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TEDEd_World_History | A_day_in_the_life_of_a_Mongolian_queen_Anne_F_Broadbridge.txt | As dawn breaks over a moveable city of ten thousand yurts, Queen Boraqchin is in for a rude awakening. A rogue sheep has slipped past her servants and guards and bolted into her yurt, where he springs into bed and bleats in her ear. Although she’s the formidable khatun of the Golden Horde, a huge kingdom in the Mongolian Empire, Boraqchin has a hands-on approach to ruling. She’s been married to Batu Khan, the fearsome grandson of Genghis Khan himself, since she was fifteen – and while her husband is out on his raids, she juggles the duties of flocks, family and empire at home. This makes her the manager – and the mover – of a city of thousands. Twice a year, Boraqchin moves the city between two seasonal camping grounds. This ensures constant water and lush grass in summer, and protection from harsh winds in winter. The whole operation requires weeks of strict planning, liaising with the other camps in her domain, strategic delegation – and the patience to move at the speed of dawdling animals. Today is moving day, and she’ll have to direct throngs of her ladies, commanders, slaves and animals up the river Volga for the summer. As Boraqchin steps outside, she’s greeted by a commotion – her unwanted visitor is now running circles around her stewards. They’re attempting to stow her possessions securely into wagons. Boraqchin orders them to get it under control – but she’s the only one quick enough to catch the stray. She next supervises her ladies who are unpinning her yurt and lifting it onto its custom wagon. It requires a team of twenty oxen to pull, and Boraqchin wouldn’t trust anyone to steer it but herself. Next, Boraqchin and her woolly companion meet with the guards. She orders them to keep close watch on her husband's special reception yurt and port-able throne during the journey. They’ll also act as outriders, and she tells them how to secure the route, surround her for safety – and keep the animals in check. But when the sheep finally breaks free and makes for the fields, the guards can barely keep up as it scampers through crowds packing up their yurts. Exasperated, Boraqchin rides down to the pastures herself. When she gets there, she catches sight of the troublesome sheep wriggling into the middle of a flock. When she follows him in, he’s nestled next to a ewe, his mother. She’s pregnant, and seems to be in pain. With a start, Boraqchin realizes that this ewe’s impending delivery has been forgotten in the flurry of moving day. There’s no time to find a shepherd – instead, Boraqchin rolls up her sleeves, greases her arm and helps the ewe give birth to two new additions to the empire. Leaving the lambs and their mother, Boraqchin dashes back to the camp. Here the final touches have been put to packing, and vehicles are starting to line up. This vast procession starts with the queen and two hundred wagons filled with her treasures. Next up are the junior wives and crew, then the concubines – and this is only Boraqchin's camp. After this comes the second imperial camp led by another senior wife, then two more camps, also led by wives. Boraqchin has been checking in with them for weeks to ensure a smooth departure and orderly queue. But they only make up the royal portion of the line – behind them winds the entire civilian city, which includes holy men with portable chapels and mosques, families, tradesmen, and shepherds. Finally, Boraqchin settles into her wagon. It’ll take weeks to reach their destination – but over the course of the journey, she’ll keep everyone expertly in check – from her proud children and attentive subjects, to the most meandering sheep at the back of line. |
TEDEd_World_History | A_day_in_the_life_of_a_Roman_soldier_Robert_Garland.txt | The year is 15 CE and the Roman Empire is prospering. Most of the credit will go to the emperor, but this success wouldn’t have been possible without loyal soldiers like Servius Felix. Servius enlisted as a legionary eight years ago at age 18, the son of a poor farmer with few prospects. Unlike the majority of legionaries, he doesn’t gamble, so he’s been able to save most of his wages. He’s even kept his viaticum, the three gold coins he received when he enlisted. If he survives until retirement, he’ll receive several acres of land. And he’s grown rather fond of a girl back home whom he intends to marry. But he’ll have to wait until he completes his 25 years of service before that can happen. And the life of a legionary is dangerous and grueling. Today, Servius’s legion, along with three others, has undertaken a “great march” of 30,000 Roman paces, the equivalent of nearly 36 kilometers. Servius’s armor and weapons, including his gladius, scutum, and two pila, weigh over 20 kilograms. And that’s not counting his backpack, or sarcina, which contains food and all the tools he needs to help build the camp – spade, saw, pickaxe, and basket. Although Servius is exhausted, he won’t sleep much tonight. He’s been assigned the first watch, which means looking after the baggage animals and keeping alert against a possible ambush. After he’s done, he lies awake, dreading the day ahead, which will force him to recall his worst nightmare. At dawn, Servius eats breakfast with his seven tent companions. They’re like a family, all bearing scars from the battles they’ve fought together. Servius is from Italia, but his fellow soldiers hail from all over the empire, which stretches from Syria to Spain. So they’re all far from home in the northern land of Germania. Servius’s legion and three others with him today are under the command of Emperor Tiberius’s nephew Germanicus, named for his father’s military successes against the Germanic tribes. Each legion has close to 5,000 men, divided into cohorts of about 500, further subdivided into centuries of around 80-100 men. Each century is commanded by a centurion. An aquilifer, or eagle-bearer, marches at the head of each legion carrying its eagle standard. The centurions march beside the legionaries belting out orders, “Dex, sin, dex, sin," “Right, left, right, left," starting with the right foot as the left is considered unlucky or sinister. Despite the strict discipline, there’s tension in the air. Last year, some legions in the area revolted, demanding better pay and a cut in the length of service. Only their general’s charisma and negotiating skills prevented wholesale mutiny. Today is a “just march,” only 30 kilometers. As the marshes and forests of Germania lie beyond the empire’s road system the men must build causeways and bridges to make headway— something they’ve recently spent more time doing than fighting. Finally, they arrive at their destination, a place Servius knows too well. It’s a clearing on the outskirts of the Teutoburg Forest, where six years ago, during the reign of the Emperor Augustus, Germanic tribes under their chieftain Arminius ambushed and destroyed three legions. Proceeding along a narrow path, the legions were attacked from forest cover under torrential rain with their escape blocked. It was one of the worst defeats the Romans ever suffered and Augustus never lived it down. Servius was one of the few survivors. Servius still has nightmares of his comrades lying where they fell. But now the army is back to bury the dead with full military honors. As he helps in the task, he can’t help wondering whether the bones he handles belonged to someone he knew. Several times he wants to weep aloud, but he pushes on with the task. The glory of the Empire can go to the crows. All he craves is to retire on a small farm with his wife-to-be, if the gods should spare his life for 17 more years. |
TEDEd_World_History | 무엇이_프랑스_혁명을_일어나게_했을까_톰_뮬레이니Tom_Mullaney.txt | What rights do people have, and where do they come from? Who gets to make decisions for others and on what authority? And how can we organize society to meet people's needs? These questions challenged an entire nation during the upheaval of the French Revolution. By the end of the 18th century, Europe had undergone a profound intellectual and cultural shift known as the Enlightenment. Philosophers and artists promoted reason and human freedom over tradition and religion. The rise of a middle class and printed materials encouraged political awareness, and the American Revolution had turned a former English colony into an independent republic. Yet France, one of the largest and richest countries in Europe was still governed by an ancient regime of three rigid social classes called Estates. The monarch King Louis XVI based his authority on divine right and granted special privileges to the First and Second Estates, the Catholic clergy, and the nobles. The Third Estate, middle class merchants and craftsmen, as well as over 20 million peasants, had far less power and they were the only ones who paid taxes, not just to the king, but to the other Estates as well. In bad harvest years, taxation could leave peasants with almost nothing while the king and nobles lived lavishly on their extracted wealth. But as France sank into debt due to its support of the American Revolution and its long-running war with England, change was needed. King Louis appointed finance minister Jacques Necker, who pushed for tax reforms and won public support by openly publishing the government's finances. But the king's advisors strongly opposed these initiatives. Desperate for a solution, the king called a meeting of the Estates-General, an assembly of representatives from the Three Estates, for the first time in 175 years. Although the Third Estate represented 98% of the French population, its vote was equal to each of the other Estates. And unsurprisingly, both of the upper classes favored keeping their privileges. Realizing they couldn't get fair representation, the Third Estate broke off, declared themselves the National Assembly, and pledged to draft a new constitution with or without the other Estates. King Louis ordered the First and Second Estates to meet with the National Assembly, but he also dismissed Necker, his popular finance minister. In response, thousands of outraged Parisians joined with sympathetic soldiers to storm the Bastille prison, a symbol of royal power and a large storehouse of weapons. The Revolution had begun. As rebellion spread throughout the country, the feudal system was abolished. The Assembly's Declaration of the Rights of Man and Citizen proclaimed a radical idea for the time -- that individual rights and freedoms were fundamental to human nature and government existed only to protect them. Their privileges gone, many nobles fled abroad, begging foreign rulers to invade France and restore order. And while Louis remained as the figurehead of the constitutional monarchy, he feared for his future. In 1791, he tried to flee the country but was caught. The attempted escape shattered people's faith in the king. The royal family was arrested and the king charged with treason. After a trial, the once-revered king was publicly beheaded, signaling the end of one thousand years of monarchy and finalizing the September 21st declaration of the first French republic, governed by the motto "liberté, égalité, fraternité." Nine months later, Queen Marie Antoinette, a foreigner long-mocked as "Madame Déficit" for her extravagant reputation, was executed as well. But the Revolution would not end there. Some leaders, not content with just changing the government, sought to completely transform French society -- its religion, its street names, even its calendar. As multiple factions formed, the extremist Jacobins lead by Maximilien Robespierre launched a Reign of Terror to suppress the slightest dissent, executing over 20,000 people before the Jacobin's own downfall. Meanwhile, France found itself at war with neighboring monarchs seeking to strangle the Revolution before it spread. Amidst the chaos, a general named Napoleon Bonaparte took charge, becoming Emperor as he claimed to defend the Revolution's democratic values. All in all, the Revolution saw three constitutions and five governments within ten years, followed by decades alternating between monarchy and revolt before the next Republic formed in 1871. And while we celebrate the French Revolution's ideals, we still struggle with many of the same basic questions raised over two centuries ago. |
TEDEd_World_History | The_history_of_chocolate_Deanna_Pucciarelli.txt | If you can't imagine life without chocolate, you're lucky you weren't born before the 16th century. Until then, chocolate only existed in Mesoamerica in a form quite different from what we know. As far back as 1900 BCE, the people of that region had learned to prepare the beans of the native cacao tree. The earliest records tell us the beans were ground and mixed with cornmeal and chili peppers to create a drink - not a relaxing cup of hot cocoa, but a bitter, invigorating concoction frothing with foam. And if you thought we make a big deal about chocolate today, the Mesoamericans had us beat. They believed that cacao was a heavenly food gifted to humans by a feathered serpent god, known to the Maya as Kukulkan and to the Aztecs as Quetzalcoatl. Aztecs used cacao beans as currency and drank chocolate at royal feasts, gave it to soldiers as a reward for success in battle, and used it in rituals. The first transatlantic chocolate encounter occurred in 1519 when Hernán Cortés visited the court of Moctezuma at Tenochtitlan. As recorded by Cortés's lieutenant, the king had 50 jugs of the drink brought out and poured into golden cups. When the colonists returned with shipments of the strange new bean, missionaries' salacious accounts of native customs gave it a reputation as an aphrodisiac. At first, its bitter taste made it suitable as a medicine for ailments, like upset stomachs, but sweetening it with honey, sugar, or vanilla quickly made chocolate a popular delicacy in the Spanish court. And soon, no aristocratic home was complete without dedicated chocolate ware. The fashionable drink was difficult and time consuming to produce on a large scale. That involved using plantations and imported slave labor in the Caribbean and on islands off the coast of Africa. The world of chocolate would change forever in 1828 with the introduction of the cocoa press by Coenraad van Houten of Amsterdam. Van Houten's invention could separate the cocoa's natural fat, or cocoa butter. This left a powder that could be mixed into a drinkable solution or recombined with the cocoa butter to create the solid chocolate we know today. Not long after, a Swiss chocolatier named Daniel Peter added powdered milk to the mix, thus inventing milk chocolate. By the 20th century, chocolate was no longer an elite luxury but had become a treat for the public. Meeting the massive demand required more cultivation of cocoa, which can only grow near the equator. Now, instead of African slaves being shipped to South American cocoa plantations, cocoa production itself would shift to West Africa with Cote d'Ivoire providing two-fifths of the world's cocoa as of 2015. Yet along with the growth of the industry, there have been horrific abuses of human rights. Many of the plantations throughout West Africa, which supply Western companies, use slave and child labor, with an estimation of more than 2 million children affected. This is a complex problem that persists despite efforts from major chocolate companies to partner with African nations to reduce child and indentured labor practices. Today, chocolate has established itself in the rituals of our modern culture. Due to its colonial association with native cultures, combined with the power of advertising, chocolate retains an aura of something sensual, decadent, and forbidden. Yet knowing more about its fascinating and often cruel history, as well as its production today, tells us where these associations originate and what they hide. So as you unwrap your next bar of chocolate, take a moment to consider that not everything about chocolate is sweet. |
TEDEd_World_History | The_Egyptian_Book_of_the_Dead_A_guidebook_for_the_underworld_Tejal_Gala.txt | Ani stands before a large golden scale where the jackal-headed god Anubis is weighing his heart against a pure ostrich feather. Ani was a real person, a scribe from the Egyptian city of Thebes who lived in the 13th century BCE. And depicted here is a scene from his Book of the Dead, a 78-foot papyrus scroll designed to help him attain immortality. Such funerary texts were originally written only for Pharaohs, but with time, the Egyptians came to believe regular people could also reach the afterlife if they succeeded in the passage. Ani's epic journey begins with his death. His body is mummified by a team of priests who remove every organ except the heart, the seat of emotion, memory, and intelligence. It's then stuffed with a salt called natron and wrapped in resin-soaked linen. In addition, the wrappings are woven with charms for protection and topped with a heart scarab amulet that will prove important later on. The goal of the two-month process is to preserve Ani's body as an ideal form with which his spirit can eventually reunite. But first, that spirit must pass through the duat, or underworld. This is a realm of vast caverns, lakes of fire, and magical gates, all guarded by fearsome beasts - snakes, crocodiles, and half-human monstrosities with names like "he who dances in blood." To make things worse, Apep, the serpent god of destruction, lurks in the shadows waiting to swallow Ani's soul. Fortunately, Ani is prepared with the magic contained within his book of the dead. Like other Egyptians who could afford it, Ani customized his scroll to include the particular spells, prayers, and codes he thought his spirit might need. Equipped with this arsenal, our hero traverses the obstacles, repels the monsters' acts, and stealthily avoids Apep to reach the Hall of Ma'at, goddess of truth and justice. Here, Ani faces his final challenge. He is judged by 42 assessor gods who must be convinced that he has lived a righteous life. Ani approaches each one, addressing them by name, and declaring a sin he has not committed. Among these negative confessions, or declarations of innocence, he proclaims that he has not made anyone cry, is not an eavesdropper, and has not polluted the water. But did Ani really live such a perfect life? Not quite, but that's where the heart scarab amulet comes in. It's inscribed with the words, "Do not stand as a witness against me," precisely so Ani's heart doesn't betray him by recalling the time he listened to his neighbors fight or washed his feet in the Nile. Now, it's Ani's moment of truth, the weighing of the heart. If his heart is heavier than the feather, weighed down by Ani's wrongdoings, it'll be devoured by the monstrous Ammit, part crocodile, part leopard, part hippopotamus, and Ani will cease to exist forever. But Ani is in luck. His heart is judged pure. Ra, the sun god, takes him to Osiris, god of the underworld, who gives him final approval to enter the afterlife. In the endless and lush field of reeds, Ani meets his deceased parents. Here, there is no sadness, pain, or anger, but there is work to be done. Like everyone else, Ani must cultivate a plot of land, which he does with the help of a Shabti doll that had been placed in his tomb. Today, the Papyrus of Ani resides in the British Museum, where it has been since 1888. Only Ani, if anyone, knows what really happened after his death. But thanks to his Book of the Dead, we can imagine him happily tending his crops for all eternity. |
TEDEd_World_History | A_brief_history_of_cannibalism_Bill_Schutt.txt | 15th century Europeans believed they had hit upon a miracle cure: a remedy for epilepsy, hemorrhage, bruising, nausea, and virtually any other medical ailment. This brown powder could be mixed into drinks, made into salves or eaten straight up. It was known as mumia and made by grinding up mummified human flesh. The word "cannibal" dates from the time of Christopher Columbus; in fact, Columbus may even have coined it himself. After coming ashore on the island of Guadaloupe, Columbus' initial reports back to the Queen of Spain described the indigenous people as friendly and peaceful— though he did mention rumors of a group called the Caribs, who made violent raids and then cooked and ate their prisoners. In response, Queen Isabella granted permission to capture and enslave anyone who ate human flesh. When the island failed to produce the gold Columbus was looking for, he began to label anyone who resisted his plundering and kidnapping as a Caribe. Somewhere along the way, the word "Carib" became "Canibe" and then "Cannibal." First used by colonizers to dehumanize indigenous people, it has since been applied to anyone who eats human flesh. So the term comes from an account that wasn't based on hard evidence, but cannibalism does have a real and much more complex history. It has taken diverse forms— sometimes, as with mumia, it doesn't involved recognizable parts of the human body. The reasons for cannibalistic practices have varied, too. Across cultures and time periods, there's evidence of survival cannibalism, when people living through a famine, siege or ill-fated expedition had to either eat the bodies of the dead or starve to death themselves. But it's also been quite common for cultures to normalize some form of eating human flesh under ordinary circumstances. Because of false accounts like Columbus's, it's difficult to say exactly how common cultural cannibalism has been— but there are still some examples of accepted cannibalistic practices from within the cultures practicing them. Take the medicinal cannibalism in Europe during Columbus's time. Starting in the 15th century, the demand for mumia increased. At first, stolen mummies from Egypt supplied the mumia craze, but soon the demand was too great to be sustained on Egyptian mummies alone, and opportunists stole bodies from European cemeteries to turn into mumia. Use of mumia continued for hundreds of years. It was listed in the Merck index, a popular medical encyclopedia, into the 20th century. And ground up mummies were far from the only remedy made from human flesh that was common throughout Europe. Blood, in either liquid or powdered form, was used to treat epilepsy, while human liver, gall stones, oil distilled from human brains, and pulverized hearts were popular medical concoctions. In China, the written record of socially accepted cannibalism goes back almost 2,000 years. One particularly common form of cannibalism appears to have been filial cannibalism, where adult sons and daughters would offer a piece of their own flesh to their parents. This was typically offered as a last-ditch attempt to cure a sick parent, and wasn't fatal to their offspring— it usually involved flesh from the thigh or, less often, a finger. Cannibalistic funerary rites are another form of culturally sanctioned cannibalism. Perhaps the best-known example came from the Fore people of New Guinea. Through the mid-20th century, members of the community would, if possible, make their funerary preferences known in advance, sometimes requesting that family members gather to consume the body after death. Tragically, though these rituals honored the deceased, they also spread a deadly disease known as kuru through the community. Between the fictionalized stories, verifiable practices, and big gaps that still exist in our knowledge, there's no one history of cannibalism. But we do know that people have been eating each other, volunteering themselves to be eaten, and accusing others of eating people for millennia. |
TEDEd_World_History | 세계_5대_종교에_대해서_존_벨라이미_John_Bellaimey.txt | Transcriber: Andrea McDonough Reviewer: Jessica Ruby In all times and places in our history, human beings have wondered, "Where did we come from? What's our place in the world? What happens to us after we die?" Religions are systems of belief that have developed and evolved over time in response to these and other eternal mysteries, driven by the feeling that some questions can only be answered by faith and based on an intuition that there is something greater than ourselves, a higher power we must answer to, or some source we all spring from and to which we must return. Hinduism means the religions of India. It's not a single religion but rather a variety of related beliefs and spiritual practices. It dates back five millennia to the time of Krishna, a man of such virtue that he became known as an avatar of Vishnu, an incarnation of the god in human form. He taught that all life follows karma, the law of cause and effect, and our job is to do our duty, or dharma, according to our place in society without worrying how things turn out. When we die, we are reincarnated into a new body. If we followed our dharma and did our proper duty in our past life, we get good karma, which sends our soul upward in the social scale. Our rebirth into the next life is thus determined by what we do in this one. The wheel of rebirths is called samsara. It's possible for a very holy person to lead a life with enough good karma to escape the wheel. This escape is called moksha. Hinduism teaches that everything is one. The whole universe is one transcendent reality called Brahman, and there's just one Brahman but many gods within it, and their roles, aspects, and forms differ according to various traditions. Brahma is the creator, Vishnu is the preserver who sometimes takes on human form, and Shiva is the transformer, or Lord of the Dance. Durga is the fiercely protective divine mother. Ganesha has an elephant head and is the wise patron of success. Hinduism is the third largest religion in the world. And although most Hindus live in India, they can be found on every continent, one billion strong. Now, let's travel west, across deserts and mountains to the fertile crescent about 4,000 years ago. Judaism began with God calling Abraham and Sarah to leave Mesopotamia and migrate to the land of Canaan. In return for their faith in the one true God, a revolutionary concept in the polytheistic world of that time, they would have land and many descendants. From this promise came the land of Israel and the chosen people, but staying in that land and keeping those people together was going to be very difficult. The Israelites were enslaved in Egypt, but God freed them with the help of the prophet Moses, who received the Ten Commandments and later hundreds more. They conquered the Promised Land, but could only keep it for a few hundred years. Israel sits at a crossroads through which many armies marched over the centuries. And in the year 70, the Romans destroyed the temple in their capital, Jerusalem. So, the religion transformed itself from a temple religion with sacrifices and priests to a religion of the book. Because of this, Judaism is a faith of symbolism, reverence, and deep meanings tied to the literature of its history. The many sacred scriptures make up the Hebrew bible, or Tanakh, and hundreds of written discussions and interpretations are contained in an expansive compendium of deeper meanings, called the Talmud. Jews find rich, symbolic meaning in daily life. At the Passover meal, every item on the menu symbolizes an aspect of the escape from slavery. The importance of growing up is emphasized when young people reach the age of bar and bat mitzvah, ceremonies during which they assume responsibility for their actions and celebrate the weaving of their own lives into the faith, history, and texts of the Jewish people. There are 14 million Jews in the world today, 6 million in Israel, which became independent following the horrors of genocide in World War II, and 5 million in the United States. But now let's go back 2500 years and return to India where Buddhism began with a young prince named Siddhartha. On the night he was conceived, his mother, Queen Maya, is said to have been visited in her sleep by a white elephant who entered her side. Ten months later, Prince Siddartha was born into a life of luxury. Venturing forth from his sheltered existence as a young man, he witnessed the human suffering that had been hidden from him and immediately set out to investigate its sources. Why must people endure suffering? Must we reincarnate through hundreds of lives? At first he thought the problem was attachment to material things, so he gave up his possessions. He became a wandering beggar, which he discovered certainly made him no happier. Then he overheard a music teacher telling a student, "Don't tighten the string too much, it will break. But don't let it go too slack, or it will not sound." In a flash, he realized that looking for answers at the extremes was a mistake. The middle way between luxury and poverty seemed wisest. And while meditating under a bodhi tree, the rest of the answer came to him. All of life abounds with suffering. It's caused by selfish craving for one's own fulfillment at the expense of others. Following an eight-step plan can teach us to reduce that craving, and thus reduce the suffering. On that day, Siddhartha became the Buddha, the enlightened one. Not the only one, but the first one. The Buddhist plan is called the Eightfold Path, and though it is not easy to follow, it has pointed the way for millions to enlightenment, which is what Buddhahood means, a state of compassion, insight, peace, and steadfastness. From the time he got up from under that tree to the moment of his death as an old man, the Buddha taught people how to become enlightened: right speech, right goals, a mind focused on what is real, and a heart focused on loving others. Many Buddhists believe in God or gods, but actions are more important than beliefs. There are nearly a billion Buddhists in the world today, mostly in East, Southeast, and South Asia. 2,000 years ago in Judaism's Promised Land, Christianity was born. Just as Hindus called Krishna "God in Human Form," Christians say the same thing about Jesus, and Christianity grew out of Judaism just as Buddhism grew out of Hinduism. The angel Gabriel was sent by the God of Abraham to ask a young woman named Mary to become the mother of his son. The son was Jesus, raised as a carpenter by Mary and her husband Joseph, until he turned 30, when he began his public career as the living word of God. Less interested in religiousness than in justice and mercy, Jesus healed the sick in order to draw crowds and then taught them about his heavenly father -- affectionate, forgiving, and attentive. Then, he would invite everyone to a common table to illustrate his Kingdom of God, outcasts, sinners, and saints all eating together. He had only three years before his unconventional wisdom got him into trouble. His enemies had him arrested, and he was executed by Rome in the standard means by which rabble-rousers were put to death, crucifixion. But shortly after he was buried, women found his tomb empty and quickly spread word, convinced that he had been raised from the dead. The first Christians described his resurrected appearances, inspiring confidence that his message was true. The message: love one another as I have loved you. Christians celebrate the birth of Jesus in December at Christmas, and his suffering, death, and resurrection during Holy Week in the spring. In the ceremony of baptism, a washing away of sin and welcoming into the Christian community, recall Jesus's own baptism when he left his life as a carpenter. In the rite of Communion, Christians eat the bread and drink the wine blessed as the body and blood of Jesus, recalling Jesus's last supper. There are two billion Christians worldwide, representing almost a third of the world's people. Islam began 1400 years ago with a man of great virtue, meditating in a mountain cave in the Arabian desert. The man was Muhammad. He was visited by a divine messenger, again the angel Gabriel, in Arabic, Jibril, delivering to him the words of Allah, the one God of Abraham. In the next few years, more and more messages came, and he memorized and taught them. The verses he recited were full of wise sayings, beautiful rhymes, and mysterious metaphors. But Muhammad was a merchant, not a poet. Many agreed the verses were indeed the words of God, and these believers became the first Muslims. The word Muslim means one who surrenders, meaning a person who submits to the will of God. A Muslim's five most important duties are called the Five Pillars: Shahada, Muslims declare publicly, there is no other God but Allah, and Muhammad is his final prophet; Salat, they pray five times a day facing Mecca; Zakat, every Muslim is required to give 2 or 3% of their net worth to the poor; Sawm, they fast during daylight hours for the lunar month of Ramadan to strengthen their willpower and their reliance on God; and Hajj, once in a lifetime, every Muslim who is able must make a pilgrimage to the holy city of Mecca, rehearsing for the time when they will stand before God to be judged worthy or unworthy of eternal life with Him. The words of God, revealed to the prophet over 23 years, are collected in the Quran, which literally translates into "the recitation." Muslims believe it to be the only holy book free of human corruption. It's also considered by many to be the finest work of literature in the Arabic language. Islam is the world's second largest religion, practiced by over one and a half billion Muslims around the globe. Religion has been an aspect of culture for as long as it has existed, and there are countless variations of its practice. But common to all religions is an appeal for meaning beyond the empty vanities and lowly realities of existence, beyond sin, suffering, and death, beyond fear, and beyond ourselves. |
TEDEd_World_History | The_dark_history_of_bananas_John_Soluri.txt | On a December night in 1910, the exiled former leader of Honduras, Manuel Bonilla, boarded a borrowed yacht in New Orleans. With a group of heavily armed accomplices, he set sail for Honduras in hopes of reclaiming power by whatever means necessary. Bonilla had a powerful backer, the future leader of a notorious organization known throughout Latin America as El Pulpo, or "the Octopus," for its long reach. The infamous El Pulpo was a U.S. corporation trafficking in, of all things, bananas. It was officially known as United Fruit Company— or Chiquita Brands International today. First cultivated in Southeast Asia thousands of years ago, bananas reached the Americas in the early 1500s, where enslaved Africans cultivated them in plots alongside sugar plantations. There were many different bananas, most of which looked nothing like the bananas in supermarket aisles today. In the 1800s, captains from New Orleans and New England ventured to the Caribbean in search of coconuts and other goods. They began to experiment with bananas, purchasing one kind, called Gros Michel, from Afro-Caribbean farmers in Jamaica, Cuba, and Honduras. Gros Michel bananas produced large bunches of relatively thick-skinned fruit— ideal for shipping. By the end of the 1800s, bananas were a hit in the US. They were affordable, available year-round, and endorsed by medical doctors. As bananas became big business, U.S. fruit companies wanted to grow their own bananas. In order to secure access to land, banana moguls lobbied and bribed government officials in Central America, and even funded coups to ensure they had allies in power. In Honduras, Manuel Bonilla repaid the banana man who had financed his return to power with land concessions. By the 1930s, one company dominated the region: United Fruit, who owned over 40% of Guatemala’s arable land at one point. They cleared rainforest in Costa Rica, Colombia, Guatemala, Honduras, and Panama to build plantations, along with railroads, ports, and towns to house workers. Lured by relatively high-paying jobs, people migrated to banana zones. From Guatemala to Colombia, United Fruit’s plantations grew exclusively Gros Michel bananas. These densely packed farms had little biological diversity, making them ripe for disease epidemics. The infrastructure connecting these vulnerable farms could quickly spread disease: pathogens could hitch a ride from one farm to another on workers’ boots, railroad cars, and steamships. That’s exactly what happened in the 1910s, when a fungus began to level Gros Michel banana plantations, first in Panama, and later throughout Central America, spreading quickly via the same system that had enabled big profits and cheap bananas. In a race against “Panama Disease,” banana companies abandoned infected plantations in Costa Rica, Honduras, and Guatemala, leaving thousands of farmers and workers jobless. The companies then felled extensive tracts of rainforests in order to establish new plantations. After World War II, the dictatorships with which United Fruit had partnered in Guatemala and Honduras yielded to democratically elected governments that called for land reform. In Guatemala, President Jacobo Arbenz tried to buy back land from United Fruit and redistribute it to landless farmers. The Arbenz government offered to pay a price based on tax records— where United Fruit had underreported the value of the land. El Pulpo was not happy. The company launched propaganda campaigns against Arbenz and called on its deep connections in the US Government for help. Citing fears of communism, the CIA orchestrated the overthrow of the democratically elected Arbenz in 1954. That same year in Honduras, thousands of United Fruit workers went on strike until the company agreed to recognize a new labor union. With the political and economic costs of running from Panama Disease escalating, United Fruit finally switched from Gros Michel to Panama disease-resistant Cavendish bananas in the early 1960s. Today, bananas are no longer as economically vital in Central America, and United Fruit Company, rechristened Chiquita, has lost its stranglehold on Latin American politics. But the modern banana industry isn’t without problems. Cavendish bananas require frequent applications of pesticides that create hazards for farmworkers and ecosystems. And though they’re resistant to the particular pathogen that affected Gros Michel bananas, Cavendish farms also lack biological diversity, leaving the banana trade ripe for another pandemic. |
TEDEd_World_History | 예술에서의_종교의_짧은_역사_TEDEd.txt | It's only been the last few hundreds years or so that Western civilization has been putting art in museums, at least museums resembling the public institutions we know today. Before this, for most, art served other purposes. What we call fine art today was, in fact, primarily how people experienced an aesthetic dimension of religion. Paintings, sculpture, textiles and illuminations were the media of their time, supplying vivid imagery to accompany the stories of the day. In this sense, Western art shared a utilitarian purpose with other cultures around the world, some of whose languages incidentally have no word for art. So how do we define what we call art? Generally speaking, what we're talking about here is work that visually communicates meaning beyond language, either through representation or the arrangement of visual elements in space. Evidence of this power of iconography, or ability of images to convey meaning, can be found in abundance if we look at art from the histories of our major world religions. Almost all have, at one time or another in their history, gone through some sort of aniconic phase. Aniconism prohibits any visual depiction of the divine. This is done in order to avoid idolatry, or confusion between the representation of divinity and divinity itself. Keeping it real, so to speak, in the relationship between the individual and the divine. However, this can be a challenge to maintain, given that the urge to visually represent and interpret the world around us is a compulsion difficult to suppress. For example, even today, where the depiction of Allah or the Prophet Muhammad is prohibited, an abstract celebration of the divine can still be found in arabesque patterns of Islamic textile design, with masterful flourishes of brushwork and Arabic calligraphy, where the words of the prophet assume a dual role as both literature and visual art. Likewise, in art from the early periods of Christianity and Buddhism, the divine presence of the Christ and the Buddha do not appear in human form but are represented by symbols. In each case, iconographic reference is employed as a form of reverence. Anthropomorphic representation, or depiction in human form, eventually became widespread in these religions only centuries later, under the influence of the cultural traditions surrounding them. Historically speaking, the public appreciation of visual art in terms other than traditional, religious or social function is a relatively new concept. Today, we fetishize the fetish, so to speak. We go to museums to see art from the ages, but our experience of it there is drastically removed from the context in which it was originally intended to be seen. It might be said that the modern viewer lacks the richness of engagement that she has with contemporary art, which has been created relevant to her time and speaks her cultural language. It might also be said that the history of what we call art is a conversation that continues on, as our contemporary present passes into what will be some future generation's classical past. It's a conversation that reflects the ideologies, mythologies, belief systems and taboos and so much more of the world in which it was made. But this is not to say that work from another age made to serve a particular function in that time is dead or has nothing to offer the modern viewer. Even though in a museum setting works of art from different places and times are presented alongside each other, isolated from their original settings, their juxtaposition has benefits. Exhibits are organized by curators, or people who've made a career out of their ability to recontextualize or remix cultural artifacts in a collective presentation. As viewers, we're then able to consider the art in terms of a common theme that might not be apparent in a particular work until you see it alongside another, and new meanings can be derived and reflected upon. If we're so inclined, we might even start to see every work of art as a complementary part of some undefined, unified whole of past human experience, a trail that leads right to our doorstep and continues on with us, open to anyone who wants to explore it. |
TEDEd_World_History | This_is_Sparta_Fierce_warriors_of_the_ancient_world_Craig_Zimmer.txt | In ancient Greece, violent internal conflict between bordering neighbors and war with foreign invaders was a way of life, and Greeks were considered premier warriors. Most Greek city-states surrounded themselves with massive defensive walls for added protection. Sparta in its prime was a different story, finding walls unnecessary when it had an army of the most feared warriors in the ancient world. So what was Sparta doing differently than everyone else to produce such fierce soldiers? To answer that question, we turn to the written accounts of that time. There are no surviving written accounts from Spartans themselves, as it was forbidden for Spartans to keep records, so we have to rely on those of non-Spartan ancient historians, like Herodotus, Thucydides, and Plutarch. These stories may be embellished and depict Sparta at the apex of its power, so take them with a grain of salt. For Spartans, the purpose for their existence was simple: to serve Sparta. On the day of their birth, elder Spartan leaders examined every newborn. The strong healthy babies were considered capable of fulfilling this purpose, and the others may have been left on Mount Taygetus to die. Every Spartan, boy or girl, was expected to be physically strong, mentally sharp, and emotionally resilient. And it was their absolute duty to defend and promote Sparta at all costs. So in the first years of their lives, children were raised to understand that their loyalty belonged first to Sparta, and then to family. This mindset probably made it easier for the Spartan boys, who upon turning seven, were sent to the agoge, a place with one main purpose: to turn a boy into a Spartan warrior through thirteen years of relentless, harsh, and often brutal training. The Spartans prized physical perfection above all else, and so the students spent a great deal of their time learning how to fight. To ensure resilience in battle, boys were encouraged to fight among themselves, and bullying, unlike today, was acceptable. In order to better prepare the boys for the conditions of war, the boys were poorly fed, sometimes even going days without eating. They also were given little in the way of clothing so that they could learn to deal with different temperatures. Spartan boys were encouraged to steal in order to survive, but if they were caught, they would be disciplined, not because they stole, but because they were caught in the act. During the annual contest of endurance in a religious ritual known as the diamastigosis, teenage boys were whipped in front of an altar at the Sanctuary of Artemis Orthia. It was common for boys to die on the altar of the goddess. Fortunately, not everything was as brutal as that. Young Spartans were also taught how to read, write, and dance, which taught them graceful control of their movements and helped them in combat. While the responsibilities for the girls of Sparta were different, the high standards of excellence and expectation to serve Sparta with their lives remained the same. Spartan girls lived at home with their mothers as they attended school. Their curriculum included the arts, music, dance, reading, and writing. And to stay in peak physical condition, they learned a variety of sports, such as discus, javelin, and horseback riding. In Sparta, it was believed that only strong and capable women could bear children that would one day become strong and capable warriors. To all Spartans, men and women, perhaps the most important lesson from Spartan school was allegiance to Sparta. To die for their city-state was seen as the completion of one's duty to Sparta. Upon their death, only men who died in battle and women who died in childbirth were given tombstones. In the eyes of their countrymen, both died so that Sparta could live. |
TEDEd_World_History | Whats_so_special_about_Viking_ships_Jan_Bill.txt | The Vikings came from the rugged, inhospitable north known today as Scandinavia. As the Roman Empire flourished further south, Scandinavians had small settlements, no central government, and no coinage. Yet by the 11th century, the Vikings had spread far from Scandinavia, gaining control of trade routes throughout Europe, conquering kingdoms as far as Africa, and even building outposts in North America. The secret to their success was their ships. The formidable Viking longship had its origins in the humble dugout canoe, or log boat. For millennia, the inhabitants of Scandinavia had used these canoes for transportation. Dense forests and tall mountains made overland travel difficult, but long coastlines and numerous rivers, lakes, and fjords provided a viable alternative. The first canoes were simply hollowed out logs rowed with paddles. Over time, they added planks to the log boat base using the clinker, or "lapstrake," technique, meaning the planks overlapped and were fastened to each other along their edges. As the Roman Empire expanded north, some Scandinavians served in their new neighbors’ armies— and brought home Roman maritime technology. The Mediterranean cultures at the heart of the Roman Empire had large warships that controlled the sea, and cargo ships that transported goods along the waterways. These ships were powered by sail and oars and relied on a strong skeleton of internal timbers fastened to the outer planks with copper, iron, and wood nails. At first, Scandinavians incorporated this new technology by replacing their loose paddles with anchored oars. This change hugely improved the crew’s efficiency, but also required stronger ships. So boat builders began to use iron nails for fasteners rather than sewing. They abandoned the log boat base for a keel plank, and the boats became higher and more seaworthy. But these early ships retained the concept of the original log boat: their strength depended on the outer shell of wood, not internal frames and beams. They were built as shells— thin-walled but strong, and much lighter than the Roman ships. Competing chieftains quickly refined the new ships to be even more efficient. The lighter the boat, the more versatile it would be and the less investment of resources it would require— an essential advantage in a decentralized culture without large supplies of people. These ships still had no sails— sails were costly, and for now the rowed ships could meet their needs. That changed after the Western Roman Empire collapsed in the 5th century. Western Europe took a heavy economic blow, leveling the playing field a bit for the Scandinavians. As the region revived, new and vigorous trade routes extended into and through Scandinavia. The wealth that flowed along these routes helped create a new, more prosperous and powerful class of Scandinavians, whose members competed constantly with each other over trade routes and territory. By the 8th century, a sailing ship began to make sense: it could go further, faster, in search of newly available plunder. With the addition of sails, the already light and speedy ships became nearly unbeatable. The Viking ship was born. Viking longships could soon carry as many as 100 Vikings to battle. Fleets of them could land on open beaches, penetrate deep into river systems, and be moved over land if need be. When not at war, the vessels were used to transport goods and make trade journeys. There were smaller versions for fishing and local excursions, and larger adaptations for open sea voyages capable of carrying tens of tons of cargo. Thanks to their inventiveness in the face of difficult terrain and weak economies, the Vikings sailed west, settled the North Atlantic and explored the North American coast centuries before any other Europeans would set foot there. |
TEDEd_World_History | The_rise_of_modern_populism_Takis_S_Pappas.txt | In the mid-1970s, after decades of political turmoil, Greece finally seemed to be on the path to stability. With the introduction of a new constitution and negotiations underway to enter European institutions, many analysts expected Greek politics to follow the pattern of the larger Western world. Then in 1981, a political party called PASOK came to power. Its charismatic leader Andreas Papandreou railed against the new constitution, and accused those in power of “national betrayal.” Opposing Greece’s membership in NATO and the European Economic Community, Papandreou promised to govern for the betterment of the “common people" above all else. He famously declared, “there are no institutions, only the people exist.” Papandreou’s rise to power isn’t a unique story. In many democratic countries around the world, charismatic leaders vilify political opponents, disparage institutions, and claim the mantle of the people. Some critics label this approach as authoritarian or fascist, and many argue that these leaders are using emotions to manipulate and deceive voters. But whether or not this style of politics is ethical, it's certainly democratic, and it goes by the name of populism. The term populism has been around since Ancient Rome, and has its roots in the Latin word “populus” meaning “the people." But since then populism has been used to describe dozens of political movements, often with counterintuitive and sometimes contradictory goals. Populist movements have rebelled against monarchies, monopolies, and a wide variety of powerful institutions. It’s not possible to cover the full history of this term here. Instead, we’re focusing on one specific type of populism— the kind that describes Papandreou’s administration and numerous other governments over the last 70 years: modern populism. But to understand how political theorists define this phenomenon we first need to explore what it’s responding to. In the aftermath of World War Two, many countries wanted to move away from totalitarian ideologies. They sought a new political system that prioritized individual and social rights, aimed at political consensus, and respected the rule of law. As a result, most Western nations adopted a longstanding form of government called liberal democracy. In this context, “liberal” doesn’t refer to any political party, but rather a type of democracy that has three essential components. First, liberal democracies accept that society is full of many, often crosscutting divisions that generate conflict. Second, it requires that society’s many factions seek common ground across those divisions. Finally, liberal democracies rely on the rule of law and the protection of minority rights, as specified in constitutions and legal statutes. Taken together, these ideals propose that tolerance and institutions that protect us from intolerance, are the bedrock of a functional and diverse democratic society. Liberal democracies helped bring stability to the nations that adopted them. But like any system of government, they didn’t solve everything. Among other issues, an ever-increasing wealth gap led to underserved communities who distrusted both their wealthy neighbors and their political leaders. In some cases, political corruption further damaged the public's trust. Growing suspicion and resentment around these politicians primed citizens to look for a new kind of leader who would challenge established institutions and put the needs of the people first. In many ways, this reaction highlights democracy in action: if the majority of a population feels their interests are underrepresented, they can elect leaders to change that using existing democratic systems. But this is where assertive, modern populist candidates can subvert democracy. Modern populists identify themselves as embodying the "will of the people," and they place those interests above the institutions that protect individual and social rights. Modern populists argue these institutions are run by a self-serving ruling minority, who seek to control the vast majority of virtuous common people. As a result, politics is no longer about seeking compromise and consensus through tolerant democratic institutions. Instead, these leaders seek to overturn what they see as a broken system. This means that where a liberal democracy has the utmost respect for institutions like courtrooms, free press, and national constitutions, modern populists disparage any establishment that disagrees with the so-called “common will." Modern populist parties have arisen in many places, but the leaders of these movements are remarkably similar. They’re often charismatic individuals who identify themselves as embodying the “will of the people." They make exorbitant promises to their supporters, while casting their opponents as traitors actively undermining the country. But whether these politicians are sincere believers or manipulative opportunists, the dynamics they unleash can be profoundly destabilizing for liberal democracy. Even when modern populist leaders don’t follow through with their most extreme promises, their impact on political discourse, the rule of law, and public trust can long outlast their time in office. |
TEDEd_World_History | The_rise_and_fall_of_historys_first_empire_Soraya_Field_Fiorio.txt | History’s first empire rose out of a hot, dry landscape, without rainfall to nourish crops, without trees or stones for building. In spite of all this, its inhabitants built the world’s first cities, with monumental architecture and large populations— and they built them entirely out of mud. Sumer occupied the southern part of modern Iraq in the region called Mesopotamia. Mesopotamia means “between two rivers”— the Tigris and the Euphrates. Around 5000 BCE, early Sumerians used irrigation channels, dams, and reservoirs to redirect river water and farm large areas of previously bone-dry land. Agricultural communities like this were slowly springing up around the world. But Sumerians were the first to take the next step. Using clay bricks made from river mud, they began to build multi-storied homes and temples. They invented the wheel— a potter’s wheel, for turning mud into household goods and tools. Those clay bricks gave rise to the world’s first cities, probably around 4500 BCE. At the top of the city’s social ladder were priests and priestesses, who were considered nobility, then merchants, craftspeople, farmers, and enslaved people. The Sumerian empire consisted of distinct city-states that operated like small nations. They were loosely linked by language and spiritual belief but lacked centralized control. The earliest cities were Uruk, Ur, and Eridu, and eventually there were a dozen cities. Each had a king who served a role somewhere between a priest and a ruler. Sometimes they fought against each other to conquer new territories. Each city was dedicated to a patron deity, considered the city’s founder. The largest and most important building in the city was this patron god’s home: the ziggurat, a temple designed as a stepped pyramid. Around 3200 BCE, Sumerians began to expand their reach. The potter’s wheel found a new home on chariots and wagons. They built boats out of reeds and date palm leaves, with linen sails that carried them vast distances by river and sea. To supplement scarce resources, they built a trade network with the rising kingdoms in Egypt, Anatolia, and Ethiopia, importing gold, silver, lapis lazuli, and cedar wood. Trade was the unlikely impetus for the invention of the world’s first writing system. It started as a system of accounting for Sumerian merchants conducting business with traders abroad. After a few hundred years, the early pictogram system called cuneiform turned into a script. The Sumerians drafted up the first written laws and created the first school system, designed to teach the craft of writing— and pioneered some less exciting innovations, like bureaucracy and taxes. In the schools, scribes studying from dawn to dusk, from childhood well into adulthood. They learned accounting, mathematics, and copied works of literature— hymns, myths, proverbs, animal fables, magic spells, and the first epics on clay tablets. Some of those tablets told the story of Gilgamesh, a king of the city of Uruk who was also the subject of mythical tales. But by the third millennium BCE, Sumer was no longer the only empire around, or even in Mesopotamia. Waves of nomadic tribes poured into the region from the north and east. Some newcomers looked up to the Sumerians, adopting their way of life and using the cuneiform script to express their own languages. In 2300 BCE, the Akkadian king Sargon conquered the Sumerian city-states. But Sargon respected Sumerian culture, and Akkadians and Sumerians existed side-by-side for centuries. Other invading groups focused only on looting and destruction. Even as Sumerian culture spread, a steady onslaught of invasions killed off the Sumerian people by 1750 BCE. Afterward, Sumer disappeared back into the desert dirt, not to be rediscovered until the 19th century. But Sumerian culture lived on for thousands of years— first through the Akkadians, then the Assyrians, then the Babylonians. The Babylonians passed Sumerian inventions and traditions through along Hebrew, Greek, and Roman cultures. Some persist today. |
TEDEd_World_History | 시저에_대항한_위대한_음모_캐서린_템페스트Kathryn_Tempest.txt | What would you do if you thought your country was on the path to tyranny? If you saw one man gaining too much power, would you try to stop him? Even if that man was one of your closest friends and allies? These were the questions haunting Roman Senator Marcus Junius Brutus in 44 BCE, the year Julius Caesar would be assassinated. Opposing unchecked power wasn’t just a political matter for Brutus; it was a personal one. He claimed descent from Lucius Junius Brutus, who had helped overthrow the tyrannical king known as Tarquin the Proud. Instead of seizing power himself, the elder Brutus led the people in a rousing oath to never again allow a king to rule. Rome became a republic, based on the principle that no one man should hold too much power. Now, four and a half centuries later, this principle was threatened. Julius Ceasar's rise to the powerful position of consul had been dramatic. Years of military triumphs had made him the wealthiest man in Rome. And after defeating his rival Pompey the Great in a bitter civil war, his power was at its peak. His victories and initiatives, such as distributing lands to the poor, had made him popular with the public, and many senators vied for his favor by showering him with honors. Statues were built, temples were dedicated, and a whole month was renamed, still called July today. More importantly, the title of dictator, meant to grant temporary emergency powers in wartime, had been bestowed upon Caesar several times in succession. And in 44 BCE, he was made dictator perpetuo, dictator for a potentially unlimited term. All of this was too much for the senators who feared a return to the monarchy their ancestors had fought to abolish, as well as those whose own power and ambition were impeded by Caesar's rule. A group of conspirators calling themselves the liberators began to secretly discuss plans for assassination. Leading them were the senator Gaius Cassius Longinus and his friend and brother-in-law, Brutus. Joining the conspiracy was not an easy choice for Brutus. Even though Brutus had sided with Pompey in the ill-fated civil war, Caesar had personally intervened to save his life, not only pardoning him but even accepting him as a close advisor and elevating him to important posts. Brutus was hesitant to conspire against the man who had treated him like a son, but in the end, Cassius's insistence and Brutus's own fear of Caesar's ambitions won out. The moment they had been waiting for came on March 15. At a senate meeting held shortly before Caesar was to depart on his next military campaign, as many as 60 conspirators surrounded him, unsheathing daggers from their togas and stabbing at him from all sides. As the story goes, Caesar struggled fiercely until he saw Brutus. Despite the famous line, "Et tu, Brute?" written by Shakespeare, we don't know Caesar's actual dying words. Some ancient sources claim he said nothing, while others record the phrase, “And you, child?” fueling speculation that Brutus may have actually been Caesar's illegitimate son. But all agree that when Caesar saw Brutus among his attackers, he covered his face and gave up the fight, falling to the ground after being stabbed 23 times. Unfortunately for Brutus, he and the other conspirators had underestimated Caesar's popularity among the Roman public, many of whom saw him as an effective leader, and the senate as a corrupt aristocracy. Within moments of Caesar's assassination, Rome was in a state of panic. Most of the other senators had fled, while the assassins barricaded themselves on the Capitoline Hill. Mark Antony, Caesar's friend and co-consul, was swift to seize the upper hand, delivering a passionate speech at Caesar's funeral days later that whipped the crowd into a frenzy of grief and anger. As a result, the liberators were forced out of Rome. The ensuing power vacuum led to a series of civil wars, during which Brutus, facing certain defeat, took his own life. Ironically, the ultimate result would be the opposite of what the conspirators had hoped to accomplish: the end of the Republic and the concentration of power under the office of Emperor. Opinions over the assassination of Caesar were divided from the start and have remained so. As for Brutus himself, few historical figures have inspired such a conflicting legacy. In Dante's "Inferno," he was placed in the very center of Hell and eternally chewed by Satan himself for his crime of betrayal. But Swift's "Gulliver's Travels" described him as one of the most virtuous and benevolent people to have lived. The interpretation of Brutus as either a selfless fighter against dictatorship or an opportunistic traitor has shifted with the tides of history and politics. But even today, over 2,000 years later, questions about the price of liberty, the conflict between personal loyalties and universal ideals, and unintended consequences remain more relevant than ever. |
TEDEd_World_History | History_vs_Henry_VIII_Mark_Robinson_and_Alex_Gendler.txt | He was a powerful king whose break with the church of Rome would forever change the course of English history. But was he a charismatic reformer or a bullying tyrant? Find out on History versus Henry VIII. Judge: Order, order. Now, who do we have here? Looks like quite the dashing fellow. Defense: Indeed, your honour. This is Henry VIII, the acclaimed king who reformed England's religion and government and set it on course to becoming a modern nation. Prosecutor: I beg to differ. This is a cruel, impulsive, and extravagant king who had as little regard for his people as he did for his six wives. Judge: Six wives? Defense: Your honor, Henry's first marriage was arranged for him when he was only a child. He only married Catherine of Aragon to strengthen England’s alliance with Spain. Prosecutor: An alliance he was willing to toss aside with no regard for the nation. Defense: Henry had every regard for the nation. It was imperative to secure the Tudor dynasty by producing a male heir – something Catherine failed to do in over twenty years of marriage. Prosecutor: It takes two to make an heir, your honor. Defense: Ahem. Regardless, England needed a new queen to ensure stability, but the Pope refused to annul the union and let the king remarry. Judge: Sounds like quite a pickle. Can’t argue with the Pope. Prosecutor: And yet that’s exactly what the king decided to do. He uprooted the country’s religious foundations and broke the Church of England away from Rome, leading to centuries of strife. Defense: All Henry did was give the Church honest domestic leadership. He freed his subjects from the corrupt Roman Catholic establishment. And by rejecting the more radical changes of the Protestant reformation, he allowed his people to preserve most of their religious traditions. Prosecutor: Objection! The Church had been a beloved and popular institution that brought comfort and charity to the masses. Thanks to Henry, church property was seized; hospitals closed, and precious monastic libraries lost forever, all to enrich the Crown. Defense: Some of the funds were used to build new cathedrals and open secular schools. And it was necessary for England to bring its affairs under its own control rather than Rome’s. Prosecutor: You mean under Henry’s control. Defense: Not true. All of the king’s major reforms went through Parliament. No other country of the time allowed its people such a say in government. Prosecutor: He used Parliament as a rubber stamp for his own personal will. Meanwhile he ruled like a tyrant, executing those he suspected of disloyalty. Among his victims were the great statesman and philosopher Thomas More – once his close friend and advisor – and Anne Boleyn, the new queen Henry had torn the country apart to marry. Judge: He executed his own wife? Defense: That…wasn’t King Henry’s initiative. She was accused of treason in a power struggle with the King’s minister, Thomas Cromwell. Prosecutor: The trial was a sham and she wouldn’t have been convicted without Henry’s approval. Besides, he wasn’t too upset by the outcome - he married Jane Seymour just 11 days later! Defense: A marriage that, I note, succeeded in producing a male heir and guaranteeing a stable succession… though the new queen tragically died in childbirth. Prosecutor: This tragedy didn’t deter him from an ill conceived fourth marriage to Anne of Cleves, which Henry then annulled on a whim and used as an excuse to execute Cromwell. As if that weren’t enough, he then married Catherine Howard – a cousin of Anne Boleyn – before having her executed too. Defense: She was engaged in adultery to which she confessed! Regardless, Henry’s final marriage to Catherine Parr was actually very successful. Prosecutor: His sixth! It only goes to show he was an intemperate king who allowed faction and intrigue to rule his court, concerned only with his own pleasure and grandiosity. Defense: That grandiosity was part of the king’s role as a model for his people. He was a learned scholar and musician who generously patronized the arts, as well as being an imposing warrior and sportsman. And the lavish tournaments he hosted enhanced England’s reputation on the world stage. Prosecutor: And yet both his foreign and domestic policies were a disaster. His campaigns in France and his brutal invasion of Scotland drained the treasury, and his attempt to pay for it by debasing the coinage led to constant inflation. The lords and landowners responded by removing access to common pastures and turning the peasant population into beggars. Defense: Beggars who would soon become yeomen farmers. The enclosures made farming more efficient, and created a labor surplus that laid the foundation for the Industrial Revolution. England would never have become the great power that it did without them …and without Henry. Judge: Well, I think no matter what, we can all agree he looks great in that portrait. A devout believer who broke with the Church. A man of learning who executed scholars. A king who brought stability to the throne, but used it to promote his own glory, Henry VIII embodied all the contradictions of monarchy on the verge of the modern era. But separating the ruler from the myth is all part of putting history on trial. |
TEDEd_World_History | Who_was_Confucius_Bryan_W_Van_Norden.txt | Most people recognize his name and know that he is famous for having said something, but considering the long-lasting impact his teachings have had on the world, very few people know who Confucius really was, what he really said, and why. Amid the chaos of 6th Century BCE China, where warring states fought endlessly among themselves for supremacy, and rulers were frequently assassinated, sometimes by their own relatives, Confucius exemplified benevolence and integrity, and through his teaching, became one of China's greatest philosophers. Born to a nobleman but raised in poverty from a very young age following the untimely death of his father, Confucius developed what would become a lifelong sympathy for the suffering of the common people. Barely supporting his mother and disabled brother as a herder and account keeper at a granary, and with other odd jobs, it was only with the help of a wealthy friend that Confucius was able to study at the Royal Archives, where his world view would be formed. Though the ancient texts there were regarded by some as irrelevant relics of the past, Confucius was inspired by them. Through study and reflection, Confucius came to believe that human character is formed in the family and by education in ritual, literature, and history. A person cultivated in this way works to help others, guiding them by moral inspiration rather than brute force. To put his philosophy into practice, Confucius became an advisor to the ruler of his home state of Lu. But after another state sent Lu's ruler a troop of dancing girls as a present and the ruler ignored his duties while enjoying the girls in private, Confucius resigned in disgust. He then spent the next few years traveling from state to state, trying to find a worthy ruler to serve, while holding fast to his principles. It wasn't easy. In accordance with his philosophy, and contrary to the practice of the time, Confucius dissuaded rulers from relying on harsh punishments and military power to govern their lands because he believed that a good ruler inspires others to spontaneously follow him by virtue of his ethical charisma. Confucius also believed that because the love and respect we learn in the family are fundamental to all other virtues, personal duties to family sometimes supersede obligations to the state. So when one duke bragged that his subjects were so upright that a son testified against his own father when his father stole a sheep, Confucius informed the duke that genuinely upright fathers and sons protected one another. During his travels, Confucius almost starved, he was briefly imprisoned, and his life was threatened at several points. But he was not bitter. Confucius had faith that heaven had a plan for the world, and he taught that a virtuous person could always find joy in learning and music. Failing to find the ruler he sought, Confucius returned to Lu and became a teacher and philosopher so influential, that he helped shaped Chinese culture and we recognize his name worldwide, even today. For the disciples of Confucius, he was the living embodiment of a sage who leads others through his virtue, and they recorded his sayings, which eventually were edited into a book we know in English as "The Analects." Today, millions of people worldwide adhere to the principles of Confucianism, and though the precise meaning of his words has been debated for millennia, when asked to summarize his teachings in a single phrase, Confucius himself said, "Do not inflict upon others that which you yourself would not want." 2,500 years later, it's still sage advice. |
TEDEd_World_History | Did_ancient_Troy_really_exist_Einav_Zamir_Dembin.txt | When Homer’s Iliad was first written down in the 8th century BCE, the story of the Trojan war was already an old one. From existing oral tradition, audiences knew the tales of the long siege, the epic duels outside the city walls, and the cunning trick that finally won the war. In the end, the magnificent city was burned to the ground, never to rise again. But had it ever existed? By the time the field of archaeology began to take shape in the 19th century, many were skeptical, considering the epic to be pure fiction, a founding myth imagining a bygone heroic era. But some scholars believed that behind the superhuman feats and divine miracles there must have been a grain of historical truth - a war that was really fought, and a place where it happened. Frank Calvert was one such believer. He had spent his youth traveling and learning about ancient civilizations before accompanying his brother Frederick on a diplomatic mission to the northwest Anatolian region of Çanakkale. It was here that Homer described the Greek encampment at the mouth of the Scamander river. And it was here that fate brought Frank into contact with a journalist and geologist named Charles Maclaren. Locals and travelers had long speculated that Troy might’ve stood on one of the surrounding hilltops. But Maclaren had been one of the first to publish a detailed topographical study of the area. He believed he had found the site – a 32-meter mound known by the name Hisarlık, derived from the Turkish word for “fortress.” Soon after meeting with him in 1847, the Calverts bought 2,000 acres of farmland that included part of the hill. Before they could explore any further, the Crimean War broke out and forestalled their archaeological ambitions for several years. After the war’s end, Frank Calvert began to survey the site, but lacked the funds for a full excavation. This was where the wealthy German businessman and amateur archaeologist Heinrich Schliemann came in. At Calvert’s invitation, Schliemann visited the grounds in 1868, and decided to excavate. Eager to find the ancient city, Schliemann tore massive trenches all the way to the base of the hill. There, he uncovered a hoard of precious artifacts, jewelry, and metalwork, including two diadems and a copper shield. Schliemann took full credit for the discovery, announcing that he had found Troy and the treasure of its king Priam. But the real treasure was elsewhere. When later archaeologists studied the site, they realized that the mound consisted of no less than nine cities, each built atop the ruins of the last. The layer Schliemann had uncovered dated back to the Mycenaean Age, more than 1,000 years too early for Homer. But inside the mound was indeed evidence for a city that had thrived during the Bronze Age, with charred stone, broken arrowheads, and damaged human skeletons suggesting a violent end. It was Troy VII, contained in the middle layers and now ravaged for a second time by Schliemann’s careless excavation. The settlement, spanning some 200,000 square meters and home to as many as 10,000 people, thrived until around 1180 BCE. Its position at the southern entrance of the Dardanelles strait would’ve made a formidable strategic location for both defense and trade. Most importantly, there are the remains of a massive fortification wall – perhaps the very same one from which Priam and Hector once watched the Greeks approach. Of course, it’s difficult to be certain that these ruins are the true remains of ancient Troy, and scholars still dispute whether the Trojan War as described by Homer ever happened. Yet the evidence is strong enough that UNESCO has labelled Hisarlık the archeological site of Troy. Regardless of its identity, thanks to persistence, a bit of faith, and a lot of research, archaeologists are bringing the long-buried secrets of an ancient, lost city to light. |
Open_Ed_Cyrus_Patell_American_Literature | American_Puritanism_III.txt | >> Lecturer: So today we're talking about Puritan poetry, which, at one point used to be regarded as if it were something of an oxymoron. How could the Puritans actually produce poetry since they seem to be hostile to imaginative literature of any kind? Puritan theologians used to warn that the senses were unreliable. It's that whole total depravity thing: if the world is totally depraved, then anything of the world is unreliable at best and damned to hell at worst. And that would include most uses of human language. You have to understand that -- the Puritan poet has a particular problem. And this is going to be true of all three of the ones we're going to look at today and I think especially true of Edward Taylor, which is this: How do you represent something divine when the tools that you have are human? How can you represent the incommensurability of the divine mind to the extent to which it is so different from the human mind when all that you have is human tools? Which again, are unreliable at best and may be worse; damned at worst. So that's one of the problems that the Puritan poet has is kind of technical problem. Figurative language the Puritans distrust. They distrust graven images of any kind. I mean, they are very much opposed to both the Catholic's and the Anglican's use of what they consider to be graven images, their emphasis on speaking eloquently at the pulpit as a way of appealing to their parishioners, the use of music and vestments in Anglican and Catholic rituals -- the Puritans are distrustful of all of this and then they don't do it. In fact in England, the Puritans become iconoclastic destroyers of religious imagery, especially during the Civil War. So they're really opposed to various kind of representation. And so Puritan doctrines were generally thought to have forbidden any kind of figurative language, except when you're using it for the purpose of religious instruction. So this would seem to be a formidable set of obstacles, you might say, to the production of anything that we might call "Puritan art" or "Puritan poetry." And there's an early statement in New England of what people have taken to be kind of principles of the Puritan use of language. And it comes from something that's called The Bay Psalm Book, which I'll show you in just a minute. But I want to show you where that fits in. So that's going to be 1640, The Bay Psalm Book. And this is roughly speaking, the chronology that we're working with over the last couple of times, right? The Bradstreet and Dudley families arrive with Winthrop in 1630. 1630 is also the time when Bradford is writing the History of Plymouth Plantation, their plantation having been there for ten years already. Hutchinson emigrates four years later. She's tried four years after that and banished the following year. 1648, that Cambridge Platform in which part of the problem that Hutchinson's Antinomian Controversy produces is a problem of: How do we know when people have been converted? This idea that conversion should be personal on the one hand, the way that Hutchinson would approve but also public. You need to make a public profession of your faith. So that's some of the stuff that we've been talking about. Bradstreet is writing poetry during these years, and she publishes her first volume there. And we'll talk a little bit more about how what we are thinking about the second half of Wigglesworth's Day of Doom is roughly contemporary with Paradise Lost and also just before the beginning of King Philip's War and the development of, you might say, the jeremiad by this time. And you might say that The Jeremiah develops in 1670, but in some sense the form is already being pioneered in not only sermons but even in a poem like the Day of Doom, which as we'll see has certain Jeremiahatic kinds of structures and sensibilities behind it. So this is roughly the chronology we're talking about. And what I'm trying to do in making this chronology is show you how the poetic productions that we'll be talking about today map onto the things that we've been talking about in the past week, that literature of settlement and then Winthrop's "Puritan City on a Hill" and Rowlandson. So you might say this week is poetry for today and then prose is what we're mapping it onto. And this will be on the post lecture notes. Now the Bay Psalm Book was a translation of psalms done in Massachusetts Bay. Its full title was The Whole Book of Psalms Faithfully Translated Into English Metre. And it's that "faithfully" that is the important term there. They had inherited -- they had brought with them -- a version of the psalms that had been used in the Anglican Church. And various clergy in New England began to think of that as overly poetic, too figurative, not literal enough. And in fact, the preface is written by John Cotton, who is a very conservative minister who had ties to Hutchinson originally and was one of the more conserve ministers in New England at the time. And his point of departure, the preface that he writes, is almost a little sermon I suppose. It certainly takes as a point of departure a particular text from the Bible, and that text is this one in Exodus 20: "The lord says an altar of earth thou shalt make unto me. And if thou wilt make me an altar of stone, thou shalt not build it of hewn stone: for if thou lift up thy tool upon it, thou hast polluted it" -- just the stone, don't chisel it, leave it alone, that's enough. And this was taken metaphorically when Cotton does his introduction to the kind of gloss of this. It's the idea that all you need is the Bible faithfully rendered. You don't have to make it more fanciful or figurative or easier to read. In that sense, there's a way in which you're polluting it. So this is what Cotton says: "Never let any think that for the metre's sake we have taken liberty or poetical license to depart from the true and proper sense of David's words in the Hebrew verses. No. But it has been one part of our religious care and faithful endeavor to keep close to the original text." Now when you're looking at something like this from the self-conscious point of view that I've been encouraging, you might want to look at first of all, what assumptions lie beneath a piece of text like this and then also what kinds of relations it sets up? What's good? What's bad? Of what does it disapprove? Of what does it approve? If you go back to the piece that we had you read from Stephen Greeblatt, that idea of culture, he talks about poems of praise and blame. And he says when you're looking at these kind of extreme forms of poetry -- poems of praise and blame -- you can quite clearly see how certain ideological points of view work their way in. The poet is trying to praise someone; you can see a certain of ideological assumptions at play. Blame -- the same thing. It's easier to see. Then he says, "look for those structures in everything that you read." So what is being praised and what is being blamed here just in this little snippet of text? Anybody? The meanings aren't hidden. They're just kind of right there. What's being praised? Yeah? >> Ordinariness. >> Lecturer: Okay. Ordinariness. What word would you use to say "ordinariness"? What? >> Unembellished. >> Lecturer: Okay, good. Unembellished. Where is "unembellished"? No, that word works from this. Like if you say, "Okay fine, the concept is ordinariness, so we need to pull our data from the actual text." What word suggests ordinariness? >> Not taking poetical [inaudible]. >> Lecturer: Okay, so ordinariness suggests "not for the meter's sake have we taken liberty or poetical license." So what's being praised and what's being blamed? Ordinary is being praised; what's being blamed? Yeah? >> Poetical license. >> Lecturer: Yeah, sure, poetical license. And not only poetical license, it's "or poetical license" but liberty. We haven't taken liberties with the text. Just think about that phrase: "take liberties with the text." Somehow that's departing from what is ordinary. It's set up, you might say, against the idea of being faithful. If you're faithful to something, you don't take liberties with it. And yet, "liberty" means what? I mean, liberty means freedom. So there's a certain sense in which there is kind of a constraint, a self-imposed constraint that's being built into this. And you might say that's part of Puritan ideology. Puritan ideology is about imposing constraints on yourself because you believe that that's the way that you should follow God's will. He goes on, "if therefore the verses are not always so smooth and elegant as some may desire or expect, let them consider that God's altar needs not our polishings." That's Exodus 20 that I showed you. This is how glosses it: "God's altar needs not our polishings." So we have respected rather a plain translation -- and see, that would be for your ordinary point. So you're going to say he's talking about the importance of ordinary language, plain translation. Remember I told you when we were talking about Bradford that Bradford and other Puritans were thought to have written in a plain style. When I suggested to you that's kind of a misreading of what they're doing. In a certain way, the diction may be plain enough, but it's built -- as I hoped you saw -- on a whole set of ideological assumptions and a symbolic structure about the old world versus the new world; the Old Testament versus the New Testament; who is the chosen people, who isn't the chosen people. And Bradford's ninth chapter is that strange little performance when he stops, addresses himself to some reader, brings in the Indians, breaks chronology, compares himself to the apostles, right? It's a very complicated piece of rhetoric -- not plain at all. And yet, critics who believe that it was plain back in the day used to take their cue from this: "We respected rather a plain translation than to smooth our verses with the sweetness of any paraphrase and so have attended conscience rather than elegance." Fidelity rather than poetry, right? That's why I'm suggesting to you that Puritan poetry was often regarded as if it were an oxymoron. It would seem that this whole idea of faithfulness is in direct opposition to some category that we would label "poetry." So we want not poetry, which somehow seems to be false, fictitious. Fidelity, in translating the Hebrew words into English language and David's poetry into English meter. I mean, there's a kind of weird slippage here, right? I mean, that portion of the Bible is poetry -- the Psalms -- and yet the Puritans are suspicious of poetry. And yet there's poetry in the Bible. What are we going to do about that? Well, we'll make it yucky to read. That will make it better or truer. "That so we may sing in Sion the Lord's song of praise according to his own will until he take us from hence and wipe away all our tears and bid us enter into our master's joy to sing eternal halleluiahs." Amen, right? That sounds like a sermon, and yet it's an introduction to this book of the Bible. So one of the things we need to see is that this, in a certain sense, is the horizon of expectations against which poets like Wigglesworth, Bradstreet, and Taylor are writing. This is what their audience is expecting to read: poetry as almost a kind of necessary evil that's tolerable only when it's in the service of religious instruction. So when people nowadays say that Anne Bradstreet is interesting to us it's precisely because they're interested in the way that she is in some sense rebelling against this. They portray her as a kind of cultural rebel, who is rebelling not only against the formal strictures against smooth verses and sweetness and poetry and paraphrase, but also against the very narrow role that the Puritans construct for women. Likewise, Edward Taylor is portrayed as somebody who isn't part of mainstream Puritan culture. He's living for the most part out in the sticks. And he's engaged in sort of theological disputes, but they're mostly in his head and through his writing. And he in some sense is kind of an outlier from mainstream Puritan society. There's a sense in which Taylor kind of knew that he was doing something that might not be regarded as strictly speaking "doctrinaire," therefore he never published his poetry. It remained unpublished -- almost lost, actually, although he carefully preserved it. It's like he carefully preserved it in these bound volumes that he handed down to his family. I think they were eventually discovered in an attic someplace and given to the Yale Library in 1920. So Taylor was not well-known in literary circles until the 20th century. So there's a sense in which you might say the conditions -- the context -- in which these two poets, especially Bradstreet and Taylor lived had everything to do according to this train of scholarly thinking with the fact that they could produce the poetry they did. Bradstreet had a more liberal father and husband who believed that women should be educated. Back in England, she was able to read truly English poetic tradition with her father. She was relatively well-to-do. She had servants. She didn't have to spend all of her time raising the children and doing housekeeping. And Taylor, off in the sticks, able to pursue a kind of quiet life of contemplation. He also was able to write these poems. And there's a sense in which, from the standpoint of what we're thinking about today, we're going to use Michael Wigglesworth as kind of the control group for us. So you might say that the kind of poetry we would expect to be produced -- if this is what our idea of poetry is, Cotton strictures about poetry -- if that's going to be the plan for producing poetry, probably is going to look something like Wigglesworth. And then we'll look at the other two as potentially departures. And again, I wanted to stress to you the idea of the jeremiad. By the time Danforth gives his sermon, "Errant Into the Wilderness" in 1670, the jeremiad has already a kind of settled sermonic form. But the logic behind the jeremiad has been there from the beginning: "We are the chosen people. We did something wrong, just as Adam did something wrong. Adam has to pay for that, he has to be tested. We often will have to be tested. In the end, because God is merciful, he redeems Adam's progenies through the agency of Christ. In the end, he will redeem us. We're certain of that. So no matter how bad things are, if we just abide by the straight and go back to the original zeal of the founders, that will be a sign if we have inclination to do this, it will be a sign that somehow God is still paying attention to us." Remember that moment from Rowlandson. The worst thing that she can imagine is not that she should go to hell; it's that God doesn't care about her, that he's just forgotten about her. So there's a sense within the jeremiad that even if you're listening time after time to the preacher, telling you about how sinful you are and the garden of the new world has become overgrown with weeds, it's a howling wilderness again, nevertheless it convinces us that all of this punishment has taken place precisely because God is disappointed, precisely because he cares. Because God has chosen the Puritans to be the chosen people. That structure goes along with Wigglesworth as well. And it's interesting to note again that Wigglesworth is 1662. John Milton's great poem Paradise Lost -- how many of you have read Paradise Lost in the context of some course here? Okay. So you know a little bit about Paradise Lost. 1667 -- roughly the same topic: paradise lost and then regained is basically the thing that both of them are interested in. But Milton looks a little bit different, you would say, from Wigglesworth. Let's take a look at Wigglesworth. This is on page -- let's take a look at the beginning of Wigglesworth on page -- sorry, I've lost my page. Let's just go to the very beginning, 218. Could somebody read the first stanza for me of Wigglesworth? Yes? Go ahead, loudly and with conviction. >> "Still was the night, Serene and Bright, when all Men sleeping lay; Calm was the season, and carnal reason thought so 'twould last for ay. Soul, take thine ease, let sorrow cease, much good thou hast in store: This was their Song, their Cups among, the Evening before." >> Lecturer: Okay, good. Interestingly, you didn't read the stuff in the margin. It's an interesting question about what relation the stuff in the margin has to the stuff that you just read. Most people would not bother with the stuff in the margin. All right, now read that, please. >> "Of Man's first disobedience, and the fruit Of that forbidden tree whose mortal taste Brought death into the World, and all our woe, With loss of Eden, till one greater Man Restore us, and regain the blissful seat, Sing, Heavenly Muse, that, on the secret top Of Oreb, or of Sinai, didst inspire That shepherd who first taught the chosen seed In the beginning how the heavens and earth Rose out of Chaos: or, if Sion hill Delight thee more, and Siloa's brook that flowed Fast by the oracle of God, I thence Invoke thy aid to my adventurous song, That with no middle flight intends to soar Above th' Aonian mount, while it pursues Things unattempted yet in prose or rhyme." >> Lecturer: Thank you. [ Applause ] Come on, give him a hand. [ Applause ] They're a little bit different, right? Okay, so let's comment a little bit. Let's start with this one because in a funny way, this is more familiar to us as a piece of great lit that we study in survey courses. What do we notice about it or what have you been told about it? This is just the first few lines of Book One from Milton. But as I said -- and it begins with all kinds of prose prefaces and stuff -- but when you look at this, there are certain grounds rules that Milton is immediately establishing, certain things he's invoking, certain styles he's invoking. So if we were going to look at this as a piece of text, we would start to catalog our data. Nothing is too insignificant to be written down in our catalog because we may not use it or we may use it. So something we notice about this? Anything? Yes? >> It has a lot more details. >> Lecturer: Okay, that's good. It has a lot more details. We don't even need to think about it in terms of Wigglesworth right now. So there are details. Would you point to any particular details that seem interesting to you? >> [ Inaudible ] >> Lecturer: Okay, so one kind of detail is particular proper names, places in the Bible, right? That good? What about this phrase, just above the one you pointed to? "Sing heavenly muse." Anybody do anything with that? Yeah? >> [ Inaudible ] >> Lecturer: Okay. It belongs not to the same tradition you might say as Oreb or Sinai, but the tradition of Greek. Greek what? Anybody? >> Greek epic. >> Lecturer: Greek epic, yes. You were going to say? >> I was going to say there's no rhyme scheme. >> Lecturer: Okay, so it was written in -- what does it mean when there's no blank [laughter]. All right, there you go. What does it mean when it's not written in rhyme? >> Blank. >> Lecturer: Okay, but what metre is it generally in if it's "blank verse"? >> Iambic. >> Lecturer: Yeah, so it's pretty much iambic pentameter. I'm trying to find a good line. "Brought death into the world and all are woe." Five feet. That's the standard English metre -- metre in English for poetry -- iambic pentameter. When you don't write in iambic pentameter, you're usually doing something for effect. So this is written in iambic pentameter. Since it's unrhymed, we call it "blank verse." Very good. So we've got unrhymed iambic pentameter. It doesn't look like it's in stanzas. We've got proper names drawn from the Biblical tradition, also a kind of invocation of Greek epic. The very beginning of epic is "sing." The beginning of Virgil's Aeneid: "I sing of arms of a man," "arma virumque cano." So he's invoking that whole tradition. And there are even uses of words like "chaos" that might be compatible with Greek epic, even though one of the things we would say is he's revising that tradition. It's a heavenly muse that's going to be linked directly to the Christian conception of God. Anything else we want to note here? How about the lines? Anything to note about the lines? Where they begin and end maybe? >> They're enjambed? >> Lecturer: Oh, very good. They are enjambed, yes. So that means what? >> It's not the end of the sentence at the end of the line [inaudible] next line. >> Lecturer: Good. So you would say that if a line is strongly end-stop, you would say the grammatical sense of it would end at the end of the line. So you would have a comma there, the cause would be complete, or something not this. "Of man's first disobedience and the fruit," and to find out the fruit of what, we have to continue on, "of that forbidden tree whose mortal taste brought death into the world and all our woe." Stop there. So part of what your job is going to be, like if enjambment were going to be one of the things you're going to be looking for on your scavenger hunt, you'd say, "Okay, that's enjambment," you'd give us an example of it, and then you'd say what the effect is. So you try to think about what the effect of this is. And it could be any number of things that you might think about it. You might say that he kind of puts you on the hook here and he asks you to keep of this, all the more to emphasize this: "our woe." That's where you get the stop. Anyway, anything else to notice about this? Okay, so when you have an enjambment like this, you usually have something else emphasized in the middle of a line. What would that be called? >> Caesura. >> Lecturer: Caesura, right? Almost every line has a kind of natural caesura in it. It's not the same as in Latin where there always is a caesura. But generally speaking, if you find an enjambment, you're going to find a caesura beforehand. So then you think about how those two work together -- what does the caesura emphasize? "A man's first disobedience" -- boom -- "and the fruit of that forbidden tree whose mortal taste brought death into the world and all our woe." No caesura there. So again, you would think about: What do think effects are? And it's going to be interpretive, right? You're trying to think about, "If this were a passage," you'd say, "well, what is the overall effect?" The last thing the poet says here in this passage is "it pursues things unattempted yet in prose or rhyme." Well, is that true? What's going to be unattempted? Is this a standard kind of style? Or is he using a kind of standard style, but within the constraints that are imposed by blank verse? Is he doing interesting things with the enjambments or caesura? Or is it maybe the project of Christian epic? Maybe that's what's not been attempted. So these are some of the things you'd want to -- and if that's what it is, how does the diction, the words that he's chosen and the ways in which he's put them down -- the syntax -- how do they help him right away to signal that something new under the sun is coming in this prose or rhyme? Just a little snippet of Paradise Lost. It's one way to go about telling this in 10 and 12 books of epic -- big. As opposed to this. I should probably have put it up here, but take a look at it again. Still was the night, Serene and Bright, when all Men sleeping lay; Calm was the season, and carnal reason thought so 'twould last for ay. Soul, take thine ease, let sorrow cease, much good thou hast in store: This was their Song, their Cups among, the Evening before." Okay. Look at that. Look at that. Now let's talk about the differences. What do we see in Wigglesworth's poem? Yes. >> There's little need for interpretation or there's no possible [inaudible] beside the One. He's telling you exactly what you need to know. >> Lecturer: So you would say interpretation by us? >> Yes. >> Lecturer: So it's much clearer than this perhaps? I mean, it seems to be more -- now why would you say that? Just the words? >> Yeah, it's hard to think that without comparing it to Milton, but -- >> Lecturer: Well, if you compare to Milton you do see some of the things we noticed, some of those details, are not there. There are no proper names invoked. There's no epic tradition being invoked. The there's no proper nouns at all, actually. So that's one thing you might say. But in terms of fixing interpretation, if you're the reader, what is it also helping to fix interpretation? Yeah? >> The singsong nature of it is very easy to -- like in the introduction, they talked about how since it was written in this sort of rhyming style, [inaudible] people to [inaudible]. >> Lecturer: Okay. So it has -- as opposed to this, which is kind of dense blank verse -- it has a rhyming style: "Wallowing in all kind of sin, vile wretches lay secure: The best of men had scarcely then their Lamps kept in good ure. Virgins unwise, who through disguise amongst the best were number'd, Had clos'd their eyes; yea, and the wise through sloth and frailty slumber'd." Well, when you put it that way, right? Okay, and in the introduction, I think they talk about it's supposed to be an aid to memorization if you keep it in a kind of simple way. Okay, so what is that telling us then? Let's do a little bit more with that. First let's talk about the rhyming scheme. What is the rhyming scheme? Look at the first couple, three verses. >> ABA [ Inaudible ] . >> Lecturer: "Like as of old, when Men grow bold Gods' threatnings to contemn, Who stopt their Ear, and would not hear, when Mercy warned them." AB -- where is the A and where is the B? Look at verse three, "Like as of old, when Men grow bold Gods' threatnings to contemn, Who stopt their Ear, and would not hear, when Mercy warned them." Yeah? >> AABB. >> Lecturer: Okay. And the AA is typically when we say we're talking about the lines, right? But in fact, there's an internal rhyme here. So it's AA in the first line, and then a B, then CC, and then the B. So it's A1, A2, maybe B; then C1, C2; and then the B again. And then the second half the stanza works the same. Okay, that's good. Seems fairly regular. He does it most of the time. So the internal rhyme aids helps with the singsong nature of it. What else helps with the singsong nature of it? How long are these lines? [ Pause ] >> Lecturer: Anybody? >> Iambic tetrameter. >> Lecturer: What's that? >> Iambic tetrameter. >> Lecturer: Iambic tetrameter, which means how many feet? >> Four feet. >> Lecturer: Four feet. Show me. Pick any one. >> "Like as of old, when Men grow bold." >> Lecturer: Okay, "Like as of old, when Men grow bold." That's iambic tetrameter. Next line? >> "Gods' threatnings to contemn." So it's trimester. >> Lecturer: Right. Good. So it's tetrameter: four iambic feet. Trimeter: three iambic feet. Eight beats in the first line, six beats in the second line -- these are called "fourteeners" because they are fourteen beats between each one. It's a kind of ballad and exactly does that. It has that kind of singsong sort of pace. The shortened line makes it easier to remember, but also when you're trying to account for it -- so it has a kind of singsong quality, or it seems plain, or it seems simpler than that, right? Each line is shorter. Plus you combine that with the rhymes. That's how he creates that particular effect. So that's one thing to notice about this. You might say it gives at least the illusion of plainness and simplicity, although I think you would say that if you're actually trying to write these damn things, you have to work on it to get that internal rhyme to work all the time. You've got a lot of stuff going on there, actually. Anything else about fixing interpretation? Yeah? >> [ Inaudible ] >> Lecturer: Okay, good. So each one of these verses you might say is then presented to us as a kind of gloss on something in the Bible or a dramatization of it. So each verse here -- or each stanza -- doesn't have to rely on its own authority; it relies on the authority of something else. We might call the stuff that's in the margin a "paratext," a text that sits side by side. So one of the things to say about this is this poem is clearly intertextual in a similar way to the way that something like Bradford or something like Winthrop is intertextual. It refers you back to some other text, without which the meaning of this wouldn't make sense. That other text completes the meaning of this poem and not the other way around, actually. And that other text is the Bible. So that's one of the things just to bear in mind about how this works. It's thought to have been something that was written primarily for instruction for children. And if you look at it, it follows that kind of jeremiadic structure, right? All of a sudden -- boom -- the day of doom is going to come and there's going to be a whole lot of suffering and stuff going on. And if you look -- I think this is not even the whole poem. They have nicely excerpted it for you. But if you look at the very end. So this is page 233, verse 218. "Thus shall they ly, and wail, and cry, tormented, and tormenting Their galled hearts with pois'ned darts but now too late repenting. There let them dwell i'the' Flames of Hell; there leave we them to burn, And back agen unto the men who Christ acquits, return." And then we get one, two, three, four, five, six verses about how nice it is for those men who are acquitted. The last couple of verses. "For God above in arms of love doth dearly them embrace, And fills their sprights with such delights, and pleasures in his grace; As shall not fail, nor yet grow stale through frequency of use: Nor do they fear Gods favour there, to forfeit by abuse." That's all doctrine. "Nor do they fear Gods favour there to forfeit by abuse." What is it? >> No good works can -- >> Lecturer: Not exactly. I think that's in here some place. It's pretty much all those principles are in here someplace, but that particular one -- "Nor do they fear Gods favour there to forfeit by abuse." You can't forfeit God's favor by abuse there because -- >> [ Inaudible ] >> Lecturer: Right. Perseverance of the saints, right? When you got it, you got it, blah, blah, blah. It doesn't mean you're supposed to go abusing it up there. Of course, you're a saint, you wouldn't want to, right? "For there the Saints are perfect Saints, and holy ones indeed, From all the sin that dwelt within their mortal bodies freed: Made Kings and Priests to God through Christs dear loves transcendency, There to remain, and there to reign with him Eternally." How many verses? One, two, three, four, five, six, seven verses about how nice it is in heaven. And really it's not -- it's kind of six and two lines. And 217 and three quarters verses devoted to hellfire and damnation. That's what people remember about The Day of Doom, right? It's all these vivid images of hell. Take a look for example -- let's pick one. I don't know. Oh, I don't know how about 17? This is on page 222. "Before his Throne a Trump is blown, Proclaiming th' Day of Doom: Forthwith he cries, Ye Dead arise, and unto Judgment come. No sooner said, but 'tis obey'd; Sepulchers open'd are: Dead Bodies all rise at his call, and's mighty power declare." It's kind of like a zombie thing, right? Cool. Or I don't know, let's take a little -- oh, this is even better, especially when you about the audience for this being children. How about on page 231, 199? Or go back to 198 about husbands and wives and then children. "He that was erst a Husband pierc't with sense of Wives distress, Whose tender heart did bear a part of all her grievances, Shall mourn no more as heretofore because of her ill plight; Although he see her now to be a damn'd forsaken wight. The tender Mother will own no other of all her numerous brood, But such as stand at Christ's right hand acquitted through his Blood. The pious Father had now much rather his graceless Son should ly In Hell with Devils, for all his evils burning eternally, Then God most high should injury, by sparing him sustain; -- you'll see there's an enjambment across stanzas there, right? "And doth rejoyce to hear Christ's voice adjudging him to pain; Who having all, both great and small, convinc'd and silenced, Did then proceed their Doom to read, and thus it uttered:" And then all stuff that he's going to say. What did they just say? "We'd rather send our children to hell and we're happy about it rather than they should be up there sullying God's grace if they are not redeemed." Every now and then, I feel like doing the same thing to my kids. But most of the time, that would be painful. Your kids. I mean, how unregenerate can they be? Well, I don't know. I guess if they haven't been converted yet and the Day of Doom comes along and -- oopsy daisy -- just didn't make it in time. Or maybe they were never meant to make it in time. Maybe we throw them into the flaming lake. So you might see that one of the things that this does if you're a child is it kind of puts the fear of God into you quite literally. I often like it to a movie, I don't know. Has anybody ever seen Brian De Palma's Scarface or anything like Brian De Palma's Scarface? I mean, we have two and some hours of unmitigated violence of all kinds, including cutting arms off with power saw. And then at the end, of course, he's a drug dealer and a bad guy and comes to no good, and he gets killed. And you can say at the end, "Look violence doesn't pay, being a bad guy doesn't pay. Everybody gets their comeuppance at the end." Official that's the moral of the story, except that you've been watching it for two hours and probably if you're a certain kind -- let's just say that when this first came out, certain friends of mine were quite taken with this movie, saw it several times, and started spending all their time talking like Tony Montana, Al Pacino's drug dealing Cuban -- "Hey man, don't fuck with me, man. Come on, man. I'll fucking fuck you up." [ Laughter ] And so you're enjoying that for two hours and then you get to say, "Oh, but of course he was a bad guy and he gets what he deserves at the end." See what I'm saying? There's a certain way in way that moral somehow seems perhaps a little insufficient, given what you've witnessed. I would say that's same thing here: 217 plus verses devoted to hellfire and damnation, and six and change to devoted to why God's grace. Of course, you have sort of doctrinaire ending and yet for the most part, the way the poem works is to put exactly that kind of fear of hellfire and damnation into you. So there's a sense in which Wigglesworth has his cake and eat it, too, just as De Palma does in that movie or any movie that's kind of like that where the bad guys get their own in the end, and yet we've been kind of following -- with probably more interest than we should -- their careers during the course of it. And I think that's one of the things to understand about the jeremiadic structure. I mean, there's a sense in which you might say it can backfire. There are problems with this. And this will come up next time when Jonathan Edwards, who is paradoxically remembered most perhaps today for one sermon that he preached, called "Sinners in the Hands of an Angry God" that uses this strategy. For the most part, he's very suspicious of this strategy. He doesn't want people to be scared into obedience; he wants you to embrace obedience. He wants you, you might say, to really take to heart those last six verses and not be so swayed by the first 217 or so. And I think that's also true of Edward Taylor the poet. One of the things that Taylor does when he's thinking about regeneration and the act of receiving grace is he fundamentally is more interested in grace itself than he is in hellfire and damnation. There's a funny way in which Wigglesworth's poem has more of a kind of tragic sensibility about it. And there's a fundamentally comic sensibility that animates Taylor as we'll see. All right. Other questions about this? I hope you've seen just some of the ways in which this poem works. It has certain tricks that it uses, and among these tricks are some that have to do with the actual words that he choses, the way the rhyme schemes are set up, and then just the larger structure of the poem, which again, we might say follows this kind of jeremiadic structure: blame, blame, blame, blame, saved. Okay. Any questions about that? All right. With Bradstreet we get something really different. I mean, there's a certain way in Bradstreet is a little bit more like Milton in terms of the ways in which she makes use of more traditional verse forms. And this is a nice stain glass window representation. I don't know the year of this. I have to find out. In England. We'll keep that up for a little bit. So one of the things again we would say and Bradstreet is that she's different. She comes from a very prominent family. She, again, is part of Winthrop's group in 1630. And there's a sense in which she, even as she's writing, there's a kind of loosening up of strictures about poetry. So she comes knowing the English tradition, in part through her father who maintained a large library in England. And by 1650, which is about ten years after The Bay Psalm Book and the year that her first collection of poems is published, there's already a kind of shift evident in Puritan attitudes towards writing. Increasingly Puritan writers felt licensed, you might say, to use what we might think of as worldly or even sensual imagery so long as it was in the service of religious purposes. So there was another translation of The Bay Psalm Book. It was revised again, this time it was 1651 by President Henry Dunster of Harvard and by Richard Lyon, who was a minister. And they claim to have had a special eye for the sweetness of the verse, so what goes around comes around. We're back to thinking again about the needs of think about capturing the sweetness of the verse of David's poetry. And in fact, Cotton Mather later said that it was thought that a little more art was to be employed upon the verses than in the previous translation of The Bay Psalm Book. So this book was published in London in that year in 1650 and it remained the first still existing book of poetry -- and we think still the first one to be published by inhabitants of the Americas. And Bradstreet was born in England, precisely in here in Lancashire and she was educated by her father who was the steward to an earl, the Earl of Lincoln. Her father was a devout Puritan, but he didn't seem to see any contradiction between having strong religious convictions and also advocating that women like his daughter should be educated. And again, that was a kind of more liberal perspective among of Puritans. So she marries her father's assistant, Simon Bradstreet, and they both immigrate to America. She is shocked by how difficult it is to immigrate to America. I was kind of making fun of Reagan's turning Winthrop into a rugged individualist and saying "little wooden bow and early freedom man." But it is true that they went through very difficult conditions. In fact, Bradstreet has a diary, some of which still remains. And she writes in the diary about missing some of the comforts of England and how she resisted the kind of new customs and manners of America. But eventually the two families -- the Bradstreets and the Dudleys -- do become very successful and they settle down in Andover. She has, let's see, eight children between 1633 and 1652, and I think some miscarriages in there as well. And she's responsible for educating them, for running the household, but she is wealthy enough to afford servants. So she's able to do this writing. First kid is 1633, first known poem that she composes is about 1632 when she's 19. And in 1645, she collects her poetry in a private, informal volume that she dedicates to her father. And her early poetry is less interesting to us. It's generally more formulaic, more dutiful, more along those kind of didactic lines that are prescribed by something like the preface to The Bay Psalm Book. But eventually she starts writing about other themes. And finally, her brother-in-law takes her poems without her permission, brings them to England, and they're brought out in 1650 without her knowledge, although they are very well-received when they come out there. So one of the things we might think about, then, is what it means to be someone in this position, to be Bradstreet, to be writing poems and then later on to find out that they've been published. Let's take a look at the very beginning of the Bradstreet section. I think it's page 188. Look at the prologue. And again, just might help us for a minute. [ Pause ] >> Lecturer: It's a little bit long. It's actually -- I think it makes sense to read the whole thing out loud. Will somebody be brave and read the whole thing out loud? [ Pause ] >> Lecturer: No one brave here? Okay. The whole thing. >> The whole prologue? >> Lecturer: The whole prologue, all eight stanzas -- loudly and with feeling. Ready? Go. >> To sing of Wars, of Captains, and of Kings, Of Cities founded, Common-wealths begun, For my mean Pen are too superior things; Or how they all, or each their dates have run, Let Poets and Historians set these forth. My obscure lines shall not so dim their worth. But when my wond'ring eyes and envious heart Great Bartas' sugar'd lines do but read o'er, Fool, I do grudge the Muses did not part, 'Twixt him and me that over-fluent store. A Bartas can do what a Bartas will But simple I according to my skill. From School-boy's tongue no Rhet'ric we expect, Nor yet a sweet Consort from broken strings, Nor perfect beauty where's a main defect. My foolish, broken, blemished Muse so sings, And this to mend, alas, no Art is able, 'Cause Nature made it so irreparable. Nor can I, like that fluent sweet-tongued Greek Who lisp'd at first, in future times speak plain. By Art he gladly found what he did seek, A full requital of his striving pain. Art can do much, but this maxim's most sure: A weak or wounded brain admits no cure. I am obnoxious to each carping tongue Who says my hand a needle better fits. A Poet's Pen all scorn I should thus wrong, For such despite they cast on female wits. If what I do prove well, it won't advance, They'll say it's stol'n, or else it was by chance. But sure the antique Greeks were far more mild, Else of our Sex, why feigned they those nine And poesy made Calliope's own child? So 'mongst the rest they placed the Arts divine, But this weak knot they will full soon untie. The Greeks did nought but play the fools and lie. Let Greeks be Greeks, and Women what they are. Men have precedency and still excel; It is but vain unjustly to wage war. Men can do best, and Women know it well. Preeminence in all and each is yours; Yet grant some small acknowledgement of ours. And oh ye high flown quills that soar the skies, And ever with your prey still catch your praise, If e'er you deign these lowly lines your eyes, Give thyme or Parsley wreath, I ask no Bays. This mean and unrefined ore of mine Will make your glist'ring gold but more to shine. >> Lecturer: Thank you. [ Applause ] That was very good. All righty. What do we notice about it? Yes? >> Well, the first thing you notice is [inaudible]. >> Lecturer: Okay. Excellent. First stanza -- Greeks, muses, and even into the later stanzas. How is she talking about it? Yeah? >> In terms of art and in terms of the way they created art and found [inaudible]. >> Lecturer: Okay. Push it one more. What is her relation to that old Greek tradition that she's invoking? "To sing of Wars, of Captains, and of Kings, Of Cities founded, Common-wealths begun, For my mean Pen are too superior things; Or how they all, or each their dates have run, Let Poets and Historians set these forth. My obscure lines shall not so dim their worth." >> She's kind of setting herself below that, saying, "Okay, they've done this. I'm just merely [inaudible]." >> Lecturer: Exactly. "My mean pen." And look at the categories. Again, we're look at systems of value -- what she praises and what she blames. She's praising the men. They belong to two categories: they are poets and historians. So if they're poets and historians, what is she? Is she not a poet? There's a weird category kind of thing going on. "But when my wond'ring eyes and envious heart Great Bartas' sugar'd lines do but read o'er, Fool, I do grudge the Muses did not part 'Twixt him and me that over-fluent store. A Bartas can do what a Bartas will But simple I according to my skill." So there's an immediately -- what would we say? Self-deprecatory tone. She's presenting herself as almost a kind of supplicant. She's humble because she's a woman, right? Women aren't supposed to do this. She's not supposed to be writing about sing, wars, and captains, kings, and all that kind of stuff. And she's suggesting it's almost like a paralypsis at the beginning, right? "All these things I'm not going to do." So she's setting out first what it is she's not going to do before she gets to what it is she is going to do. And look at the self-deprecation continue in the third stanza: "From School-boy's tongue no Rhet'ric we expect," -- because they're too young; they're not educated -- "Nor yet a sweet Consort from broken strings," -- if the instrument's broken, it's just not going to make good music. "Nor perfect beauty where's a main defect. My foolish, broken, blemished Muse so sings, And this to mend, alas, no Art is able, 'Cause Nature made it so irreparable." "I just don't have the tools, I don't have the talent, I'm kind of a housewife." It's a set up for what she's trying to do. All right. Just some of the formal stuff. What will we know to say, if you need to, in comparison to these lines, this invocation of the epic tradition? How is hers different? Yeah? >> Iambic pentameter. >> Lecturer: That's also iambic pentameter, good >> ABABCC. [Inaudible] >> Lecturer: Good. These are all things you should notice. So it ends with pretty much a heroic couplet, they're strongly end-stopped for the most part. Anything else? One of the things we might say about it is it's so standard that the form is not supposed to be an issue. Now you might think of this as a strategy, right? Because look what she says later on. She says: "I am obnoxious to each carping tongue Who says my hand a needle better fits" -- what are you using a pen for? "You're a woman, use a needle, sew. That's what you're supposed to do. Or cook." "A Poet's Pen all scorn I should thus wrong, For such despite they cast on female wits." Females aren't smart enough to do this. "If what I do prove well, it won't advance." So then even if it's good, people will say I stole it or by accident, just a one trick pony. Can't do it again, right? And then she makes another comparison. But think about again the way she's making comparisons to the way that people that we've seen -- Bradford, Winthrop, even Rowlandson are making comparisons. She's not comparing herself to the apostles here; she's going back to the antique Greeks. And she's even suggesting that those antique Greeks -- presumably less enlightened than the Puritans -- are much kinder to women than the Puritans are. "Why feigned they those nine And poesy made Calliope's own child?" And one of the things to look at here is there's a certain way in which this and in a poem that I'll ask you to look at in section this week is a kind of rewrite of this that's called The Preface. She writes it for her second volume. Think about the rhetoric of producing children that's at stake here and then even more so in there. So one of the things you might see here early on is what we'll later on in the 19th century be called the "separation of spheres" as if there is a sphere of men, and that is a sphere of pick it: politics, economics, government, public life, and a sphere of women that has to do with private life, domesticity, religion, education. Obviously religion is a bigger part of public life for men in this period than it will be then perhaps. But that idea of a separation of spheres is something she ostensibly accepts: "Men do this stuff and they do it well. Women are not thought to do this. And what whatever it is I'm doing, let's not call it poetry, let's not call it history, but whatever it is I'm doing, don't feel threatened by it, you men. I'm doing my own little thing here. I wish they had given me more talent, but they didn't so I'm doing my own little thing here." "Let Greeks be Greeks, and Women what they are. Men have precedency and still excel; It is but vain unjustly to wage war. Men can do best, and Women know it well. Preeminence in all and each is yours; Yet grant some small acknowledgement of ours." And now she's being a little bit cunning, right? "And oh ye high flown quills that soar the skies, And ever with your prey still catch your praise, If e'er you deign these lowly lines your eyes, Give thyme or Parsley wreath, I ask no Bays." What does that mean? Who gets bay leaves? What's that? >> Poets. >> Lecturer: Yeah, poets. And when you won the tragic festival, you got the bay leaves. That was a sign of your achievement. She's not asking for that. "Give me the herbs that suit my situation as a woman, and a housewife, and a mother, and a wife. Give me time, give me parsley." I want you to see that this poem drips with irony in the sense that what it is trying to convey is precisely the opposite of what it is saying. She's saying, "Oh, I don't have any talent," and yet it's a very cunningly put together poem. She's saying, "Oh, I can't really be a poet," and yet it absolutely follows various incendiary, recognizable rules for the creation of poetry. There's no question that you would look at the form of this and say if you were reading this 1650 "that's a poem," -- depending on what you think, a pretty good poem. "Give thyme or Parsley wreath, I ask no Bays. This mean and unrefined ore of mine Will make your glist'ring gold but more to shine." Kind of raw material you have polished. And yet you might see that as a prologue to a set of poems, this idea of it as "ore that can be refined" is precisely what the poetic project is going to be. So then when you go back and look at The Preface and see the way in which she rewrites this, I want you to realize that what that poem is actually about is precisely rewriting this. So keep an eye on that for section meetings on Friday. One of the things we would say about this then is what Bradford is doing trying to carve out a space for the practice of -- she's not calling it "poetry," but it is poetry by women within Puritan culture. She's registering awareness of the Greeks. She's showing that she's educated, but she's being suitably self-deprecatory. And one thing to say is that she feels in the same position that we saw Mary Rowlandson in. Mary Rowlandson needs to be licensed to speak, quite literally. Increase Mather has to say, "Go and write this," and her husband has to say, "It's okay." And to make sure that we all understand what it is we're reading, we put a foreword and an afterword to bracket her. And the title, The Sovereignty and Goodness of God Rowlandson is afterwords. She's hemmed in. And there's a certain way in which she is supposed to put her personal feelings, her own grief, her personal experience submerged to the doctrinaire read: kind of masculine authorized set of meanings. Bradstreet is working against those conventions as well. And so what we want to be looking for when we look at her poetry is the way in which she is, in fact, playing with some of these conventions. So something teasing here. But you might say it's ironic precisely because it says, "I'm humble. I have no talent." But really, it's a demonstration that she does have talent and perhaps she's not quite as humble as we think. If you look at her other poems that we had assigned, we will find that some of them seem to be very little about authorized Puritan subjects, especially the ones that are about her husband. Let's see. Let's take a look at To My Dear Loving Husband on 206. And the one you'll do in section is Author to Her Book, which is on the previous page. "If ever two were one, then surely we. If ever man were lov'd by wife, then thee. If ever wife was happy in a man, Compare with me, ye women, if you can. I prize thy love more than whole Mines of gold Or all the riches that the East doth hold. My love is such that Rivers canneot quench, Nor ought but love from thee give recompetence. Thy love is such I can no way repay. The heavens reward thee manifold, I pray. Then while we live, in love let's so persever That when we live no more, we may live ever." Nice little poem to her dear and loving husband. So where's the religious instruction in there? Anybody find it? Well, it does say heaven -- "The heavens reward thee man fold I pray." What's the difference between "heavens" and "Heaven" with a capital H? Are they the same? I don't know, one of them is a little more colloquial. One of them cuts. You'll see this later with Franklin. He has a way of using what look like religious words, but he cuts them down to size very cunningly. Yeah? >> Yeah, I think that also is there when she talks about death. She says "Thy love is such I can no way repay," instead of referring to Christ [inaudible]. >> Lecturer: Right. I mean, you know, the doctrinaire kind of love -- who's everybody's bride groom? Christ. Christ is your real bridegroom. Earthly love is earthly, right? We know about the earth, it's -- say it with me -- "depraved and damned." So earthly love, that includes the chaste love of the husband for the wife. That's damned, too, apparently. Right? How is this square with that? Maybe this is it: "Then while we live, in love let's so persever That when we live no more, we may live ever." Wait a minute. Is that right? You get to live forever because you are so loving when you were -- one of the things I wanted you to see is that she's a far more complex and contradictory poet than we might say should have existed in Puritan America, if Puritan America was such a monolith. So I want you to see that in a sense that there is a way in which Bradstreet is extraordinary because she is a woman poet writing all of these things. But you can see that maybe one of the things we should also think is that if we look at Bradstreet's poetry, we learn something else about the context in which she was writing. Maybe it's not all John Cotton-based psalm based strictures. Maybe it's little bit more open than we had thought, less monolithic, again, that reciprocal relation from the Greenblatt essay between text and context. So think about that. Think also perhaps about moments in some of the other poems. I'll just point to you the one on page 212. The Verses Upon the Burning of Our House. Ask yourself whether -- from what you know -- the house burns and she says, "Okay, but they're just earthly things. And so what's really important is has up there in heaven." Fine. So ask yourself: Is she convincing when she does that? Or is it maybe something like Rowlandson's poetry whereby somehow real feeling and grief and affection is seeping through? What does she place emphasis on? What poetic devices does she use in the middle of that poem that would suggest it ain't quite so easy to part with the stuff as those Puritan ministers want you to think? Yeah? >> [ Inaudible ] >> Lecturer: Right. I mean, that's the doctrinaire reason. That's it. "It happened to me for a reason. It just teaches me that again, I can't put store on earth as a line for that we'll encounter when we go back to Moby Dick. "Lay not your treasures here on earth where moth and rust do corrupt, but lay thy treasures in heaven where moth and rust do not corrupt." Okay. Supposed to be [inaudible] the meaning. And yet -- and yet. Read through it and see the experience of reading it. Is that the only thing the poem is conveying? Officially, yes, but -- yes? >> I felt like there was, like, compulsory initial reaction to the Divine Providence and she slips into these lines. >> Lecturer: Which ones? >> "But yet sufficient for us left. When by the Ruins oft I past My sorrowing eyes aside did cast And here and there the places spy Where oft I sate and long did lie." And then it continues where she's just, dwelling in what was lost. >> Lecturer: Right? I mean, if you were really going to do it, you'd minimize what was there. But she just remembers the specific objects. Now, there's another way to read it. You could say that she still has to get over it. That's a sign of how difficult it is to get over that. But ask yourself that. The extent of the specificity: "Here stood that Trunk, and there that chest, There lay that store I counted best, My pleasant things in ashes lie And them behold no more shall I." But then -- okay, she said, "All right, fine." But look at what she does next with the anaphora, with that repetition of the form at the beginning of the line: "Nor at thy Table eat a bit. No pleasant talk shall 'ere be told Nor things recounted done of old. No Candle 'ere shall shine in Thee, Nor bridegroom's voice ere heard shall bee." I mean, there's a kind of emphasis there in the form which possibly belies what she's ostensibly officially saying. That's what I want you to think about when we think about the relationship between what they're saying "content or theme" and "form." How does sometimes they don't actually always work in tandem or complimentary? Sometimes conflict works its way in there. And that's part of the meaning of the poem. One thing I just want to point out again is the next poem, As Weary Pilgrim. It's written -- we think it's the last poem she wrote. It's the last one that survives. So it's three years after the previous, roughly speaking. She's sick at this point and has an awareness. She dies some three years later, I think. But anybody read Chaucer? [Inaudible] read Chaucer? How much Chaucer did you read? Knight's Tale, [inaudible]? Does anybody still read The Retraction? You know what that even is? Okay, it's the last thing in there, right, in which he says, "You know those things I wrote? Forget about those except maybe all the really boring stuff." Like, what was the -- I forget, The Parson's Tale. He says, "These are the ones you ought to read." That's again, you can say like having his cake and eating it, too. But there's a sense in which we always tend to think of Chaucer as really modern, right? I mean, he's got a modern comic sensibility; he's got a sexual frankness; blah, blah, blah, blah, blah; character; details; okay fine. The Retraction, you read it and if you take it seriously -- I think scholars would say it's not a joke. Chaucer is a person of his age, full of contradictions perhaps or struggling, you might say, against the ideological boundaries of his age. And Bradstreet does that, too. But at the end of his career and at the end of her career you might say they find comfort in the doctrinaire and the ideological. So I would suggest to you that we ought to read As Weary Pilgrim not ironically but think of it again as an indication, part of a contradictory nature of Bradstreet that in fact, she is a person who belongs to Puritan America, who is wholly a part of that whole idea of religious instruction and religious belief that Bradstreet, Winthrop, Rowlandson, Hutchinson all belong to. She is not completely out of it. She has her moments where she's exploring other things, pushing the ideological boundaries. At the end of her career, when she's sick, where did she turn for comfort? Precise idea of Christ as your bridegroom of the everlasting life. So just something so bear in mind. I think it's a wonderful poem, actually. Which leaves us just a few minutes for Taylor. So we'll probably do a little more Taylor next time because he's so cool. English metaphysical poetry. Anybody read that stuff? Yes? So what do we know about English metaphysical poetry? Who blamed them really severely? There was one really famous critic in the English tradition who wrote a famous essay on metaphysical poets. Tell me you've read -- how many of you have taken Brit Lit? Okay, what percent would you do it in? It's got to be one still. Or maybe not, maybe it got caught in the split. Where did you read Donne? >> In One. >> Lecturer: In One? Do you read Johnson when you read Brit Lit when you read Donne in Brit Lit One? The phrase "The most heterogeneous ideas are yoked by violence together" -- does that ring a bell? So Johnson writes the The Life of Cowley. God, you all should read this. The Life of Cowley -- maybe you'll read it when you get to Johnson. But it would be really more effective to read it with Donne. He talks about metaphysical wit. And he talks about what they do. The trick behind the metaphysical poets is to try to represent what hasn't been represented before. So it's the matonic project sort of, but through really weird images and they call that "wit." And it's the bringing together of things that you wouldn't associate together. You put them together and you think, "Wow, that's a kind of new thing." So Johnson says, "That's not doing anything new; it's just perverse most of the time. The most heterogeneous ideas are yoked by violence together." And he liked Shakespeare's use of puns. So he loves Shakespeare, but he says Shakespeare never met a pun he didn't like and he just writes too many of them. And it kind of detracts. So here's a famous one. You guys read this? A Valediction Forbidding Morning? This is a poem that's ostensibly about -- oh, I don't know -- chaste love. But let's look it. "As virtuous men pass mildly away, And whisper to their souls to go, Whilst some of their sad friends do say, "Now his breath goes," and some say, "No." So let us melt" -- typical metaphysical -- "make a" and "as," therefore so. Make the comparison. It's kind of a simile structure there. "and make no noise, No tear-floods, nor sigh-tempests move; 'Twere profanation of our joys To tell the laity our love. Moving of th' earth brings harms and fears; Men reckon what it did, and meant; But trepidation of the spheres, Though greater far, is innocent. Dull sublunary lovers' love -- Whose soul is sense -- cannot admit." What does "sublunary lover's love" mean? What's "sublunary"? >> [ Inaudible ] >> Lecturer: Not a word you've ever said in your life unless you've read this poem. Something under the moon, right? So it's earthly love. We might call this "periphrasis," all right? Wordiness or finding -- again, my favorite one from the 18th Century is Joseph Wharton writing about fish, the finny tribe. The finny tribe. The sublunary lover's love. "Dull sublunary lovers' love -- Whose soul is sense -- cannot admit Of absence, 'cause it doth remove The thing which elemented it. But we by a love so much refined, That ourselves know not what it is, Inter-assured of the mind, Care less, eyes, lips and hands to miss." And here we go. This is the one that everybody remembers. "Our two souls therefore, which are one, Though I must go, endure not yet A breach, but an expansion, Like gold to aery thinness beat. If they be two," -- our two souls -- "they are two so As stiff twin compasses are two; Thy soul, the fix'd foot, makes no show To move, but doth, if th' other do." And I screw that up. "And though it in the centre sit, Yet, when the other far doth roam, It leans, and hearkens after it, And grows erect," -- and there's no pun there -- "as that comes home." [ Laughter ] All right, maybe there's a pun there. I mean, Donne is famous for playing kind of lacing his poems with kind frank sexual [inaudible] -- just talking about Christly love. It's chaste love, no problem -- faithfulness, fidelity. But the whole idea of the lovers as a compass is a very famous metaphysical image. And that's the trick of Taylor's poetry as well. So Taylor ought to be read within this metaphysical tradition. And some of his poems actually exist. I said they were written out. They're in the Yale Library. This is Meditation 38. And you actually can see it dated up here. I think it's the 6th of July, 1690. Some of them actually have dates. And again, the thing about Taylor is he's this Orthodox Christian guy. He has written the Preparatory Meditations -- so this would be on 268 of your text -- as a way of preparing to give a sermon, ostensibly, right? He writes the poems to help him think about the sermons. So each of the poems takes a piece of text as its -- well, as almost the text the poem is then going to explicate. But you might say one of the things that he does is he tries to show something about divine grace while fully being aware of the fact that he's using again as I said before this kind of human, therefore unreliable form, which is language. And even if you think it's reliable, you would say it's still not so easy to use, right? Sometimes there are things you want to express and you can't just do the Wigglesworth thing and express plainly, can't even do the Bradstreet thing. You need funky, weird images and lines that you can't say. And in fact, Taylor's poems are hard to read in part because the intention seems to be he wants them to be hard to read because that gets the sense of how difficult it is to have this earthly existence, how you still have so persevere all the way through it. What's metaphysical about him is a funny way in which there's a kind of funny interplay of the metaphorical and the literal. And I'll end with this point, and then we can take it up next time. The literal in which he takes things that were dead metaphors or so familiar from the Bible that when you hear them they become kind of formulaic. An example would be page 270, Meditation Eight: "I am the living bread, Christ is the living bread." Okay, okay we get that. So he asks, "What would it mean if we actually thought about Christ as the living bread?" That means if I'm going to write about that process, I would think about eating him, and chewing him, and digesting him. And therefore even though people want to say that this phrase really means the seat of tender and sympathetic emotions, in verse four: "In this sad state God's tender bowels run out streams of grace." Now okay, fine. It doesn't maybe mean digestion or doesn't it? I mean, he's talking about eating. That's what he does. Dead metaphor, Christ is living bread. Let's make it alive by really thinking about it as literally as we possibly can. So you might say that one of the projects that Taylor has is how to use this debased form -- language -- to talk about something that is wonderful and divine and above language, such as grace. And part of his strategy is going to be how you might find new and interesting ways to talk about the need to be humble. So from the very beginning of Preparatory Meditations, the prologue on 269: "Lord, can a crumb of dust the earth outweigh, outmatch all mountains? Nay, the crystal sky. And bosom designs that shall display and trace into the boundless deity? Yea, hand append whose moisture doth guide or eternal glory with a glorious glore." Right away, the project of writing. "If it is pen had of an angel's quill and sharpened on a precious stone ground tight and dipped in liquid gold and moved by skill in crystal leaves should golden letters write, it would but blot and blur, yea jag and jar unless thou makes the pen and scrivener." That's the project right there of Taylor's poetry -- how do we use these things that are earthly without God's guidance? So we'll talk a little bit about that. As you read Edwards for next time, I want you to think about how he has the same problem of language. How do you convey what's divine using human language? And we'll leave it there for now. Thank you. |
Open_Ed_Cyrus_Patell_American_Literature | American_Transcendentalism_I.txt | >> Alright, let's get started. We have got a lot to get through today and all of it will be on the mid-term. Speaking of which the midterm, I had advised that you look at the Edwards' lecture before the mid-term. I still advise that. if anyone is having a technical difficulty, make sure that you have the latest version of Real Player for either Windows or the Mac. Real Player is now available for the Mac and it does work, since that is the way I look at it. of course, I find it a little bit horrifying to look at so I don't look at it very much. Nevertheless, it is there. The second thing, have we talked about the format of the mid-term? Pretty easy English majoring type of midterm, but for those of you who are interested in not being surprised, part one is terms, names, blah, blah, blah, things like Alexander Pope or the Covenant of Grace, okay. So I want you to identify what they are, but more importantly I want you to explain what the significance of the item is to the narrative that we are generating in this course or the set of narratives, right. Significance is everything, four out of five or six. So you will do four that should take you about 10 minutes, so don't spend a lot of time on it. The next part is basically the reading check and we will ask you to do 10 out of 12 passages that we will give to you. They are reasonably biggish, like that biggish, not that you can really see. Say three of them fit on a page, something like that, a whole variety of different genres and things like that. we will ask you to identify 10 out of the 12 by author and title, very simple. We don't want you to spend a lot of time on it, we say 20 minutes. Don't spend anymore than 20 minutes and try to make time on that section. We are giving you passages that we think are distinctive, stylistically and thematically. They will either be things that we have highlighted in lecture or that are you know at the beginning of an important section of whatever we are reading or just one of those highlight me moments, okay. Not really trying to fool you, not going to find the one passage of one poet that happens to look like another poet. That is not what we are interested in, we are interested again in the rhetoric of exemplarity so we are trying to give you exemplary moments to look at. We will ask you to identify 10 out of 12. There is no extra credit. You may answer all 12 and we will take your best 10. So do not worry if you answer 12 and you miss two of them, we will not hold that against you, unless they are really, really stupid. [ Laughter ] Then in that case, we will just make a note on a secret special grade books and say okay this is just clearly evidence of moronic behavior, no 10 out of 12, we will pick your best 10. And then we will ask you to choose four of those passages and this is the real meat of the exam, take four of those things and talk about them and we will want you to talk about them guess what, in ways that will pay attention to style and form on the one hand and thematic and other forms of content on the other. We are really interested in the way in which these things go together. I will list them for you in three different sections. It says a) comment on the rhetorical techniques used in the passage, paying attention to such matters as diction, rhythm, rhyme scheme, scantions, figure of language is appropriate, form, literary in term stuff. Then comment on the ways in which the passage dramatizes a major theme of the text from which it comes, okay. So if you get a passage from Emerson's nature, you will be wanting to talk about the ways in which it uses those formal things that you have just identified in order to talk about or just more largely just to talk about how this passage gets at something. You might think of it this way, why is this an exemplary passage from nature, for example. And then we ask you to compare the treatment of the theme that you have identified there to its treatment in another text by another author. So nature, who Emerson thinks nature is great, Bradford really thinks it is not. That would be an example, but you can't just say that. I need a few more sentences really showing me that you can think about what is going on in Bradford. For example, he invokes the howling wilderness or he invokes the native Americans before he has even met them. That would give me refer to specific moments. You don't have to quote them, but just point to specific moments, so that we know you have read and thought about the text. And if you have world enough and time, you would be able to expound eloquently at great length, but this is shorthand. Okay, any questions? Is there an extra credit, there might be, but you shouldn't worry about it. okay, if you want to worry about it, I am not interested in dates per se, but I am interested in the fact that certain writers come before other writers, certain texts came before other texts. So I am interested kind of in sequence, you need to know something about sequence, so you know who influenced who and what [inaudible]. Okay, so words to the wise. Any questions, yes? >> [Inaudible ] >> Yes, it is true, it will be up tonight at say 9 o'clock. I will even send them all to you, so make sure I will have to send them separately. Apparently people have trouble when I send more than one document via blackboard, so I will send them in separate messages, okay. The terms will probably come from there, so you might want to just have a gander. Sorry that I have been a little bit slow, I have been changing things around so that what I wrote before doesn't apply and then I have to go and do it and they pile up and you know the way it goes, right. Alright, any other questions? >> [Inaudible ] >> Remember this was boot camp, I am actually feeling like I am taking it easy on everybody this year, but alright fine. Try to get here early, I mean my exams in this course are long and they are going to make your hand hurt and you may want to build an extra blwoing on my hand time or whatever, just try to get in here early. We are a little crowded. I have decided not to go for another room so we can have double seating, but that always confuses people and people don't show up. >> Alright let's do some work, this is Emerson from a degara-type [ph] in the 50s I think. Now I am going to start with a way, one of the things that you have probably gathered is that I am kind of interested in the way in which cultural forms, ideas, figures get transmitted through time, right. So we have already talked about kind of contemporary appropriations of some of the ideas that we have been thinking about. So how Winthrope is appropriated by Ronald Reagan for example, it is a very showy example of how cultural forms can change and although ultimately when we get to the Scarlett Letter we will see that is what that book is fundamentally about in many respects. How do you try to script something and then have that script go awry. Once you put a cultural symbol out there, once you write a book, how can you control the meanings? I want to suggest to you that Hawthorne knows that you can't control those meanings. You know you are a writer, you write with an eye toward a horizon of expectations, but it in an exact science. You may intend to meet it head on and find that there is something about that horizon that is changed and your book will not have the reception that you thought it would and that can be good or bad. Make the movie you want to make, don't do any prescreening, just make it, make it Indie, do what you want and who knows, you might win best picture, usually it doesn't and the fact that I don't know it made 20 million dollars usually is a problem, but maybe not anymore, so anyway, horizon of expectations, right, okay. So I want to talk about a moment of Emerson's reception that comes from around the time of Reagan, because you might imagine that Reaganism with its stress on individualism and Emerson would go together, although Reagan I guess maybe Emerson wasn't Christian enough for Reagan or something, his speech writers didn't tend to ever invoke him. But in the fall of 1988, the Reebok corporation ran an advertising campaign, which has become kind of infamous among people who study these sorts of things. It was based on the slogan, Reeboks let you be you, okay. Reeboks let you be you and the television commercials that spearheaded this campaign were shot in bright primary colors over a soundtrack of tango music and there were brief scenes, each one had a spoken caption that came from Emerson's self reliance. So it was meant to dramatize kind of idiosyncratic behavior that was nevertheless linked to individualism, so thinks like who said it would be a man most be a non-conformist, a foolish consistency is the hob-goblin of little minds, to be great is to be misunderstood. I think there were 10 themes in the long commercial and 10 captions. And for years, I had this on some videotape that I was trying to rustle up and I probably taped Star Trek: the Next Generation over it or something like that. in any case, it is now on You Tube, we love You Tube. So I am going to show it to you, I hope. All things being equal, you will get a sense of well let me just show it to you. [ Playing video] [ Laughter ] Apparently people found this campaign somewhat enigmatic. They may not have recognized, anyway, there is a whole bunch of them. So if you like these things, they are kind of cute. I will post a link and actually I might even post the actual thingamajig on my blog. Nevertheless, we have it now, so fine where were we? So Emerson right, so that ad campaign is using Emerson, the quintessential prophet of American self-reliance or as we would say individualism to sell sneakers. So now this ad campaign actually raised the heckles of an editor at the Daily Newspaper where Emerson had gone to college. The Harvard Crimson ran an opinion piece that was entitled stomping on individualism that deplored the appropriation of the work of the man whose name that adorns that universities philosophy's building. Emerson Hall is where they teach philosophy at Harvard. Although interestingly, they rarely teach Emerson in Emerson Hall, I mean certainly back in the day, there was an oddball philosopher who was interested in aesthetics and literature, one of those types. His name was Stanley Covell and he taught Emerson, but for the most part Emerson has had a kind of renaissance since this time, but even still people regard him in professional philosophy departments, they regard Emerson with suspicion. I don't think he is on any syllabus that gets taught here at NYU. He is just not analytical philosophy at all and I think we will try to understand why. Although it was commonplace to say at the turn of the 20th century that Emerson was the America's greatest philosopher, in the first Cambridge history of American literature from about 1917 that is how he is called. He is denoted as America's great philosopher, so something has happened to the disciplined philosopher. You might say the horizon of expectations for what constitutes legitimate academic philosophy has changed. Okay in any case, this editorial writer deplored the appropriation of Emerson's work. And she wrote this, the post modern randomness of the ads is meant to stress individuality and uniqueness, as does Emerson's philosophy, individuality and uniqueness. But she complains, the ads distort that philosophy by implying that Emerson's self reliance can be found in of all things, sneakers. And she describes Emerson as the quintessential American philosopher, which as I said is a dispute claim in many philosophy departments and she points out that the campaign emphasizes what she calls the crucial American dialectic of individual versus community, what we talked about with Reagan and with Winthrop. She argues though that the ads are based on a duplicitous premise, as if they, she says they definitely obscure the fact that buying Reeboks is not an act of individualism, but an act of conformity. Okay, so buying shoes to express your individuality is especially mass produced shoes, made by sweat shops and whatever is probably not a legitimate way to express your individuality or is it. I mean what do we mean by individuals. Oh by the way though, the author of this piece went on to become a screenwriter, her name is Aileen Brosh, ring a bell, anybody? She wrote a movie. It was celebrated when it came out, it even had some Oscar nominations. I think it might have even won the screenwriting award. It was called the Devil Wears Prada. [ Laughter ] Have you seen the Devil Wears Prada? It is good. Okay, so you refers to Emerson as the quintessential American philosopher, right that was when she was a young tyke, about your age, extolling the virtues of some kind of authentic American individualism, as if there were such a thing and sneering at conformity. Okay, so individualism, not conformity and I would suggest to you that places her and the Crimson editorial that she writes within the kind of main line thinking of American political and cultural philosophy that has dominated American culture since at least Emerson, but probably we should go back to Franklin and we should see glimmerings of it all the way back to something like Winthrop that dynamic of individual versus community. How are we going to harness the individual's energies that Winthrop is trying to work with? What I want to suggest to you therefore from what we have seen already is that what she misses is that individualism and conformity or let's call it community are inextricably linked. And what is at stake really is the link that you are going to make, how are you going to depict that link. Remember Emerson is going to follow Franklin in trying to put individual first and society second. Winthrop is going to put community first and individual second. Community is supposed to infold, bind, remember the ligaments of Christ's love. That is going to bind the individual to society. So you might say conceptions of the individual are probably a necessary conception to the modern 17th century, whereas for Franklin and then for Emerson society itself is the necessary contention. It is a second order construct. I will talk a little bit more about this. It is a second order construct kind of necessary evil, right. So that is what we want to be thinking about. Did you notice the word individualism in your reading of Emerson for today? Anybody? I would hope not, because it is not there. It is not available for him for use, it is such a new term. It is this idea that the individual has an optimum and primary reality, society is a second order derived construct. This idea is really new at the beginning of the 19th century, but it is becoming a kind of Bedrock principal of American liberalism or of liberalism more generally, but it is so new that there isn't actually a word for it and it probably comes into American usage when democracy in America is translated for an American audience in 1844, oh no 41 was the first time it was published in the United States. And Tocqueville here in the second volume, you know about Democracy in America right, Alexis de Tocqueville comes in the 30s and he looks around and he goes on kind of a long tour. He is obstensibly supposed to study I think the prison systems as a source, but he starts generalizing out and broadening out and he is looking to understand what he sees to be the future. The enlightenment has taken hold, democracy is what is going to be the form of culture. There are some people who comment on Tocqueville as saying he is actually very sympathetic still to the old Aristocracy, the old regime and therefore he is trying to look for grounds of hope for those who are still interested in [inaudible] structures, where can we find the vestiges of Aristocracy in the United States and that is part of what he keys on in those particular moments, but he really thinks that democracy is the wave of the future and with it a number of other concepts that go with it. individualism is one of them, so he says it is a word recently coined to express a new idea. Our fathers he says only knew about egoism, some translate it egotism. The translator of that first American edition writes a foot note in which he apologizes. I adopt the expression of the original, however strange it may seem to an English ear, because I know of English word exactly equivalent to the expression, right. It is a brand new word. It is so new that Emerson doesn't have it in self-reliance. He doesn't have it to use. In fact, the first time this is why I was thinking 44. When he publishes the series of essays in 42, it is not in current usage. By the time he gets to 1844 and publishes an essay called New England Reformers, he does have the term individualism available, right. So this is part of this new intellectual technology. This is how Tocqueville defines individualism. He calls it a calm and considered feeling, which exposes each citizen to isolate himself from the masses of his fellows and withdraw into the circle of his family and friends. With this little society formed to his taste, he gladly leaves a greater society to look after himself. So there is a difference between individualism and egotism or egoism, it is not only self centeredness. In fact, it isn't primarily that, it is a way of approaching society that involves isolation from the mass and it is a social concept, even in Tocqueville's terms, because you gather a close community around you, your family maybe some of your friends and then you start to look after yourself. And he thinks this is a problem, egoism he says springs from a blind instinct, while individualism is based on misguided judgment rather than depraved feeling. But in the end, they boil down to the same thing. Egoism sterilizes the seed of every virtue, individualism at first only dams the spring of public virtues, but in the long run he says it attacks and destroys all the others too and finally merges in egoism. So ultimately, you want to say they boil down to the same thing. Finally, one of the things he is talking about in terms of Aristocracy is he thinks about the ways in which this is a new phenomenon and one of the things that he says you might think about how this is compatible with the argument that Winthrop makes at the beginning of a model in Christian charity about hierarchy is that in Aristocratic society is there was a hierarchy and a set of obligations and everybody knew who owed what to whom. Democracy changes that. He says democracy breaks the chain, frees each link and thus it's socially quality spread through out more and more people who, though neither rich nor powerful enough to have much hold over others, have gained or kept enough wealth and enough understanding to look after their own needs. Such folk owe no man anything and hardly expect anything from anyone. They form the habit of thinking of themselves, again that word, in isolation. And imagine that their whole destiny is in their own hands. I think leave the idea of the community behind. Each man, therefore he says, is forever thrown back on himself alone. And there is danger that he may be shut up in the solitude of his own heart. Dramatic description. And he probably sees this as exactly the problem that he's talking about. Right? Emerson's favorite lines from Self Alliance. To believe your own thought, to believe that what is true for you in your private heart is true for all men, that is genius. Speaker [inaudible] conviction, and it shall be the universal sense for the in most in due time becomes the out most. And our first thought is rendered back to us by the trumpets of the last judgment. This is what I'm thinking that you will probably be thinking. In those moments when you don't say something, when I ask a question, and then somebody else says exactly the same thing that you were thinking. Emerson says believe in yourself, reverence yourself, right. Speak up, speak out. Your first thought is probably the right thought. And if you change your mind tomorrow, we'll talk about this later on, your first thought tomorrow is the right thought for tomorrow, even if it contradicted your first thought today. But we'll get to that. This would drive Topfield [assumed spelling] nuts. Right. I mean this is exactly the kind of problem that he's pointing to. Think that what's true for you is every, is true of everybody. Again you hold your destiny in your own hand. But you know what? Almost immediately in the context of U.S. discourse, [inaudible] insight and I think it is an insight into the way Democratic societies work, was immediately appropriated and given a new meaning. Right. So in a very early review, or a very early piece that's related, even precedes Topfield's own publication of the second volume. There's an anonymous piece of the Democratic Review that writes this. The history of humanity is the record of a grand march, at all times leading to one point. The ultimate perfection of man. The course of civilization is the progress of man from a state of savage individualism to that of individualism more elevated, moral and refined. Right. So we want to move from the state of nature's version of, from individualism to produce societies that are going to cultivate a new kind of individualism that can be elevated, moral, refined, civilized. And Emerson's thinking in this period, you might say, has a lot of affinities with that kind of belief. This is a journal entry from 1833. Democracy, freedom has its roots in the sacred truth that every man have in him that define reason, or that all men are created capable of so doing. That is the equality and the only equality of all men. To this truth we local me say, reference thyself, be true to thyself. Today Emerson would probably have a blog. But one of the things that he did was cultivated the habit of keeping a journal constantly. And he drew on these journal entries for the lecture the public performances that he gave. Right. So that's one of the things to understand a little bit. We'll say more about this. But one of the things about, what's weird about Emerson's writing is that it almost seems like greatest hits of my journal. Like where'd I get, you know, if you had God, who knows what would have happened if he had had word processing and it was easier to synthesize things. Maybe he still wouldn't have done it. But I mean you know the idea of going through his journal entries and thinking you know like what's, what have I been thinking about the individual? And pulling these things together. It's often times that you get the paragraphs have kind of leaps of thought. They don't necessarily have smooth philosophical transitions. They don't seem argued. It's kind of like insight after insight after insight. But you can see that that's kind of what he's interested in. He's interested in the idea of revelation which he believes the enlightenment holds strains of enlightenment philosophy, have unjustly de-emphasized. That's one of the important things to understand about Emerson. So who so would be a man must be a nonconformist. He who would gather a mortal palms must not be hindered by the name of goodness, but must explore if it be goodness. Does that remind you of anybody that we've read? Must not be hindered by the name of goodness, but must explore if it be goodness. Does that sound. Does that remind you of anything? If we were looking for an antecedent to this thought, where would we find it? [ Silence ] So on Wednesday if there's a passage from Emerson and it's not appropriate to compare it to Bradford, you might want to think about comparing it to this guy. Might remember that moment when he's talking about he doesn't, doesn't believe that you should do things from precept. But on the other hand he thinks it's probably good, there's probably good sense behind many of the precepts. He wants to test those precepts out for himself. He's probably going to do, for example, what the preacher would tell him to do. But he's not going to do it because the preacher told him to do it. Emerson you might say he's taking that slightly farther. Right. Who so would be a man, must be a nonconformist. He who would gather immortal palms must not be hindered even by the name of goodness. I'll interpolate the even. Even by the name of goodness. But must explore the be goodness. Just because they say it's good, I can think. And remember this idea here, right, the equality of men is that everyman hath in him the divine reason. All right. So we're seeing that Emerson is taking off from those strains of enlightened philosophy that say reason is a faculty that God gave us. And we need to use it. Emerson goes further. There's a lot of references to the soul in all of the writings that you looked at. He thinks that everybody's soul is almost like a direct communication line to the divine. That we all have some of the God stuff in us. Sometimes he'll call it the soul, sometimes he'll think of it as reason for him to kind of interconnect it. You would be doing an injustice to what is divine in you to mistrust yourself. And if you were going to subscribe to that total depravity thing, oh come on. How can having part of, how can having a soul be squared with the idea of total depravity? See that's the thing about Emerson, he's, he's not interested in those kinds of arguments about the fall and nature of man. And you'll see that he makes references to the fall of man. But the references that he makes to the fall of man are completely compatible with the kind of thinking that we saw in Cant. Right. That enlightenment is the process of arising, of, of moving out of your own self incurred immaturity. When you don't dare to think for yourself. Cant says dare to be wise, Emerson would agree. And that's because Emerson frankly is a kind of American [inaudible]. Right. So one place to think of is that Emerson is inheriting from Franklin, and maybe even moving a little bit further. I would suggest to you that the difference between these two lies in their attitudes towards religion. Right. Remember what we talked about. Edwards and Franklin, sat on a cusp between Calvinism or New England Congregationalism and the Enlightenment. Edwards is trying to find a way to manage the new enlightenment technology to make it compatible with the old religion. Franklin is trying to wait a minimize the damage that thinking along the lines of the old religion can do to keep us from moving forward. So he really is trying to deemphasize religion. Think back to that passage when he talks about providence, or a guardian angel, or some unexpected chance. All of these things might have saved me from what would have gone wrong you would expect from my want of religion. Right. For him they're all equal. Providence, which is destiny and forward, and things being for ordained for chance. Who knows. And by virtue of putting those things together in the same sentence, not along as if they were co-equal, is a radical destabilization of the idea of providence. For Emerson you might say enlightenment is going to far. Emerson is a Unitarian. So that is, we might say it's an early 19th Century descendent of New England Congregationalism. But it is a far more liberal version of that in the 19th Century. Right. You want to say that Calvinism as we've seen it stresses overall Christ love as expressed through his sacrifice on the cross. And it comes with it, it comes with this idea of the depravity of human kind, and the necessity of God's intervention in order for us to be saved. We don't deserve anything. There is no way for human beings to perfect themselves except through the reception of God's grace which God gives as he sees fit. Emerson and the Unitarians stress not the death of Christ, but the life and teachings of Christ. So it isn't Christ's death that is the model finally of his love, but his life. The things that he teaches. The example that he sets of good behavior. Right. And Emerson enters Harvard College, which at the time is, he's the second of his brothers to attend the school. It's still a place where he, it's still a place where he was expected probably to become a minister. He wasn't, it might make you happy to know, wasn't a particularly good student at Harvard. So you can be a great intellectual and not necessarily be a good student in college, although I wouldn't recommend it. He did win prizes for writing. Including one of which I, myself, am particularly fond. It's called The Bowden Prize for Writing, and Emerson was one of the, the winners of it. In any case, he leaves Harvard with a suspicion you might say of organized religion. So he tries his hand at school teaching. He begins to study for the ministry more seriously at 1825. And he begins a practice of keeping journal entries to try to produce a new sermon each week. His father had been a Unitarian clergyman. But again, you know, if we think about this is a progression from conservative to liberal, there are certain ways in which we might say Emerson is even a further, a further progression to more liberal. Right. Any kind of organized religion, even Unitarianism comes to seem kind of binding to him. And he has a dispute with the ministers at Harvard, and in Boston, about the Lord's, celebration of the Lord's Supper. And that leads him to be, you know, banned from Harvard for a while. But you might say that the Unitarians become very interested in lock in psychology. The stuff that we, that also interested Edwards. Right. And they are really thinking about using enlightenment, thinking as a way of combating what they thought of as Calvinist superstition. They were, therefore, a kind of liberal denomination. So you would Emerson through the rut, well if moving from liberal to more conservation to liberal. Emerson would probably be out here. And yet, it's more complicated than that. Because even while he finds Unitarianism which is an enlightenment influenced version of New England Congregationalism as opposed to this, which is a strongly Calvinist inflected version. Emerson thinks that Franklin's account of enlightenment is impoverished. There is something wrong with the way the enlightenment has put so much stress on both human consciousness and on materialist, philosophically materialist modes of thinking. Something is missing. It's not enough. And that something is what religion is supposed to do. So there's a way in which organized religion is too, is too strict for him. But the enlightenment is too impoverished for him. He doesn't give you a full account of the human life, human consciousness. He wants to restore something of that idea that the central drama of the human existence has something to do with God and spirituality. He just doesn't find any account of it that he's read to be fully satisfactory. So there's a way in which I want you to see these essays as a kind of American religion. This is a kind of new religious text and Emerson is part of that. On the other hand, he is very much thinking about building on enlightenment philosophies, and particularly the kind of philosophy that we would see in something like Emanuel Cant. So his first major philosophical text is nature from 1836. And it really, you know, we, we would identify it as, as what we would call a piece of American transcendentalist thinking. What I want to suggest to you is that transcendentalism in the U.S. does draw on German idealist philosophy, the transcendentalism of Emanuel Cant. Most, although Cant, Emerson gets Cant less from Cant than from the way it was processed by thinkers like Coolidge and Carlisle. Nevertheless Cant is in the background of it. And he always says whatever Emerson's larger project is is to kind of domesticate Cantient [assumed spelling] thinking for American soil. And one way of, of thinking about it therefore, is that part of what he really brings into it that Cant doesn't have so much, is the idea of religion or spirit or revelation. Okay. Revelation I compatible with Cantient most think. But Emerson wants to stress that further. So you might say that what we find is a kind of battle between European, Unitarian Epistemology, so the Unitarian account of the way that knowledge comes about. And also lock in psychology. Right. So there's a sense in which Unitarian Epistemology is really, I probably shouldn't have written versus up here. They really kind of go together. Unitarians believe that knowledge comes about in part through the way in which Lock describes sensory understanding. Right. That part of what we, what we, what we come to understand is what's written on our senses, as the first kind of, you know, sensory perception becomes the first data that we use. Then we use reason to, to, to work on that. In Emerson's terms, coming from Coolidge, he would interpose one thing in between there. He would say that we get sensory data. We apply our understanding to it. But then we finally go and apply this extra super faculty that's called reason. And that's the thing that sparks some of the design. So this, there's a trend, there's a constant, there's a, you might say a concept that Emerson is domesticating from Cant that is something like a kind of higher reason. So that's one of the things that we're seeing. Transcendentalism in the United States becomes almost a kind of quasi-religious movement. Although, you know, if you asked somebody like Thero [assumed spelling] who is constantly identified as a, as a transcendentalist he probably would deny that. So it's Cant as interpreted by people like Cunta, Carlyle and Coolidge. This becomes the way in which, it works its way into Emerson. And again, understanding as a first faculty, but Emerson wants reason to mean even more than other enlightenment thinkers want it to mean. Reason is somehow going to be linked to the soul. All right. Let's take a look at some text here. How about page 1131 in the Norton. This is the section of nature that's called Idealism. And I think this might, you might get a sense of what he's talking about if we look at the text more closely here. On page 1131 this is the first full paragraph. It appears that motion, poetry, physical and intellectual science and religion all tend to affect our convictions of the reality of the external world. But I own that there is something ungrateful and expanding too curiously the particulars of the general proposition that all culture tend to imbue us with idealism. Right. I want to focus on this. We've talked about idealism a little bit when we talked about Winthrop. Idealism is not the idea that philosophical idealism is not the idea that we should pursue a certain ideal. Right. It's not the same as, as good behavior you might say. It's rather a way of thinking that presupposes a difference between appearance and reality. And remember we talked about that. The periods are deeply suspicious of appearance in the world for the reasons that we've outlined that have to do with their idea of the fall of human kind. And they believe that the world that you can't see, the invisible church is in fact the real world. So they will be classed as philosophical idealists. They are interested, I'll give you these terms now so you can see them. They are interested as many later idealistic philosophers are in this distinction between the phenomenal and the nominal. The phenomenal is the world of phenomena and matter. The world that we see. The nominal is the world of spirit or ideas or the soul. It's the world that we don't see. Right. So generally speaking, idealism, philosophical idealism in Emerson's day maintains that what is real is in some sense going to be this nominal world, and then it gets even more complicated. Because how do you have access to the nominal world? Well even if you believe that you have a soul, your access is going to be through your own mind. So you might say that the first true philosophical idealist is somebody that's mentioned a few pages earlier. This is page 1126 in the footnote number three. It's Bishop Barclay who takes off from Lock's descriptions of sensory experience in the essay on human understanding. And he says here, the footnote says that Emerson uses Bishop George Barclay as a representation of the notion that we can not know ideas, that we can know ideas only in the mind and cannot know things, material things in themselves. And just to say a little bit more about this, Barclay is extending this to all perception. And he's arguing that only sensations or ideas are real. All right. I don't want to get too far into this. But this is what, this is the philosophical discourse that Emerson is inserting himself into. And that's what he means on page 1131 when he says, he says that a little bit further on from the part. So it's the beginning of the second full paragraph. It is in fact the view which reason, both speculative and practical, that it is philosophy and virtue take. That is philosophy and virtue take. For seen in the light of thought, the world always is phenomenal and virtue subordinates it to the mind. Okay. Then he goes on, 1132, this will start to become a little clearer, I think. When he goes on to the fact that the, the idea of spirit. So we've move from, you might say, in the progression of chapters in nature, we've moved from something that looks like, you know, the world itself. To the idea of idealism and finally to another chapter here on spirit. Take a look at the, one, two, three, fifth paragraph. Three problems are put by nature to the mind. What is matter? Whence is it? And whereto? The first of these questions only the ideal theory answers. Idealism say matter is a phenomenon and not a substance. Idealism acquaints us with the total disparity between the evidence of our own being and the evidence of the world being. Right. He says the idealist would suggest that we could really only know ourselves. We can really only know what's in our mind. Because everything that we see is filtered through our perceptions. So our mind is perfect. The other flaw at best, we can't really be assured about it at all. The other he says is incapable of any assurance. The mind is a part of a nature of things. The world is a divine dream from which we may presently awake to the glories and certainties of day. Again. See how he's twisting that rhetoric of enlightenment that we've seen in places like, people like Jonathan Edwards. Idealism he said is a hypothesis to account for nature by other principles than those of carpentry and chemistry. And by that, by carpentry and chemistry and kind of mathematical view of the world, he's talking about materialist philosophy. So in short, what he's saying is look idealism is trying to get us beyond the limitations of materialist philosophy. But guess what? There are limitations to idealist philosophy as well. All right. So that's what's going to move him into this realm of spirit. It's in the next sentence. Yet if it only deny the existence of matter, it does not satisfy the demands of the spirit. It leaves God out of me. It leaves me in the splendid labyrinth of my perceptions to wander without end. Right. So look where he's gotten to. Materialist philosophy not enough. Idealist philosophy okay that's an improvement. It says to just a more supple way about the way in which we, we understand the world. It makes us realize that you know the importance of our perceptions. But what guarantees are there about anything that we think? I mean you know, everybody wonders this at times when I say red is it really the same thing that she means when she says red? How do we know? You know how do we know that we're seeing the same things? How do I know that we are not, that I am not actually at this moment, this is a famous thought experiment by Robert Nosick [assumed spelling] of lay, who used to teach at Harvard. It's like, how do I know that at the very moment, or how do you know that at this very moment you're not actually somewhere in a vast, call it Mars, the subject of an experiment that Martians have plugged into you and have simulated your own reality. But knows it's [inaudible] thought experiment. This is before the Matrix. Anybody see the Matrix? Matrix One of course. I actually like two and three fine. They missed an opportunity. We'll talk about this some other time. They missed an opportunity by going all bang, bang, bang. But, nevertheless, how do you know that you are not part of some Martian experiment? That every single thing you encounter is an incredibly elaborate simulation. That how do you know in fact that in those terms that you're not part of the Matrix? That's a problem philosophically, right? How can you be sure? Emerson knows. Emerson is sure. But what does he need in order to be sure? He needs God. Right? So that's it. He needs this idea of spirit because otherwise you're just wondering around in this maze of your own, thinking. What's going to guarantee if, if you might say it's a reconfigured version of providence. Right. If it only denied the existence of matter, it doesn't satisfy the demands of the spirit. It leaves God out of me. It leaves me in the splendid labyrinth of my perceptions t wander without end. Then the heart resisted because it balks the affections and design substantive being to men and women. Okay. So this is an expression of Emerson's transcendentalism. He's telling us that no religion, or philosophical system, and by this he's, you know, placing a lot of enlightenment theories in this, into this idea. That places God outside of the self is going to be acceptable to him. God is inside. Truth of reason. Through the soul. And that gives you a guarantee that you are not wandering only in the labyrinth of your own mind. Right. So what are the things that we want to say is that Franklin, and others, are trying to get the revelation out of philosophy. You look at Brown's novel, you're like wow, revelation there is unreliable at best. And sometimes it's, you know, conversion to the dark side. Right. You got to start killing panthers and eating the reeking fibers of the, okay. I mean that's not necessarily the kind of version we're all hoping for. Emerson says, wait a minute. I want to, I want to, I want to bring back revelation. Emerson is fundamentally more optimistic you might say than other romantic writers that we've started to look at about human nature. And he's more optimistic about human nature than the Calvinist were. He, there's often a word that's associated with him. It's the [inaudible] mood. Emerson and he doesn't mean optimistic. But Emerson is interested in the kind of language and the way, the language of possibility. He's interested in process as we'll see. Okay. Before we look a little bit more closely at nature, I do want to say something about Emerson's style of writing which you might find disturbing or even annoying. So I want, I've started to talk about this. Emerson was part of what was called a lyses movement. So it means he gave, he got you know, communities were interested in self improvement. Today we have book groups. Then people would spoil, would pool their monies together and hire a speaker. And come and give lectures on subjects. Of course philosophy you'd hire Emerson to come and he'd speak to you in a lyceum, in an auditorium and you would listen and you'd have kind of these edification, these socially, you know, called intellectually edifying moments. Fine. Emerson actually tried to make a career out of this. And for 25 years, after the death of his first wife, and he goes to Europe, he comes back. He's part of this lyceum circuit. So you might say that instead of giving sermons, he's now giving public lectures. But the lectures take a slightly sermonic form. He's often able to choose his own topics. But always there's a kind of doctrine that he is trying to promote. But I wanted to say something about this style. Again he's picking out nuggets of thinking from his journals. He's also thinking a little bit on his feet as he writes these things. And he writes them up and he puts them into essay form. But the essays that we have bear some of the hallmarks of oral delivery. Especially in this leaping from one idea to another. Or an almost a sometimes transcendental or associative train of thought, rather what we might think of as something that's strictly logical or syllogistic. Or if you want to say, it's a different kind of logic. It's an associative kind of logic. Let's take a look at page 1168 and I'll give you a, a famous passage that kind of embodies what it is that I'm talking about here. [ Sounds of pages turning ] Again, one of the things about Emerson is he's asking you to think anew. And sometimes the price of thinking anew, and this is why I think that Emerson is, is closed. He makes an approach to what we might call a kind of cosmopolitan mode of thinking that stresses the importance of understanding fablism. At the top of 1168, he's worried about all the things that we thought before. Why should you keep your head over your shoulder? Why drag about this monstrous corpse of your memory, lest you contradict some what you have saved in this or that public place. Suppose you should contradict yourself. What then? It seems to be a rule of wisdom never to rely on your memory alone. Scarcely even on acts of pure memory will bring the past for judgment into the thousand eyed present to live ever in a new day. Trust your emotion. In your metaphysics you've denied personality to the deity, yet when the devote motions of the soul come, yield to the hardened life, though they should clothes God with sharpen color. Leave your theory as Joseph his coat, in the hand of the harlot. And flee. And then this is the famous passage. As foolish consistency is the hob gobble of little minds. Adored by little statesmen and philosophers and divine. Little ones. With consistency, a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Out upon your guarded lips. Sew them up in the pack for a dew, else if you would be a man speak what you think today, in words as hard as cannon balls, and tomorrow speak what tomorrow thinks in hard words again, though it contradict everything that you say today. Ah, the next claimed the angel ladies, you shall be sure to be misunderstood. Misunderstood? It's a right fool's word, Emerson says. It's so bad then to be misunderstood? [Inaudible] was misunderstood, and Socrates and Jesus and Luther and [inaudible] and Galileo, and Newton. And every pure and wise spirit that ever took flesh. To be great is to be misunderstood. Anyway [inaudible] go back and think of the model of Jesus in the, in the New Testament. Jesus speaks how? How does he teach? It's a form that Jesus uses. >> [Inaudible]. >> Yeah he uses a parable. Why does Jesus speak in parables? Why not just say it? A new, this is, you know, we're not. Just do in two minutes what theologians spent careers and what not. People have probably been burnt for less. But, but why speak in parables? Why not just say it plainly? Well if you're interested in this, it's different in the different gospels. I mean one, one thing you would say appeal to, well it's story telling. Draws you in to understand. People can link to their experience. They understand and then they say oh. Rather than just a dry precept. You illustrate with a story. But there's a moment in Mark, this is fascinating for those of you. You go to Mark, and he does this first bit of parables and then he explains the parables not to his audience but to his disciples so that the disciples kind of have an inside knowledge. It's like they get the cliff notes. And he says, but when we speak outside, we'll speak open, when we speak other than openly. It's an interesting thing. There's a certain way in which Jesus is thereby leaving himself open to being misunderstood. And you could potentially argue that there's a whole lot of misunderstanding in the way that Christianity becomes institutionalized so that somehow the religion that's supposed to be turn the other check, the religion of charity, of humility and humbleness, became, well the great institutionalized structures that the churches became that were all about pomp and circumstance. And I mean today sometimes may lose track of their, their mission. In any case, Emerson has good presence for thinking about this. But that's what he thinks. Emerson says to be great is to be misunderstood. He's willing to take the chance. He's willing to contradict himself. So I want you to understand that one of the things that Emerson does, typically, his mode of faking is to take what would seem to be a kind of liability and turn it to his advantage. A French critic named Maurice Ganough [assumed spelling], published a very big study that was called An Uneasy Solitude. And he said this, a French mind, however open or unprejudiced it might be, is hardly ever comfortable with Emerson's thought. Fragmentary in the extreme, weak in structure, even when striving for order, fertile in contradictions and second thoughts and non-[inaudible] and so indifferent to logical rigor as to seem positively unsound. Emerson, this guy Ganough says was no Pascal. And therefore, he says, one has to try to read Emerson with a virgin mind, so to speak, following the movement of his thought, experiences the alteration of the inward tides if one wants to catch the original quality of the work. And you can see that's why it doesn't look like philosopher, philosophy to most professional philosophers. It looks like something else. Think of that it's a good metaphor I think. Title. It's fragmentary. It jumps. You'll eventually see when you read Whitman's poetry why Emerson was such an inspiration. Because Whitman also has a kind of ebb and flow in his lines of poetry. It's almost like Whitman does to poetic form in terms of opening up the constraints of, Brian starts opening up the constraints. Whitman blows them open. And Emerson is one of people's who serves as his kind of guru. Quite literally. He hears Emerson speak about the poet. We'll read that essay when we do Whitman. And has his mind completely, has, is completely transformed. Take a look then at page 1172 in the, later on in, in self alliance. Emerson writes in the journal from 1837, you know, can I now concede the universe without contradiction? And his answer is no basically. But that's not going to be a liability for him. He embraces contradiction. And he embraces contradiction because he thinks it's a crucial part of process of what we might call the process of enlightenment or spiritual awakening, or you know learning to use the reason, or Emerson would probably say learning to be self reliant. Okay. So look at the bottom of 1172. Life only avails, not the having lived. Power ceases in the instant of repose. It resides in the moment of transition from a past to a new state in the shooting of the gulf, the darting to an aim. This one fact the world hates, that the soul becomes. For that forever degrades the past, turns all riches to poverty, all reputation to a shame. [Inaudible] saint with the rogue shows Jesus and Judas equally aside. Why then do we pray to self reliance? Inasmuch as the soul is present there will be power not confidence, but agent. So talk of reliance is a poor external way of speaking. Speak rather of that which relies, because it works, and it is. So I want you to remember those words. Power ceases in the instant of repose. It's almost like a kind of shark like view of power. It consists of a darting to an aim. The cross. See that's why I think there's almost a kind of cosmopolitan thinker. He's thinking about bridging gaps. Not closing them necessarily. But trying to think about the ways in which you might forward gulfs of thought. Make unlike things have a connection to one another. And one of the things you might say about Emerson is that what links all of this together is the sense that you get in his writings of his own mind. I mean his mind is what unifies all of these things together. And therefore his writing becomes an almost kind of object lesson in how you too can make sense of contradiction in the world around you. Not by listening to everybody else. But by thinking for yourself. Trusting yourself. Being the thing that unifies. Different modes of thinking. Different kinds of ideas. Different kinds of contradictions. All right. So that's, I just wanted you guys to see that as kind of a bedrock Emersonian concept. This idea of contradiction. It's going to be problematic, and then we can start to argue about it. Well wait a minute. You just said contradiction. But what does it mean to say that he, isn't he kind of unifying and therefore subsuming contradiction? And yes. So there's almost a kind of contradiction in what I just said about his using contradiction, which I think Emerson would be very happy about. So let's go back to Nature. 1836, this is page 1110. And again, you'll start to see now that having talked about some of these things and the trajectory of his thinking, you'll start to see what he's up to in this book, Nature. [ Sounds of pages turning ] The epigraph comes from Plotinus. Nature is but an image or imitation of wisdom. The last thing of the soul. Nature being a thing which doeth only do and not know, but not know. Now Plotinus is interesting for Emerson because Plotinus is a, is thought of as one of the originary neo platonic thinkers. Plotinus is also important for people like Winthrop. Remember I talked to you a little bit about the ways in which the kinds of philosophy that would be identified as platonic would be idealistic, as opposed to Artostilian materialistic philosophy. That's good for Puritans insofar as Plato. Things that the real things or ideas. Not the particular manifestation of the table, but the idea of the table. It's that idea that's real. Puritans can work with that. But part of what enables them to work with that is Plotinus who starts to translate Plato's thought into a Christian context. Okay. He's important for Emerson as well. So immediately Emerson is using the epigraph to signal his philosophical relationships. Establish his inability and also genealogy of thinking. Our age is retrospective. It builds the cepelcurves [assumed spelling] of the fathers. The tombs of the fathers. It writes biographies, histories, and criticism. And remember, what do you think about those genres? Remember isn't that what I said was exactly the modes of what, if we had to call something literary in the 17th Century, it would be genres. The Bible sure, and then biographies, histories. A little bit of criticism perhaps. The foregoing generations, Emerson writes, beheld God and nature face to face. We see through their eyes. Why should we not we also enjoy an original relation to the universe? Why should not we have a poetry and philosophy of insight and not of tradition? And a religion by revelation to us and not the history of theirs. Right? Where have all the miracles gone? How come they were just then? Aren't there miracles going on now? How come we don't get any? Emerson probably is trying to suggest to you that we do, but we're not able to notice them. We've lost faith in them. We need them. And [inaudible] for a season and nature who's floods of life stream around and through us and invite us by the powers they supply to act in proportion to nature, why should we grope among the dry bones of the past? Put the living generation into masquerade out of its faded wardrobe. Now he's talking about thought in philosophies. These other genres, biographies, history, criticism. Right. We need new. New stuff for the new age. The sun shines today also, not just on them. We can have revelation too. There is more wool and flax in the fields. There are new lands, new men, new thoughts, let us demand our own works and laws and worships. Right. So one of the things that you would say about Emerson is he is, he is adopting this idea that is, that is a common place. That we are belated. We've come late into the world. And what Emerson will say is, there's the fall of man right there. It's the fact that we are bound to what other people have thought. We don't think for ourselves. We don't think the way they used to think. We don't experience the world the way they used to experience the world. We need to do that. And for him the way is through self reliance. And here you, just look at the boundless faith in human nature that seems to be here in these passages. Going on. Undoubtedly we have no questions to ask which are unanswerable. We must trust the perfection of the creation so far as to believe that whatever curiosity, the order of things has awakened in our minds, the order of things can satisfy. You have to imagine that, that one of the things that Emerson and many of the other writers of this period are thinking about is the fact that Champollion has deciphered Egyptian hieroglyphics very recently. It's kind of a big discovery. These things that were completely mysterious now turn out to be a language you can, it gives them hope. The Rosetta Stone, right. In which certain hieroglyphics were translated to Greek and we could read that. So we were able to understand it. Emerson uses, this is an example of the new way of thinking that the 19th Century is making available. Every man's condition is a solution and hieroglyphic to those inquires he would put. He acts in his life before he apprehends it as truth. In like manner, nature is already in its forms and tendencies describing its own design. All right you can see how this is linked to, what an extension of that kind of deism that I described with, deism that I described with Franklin. Right. The idea that, that we deduce the, in the, the existence of God by looking at manifestations of what has to be intention in, in the world. Emerson says this, let us interrogate the great apparition of signs so brief peacefully around us. Let us inquire to what end is nature. So that's where he's starting off. But I want you to understand, this is, is taking off from natural philosophy, but it's really an inquiry into the self. This is a treatise that paves the way for the later thinking about self reliance and modes of being of reliance. So you see not only in that essay, but in the American scholar and other things that we're going to be reading of his. All science is one aim. Namely to find a theory of nature. We have theories of races and the functions, but scarcely yet a remote approximation to an idea of creation. We are now so far from the road to truth, but religious teachers' dispute and hate each other, a speculative manner esteemed unsound frivolous. But to a sound judgment the most abstract truth is the most practical. Whenever a true theory appears, it will be its own evidence. Its test is that it will explain all phenomena. Now many are thought not only unexplained, but inexplicable as language sleep, dreams, beast, sex. I mean put this in the context of Brown. Right. Emerson believes that things like sleep walking, the unconscious give us time, give the world time, we'll be able to answer these kinds of questions. He does not, in other words, believe that there's some kind of flaw in human psychology, human consciousness, or human reason. We just don't know enough yet. That will be his reply. So you might say, the gothic. Emerson is an absolutely non-gothic thinker. Although as we'll see, most likely after the break, that, that he has a gothic moment or two. But then he turns around and makes a reaffirmation of his individualistic philosophy. All right. Here's a tough paragraph. Let's take a look at it. Philosophically considered the universe is composed of nature and the soul. Strictly speaking therefore, all that is separate from us, all which philosophy distinguishes as the not me, that is both nature and art, all other men in my own body must be ranked under the name nature. In a new way, the valleys of nature and casting up, there's some actually use the word in both senses. In its common and in its philosophical import. Much the way we've been talking about materialism or idealism. An inquiry so general as our present one, the inaccuracy is not material. No confusion of thought will occur. Nature in the common sense refers to essences unchanged by man, space, the art, the air, the river, the leaves. Art is applied to the mixture of his will the same things, as in a house, a canal, a statute, a picture. But his operations taken together are so insignificant, a little chipping, baking, patching, and washing, that an impression so grand as that of the world on the human mind they do not vary the result. All right. There's a couple of important things to, to note in there. For one thing, what the hell is he talking about? What is nature in the philosophical, what counts as nature in the philosophical definition that he's invoking? Yeah. >> Everything that's not [inaudible] is that [inaudible]. >> Okay. Everything, that's good. Everything that is not his consciousness then in some sense his consciousness can't change or that he takes as a kind of given. Including what? Surprisingly at the very end of the paragraph. His own body. Okay. So all that makes sense. Body biology, part of nature. But then, take a look at what he says a little bit. All right. Well let's, let's stay with our. Is there anything else to add here that we might want to say about this philosophical conception of nature? Yeah. >> [Inaudible]. >> Okay. So nature and art. Nature is essences unchanged by man. Art he says is a mixture of his will, the same thing. Now again, hovering in the background, the locking account of property. Remember what I told you. Where does property come? It's because you're born with property, it's called your body. When you mix your body's ability to labor, which is part of you, with nature, you get, not art, property. More property. So think about what is going on in the translation of this from nature and property to nature and art. Is it not unlike, we might ask, life, liberty and property from Locke? Life, liberty and the pursuit of happiness from Jefferson. Is it what? Is it an idealization of this? Is it covering up something that would be, we'd rather not talk about that's a little inconvenient. And one thing to bear in mind, people would say, I mean just take a look at this. But is operations taken together are so insignificant, a little chipping, backing, patching and washing, that an impression so grand is that of the world on the human mind, they do not vary in result. People would point to that and say, oh Emerson, gees. 19th Century thinker. He had no idea. This is all preindustrial. He thinks the railroad is a good thing. If he could wake up today, and look what we've done to nature, he'd realize that he was completely wrong. Right. I mean we can change nature. We can destroy the world. We are destroying the world. I believe in global warming. You know, personally, and you know we've done that. Right. Yeah. >> [Inaudible]. >> Well I guess you know he, he would say well gees I guess we made a lot of art. [ Chuckles ] [ Laughter ] All right. But having said that, anybody ever go to planetarium shows or look at pictures from the Hubble telescope? Or just think about all the freaking nature that's out there? What have we done to affect that? Come on. We are insignificant in a certain way. So Emerson is interested. So Emerson would say, you know, he would probably say that's probably exactly what he'd say. He'd say look, we have not affected. And yet, that's not where he wants to end up. Where he wants to end up is the fact that we are not only not significant, we are absolutely significant and that's because, again, not of what we do to nature, but of our connection to God. Last thing I want you to see. Philosophically, the not me, expand on what you're saying so we're absolutely clear on it. The only thing that is you, the only thing that is the me, is my soul or my consciousness I suppose. But my soul. Everything else is part of the not me, even my body. Now think about that. When you look in the mirror, what do you think of as yourself? Would you be the same person if your, you know, I mean maybe, maybe people, I don't know. I've never actually bleached my hair blonde or something. But if you were to change the way you look radically, and have plastic surgery you would say well it's just my body. It's not, maybe, maybe we're more, you know, it's more, more, we're more intoned with that idea. But what he wants to suggest is that the body is just a contingency. It's not really you. What you look like, what your gender is, you can extrapolate from this. What your sexuality is. What your race is. All this kind of stuff. The idea that but he's pushing is that all of these are contingent. That is what you might say puts him in a certain line of American philosophy that we would call individualistic. And I would even call ontologically individualistic. Right. The society exists only afterwards. And all these things. But not only society, everything exists only after. You are your soul first. That's you. And then a whole bunch of stuff gets added on like a box to contain your soul and it has to go with, you know, your beautiful blonde hair, or your beautiful brunette hair, or your beautiful blue eyes, or your beautiful brown eyes, or your beautiful mind. All of that stuff is extra. I just want you to think about that, because it's a really strange way of thinking. It's not a way that any of us experience being in the world. We are all born, as Emerson would say, belatedly. We're born into families. We're born into communities. We're born into a nation. We're born into a world. Really crappy things have happened in the world before us that we have had, you know, nothing to do with, and yet have to live with the consequences of. That question of belatedness is a big one for Emerson. And what Emerson does not want, Emerson wants to find modes of thinking that will keep us from being hampered, harnessed, constrained by that idea of belatedness. Okay. So one of the things Emerson would say is that idea of the me, we need to hang on to. The me is connected to the reason, to the soul. Later on in some of his essays he goes on to develop and idea that he calls the over soul. It's kind of like the sum total of all souls. And it's the thing that, in some sense, is a conduit between human beings and the divine. So I want you to see that Emerson is pushing these individualistic ideas farther than any puritan would. But even further than Franklin would. He's giving them a kind of inflection. So you might say, this is another solution to the problem of religion and enlightenment. Or spirituality and enlightenment right. Edwards has one solution, Franklin has one solution, Emerson had another solution. All right. I'm going to skip over talking about Siedenburg because I don't think it's as important as thinking about that image. And then we'll end there for today. Anybody remember this? This is one of the famous moments in nature. And as you can see, it was quickly caricatured in the popular press. This is on page 1112. Now again, think about your Edwards as a proto-romantic thinker. Edwards Bell rises nature, nature becomes an example that he can use. He gives his models for enlightenment. Edwards already is veering away from Bradford. Emerson's going to push it even further. Nature becomes the grounds of revelation. We study nature. We study itself. Nature becomes our conduit to the self. By studying the self we study the divine. Okay so nature is not to print. We are not to print. In fact nature becomes a form, a place where revelation can happen. Emerson is a romantic thinker insofar as he also agrees, you might say, that, that somehow adults have forgotten. Right. The children are closer to the God had. There's that wonderful poem that words with rise, intimations, the ode intimations of immortality. Right. People have read that? In [inaudible]. Intimations of immortality. It's about how the child comes down and you know screaming all these kind of God like qualities. And then he gets kind of really depressing, because all of a sudden as the child gets older, gets more constrained. And Emerson, and words just kind of stop. Couldn't figure out where to go next. It's like got himself into a real deep writing funk because he couldn't figure out what to do. He's painted a situation in which you're only getting further and further from this God, from God as you grow older. And finally, there's a moment, it's kind of breaking from him, and then he says oh but in those embers, like the fire's going out. No. But there's a little bit of embers, we can rekindle it. And that's, I guess, what poetry does. So Emerson is along the same lines here. To speak truly few adult persons can see nature. Most persons do not see the sun, at least they have a very superficial seeing. The sun illuminates only the eye of the man, but shines into the high and heart of the child. The lover of nature is he whose inward and outward senses are still truly adjusted to each other, who has retained the spirit of infancy, even into the era of manhood. All right. Now skip a few sentences on. Nature is a setting that fits equally well, a comic or a morning peace. In good health the air is a cordial of incredible virtue. And he's going to explain that. Crossing a bear common, and people often think of this transfer an eyeball thing takes place in the woods. Not necessarily. It can happen in the common. People think this was Cambridge common. It's kind of like Washington Square Park. Crossing a bear common in snow puddles of twilight under a clouded sky without having an in my thoughts any occurrence of special good fortune. And again, think of Edwards with the sun, with the thunder. Right. This is going to be a moment of revelation. I have enjoyed a perfect exhilaration. Almost I fear to think how glad I am in the woods too. So also happening in the city, it can happen in the woods. A man casts off his years as the snake is slough and at what period so ever of life is always a child. In the woods it's perpetual youth. Within these plantations of God, a decorum and sanctity rain, a perennial festival is dressed, and the guest sees not how we should tire of them in a thousand years. In the woods, we return to reason and faith. There I feel that nothing can befall me in life. No disgrace, no calamity, leaving the eyes. Right. So eyes is a privilege sense for him. We'll talk about that more. Which nature cannot repair. And then here's the moment. Standing on the bear ground, my head bathed by the blithe air, uplifted into infinite space, all mean egotism vanishes. Note the words. It's not all egotism that vanishes. It's all mean egotism that vanishes. We still keep some egotism. I become a transparent eyeball. I am nothing. I see all. Think back to your Edward Taylor. Isn't this kind of a weird Taylor-like image? And it's again that contradiction. I see nothing. Right. I, excuse me. I am nothing. I see all. The currents of the universal being circulate through me. Yet he is talking about electricity. It's Franklin in too. I am part or partial of God. The name of the nearest friends sounds then foreign and accidental. To be brothers, to be acquaintances, masters or servants is then a trivial and a disturbance. Think of Hutchinson or Sanctification. All this stuff is extra. I'm just having this moment. To be brothers, to be acquaintances, masters, or servants is then a trivial and a disturbance. I am the lover of uncontained and immortal beauty. In the wilderness I find something more dear and [inaudible] than in streets or villages. Again it's society, unnecessary evil. In the tranquil landscape and especially in the distant line of the horizon man beholds somewhat as beautiful as his own nature. His own nature. Nature out there is a poor copy of your own nature. I want you to see this as a kind of synthetic moment where a lot of the building blocks hat we've been investigating up until this point are re-synthesized into something else. Into an Emersonian philosophy of self reliance. All right. We're going to leave it there. Because we do not finish with Emerson, no American scholar, no experience on the midterm. We will only, only nature and self reliance are fair game. And one of them will be there in the passages. So hope you've thought about what I've been saying. But not the other two. Just those two. All right. Good luck with your preparation. I'll see you here bright and early before 2:00 on Wednesday. |
Open_Ed_Cyrus_Patell_American_Literature | American_Transcendentalism_II.txt | >> Everybody have a good spring break? Anybody go anyplace warm? >> New York City. >> So I was told. I was in someplace warmer about 13 hours away. Ok, good, lets, I hope everybody came back energized and ready for the second half of the course which contains the good stuff as far as I'm concerned. You didn't hear me say that. But I do want to go back and make sure to reinforce certain points about Emerson because there's a certain way, which Emerson's going to frame our thinking for the next few days and certainly even, maybe even few weeks. And so we'll continue on with Emerson today, maybe set up Thoreau, and then spend all of next time talking about Thoreau's two pieces that we read, Resistance to Civil Government and Walden. So we'll go back to that idea of contradiction, right? The idea that Emerson somehow uses contradiction as a kind of organizing principal in the sense that a mark of genius is to be able to hold contradictory ideas in your mind and not go mad. We'll find that later on when we get to Moby Dick, the whale, who the narrator Ishmael, thinks of as somehow having a brain that perhaps exceeds the human brain because it's able to process two diametrically opposed views. The views out of its eyes, which are, as we know, precisely where our ears would be, so they see completely different perspectives. That idea is something that I think we'll want to carry over from Emerson when we get to that moment in Melville's novel. So one of the things I want to suggest to you is Emerson thinks about the contradictions in his writing as a byproduct of what we might call the dynamic nature of culture and of the individual. So throughout his writings there's an emphasis on process. That idea, as he says, that power consists in the shooting of the gull. The kind of darting to a name as if he's less really interested in the theology of his thinking than in the process of getting to some kind of end. There's a good example of that in Self Reliance so maybe we should take a look at it. It's a well-known passage at the bottom of 1172. In which he says this, Life only avails, not the having lived, is exactly the moment I was referring to. Power ceases in the instant of repose, it resides in the moment of transition from a past to a new state in the shooting of the gull, in the darting to an aim, this one fact the world hates that the soul becomes. For that forever degrades the past, turns witches all witches to poverty, all reputation to a shame, compounds a saint with the rogue, shoves Jesus and Judaist equally aside. Well I referred to this passage before the break but I wanted to make sure to kind of engrave it in your mind. Why then, he says, do we prate of self-reliance? It is much of the soul as present there will be power not confident but age. All right, he's interested in the soul's ability to act. Confidence it seems, he means here it would suggest something less than dynamic; something static. He's interested in the acting of a soul. The talk of alliance, he says, therefore is a poor external way of speaking. Speak rather of that which relies because it works and is. Who has more of a soul than I masters me, though he raise not a finger. Right? So Emerson locates the key here in progress and the fact that the soul becomes, it's forever changing. And that he believes saves the individual from a kind of slavish devotion to the past and from the restrictions that a rigid conformity would sort of impose, right? You might call this a problem of belatedness. Emerson understands us to be belated beings. We come late into the world. Many things have already happened, right? In one account that we've been looking at this term, right, the puritans account of the world, we are so belated that we're all born damned, unfortunately for us. We're born after the fall of human kind. Emerson doesn't believe in that and he wants us in some sense to think about the ways in which we might overcome this problem of belatedness. Manifest itself in the idea as he says at the very beginning of Nature, and since we're going to be looking at Nature this might be a good time to turn to it on page 1110. He says our age is retrospective. It builds the sepulchers of the fathers, right. It's an age, intellectually of tomb building, memorials rather than thinking for ourselves. And that's the problem, right? Emerson as you no doubt have noticed, has a very exalted view of the individual. He thinks of the individual as the arbiter of meaning, right? At one point, he says suppose you should contradict yourself, what then? And he's not afraid, in other words, to face up to the fact that individuals are frequently in what we might call contradictory subject positions, right. They're pulled one way and another by different systems of thought, by different experiences in their own life. And one of the things I want to suggest is Emerson's writings attest to the power of the individual human mind to, if not necessarily resolve these contradictions, to be able to maintain them and work through them. As we might say to contain them. So quite literally the contradictions that are contained in his writing become a model for the way, which the human mind itself, might contain appropriate, maybe even be energized by the fact of contradiction. Another thing we might say about Emerson's writing, that along with being, giving itself a free license to explore contradictory impulses, it's also deeply illusive and intertextual. So if you turn to any essay you might find passages in which you're going to get illusions from, I don't know, the bible, from Shakespeare, from Conte Coleridge or Swedenborg. From Hindu, [inaudible] even philosophies, in the first. In one very famous paragraph, in the Beauty section of Nature, Emerson quotes, let's see, shallast [assumed spelling] given, he sights the Spartan King Leonidas, the Swiss patriot Winklereed [assumed spelling], Christopher Columbus, Henry Vein, the Parliamentary and William Russell, and finally ends the paragraph by making reference to Homer Pindersucks, Socrates Position, and Jesus in quick succession. Very elusive, now you might think of this as somewhat contradictory. Why is he quoting all these guys if he says, what we're not supposed to be doing is building sepulchers to the past. Shouldn't we just ignore them? Right. So this is another point I want to make. Some people say that, you know, Emerson kind of has infected us with a scorn of the past. I think Bart Giamatti who was once president of Yale and was then even more importantly commissioner of Major League Baseball, or president of the National League. I guess he was MLB commissioner as well; he's the one who banished Pete Rose from the game forever. He said that about him, didn't like Emerson. Liked baseball, thought Emerson could have learned a few lessons from baseball about the interplay of the individual and the community. But he said that Emerson infected us with a score of the past. But I want to kind of suggest that as a misreading of Emerson. One that Emerson himself leaves himself open to. But I think it's not about scorning the past, it's about not being tyrannized by the past. In fact being willing yourself to tyrannize the past. He says that in one moment. We'll take a look at that when we get to essay The Poet when we read Whitman. But we need a poet with tyrannize. Alright, somebody who's not afraid to take what he wants out of history, culture, the past and remake it anew. So Emerson feels free to quote from all these authorities, except he doesn't think of them as authorities. They are just other thinkers of whom he might say he is not only the equal, but in some sense superior because he's quoting them. You should take this as a lesson for how you should write papers as an English major. The thing you should not do from Emerson is be very contradictory and kind of meandering and jump from high point to high point. We probably require you to build a more orderly argument than that. On the other hand, you should feel free to tyrannize your sources in the sense of making them subordinate to the arguments that you make. That's what I would advise you. In a poor strategy to set up some poor critic as a strong man and then just kind of bash him and then just get your own argument in sideways. Or even worse to cobble together a paper that is a series of other peoples insights. Emerson would hate that. So there is something that we can learn from Emerson, right? Get their insights, but subordinate them rigorously to your own argument. When you write a paper, make sure it's not being driven either by the insights of others or by just something like the sequence of attacks. So find ways, we can talk about this; find ways to subordinate rhetorically what other people have thought. You got to bring in a critic or proof, or to show that you've done your homework. Don't set them at the beginning of the paragraph. Put your argument first and then set the critic into a subordinate position. They're helping you make your argument. They've already made theirs; they don't care about you. Ok. So that to the side, I want you to see that Emerson wants us to make use of the past. And therefore, he thinks, as he says, that there is not only creative writing, but creative reading. And that's part of what he is trying to get you to do even to him. Ok. So that's one thing I want you to understand that because of his process of creating reading, contradiction is contained and in a certain way the paradoxical effect is that we all get a certain kind of uniformity rhetorically in Emerson, right. It comes from all these different sources and somehow it all becomes Emerson. It all is subsumed into Emerson's consciousness. And I think that's one of the strengths in some of his writings. And it may also be one of the limitations. A little bit later on, we'll get to why I think there's a set, a kind of missed opportunity in Emerson's writing, which has to do something with a cosmopolitan impulse that's ultimately thwarted. But before we can get to that, I want to take a little bit more time to look at Nature. We did manage to look at some bits of it last time, but I'd like to think about it again before moving onto the American Scholar and Experience. Right. So one of the things to say about Nature is that even though it's Emerson's first major text, there's a sense in which it is, I would argue, not entirely characteristic of all of his writings. In part because it seems to have a formal structure in which one chapter builds on one another. It's influenced you might say, because its subject is nature, by thinking of natural historians or scientists. So that natural history becomes one way for him to think about transforming nature from just lots of data to be collected into some kind of truths that we can read. So you can see if you read Emerson's journal that he's kind of working on this and sometime around March of 1836, in his journals he records that he's hit on this kind of scheme that allows him to talk about his subject. Right. So we get a bunch of chapter headings after the introduction that would seem to mark a kind of ladder of thought and a scent of a kind of moral and spiritual ladder from something that's lower to higher. Or you might say after the introductory chapter on nature itself, we move finally from you might say commodity to higher levels of abstraction all the way up to idealism and then finally spirit. And then each of the chapters, many of them are themselves divided into numbered sections. So that would seem to be a little more orderly than other forms of Emerson's writing that we've encountered. It doesn't have that kind of associative quality. Those kinds of leaps of thought that we might see either in the American Scholar, or especially in something like Self Reliance. But one of the things I want to suggest to you is in fact if we look at this kind of structure of leaping rhetorically, we see that in a sense the structure of nature contradicts itself. But there is this kind of leaping that goes on in almost every chapter. So in some sense every chapter replicates this structure of associative thinking. Emerson in other words seems to build his arguments in each of the individual sections. Not necessarily through progress but through something that we might think of more as some kind of accumulation, the accumulation of ideas rather than a strict sequence. In effect, you might say every chapter then recapitulates the others in having this kind of structure of an ascent up a ladder and that's one of the things I want to suggest to you. That's why many people actually think that despite the apparent projectory in the book as a whole, many of the chapters seem somewhat interchangeable with one another. It's often hard to figure out, as you'll remember reading something in Nature and sometimes it's hard to pinpoint where it is if you haven't been keeping careful track. And I think that's an experience that many of us who have spent a lot of time reading Emerson, often have. Like, you know that's in there someplace but you can remember quite where it is. All right, so that's one of the things I want to suggest to you, that Emerson is looking for a structure because at this point in his career he thinks it will help him articulate. But ultimately, he's going to chuck that idea of structuration all together. Now I said last time, and I didn't have a chance to talk about it very much, that the epigraph to the book sends an important clue and it comes from Plotinus who is one of the first great neoplatonic thinkers. The epigraph on page 1110 is this; nature is but an image or imitation of wisdom, the last thing of the soul. Nature being a thing, which duct only do but duct not know, right. And I think that that's a signal that Emerson is sending that he is writing not only something that's going to be a contribution to natural history but also a contribution to theology and to neoplatonic philosopher. Plotinus, as I think the footnote tells you, actually it doesn't tell you very much. It tells you about when he lives; I think roughly 205 to 270 after the Common Era. So he's living about 200 years after Christ and he's regarded as the first neoplatonic philosopher. And so there are certain characteristics that we might say that Emerson is signaling that he thinks he shares with Plotinus. Especially the idea that there's some kind of higher level of reality other than what you can see and touch and taste and hear. Other than, you might say, the visible or the sensible. So this is the platonic belief in forms or ideas that have a higher reality. Right, we remember the whole; we don't have to go through it again, right? The platonic idea of the table, this is one manifestation of a table but it's false to many other manifestations of the table. So what's really real and true is the idea of the table, which exists. I don't know. Somewhere in the ethos [inaudible] or in our minds. Ok. So Plotinus is kind of taking that and mapping it in some sense onto Christian theology and he becomes an inference for the Puritans as well, who believe fundamentally, that what exists in heaven is what's real and what exists on earth is false and any number of ways. So that's one thing that Emerson is signaling. Also perhaps, several other things. A belief that the universe is fundamentally good. That's one of the kind of Plotinian revisions I suppose. And, or one of the things that exist in Plotinian accounts of Christianity that then get somewhat sidetracked later on by Calvinism. And a kind of preference for what we might call intuition or revelation above simply empirical investigation. So empirical investigation, being a kind of materialist philosopher is the only place to start. It's just gathering data. But ultimately, we're looking to create a fertile ground for revelation. All right, so one of the most famous moments of revelation is one of the ones we looked at last time. That idea of the transparent eyeball when Emerson's walking through the bear colony all of a sudden gets short, has the currents of the universal being flowing through him becomes his transparent eyeball, wonderful. So that's a moment of revelation. That's the kind of thing that Emerson is looking for. You go wandering around, but not even, you don't have to wander around, you don't have to leave your room. You can have these things so long as you are not tyrannized by the past all the bad stuff. In other words Emerson believes that each of us has a soul that's connected to something that later on he goes on to call the over soul. And that you might say, you'll get to this especially when we start reading the essay called The Poet, is one of the things that's a goal of poetry. To help us with our individual souls connect to that larger over soul. And when we can make that connection, then we can, you might say participate in this economy of revelation. So poetry eventually helps us to experience revelation. Or at least the kind of poetry that Emerson has in mind that he hasn't found yet, that he is happy to find when Walt Whitman sends him a little book of poems called Leaves of Breath. But we'll get to that. Ok, another influence that I didn't get to last time, but I just wanted to register, is Swedenborg; who's more important really in the early Emerson. So he gets quoted here and then some of the essays that we read then in the later. It's a kind of Christian reinterpretation of neoplatonic thoughts. So it takes some of the insights of Plotinus and really Christianizes them. He was a, lets' see, a Swedish scientist, Christian mystic, theologian philosopher who lives in the late 17th century; 1688 and into the 18's, up all the way to 1772. And so Swedenborg very quickly maintains that, you know, there's a kind of infinite and indivisible power and life within all creations and that is God. And so he believes creation has its origin in the kind of divine love. He says that all created things are there for forms or manifestations, fundamentally of that love and wisdom. And therefore, he comes up with the doctrine that gets known as the doctrine of correspondence. They correspond on the material plane to some kind of concept on the spiritual plane. So when Emerson talks about this idea of correspondence all over nature's data, in some sense, is where he's getting it from. I guess one example of that, a good example, would probably be the chapter on language when he talks about the ways in which, let's take a look at that on page 1118 he says a third use which nature subserves to man is that of language. Nature is the vehicle of thought and a simple, to a simple double, simple double and threefold degree. So then, he goes on to say that, words are signs of natural facts. Right. He's thinking about the process of what we now call signification. Now word is a kind of arbitrary sign, why should any set of sounds ands set of symbols correspond to an idea. So it's only a sign of some other facts. But then he also thinks that those facts themselves are merely symbolic of spiritual facts. So therefore, he says nature ultimately has a kind of symbolic function, it symbolizes this other world. And that's all stuff that he gets from Swedenborg. Just so, you know, that's where a lot of this is coming from. Now, nature, therefore I want to just suggest to you, brings a lot of these things together, this little volume. It begins, we might as well take a look at the beginning again because I think it kind of helps us to get an idea of the way an Emerson, Emersonian kind of rhetorical strategy works. He begins it somewhat conflictually. Right? I mean he sets up a kind of problem we've talked about this several times. Our age is retrospective; it builds the sepulchers of the fathers. It writes biographies, history, criticism right. So the subject of criticism arises immediately in Nature, in the volume Nature, only to be scorned right away. Right, so there's a whole set of undesired, and I said don't set up a strong man, well he does actually. He sets it up to be these old genres. These are the false ones. Biographies, history, and criticism is a true one, are the ones he wants to promote. They are genres of insight he says, revelation. Those kinds of genres, and he's thinking, therefore about somewhat discredited genres still like poetry. So he's interested in originality rather than retrospection. Revelations shouldn't only be something that we assume is in the past, but that we should think of as possible, not only possible in the present, but possible if we promote a certain view that he comes to call self-reliance. So you might say that in contrast to some of the other writes that we were looking at before the break, like Charles Brockden Brown perhaps or Edgar Allan Poe who are suspicious of human consciousness, who worry about the limits of consciousness to control thought, or what happens when we go to sleep, or what happens when we're dreaming, or what happens when we go mad? Emerson, you might say perhaps too easily, that's one critique of Emerson. Emerson pushes some of those concerns aside. He celebrates the individual's power to conduct reasoning. And he believes that reasoning is a high faculty that comes essentially from the divine. So he refuses to acknowledge that there's any phenomena that human beings can't eventually figure out. Nothing, he says, that really could be called inexplicable. Take a look at the second paragraph of Nature on 1111. Undoubted we have no questions to ask which are unanswerable. We must trust the perfection of creation so far as to believe that whatever curiosity, the order of things is awakened in our minds, the order of things can satisfy every mans condition is a solution in hieroglyphic to those inquiries he would put. He acted as life before he apprehended his truth. And that's part of why there's all this stress in Nature. It's almost like our actions, become our, we have to figure out how to understand our actions and the way we live as symbolic as something else. The truth is inside us, we don't realize it. We act, we need to step back and think about what the truth is that's contained inside all of those actions. Right? And again, this is leading to a rather abstract understanding of what the individual is. Right? In the next paragraph he talks about the aim of science, being defined a theory of nature. He says we have theories of races and of functions but scarcely at a remote approximation to an idea of creation. Clearly indicating that the biblical idea of creation is insufficient. We are now so far from the road of truth that religious teachers dispute and hate each other. And speculative men are esteemed unsound and frivolous but to a sound judgment, the most abstract truth is the most practical. Whenever a true theory appears, it will be its own evidence. Its test is it will explain all phenomena. Now many are thought, not only unexplained but inexplicable. And these are some of the things you might say that, some of the things that were in those other writers that I mentioned, Brown and Poe and others. Language, sleep, dreams, beasts, sex. Emerson says they're not, they shouldn't be, we shouldn't worry about them because if we spend enough time on it we can answer these things. And then he goes on at the end of this to talk about this really constrained conception of himself. The me is only the soul. Everything else belongs to nature and its therefore separate from me. So he divides everything philosophically into the me and the not me. And what I want you to do is really think about the strangeness of that. It means that you, what you typically look at in the mirror is not really you. I mean it's just sort of a contingent aspect of you. You happen to be a woman, you happen to have brown hair, you happen to be 5 foot 3, you happen to have light skin. All of that is contingent, it isn't you. Now typically we think in a different way. We think about what makes us unique, we look at many of those characteristics. And he would have said even beyond that, a certain characteristics of mind or thought. So it's a rather abstract version of the individual. And what I want to think about a little bit is the way in which that is highly compatible with a kind of strain of liberal philosophy about the individual that is proven to be very powerful. Right. So there's a certain way in which you might say, Emerson is in parts in cahoots with kind of a discourse of individualism that in other times he would seem to scorn. So, any questions about that so far? About these ideas of nature itself, individual contradiction. Are we good? Ok, let's take a look, oh I don't know, let's take a little bit of a look inside nature and maybe a place to go would be this chapter on beauty. This starts on page 1114, 11 yeah. He's trying to understand beauty, right. To think about, so this we might say is the idea of aesthetics here. And one of, the only thing I want, what I want you to see is just part of the way in which the rhetoric works through a kind of weird confusion of what we might call the natural and cultural. And there's asens in which Emerson is doing is pushing all of those things aside on the not me side of the ledger. So take a look at the top of 1115. In other hours, nature satisfies the soul purely by its loveliness and without the mixture of corporeal benefit. I have seen the spectacle of morning from the hilltop over against my house from daybreak to sunrise with emotions, which an angel might share. The long slender bars of clouds float like fishes in the sea of crimson light. From the earth, as ashore, I look out into that silent sea. I seem to partake its rapid transformations. The active enchantment reaches my dust and I dilate and conspire with the morning wind. How does nature dayafy [assumed spelling] us with a few and cheap element. Give me health in a day and I will make the pomp of emperors ridiculous. The dawn is my Aseria, the sunset and moonrise my papoose, and unimaginable realms of fairy broad noon shall be my England of the sense and the understanding. The night shall be my Germany of mystic philosophy and dreams. Now this is supposed to be a section about beauty that's about simple perception of natural form, right? And he starts that, he's looking at the sunrise, but look how immediately his mind leaps. His mind leaps into the past of humanity. And while he's setting nature up over against the kind of traditions of history and thinking, he might say there's a certain way in which his perceptions of those things are never the less parasitic on an understanding of history and culture. So one of the things we might suggest here is that nature is quickly in Emerson's thought incorporated into a kind of cultural system that then spread out and comprehends all of western and eastern civilization. So you might say that one of the things it's doing, we have the mind here unifying things that are often kept apart, nature and culture on the one hand. And then you might say not only bring them together but separating them off from thyself. Both of them become the grounds for which we might call self-investigation. So that's one of the thing is want you to see. If you should look through these pages, you will see that different kinds of boundaries that we typically keep apart or use to separate things, Emerson pushes together on the one hand and then puts them all out there as if they were all simply the grounds for what he calls self-reliance. They become, nature and culture equally become the grounds through which we explore the self. There's a funny way in which Emerson is using both culture and nature what we might call instrumentally. They are just, you know, things according to which you might want to apply this idea of the tyrannize eye that he talks about in the essay, The Poet. Now let's look at the end of this. It's a little bit strange. It's a section that's called Prospects and it starts on page, I think, well let's go to page 1132 that seems like a good place. That's where, yeah ok, in fact we'll just go to prospects. One of the things about prospects was it was the final chapter. Is it Emerson says at the end we're still very far away from a true theory of the universe, right. So you might say there's a sense we've been building up through this, what I said was a kind of seeming progression of thought. Upwards, up a ladder of moral and spiritual philosophy. I suggested that the structure of each individual chapter be looked at. That each of them is built on these leaps. But finally one of the things that these prospects are looking for, this chapter suggests, there's been something inadequate about the whole scheme all together. Or you might say there's something inadequate about natural science itself. So he forced to do something other than strictly speaking natural science and what he does is to tell a fable. And this is a characteristically Emersonian moment and one that next time we will see, we will see Thoreau make use of as well. So take a look on page 1135. The middle of the page, he says I should therefore conclude this essay with some traditions of man and nature, which a certain poet sang to me. And which as they have always been in this world and perhaps we appear to every borrowed maybe both history and prophecy. And of course, the footnote tells you that the poet is Emerson himself. And this poet gets described as later the orphic poet. But take a look at what the poet says. Perhaps we don't want you to read it all but maybe the bottom of the page, second to last paragraph. A man is a God in ruins. When men are innocent, life shall be longer and pass into the immortal as gently as we awake from dreams. Now the world would be insane and rabid if these organizations should last for hundreds of years. It is kept in check by death and infancy. Infancy is the perpetual Messiah, which comes into the arms of fallen men and pleads with them to return to paradise. Man is the dwarf of himself. Once he was permeated and dissolved with spirit, he filled nature with his overflowing currents. Out from him sprang the sun and moon, from man to sun, from woman to moon, the laws of his mind, the periods of his actions externalized themselves into day and night, into the year and seasons, but having made for himself his huge shell, his waters were tired. He no longer fills with veins and veinlets [assumed spelling]. He shrunk to a drop. So what we have here is a kind of alternative creation. Emerson suggests that we live in a world that fundamentally we have forgotten we created. And part of his goal is for us to remember that we've created these things. And again this is somewhat counter intuitive, especially for a thinker who believes in something that he calls God at times and the over soul who believes in the soul. But again, you can think of it as a number of different ways. You can say of course we created it because again part of us, the most important part of us is linked to the divine. Is consubstantial with the divine. So we participated in the creation you might say of ourselves. But now as he tells us where we've become timid and apologetic and even forgetful. We've forgotten that his essays are an attempt to get us to rethink our paradigms, to get us to rethink our relationship to nature and to take dominium over which is ours. And there's a sense in which Emerson picks up the idea of dominium that we find in the first chapter of Genesis and invokes it at the bottom of 1137, at the end of the essay. Landowners let's take a look at that, it's about, well, just we'll do the second line from the bottom of 1137. The kingdom of man over nature which cometh not with observation, a dominion such as now is beyond his dream of God. He shall enter without more wonder than the blind man feels who has gradually restored to perfect size. And in that idea of dominium and then that idea of being beyond his dream. Which cometh not with observation. Which that phrase comes from Luke. Emerson is creating a kind of idea that suggests that finally what we need to do is take control of nature for ourselves. And it's hard to tell at certain moments where Emerson is thinking kind of metaphorically, nature, philosophically, or whether as some people have suggested, that it fundamentally puts in, one of the things that Emerson has been compatible with is a certain kind of materialist use of the natural. Which makes him anything other than a kind of naturalist. So we'll talk about that next time when we think about the uses to which his disciple Thoreau puts nature. But one of the things I want you to see. This is what I mean when Emerson uses nature instrumentally. It's a tool only to be, that's interesting not for its own self but only because of what it tells us about ourselves as human beings. The kinds of insights it can be fundamentally, therefore Emerson, I would suggest doesn't care about nature, he cares about people, himself, and individuals. Now, The American Scholar's a little bit different. It's a speech, it was given for an occasion but there are certain ways in which it picks up exactly where he leaves off at the end of nature. I mean it's delivered the next year, a year after Nature is written. A year after it's published. It's delivered at an annual Phi Beta Kappa address at Harvard University. And it's supposed to be a kind of, perfunctory, well not perfunctory but there is a certain genre to which it belongs of the commencement speech and there's traditional topics. One of them is the place of the Scholar in an American kind of commercial society. That's the kind of typical topic. Another you might say is the state, probably the low state of American literature. One of the things that Emerson does is to combine these topics, the function of a scholar, the idea of an American literature. Under the rubric of what he comes to call here, the problem of self-distrust. All right, in the positive sense, you might say it's self-reliance. And that's an organizing principal for all of Emerson's writings in this period from about 1837 through the publication of the first series of essays and Self Reliance comes from that series of essays. It's a certain kind of egoism. Remember in Nature, in the moment of the transparent eyeball, he says all mean egotism vanishes. That doesn't mean all egotism vanishes, we need some of it. We just don't want it to be. There's a kind of idealized egotism that Emerson finally calls self-reliance. The problem with American thinkers in this moment is that they lack self-reliance. In a way there are things that he says now about intellectuals, one of the things to know about this essay is it's written in the, in a moment of economic decline. There's a panic in 1837, which makes prospects for the scholars, for people graduating from school seem even dimmer than usual. And one of the things Emerson is suggesting is that you need to not be afraid as a scholar, as somebody graduating from a school like Harvard. Even in the face of a commercial society that generally scorns what you do and also is proving itself to be somewhat unreliable. So, he takes up the idea here of creative reading and he sets up the idea of process. So he's all about certain kinds of redefinition and part of the reason I say he takes up where he left off in nature is that in nature he ends with the idea of the orphic poet, he beings American Scholar with another fable. Take a look at it. It's at the bottom of 1139. He says I'm going to tell one of those fables, which out of an unknown antiquity can convey unlooked for wisdom. That the gods in the beginning divided Men in men that he might be more helpful to himself just as the hand was divided into fingers, the better to answer it's end. And then he goes on. The old fable covers a doctrine ever new and sublime. That t here is one man present to all particular men only partially. So partially, wants you to see the kind of neoplatonic way of thinking. There's an idea of man, each one of us is not only a particular manifestation of that idea of man, but we only get a little part of it. We're definitely partial. I guess in the same way that that table is partial. It has wheels instead of legs, it just belies a lot of other kinds of tables. You must take all of the society to find the whole man. So he says man is not a farmer or a professor or an engineer, but he is all Man with a capital M. Man is priest and scholar and states man and producer and soldier. But now look at what he says, in the divided or social state, these functions are parceled out to individuals, each of whom aims to ado his skint of a joint work while each other performs his. Remember I said last time that in the kind of individualistic idea of society that Emerson is drawing on and then pushing forward, society is regarded as a secondary thing. It's a kind of necessary evil. So look at what he calls it here. Society the social state is the divided state. And he means that in kind of a double way. We divide people up so that each person has a particular function professor, scholar, statesman, producer, soldier, whatever. But there's also the implication that we are divided beings. We are divided from our true nature. And he goes on to talk about that. The fable and prize of the individual to posses himself must sometimes return from his own labor to embrace all the other laborers. But unfortunately, this original unit, this fountain of power has been so distributed to multitudes, it's been so minutely sub divided and peddled out that it is spilled into drops and cannot be gathered. The state of society is one in which the members have suffered amputation from the trunk and strut about so many walking monsters, good finger, a neck, a stomach, an elbow, but never a man. That's kind of a literary device. What it is? If you have to identify that with a literary device, what would you call it? Yeah? >> Synecdoche. >> Yeah, it is a synecdoche. Good one to know. Synecdoche, part for the whole. So you might say that something has happened, it's a kind of weird process of metaphorization that's going on. We've all become synecdochised [assumed spelling] in the social state. We've just become partial, which is bits and pieces walking around. And as a result, he goes on, man is metamorphosed into things, into many things. So we started as [inaudible] synecdoche happened and it gets even worse because now we are people to who metonymy has happened. Right? The association of one thing with another in which it is continuous in our experience. So man is metamorphosed into a thing, into many things. The planter who is set out into the fields to gather food is seldom cheered by any idea of the true dignity of his ministry. He sees his bushel and his cart, and nothing beyond and sinks into the farmer instead of man on the farm. So I want you to see how that works, right. Partly synecdoche, we are like a pinky walking around or a nose or our hands. And remember I told you at some point, I know I said that one. When we think about synecdoche, we think all hands on deck. But that's not ideologically neutral. It suggests that we are in fact valued when we're a sailor and said all hands on deck, it's because we're only valued for our manual labor. That's part of what's going on here. But look at this, metonymy means now we don't think of ourselves even as that. We're completely alienated. I'm a farmer, I just think of myself in terms of my cart. I mean, how bad is that, right? The tradesman scarcely ever gives an ideal worth to his work but is ridden with the routine of his craft and his soul is subject to dollars, the priest becomes a forum, the attorney a statute book, the mechanic a machine, a sailor a rope of a ship. This is what the divided or social state has done to us. It's synecdochised us, it metonymies us and it's therefore alienated us from our true nature. In this distribution of functions, the suckaller [assumed spelling] is the delegated intellect. In the right state, which is not this divided social state, but in his right state he is man thinking, right? So Emerson wants to stress the participle. Thinking is process. Yes? >> I hate to be that student, but a lot of what he's saying here and a lot of language you use like [inaudible] >> Anticipates Marks? >> I guess, I guess so. >> Yeah, I think that's right. I think he's compatible with Marks. If fact I'll go on to say a little bit more about that. You think that's a bad thing? >> No, I do not know like you said [inaudible] >> I mean you know, Marks is partially, Marks is interested in a critique of what's happened in this divided or social state, right? Later on Lukash will go on to talk precisely about the thing that Emerson is talking, and it was Lukash's idea of reification [assumed spelling] as well. We've all become thingified [assumed spelling]. Lukash talks about that as a result of the kind of labor that we do. I mean it's even worse, this, what Emerson is talking about here becomes only intensified by the industrial revolution. One of the things is the critique of Emerson, when he says things like, we can't, all of our operations taken as a whole don't affect nature. We can say, well he has no idea, right, about the extent to which we're able to affect nature. And yet you can see that there's a funny way in which he's a little optimistic perhaps about what man can and can't do to damage nature. But there's a sense in which he anticipates some of the kind of late 19th century disasters in the making. So I think you're absolutely right that he is compatible with a certain line of Mark's [inaudible] thinking. And so Marks again is interested in trying to find a social system that will enable us to get back to what he calls our species being. All right. And that's, again if you look at some of that language, it's, where's it going to be different? The fundamental difference between Emerson and Marx; where's that going to be? >> Individually. >> Yes, that's right I suppose. That's right although Marx, what I'm suggesting to you is that this is a weird kind of individualism right because there's a something communal built into his idea of the individual, right? He's talking about we are individuals but we are linked to some larger fountain of power, we need to right? Ok. But no, now where is the real difference going to be? And even that difference is mitigated somewhat. What is it that Mark calls the opiate of the masses? >> [inaudible] >> [inaudible] right. So Emerson has a, Emerson has a distrust you might say of the ways in which religions have been organized. But fundamentally, he remains a religious thinking. Wouldn't you say? I mean his language is shot through with the soul. And the thing that we talked about last time we were talking about Emerson, the problem with idealist philosophy is that it leaves the God out of me. That is not something that Marx would write. So there's where you would draw the line between them. And yet you might say that Emerson is also a dissident. Marx wants to chuck religion all together. He thinks it's the opiate of the masses; it's a tool of social control that the upper classes have used to help with this creation of false consciousness so that the lower classes think that the interests of the rich are their own interests. And religion becomes one tool so that that happens. Excuse me. [ Door slams ] But Emerson has more of a, so Emerson doesn't believe as Marx seems to that God is a fiction created by the, you know, one class to keep another in control. Emerson really believes in God in some kind. So there we would draw the line but yet he like Marx is dissatisfied with the state of things in the culture he loos around and a lot of that dissatisfaction comes from the idea of the ways in which the soul, as he puts it here, is subject to dollars. And this isn't what I was going to do, but why don't we do it now anyway. Let's take a look at; well no it's all right, in fact, thank you for that, that's not a bad way of getting to this. One of the things I want to suggest to you is that there is a certain way in which Emerson is compatible with a form of Lockean thinking that he would seem to be critiquing, right? Locke, as I said, and the you had a little, we had a little handout electronically that had excerpts from the second treaty of the government. But the basic idea that I wanted to get at is that Lock comes up with an idea of the self that is based fundamentally on the idea of property. And that's what the Mark, the Neil Marxist political philosopher, Crosserd [assumed spelling] calls possessive individualism. So when we talked about this with Jefferson. Lock has this idea, life, liberty, and property. Those are the things that we want to be able to guarantee. And he thinks of them as inextricable. Why would you include property? Well remember where he's coming from, all right. English Civil War, lots of unrests, so Hobbes is kind of mortified by all this. [Inaudible] looks for a philosophical basis to justify absolutism and yet still keep some idea of the concept of the government. So Hobbes famously says that the war, that the state of nature is intolerable. It's the war of all in which the life of man is nasty, brutish, and short. So in order to avoid lives that are nasty, brutish, and short, we give up some of our freedoms in order to preserve [inaudible], right. Typical social contract theory. And it becomes, so what we do is we delegate it all, we give all of our power to the King and he acts as our agent, so in some sense he's our delegated agent. Of course, once we've delegated our agency, our agency is delegated and it's gone. So it becomes a kind of round about defense of the absolutism in which basically, we have delegated all of our ownership to the king and then the king can delegate it back or not. Lock isn't like that. Lock wants to find a way of creating, siphoning off some of that property for us as individuals. So he comes up with this idea that in fact property is something that you are born with and the first property you have is your body. Then again map this onto the kinds of things, you know, see think about how does that work with what Emerson is saying. Your body is not really yourself. Well hasn't Lock alienated the body from you, as well by suggesting it's the property that you own. But what McPherson means by possessive individualism, is that there's a funny logic of fundamentally who you are is what you own. Or you can be who you are because of what you own. Taken too far, this leads to shopping at I don't know where and accessorizing and what Beverly would later call conspicuous consumption. Think about it, your property is your body. Because you own this body, you get to own other stuff. Why? Because your body can do stuff. You can own what you do. You own your labor. When you take nature stuff and use your labor to effect nature, you're creating more stuff and that stuff is yours, its property. So the mixture of labor and nature creates more property. And it's all based on the property that is self. McPherson doesn't like that idea, and in a way, McPherson the Marxist thinker is entirely compatible with Emerson, the non-Marxist thinker because they both think that's a degrading way of living and seeing yourself. That it is reducing you to just a set of market relations. That's what Emerson means when he says the soul is subject to dollars. He doesn't think that's the right way of thinking at all. So he actually goes after, precisely this sort of thing. Let me see if I know where the, take a look at, to get a sense of what this is let's take a look in Self Reliance, maybe. How about 1173 after the place where we were before. Right, so again if you're interested in points of contact in Emerson and then later Marx, you might thing about this passage here. It's in the middle of 1173. But now we are a mob. Man does not stand in awe of man nor is the soul admonished to stay at home to put itself in communication with the eternal ocean. But it goes abroad to beg a cup of water of the earns of men. We must go alone. Isolation must proceed through society. I like the silent church before the service begins better than any preaching. How far off, how cool, how chased a person's look, begirt each one with a precinct or sanctuary. So let us always sit. Why should we assume the faults of our friend or wife, or father or child because they sit around our hearth or are said to have the same blood. All men have my blood and I have all men's. Not for that will I adopt their petulance or folly even to the extent of being shamed of it. But your isolation must not be mechanical, but spiritual, that is must be elevation. So I think Marx would probably find that problematic, right? There's a sense in which one of the things that Emerson is doing is he sort of says that various ones disavow all of these social relations. So that would seem to be, so the idea of what, you know the, that Marx is developing is the idea of the math in which there will be power, if mass can learn to work together. For Emerson only becomes the mob. What I want you to see is, and so people will point to this and say this is Emerson, he's anti-society, he's all about egotism, but [inaudible] is that this is kind of a process of deconstruction and reconstruction. Now we are a mob. In order to reconstitute ourselves, as you might say, the right state of society, we need to disengage, think for ourselves, create the sense of isolation; but it's a weird kind of isolation, or special kind. It's going to be spiritual, not material. So for him, the material is a problem. So that's where he shares with Marx. The solution is going to be different. The solution is a kind of weirdly individualistic grass roots solution. And therefore you might say it draws on the logic of Lessays Fier [assumed spelling], but in a kind of idealized way. All right, so that's, it's getting a little bit more abstract than I intended, but. So Marx wants to reject the logic of Lessays Fier, that we find in Adam Smith, right. The idea of the somehow capitalism is a sum total of Market relations if everybody maximizes his own self interest, the whole society's self interest is maximized and the system will regulate itself through what he calls the invisible hand. It's a very nice story. Emerson is drawing on that, but again, and he's drawing on the logic of the marketplace to launch a critique of the marketplace. So he's trying to make a market in something else and that market is in individuality. So it's almost like a kind of grassroots thing. Everybody's got a seed of their own self-reliance and eventually we're going to renovate the domestic state. Another place to look, let's take a look on back, I'm skipping around a little bit, but let's take a look back in The American Scholar. This is on page 1147. This is the other moment of massification [assumed spelling]. In the middle of the page, he's talking about men in history as the herd. This is the kind of passage that Nietcha [assumed spelling] liked, because he agreed. Men are, begins in the first full paragraph, 5 lines down. Men are become of no account. Men in history, men in the world today are bugs, are spawn and are called the mass and the herd. In a century, in a millennium, that is to say one or two approximations of the right state of every man. All the rest behold in the hero or the poet their own green crude being. Ripened, yes, and are content to be less. So that may attain to its full stature. Any Yankees fans? Do you see A Rod and think oh its ok that he makes all that money because, never mind. Mets fan, sorry. [ Laughing ] I'm not going to say that rooting for the Yankees is a little bit like rooting for Microsoft, I mean. [ Laughing ] I wouldn't think that, would I? All right, where were we, yes. All the rest, can we cut that out of the tape? [ Laughing ] Actually, keep that in the tape, fine put it up on YouTube. All the rest behold. What a testimony full of grandeur, full of pity is born to the demands of his own nature by the poor clansman, the poor partisan who rejoices in the batting average of his chiefs. [ Laughing ] The poor and the low find some emends to their immense moral capacity for their acquiescence in a political and social inferiority. So that kind of hero worship, again you can think of Emerson and his resiliencies with Carlisle [assumed spelling], Carlisle's hero and hero worship. That's not good. What we need to find is the heroic in all of us. What's keeping us from doing that? It's this divided or social state, which is so linked to economy. So the next paragraph. Men such as they are very naturally seek money or power. Power because it is good as money. The spoils, so called, of office. And why not? For they aspire to the highest, and you might think of Edgar Huntly here, and this in their sleepwalking they dream is the highest. All right, now like that invocation of sleepwalking, but again, why I want you to see the fundamental difference is for Browne, sleepwalking is a kind of allegory of the human consciousness, of the limitations of it. Edgar has no idea that he's asleep, he walks around, he mucks up everything, and he learns nothing by the end of the novel. Emerson thinks that sleepwalking is like one of these errata that Franklin has identified. You can fix it; all you need to do is have more self reliance, to think clearly, separate yourself out from the mass or the herd, create this kind of spiritual separation, connect up to the over soul and the idea of where you came from, and you will realize what the true goods are. Wake them he says, and that's his job. They shall quit the false good and leap to the true and leave government to clerks and desks. This revolution is to be wrought by the gradual domestication of the idea of culture. The main enterprise for the world, for splendor for extent is the up building of a man. Here are the materials strewn on the ground. The private life of one man shall be of more illustrious monichy, more formidable to its enemy, more sweet and serene in its influence to its friends than any kingdom in history. Right. This is what Emerson at one point in his journal has called the infinitude of a private man. Right. So what I want you to see is there's a funny thing going on here. In a certain way, it's a rejection of the idea of possessive individualism. In some sense, it's a kind of idealization, or sitting it on a higher plane, or trying to understand the idea behind the idea of possessive individualism. And yet other people would say because it draws on the same kind of logic, it's strangely continuous with it. It's strangely; it's almost parasitic on that thing that it would disavow. One of the things that Emerson says at one point is that society is a kind of Joint Stock Company. In, that is in Conspiracy Against the Manhood of its [inaudible]. I believe that's in Self Reliance. Let me see if I can find it for you quickly. [ Flipping through pages ] And what I want, when he says that about the joint stock company, he is in some things making reference back to the model that we saw earlier on, which I think I brought for you today. Yeah, remember this moment in Winthrop? Right. Thus stands the God, the cause between God and us, we are entered into covenant, right? Winthrop is worried that his brethren are going to devote too much energy to upward mobility and individualistic things. And I suggested, when we talked about it here, that Winthrop is making use of a kind of logic of covenant and a logic of contract in order to create this larger sense of community, right. So you might say that Winthrop is trying to harness the language of materialism in its double sense. Right? Materialism as in acquisitiveness and also materialism as in this kind of philosophy that's rooted in the world. Harness it but ultimately push a kind of idealistic metaphor. And again, I think the, one way to think about that fable at the beginning of The American Scholar, the doctor never knew in sublime that there was one man, is to think of this as Emerson's take on this particular moment. One of the things that Emerson is trying to do is also present a way of thinking about society that can kind of harness the energies of materialist modes of thinking. But ultimately set them in the service of kind of idealist modes of thinking. So that's what, that might be an Emersonian rejoinder to the critique that he is too compatible with these kind of locked in modes of thinking. Emerson would say he's appropriating these locked in modes of thinking in the service of something else. One of the things I want to suggest to you about Emerson is that fundamentally, he has a kind, there is a kind of cosmopolitan opportunity that's being presented in his writing. And I've talked; I think I've talked a little bit about cosmopolitanism before. This is a quote that comes from the intellectual historian, David Hollinger, and he suggests that there's a difference between cosmopolitanism and universalism. And I'm thinking that we might think of Emerson fundamentally as a kind of universalistic thinker. If you look at his technique, he is trying to think about ways in which we are all alike. So he's trying to offer prescriptions about society that are going to be rooted in the individual. And fundamentally, what he wants to do is shift the grounds of inquiry away from the social, to the individual in order to be able to make generalizations about society. So for common denominator can be the soul, and if we all have that, that underwrites his understanding of society. You can make generalizations about each individual as human being and they become true of all human beings and that's what makes him a kind of Universalist. And so for him, the ways in which we are different, are actually a problem, Hence the me and the not me. If we have that very rarified understanding of what the me is, we get rid of the problem of difference. Difference becomes contingent, incidental; we don't have to worry about it. What Hollinger says, is that for cosmopolitans, diversity is not something contingent that you can pair away. So cosmopolitism starts out as a critique of nationalism but ends up being something more. It becomes an understanding of the way universalism is kind of, is problematic. If you think about it, one of the reasons that Emerson might seem dated to us today, is that he tells us a lot about the ways that we're the same but he gets short drift to the ideas and ways in which we're different and were at a moment where we're trying to think more, in terms of cultural criticism, as you might say about the interplay of sameness and difference. But what I want to suggest to you is that there's a funny opening in Emerson's writing for cosmopolitism. I mean think about the way in which he brings a variety of different sources into his writing. His writing is extremely eclectic. I would go so far as to suggest to you that Emerson is a kind of rhetorical cosmopolitan. And yet such is the way in which American audio logical structures are created still in the 19th century, that Emerson isn't able to make that final leap to something that we might think of as a true kind of cosmopolitan appreciation for difference. When push comes to shove, he rejects the opening of a cosmopolitan appreciation for difference and ultimately remains a kind of universalistic thinker. And that's one of the paradox's I was referring to earlier on. He's very eclectic, he's very intertextual, he draws from the east, west all kinds of philosophical conditions. But in a certain way, it all comes out Emerson in the end. It's like that joke about the melting pot. Remember I told that in here. I told probably [inaudible]. You know everybody comes from where ever they come and they go in the melting pot and they all come out Presbyterian. So Emerson, it all comes out Emerson in the end. Here's a, here's an example of him thinking about these things, right. In this continent, this is a journal entry from 45, so it's after the stuff that we've been reading. Asylum of all nations, the energy of Irish, German, Swedes, Poles and the [inaudible] and all the European tribes that the Africans and the Polynesians will construct a new race, a new religion, a new state, a new literature, which will be as vigorous as the new Europe which came out of this melting pot of the dark ages or that which earlier emerged from the polangic [assumed spelling] and Europe trust in barbarism [assumed spelling]. One of things I want to suggest to you is that Emerson is on a cusp of a kind of cosmopolitan awareness. But it remains in our course for that to be realized more fully by Whitman, that' quite, that people, that's it's not controversial to call Whitman a cosmopolitan thinker. And Melville and it is a little more controversial to call Melville a cosmopolitan thinker. And we'll go on to explore that idea a little bit later on. Now the test of any true philosophy, Emerson himself says, that it will explain all phenomenons. So that it should work. And there's a certain way in which in the readings that you have, Emerson provides that kind of test for himself. Right. And that's in the essay that's called Experienced, which you might say is a kind of recasting of some of the stuff from the earlier essays, but in a very dark vein. Let's take a look at the beginning of that essay very quickly at the, on page 1195. Now I talked about the problem of belatedness, right? Emerson has confidence that we can conquer this problem, we can conquer, we conquered the riddle of the sphinx. There's nothing that we can't ask that we can't eventually answer. Pooh on belatedness. But look at this, 1195. 1195 yes. Where do we find ourselves? In a series of which we do not know the extremes and believe that it has none. We wake and find ourselves on a stair. There are stairs below us, which we seem to have ascended; there are stairs above us, many one which go upward and out of sight. But the genius which, according to the old belief, stands by the door by which we enter and gives us the leafy [assumed spelling] to drink. Right? He's talking about waking up from dreams leafy's the forgetfulness of the river, of the [inaudible]. That we may tell no tales. Mixed a cup too strongly and we cannot shake off the lethargy, now at noon, day sleep lingers all our lifetime about our eyes. As night, hovers all day in the bows of the fir tree all things swim and glimmer. Our life is not so much threatened as our perception. Ghost like, we glide through nature and should not know our place again. Right. I've just finished saying that you know, conjuror Charles Brockden Browne, he doesn't think of sleepwalking as a kind of metaphor for the human condition, but as a problem to solve and then this, in which sleepiness, drowsiness, disorientation seem to be what he's saying is a condition of human life. How do we get from there to here? Ghost like we glide through nature. It almost seems like the beginning of a Poe story. Did our births fall in some fit of imagince and frugality in nature that she's so sparing of her fire and so liberal of her earth that it appears to us that we lack the affirmative principal. And though we have health and reason, yet have no [inaudible] fluidity of spirit for new creation? We have enough to live and bring the year about, but not an ounce to impart or to invest. Ah that our genius were a little more of a genius. We are like millers on the lower level of the stream and the factories above them have exhausted the water. We too fancy that the upper people must a raise their damns. And again, I want you to look at that. I mean if you were going to, if I was going to ask you to do a close reading of that, one of the things you should probably notice is the way it shot through with a kind of economic language. Precisely the things that Emerson would seem to be disavowing, that I've just been arguing he's been disavowing, seems to now he's using as almost a kind of constitutive metaphor. So what's going on here? This essay is written in the aftermath of the death of his child. And you know, you're too young all of you, but one day you'll come back to this essay maybe, and you'll have children and you'll think about what it might actually mean to have your beliefs tested in this way by something like the death of a child. So there's this kind of shocking moment. It's weird, I guess when you're older it really is shocking what he says on the middle of page 1197. It's about 10 lines from the break. He says grief too will make us idealists. In the death of my son, now more than two years ago, I seem to have lost a beautiful estate. No more. I cannot get it nearer to me. If tomorrow I should be informed of the bankruptcy of my principal debtors, though loss of my property would be a great inconvenience to me, perhaps for many years, but it would leave me as it found me. Something, which I've fancied, was a part of me, which could not be torn away without tearing me, nor enlarged without enriching me, falls off from me and leaves no scar. It was catechus. I grieve that grief can teach me nothing. Though carry me one-step into real nature. The Indian who was laid under a curse with the wind shall not blow on him, nor water flow to him, nor fire burn him is a type of us all. The dearest events are summer rain. And we the paracoats [assumed spelling] that shed every drop, nothing has left us now but death. We look to that with grim satisfaction saying there is at least reality that will not dodge us. I take this evanescence and lubricity of all objects which lets them slip through our fingers then when we clutch the hardest to be the most unhandsome part of our condition. [ Book closes shut ] What does that mean? In the death of my son, I seem to have lost a beautiful estate. What could that possibly mean? What's the logic of that? Anyone? Grief to will make us idealists. Yeah? >> [inaudible] more valuable then [inaudible] >> Ok, and how does it affect him? >> [inaudible] >> He transcended the material things that he had. Isn't the argument that it's kind of like the material things that he had. If he loses his estate, he's going to be inconvenienced, but ultimately what has he lost? You know the way people say, it's just things. You wrecked your car, thank God, you weren't hurt. It's just a thing after all. Sorry that you lost your I-pod, but it's just a thing. Sorry that you lost your son, but frankly, he wasn't you. Yeah? >> [inaudible] kind of a parody I guess that he was saying that if God would hear him >> That's right. He finds himself surprised that he's intact. It hasn't changed him fundamentally. Why is that? Because his child, as dearly, I mean, think about the residences with other things that we've looked at. Remember the Puritans were willing to cast their children into the fire so long if they're sinful and not saved. So long as the idea of God is not going to be sullied by them. I mean this is the kind of weird recasting of that too. We cast off, you know we lose property, we get that but that doesn't affect us. Why? Because property was clearly part of the not me. Well guess what, your son is part of the not you too. I mean if your body is part of the not you then certainly your son isn't. So these are still going to be external relations. This is you might say the test, the limit case of his own belief. If my theory is true, it's going to apply even here. That my worldly, my love for my son is part of an external relation to me. That's part of what motivate, you might say this is a test of the philosophy and Emerson can't believe it but the philosophy passes the test. Later on, he goes on to talk about in this essay, he goes on to talk about a recasting of the story of the fall. And we'll end with this. This is page 1207. It is very unhappy, but too late to be helped. The discovery that we have made that we exist. That discovery is called the fall of man. Ever afterwards, we suspect our instruments. We have learned that we do not see directly, but mediately. Though we have no means of correcting these colored and distorting lenses of which we are or of computing the amount of their errors. Perhaps these subject lenses have a creative power, perhaps there are no objects. Once we lived in what we saw, now the rapaciousness of this new power, which threatens to absorb all things, engages us. Nature, art, persons, letters, religions, objects, successively tumble in and God is but one of its ideas. Nature and literature are subjective phenomena, every evil; every good thing is a shadow, which we cast. Right. So this is a retelling of the fall of man, post enlightenment in terms of human consciousness. We understand that we don't see directly. This is kind of, if you want to talk about anticipations right, if there are moments when he seems to be anticipating Marx in terms of his critique of [inaudible], this seems to be interpreting, anticipating Marxist critique of ideology. Even more advanced, or neo-Marxist ideas about ideology in which say there is no outside to ideology. Or even Heisenberg's uncertainty principal. The idea that we can't, that our very presence in an experiment changes the nature of the experiment. So I want you to ask yourself, and we'll start here next time. What is the way out of this problem? What is the way out of the problem of this rapaciousness here. We'll go on to talk about Thoreau next time also. So as you think about what you read and finish up the Thoreau, I want you to think about the ways in which Thoreau's writing maps onto Emerson's. Particularly that Resistance to Civil Government is his version of the American Scholar. And this text, Walden, is his version of Emerson's Nature. All right, we'll take it from there. |
Open_Ed_Cyrus_Patell_American_Literature | Uncle_Toms_Cabin_II.txt | [ Background Noise ] >> Alright, let's get started. So let's continue on with Uncle Tom's Cabin. I wanted to just go over some of the things I said last time at the end. Remember, just a few things to bear in mind structurally about the novel. The first is that it has this kind of double plot, so it's moves both north and south and again that's another way of reiterating the fact that slavery is a national problem. It's not simply something that is a Southern problem that they need to deal with in a way Stow wants to indicate that the entire country as Emerson came to realize after the passage of the fugitive slave law, is implicated in slavery. And I think that's one of the reasons that not only she creates the double plot but has the worst villain in the novel and argue, the worst villain in nineteenth century American literature, Simon Lagree, hailed from the north and to be the embodiment of a certain kind of market capitalism that just happens to seize on trafficking human bodies as it's, as it's object. Another thing that I want you to think about, structurally was to think about the way in which the idea of Uncle Tom's Cabin, the title of the book, suggests that there's something important about, you might say domestic situations. This is a domestic novel. And it's a domestic novel that falls into the sentimental tradition, which means is that it's a novel that's intended probable, one way to think about what sentimentality does is that it is intended primarily to appeal to the reader's emotions rather than the intellect first. I'd say it's, you might say it's a variation on the old, the old idea that the goal of poetry used by [inaudible] Johnson or Samuel Taylor Colege [assumed spelling], well expressed. The idea is to instruct by pleasing, right, that literature has, is taken in the eighteenth century to have adaptic function, but what separates it from other forms of writing is that it pleases the reader first. You, you enjoy reading it and then you realize that you've had found, had some kind of educative experience at the, after you're done. So this is a very [inaudible] item, what Stow was going to do is she has a kind of analytical point to make, she has an intellectual point to make about the evils of slavery. But the way that she's going to make that point first is by getting you in the heart strings. She's going to grab onto those, pull those and then finally make her intellectual point. See its sentimental fiction, is a form that appeals first and foremost to sentiment, to feeling and secondarily, but very importantly, to intellect after that and it's linked in the nineteenth century to the idea of domesticity. So domestic life as this fear of sentiment as opposed to the life of the economy or of politics, which are meant to be linked to the life of an intellect or of abstraction, you might say. Remember she's interested in emotions and a kind of palpable feeling. That's what she wants to do. She wants to create for her readers, something that is like the experience that Senator Byrd has when having thought about fugitive slaves in charactertures or as abstractions or as you know the, the people you would read about in court cases, opens his back door and sees a young woman with a young child. And then sees that child dressed in his dead son's clothes, has a kind of visceral, emotional experience, that in the end trumps his intellectual, his intellectual experience. And for Stow, you will remember, that is a way, that is a, a form of improvement. It's a mirrortive moment when he moves from being simply a senator who thinks in legal abstractions in laws and about caricatures from the press to someone who is in some sense a man and can feel more fully. So that's one of the other things that we want to say. The house calls up the domestic situation, the domestic situation brings in this whole discourse of sentimentality, but also this therefore the house becomes one of the central ways in which the nor, novel is organized. So what we are really seeing is and we'll go through this in a little bit more detail today is a kind of series of domestic situations. So we have a kind of opening domestic situation on the Shelby Plantation and that presents us with in some sense a kind of preparation of spheres. Mr. Shelby is the man who runs the business, apparently not very well since it's not doing very well and he's having to sell his slaves. His wife is a little bit cowed by his, isn't able really to intervene on behalf of the slaves that she's been trying to raise. We see a variation on that in the Byrd household later, where Mrs. Byrd is able to slowly but surely what [inaudible] calls influence on her husband. And we talked last time about the way in which the novel seems to accept the separation of spheres into a masculine sphere of economy and business, of politics and abstraction and intellect on the one hand and a domestic, feminine sphere that's about education and religion and feeling and sentiment. And one of the things that she's proposing is that in the right state of affairs, the domestic sphere should promote a strong influence on the masculine sphere, not that it doesn't seem to propose to us ever that women should up and becoming politic, politicians and actually, literally intervene. Instead, perhaps, that should work as Mrs. Byrd does, right? That is another variation on the Shelby household and we see a variety of these different variations as the, the novel progresses. That's another structuring thing I want you to think about. When a novel does something like this, you might say it works in a kind of factorial way. The sum total of a novel is, is, is the product of a number of factors which are in sometimes variations on a single idea. This could be in terms of character, could be in terms of settings, scenes like this. We, we, you want to think closely about how the novel has created a system of value and then explored this system of value by setting up variations on how these values might be mixed together. Right. So I said, there's a masculine sphere and a feminine sphere, the novel clearly prefers many of the aspects of the feminine sphere. Right. But not every woman has the virtues of femininity. It is not enough just to be a woman, in other words and there are many men in this novel who do have some of the virtues of femininity and we see this very clearly in Saint Claire. Saint Claire household where Augustine and his wife really seemed to almost switch places, it's almost like she's the man of the household who thinks in these kinds of abstractions, even though she constantly appeals like oh, oh if you were a mother you would understand, you know. We understand who the real mother in that household is and it is not Marie. It may be Augustine, probably more likely it's Mammy, right, so there's a, there are interesting things going on in, in these households in which these, these elements of masculine, feminine are being reorganized and tested as a result. Right? One indication perhaps that the feminine sphere alone isn't sufficient is that you might say that part of, of what brings down the Saint Claire household is that Augustine Saint Claire lacks a little bit of a kind of masculine, let's do it now. He's kind of not enough of a man of action and that proves to have a kind of tragic result. And so again Stow is interested in the inter play of these different values. She believes in the separation of spheres, but she believes in a system in which both spheres are necessary. But there needs to be the correct relationship between them and at the beginning of the novel that relationship is a myth. There's something wrong with it, okay? That's one of the things that we want to say. The third thing to say is that there is a kind, there are sort of three major parts and this is kind of the opening part, which focuses primarily I suppose on the Harris' story. Then that long second part which is about the time in New Orleans and the Saint Claire household, which I suggested to you last time is much longer than it really should be if we were going to have a well proportioned narrative in terms of what action takes place, in terms of, we need to have to tell a tight story, there shouldn't be that many chapters. But it becomes, you might say, the time when the novel is, seems to warm to her subject in which she creates some of these indelible characters that people tend to remember and when she allows these characters to start to in having, become appealing to the reader if everything is working in your, your, you're reading according to her plan. She's then able to bring in kind of some intellectual discourse that she wants to have. But then there's this third section that happens after the death of Saint Claire, the death of Eva and the death of Saint Claire in which we, we move into one of the darkest phases of slavery. And there's an interesting thing, just to give you an overview, the interesting thing that seems to happen at the end of the novel in which the very premises or sufficiency of sentimentality itself are in question. Maybe sentimental isn't enough, maybe you need other literary technologies and in this case it turns out to be gothic. As the story starts to explore about what the relations between the sentimental and the gothic might be and then we'll see at the end how you might say she resolves a potential conflict between these two things. Alright. Just a couple, just to get us back up to speed so we remember where we were last week, remember that Stow thinks of writing instrumentally, right. She doesn't mean to be thought of as an artist, she doesn't have those kinds of aspirations in the way that somebody might, Hawthorne or Melville might have been said to have. She thinks of writing instrumentally at first to earn money, right, she wins fifty dollars in a prize wheel and realizes that she can supplement her family income through writing. That's one thing. It's an extension of her motherly duties there, to help out in that way and later when she writes Uncle Tom's Cabin, she concedes it as a further extension of her maternal duties, right. She writes the editor of The National Era in 1851, up to this year I have always felt that I had no particular call to meddle with this subject. And I dreaded to expose even my own mind to the full force of its exciting power but I feel now that the time has come when even a woman or a child who can speak a word for freedom and humanity is bound to speak. We can no longer sit on the sidelines, right. It's come time, the men, the, the inference here that we might have is that men and ministers, you know all of these things that are part of the masculine sphere are letting the country down. Now it's come the time that even women and children have to speak. Alright, so that's one thing. Retrospectively she comes back to think of this later on when she writes a preface to an 1879 edition. I think I told you later on in her career, when she's very much the woman of letters, she likes to write about herself in the third person, so she says, she was convinced that the presentation of slavery alone in its most dreadful forms would be a picture of such unrelieved horror and darkness as nobody could be induced to look at. Of said purpose, she sought to light up the darkness by humorous and grotesque episodes in the presentation of the milder and more amusing phases of slavery for which her recollection of the never failing wit, that should be wit, and drollery of her former colored friends in Ohio, gave her abundant material. And this is exactly the kind of statement that people subsequently find problematic, right? I mean the idea that there could be any milder or amusing phases of slavery, something that seems anathomous to us now. But you can imagine it, that one of the things she's do, she does to both appeal to the emotions, it's not only going to be to the tragic emotions, but she's going to try to create things that you can enjoy, is to appeal to certain kinds of essentialist stereotypes. Which have to do with the way in which African Americans sing or dance or certain, you know, certain kinds of down home practicalities, for example, in Mammy, in Chloe's kitchen or Mammy's kitchen are, are things that Stow uses to kind of leaven the story up and make it seem a little bit less oppressive than it might be. And that's one of the things that we should remember about the, the strategy of the novel is that in some sense one of the things she's doing is suggesting that this is a time when these three oppressed groups, women, children and slaves actually can have a voice. Needs intervene, but again the style of the novel goes along with this general idea about influence, they're not going to intervene directly, bless you, we're not going to write a tract. We're going to write a fiction which can exert a certain kind of influence and part of the necessary trickery of that fiction is that we're going to have to present, we're going to have to have some comic relief. For her, the ready to hand comic relief comes really in the wit that she finds in African American culture. Again, today that wit puts us off because it's been exaggerated so much in the later part of the nineteenth century in things like Tom Shows and other forms of, of minstrels on stage that we find it kind of off putting, right. So I want you to again think about the ways in which Stow is finding a set of, you might even call them kind of literary tactics that she can deploy and I would suggest to you that she deploys them rather consciously. Again, I suggested last time that she was deploying these as part of emotive act of sentimentality that she learns from Stern and Dickens, and very much Dickens. Right, right, if any of you have read Dickens, either in high school or the context of a Lit course here, you'll remember that you know, Dickens has, is a social reformer in many ways. And there's some very dark things in Dickens, just you know, think about child abuse in Hard Times or in Oliver Twist and all of these novels are lightened by kind of moments of comic relief and by comic characters. There's a sense in which Stow is trying to translate the Dickensian idiom into American letters and that's part of what her project is. Alright, one of the things to bear in mind then is this idea of the lowly. And for her the lowly means not only Africans who are enslaved in the United States but also other people who are set aside. Women and children and so these three groups are very much linked together in the novel's imagination. And I want you to understand that they are not incidentally linked together, it's very much, it seems to be by design. The novel creates moments of comparison among these different groups. And we might say it's, it's a dangerous strategy, not just for, for you know, the picture of African American culture, alright, I mean, not just because in, we can see in the subsequent career of the novel for African American intellectuals. This novel became an [inaudible] because it seemed to portray it as a desirable cultural affect, the subservience of African American men and, and women to some other set of values. But you can see how even in terms of the novels secondary, but still important, feminist agenda, this idea of submitting forms possibly a new rational for the submission of women, right? And we're writing in a time when women still have not achieved equal rights, so you might say for awhile this novel became not at all useful for feminist thinkers or for people who were interested in promoting women's suffrage or other kinds of feminist causes. And again it's only later on in the middle of the 1960's really that it starts to be reclaimed as part of a general reclamation of thinking about kinds of writing that don't fit a kind of modernist prototype, right? So these are all some of the things that I want you to be bearing in mind as we think, as we look at a few of the more details, right. So one of the ways, to put this in a nutshell, I will suggest to you that this is a novel that is deeply critically of and even sets itself against forms of racial and patriarchal oppression, okay. I said, I'll say it again. It sets itself deliberately against forms of racial and patriarchal oppression. It does so by tactically making use of a number of stereotypes that we would think of as racist and sexist. Okay, it's using what today we would call racist and sexist stereotypes, I would call them modes of essentialist thinking. But it's using the essentialist modes, which are typically thought of as inclusion with patriarchal and racial oppression against patriarchal and racial oppression. So for example, let's take a look at some examples of this and you'll see what I mean, I think, very vividly. Take a look on page, oh how about page forty four, this is an early example about this, of this. The little boy walk, comes in, Mr. Shelby says hello Jim Crow, whistling and snapping a bunch of raisin [inaudible] and pick that up now. The child scampered with all his little strength out for the prize while his master laughed. Come here Jim Crow, he said. The child came up and the master patted the curly head and chucked him under the chin. Now Jim, show this gentleman how you can dance and sing. Alright, so that is the master's behavior. This is the nararator. The boy commenced one of those wild, grotesque songs common among the Negroes in a rich clear voice, accompanying his singing with many comic evolutions of a hands, feet and whole body, all in perfect time to the music. The boy commenced one of those wild, grotesque songs common among the Negroes. So today we would say, hum, that seems that like kind of has a racist tinge to it. Now, what I want you to see is that, I don't think this is racist because it's not disapproving of it, it's not meaning to use this representation as a, as a rationale for the subjection. Of anything, of, of African Americans, anything, it's quite approving of the fact that there's something melodious about their culture that they have. And again, you might imagine it as being all part of the domestic sphere over against a masculine sphere that doesn't have time for things like this. Alright, so again, this is, this is again a moment in which the novel is making use of an essentialist stereotype that African Americans are have, have a naturally gift, are naturally gifted as singers or have a natural affinity towards music. Things like that. Let's find another one. How about page seventy seven. This is singing also. There getting together to celebrate. Middle paragraph, after awhile the singing commenced to the evident delight of all present. Not even all the disadvantage of nasal intonation could prevent the effect of a naturally fine voices in airs it once wild and spirited. I take it that that means, you know, they're not trained, they still have nasal intonations, they're not tutored in singing. Never the less they have the kind of natural advantage, naturally fine voices. The words were sometimes the well known and common hymns sung in the churches about, sometimes of a wilder, more indefinite character picked up at camp meetings. The chorus of one of them, which ran as follows was sung with great energy and function. Die on the field of battle, die on the field of battle glory of my soul. That's such and such, so it goes on in this kind of mode. See if we go on, we could even go on, there were others which made incessant mention of Jordan's banks, Canon's fields and the New Jerusalem. For the Negro mind, impassioned and imaginative always attaches itself to hymns and expressions of a vivid and pictorial nature. And as they sung, some laughed and some cried and some clapped hands or shook hands rejoicingly with each other as if they had fairly gained the other side of the river, right. And we would say there's something slightly patronizing perhaps, about that description. But one of the things to say is, the novel in so far as a novel is attributing something childlike to the African American temperament, to the African American intellect, it thinks that's a good thing. The two most Christ like characters in the novel Tom and Eva, both have a kind of childlike appreciation for the world and for other people, right? So the novel is deliberately making a link between Tom and Eva and parted lays the ground work for that by creating the slightly and tantalized idea of what the Negro mind, as it would put it, is all about. Let's see, this becomes explicit actually in the next example that I've got for you, page 135. This is in Eliza's, this is Eliza's escape, so it's about twelve chapters into eight, twelve pages into Chapter eight or so. In this edition, it's the middle of 135. Now there's no more use in making believe be angry, in making believe be angry with a Negro than with a child. Both instinctively see the true state of the case, though all attempts to affect the contrary. And Sam was in no wise disheartened by this rebuke, though he assumed an air of doful gravity and stood with the corners of his mouth lowered in most penitential style. Master quite right, quite, it was ugly on me, there's no disputing that, [inaudible] master and misses wouldn't encourage no such works. I'm sensible, that all about a poor nigger like me, [inaudible] attempted to act ugly sometimes when fellars will cut up such shines as that master [inaudible]. He ain't no gentleman no way, any ways been raised as I have been can't help but seemed alright. Right. So there's a deliberate [inaudible], deliberate bringing together of these two forms of representation. And you can go on and on, right, the page 253 in this, I'll, I'll put some notes afterwards that African Americans are described as exotic. A little bit later on, cooking is described as an indigenous talent of the African race, right. So I want you to see is the kind of racist and sexist stereotypes are pretty much identical in the novel. They're clearly mapped onto one another and the masculine characteristics of white male characters are often and, are often and almost consistently contrasted with the feminine qualities, not only of white women but also of black men. Let's take a look in chapter ten, this is page 162. I think it's probably the third paragraph of chapter ten. Let's start with the second. Tom sat by with his testament open on his knee and his head leaning upon his hand, but neither spoke. It was yet early and the children lay all asleep together in their little rude trundle bed. Tom who had to the full, the gentle domestic heart, which wove for them, has been a peculiar characteristic of his unhappy race, got up and walked silently to look at his children. It's the last time, he said. Now again, this is a moment when we see this kind of mixture of things, so again, you're going to say there's something patronizing about this. The peculiar characteristic of his unsym, his unhappy race, right. It's written from a seeming vantage point of white narrative superiority and yet this is a moment of deep path thoughts in which the narrative has profound sympathy for Tom and the plight that he has. Alright, again, I want you to see how this is working. These are passages that are designed to create sympathy for Tom. And you might say in so far as Eva and Tom are set up to be kind of Christ like figures, the function that Eva plays in the novel, is in fact not only Christ like but in the certain sense, she plays the role of John the Baptist. We affect really, onto her, we, we, invest her, we have a lot of our emotions as readers get. They get focused on her and when she dies, they focus some place else and it's almost as if we've been taught now to have a focus on Tom. And there's a sense in which his death replays her death. Lives up even to the promise of, of selflessness that her death implies, and in some sense, the novel helps us to appreciate Tom by first finding someone with whom we more readily appreciate, a young innocent girl who's all dressed in white. Shouldn't have that much, almost always dressed in white, as opposed to Pearl who you'll meet in like next week, almost always dressed in red. They make an interesting contrast. Please don't write a paper about that, please. But there's a sense in which part of [inaudible] function is to prepare us for Tom. That she sucks us in by getting us used to think about Ava and then we transfer many of those same emotions onto Tom. There is a slave who defies the stereotypes that I've just been talking about. Anybody think of an example? Yes? >> [inaudible] >> George Harris. Right. So George Harris would seem to be an exception to this rule. Except why is it that George is different? Remember anything about George that makes him particularly interesting or different from Tom? Yes. >> [inaudible] OK. >> [inaudible] >> And? >> [inaudible] >> OK, he's and there's something else about him too. His genes. >> [inaudible] >> Right. He's Malato [assumed spelling]. Take a look at page 182 in the chapter that's called, An Improper State of Mind. It's about ten pages into chapter 11. So this is at the bottom of 182. We were remarkable pason [assumed spelling] that George was, by his father's side of white descent. His mother was one of those unfortunates of her race. Marked out by personal beauty to be the slave of the passions of her possessor and the mother of children who may never know a father. From one of the proudest families in Kentucky, he had inherited a fine, set of fine European features and a high, indomitable spirit. From his mother he had received only a slight Malato tinge, amply compensated by it's accompanying rich, dark eyes. A slight change in the tint of the skin and the color of his hair, had metamorphosed him into the Spanish looking fellow he had then appeared. And as gracefulness of movement and gentlemanly manners had always been perfectly natural to him, he found no difficulty in playing the bold part he had adopted. That of a gentleman traveling with his domestic. So I want you to see here how he's in some sense the exception who proves the rule. He has inherited not only European features from his white father, but that kind of high, indomitable spirit. OK? I want you to think about that and think about whether it is that the Harris', that George Harris is in some sense the hero of the novel or whether in fact, it is kind of a very mixed blessing to have inherited these things. Right? Part of what we realize in the novel is that there isn't, the novel at the end cannot imagine a place for the Harris' in the United States and they are in some sense relegated off to Liberia. Part of it is this kind of weird mixture of George. One thing that George, George is not the natural, George isn't something that's not the natural Christian that Tom is and that works against him in the imagination of the novel. Let's take a look at one of these other households that we haven't had much of a chance to talk about yet. This is the quaker settlement and it's in chapter, well it starts, it's chapter 13, which is 214 in this edition. Let me. This is an illustration of characters from the quaker settlements and again, that's Maliza [assumed spelling] right. So we're meant to understand that Maliza also is very fair. Now, let's take look at page 222 here. There's an interesting passage here for us to look at. Bottom of the page. So this is about again, twelve pages into the chapter maybe. It comes after a break. The chapter, the paragraph begins the next morning was a cheerful one at the quaker house. A little bit further on. While therefore John ran to the spring for fresh water and Simeon the 2nd sifted meal for corn cakes and Mary ground coffee, Rachel, Rachel Holiday, moved gently and quietly about, making biscuits, cutting up chicken and diffusing a sort of sunny radiance over the whole proceeding generally. If there was any danger of friction or collision from the ill regulated zeal of so many young operators, her gentle come come or I wouldn't now, was quite sufficient to allay the difficulty. Bards have written of the sestus of Venus, that turned the heads of all the world in it's successive generations, we had rather, for our part, have the sestus of Rachel Holiday that kept heads from being turned and made everything go on harmoniously. We think it is more suited to our modern days, decidedly. Right? So she has a kind of matriarchal authority. It seems to work effortlessly, but does it work through direct punishment? Not exactly. It works with something that's much more like influence. Come come, she says or I wouldn't now. Right? Gently. Just kind of, it's almost like you have, she's just kind of keeping order on a kind of a system that's chaotic or entropic of all these particles. She keeps them from colliding from one another, with one another. Interestingly, her authority never seems to be challenged by the quaker men in the settlement. Next paragraph. While all other preparations were going on, Simeon the elder stood in his short sleeves before a little looking glass in the corner, engaged in the anti patriarchal operation of shaving. The anti patriarchal Why is that, anti patriarchal? Another joke. What? Yes? >> [inaudible] >> Yes, I'm just, think about old testament patriarchs too. Long beard, right? So if you shave, it's being anti patriarchal That's kind of a joke right, but it's one of the things that signals that the whole idea of what constitutes a patriarch and who usually runs settlements like this, is on the novels mind. Just through that little grace note. If you will. Everything went on socialably. So quietly, so harmoniously in the great kitchen. It seemed so pleasant to everyone to do just what they were doing. There was such an atmosphere of mutual confidence and good fellowship, everywhere. Even the knives and forks had a social clatter as they went on to the table and the chicken and ham had a cheerful and joyous fizzle in the pan, as if they rather enjoyed being cooked than otherwise. Seems like a little one of those kind of like Warner Brothers cartoons. Right? Something happy about it. It's just about as unrealistic as a cartoon as well or you might say, for the novels imagination, it understands it as a kind of Utopian space. It's not really, genuinely possible and it is impossible for the Harris' to stay here for very long. And when George and Eliza and little Harry came out, they met such a hardy rejoicing welcome, no wonder it seemed to them like a dream. And as far as they are concerned, it is a dream. Right? So one of the things to say within the topographical imagination of the novel is that to move, move north, away from Ohio and Kentucky, to move north towards Canada, is to move towards freedom. That's one thing that we would say is going on. There's also a hint that it's also doing something else. It's to move from the public world of a plantation or a senator's house, to something more private. A kind of settlement and a matriarchal settlement. So to move from a world of power, in the senator's household, to a world where power is exerted differently here, through feminine influence. And one of the things we might say is that the ultimate result for George Harris of this move northward, is the increasing influence of this feminine influence on him. So at the end, something about that high, indomitable spirit of his leads him to be tempered a little bit. And we'll take a look at that again. OK? Thus, the movement north. The movement south is a little bit different and it's a little bit strange as well. New Orleans house of Augustine and Marie St. Clair, is as I suggested already, a kind of strange variation on the opening domestic situation. In fact, it's probably the most unusual one because the masculine, feminine seems split up in interesting and different ways. Let's see, I think I have, now one of the things to notice about this. Is that it is a courtyard in the Moorish style. Right? So one of the things that we would say is it's kind of elaborate. Its even baroque. There's something voluptuous about it. These are words that Stowe uses and one of the things to suggest about that is that it is in some sense a kind of reflection of St. Clair's personality. To have this kind of household. Of house. All right? I want you to remember this though, this image. We'll come back to it. It's got the courtyard, it's got fountains inside, it's got this enclosed garden space, got these arches here, these kind of terraces on the top. OK, that's the way it looks. We'll see another house a little bit later on that's a variation on that particular situation. Now inside the house we have Marie and Augustine and as I suggested to you, there's a funny way in which when the values were poured into each of them, they didn't get poured in exactly the way we'd expect. Marie is kind of selfish and masculine. And Augustine has a lot, where his greatest influence comes, not from his father he says, but from his mother, he tells us. Let's take a look at the chapter that's called, Tom's Mistress and her Opinions. This is well, let's take a look on page 277 of this edition and that is I don't know, about seventeen or eighteen pages into chapter 16. Right? Again think about how I've mapped things out right. Where does religion belong in going to church, which sphere does those belong to. Marie kind of knows what the values of the feminine sphere is supposed to be. She knows what she's supposed to be, she just in some sense chooses not to do it or rather she chooses to manipulate those values to generate sentiment or sympathy for herself. Right? As opposed to someone earlier, even Emily Shelby and certainly Misses Bird, these are values in which they seem sincerely to live, Marie's seems to have kind of a relationship to bad faith to some of these values. So, top of the page. Ava looked down, cast an aggrieve and turned slowly. I say, Marie, let the child alone. She shall do as she pleases, say St. Clair. St. Clair, how will she ever get along in the world, said Marie. Well, Lord knows, said St. Clair, but she'll get along in heaven better than you or I. Oh papa don't, said Ava, softly touching his elbow. It troubles mother. Well cousin, are you ready to go to the meeting?, said Miss Ophelia [assumed spelling], turning square about on St. Clair. I'm not going, thank you. Ah, I do wish St. Clair ever would go to church, said Marie, but he hasn't a particle of religion about him. It really isn't respectable I know it, said St. Clair. You ladies go to church to learn how to get along in the world I suppose and your piety sheds respectability on us. If I did go at all, I would go where Mamie goes. There's something to keep a fellow awake there at least. What? Those shouting methodists. Horrible, said Marie. Anything but the dead sea of your respectable churches Marie. Positively, it's too much to ask of a man. Ava, do you like to go? Come stay at home and play with me. Thank you papa, but I'd rather go to church. Isn't it dreadful tiresome, said St. Clair? Well I think it is tiresome some, said Ava, and I'm sleepy, too. But I try to keep awake. Right out of the mouths of babes. What do you go for then? Why you know papa, she said in a whisper. Cousin told me that God wants to have us and he gives us everything you know. And it isn't much to do it if he wants us to. It isn't so very tiresome at all. You sweet, little obliging soul, said St. Clair kissing her. Go along, that's a good girl. And pray for me. Certainly, I always do, said the child as she sprang after her mother into the carriage. Right? So there's a whole set of things that are being laid out here. A whole discourse of respectability and that's part of the discourse that Stowe is taking aim at. She hates this idea of Christian respectability. All these women like Marie who go to church and listen to ministers and do nothing, at best, about slavery and at worst, are actually promulgator of slavery in the way that Marie turns out to be. Right? So there's one thing. There's the idea that there's a more authentic form of Christianity that is available here. It isn't the church that Marie goes to, it's the one that Mamie goes to. And immediately you see here, as in elsewhere in this section, a kind of comparison and contrast set up between Marie and Mamie Who's the real mothering figure in this household? Well there's actually several and they learn from Mamie Mamie will be one of them. St. Clair might be another and Ava herself might be a kind of mothering figure by the time we're done. Let's take a look a little bit earlier on to get a contrast between Marie and St. Clair. Let's see. Or actually no, just let's press a little bit further on this idea of Christian respectability. This is page 208 in Incident of Lawful Trade. And it's a moment that should remind us of the way in which, this should remind us in the way that, that Stowe abraids the south for their attitudes and the moment then she props up senator Bird. This is 208 in the chapter called, Incidents of Lawful Trade, about sixteen pages in or so. The traitor had arrived at that stage of Christian and political perfection, which has been recommended by some preachers and politicians of the north lately, in which he had completely overcome every humane weakness and prejudice. His heart was exactly where your sir and mine, could be brought with proper effort and cultivation. Right? So this is the effect of respectability. This is the effect of civilization. We have the kind of Christian that this traitor concedes himself to be. The wild look of anguish and utter despair that the woman cast on him, might disturb one less practiced, but he was used to it. He had seen that same look hundreds of times. And then she addresses the reader. You can get used to such things too, my friend. And it is a great object of our recent efforts to make our whole northern community use to them, for the glory of the union. Right? So she takes a dig again at the fugitive slave law. And this is an example then again about what the purpose of the novel is. People like Marie, people like this traitor, have become the dominant representatives of respectable Christianity We need something else other than that. OK, so that's one thing to bear in mind. Let's go back now to just, let's go back to take a look at Marie one more time. This is on page 268. OK and I want to you know, to set a contrast of the novel as taking off. Right? So that's a form of respectable Christianity And there's different forms of motherhood. There's kind of respectable motherhood, I suppose in the way that Marie practices it and there's real motherhood. On 268, this is in the chapter that's called, Tom's Mistress, about eight pages into it. Don't you believe that the lord made them of one blood with us, said Miss Ophelia shortly. No indeed, not I. Pretty story, truly. They are a degraded race. Don't you think they've got immortal souls said Miss Ophelia with increasing indignation. Oh well, said Marie yawning, that of course. Nobody doubts that. But just putting them on any sort of equality with us you know. As if we really could be compared. Why it's impossible. Now St. Clair really has talked to me as if keeping Mamie from her husband was like keeping me from mine. There's no comparing in this way. Mamie couldn't have the feelings that I should. It's a different thing altogether. Of course it is and yet St. Clair pretends not to see it. Right? So that's one of the things. Again that's a moment of a little irony, in which we the reader, clearly see it and St. Clair is not only, is not exactly pretending not to see it, but there's a sense in which you might say that what St. Clair is attempting to do is operate in the way that somebody in the feminine sphere might do. Through influence. And we might say that that perhaps isn't' quite good enough. All right, let's talk about one of the more disturbing representations of childhood and femininity and that's Topsy Topsy of all the characters in the novel, is most likely to offend people as a kind of racist representation. Right? And there's clearly I mean, is as far as the novel is all about setting up contrasts, there's clearly a contrast that's set up between Topsy and little Ava. I mean Topsy is really dark and little Ava is really white. And Topsy and little Ava is really well behaved and Topsy is really not. OK. Let's take a look in chapter 20, this is page 364 in the OK and we'll see how Miss Ophelia, who takes up the care of Topsy, decides. Now Miss Ophelia is a woman from the north right, she's a reformer. She comes in with systems right. There's not that funny moment when she tries to make Dinah's kitchen, systematic and of course, it's disastrous Top of 364. It's your system makes such children, said Miss Ophelia I know it, but they are made. They exist. What is to be done with them? Well I can't say I thank you for the experiment, but then as it appears to be a duty, I shall persevere and try and do the best I can, said Miss Ophelia And Miss Ophelia, after this hour, did labor with a commendable degree of zeal and energy on her new subject. She instituted regular hours and employments for her and undertook to teach her to read and sew. Now, Topsy has her preferences. She's not just some wild child and these are the preferences. In the former art, reading, the child was quick enough. She learned her letters as if by magic and was very soon able to read plain reading. She's a little natural Frederick Douglas, right. But the sewing was a more difficult matter. The creature was as live as a cat and as active as a monkey and the confinement of sewing was her abomination So she broke her needles, threw them slyly at the window, down in chinks of the walls. She tangled, broke, dirtied the thread or with a sly movement would throw away a spool altogether. Her emotions were almost as quick as that of a practiced conjurer and her command of her face quite as great. And though Miss Ophelia could not help feeling that so many accidents could not possibly happen in succession, yet she could not without a watchfulness which would have leave her no time for anything else, detect her. What's going on there? In that passage. I mean, what are Topsy's preferences all about? What does she like? Reading. With what is that associated? Man the masculine sphere. About getting out of slavery from Frederick Douglas. What doesn't she like? Sewing. Right? What is sewing associated with? Women's work. Right? Topsy is a little rebel and there's a funny way in which she's behaving according to a set of principles. So I want to suggest to you that even here, Stowe is reinforcing her method. Right? Topsy and Topsy becomes a prime example of the way which some of these values of masculine feminine can be interestingly blended and there are certain kinds of relegation of women to certain kinds of work, such as sewing, that make, it's another way of saying that there's a tie here between slavery and what Stowe refers to as domestic slavery. Right? Now a very interesting thing happens with Topsy and Miss Ophelia I asked you to think about this. So the irony of course about Miss Ophelia is a couple of things. She walks into the St. Clair household and immediately she sees Ava kissing Mamie and she's like, ugh. You know, well your young southern girls do something I couldn't possibly do. Right? So clearly Miss Ophelia is a racist. She's a northern, anti slavery, abolishist, but former racist. OK. So what does Miss Ophelia need to learn to do? She needs to get beyond that category of race or that thing that puts her off. She needs to be able to touch and embrace. She needs the magic of the real presence of distress. Right? And she is transformed by the death of little Ava. She actually, it becomes a transformative thing. She manages to embrace Topsy. And to be a real mother to Topsy. Right? That's the story. Except it's not quite that simple. There's one step that needs to be taken between having, you know, doing that you know, being able to be Miss Ophelia being of a kind of a real mothering figure for Topsy and where she was before and it's a legal step. So what is it? What does she have to do? What did she have to do? Yes. >> [inaudible] >> Very good. She has to own Topsy. Right? So the white, northern, abolishonist lady, who reads all the good things, pilgrims progress and you know, [inaudible] and all this kind of stuff is on her bookshelf. She has to gain possession. She tells St. Clair, I want to do it, we need to do it. He's like all right, we'll do it. No, do it now. Right? She has a little, enough of that kind of masculinity in her, she says, well do it now. Would that he have done it now for all of his slaves? But Topsy is saved from the dissolution of the south household, because Miss Ophelia has to become the thing that's an aphama to her. She becomes a slave owner, in order she can gain possession of Topsy and free Topsy. So she works within the system, but that becomes the irony. Again, northerners, if they want to make a change, have to admit that they are implicated in slavery. They have to own up to it. Literally. And then they can actually do some good. Right? So that's not accidental again. It's part of a very complicated way in which the narrative has set up, to implicate both southerners and northerners. And again, the most famous northern implication is Simon Legree [assumed spelling]. A northerner and ardent capitalist who cares more than anything else, about making money. There's a way in which the greed hasn't quite eternalized the anti black racism that seems to motivate many of the characters, but he's happy to use it as a kind of tool. Let's turn to chapter 31 now, the second, this is the last part of the novel. It's page 480 in the Penguin. This is a part of the novel that portrays slavery at it's most corrosive. It's called, the middle passage, and it's designed to in some sense, suggest that Tom's final passage to Legree's plantation is a recapitulation of the horrible middle passage from Africa to the new world that captured Africans were forced to endure. Many of them dying on the way. I mean, packed like sardines into these ships. Influence may not be enough in this section of the novel. Right? Read the first three paragraphs of chapter 31. On the lower part of a small, mean boat on the Red River, Tom sat. Chains on this wrists, chains on his feet and a weight heavier than chains lay on his heart. All that faded from his sky, moon and star, all had passed by him as the trees and banks were now passing to return no more. Kentucky home with wife and children and indulgent owners, St. Clair home of Ava with saint like eyes. The proud, gay, handsome, seemingly careless yet ever kind St. Clair. Hours of ease and indulgent leisure. Novel has been recapitulated for us. All gone. And in place there of what remains? Another novel, narrator steps back. In personal construction. It is one of these bitterest apportionments of lot of slavery and again, we're going to have one of these essentialist summing up moments, that the Negro, sympathetic and assimilative after acquiring [inaudible] fine family, the taste and feelings which formed the atmosphere of such a place. Is not the less liable to become the bond slave of a coarsest and most brutal. Just as a chair or table which once decorated the superb saloon, comes at last, battered and defaced, to the bar room of some fility tavern or some low haunt of vulgar debauchery. And again, I want you to see how this works. Right? It seems to be patronizing, but it's making the same point you might say, that Phyllis Wheatley [assumed spelling] makes in that poem on being brought from Africa to America. She even uses the same word, refined. The African American is sympathetic and assimilative. These are good things. All right? They are clearly educable. A naturally take to these kinds of refinements. But the logical possessive individualism is such that if you aren't free, you're no better than a chair or a table and subject to all of the kind of vicissitude the property is subject to. The great difference is that the chair and table cannot feel and the man can. Right? So what do you see out of that category now? Established earlier on in the chapter with senator Bird, is being redeployed here. A man can feel. For even a legal enactment that he shall be taken reputed and judge in law to be a chattel personal, cannot blot out his soul with it's own private little world of memories, hopes, fears, loves and desires. Right? So clearly there's a kind of natural law that's being in some sense contradicted by the laws of the land. Mister Simon Legree, Tom's master, had purchased slaves at place and another in New Orleans, to the number of eight and driven them handcuffed, in couples of two and two, down to the good steamer pirate, which lay at the levee, ready for a trip up the Red River. OK, no accident that it's called the Red River. No accident that the ship is called the pirate, the steamer is called the pirate. Right? Probably it's an actual reference to the moment in Douglas' narrative where he thinks about the right or his owner to own him and take any of his wages as simply the right of the pirate on the high seas to take by force. Right? Let's go about seven pages on to a description of the landscape in the, actually it's the beginning of the next chapter called, Dark Places. They're now off the river and onto the landscape. It was a wild forsaken road, now winding through dreary pine barons, where the wind whispered warnfully. Now over long causeways through song cypress swamp, the doleful trees rising out of the slimy, spongy ground, hung with long wreath of funeral brack moss. Whatever [inaudible] loathsome form of the moccasin snake might be seen sliding among broken stumps and shattered branches that lay here and there, rotting to the water. The approach to Legree's plantation in other words, which is very deep in these kind of eerie, Louisiana, swampy wilderness, draws on Gothic conventions. I mean, this is kind of a mild version of that disgusting passage that I read you from Monk Lewis. Right? Think about it. It's a kind of dream landscape, a closed world that's separate from the world of the everyday, somehow cut off. Repeated images of darkness and death, decay. Kind of sense of evil portrays this whole thing. And then we get to the, let's see, that's Dark Passages. Let's take a look at Legree's plantation. OK. Legree's plantation is an interesting thing. It seems to embody decay itself. Take a look on page 491. Actually bottom of 490. There's about three, three and some pages into this chapter. Legree had been drinking to that degree that he was inclining to be very gracious and it was about this time that the enclosures of the plantation rose to view. The estate had formally belonged to a gentleman of opulence and taste. We've seen a gentleman of opulence and taste, right? Augustine St. Clair. The estate had formerly belonged to a gentleman of opulence and taste, who had bestowed some considerable attention to the adornment of his grounds. Having died insolvent, it had been purchased at a bargain by Legree, who used it, as he did everything else, merely as an implement for money making. The place had that ragged, forlorn appearance, which is always produced by the evidence that the care of a former owner has been left to go to utter decay. Right? It's decay embodied. What was once a smooth shaven lawn before the house, dotted here and there with ornamental shrubs, was now covered with frousy tangled grass, with horse post set up here and there in it. Where the turf was stamped away and the ground littered with broken pails, cobs of corn and other slovenly remains. Here and there a mildew Jessamine or honeysuckle hung raggedly from some ornamental support, which had been pushed to one side by being used as a horse post. What once was a large garden was now all grown over with weeds, though which here and there some, through which here and there, some solitary, exotic reared it's forsaken head. What had been a conservatory now stood, had now no window shades and though the moldering, moldering shelves stood some dry forsaken flower pots with sticks in them, who's dried leaves showed that they had once been plants. Now Stowe was drawing here again, on the whithered garden. Right? It goes back all the way to puritan record. The idea that the new world had been a wilderness. It had then become a garden. But then through spiritual neglect and decay, it's become this horrible wilderness again. Right? That whole period of the Jeremiah, is in fact being evoked by this. And the topographical imagination of the novel continues to think about the ways in which houses might be expressive of some kinds of larger spiritual states. In that sense, you might say, this is a Gothic landscape. It seems to express the interior decay of Legree himself. Skip a paragraph. The house had been large and handsome. It was built in a manner common at the south. A wide veranda of two stories running around every part of the house in to which each outer door opened. The lower tiers supported by brick pillars. But the place looked desolate and uncomfortable. Some windows stopped up with boards, some with shattered panes and shutters hanging by a single hinge. All telling of coarse neglect and discomfort. Now I want you to think about this. It's built in a manner common in the south. It's a wide veranda of two stories, running around every part of the house into which the outer door opened. Right? So you can see the veranda out there. Does that remind you of anything else? I should have put the slides right next to one another. But to me it seems like a deliberate inversion of this house. Which is also two stories. Owned by a person who has a kind of rich sensibility. Has a broke, well cared for garden on the inside. Legree's house has the veranda on the second floor, going around on the outside. And I don't think that little detail is in fact incidental. I think what these two houses compare to one another are meant, it's meant to suggest, what happens to something like the St. Clair mansion, when it's not run by somebody like St. Clair. It too easily forms the kind of decay. It becomes something that is an embodiment of the worst places of slavery, like that. So you could see in them a kind of progression. We move from one place that seems pretty good, to another place that's awful. And yet, I think the novel is suggesting even more than that, by having this kind of inversion you might say. It's as if this is the St. Clair household turned inside out. And when you turn the St. Clair household inside out, you not only get the verandas and garden on the outside, but what you get is what was at the dark heart of the St. Clair household all along. Right? You turn it out and it's a slave holders house. All right, one of the things you might say is that Legree, this you know, it's almost in a sense then that St. Clair and Legree's plantations, function as almost like type and anti type. St. Clair's is the type, the fulfillment of it, the true meaning of it is not understood until we get to Legree's plantation and we realize these are both slave holding, slave holding plantations, households. And it looked kind of nice, because St. Clair seemed like a kind of good guy. But he was irresponsible in a certain way and his actions or lack of actions have led, have led to Tom's being relocated from the one to the other. But I want to think the novel is creating a certain kind of equivalent. It's only a hop, skip and a jump and an accidental stabbing perhaps, to go from one phase of slavery to another. And the over arching point is that they are both phases of slavery. All right, so I think that Stowe was very careful in the way that she describes this house and the way in which she puts these things together. Let's take a look on page 512, a little bit further on. Cassie tells Tom about precisely how isolated he is. This is in the quadroon story. Right? And Cassie and Tom were having this kind of interaction together and she tells him about how bad things really are. You see, said the woman. You don't know anything. Let's see, here's Cassie talking to Tom. I do. I've been on this place five years, body and soul, under this man's foot and I hate him as I do the devil. Here you are on a lone plantation, ten miles from any other. In the swamps. Not a white person here, who could testify. Again invoking the conditions of future slave law. If you were burned alive, if you were scalded, cut into pieces, set up for the dogs to tear or hung up and whipped to death. There's no law here of god or man, that can do you or any one of us the least good of this man. There's no earthly thing that he's too good to do. I could make anyone's hair rise and their teeth chatter, if I could only tell what I have been seeing and knowing to hear. And so she resolves to kill Legree and Tom talks her out of it. Right? There's a part of what he's learned from little Ava. So she does something else. What does she do? She mobilizes one phase of the Gothic Right? She mobilizes that kind of hoax Gothic that we saw and we've talked about it in terms of Ann [inaudible], we saw in Washington Irving's, Legend of Sleepy Hollow. Right? So just as Brawn Bones impersonates Ichabod Crane, the headless, I mean impersonates the headless horseman in order to drive Ichabod Crane off, Cassie impersonates a ghost as well. Somebody out of this term. Legree's past, in order to frighten Legree and enable her own escape. And one of the things I want to suggest to you is that Stowe is making use, deliberately making use of that tradition of Gothic fiction. She's not interested in the, she's not interested in the kind of charnal house, disgusting Gothic of Lewis and Walpo [assumed spelling] and all these other writers. Rather she sees that that's what slavery is about. So again, you might say Stowe is manipulating literary forms. She's suggesting that slavery is embodied by that kind of Gothic fiction. She takes another kind of Gothic fiction, the hoax kind of Gothic fiction and turns it against that other kind. Right? And enables, therefore you might say, to have Gothic fiction become compatible with sentimentality. Finally, towards the, so that we get that, right. Cassie haunting Legree. And one of the things to notice about this, this the way in which this works, is that it isn't quite so clear right. I mean, think about how it works psychologically. Tom is carrying around a relic, a kind of talisman. Right? You people, do you remember what it is that he's carrying around? Something that he received. What's that? >> [inaudible] >> And what else? >> [inaudible] >> A lock of Ava's hair. Right? This beautiful, gold hair. And when he sees it, Legree has this kind of freak out moment right. For one thing it reminds him of the moment when he received a lock of hair from his mother whom he clearly you know, was a Christian woman whom he clearly didn't treat very well and whom he deeply disappointed. And he's racked by a certain kind of guilt. So that in this context, you might say in the very deepest form of context, something weird happens to the idea of influence. It isn't so much that the outward force has changed, but it's the way in which they are able to perceive changes. So that even saintly little Ava's lock of hair, becomes this kind of weird, sinister thing in Legree's imagination. He imagines it just kind of curling around his fingers if it's alive. You might say that is a sign, that he is beyond redemption. He can't actually be saved. Right? And so that's one of the things that, I think one of that things that, one of the reasons that Stowe brings the Gothic into this sentimental fiction at all is to suggest the limit of sentimentality and also the limits perhaps even of Christian sensibility. There are some people who are going to go to hell. There are some people who cannot be saved. And perhaps what the novel suggests is that we need to concentrate on saving those who can be saved and not worry about those like Legree. We get to the final moment of the novel, the one that you might say is the final building block that Stowe needs before writing on. Right? Remember I told you she has this vision that the communion table, after her son has died of her, of a slave being whipped to death by his master and forgiving that slave, that master with his dying breath. And that's what we see. Although again, mostly the very worst part of it occurs off stage. Again, Stowe is not really interested in dramatizing that for us. We only see sometimes the aftermath of Tom's fatal, final beating. But here's a funny, OK, so we don't need to belabor that. And I take it all of you are too hard boiled. Nobody shed a tear when they look at that. Sad. But think about this from a narrative point of view. That should be the climax of the novel right. But it isn't the climax of the novel. Why is that? Possibly it's to suggest that if Tom is a kind of Christ figure, we don't, we can't culminate in his death. We need to see what he might say is the most important thing about the life of Christ and the life of Tom, the after effects that it has. And what are the after effects that we have here? Cassie is saved. Cassie does not become a murderous, Cassie is saved. Right? Tom presumably goes to heaven and or is you know, within the imagination of the novel, he also acts as a kind of force for redemption, even the other slaves who are complicit in his death, are kind of awed by his behavior. But the final thing that we see is that at the end of the novel, he emerges almost as a kind of symbol. I mean, there's a kind of weird resurrection of Tom at the end, when young George Shelby manages to return and we find out that all this stuff has been going on in the back story. We kind of come around full circle. We come around back to uncle Tom's cabin, once again. And we see that the cabin is in some sense set up as the final, it's almost like the first domestic situation we want to think about but from the beginning of the novel is Uncle Tom's Cabin, it becomes a kind of symbol at the end. And there's a kind of [inaudible] that takes places here. Right? So this is where we would say, oh like sentimental fiction, all of this is truly unbelievable. How could all of these people have been related? That's part of the sentimentality, that's part of what puts audiences today off I suppose, is that it all gets tied up neatly. But one of the things that Stowe would answer if she was a novelist behind this, is she would say, there's a reason that all these extensible coincidences come to pass at the end. There's a reason that there's been a kind of controlling, there seems to be a kind of controlling force in the background waiting, you know, happening with the Shelby's, even though we don't know about it. What's the name that we would give to this? The name that we might give to this is providence. Right? I mean ultimately I want you to see that Stowe would say that there isn't a such thing as coincidence within sentimental fiction. There's a sense in which all of this is part of a kind of larger Christian plan. And so finally where Stowe ends up here, in her concluding remarks section, is in some sense to break the fiction entirely. The last image that we have in the chapter that's called, The Liberators. That's the second to last chapter, is this image of, let me see if I have it for you. Uncle Tom's Cabin. Right? George is able to reinvoked uncle Tom, now just kind of a ghostly spiritual presence. It was on his grave my friends, that I resolve before God, that I would never own another slave while it was possible to free him. And nobody, through me, should ever run the risk of the being parted from home and friends and dying on a lonely plantation as he died. So when you rejoice in your freedom, think that you owe it to that good old soul and pay it back in kindness to his wife and children. Think of your freedom every time you see Uncle Tom's Cabin and let it be a memorial to put you all in mind to follow in his steps and be honest and faithful and Christian as he was. Right? And that is the form that Tom resurrection you might say, takes place in that. One of the things that we realize at the end is that we've been reading this very long novel, that we thought was a kind of fiction and in the end, it may be a fiction but it also takes the form of something else. A sermon. And so Stowe in some sense, breaks the, she breaks the frame of the fiction at the very end and goes and it's like all those little bits and pieces of direct address to the reader come front and center at the end and we find out who the audience for this really is. Right? So page 621. It's about five pages into the conclusion. She writes about herself in the third person. No longer as the kind of, now the narrative voice takes on the voice of the author. The author hopes she has done justice to that nobility, generosity, humanity, which in many cases characterize individuals at the south. Such instances save us from utter despair of our kind, but she asks any person who knows the world, are such characters common anywhere. For many years of her life, the author avoided reading or put illusion to the subject of slavery considering too painful to be inquired to. Right? It's like that think I showed you from the 1879 preface. And she goes on, as the concluding remarks continue, to basically offer up her final suggestion of what people can do. And as I told you last time, if you're expecting some kind of legislative programs, some alternative to the future slave law, you're going to be disappointed. The bottom of 624. She has addressed herself now to the mothers and daughters of the free states. But she asks at the bottom of 624, what can any individual do, of that every individual can judge, there is one thing that every individual can do, they can see to it that they feel right. And I want you to think about a pun that might be implicit in those worlds. It isn't quite grammatical, but I think it's a pun nevertheless. An atmosphere of sympathetic influence encircles every human being and a man or woman who feels strongly, healthy, healthfully and justly on the great interest of humanity, is a constant benefactor to the human race. At the end, what this novel is promoting, is a kind of grass roots movement, linked to Christianity, linked to the idea of feeling and then feeling correctly and then feeling that you are right. And it has tried to teach you how to feel properly, to create that sense of understanding things, not in terms of abstractions, but in palpable realities. It's taught you how to respond to narrative, not primarily first through the head, but through the emotions and in the end the novel is suggesting that if you take that approach to reading and to life as a whole, you will in the end find that you feel right. That you are in the right and if everyone did this, it would be a radically different country. OK, we'll leave it there. As you go on to Hawthorn, I want you to think about the differences between Hawthorn's technique and Stowe's. How does Hawthorn seem to make use of allegory while demonstrating it's limitations? |
Open_Ed_Cyrus_Patell_American_Literature | Edwards_and_the_Transition_to_Enlightenment.txt | >> I'm going to play you Whitney Houston's version of the Star Spangled Banner. [ Cheer ] And then I want you to listen to it, and then I'm going to play you a clip from a film. This film is called The Sum of All Fears, has anybody seen it? It stars Ben Affleck, you know, an adaptation of Tom Clancy's novel. And you'll see immediately why I'm playing you the clip, I want you to look at it and tell me what you noticed about it, alright? So let's first listen to Whitney. [ Music ] >> Alright, please try to get me to [inaudible], [ Music ] [ Applause ] >> Alright, so what did you noticed about that? Yeah, >> In both versions they have drums, and they, >> In both versions they have drums, ok, what do you mean? What do you mean in both versions? Ok, Very good. What he sang in the film clip was not the Star Spangled Banner. It was the verse four of the Defense of Fort McHenry which was the poem, from which the national anthem, the Star Spangled is taken. And most people don't realize that in fact, the Star Spangled Banner is only one verse of a longer poem that was written after a battle during the war in 1812. And one of the things I'm going to try to argue for you in the course of the hour is that, people have said that Star Spangled Banner maybe that should not be the national anthem and not only because it's hardly sing able by any, you know, normal human being. Ever tried singing it before a ball a ball game? It's very difficult; especially when somebody is doing it in a high key with lots of flourishes on top. And actually there is a good reason to think that it shouldn't be the national anthem seeing it, as it comes more of a British drinking song. Ok, but also, people say, well it's about war. And why should our national anthem be about war; shouldn't we have something like God bless America; or America the beautiful; something that celebrates the land. And what I would want to suggest to you is that it's only in part of the poem that is about war; and that what it also is, in fact this what I would want to suggest to you is, what it primarily is, is a poem about the process of enlightenment. Now we might decide it for other reasons, we don't want to have a poem that is about enlightenment, to be the national anthem, but I think we should think about that in a different way. Ok? So, one of the things I want to do for you today is to sketch briefly, what we mean by enlightenment. We didn't have a lecture last week on Edwards, 'cause it's usually where I would introduce the concept of enlightenment. And just as you all remember, I'm going to do that lecture next Monday, for those of you who can attend at 12:30 in this room; so right before our normal meeting time, and then we'll go from that, we'll have a break, and then we'll go into the lecture that's about the American enlightenment of Franklyn and Jefferson. But I'll tell you a little bit about Enlightenment now, coz it should in some sense, remind you of the things that you've done in the supplementary reading, particularly that piece written by Leonard Mercek. But the enlightenment, you might say, is a moment of profound intellectual and cultural change; and one way of thinking about enlightenment, that I think might be useful for us, is to think of it in terms of that model of dominant residual and emergic cultures, that I mentioned and have been talking about since the beginning of the term. Well I wish there was some kind of dominant consensus that becomes, you might say, the core of the culture. And that dominant consensus is always part of the process; it's always changing; it's always sending off challenges; challenges from older belief system that might still be around. Challenges from newer belief systems. So the context of our course, we might say that the dominant culture in the 17th century, where we've been spending a lot of our time recently, has to do with, something that has to do with religious experience particularly in New England; and the Northeast with Calvinism; American Puritanism; but at the same, there are whole other set of intellectual development that are going on, in their accelerated way, in England and the continent; but eventually they make their way over here. We'll talk about it a little bit more next week, but it's a culture, where we might call Belle Letra, right? And with that kind of, which literally means beautiful letters, but certainly, it means kind of fine writing; writing for almost its own sake; Belletristic writing is often about, is often a kind of essay writing that we would associate with something in English context like, In a Joseph Ashton for example. That is a thing that is happening at the same time, as Jonathan Edwards is being educated in a school for ministers called Yale. And one of the things that happen to Edwards, he happens to read some of John Loft, we'll talk a little bit more about it next time, and he kind of sees, all of a sudden, something very exciting in Loft and something really scary, because Edwards is raise as a kind of old time Calvinists. In fact he's even a little bit more doctrinaire than his uncle, who was a famous preacher; but who was pushing Calvinist doctrine a little bit towards the enlightenment, Samuel Starter. Edwards has some sense of retrenches and wants to become conservative, but he sees what we might think of as a kind of emergent culture, around the ideas of the enlightenment; which is clearly going to pose the threat to the old time religion. Mind him, that he's going to realize that, if he wants to continue preaching the Calvinists way and sustain Calvinists belief; he has got to find a way to retrofit it; to take this new technology and make it compatible with, or at least not a threat to the Calvinism, which he so firmly believe. So everyone has become his very strange cost figure. And one of the things to remember about Edwards is that, he's almost exactly the contemporary of Benjamin Franklin. And the two men -basically, Franklin lived longer, 'cause Edwards died prematurely of slob pox, but they were living at the same time. And they were both looking to strike a balance between old time ideas that grew out of New England: Puritanism and other forms of Religion and Religious influence, up and down the Eastern Seaboard; and this new idea of the enlightenment. And one of the things that I would say about the shift that is placed with the enlightenment; Enlightenment is really about moving about from a conception of the primary drama of human life being spiritual and taking place, you might say, in God's consciousness. To the primary drama of human life taking place in our own consciousnesses; life becomes infra eccentric, human centered, understanding of the nature of the Universe. And different enlightenment thinkers would try to square that was a belief in God in different ways. Some people like John Loft will find it completely compatible with belief in a deity, in a Christian deity, particularly. I mean, you could say bluh, is a revelation, miracles; that way of attaining knowledge, that's still, you know, if you could get that, that's the best way. It comes directly down from the pipeline from heaven, that's the best way to get knowledge, but how often does that happen? How often does that happen in modern 17th century times? Not so often. So it's not the most reliable way to get knowledge. On the other hand, if God gave us souls; God gave us the minds; God gave us everything that comes with them, then he gave us the power to reason. So the sense of this power to reason is divine and we have to make use of it. So there's no incompatibility for somebody like loft between belief in God and you might say, using human reason to discern things about truths, you know, larger truths, as far as scientific principles, understandings of the way the world works. Now obviously that's a big shift in the premisance [assumed spelling], and when the premisance obviously change, we're not automatically believe that the world is somehow deprave and completely unreliable and that we, as human being, are depraved and completely unreliable. And that we we're going to say No, in fact we are connected to God, and therefore, there is some sense of divine sanction for things like scientific research, and scientific belief, some enlightenment think we'll go even further, they become ascious [assumed spelling], as see what, well we'll talk about Franklyn's particular take on this next time. But one of the things that I see is some kind of a spectrum of responses, but all of these are part of a larger trend in thought in which we might say the human consciousness. After they cart the human consciousness is where the action is. It's what becomes the center you might say of culture in a way that it hadn't been before. So there's a number of principles of that we might think of when we think about the enlightenment. But one of the most important I want to understand is that many of these thinkers think of enlightenment not as an end result but constantly as a process. And in that sense, the way that people like can't even have talked about enlightenment is very compatible with this idea of a model of culture that is constantly in flux and part of a process. A dominant, residual, immersion culture struggling to control and be persuasive to create new practices that will become the dominant practices that is compatible with this idea of enlightenment. So one of the famous statements about the enlightenment comes from Cant. He even uses the term that sounds similar to this idea of the emergent although it's not the same term. Emergence. Enlightenment is man's emergence from his self-incurred immaturity. Automatically, you can see that it's the self that becomes the most important thing. It isn't emergence from the state of nature or from the ignorance of Garden of Eden. It's self-incurred. Why? Because he says, Immaturity is the inability to use once own understanding without the guidance of another. This immaturity is self-incurred if it causes not lack of understanding but lack of resolution and courage to use it without the guidance of another. The model of enlightenment is therefore sacra auda, which literally translated from the Latin word meaning dare to be wise, right? Have courage to use your own understanding. And when we get to Ralph Waldo Emerson, you will see what many people have regarded. Emerson is a kind of content thinker. Somebody who has taken a lot of transcendentalist philosophy that is associate with Cant and other German primarily thinkers and somehow domesticated it, made it suitable for an American audience. But that idea of have courage to use your own understanding, that could easily be paraphrased. A paraphrase for Emerson's entire essay Self Reliance. Emerson is all about the problem for Emerson would be something like self-distrust, being afraid to trust yourself. We'll talk about that. I want to lay that note out there for you to listen to now and to strike to the note again later on. Jefferson, some 40 years later after we might say the American enlightenment has become the dominant culture, has become the dominant consensus reflects back on it. And he says this in 1826, All eyes are opening to the rights of man. The general spread of the light of science has already laid open to every view and the powerful truth that the mass of mankind has not been born with subtle on their backs nor a favored few booted and spurred ready to ride them legitimately by the grace of God. These are grounds of hope for others. What is he talking about here? What is he actually referring to? First of all, the metaphor? What is the metaphor? Yes. >> A horse. >> Who is the horse? Mankind is the horse. Good. And who's riding mankind therefore? Yes, I heard it. The favored few booted in spur. Who are the favored few? Excuse me? I think what he is suggesting is that enlightenment is a process that will allow these people to no longer be the horse, right? So it really wouldn't be the enlightened, if it wouldn't be enlightened. Who would the favored few be who have this, what's that? Well, I guess if you're a Puritan, it would be the elect and I suppose you might say if you think, I haven't thought of that. But I think that's good so far as you're thinking. Give it a kick, if you are, several kicks. Put it in spur. There you go. Thank you very much. If you are thinking for a Puritan standpoint, you will say yeah. Actually, the Puritans think of themselves as the favored few. They have the grace of God. And who were their writing and spurring? Probably the natives like non-elect people. So that's good. Although, I'm not sure that's Jefferson has in mind but it's good for our course. Yes? Yeah the aristocracy and maybe kings as well, right? The divine right of kings, the aristocrats are supposedly given divine sanction, right? Remember go back to Winfra. Inequality is something that is given by God. Its part and Winfra comes up of these arguments about mutual obligation, the promotion of charity. He says that this is why God has created this system but exactly the divine right of kings. I mean one of the things that we will talk about a little later on is the way which locks second treaties of government is really designed to make the counter argument and prepare the way for this. You might say in the aftermath of the English revolution, Hobbs created justification in understanding of the statement which says like look he's really trying to create order and he says, Everybody is born but what happens is once you are born may immediately delegate you're authority to this larger thing. He calls it the laviton by which means the state, which is, personified the king. So effectively, everything belongs to the king. Lock comes up with the rational for understanding why everything does not belong to the king. Even if you have a king, the king doesn't own everything. Property has a different basis than the divine right of kings. We will get to that but it has everything has to do with property in the body. You have property in the body first. Because you have property in the body, you own your own labor. When you mix your labor with nature, you get more property. That's yours. That's the theory behind it. That means God has sanctified kings but not given them everything. But the enlightenment starting taking them as the starting point, Jefferson is looking around and says look with the ideas of the enlightenment, what we are seeing is first of all we talked about the rights of man. In many cases, it is philosophically justified through property rights. The idea of science and constantly enlightenment things are using the actual metaphor of light itself, the light of science. Because of the light of science, you can see better. When you see better, you get this truth. And what the truth is, one that's fundamental for him, is that enlightenment means we need to get rid of aristocracy. That's why the most enlightened country is the United States in this early national period not a favored few who are going to ride legitimately by the grace of God. But in fact, Jefferson would believe in a certain kind of meritocracy that those who have certain kind of gifts will raise to the top but it won't be on the basis of whether your family has descended from kings or aristocrats urban property called it, right? That's part of what Americans are thinking about. And by this time in 1826 we would say the enlightenment has become complete. We might also think about the fact that therefore the moment of the Declaration of Independence losing up from there through the constitution and into the early national period is the moment of the American enlightenment. Therefore, you might say this country is founded on the principles of enlightenment. The Declaration of Independence is often taken to be and we will talk about it next week as a statement of the principles of enlightenment. One of the things to notice about Jefferson, one of the reasons that we look at it is that we will see that it's a kind of compromised document. When you read the account of the Declaration of Independence that's in Jefferson's autobiography you'll see that he trying to tap the original because he wants you to see where those damn politicians have made compromises especially those southern ones, other southern ones. But one of the things we can see that Jefferson was not trying to think of anything radically new when he wrote the Declaration of Independence. I think it's a brilliant document rhetorically. I'll be little harsh about Jefferson a little bit later on today. But I think Jefferson was a brilliant thinker, contradictory complex. But what was he trying to do with the Declaration of Independence was create a document that you wouldn't be able to argue with because it embodied common sense, the common sense of the enlightenment. And one of the things to say is whatever or anybody involves common sense is always in some sense the height of ideology. So by looking at the document that is supposedly embody in common sense, we can learn a lot about the moment in which it was written, the kind of assumptions behind that moment, alright? There are certain doctrines that come with enlightenment thinking. Among them is this, which would be almost direct encounters to the period that we've been looking at, the natural goodness of human being. There might even good ones but that didn't last very long. Enlightenment thinkers don't tend to believe in the total depravity of human kind. In fact, they believe in its opposite, in the perfectibility of the human race. We are getting 180 degrees shift here away from total depravity, embracing something that might look to appear like there are many inherency, we can perfect ourselves, and good works can be rewarded. There's an emphasis on reason in the ways that I suggested to you. Reason is the divine faculty. It can end up in different variants. We'll talk about some of these next weeks. But for many it's still compatible with belief in God because it's God given. But what Jefferson's quote is telling us really , is that along with all these things we need a doctrine of equality, equality before the law based on the right individual liberty because the system of natural rights was put into praise. Once you have equality, you already start to understand. You need to be tolerant over the people. So this is all the moment where there is greater emphasis on religious toleration. We usually in the American context would mean something like toleration for various kinds of Christian beliefs. We just suppose to step forward. Along that I got an idea of universality or what's the universal brotherhood of all rational beings and I used that term brotherhood intentionally because again it's a certain way in which many of these ideals are expressed in terms that are absolutely masculine and it is often questioned to what these thinkers actually believed that women could participate in enlightenment thinking as fully as man could and that's you might say a problem that is sort of set aside by the founding doctrines of the country and left to be dealt with later on and along that with that the idea of science and progress if reason is defined the application of reason to the data and material observations that we might make is also divine. and so therefore science that is something that is emphasized throughout all, the key principles we would want it keep in mind now just to give you a sense of how this will translate into poetic practice which is our subject for today want you to take another look or a closer look at something that I mentioned to you before in conjunction with the metaphysical poet and I was suggesting to you when I cited Johnson asked if you have read it, the idea was to understand something about metaphysical poetry and how it worked. Now I'm asking you to look at it from a slightly different point of view I'm asking you to think about what kind of a sentence about a nature of poetry intellectual thought like behind this so when I said this is an 18th century text we use it to try to get an insight into a 17th century set of text but now I want to think about the 18th century right so this is what Johnson write from The Life of Culley, with the given subject of nature to the choice of the man, has it changes in fashions and has different time takes different forms at the beginning of the 17th century writers turned the metaphysical poets all metaphysics in The Life of Culley. It is not improper to give some account and Johnson was one of the great 18th century pro star, so we're going to give it a chunk of, I want you to see how it works and I'm going to ask you when we're through of sets of paragraph here to tell me what you think are some of the literary values that the pros itself would seem to exemplify it is not improper to give some account the metaphysical poet and to show their learning was their whole endeavor but unluckily resolve to show it in rhyme instead of writing poetry they only wrote verses and very often said verses as to the trial of the finger better than the ear for the modulation was so imperfect that they were only found verses by counting the syllables what was that mean? Is it all clear, what we're talking about here? Yeah, alright. So it's technically its poetry because why it scams theoretically right? That what he means by the finger better than the ear right you can see the beats but it doesn't sound good. So that's something to bear in mind there's something to do that poetry has something to do not only with metro pole measurements but something to do with the way things sounds modulation that's what they call it. Okay. if the father of criticism by whom he means Aristotle if the father of criticism has rightly to nominate a poetry an imitative art like Aristotle talks about the principle of my nieces art as representation through imitation these writers will without great wrong lose their rights the name of poets they cannot be set to imitate anything their neither copy nature nor life neither painted the forms of matter nor represented the operations of intellect those however who deny them to be poets allow them to be wits. Again, we were thinking about metaphysical poetry, driving one's to say, and poetry on the one hand wit on the other and the term rarely meets. Driving confesses of himself fall below down in wit maintains that they surpass them in poetry. Is wit been well described by poetry as being that which has often been taught but never before so well expressed that's one definition of wit? They certainly never changed nor ever saw it, for they endeavor to be single in their thoughts and were careless of their diction but poet account of wit was in doubt of the erroneous he depresses it below his natural dignity and reduces it from strength of thought to happiness of language. Okay so there's a way the Johnson is being critical also of some of the poetic practices of his day by you know or poet of the day the one that is taught to be the model very model of modern nature poet pope. If I am more noble and more adequate conception that be considered wit which is at once natural and new that was not obvious is a poet's first production that knowledge to be just, if it be that would she that never found it wonders how he missed to wit this kind the metaphysical poets have seldom reason there thoughts are often new but seldom natural they are not obvious but neither are they just and the reader far from what he missed them wonders more frequently by what the version of industry they were ever found but wit abstracted from facts upon the hearer maybe more rigorously and philosophically considered as kind of Discordia concourse a combination of similar images or discovery of a cult resemblances in things apparently unlike and then the final famous statement. A wit does defined they have more than enough the most heterogeneous ideas are yoked by violence together nature and art are ransack for those stations, comparisons and illusions they're learning instructs and their subtlety surprises but the reader commonly thinks his improvement dearly bought and though he sometimes admires is seldom pleased. Alright, that's a chunk of pose, very Johnsonian poses, what literary values does it seem to embody does it promote not only by what it says but we consider what says but how it says it? You can do both those things. What and how? What literary values if we were going to discern what Neil classicism is as a set of principles from just this passage what would we say about it? If anybody needs me to go back to a phrase I can do that, Yes? >> [Inaudible] >> So, I want you to what, >> [Inaudible] >> Okay. What are some instances? Can you think of, ? I think there's fairly a better one. >> [Inaudible] >> Alright what do you mean? You're right about synthesis; we're using it a lot. What is synthesis? >> [Inaudible] >> Well, look at this one, if the father of criticism has rightly denominate our poetry and imitate of art these writers will without great wrong lose their right to the name of poets for they cannot be set to imitate anything so that antithetical set up this is what poetry is, these people are not bad. You might say one of the things that come along with various kinds of antithetical statement is a certain sense of balance right this but not this but not this a synthesis often goes along with parallelism you have parallel statements set up so what we might say about that kind of pose, an ant synthesis comes up with a certain kind of philosophical argumentation right so the pose immediately in it's very diction and some philosophical even to a sentence like this one about the beginning of periods and letters that maybe through metaphysical that whom in criticism of the word, it is not improper to give some account. It is not improper right? That's a double negative It might all has to be considered to be a lit odious what's a lit odious? [ Silence ] >> Literal interpretation folk to talk to them about no, Yes? >> [Inaudible] >> Okay so what is not bad instead of good mean? It's even better than. It's just like that as fabulous, and you'd go, oh not bad, >> [Inaudible] >> Okay that's good underestimate we would say it's a form of understatement. We will say it's a form of understatement, right, that makes use of a double negative construction. By understatement it means really good, actually, it's not just good, if you are saying it's a litotes you will say it's not bad, it's a way of indicating that something is really good. It is not improper to give some account, but you just have to think about what it is. There is a certain kind of formality that makes it sound kind of philosophical, that gives it certain kind of authority and finality, and then he can go on to explain that account. So Johnson's prose is all about kind of balance, what he would call decorum, right? It's about carefully balancing sentences. And I don't know if there is a typo, just couldn't read it quite right, but there's a sentence in here where he talks about, this one: If by a more noble and more adequate conception that be considered as wit which is at once natural and new, that which though not obvious is, upon its first production, acknowledged to be just; if it be that, which he that never found it wonders how he missed; to wit of this kind the metaphysical poets have seldom risen. There's a very strangely content little sense, I don't think it actually works, it think there's something wrong but can't exactly figure out what it is. But even if we had it all perfect up here, I think we would say he's doing a kind of balancing act for a certain kind of emphasis, he wants to juggle rhetorically certain things until he gets to this: to wit of this kind the metaphysical poets have seldom risen So Johnson is a pro stylist who is above all interested in a certain kind of promotion and in a certain kind of decorum, it's exactly that kind of decorum that he says the metaphysical poets don't have. The most heterogeneous ideas are yoked by violence together, or you know, you wonder by what per verses of industry these metaphors ever found, I mean who ever thought of lovers as the feet of a compass, or what was that, the lights of a compass. It's like who would have thought of that, does that makes sense, does it really tell us anything? Johnson would say no. So one of the things we might say is that, for thinkers like Johnson who are talked about as neoclassical thinkers, you say, there is, in some sense, some interest in going back to the moment of Aristotle, to thinking very seriously about the kinds of principles of writings that Aristotle exposed, and that you could find in other works of the classical Greek and Roman period, right? So it's a Neoclassicism, it's a new classicism and it accompanies the enlightenment because it seems to be the translation into poetic practice of certain kinds of enlightenment ideals, right? So they start with the idea of imitation from Aristotle meaning poetry is mimetic, and therefore think that poetry ought to imitate human life. And what they what to do is to assimilate certain classical ideas and make them more modern, rewrite them for the Modern Age, which is the 18th century; in part of the epic, but even more of some of the minor Classical authors. This becomes their way of reconstituting what they think it was ancient, literally valued. So you can say that, how is it connected to enlightenment and thought? Well, you might say that if we are outside of the tyranny of Christianity as a cultural system we are now free to explore some of the ideas that people like the Calvinists wanted us to shut down. We can go back to the Greek past and rethink the meaning of some of their ideas. This is coming right after two things, right? First, the achievement that anyone who was a thinker about English letters in this period would acknowledge, the achievement of Milton in Paradise lost. It's really epic, and I'm not going to do so much epic, because it's hard to get beyond the achievement of epic of Milton. Plus , to us, I think this spiritual lesson is tenacious than Shakespeare and that's also Lumus law, and that also Shakespeare has sensed something as the great master of drama, drama is going to be a little bit harder to really conquer and some of the 18th century people try as much. And also they are reacting against, what we would think like as the achievement of the metaphysical poets, right. They don't like it, they think it's undisciplined, instead they would rather have what they called decorum, and well that's restraint, simplicity, impersonality, decorum, right. That's seems impersonality, it would not be a mist too. It would not be improper to clearing a some sort of authority, we might say, that was really grounded in the self but you'll try to masked that authority, and we actually against various kinds of ornamental obscurity, you know, excess of personality, so you don't want something right done into poetry, that's the whole point of Johnsons Life of Poetry, which you want instead is a kind of truthful representation of nature and in kind of larger terms, and this is what really squares it with the enlightenment, the idea of humanism. And in some sense what we are interested in is the development of humankind, from various kinds of forms, and poetry would be one of them, right? And as a result of that it draws of some of the ideas of enlighten. The idea of universal brotherhood that I talked to you about becomes an idea about the power of the universal, rather than the particular. We're more interested in what is universally true than in we're literal [inaudible]. One thing that Johnson said in his prepositions in Shakespeare is that Shakespeare is a master precisely because he is able to address the species whenever he is depicting an individual. In other words, all these characters seemed unique, Hamlet, Macbeth, whoever, and then you realize that they are embodying some larger set of traits which we can recognize in human beings as a whole, right? So Shakespeare manages to do both. He gives us the individual and the species in that is almost unique genius. Poetry, finally, should be didactic. I mean you go back to the last thing that he said. The improvement is dearly boss, no matter if it is physical poetry or they teaches something but it's dearly boss, it's expensive; you spend a lot of your own mental capital on it. Why? because you admire it but you are not pleased by it. Didactic poetry should be didactic for a chameleon faster finger but it should instruct by pleasing. It is one of the important things. Now if you want create an art that is pleasant to the ear, it goes down smooth, and therefore you ingest as it were the principles behind it much more easily, just a spoonful of sugar makes the verses go down, right? So that is basically in a nutshell some of the principles of English neoclassicism. I think you can see them, I'll put this close up for you and I think you'll seize it if you see that some of the principles are in fact embodied in Johnson's writing. All of these stuff makes it way over to the America's, starting, you might say in the time of Edwards' and then becomes a large part of American revolutionary discourse and the discourse of the early national period. In fact, poetry is pretty much everywhere in the early national period. It's funny to think about it, but it was about, it is a way which was the period of the founders, maybe has a high point of American intellectual culture, right? I mean these essential people who were reading and talking about ideas people, right? There were fewer of them and fewer of them who got countless people but leave that alone, we would say that there was a, you know, the life of the mind was evident in the popular culture. So poetry was everywhere, you would find it in newspapers, you would find it in public performances, you would find it in [broad sides] like this one, like the defense of port McHenry is a broad sign. It was published in a large, by which it was published in a large sheet of paper that was published made available for sale very cheaply, or poet even posted someplace, right? So you would say that poetry was kind of everywhere. And it was in all kinds of occasions, you know, somebody died, you just made a poem; somebody is born, you made a poem; somebody who got married, you made a poem; somebody did something else, you make a poem. And do you remember Huckleberry Finn? I forgot her name, what's her name? That character, that she sat somewhere half in the novel; who is always writing poems, for every occasions [inaudible] the feud episode. There's this woman, who just kind of writes poems at the drop of the hat she is always writing her poems for everybody. That is the satire of the, you might say, the tail end of this kind of public culture of poetry. But what I want you to understand is that, poetry still doesn't mean what we think poetry means. Like I said before, the period of poetry was a kind of oxy-moron and then Venice starts to open up a little bit and that there is attention in the work of Brad's Steet, for example, between the Doctrinaire theological impulse, and a kind of more personal impulse to explore both earthly love, love for your husband, grief when your children die, when the house burns down; that kind of attention is still very much attention of what we might think of these public and private lives; and that is still going on in this period. So poetry so a site of private imagining, or lyric, or you know, working out problems in your head, No, that is not what poetry is. Poetry is meant, poetry in this period is thought of us public, communal, didactic, it's out there in public, it's part of the social life of this period. And therefore, some of the great poets are re-interpreted to be these kinds of public poet, right? So Shakespeare as thought of in the early national period, for example, as a great writer because he is a writer who constantly opposes tyranny of all kinds. He depicts the problems of, death becomes a kind of a cautionary tale to the English monarch of , and people still talk about this today but what goes wrong when you abuse power. Shakespeare Milton becomes a friend of religious liberty, to try to open Puritanism up to a larger audience and then uses the form of epic and so, one of the things we might say is that the Augustan style in England during the first half of the 18th century is precisely what makes it way over to the Americas throughout and it becomes important throughout the early years of independence. We might think of the directions that Joe Barlow gives for making pudding in Hasty's Pudding. I think somewhere around Line 310 , this stanza here. Some with molasses line the luscious treat and mix like bards the whole the youthful with the sweet, a wholesome dish and well deserving praise, a great resource in those bleak wintry days when the chilled earth lies buried beneath deep in snow and raging Boreas drives the shivering cow. A wholesome dish, bards, mix the youthful with the sweet , that's what poetry is supposed to do. It's supposed to please but it's also supposed to instruct by pleasing and part of what the poets were writing in this period or trying to do is create something that we might call kind of American national poetry that will, in some sense, celebrate some of the great achievements of American culture up to this date. Something like The Life of Washington or Battles of the Revolution were popular, subjects for poetry in the early national period. Couple of things though. In England, because it had an aristocracy and continues to have an aristocracy, if you were a poet, you would be part of a patronage system. Typically, you would think that a poet is either going to be one of two models. Poet , you can be some sort of nobleman like Sir Phillip, who's got time to write because he doesn't have to earn a living. So he's got time to write in his leisure time or someone who's kind of an impoverished artist figure who then finds a great man to be his patron, and therefore sustain a kind of part of court to be or to produce [inaudible]. So you have a system of patronage, doesn't work in revolutionary America and in the early national United States. There's no more aristocracy. We're not going to be booted and spurred anymore but we're also not going to pay you for making poetry. So there's a kind of problem there, you might say. Increase me what's going to happen, and this will be a subject for us in the next couple of weeks, is that one of the things that's becoming emergent in this period is a system that we might call the literary marketplace in which poets and novelists are going to realize that they've got to figure out how to sell their stuff if they want to continue to write it and make a living for it. And it's difficult enough for the novel, we will see. There are your [inaudible] who's wonderful gothic novel Edgar Huntley that we're going to read in a little bit that tries and fails to make a professional career out of being an imaginative writer, Washington Irving is the first one that really manages to do it. It's even harder for poets. That's another thing that they get , along with these ideas of style, philosophical content, didactic poetry. Certain models for what it means to be a poet. And the problem is that neither of these models, neither of the gentlemen amateur or the hanger-on or the someone who has Aristocratic patrons quite fit the actual situation that you have in the United States in the early national period. So that's part of what we'll see, I think, in the couple of the lives that we're going to be talking about today. Let's talk about this thing. The defensive Fort McHenry , if you look at the head note of it, it tells you, I'll give you the link that you can find it. The thing is from the , can't remember it. The Marilyn Historical Society has a copy of this. It says the next song was composed under the following circumstances. A gentleman had left Baltimore in a flag of truth for the peppers of getting released from the British fleet, a friend of his who had been captured at Marlboro. He went as far as the mouth of Patuksik [assumed spelling] and was not permitted to return unless he intended an attack on Baltimore should be disclosed. And the British Admiral had voiced that they would take over the fort lickedy-split in no time at all. He was therefore brought up to the bay to the mouth of the Patapako [assumed spelling] where the flag vessel was kept under the guns of the frigate and he was compelled to witness the bombardment of Ford McHenry which the admiral will have boasted , there it is - he would carry in a few hours and that the city must fall. He washed the flag at the fort through the whole day with an anxiety that would be better felt than described until the night prevented him from seeing it. In the night, he washed , >> The bombshells and at early dawn his eye was again greeted by the proudly waving flag of his country. The British were in fact repulsed, and the naval occupation of Baltimore doesn't happen. To Anacreon in Heaven, again that was a drinking popular in an English pub called the Anacreontic Society. I think it's written by this guy John Stafford Smith for the Anacreontic Society, and this is a copy of the manuscript. This is definitely in the Maryland Historical Society. Okay, I want to read it and then I want about how it does, want to think about what it does, and how it does what it does. I think it's slightly cut off, but I think we can read it well enough. And if you have it, you might find it easier to look at it on paper actually if you printed it out. Can somebody read it for me? Yes. Loudly and with, >> Want me to read the whole thing? >> Yes I do want you to read the whole thing. Now, okay, as I want you to read, I want you to read the whole thing, and I want you to pay attention as she does it to the ways in which certain elements of the poem are repeated but with a difference. Immediately you should notice something about the first stanza that most people listening to the Star Spangled Banner do not know. Take it away. >> Oh say can you see by the dawn's early light. What so proudly we hailed at the twilight's last gleaming? Whose broad stripes and bright stars through the perilous fight o'er the ramparts we watched were so gallantly streaming. And rockets' red glare, the bombs bursting in air, gave proof through the night that our flag was still there. Oh say does that star spangled banner yet wave. O'er the land of the free and home of the brave. On the shore dimly seen through the mists of the deep. Where the foe's haughty host in dread silence reposes. What is that which the breeze o'er the towering steep, as it fitfully blows, half conceals, half discloses? Now it catches the gleam of the morning's first beam, in full glory reflected now shines in the stream. Tis the star spangled banner, oh long may it wave o'er the land of the free and the home of the brave. And where is that band who so vauntingly swore that the havoc of war and the battle's confusion, a home and a country should leave us no more. Their blood has washed out their foul footsteps' pollution. No refuge could save the hireling and slave from the terror of flight or the gloom of the grave. And the star spangled banner in triumph doth wave o'er the land of the free and the home of the brave. Oh thus be it ever when freemen shall stand between their loved home and the war's desolation. Blest with victory and peace may the heaven rescued land praise the power that hath made and preserved us a nation. Then conquer we must when our cause it is just, and this be our motto, in God is our trust. And the star spangled banner in triumph shall wave o'er the land of the free and the home of the brave. >> Give her a hand please. [ Applause ] >> Thanks a, well done, and of course what was in the Tom Clancy movie was that last bit. And conquer we must when our cause it is just and this be our, okay. By the way, I went back and got the DVD of the commentary. There are two commentary tracks. One with Clancy and the director and one with the director and the screenwriter. Looking for some interesting tidbits about why they chose this, alas none to be found so don't bother unless you. The movie's fine as that kind of thing. It's one of these movies where you say oh they're not going to do that. Oh they really do that. Wow, okay. And then the movie goes on from there. But Clancy was more concerned about the incorrect direction that the President's motorcade was driving when they're getting to the stadium, because, he's from Baltimore. And the director's like, gee I didn't even know that there was another verse. So, no, I have yet to find out why that's in there or who's idea it actually was. What do we notice about the first stanza? Yes. >> It ends in a question. >> It ends in a question, right. I mean when Whitney Houston is singing that, does that sound like a question to you? It's like no, I mean there's like, there's often that flourish at the top when they go, you know. It's a question. Oh, say does that star spangled banner yet wave or the home of the free and the whatever, the land of the free and the home of the brave? Asking a question. Now let's look at the things that are repeated in the poem. What is repeated in the poem? >> The land of the free and, >> Okay, so this stuff. Like the last couplets. >> What does it hear? 'Tis the star-spangled banner, oh, long may it wave O'er the land of the free and the home of the brave! then and the star-spangled banner in triumph doth wave O'er the land of the free and the home of the brave and then finally and the star-spangled banner in triumph shall wave O'er the land of the free and the home of the brave. What's going on there? What's different amongst those lines? >> Well in sentence it is more of like discovery >> Ok >> It will keep waving and the three the same establishing that there is triumph in the moment and it don't wave then and in the fourth it's, >> Good, very good so we have a difference in mood of the verb and an intense interrogative here questioning declarative of somewhat subjunctive conditional here all along here how may it wave to firmly declarative the star-spangled banner in triumph doth wave to something that we might think of as future tense or even prophetic it shall wave right? Suggesting that little change we can see a progress and that progress is from questioning uncertainty to certainty right there, that's the process of enlightenment and then something else, you might say the projection of enlightenment out This be our motto In God is our Trust: and the star-spangled banner in triumph shall wave right? Then conquer we must, When our cause, it is a just But I also want you to think also about the pattern of imagery that we've got here because as the head note, right? This head note tells you the story I mean he is looking at this; again we don't hear this song anymore because it's so overplayed and there was a period of time when many of us in the country didn't really like hearing it played because it reminded us of a particular version of American patriotism, that might not have been the particular version of American patriotism that we may believed in easier these days maybe. In any case it's also you grow-up with, it's kind of remote of the past, remote of the past? Densely like? Come on. Remote of the past? If you have read books when growing up. She kind of hears it , She is like what is denser, densely, densely like? It is just syllables so to hear it again we need to see it in some way that we hear it again, see what is doing, it's asking a question, right? Its night time, the four is being bomb, if the four falls, the British take over the city. How will you know the fourth falls? The flag, right? The star-spangled banner is the flags, you are looking to see if the US flag is still up there or its going to be replaced by the British flag and imagine the city at night, its dark and you can't really see so you've gone from light to dark and with dark comes non-lightning but obscurity questioning uncertainty, there are slashes of illumination whose , , . The rock its red glare gave proof through the night so BOOM! FLASH! You can see that that flag is still there so BOOM! FLASH! You can see that the flag is still there and then what happens? You get through the night and gradually you have the coming of the dawn, you have the rising of full light and when you have the rising of full light, you get a literal process of enlightenment and watch this close that the flag is still there. Now, it catches the gleam of the morning first theme in full glory reflected now shines in the stream of 'tis star-spangled banner right? And now you have that certainty that you didn't have before so the poem's movement is not only about the battle but there is a way which the battle becomes a kind of metaphor for this process of enlightenment that goes along with, it's kind of philosophical under pinning's of early national period. How can we move from questioning and uncertainty to certainty? What will give proof through the night? And you might think of this more generally, it's not just being about this specific battle but about being a law of being the larger national project of the United Stated and eventually almost predictably you move in to a kind of prophetic mode, right? The battle is pretty much over there, right? We see that the flag is still there, we start to think about all the sacrifices that have made and then we go in to our prophetic mood thus be it ever when free men shall stand between their loved home and the wars desolation plus victory and peace made the heaven rescued land, pray the power that has made and preserve us a nation and conquer we must. Ok so I want you to see that's the path of a larger pattern of a poem and part of the trick of the poem is you do it through the tenses and moods of its verbs in the last complex. Questioning to the subjunctive, to the fully declarative, to you might say the future tense or prophetic. Who wants to scan online? Anybody? How about second sentence, I think that's easy. On the shore, dimly seen through the mists of the deep where the foe's haughty host in dread silence reposes, what is that which the breeze, o'er the towering steep, as it fitfully blows, half conceals, half discloses? On the shore, dimly seen through the mists of the deep >> Trochaic >> Trochaic alright, how would that scan out? >> Unstressed, unstressed, stressed >> Wait, say it again. >> Unstressed, unstressed, stressed >> Ok, unstressed, unstressed, stressed on the shore. What's the next one? >> It's the same >> Unstressed, unstressed, stressed. What is that? It's not a trochee; it's an anapest, YES! This is anapestic tetrameter, a rare meter in English, it's called the galloping rhythm and you can see why, it gallops, it moves on the shore, dimly seen, through the mist of the deep where the foe's haughty host in dread silence reposes. Then you can throw and respond on two periodically but it is different in the kind of stately rhythm of heroic complex dada dada dada dada, right now! Dadadan dadadan dadadan dadada, so that's another one of the tricks of the poem, right? It gives you that sense of drama of kinds of heightens passion precisely through its use of metrical feet, anapest for the scavenger hunt, anapest and this poem are now out of bounce, you can't talk about anapest in the defense of form cannery. Oh well, there are other anapest can be found but this the famous example in U.S. Literature that I know of anapestic tetrameter, right for that we mean four anapestic feet on the shore, that's one, dimly seen, through the mists, of the deep, questions and thoughts about this and anything else to say? I don't know if I have made you think of this differently but you can see that it's a very complicated poem and it's a poem re-wears repays thinking and I think it's a good example of post-neo classism and either more so enlightenment thought in less, it's not as good an example of Neo-classism as a poetry by Swiftly impart because it gets away from the kind stately iambic contender that weekly picks up from Alexander Pope so in that sense in terms of metrical form, I don't think the defense of form typical but its theme of enlightenment, its belief that poetry can be public and didactic and then you know through that way which is meter works it's kind of sweetened that message I think it is a very good example of new classical poetry. Alright, Seewess Swiftly is an interesting character because she is both the most neoclassical of poets and the most exceptional of poets in the neoclassical period why that would be? In what way is she exceptional? Yeah >> She was a slave >> Well she was a slave, Ok that's true, anything else? Yes >> She was a she >> And she was a she, YES! Rights of impulses I mean, ok we have just think of her as a belonging impart tradition and would include Mary Rowlens and Alexander Poet and Bradstry. Alright, Bradstry is also trying to carve out of space for female poetic practice. Don't worry I am not threatening your epic poets, don't worry about it I am going to carved out my space Wow! You know, I suggest she was a kind of subversion of normal poetic expectation on Bradstry's part so we belongs to that kind of tradition, one of the things that we might say is that It's important for her to have this identity so poems on various subject religious and moral, Phillis Wheatley, Phillis is the name of the ship of which she came note the spelling; there's no y in it. Wheatley is her master, Negro servant to Mr. John Wheatley of Boston in New England. And this is published according to an act of parliament 1772, so it's published in London right? England and that's important. So, Wheatley is exceptional in that way. Why would she be therefore be the most in substance being paradigmatic in being classical poet? >> [assumed spelling] >> Okay, so she's aspiring to some of the values of within you class, she's looking for truth and wisdom in her poetry. Yes, let's do a little more with that. Do you want to add? Nope! Anybody? Yes! >> [assumed spelling] >> Very good! Okay, in fact, let's look at that, we can read the whole thing; let's just talk the way this works. You want to read that one? >> [assumed spelling] >> Thank you very much! So, what is this? This is exactly about that process being enlightenment that you were referring to, right? >> Where was she? >> Africa >> And what was she when she was in Africa? What's the adjective she uses? >> Pagan >> Pagan is one >> Benighted >> Benighted, Benighted, Right? That means literally in the dark, and when she comes, she's no longer benighted, she's in the light! So quite literally, it draws on the same tropes of enlightenment that we see in Jefferson's paragraphs, that we see in the defense of Fort McCannery, plus mercy brought me forth my pagan lab, right? Bless you! So, what else might we say about this? There's a kind of trick in this poem, as I said there was some tricks in the other poem, there's a trick in this one too. What is it? Yes? >> That she might not be entirely grateful of the way she was brought in to America because she said remember, Christians, Negros black is cane that you're violating Joe and Jane Cane. >> Okay, why would you do that? >> I feel like she's attracted to dress that becomes so accusatorial and becomes, >> Accusatory of what though? >> Of, hers not still not was being appreciated in the society, >> That's correct! I mean, I think that's right. There's clue that we see that there's a problem here that she's addressing. But, does that idea, if it's there that there's something, some blame that Christians have to accept. Does that contradict that idea? That, plus mercy brought me from my pagan land? Would she rather have stayed there, according to this poem? >> No. >> No! You're right! She don't think so, I mean, there's no way in this poem that suggests that she has been available about that. It was mercy who brought me from my pagan land taught my benighted soul to understand that there's a God, that there's a Savior too, once I redemption neither sought nor knew. Boom! Period! Right? So that's a sentence. Boom! Half of the poem! Second half of the poem, as you're pointing out has a kind of turnaround to it. Some and we don't know who the some are yet. Some of you are sable, I know, I mean, look at all the words for black that there's some of you are sable with scornful eye their color is diabolic dye. But again, I think I mentioned this earlier when I was talking about Ishmael and Moby Dick, that some people thought that people from Africa where descendants of the race of Cane and that they were marching that way, that might be one thing, they might be descendants of Ishmael so they are also still from the outcast. In our case, there are various ways of thinking biblically about why it would be okay to enslave Africans. Their colors diabolically this may be black, you know. Their colors are diabolic dye. Remember, Christians, Negros, black is Cane, may be refined and joined the angelic train. The trick is in the second half of the poem. Yes? >> It just seemed she's so racist in the writing because she was saying that there should be acceptance should be that, how she is sure that blacks could be refined. That there is something completely wrong because they are not, of you knows, of for being effective of the question of being refined and that all black is Cane. >> Uhm, Yeah, >> Specially causing the angelic train, is the that, describing the angelic [inaudible] >> We would treat it as a racist if; I suppose we would say it's racist if we think there's something wrong with black people, just because there is. We are treating things that there's something wrong with black people if they come from Africa and the reason there's something wrong with black people if they come from Africa was because they neither have redemption neither sought nor knew. Anyway, Wheatley is a person of her, you might say her context, and she's Christian. She's really Christian; she thinks it's good to be Christian. I mean, again this is some of the power, right? She's a new and classical poet, but you still see the power of Christianity in her thinking. When writes the poem to Reverend Whitfield, of who I'll talk a little bit more about next time. Again, it's part of her commitment to Christianity. So, what's wrong with black people is if they came from Africa, they didn't know God. So, that was a mercy, that was God's, you know, you can think of a role in center, God has supposed in me, you know God has been merciful to her because He brought her and she didn't talk about how it happened but it was a mercy, it was difficult but she's gone through it. For that some kind of role in same kind of logic, that's not what the problem is. The problem is this, that's some of you are sablewayed [assumed spelling] to scornful eye, period! As if there were periods! Their color was a diabolic dye period! That's it! That's where they would stop. Where does she go? She goes further than that period. Right? Remember Christians, Negros, black is Cane may be refined and joined the angelic train. Now you may say if, you're right to say, I suggest that there's something wrong with black people. I would say that the basis of what's wrong is that race, however, the basis of what's wrong is that they haven't been redeemed, what's wrong with the Christians, is that they seemed to have either forgotten or willfully wished to deny the fact that Negros, black is Cane may be refined and joined the angelic train. Onto the racist are here, but I would argue that the poem is not racist, the poem is actually an attack on racist who believe that black people or African people cannot be Christianized. She would say that everyone can be Christianized. But if wanted to take the extra leap and say for a minute that why everybody has to be Christianized, can't they be something else. That's not going to happen, I mean, that's not who she was. Some people get upset about that, asking why is not she more like pagan, why didn't she celebrate her paganism? Or why does not he become a socialist, why does he, you'll see, why does he not, why does he not characterize like some kind of economic individualism. This is the way that we see as the delimitations of cultural context. Wheatley is a progressive thinker and she's for anti-slavery, and anti-racism, but she is firmly committed Christian. But we still haven't gotten to the trick. So, what's the trick? Yes? >> [inaudible] >> That's good! That's very good! There is a weird ambiguity of this punctuation. At the very least you would say that there is a syntactical complication that makes you pause and wonder. Remember Christians, Negros, how we addressing the Christians and the Negros? No, I mean possibly, but not really but you have to go back to make sure, remember Christians, Negros, but what they've done, what I think you're pointing to is there's a certain kind of syntactical equivalence created here, this are both enclosed by comma's and syntactically they seemed to have the same weight within the sentence and look how the poetry slows down, remember, Christians, Negros, like three, sazurels, right there! Slows it down and creates some kind of weird syntactical equivalence betweens these things possibly. In actual you say no, remember Christians, Negros may be refined and join the angelic train. That's the actual sentence, but the weird punctuation makes you pause and worry a little bit about that. I think that's one of the tricks. Although, I don't think that's the trick. Yeah? >> You can't be referring to some? >> Who? Some? >> You were referring to the some? Because you know, >> Yeah, but who is the some now we know? >> We thought that was Christian, >> Well, Well, it's still is. Alright, some of you are simple ways to score a fly. So, the Christians are clearly being implicated in this. Alright? Some of you , and she's not going to say all Christians, she's not getting it all , 'some'. But then, there's a kind of implication that way , syntactically , that way too many Christians believe this. Some of you are simple ways to score a fly. Remember Christians, And there's a sense in which it's almost assumed that the Christians are not the ones. If they need to remember it, they forgotten it. That would be a good way of thinking about it. Possibly, they're even denying it. That would be the bad way of thinking about it. That's what these are. Here, The fact that this is probably Christians is diabolic. Right? They're the implications of what seems to be biblical thinking here by these 'some.' That's still not the trick. Now we're running out of time. We're going to have to end on this. Yes? [Inaudible]. >> It's possible. It's, Remember what we said about the coin, except, that's what they're talking about. There's a pun on 'dye' end with 'Y-E' and , I think that's right. And, maybe also 'die' too. >> [inaudible]. >> I think the pun is they think that it's not only 'dyed' , that they're dyed in terms of their color , but they're stamped that way. So it's final and done. That's not the only pun in here. Come on, we're running out of time. Yes? >> [inaudible]. >> Possibly. Have to do with, >> [inaudible] >> Very possibly, although we're pre-industrial. But, yes, there is that sense of refinement, go , What needs to be refined? >> [inaudible] >> Right. But, in life, what are the things that need to be refined? I'm not calling on anybody else yet. >> [inaudible] >> Uh huh. >> [inaudible] >> Negroes. You're saying , right? They're black as what? >> [inaudible] >> Right. It's spelled 'K' as in cable but if you hear it, you don't necessarily hear it that way. Remember Christians, negroes black as cane, as in cane sugar, which is related to slavery , clear to everybody who knows that sugar trade is one of the reasons for slavery , , they're black as cane, they may be refined and join the angelic train. Right? So, it invokes the pun is on cane. It invokes that kind of purification of sugar. It also indicts the slave trade all extremely economically. You didn't believe she could do poetry? You didn't believe that a black woman slave could do poetry? All you have to do is see the way this poem works and you know that she can. Alright, we're going to take a 'borrow' then next time. I'll work it into one of those lectures. Alright, thanks a lot. |
Open_Ed_Cyrus_Patell_American_Literature | Frederick_Douglass.txt | >> In the first chapter of the narrative of the Life of Frederick Douglass, an American Slave written by himself, the ex-slave describes one of his earliest childhood memories which in fact turns out to be a scene as disturbing and gory as anything you might find in the work of Edgar Allen Poe. This is near the end of the first paragraph on page 2074 of your text. Douglass writes I was quite a child but I well remember it. I never shall forget it whilst I remember anything. It was the first of a long series of such outrageous of which I was doomed to be a witness and a participant. It struck me with awful force. It was the bloodstained gate, the entrance to the hell of slavery through which I was about to pass. Now what Douglass is remembering here is the flogging of his aunt by the overseer Mr. Plumber which he's described already a little earlier in the paragraph. This is Douglass. I have often been awakened at the dawn of day by the most heart rendering shrieks of an own aunt of mine whom he used to tie up to a joist and whip upon her naked back until she was literally covered with blood. No words, no tears, no prayers from his gory victim seem to move his iron heart from its bloody purpose. The louder she screamed the harder he whipped and where the blood ran fastest, there he whipped the longest. He would whip her to make her scream and whip her to make her hush and not until overcome by fatigue would he cease to swing the blood-clotted cow skin. Douglass concludes finally it was a most terrible spectacle. I wish I could commit to paper the feelings with which I beheld it. Now Douglass' work and career like those of other escaped slave and of abolition workers posed for us very probing deep questions about the meaning of America which we discussed early in the course as a kind of trope, an example of figurative language. Douglass' text brings up issues that the Declaration of Independence conjures up but ultimately refuses to address. They ask in other words what the term freedom equality might mean in a country that practices slavery. Now when the narrative originally appeared in Boston it appeared under the imprint of the anti-slavery office. This was 1845 and it made a powerful impact. In part because the reputation that Douglass had already achieved as an abolitionist speaker and in a way what the autobiography is designed to do is to show how it is that Douglass, an ex-slave could become that kind of powerful speaker. It appeared at a moment when anti-slavery activity was very strong but also factionalized. People couldn't come to an agreement over issues like how important nonviolence was to the movement or what women's participation should be in public protest, what the role of churches might be and about the role of Northern racism, the kind of problems that bedeviled the anti-slavery movement. The narrative was 125 pages in its first edition. It sold for fifty cents and it sold about thirty thousand copies in the Unites States and Europe within five years. It was soon translated into other language and it was different from other anti-slavery text because of the way in which Douglass wrote it making self-conscious use of literary devices and literary techniques that immediately added to the authority of the text and that distinguished it from many of the narratives that were had appeared by the time by even the middle of the 1850s by the time that Stow had written her narrative a few years later. Alright so I want to emphasize that for you. This is a self-consciously literary text in the sense that literature is starting to emerge in the beginning of the nineteenth century. Something that does not necessarily include history although and it does not necessarily mean history although it includes elements of the historical. Is not the same thing as a sermon although it will clearly include sermonic elements but something that is more related to the uses of language in esthetic ways and also to exploring the province of imagination right? This is a personal narrative but it is drawing, you will see in crucial moments, on literary devices and part of the power of the narrative is that it can be seen by its readers to be drawing on those devices. Douglass knows exactly what he's doing in other words as he draws on certain kinds of literary devices like personification or apostrophe or when he creates sentences that are clearly kind of baroque and yet in control right. Part of his project here is to demonstrate that blacks are in no way the field the intellectual imaginative moral inferiors to whites that they are equal in every way and so the proof of the pudding is that an African American can actually write a text like this one. Part of the question, part of the reason that Douglass writes the narrative is the question that people don't believe that he's an actually an ex-slave or that he could have had the history that he claimed to have. So, its in writing the story of his life you might say that he validates the story of his life. That narrative becomes its own emerges as its kind of own authority through its ability to not only make use of elements of personal but also to be you know rhetorically sophisticated to invoke the Bible, to pitch itself basically as a literary text and if that's not enough the letter, the narrative is also prefaced by respected abolitionist figures. It includes letters from William Lord Garrison and Wendell Philips to further testify to its authenticity and even to its power. There's a way in which part of one of the job of those letters is to teach you how to read the narrative so in that sense it should remind us of a couple things that we've seen. What other text have we looked at that required a certain kind of authorizing from others besides the writer? Remember any? Yeah. >> [Inaudible] Rose >> Roleton [assumed spelling] to be one, right. Increase manor ad her husband bookending the thing and authorizing her to speak. Another? Remember Phillis Wheatley? I mean her owner testified to the fact that she is in fact a slave, African American slave brought to the United States who is writing these poems, right. There's a sense in which part of the interest of Wheatley's poetry is the fact that they could be written by somebody who it was not believed could actually write poetry and certainly not good poetry, right and we talked about the ways in which one of the things Wheatley had to demonstrate was that she could write poetry that could be recognized as poetry. So she didn't have the luxury of being able to do the kind of formal experimentation that we would see in someone like Taylor. Likewise we will see in Douglass, certain choices that he makes that are designed to demonstrate his awareness of what we might call literary history. Certain choices that he makes that demonstrate that he is a literary writer and that therefore that he can be inserted into a larger intellectual tradition. That's part of the project you might say of the narrative. Which means that one of the things that Douglass is doing it is suiting himself into what we might think of white literary culture or white literary history. Its precisely to appropriate that white literary history, to make white literary culture or even more largely white culture itself his ally perhaps to spite itself. In other words he's going to be using means that come out of the tradition that has been oppressing him, precisely to show what's wrong with that tradition and to try to lessen some of that oppression. I mean it's a long-standing question within African American studies about whether you can use the master's tools to dismantle the master's house. Douglass would say yes you could although his goal isn't exactly to dismantle the house, as we'll see. His goal is simply to allow that house to become a place where people like him are welcome. So he doesn't want to challenge what we might think of as a major positive enlightenment ideal of the United States. He simply wants them to be extended to everyone regardless of race and you know creed and gender, all of these things although there are clearly certain priorities. He's most concerned about race. So part of what he's trying to do in the narrative is take the fact of his life as representative and again this is something we would see in personal narratives by Edwards or Franklin or even Thoreau whom we've read most recently, right? Or even Whitman I suppose would be another person who takes the facts of his life and tries to make them into something larger, to use them as representative or exemplary a larger cultural and political forces. In this case, it's the forces that constitute the nation's crisis over slavery. So you might say that he is in some way designing his narrative to create a kind of embodiment of exactly the forms of writing and speech that are typically denied to slaves, right. In a sense, what we'll see is that he proves all of the arguments that are made against educating slaves to be correct. You shouldn't educate slaves because once you educate slaves they start to think and once they start to think they think about the things you'd rather they didn't think about. They think about what's wrong with the slave-holding society that is the United States and they're able to write persuasive documents like this, right. So I told you way back when that one of the reasons we might say text is so important to the Republic is that or a sign of that is that we venerate the date of the Declaration of Independence with a sign. We venerate the date that that text became official and I suggested to you that a culture that could create a text like that one was in fact a culture whose time had arrived. I think we could say the same thing about Douglass' project here. Douglass wants to show that someone like him can create a text like this that is perhaps the most powerful in-justification for freedom that we could possibly offer. He goes on by the way and a little bit like Whitman writes it again a couple of times. There are two other versions. He expands his life story in My Bondage and My Freedom which is published ten years later and the person who introduces that volume hails Douglass as a kind of representative American to use the language as active [inaudible] he calls them a type of his countrymen and Douglass publishes a third version of his life much later in 1881 which is called The Life and Time of Frederick Douglass, right. In fact, in The Life and Times of Frederick Douglass he reveals something that he kept suppressed in the earlier version which was how it was he actually escaped from slavery to freedom. He doesn't tell you in the 1845 narrative because he wants to keep that possibility, that avenue open for others. Take a look on page 2122 and you can immediately see something of the self-consciousness of the narrative and also about the ways in which the narrative like the author of the narrative is a kind of constructed figure. So I would suggest to you that Douglass wants us to see that his very name Frederick Douglass is a kind of epitome of his project. So, top of 2122, we know begin to feel a degree of safety and to prepare ourselves for the duties and responsibilities of a life of freedom. On the morning after our arrival in New Bedford while at the breakfast table the question arose as to what name I should be called by. The name given me by my mother was Frederick Augustus Washington Bailey. I had however had dispensed with the two middle names long before I left Maryland so I was generally known as by the name of Frederick Bailey. I started from Baltimore by the name Stanley. When I got to New York I again changed my name to Frederick Johnson and thought that would be the last change but when I got to New Bedford, I found it necessary again to change my name. The reason of this necessity was that there were so many Johnsons in New Bedford. It was already quite difficult to distinguish between them. I gave Mr. Johnson the privilege of choosing me a name but told him that he must not take from me the name of Frederick. Why, because I must hold onto that to preserve a sense of my identity. Frederick is his given name, not the surname right. There's someway which he identified with Frederick. The other stuff can be part of his shaped personality. Mr. Johnson had just been reading The Lady of the Lake and at once suggested that my name be Douglass and the footnote tells you that that plot of The Lady of the Lake is loosely pertinent it says to Frederick Douglass' life civilization but also in Gaelic, Douglass connotes blackness alright. So it works nicely in that sense. And from that time until now I have been called Frederick Douglass and as I am more widely known by that name than by either of the others I shall continue to use it as my own, alright. So one of the things we might say is the dynamic of moving from slavery to freedom is a dynamic of moving from the lack of choice to the ability to choose. To choose certain things for yourself. Out of servitude you can now choose to create yourself again and so having a new name and particularly a name that draws on. It's inter-textual with white culture is exactly a sign of the way in which Douglass is trying to use white culture to appropriate white culture almost against itself. In order to, again, not tear it down but to make sure it lives up to its promises right to extend the conception of freedom that is ostensibly implicit in the founding of the United States. Right. Think about all that rhetoric, our freedom from the enslavement by Britain. I mean people often wondered didn't the founding fathers know when they used all this rhetoric about freeing themselves from the bonds of England that they were in some sense being quite hypocritical. Sure they knew but there were certain things they were not willing to do or not willing to do with or you might say they had ways of rationalizing it. Individuals, men had to be free but black men didn't count as either of those things neither as men nor as individuals. Alright. Douglass wants to extend that. You might say he will probably be one of those people that would say you know like life, liberty and the pursuit of happiness all men are created equal. We just want to make sure we live up to that, that men in some sense should become a kind of generic term for all individuals. Ok. So I want you to think about that. Douglass is in some sense trying to use white culture to perfect the project of America, not to radically alter it and as so therefore it's useful I think for us to think of him as, his narrative as part of a trajectory of personal narratives that we've had in the course that would certainly include Edwards and Franklin and possibly also include Thoreau and Whitman. Alright. People who are using their lives as exemplary but there are particular ways in which it is useful to think of two selves who are at work in the narrative, two versions of Douglass' self, two strings you might say of of, of self-creation that sometimes work in tandem and sometimes works separately. So shorthand I think it might be useful to think of it in these terms right. The Jonathan Edwards self and the Benjamin Franklin self and we'll try to trace these two motifs through the course of the narrative. So the Edwards self follows kind of a developmental history that leaves you might say from Christian enlightenment all the way to the establishment of Sunday school, Sabbath school for fellow slaves, to a career as a kind of abolitionist and preacher, almost you might kind of say a messiah on behalf of abolitionism. That's the Edwards trajectory. The Franklin trajectory for follows a career of self-making that really begins with kind of self-teaching, auto-didacticism in the way that Franklin did and culminates into what we might think of as a kind of active economic self-possession and the ability therefore to make contracts. Ok. The central moment in the first story, the story of Edwards, so that's Franklin. So let me just see what. You know let's go back. Just keep that up. The central moment of the Franklin story is the battle with Mr. Covey. Take a look at page 2101 and we can take a look at that. [ Pages turning ] At the bottom. At the top of the page it says I've already intimated that my condition was much worse during the first six months of my stay at Mr. Covey's than at the last six. The circumstances leading to the change in Mr. Covey's course toward me formed an epic in my humble history. Right and again even in thinking about himself having a history that can have epics is a sense of conveying that this history is more than just a personal history. It's also kind of a larger dynamics of history are at work here and then the sentence that is often quoted, you have seen how a man was made a slave. You shall see how a slave was made a man and in Douglass' account this happens by violence. Right. He kept his slaves in slavery by violence. It's through violence that he finds a kind of escape. In this case it's kind of a protracted, physical resistance in a fight against a man who was entrusted with the project of breaking his spirit, breaking down any possibility of resistance. This is what Douglass does. He resists precisely this person and you can see how Douglass is drawing on the Old Testament for this. People will often identified this as a kind of [inaudible] figuration of Jacob's wrestling with the angel in the Old Testament and I think that's certainly part of what Douglass is trying to get across. Let's skip ahead a little bit further and look at [ Turning pages ] The top of 2104 and you can see the way in which Douglass is using this kind of language of the Bible so after the fight is over and you can by the way if you're interested look at the language of the fight on page 2102 to 2103. It's a one long huge paragraph alright. There's a kind of intensity to this as if the paragraph itself signifies that once Douglass is in it he's in it until you know for the long haul until he breaks or breaks the resistance of his of slave master or until his own spirit is broken. But here he says this, fighting with Mr. Covey was the turning point in my career as a slave. So this is what he had in fights as the turning point here although I would suggest to you that it's simply one turning point. It rekindled the few expiring embers of freedom were revived within me a sense of my own manhood and again that's not accidental. Part of the way in which Douglass' narrative works is that it suggests that one of the crucial things it's being denied to, to slaves, especially male slaves is their masculinity, their manhood and that's one of the things in some sense sometimes bothers feminists who read this. That it's a very masculinist [assumed spelling] narrative. In some sense it's interested in women by implication but it's primarily interested in African American masculinity, the reassertion of this, the way in which slavery has feminized them, alright. So part of what Douglass suggests is that part of his. He quite means. He means it when he says you've seen how a slave is made of, a man was made a slave you want to see how a slave becomes a man, he means that, man in that kind of full masculine implication of all of that. He says it recalled the departed self-confidence and inspired me again with a determination to be free. The gratification afforded by the triumph was afforded the full compensation for whatever else might follow, even death itself. He only can understand the deep satisfaction which I experienced who was him, has himself repelled by force the bloody arm of slavery. Again this is the kind of moment, you might say it's a problem of representation in which he can simply only point to, use language to point to that experience. Looked a little bit like Edwards talking about in the divine and supernatural life about grace in terms of sweetness, right and you can have an intellectual idea of sweetness without ever having tasted honey but once you do taste honey you're understanding of the concept is completely transformed. You know there's a kind of experiential basis that is necessary for a complete understanding. Same here. You can't really understand it unless you've been a slave but he's going to try to point you in that direction and the way he can point to that direction is to use a story that everybody knows and one in which he firmly believes. I felt as I've never felt before. Right, it's a moment of conversion but in some sense it's the ultimate moment of conversion, the one that we see at the end of the life of Christ from death in this case, living death, to life itself. It was a glorious resurrection from the tomb of slavery to the heaven of freedom. My long crushed spirit rose, cowardess departed, bold defiance took its place and I know resolve that however long I might remain a slave in form that day had passed forever when I could be a slave in fact. I did not hesitate to let it be known of me that he white man who expected to succeed in whipping must also succeed in killing me. So he's still a slave in outward appearance when this was done but he knows that fundamentally something has changed in him. He is no longer a slave and he dates his transformation to this period. Let's follow out this line of imagery a little further and turn to page 2124 near the end of the narrative and you'll see how it kind of comes to us. It's far less dramatic than this but it comes to a kind of conclusion that we might expect here. [ Pages turning ] Last paragraph in this. This is the conclusion of the narrative proper before the appendix. I had not long been a reader of the Liberator before I got a pretty correct idea of the principles, measures and spirit of the anti-slavery reform. I took right hold of the cause. I could do but little but what I could I did with a joyful heart and never felt happier than win in an anti-slavery meeting. I seldom had much to say at the meetings because what I wanted to say was said so much better by others. Right again, problem of representation. He isn't quite there yet. He isn't quite the self that has had such a transformation that he's himself able to express himself, speak in front of others, write this kind of narrative but while attending an anti-slavery convention at Nantucket on the eleventh of August, 1841. Right so he specified the details of the day because it's important. I felt strongly moved to speak and was at the time much urged to do so by Mr. William C. Coffin a gentlemen who had heard me speak in the colors peoples meeting at New Bedford right. So again it's the content that's separate. He feels comfortable speaking in front of other African Americans, less so in front of white abolitionists, but he does and here's the culmination of the imagery. It was a severe cross but I took it up reluctantly and I took it up reluctantly. The truth was I felt myself a slave and the idea of speaking to white people weighed me down, right. So in a sense right he said glorious resurrection, massive moment, you're going to have to kill me in order to whip me. I'm not a slave anymore but there's a certain way in which he still remains a slave. It's almost like Edwards again. Edward points to a moment where he starts to see the beauty and the awesomeness of the thunder but it's not a one-conversion moment. There are others that come afterwards and this perhaps is the culmination of a series of conversion moments for Douglass. [ Coughing ] He takes up the cross of speaking publicly. I spoke but a few moments when I felt a degree of freedom and said what I desired with considerable ease. From that time until now I have been engaged in pleaing the cause of my brethren which what success and with what devotion I leave those acquainted with my labors to decide. Right. So that in some sense is the culmination of the set of Christian images with which Douglass surrounds himself in the narrative and one of the things we might say about this particular version of Douglass' self is that it is outward looking. The central experiences of the Edward side of Douglass' self are oriented not towards self but towards other people right. So here in a moment of speaking out to other people. Earlier on let's take a look at [ Pages turning ] Let me see, where is this. Didn't note it down on the page but the, the moment of the Sabbath school right, when he talks about. I did bring the quotes. Listen to it. He says I look back to those Sundays with an amount of pleasure not to be expressed. They were great days to my soul. The work of instructing my dear fellow slaves was the sweetest engagement with which I was ever blessed. We loved each other and he goes on to say every moment that we that they spent in that school they were libel to taken up and given thirty-nine lashes. Right, again the same imagery that comes from the crucifixion. They came because they wished to learn. I taught them because it was the delight of my soul to be doing something that looked like bettering the condition of my race and then in the next paragraph he says this. We were linked an interlinked with each other. I loved them with the love stronger than anything I have experienced as a slave. Right. So that outward feeling, that's part of you know there's a sense in which Douglass is drawing from a long tradition of Christian imagery that we looked a little bit in at in this class right but the idea between [inaudible] of Winthrop right? The bonds of crisis love. The community first, the individual second. That is the Douglass side of this narrative. I mean the Edward's side of the narrative and it's an important thing to think about. There is another side to his narrative and we might think of it again as the Franklin side to this narrative. In part it is, is not unrelated to the idea of communal bonds as well because one of the things that Douglass points out at the very beginning of the narrative is that one of the things that he points out to us is that he is prevented from starting out with a kind of normal, familial bonds that whites who are free simply take for granted. Let's take a look at the very beginning. This is chapter one. [ Pages turning ] And he says this. I was born in Tuckahoe. This is on page 2072. I was born in Tuckahoe, near Hillsborough about twelve miles from Easton in Talbot County, Maryland. I have no accurate knowledge of my age neither having seen any authentic record containing it. By far the largest part of the slaves know as little of their ages as horses know of theirs and it is the wish of most masters within my knowledge to keep their slaves thus ignorant. Alright. So some of the bare facts of his birth remain unknown to him. I do not remember to have ever met a slave who could tell his birthday. They seldom come nearer to it than planting time, harvest time, cherry time, springtime or fall time. You see that from the very beginning, slaves are made to exist in a different sense of time other than the kind of teleological time that marks not only western thinking but even Christian thinking, right. It's cyclical and it's oriented around the idea of labor here. A want of information containing my concerning my own was a source of unhappiness to me even during childhood. The white children could tell their ages. I could not tell why I ought to be deprived of the same privilege. I was never able allowed to make any inquiries of my master concerning it. He deemed all such inquiries on the part of a slave improper and impertinent and evidence of a restless spirit. The nearest estimate I can give makes me now between twenty-seven and twenty-eight years of age. I come to this from hearing my master say sometime during 1835 that I was about seventeen years old. Even more is denied to him. My mother was named Harriet Bailey. She was the daughter of Isaac and Betsey Bailey both colored and quite dark. My mother was of a darker complexion than either my grandmother or grandfather. But then he goes on to say this. My father was white man. He was admitted to be such by all I ever heard speak of my parentage. The opinion was also whispered that my master was my father but of the correctness of this opinion I know nothing. The means of knowing was withheld from me. My mother and I were separated when I was but an infant before I knew her as a mother right. So part of what we are seeing right at the outset here is that the institution of slavery depends on the disruption of familial bonds. The kinds of thinks that any average American can take, free American in the United Stated can take for granted are denied to the slave. You don't know when you're born. You don't even know who your parents are. Think about Benjamin Franklin's autobiography right. He talks about the fact that he comes from relatively humble origins. He's not. I said at the time he's not like Jefferson. He's not like Adams, men who are born to wealth, who take a college education as their due. Franklin has to work. He has to apprentice himself to his brother. He has to teach himself. It's not encouraged but he begins that narrative how, by addressing himself to his son. He takes pride therefore in his family history, in his family genealogy and he's relatively certain that you might say he can pass on this lineage to his son. So if we're thinking about Douglass as Locke [assumed spelling] puts it, a kind of Negro edition of Ben Franklin, one of the things we would see here is that in some sense in terms of humbleness of origins Douglass is more Franklin than Franklin right. The humbleness of Douglass' origins far outstrips those of Douglass. There's no more obscurity that's darker in American culture at this time than that of a slave and that's one of the things that Douglass points out to him. He's born into a kind of limbo where he doesn't have information. He has to listen to it by hearsay. He's certainly not secure in his birth records and in his genealogy. Interesting thing to note, by the time this narrative is published, Douglass is already a father. I mean he has a family. He's free. He has a family. He doesn't address the narrative to his child. It's a way of making a point that for most people like him, ancestry is a question and posterity you might say is in jeopardy. The problem with family is therefore one that is acute for the slave and in this very first paragraph I think Douglass shows us how individual identity is restricted by the ignorance that comes with being a slave. Ok. So that's one of the things to bear in mind at the outset of this story of Douglass as a kind of Franklinian figure. He's more Franklinian than Franklin himself even in the next stage of his career right. One of the other things we think about Franklin is that Franklin is an autodidact. He's someone who is self-educated, who teaches himself. Well Douglass is more of an autodidact than Franklin. Douglass is. Douglass outstrips Franklin. Why? Because frankly it was just hard to do. It wasn't encouraged. For Douglass it was actually illegal. It was something with which he could be punished by whipping or you know death. There was way in which to take the chance of educating himself was precisely the thing that Douglass decides he has to do in order to transform himself into something other than a slave. So what's difficult for Franklin is dangerous for Douglass. Let's take a look at in the fifth chapter no in the sixth chapter, 2086. [ Pages turning ] Alright. He goes to a new place and he's in the presence of somebody's who seems like a very kindly mistress, Mrs. Auld and he says very soon after I went to live with Mr. and Mrs. Auld she very kindly commenced to teach me the A, B, C. After I learned this she assisted me in learning to spell out words of three or four letters. Just at this point of my progress Mr. Auld found out what was going on and at once forbade Mrs. Auld from instructing me further telling her among other things that it was unlawful as well as unsafe to teach a slave to read. To use his own words further he said if you give a nigger an inch he will take an ell. A nigger should know nothing but to obey his master. To do as he is told to do. Learning would spoil the best nigger in the world. Now said he if you teach that nigger, speaking of myself, how to read there will be no keeping him. It would forever unfit him to be a slave. He would at once become unmanageable and of no value to his master. As to himself, it could do him no good but a great deal of harm. It would make him discontented and unhappy. Now, the key thing is he is ninety percent right. If you want to keep an African American as a slave or to keep somebody a slave, don't teach them to read. Don't teach them to read because with reading comes a certain kind of self-confidence comes kind of thinking right. He would become at once unmanageable and of no value to his master. That is true but the one place where he gets the ten percent maybe that he gets wrong as to himself it could do him no good but a great deal of harm. That's where Douglass would choose to disagree alright. Douglass would realize how dangerous it is and from a certain point of view you might say it's a point just to keep him contented in his lot it is harmful for him to learn to read. But if you're talking about the project of creating yourself as a as someone who is freed, someone who's going to be an individual, reading is absolutely necessary. So he realizes a valuable lesson. The most valuable lesson he gets on this page comes not from the mistress but from the master himself. From that moment and he goes on. It was a new and special revelation and again even though I'm tracing this as part of the Franklinian side I guess that you want to see that it's never really separable from the biblical side, from the Edwards side. Again this language of revelation. He goes on to say it was a new and special revelation explaining dark and mysterious things with which my youthful understanding had struggled but struggled in vain. I now understood what had been to me a most perplexing difficulty to wit the white man's power to enslave the black man. It was a grand achievement and I prized it highly. I mean it's the same kind of language that he uses in the struggle with Mr. Covey. From that moment I understood the pathway from slavery to freedom. It was just what I wanted and I got it at a time when I least expected it. Whilst I was saddened by the thought of losing the aid of my kind mistress I was gladdened by the invaluable instruction in which by the merest accident I had gained from my master and then he goes on. Thought conscious of the difficulty of learning without a teacher, I set out with high hope and a fixed purpose at whatever cost of trouble to learn how to read. The very decided manner he says with which he spoke and stove to impress himself, press his wife with the evil consequences of giving me instruction served to convince me he was deeply sensible of the truths which he was uttering. It gave me the best assurance that I might rely with the utmost confidence on the results which he said would flow from teaching me to read. What he most dreaded that I most desired and this is another one of these self consciously literary moments. I mean look at the cadence that he sets up here. It's meant to be the culmination of this revelation. Look how he sets up the kind of parallelism here. What he most dreaded that I most desired. What he most loved that I most hated. That which to him was a great evil to be carefully shunned was to me a great good to be diligently sought. See. Look at the expansion of the structure there. And the argument with which he so warmly urged against my learning to read only served to inspireme with a desire and determination to learn. In learning to read I owe almost as much to the bitter opposition as to my master as to the kind of my master as to the kindly aid of my mistress I acknowledge the benefit of both. That's kind of a bravura moment right when you can already see forecasted the end result of this moment in which he decides he has to read. The end result of learning how to read is being able to write sentences like those to culminate a description in a moment like that right. The use of antithesis here in other worlds in this passage shows us the kind of his budding awareness of what we might call a paradox of slavery but it also forecasts the end result of what he resolves to do here. So we might say that if the fight with Covey is the basis for his kind of spiritual regeneration, the act of reading here becomes the basis for the intellectual basis for his quest for being free or for liberation. Take a look at a couple of pages on for example at the top of page 2089. [ Pages turning ] This is one of the moments that people point to and again in the practice of his reading. Actually go to the bottom of the previous page. I was now about twelve years old and the thought of being a slave for life began to weigh began to bear heavily upon my heart. Just about this time I got hold of a book entitled The Columbian Orator. Every opportunity I got I used to read this book. Among much of other interesting matter, I found in it a dialogue between a master and his slave and the footnote tells you that this was a popular anthology of pieces for recitation that was compiled by a Massachusetts teacher and writer named Caleb Bingham. It was used widely in this time, in the 1830s, as a kind of educational text and it really was a work of republican education right. It was designed to implicate Democratic and Republican principles and therefore it contains arguments against slavery. Although in the context Douglass has to translate the context because here the context he understands is that of Catholic emancipation in Ireland. So he says this. The dialogue represented the conversation which took place between them when the slave was retaken the third time. In this dialogue, the whole argument in behalf of slavery was brought forward by the master, all of which was disposed of by the slave. The slave was made to say some very smart as well as impressive things in reply to his master, things which had the desired though unexpected effect for the conversation resulted in the voluntary emancipation of the slave on the part of the master. This is something that outstrips Douglass' experience and then here is the business of Catholic emancipation. In the same book I met with one of Sheridan's mighty speeches on behalf of Catholic emancipation. These were choice documents to me. I read them over and over again with unabated interest. They gave tongue to interesting thoughts of my own soul which had frequently flashed through my mind and died for want of utterance right. So he's keenly aware here that your ability to control language limits will enable your ability to think. You can't complete your thought if you don't have the words in some sense to complete it. That's why reading is such an important part of the process of no longer being a slave. The reading of these documents. Oh he says what I got from Sheridan is a bold enunciation of slavery and a powerful vindication of human rights. So this is what comes of reading. It's exactly what Mr. Auld predicted. The reading of these documents enabled me to utter my thoughts and to meet the arguments brought forward to sustain slavery but while they relieve me of one difficulty they brought on another even more painful than the one of which I was relieved. Exactly what was predicted right. The more I read, the more I was led to abhor and detest my enslavers. I could regard them in no other light than a band of successful robbers who had left their homes and gone to Africa and stolen us from our homes and in a strange land reduced us to slavery alright and later on he says. He goes on in this vain as I writhe under this burden it opened my eyes to the horrible pit but to no ladder upon which to get out. In moments of agony I envied my fellow slaves for their stupidity right. So there's a problem and you might say that once again even though I'm tracing this out as the kind of Franklinian side you can see a Calvinist motif here. There's a certain kind of fall that's at stake here. A fall for what you might call ignorance and to knowledge just as the fall of human of the fall of Adam was from a certain kind of ignorance into knowledge and things get worse and things get painful but ultimately things get better. So, there's that kind of Calvinist logic of being of struggling to achieve something that will be better than when you started out. So that you might say that learning to read is a part of both of these stories fundamentally and for Douglass it's literally kind of a means out of bondage. Learning to read leads to learning to write and you will see in the course of the narrative that there are certain kinds of documents, written documents that Douglass chooses to reproduce here. Take a look at a couple of pages on here and we see kind of in poignant terms what it is that Douglass has to do in order to learn. Top of 2091. During this time my copybook was the board fence, the brick wall and pavement. My pen and ink was a lump of chalk. With these I learned mainly how to write but think about that image right? There's a certain way in which what Douglass is doing is writing on fences and on walls he is literally inscribing himself onto the country around him. Even more than that, I then commence and continue my copying the italics in Webster's spelling book until I could make them all without looking on the book. By this time my little master Thomas had gone to school and learned how to write and had written over a number of copybooks. These had been brought home shown to some of our new neighbors and then laid aside. My mistress used to go to class meeting at the Wilk Street meetinghouse every Monday afternoon and leave me to take care of the house. When left us I used to spend the time in writing in the spaces left in master Thomas' copybook copying what he had written. I continued to do this until I could write a hand very similar to that of Master Thomas. Thus after long tedious effort for years I finally succeeded in learning how to write. Alright. So think of those two images. He's writing his name on chalk all around outside. Inside he's literally taking the cast-offs of white culture alright. The book, the textbook that the little boy doesn't need anymore. These textbooks are written all over almost like American culture, full up right and yet there is room in the margins. There is room for Douglass to re-write, to copy and re-write and inscribe himself in that book as well. You might say that that little moment there at the top of 9021 is again one of these exemplary moments that ought to shout out at you. It sort of embodies within it and it's meant to by Douglass, to embody within it the entire dynamics of this narrative and really of the process of emerging out of slavery. It's another way like his name and like the, you know, generally the ability to insert himself into literary culture in which we might see Douglass taking white culture and making it his ally despite itself. The masters have no idea. If they had any idea that these books that they put out as trash could be made use of by Douglass they would certainly have gotten rid of them. So that's part of the project here and part of the project is not is then to extend that further and to show throughout the narrative that Douglass can make use of that language in terms that would do the Columbian order proud right? I mean the Columbian order is the text within white culture of Republican education; he wants to produce a text that is similarly educative. Alright a text that can educate his wide readership and eventually serve as a kind of, of something that his fellow ex-slaves or once they're no longer slaves that free blacks will be able to learn from and pattern themselves on. In order to achieve that goal I'll say it again he needs to write a text that can be demonstrated to be literary. So there are certain little tricks that he uses. A little bit further on, on 2093 look at this moment. Now give me the ok this is symptomatic of his, you know, he's still learning. He doesn't have full control of language. There are certain. There are certain ways in which he's going to defer to [inaudible] or it doesn't quite have the words for it but look what he does, he's talking about his poor grandmother at the top of 2093. [ Pages turning ] Getting a running start tat the bottom of page, her present owners finding that she was of little value, her frame, top of 2093 already racked with the pains of old age and complete helplessness fast stealing over her once active limbs, they took her to the woods, built her a little hut, put up a little mud chimney and then made her welcome to the privilege of supporting herself there in perfect loneliness thus virtually turning her out to die. If my poor old grandmother now lives, she lives to suffer in utter loneliness. She lives to remember and mourn over the loss of children, the loss of grandchildren, the loss of great grandchildren. They are in the language of the slave's poet, wittier and then he quotes wittier, gone, gone, sold and gone to the rice swamp dank and lone where the slave-whip ceaseless and etcetera. Ok. So he quotes a bit of and you ask why quote Whittier there? I mean he's got a, had a steam rope rhetorically right. He's gotten this gradual emphasis of loss of children, loss of grandchildren, loss of great-grandchildren, why give up his own voice here in the moment and quote the Stanza from Whittier? Well it's kind of like a name check, alright. It. He manages to get Whittier in and Whittier is a recognized abolitionist figure. It becomes a way for Douglass both to signal his affiliations but also you might say to make it clear that he understands some of the dynamics of American literary culture right. He becomes a way of signaling that he is part of that literary culture so there's a kind of interplay here. We give up a little. He gives up a little bit of voice in order to gain something else. Something of the prestige you might say that belongs to Whittier's voice. Well earlier on there's a wonderful moment. [ Pages turning ] No, this is a little bit later on. Let's see. It's the moment in Chesapeake Bay. Let me see if I can find it for you. [ Pages turning ] Guys know where it is? [ Pages turning ] Another one I forgot to note down. [ Pages turning ] [ Coughing ] Sorry about that. I just think it's worth my finding it although. Alright. Here we go. I think it's on, yeah, 2100 to 2101. Alright. This is a famous moment in the text and it's interesting because it is one of the most self-consciously literary moments in the text. So he says here in the second full paragraph on page 2100, our house stood within a few rods of the Chesapeake Bay whose broad bosom was ever white with sails from every quarter of the habitable globe. Those beautiful vessels robed in purest white, so delightful to the eye of freeman were to me so many shrouded ghosts to terrify and torment me with thoughts with my wretched condition right. Now you can say this is a little bit of overwriting here. Right, again he makes use of antithesis. It's a device that he uses constantly throughout the narrative. But listen to this. I have often in the deep stillness of a summer's Sabbath stood all alone upon the lofty banks of that noble bay and traced with saddened heart and tearful eye the countless number of sails moving off to the mighty ocean. The sight of these always affected me powerfully. My thoughts would compel utterance, and there with no audience but the Almighty, I would pour out my soul's complaint. What's a complaint? In literary terms. Is that [inaudible] now? People are always writing complaints in the form of sonnets. Lover will typically write a complaint to and you know as part of unrequited love right. You'll write a complaint to your lover if we're not paying attention or something like that. This is a complaint that he's writing except in the case of it's not unrequited lover. You might say the un. Not being requited by the Almighty. He's trying to ask what it is and he creates a moment of apostrophe here in which he addresses these ships that he sees out there. It's a self-consciously literary moment and he knows it's an apostrophe because he uses the term. I will pour out my soul's complaint in my rude ay with an apostrophe to the moving multitude of ships and he goes on. You and again look at all the antithesis. You are loosed from your moorings and are free. I am fast in my chains and am a slave. You move merrily before the gentle gale and I sadly before the world. I am confined in bands of iron and oh you are freedom's swift-winged angels that fly around the world. I am confined in bands of iron. Oh that I were free. Oh that I were on one of your gallant decks and under your protecting wing. Alas. Betwixt me and you the turbid waters roll. Go on, go on. Oh that I could also go, etcetera, etcetera, etcetera and it goes on quite a t length here alright. It's one of these moments that if you look at 2068 here. [ Pages turning ] Which is in the preface that Garrison's writes to the narrative. He calls our attention to this passage and in doing so you might say he teaches us. Garrison was trying to teach us how to read this narrative. So you might say the fact that Garrison is calling attention to this passage is proof that the passage in some sense does its job. It's overwritten to be sure but he calls attention to itself and it calls attention to itself as literary. So this is what Garrison says on 2068. This narrative contains many affecting incidents, many passages of great eloquence and power but I think the most thrilling one of them all was the description Douglass gives of his feelings as he stood soliloquizing respecting his faith right. Soliloquizing, a word that comes from drama, you know, associated with Shakespeare. Again we're getting across the literary nature of this narrative. The chances of his one day being a freeman on the banks of the Chesapeake Bay viewing the receding vessels as they flew with their white wings before the breeze and apostrophizing them as animated by the living spirit of freedom. Who can read that passage and be insensible to its pathos sense sublimity compressed into it is a whole Alexandrian library of thought, feeling and sentiment. All that can, all that need be urged in the form of expostulation and treaty rebuke against that crime of crimes making man the property of his fellow man right. It's almost as if he's saying about that moment what I said about the narrative as a whole. That in some sense it is itself an argument against the institution of slavery. How could you possibly enslave anybody who can think and feel this? Right. So that's part of the way this works alright. This is exactly the kind of moment we would say Douglass probably learned from the Columbian order. Alright. This is exactly the kind of thing that the order was designed to teach. Alright. So that's one way in which we would say this Franklinian self progresses. It learns to make use of rhetoric and it uses it in a kind of crafty way. Alright. So it's not at all like Wheatley demonstrating that it can be literal but it's even like Franklin. It's kind of using the narrator, the reader's expectations almost again so you remember that moment from Franklin when he talks about well he had this want of religion and he was preserved from the probable go to effects by well what was it? Providence or some guardian angel or maybe just kind, happy, accidental chance, something like that right and then you see how you've been manipulated as a reader. You've gone from Providence to chance which is diametrical opposite and you're kind of like merrily going along because it all seems so reasonable. There are instances where Douglass is cautiously aware of the ways in which he can manipulate the reader as well and that's part of the work of the hallmarks of this book. There's one other thing to mention along with this Franklinian side and it has to do with something that I've already talked about but it has to do with this idea of individualism. I mean one of the things that we've talked about already is that the American liberal tradition in our course most perhaps openly theorized by Ralph Waldo Emerson is really a tradition in which we believe in the individual first and society second. Alright. It's an envision of the value that Winthrop had. Emerson would argue that you are first of all a soul and second of all a member of society and for the most part that being a member of society is not such a good thing right. He thinks of society of as a kind of joint stock company in which every member is a conspiracy against the manhood of the members of the society. Society in other words is a kind of necessary evil that we are forced to create and I said to you that in some sense both the Declaration of Independence and Emerson's thinking grows out of John Locke's understanding of property in the two treatises of government alright, just to remind you. You, property exists because everyone is born with property. That property is your body. You own it. Because you own it you own your labor. Because you own your labor if you mix your labor with nature you create more property and you're entitled to that. Locke designed it as a defense against the kind of absolutism of the monarch that Hobbs is essentially defending in which he basically says we delegate all our agency away and it's for our own good that we do this. Locke want has a different idea in mind. So, Locke says every man has a property in his own person. This nobody had any right to but himself. The labor of his body and the work of his hands we may say are properly his. Right. This might be thought of as ontological individualism. Ontologically, in terms of our states of being we are selves first and members of society second. The self exists priory, to use the language of philosophers from before. People have been less enamored of this. Particularly a whole Marxist [inaudible] have called this possessive individualism because it's a form of individualism that takes as its root idea the idea of possession. You're an individual because you possess your body which is all well and good but some would say you know that kind of reduces things down to a series of market relations. Do we really want our culture to be reduced to a set of market relations which we are conceived of our primary social relations as transacting of business to one another. Certainly Emerson hated that. That's the whole force of his joint stock comment but I think we've seen in the past there are ways in which given the cultural context, economic relations can in fact be what we might think of as progressive or at least they can allow us to think in new ways. Remember those moments in Mary Rawlinson right. It's precisely the moments which she can engage in trade or barter with the natives that they become personalized. They become people. She could engage in contract with them. Once she is able to engage in contract with them, she's able to think of them as people. Now she clamps down at the end of the narrative but those moments are there so we can see that then market treating people which is of market relations can be enabling rather than simply disabling. Now, one of the things we might say about the slave. What is it about this that doesn't work for the slaves? What doesn't the slave get to own the moment he or she is born? His or her body. Right. Possessive individualism in this account suggests what makes a slave a slave is the fact that the slave does not own his or her body and one of the things that we might say about this and the sociologist Orlando Patterson has written at length about this. He said as a result of this, slaves are actually born dead. Socially dead. They do not have a kind of social life because they don't have access to property. The property of themselves. They are owned completely by somebody else and so that's one of things that we want to bear in mind here that these kinds of dynamics here. One of the things that Douglass intuits in this narrative is this dynamic. He doesn't have words for it in the same way but he realizes and this is part of the you might say Franklinian story, the importance of property and the importance of the fact that he is property. So slaves are socially dead. One of the things that Douglass realizes he needs to do if he's going to become alive is to own property and when we think about that is why it is transformative for him. Another thing along those he is able at a certain point to remember to be hired out by a slightly more enlightened master for wages. Not only that, the master thinks oh well you know, you can get to keep a few of them. Keep some of your wages and Douglass has a fundamental realization when that happens. He says the fact that he had the that I had the right to any of them means that I should have had the right to all of them and that the right that his master had to take them was simply because he could compel me to take them. Right. So remember that moment? Why is that? The theory of possessive individualism in a social death explains that. The logical contradiction is if you are socially dead, you can't own property. You can't keep your wages. You can't keep the money. You're not allowed to in some way. It's a contradiction because you are. Because you are property, you can't have property. if your master is willing to let you have some property, to keep some money, it's an admission, one that he shouldn't be making but an admission that he is in fact that you are in fact something other than property and that's why that is transformative for Douglass. Now, again critics of this narrative suggest that there's Douglass doesn't go far enough. It's the same kind of thing people say about Wheatley. Oh come on, Wheatley, why does she have to be Christian. Why couldn't she you know be promoting some kind of revived African religion or something like that. What is all this Christian stuff. Does it mean she's a part of a colonized mind? They would say the same thing with Douglass. He's trying you know why is he not stepping outside of the box of this whole set of market relations in American individualism? Why isn't he a socialist? Why does he trade one form of slavery for another form of slavery, right? From being an actual slave he goes to become a wage slave in the north and I guess what I want to suggest is that's kind of a luxury position right, to be able to make that critique. That in fact, there's a large difference between the actual slavery in which you have no rights and have no ability to own property legally and the fact that you may have to work for a job that you don't like but that you're still able legally to own property. Douglass gladly transformed, trades the former state from the latter state. There's an anecdote that the a kind of brilliant legal thinking named Patricia Williams tells about that has something to do with this I think. She writes a book called the Alchemy of Race and Rights. I think she teaches at Columbia, up at Columbia Law School now and she says there is one moment where she has this friend who named Pitter Gable who is a deconstructionist kind of fancy, critical legal theorist right. He's all about deconstructing the language of rights and they're good friends. They're both going to sublet an apartment. Some of you have had experience. They're going to sublet an apartment in New York over the summer, fine. So he kind of looks at it and calls up these people. They come to an agreement and he doesn't know them but he's saying ok I'm going to do this, send you my money. He shows up. The key's waiting under the mat and it all works out well for him. She's appalled by this. She says how could you possibly do that? She says why didn't you sign something. No, no, signing would infringe on my sense of self. I believe in kind of trust relations. You know, he's a white guy so you know and she thinks wow you know because I'm subletting an apartment from a good friend that I've known for years and we were very careful to create a contract and to sign it and have everything by the numbers and legal and she said the two positions you might say are radically different. You might and one of the things to suggest is that for somebody like Patricia Williams who is an African American whose you know not too long in her genealogy. She is a descendent of slaves. The very ability to define yourself according to contract, the thing that Gable would find restricting is exactly the kind of thing to which African American slaves aspire. The ability to become recognized as contracting agents so what is liberating for her is constricting for him but it's almost like it's a necessary stage for her to go through in order to feel like her subjectivity is doubted. I think there's a similar analogy to be made about Douglass and I would suggest to you that that is why at crucial moments documents are reproduced in this narrative. First off is the pass that he's able to write you know, that he tries to use two to get free the first time. It doesn't work but the ability to write that is marked in the text simply as a kind of stage of his development. Likewise you might say that the act of culmination of all of this imagery, this Franklinian side, all this learning, all of this reading, this writing and all of this coming into self possession through economic means, it culminates on page 2121 in this little indented paragraph. This may certify that I joined together in holy matrimony, Frederick Johnson and Anna Murray as man and wife in the presence of Mr. David Ruggles and Mrs. Michaels. James W. C. Pennington, New York, September 15, 1838. Why would you reproduce that? It's almost like reproducing the marriage contract. It isn't even a piece of Douglass' own writing so what's it doing there? One of the things that we might say about it is it is the moment in which Douglass most fully becomes a person. It shows that he is able to be a contracting agent. He can exist in a situation in which he is able legally to make a contract and not just any kind of contract, the marriage contract, which from medieval times on has been thought of as the very type of the social contract alright. It's a version of a larger contract that you make when you enter into society. There's a contract between the king and his subject which is and often times medieval legal theorists would think of it on the pattern of the contract that the wife makes to the, to the husband right. You give away certain rights. You have certain protections as a result. So in reproducing this, this is the moment when Douglass arrives as a kind of contracting agent and more than that we might think beyond that. The ability to be married in the culture suggests that you are therefore part of that culture and able to reproduce. It's kind of why in a novel of marriage, marriage is almost always the end point. Who gets in? Who's affirmed as part of the tribe? Those who get to marry and there's a sense in which this is therefore presented to us as a kind of trophy, a textual trophy that shows the moment that Douglass has arrived right and it therefore comes as I think as a culmination of all of these different discourses. It brings together the Franklin imagery which has to do with learning and also economic self-possession and it brings it together with the Edward's self because it's a kind of sacred act in which you are joined in holy matrimony. I joined together in holy matrimony so all these things come together at this point. Ok. One last word about this text. Does anybody know how Douglass finally escapes? It's another example of using white culture against itself. In this case the very emblem of nineteenth century American progress. The train. He goes off to work for the day in Baltimore. He forges a pass that says he's a soldier on leave. He manages to board the train and by the time he is revealed to be missing, the train has whisked him up to New York City and he writes about coming up and being in New York City. So you might say it is a version once again in his life, its kind of a [inaudible] of using the very emblems of white culture against itself. Alright. We'll go on from here to talk a little bit about slavery in general as we go on with Harriet Beecher Stowe. |
Open_Ed_Cyrus_Patell_American_Literature | MobyDick_II.txt | [ Silence ] >> All right let's get started. Actually, I want to begin by thanking everybody who had the last class hour free and chose to spend it here in this rather stuffy room with me. Thank you very much. I understand it was a sacrifice, having just walked outside, it's nice out for now at least. So thank you. I think the rest of you, when you hopefully have a chance to watch that lecture online. I asked them to make that available by blackboard as well. Will find that it's less terrible then it might have been had I've been speaking simply to an empty room. So I do appreciate it. And we were speaking a little bit about how for Hawthorne [assumed spelling] romance is a kind of integrated mode that brings things together. Speaking about, thinking about a logic of both and as opposed to a kind of either or of allegory. And thinking about what kinds of constraints might be in place when you apply a logic of both and. Both and means you can't get rid of either term and there are certain ways that in which both than may not be a fully receptacle relation. One part of the, of the binary may end up coloring towards then what's going on elsewhere in that system. And I think that's something we really want to be thinking about as we finally, finally turn our attention back to Melville [assumed spelling]. Bless you, bless you, believe me I sympathize. The, so we're thinking about Hawthorne as kind of an older writer pioneering in romance as far as Melville is concerned. And, and Melvin you remember when we, when we turned to Melville on the second day of class I suggested that we would be thinking about Moby Dick as a kind of framing text cross. And that in many ways we were going to think about it as summing up, encoding into it, in that green black sense of a great novel or great work of art encoding many of its cultural context into its own texterality [assumed spelling]. Decoding of lot of what's going on in the United States in the middle of the nineteenth century. And really in the literary history that takes place in, in the seventeenth to the nineteenth century is that what we've been trying to chart. So this is our moment really to kind of sum things up in the course. And hopefully our reading of Moby Dick will allow us to do that. You remember last time though, we started off by thinking about this statement from Hawthorne and his Mosque. You remember the story that Melville had recently decamped from the York. He's gone up to live in the Berkshires. He meets with Iya Hawthorne in a picnic. He's been writing this whaling voyage. At this time in his career, he's known as somebody that writes narratives of the sea from the most part inflexed by his personal, his personal life story. They tend to be presenting in some since as personal narratives, although there's clearly a, a kind of fictionality [assumed spelling] that's imposed. In fact there's some controversy over rather type p is perhaps too fictionalized or presented under false auspices. But he meets Hawthorne and the story goes that Moby Dick changes as a result, and it starts to do something quite different. And he meets Hawthorne, he goes back and he reads Mosques from the old man and he writes a review. And it's published really, and he writes it a couple of weeks, really quickly, it's published in two parts. And as we said then, it is a kind of program piece for what an American literature might look like. So we haven't read to, I haven't to oppose too many of them on you here. We might have to think of it as something would be an align of manifesto's that would include such things like Bryan's Tricolavic [assumed spelling] Meter Essay, Emerson's [assumed spelling] American Scholar or Self Reliance, Whitman's [assumed spelling] preference to the eighteen fifty five Leagues of Grass. Hawthorne in his Mosque's is that kind of piece. It's extensively a review, but what it really is, is a manifesto for the new kind of literature, an American literature masquerading as we review. He has a particular way of reading Hawthorne. And you know we were just talking in the last hour about that moment which you should all review in the custom house preface when Hawthorne talks about the affect of moonlight on a room. How a room that looks one way, a drearly domestic kind of, very much in cahoots with the kind of numbing that's the banality of life in the nineteenth century in the United States is transformed by the moonlight. Become as what Hawthorne calls as neutral territory, where the imaginary and the actually imaginary they meet and imbuest [assumed spelling] each other with aspects of one another. Melville picks up on that, that imagery of light and dark. So in the course of this essay as this moment he's been talking about the kind of sunny side of Hawthorne. But that doesn't interest him as much, as this, despite of the Indian summer sunlight on the hither side of Hawthorne soul the other side like the dark half of physical sphere is shrouded in the blackness ten times black. But this darkness gives more effect to the ever moving dawn that further advances through it, has circum navigates the world. Let's think about image [inaudible] I mean half the world is always covered in darkness but the world is being circum navigated by darkness. In a sense this is a very, this is a very powerful image for Melville, whether Hawthorne has simply availed himself of this mystical blackness as a means to the wondrous affects he makes it to produce in his lights and shades. Or whether there really lurks in him a touch of pure tainted gloom this I cannot altogether tell. But I'm hoping that by now a pure tainted gloom means something different to you. It could be the state that was induced after your midterms, perhaps. [ Laughter ] Hopefully we'll be moving towards a more frankleneon [assumed spelling] mode of perfectionism if that's the case for the final. But Melville said that certain as it is to have this great power of blackness in him to rise its force from its appeal so that Calvinistic sense of innate depravity an original sin. Right, so remember that. It's one of those things that Melville is doing is looking back to puritan inheritance that he believes that U.S. culture has. Particularly the idea of total depravity as a result of original sin or too it as long as principles flow out of this. And the only thing that happened is that they haven't disappeared. I mean you read Emerson [assumed spelling] and you think, oh, I just retrospected, he builds on circles of [inaudible] of do everything again. Look start again, don't be coward by the pass. Forget original sin, we believe in perfectionism. Thank him, we believe in perfectionism. Hawthorne and Melville both never said, let's wait a minute maybe that's too fast. Like there's the moment I referred to in the last hour of Hester Prim urging the Dimisdale [assumed spelling]to begin all anew. And that's not possible. That can only happen in the enchanted space of the forest that they all have to leave. And she by the end comes to realize that true wisdom suggest that you cannot begin all anew. That you are bound to history, and you can be bound to history in a way that's completely constraining, or you can be bound in a ways that can be constructive and forward moving. But it isn't quite so easy to cut the ties as Emerson might suggest. So Melville is thinking a similar things. Innate depravity an original sin from whose visitations no deeply thinking mind is always unholy free. For the certain modes no man can wade this world without throwing in something, somehow like original sin to strike an uneven balance. And there's something frankleneon perhaps, maybe even Hawthorne it about something, somehow like original sin. Which two hundred years later is not going to be original sin, but we just can't dispose of it. We need something, the puritans was on to something. Something has to take that place, you know in our imaginations, otherwise things are out of balance. The worlds don't work that way, right. If you think about that image of the glow, the glow was always half-and-half. Half-light, half-dark, it's balanced in that way. Original sin is necessary sometimes to keep us conceptually balanced, that's what's Melrose arguing. Remember when I suggested to you earlier on therefore that Melville is kind of haunted by the residue of this puritan imagination that the article as we traced from Bradford and Winthrop [assumed spelling] on, right. So I ask you to then think about the relationship between their modes of using the bible. Winthrop and any of the other puritan thinkers, Wigglesworth for example, even Bradstreet [assumed spelling] or Taylor, would they have a relationship with the bible that is mutually supportive. Winthrop has something to say because there is a book called the bible. And he is then, you might as well say the moments in his sermon are authorized by his engagement with and his apparent knowledge of the bible. He can almost use a kind of shorthand as can Wigglesworth, just to refer you to the bible. Refer you to passages to delegate what he's saying. Right, so the two have a relationship of intertextuality [assumed spelling], you might say that's complimentary. Is that what's going on in Moby Dick? Certainly it has a relationship of intertextuality to the bible among a host of other books, but perhaps first and foremost the bible. Meanings of Moby Dick are not going be Complete if you don't know the book call the bible exist, But what is that relationship. Is it a relationship of Complimentary the way this one is, or is it something else You remember I suggested that Melville inherited from his mother this sense a Calvinistic sense, or Calvinistic approach to Christianity and therefore he knew the bible. I mean scholars have said that you know Melville imagination is bible trends that he can quoted it, you know. Yes ok but from his father a certain kind of skepticism a willingness to play along but we think not entire you know not a really full belief to go thru the rituals but perhaps not believe in the same way. And that tension seem to work its way into Melville's text practically in Moby Dick likewise I told you that the family had a considerable hardship. Alan Melville signs his name without an e that because in some sense after his death. Maria supporting Melville as the eve to destroying, in part to distinguish the family's future from the family's past. They have incredible financial hardship and Melville as well has a deep imbeviance [assumed spelling] to the world of business and finance. He's forced to cease his education in order to help support the family, he tried to be a schoolteacher and then he goes to sea. But, Moby Dick is marked therefore by a number of context, and one of them is the biographical. Another context may I say is the moment in history that we've been talking about. So precisely that moment of eighteen fifty, remember I told you that yet Lameul [assumed spelling] Shaw, who is Melville father in-law was the judge who first upheld the fugitive slave law. And felt in, in return the slave named Thomas Simms back to the south from Massachusetts. All right, so there's that context as well. And then there's a whole context of literary history kind of leading up to this, all right. Melville himself is trying to evoke a since of context for what he's doing. That's why we have these strange chapters at the beginning called anemology [assumed spelling]an extracts. And particularly extracts you might say is setting a kind of intellectual history. And also you might say putting us on notice that this is not going to be a standard novel. This is going to be a novel that has certain kinds of encyclopedic aims. It's going to be a novel that in some since might like the whale swallow up for a variety of previous forms of writing. So these are signals that the novel is sending to us again. And I suggested in the last hour that either the Scarlett Letter is a novel begins three times. It begins with the custom house preface, it begins with the first chapter which is kind of short an anematic [assumed spelling]and focused on the weather beaten door and invites us to a certain kind of allegorical reading which we were able to make immediately problematic. And then it begins again when Hester Prim actually comes in the sub narrative and starts proper. Moby Dick begins three times too, four if you count the dedication to Hawthorne which for us is a crucial context. But begins with it has its anemology section in which you know, it's clearly not just a list of words, right. He's starting to do some actually imaginative writing here, anematic as it might be, there's the abstract section, and then there's Call me Ishmael. Right, that chapter called Loomings that I spent a lot of time on last time, and so one of the things that I want to suggest is that this is a novel that in some since is immediately putting us on notice that's it's going to be a strange kind of novel. It begins three times it seems to set a set of ground rules for us. It's going to have these encyclopedic aims, it's going to be fictional but maybe not entirely fictional. And it's going to have this serious engagement with the bible. So the first of the abstracts is from Genesis, and God created great whales. The first sentence of the narrative proper, call me Ishmael immediately invokes a kind of biblical context. And I suggested that we ought to think kind of carefully about what it means to begin a novel with Call me Ishmael. It's different than my name is Ishmael. This means we don't know what his name is. Call me Ishmael, there's something a little bit chatty about it, maybe, maybe something a little bit pushy you can dramatize it in different ways. Certainly Ishmael suggests the outsider, somebody who is not part of the biblical tradition, the mainstream biblical tradition, although he is crucial to the Muslim tradition. We'll talk a little bit about Melville engagement with Islam perhaps in a couple of lectures from now. Someone who certainly is a wonderer, all right, so these are some of the context, of course you don't know that if you don't know about the bible. So you kind of need to have, this is something that Melville is immediately putting you on notice that he is drawing on a biblical tradition. But that Ishmael thing should give us pause, it's not the same as call me Jacob. I haven't been keeping up with Lost so I have no comment on any of that. [ Laughter ] Should I, should I, like five episodes in the bank, should I keep writing. Yes, ok, I'll blame you. [ Laughter ] No, I always enjoy binging on lost whenever, I know exactly when I want to do that, May tenth at around five pm. [ Laughter ] Ok, so call me Ishmael suggest that we should be a little nervous. And then the implication of death, you know he's being funny but he's trailing after coffins and he's talks about committing suicide or not and there's a kind of weird thing that's going on. So that's part of what I suggested to you. I also told you the story about the asters you remember, Melville hears about the story of the Essex [assumed spelling], the whale ship in the eighteen thirties that was famously sank by a whale. That seemed to sink it with intention, not just by accident or by instinct, but to actually come around and whack the boat deliberately. And at the result of that was that these sailors, the captain, and the first mate were ended up in long boats. The whaling boats, an I'll show you pictures of a lot of what that looks like and maybe a little clip of what's called a Nantucket sleigh ride when the, when the boat gets pulled by the whale. And they do the crazy thing of trying to get to the western coast of South America, rather than the most closer Markazian [assumed spelling], because they are so afraid of meeting cannibals in Markazia. And then of course in one of those dramatic ironies that life often presents, they become cannibals in order to survive. And they eventually make it home but not after becoming the very thing that they sought to avoid. Melville reverses it, he has Ishmael go the other direction and he has him meet the cannibal right away. We'll get our cannibal out of the way, we'll meet the whale later. So there's something funny that Melville is doing from the very beginning with the idea of personal narrative as well. And I suggested to you that at the end of the Looming chapter one of the things that's being evoked as an addition to the kind of weirdly proleptic [assumed spelling] contested election and battle for Afghanistan and all these thoughts about people on all paranormal had after nine eleven, that this was some kind of like weirdly prophetic Nostradamus like book. Beyond that the extent that Ishmael is a kind of cosmopolitan. He's interested in things worldly. What he calls baberish [assumed spelling] shores. He says I love to, this is on page twenty two, I love to sail forbidden seas, for that I'm tormented with an everlasting itch for things remote and landing on baberish shores, coasts not ignoring what is good, I'm quick to perceive the horror and could be social withered would they let me, since it is but well to be on friendly terms with all the inmates of the place one lodges in. World is a madhouse or prison, interesting, right. By reason all, all these good things he goes away on the voyage. And I suggested to you like, why does Melville begin it once, what in Manhattan. I mean once because I've already began the book in Manhattan, so it kind of pays homage because he already began the book in Manhattan. But he's only putting so many aspects of his personal life up for grabs. Why begin it there? Why not just begin in New Bedford or in Nantucket. Why begin in the island of Manhattan. I wanted to suggest, I suggested to you that maybe it's a way of signaling a certain drawing on a cosmopolitan history that already is associated with New York, and maybe signaling a kind of a way of thinking about this novel, which then quickly leaves the scene of cosmopolitan New York and becomes something else. Ok, so I want to take a look at some of the chapters that go further on here and we're think a little bit more about what's going on here. How much objective mind, did I talk to you about The Spouter Inn? Does that ring a bell? Did I show you that picture? All right, we'll do that then. So, The Spouter , so Ishmael goes, right, and he's looking around for a place to stay. He has this tendency you might say to think about the world, at, in not in allegorical terms but in least in symbolic terms. And he always position, I mean he's named Ishmael, it belongs to a tradition that has a sub imperialism were names seem to be significant. This is on page 24 for example, he's looking for a place to stay. Hah, said I, Hah as the flying particles almost choked me, are these ashes from that destroyed city Gomorra but the crossed harpoon and the swordfish, this then must be the sign of the trap, doesn't really want to stay in any of these places. Moving on I came out last keen to a dim sort of out hanging light not far from the dock and heard a fro long creaking in the air. Looking up, saw a swinging sign over the door with a white painting upon it, fairly representing a tall straight jet of misty spray, and these words underneath, The Spouter Inn, Peter Coffin. A coffin is actually a good old Nantucket name. So it's kind of one of these happy accidents from Melville's, what's the name of this guy Peter Coffin, Coffin, Spouter, rather ominous in that particular connection said I, but it is a rather common name in Nantucket they say. And I suppose this Peter here is an immigrant from there. As the night look so dim and the place for the time looks quite enough in the dilapidated little wooden house itself, looked as if it might have been carted here from the ruins of some burnt district. And as the swinging sign had a poverty sort of stricken creak to it, I thought that here was a very spot for cheap lodgings and the best of pea coffee. All right, so he goes into the Spouter Inn. Entering, this is the next page, entering the gabled, entering the gable of the Spouter Inn you found yourself in wide low straggling entry with old-fashioned wainscot reminding one of the bullocks of condemned old craft. On one side hung a very large oil painting so thoroughly besmoked, and every way defaced, that in the unequal cross lights by which you viewed it. It was only by diligent study and a series of systematic visits to it, and careful inquiry of the neighbors, that you could any way arrive at an understanding of its purpose. Now, once again artwork represented in a piece of writing or piece of art we should pay attention. This is a moment of what's called effaces, the representation of visual art in a text. A classic representation it should be, we should think of it as again a moment when the novelist is able to comment on acts of interpretation and therefore suggest to you things about how you maybe should interpret the text that you're reading. So let's see how he comes to meaning here. And this is by the way people think that this is not, not necessarily this one but when Melville went on his trip to Europe, before writing Moby Dick, one of the things he might, he saw was paintings by the, the, kind of the, the romantic portrait, landscape painter Turner. And this seems to be a fairly reasonable representation of the kind of thing that Ishmael is probably seeing here, okay. Such unaccountable masses of shades and shadows, that at first you almost thought some ambitious young artist, in the time of the New England hags, had endeavored to delineate chaos bewitched. But by dint of much and earnest contemplation, and oft repeated ponderings, and especially by throwing open the little window towards the back of the entry, you at last come to the conclusion that such an idea, however wild, might not be altogether unwarranted. Nice Hawthornian [assumed spelling] sort of sentence. So how are we going to go about doing our interpretation. What do we need to do? What most puzzled and confounded you was a long, limber, portentous, black mass of something hovering in the center of the picture over three blue, dim, perpendicular lines floating in a nameless yeast. Let's call those the three dim blue perpendicular lines. A boggy, soggy, squitchy picture truly, enough to drive a nervous man distracted. Yet was there a sort of indefinite, half-attained, unimaginable sublimity about it that fairly froze you to it. Till you involuntarily, involuntarily took an oath with yourself to find out what that marvelous painting meant. Ever and anon a bright, but, alas, deceptive idea would dart you through. It's the Black Sea in a midnight gale. It's the unnatural combat of the four primal elements. It's a blasted heath. It's a hyperborean winter scene. It's the breaking up of the icebound stream of time. But at last all these fancies yielded to that one portentous something in the picture's midst. That found out, once found out and all the rest were plain. But stop, does it not bear a faint resemblance to a gigantic fish, even the great leviathan himself? In fact the artist's design seemed this, a final theory of my own, partly based upon the aggregated opinions of many aged persons with whom I conversed upon the subject. The picture represents a Cape-Horner, so it's a type of whale ship, in a great hurricane. The half-foundered ship weltering there with its three dismantled masts alone visible, and an exasperated whale, purposing to spring clean over the craft, in the enormous act of impaling himself upon the three mastheads. Now, what do we make of Melville? How does he arrive at his meeting? That's the process of interpretation here. If this is supposed to be an act of interpreting of meaning making, how's it working? Does he come up with it all by himself? Yeah. >> [inaudible] >> Sure, that's good, he brings at it from other kinds of angles. He even has to change the lighting a bit. He has to throw open a, you wonder how he's actually standing there, he has to throw open a window in the back some place. What do you mean by other context? >> I don't know like, he's talking about like the winter scene and breaking open the ice, and then >> So there's a lot of interpretive possibilities here. How did he settle on his final meeting? Yeah. >> He [inaudible] asked others opinion. >> So he asked other opinions. So there is a kind of collaborative moment of meaning making here. I have a theory of my own partly based upon the aggregated opinion [inaudible] and then he decides that it's a whale leaping over the mast of a ship. Which seems kind of more outlandish than the other possibilities, again leading you to wonder, to what extent is he, in fact, imposing his own perspective on what's going on. He's whale obsessed, maybe everything looks like a whale to him. He claims to have consulted a lot of people. He claims to have tested out lots of things. This would extensively make it seem like an authoritative rendering of the scene. But I think we should ask ourselves are there limits to the mode of interpretation that's going on here. There's one possible interpretation of course that he doesn't bring up. Does that remind you of anybody? Or of anything, that picture? [ Silence ] No, don't remind you of anything. Yeah. >> The three masses of [inaudible] >> The three masses of sister ships. Ok, it could be Columbus, I guess, maybe, possible, sure. >> [inaudible] >> Yes, it's possible, I mean, whatever we're just speculating here as it turns out Ishmael is [inaudible]. Yeah. >> [inaudible] >> Kind of like go with a, I used to dramatize it this way, ship, whale. [ Laughter ] Sinking. [ Laughter ] But he doesn't say that. Why doesn't he say that? Right, I mean it's a bible, he's bible obsessed. It's a bible obsessed book. Why does he leave out the biblical interpretation? Maybe the professor is just reading in, maybe not, maybe this is Melville having an end joke you might say at Ishmael expense. In any case obviously the scene is an important one. Whatever you make of it, it's a scene about not only interpretation and modes of interpretation. But you might say the subjective nature of interpretation and the limitations of interpretation. And it also might be a way of getting at the thing I was talking about on the second day of the course. Which is, how can a first person novel know more than its first person narrator is that possible. And is Moby Dick an example of that. So that's one of the things we might want to ask over the next few times. Is there a way in which Ishmael, who seems to take up all the air in the room, is it possible that there are things that Ishmael doesn't know yet, that the novel is conveying to us. I suppose that further iteration might be Ishmael older writer knows them but Ishmael character being dramatized here doesn't know them. We want even get into the further level of complexity would be are there things that Ishmael older novel writer still doesn't know that Tex knows or Melville knows. We'll get to that later, anyway I want you to be in tune to this, there are many of these in Moby Dick. Moments when we ought to be saying, oh this is a scene, it's a inset story, it's a kind of dramatization when the novel is self consciously reflecting on its own means of generating representations, and of the ways in which those representations are likely to be interpreted. Alright, do we need that, we don't need that, don't want that, ok so Ishmael goes right, he goes in to the inn and he meets Peter Coffin and he is trying to figure out where to stay. And Peter Coffin says, well there's not really a place for you to stay. Well you could stay with this harpooneer. Ishmael doesn't really want to do that. Bottom of 29, no man prefers to sleep two a bed. In fact, you would a good deal rather not sleep with your own brother. I don't know how it is, but people like to be private when they are sleeping. And when it comes to sleeping with an unknown stranger, in a strange inn, in a strange town, and that stranger a harpooneer, then your objections indefinitely multiply. Nor was there any earthly reason why I as a sailor should sleep two to a bed, more than anybody else, for sailors no more sleep two in a bed at sea, than bachelor Kings do ashore. To be sure they all sleep together in one apartment, but you have your own hammock, and cover yourself with your own blanket, and sleep in your own skin. So, he goes to plan B. Landlord I changed my mind about that harpooneer, I can't stay with him. I'll try the bench here. So he goes and tries to sleep on the bench, this is a scene of comedy, alright so one of the things to know then about what Melville is invoking is, that there is a kind of urging like narrative voice that Ishmael has. It should remind us a little bit of Geoffrey Crayon and the Voyage perhaps. Irving, Ishmael had, he just seems a little bit like a kind of hypochondriac. He seems a little bit depressive, but there is also another stream of magazine writing that Melville seems to be invoking. It's called down east humor. Down east humor typically has somebody with, who is kind of like a country bumpkin coming to the city and making a fool of himself. And it pretty much uses a kind of ridiculous Yankee biblical names like, Hezekiah, or Ezekiel, or Ishmael, things like that. That's what's being invoked in this chapter. All right, so we get a kind of slapstick moment here. This is the start of it, he's like, I'm not going to sleep, Melville says okay, I'll shave down that, the thing that make him more comfortable, start shaving it down in between service and he hears a knock, which kind of makes it worse and he says forget it, I'll sleep with the damn harpooner. So he goes and he sleeps with the harpooner. And I want you to look the way in which the scene progresses, because it should be telling you something about the way that Ishmael thinks. And is it a part that tells you something about the way that Ishmael thinks, it should make, should give you an idea whether this is a narrator that you can trust, or not. So he goes back, bottom of 32. There, said the landlord, placing the candle on a crazy old sea chest that did double duty as a wash-stand and centre table, there, make yourself comfortable now and good night to ye. I turned round from eyeing the bed, but he had disappeared. You know what happens later own, but I always had like a picture in my mind that he's kind of got his eye on that keyhole looking and listening at the doors to see what's going on. Because clearly there's a since in which Peter Coffin is acting as a kind of stage manager here. This is a moment of dramatic irony which he knows things that Ishmael doesn't know and he's, he's you know setting up a scene you might say that's going to play out in front of us. Folding back the counterpane, right, the comforter, I stooped over the bed. Though none of the most elegant, it yet stood the scrutiny tolerably well. I then glanced around the room; and besides the bedstead and centre table, could see no other furniture belonging to the place, but a rude shelf, the four walls, and a papered fireboard representing a man striking a whale. Of things not properly belonging to the room, there was a hammock lashed up, and thrown upon the floor in one corner; also a large seaman's bag, containing the harpooneer's wardrobe, no doubt in lieu of a land trunk. Likewise, there was a parcel of outlandish bone fish hooks on the shelf over the fire-place, and a tall harpoon standing at the head of the bed. So far, so good, all things within a typical seaman's experience. But what is this on the chest? I took it up, and held it close to the light, and felt it, and smelt it, and tried every way possible to arrive at some satisfactory conclusion concerning it. It might remind you of Edger Huntley and his box, right, he is going to try to use empirical investigation, rational experience to figure out what this thing is. He can't, it's outside the realm of his experience. So again we might, in tying things back, you know he talks about the painting is marvelous, he talks about the novel is going to depict a wonder world. There's a since in which Melville is also drawing on that discourse of the wondrous and the marvelous that we say in some of the sentiment narratives. And Ishmael portrays the same kind of logic that someone like Columbus does in his letters. We have a template, we apply it to experience. We try to shoehorn experience into it even when it doesn't quite fit. I can compare it to nothing but a large door mat, ornamented at the edges with little tinkling tags something like the stained porcupine quills round an Indian moccasin. There was a hole or slit in the middle of this mat, as you see the same in South American ponchos. But could it be possible that any sober harpooneer would get into a door mat, and parade the streets of any Christian town in that sort of guise? I put it on, to try it, and it weighed me down like a hamper, being uncommonly shaggy and thick, and I thought a little damp, as though this mysterious harpooneer had been wearing it of a rainy day. I went up in it to a bit of glass stuck against the wall, and I never saw such a sight in my life. I tore myself out of it in such a hurry that I gave myself a kink in the neck. All right, again it's a common theme. He sees this pretty mat, he's putting it on and he's acting like an idiot. But he's trying to figure it out. Ok, yes in bed, and then, bottom of the page. I heard a heavy footfall in the passage, and saw a glimmer of light come into the room from under the door. Lord save me, thinks I, that must be the harpooneer, the infernal head peddler. Because he has been told that this guy has been going off and selling heads around the town. But I lay perfectly still, and resolved not to say a word till spoken to. Holding a light in one hand, and that identical New Zealand head in the other, the stranger entered the room, and without looking towards the bed, placed his candle a good way off from me on the floor in one corner, and then began working away at the knotted cords of the large bag I before spoke of as being in the room. I was all eagerness to see his face, but he kept it averted for some time while employed in unlacing the bag's mouth. This accomplished, however, he turned around when, good heavens, what a sight, such a face. It was of a dark, purplish, yellow color, here and there stuck over with large blackish looking squares. This is bad, but know where in the realm of my understanding right. Yes, it's just as I thought, he's a terrible bedfellow. He's been in a fight, got dreadfully cut, and here he is, just from the surgeon. Ok frame of explanation one. But it doesn't quite fit. But at that moment he chanced to turn his face so towards the light, that I plainly saw they could not be sticking plasters at all, those black squares on his cheeks. They were stains of some sort or other. At first I knew not what to make of this, but soon an inkling of the truth occurred to me. For readers of Tepee [assumed spelling], they would notice this, this is exactly the thing that the narrator in Tepee is afraid of. That these people, one of things while he's most afraid of that they're going to eat him. But beyond that he's afraid that the cannibals amongst, what he thinks are cannibals, amongst whom he has, will tattoo him and disfigured him, especially his face. He's happy to have tattoos everywhere but not the face. I remembered a story of a white man, a whale man too, who, falling among the cannibals, had been tattooed by them. I concluded that this harpooneer, in the course of his distant voyages, must have met with a similar adventure. And what is it, thought I, after all. It's only his outside, a man can be honest in any sort of skin. Now that is a nice platitude. And in a way if you think about it, especially given the context of eighteen fifty and racism and slavery and that's not a bad thing to be thinking about it seems like, ideologically progressive. Can we take it seriously in this narrative context? That's part of the challenge of these early chapters. There full of comedy, the comedy subvert what we might think of as cosmopolitan principles, or principles of toleration equality of the novel. And Ishmael seems to be putting forward. What's the relationship between these moments of philosophical thought and comedy? To be sure it might be nothing but a good coat of tropic, but he said, but then what to make of his unearthly complexion, that part of it, I mean lying roundabout can come completely independent of the squares of tattooing. To be sure, it might be nothing but a good coat of tropical tanning, but I never heard of a hot sun's tanning a white man into a purplish yellow one. However, I had never been in the South Seas; and perhaps the sun there produced these extraordinary effects upon the skin. Right again, trying to be rational, hycephic [assumed spelling], empirical. Now, while all these ideas were passing through me like lightning, this harpooneer never noticed me at all. But, after some difficulty having opened his bag, he commenced fumbling in it, and presently pulled out a sort of tomahawk, and a seal-skin wallet with the hair on. Placing these on the old chest in the middle of a room, he then took the New Zealand head, a ghastly thing enough, and crammed it down into the bag. He now took off his hat, a new beaver hat, when I came nigh singing out with fresh surprise. There was no hair on his head, none to speak of at least, nothing but a small scalp-knot twisted up on his forehead. His bald purplish head now looked for all the world like a mildewed skull. Had not the stranger stood between me and the door, I would have bolted out of it quicker than ever I bolted a dinner. Again, that's a kind of therovian [assumed spelling]moment right, but it's part of the comedy here. So look what's going on Ishmael is trying to make himself comfortable. He's put himself in a new situation, thinks he can handle it. He looks for the most comfortable frame of explanation. Staving off what he knows is the truth, and what we already have realized is the truth about this person here. Even as it was, I thought something of slipping out of the window, but it was the second floor back. I am no coward, but what to make of this head peddling purple rascal altogether passed my comprehension. Ignorance is the parent of fear, and being completely nonplussed and confounded about the stranger, I confess I was now as much afraid of him as if it was the devil himself who had thus broken into my room at the dead of night. In fact, I was so afraid of him that I was not game enough just then to address him, and demand a satisfactory answer concerning what seemed inexplicable in him. Alright, so he's going on, he's got this tomahawk, Ishmael is scared you know, blah, blah, blah, blah, blah. We go on to the next, let's go on to the next page. We'll go to the bottom of the page, next page. In the interval I spent in deliberating what to say, was a fatal one. Taking up his tomahawk from the table, he examined the head of it for an instance, and then holding it to the light, with his mouth at the handle, he puffed out great clouds of tobacco smoke. The next moment the light was extinguished, and this wild cannibal, tomahawk between his teeth, sprang into bed with me. I sang out, I could not help it now, and giving a sudden grunt of astonishment he began feeling me. Stammering out something, I knew not what, I rolled away from him against the wall. And then conjured him, whatever or whatever he might be, to keep quiet, and let me get up and light the lamp again. But his guttural responses satisfied me at once that he but ill comprehended my meaning. Who e debel you? He at last said, you no speak e, dam me, I kill e. And so saying the lighted tomahawk began flourishing about me in the dark. Landlord, for God's sake, Peter Coffin, shouted I, landlord, watch, Coffin, angels, save me. Speak e, tell e me who e be, or dam me, I kill e. Again growled the cannibal, while his horrid flourishings of the tomahawk scattered the hot tobacco ashes about me till I thought my linen would get on fire. But thank heaven, at that moment, and I tell you, he's outside at the door listening, the landlord came into the room light in hand, and leaping from the bed I ran up to him. You can imagine him doing a Yogi Barra and like, you know putting all his legs around him perhaps. Don't be afraid now, said he, grinning again, Queequeg here wouldn't harm a hair of your head. Stop your grinning, shouted I, and why didn't you tell me that that infernal harpooneer was a cannibal? I thought ye know'd it, didn't I tell ye, he was a peddling heads around town, but turn flukes again and go to sleep. Queequeg, look here, you sabbee me, I sabbee you this man sleepe you, you sabbee? [ Laughter ] Humph, me sabbee plenty. [ Laughter ] Grunted Queequeg, puffing away at his pipe and sitting in bed. You gettee in, he added, motioning to me with his tomahawk, and throwing the clothes to one side. And now look at what's happened. Think about Ishmael train of thought. He's tried to make since of the situation in which things are just beyond his experience. He has no idea what these cannibals possessions are, he tries to keep the knowledge that he's with a cannibal off as long as possible. He finally has to admit that's what it is. And then all of a sudden there's a really quick about face. He really did this in not only a civil but a really kind and charitable way. I stood looking at him for a moment. For all his tattooings he was on the whole a clean, comely looking cannibal. What's all this fuss I have been making about, thought I to myself, the man's a human being just as I am. He has just as much reason to fear me, as I have to be afraid of him. Better sleep with a sober cannibal than a drunken Christian. Ok, that sounds like good advice, I guess. [ Laughter ] Landlord, said I, tell him to stash his tomahawk there, or pipe, or whatever you call it. Tell him to stop smoking, in short, and I will turn in with him. But I don't fancy having a man smoking in bed with me. It's dangerous. Besides, I ain't insured. So he makes a joke. He takes the thing that's worrying him an deflates attention away from it to something else that's extensively the thing that worries him the most. Now, again this is just a little thing, but its characteristic, and we'll see this in a moment, of the way in which the novel shows us characters who for various purposes of persuasion, shift the ground of debate from one arena into another. So he's worried about cannibalism but he claims to be worried about, you know, smoking in bed. And this you might say is a kind of technique that we will see other people use in novel. The novel is sort of making us attune to it at this particular moment. This being told to Queequeg, he at once complied, and again politely motioned me to get into bed, rolling over to one side as much as to say, I won't touch a leg of ye. Good night landlord, said I, you may go. I turned in, and never slept better in my life. Now, I want to ask you what you think of that scene. Alright its meant to be funny. So that's one of the signals that the novelist that the novelist done, this can actually be a funny novel. If you can get beyond the fact that it's all these pages and it's this nineteenth century American classic that everyone talks about. And it's been assigned in this ridiculous course that's going to have an exam at the end, if you can get beyond all that. [ Laughter ] You can realize it's actually fun to read this damn thing. And its irreverent and has some social overtones which push the boundaries of, of the exceptual ideas in the nineteenth century and it is blasphemous in many places. It makes fun of the bible, it has a lot of kind of dirty jokes that are based on biblical culture. And the fact that people probably don't bother to look things up, or don't know it quite as well as Melville does. Ask yourself how we are supposed to take this idea. Better sleep with a sober cannibal, than a drunken Christian. Are we supposed to take that straight up, or with a grain of salt. Are we suppose to think that Ishmael has come around to the right way of thinking that this is a kind of image of cosmopolitan tolerance, or has he been too quick to rationalize things. Has he not actually thought all this through, is he too quick to jump into something new. Is there a problem here with the narration that we're seeing. Ok, that's one seen I think is somewhat iconic for this narrative. And I think it says a lot of things in play for us to be attune to as we go on. Ok, let's take a look at the chapel, the chapter that's called chapter seven. The cenotaphs, I mean The Chapel. And what it does is present us with a set of cenotaphs. A cenotaph is a kind of funereal marker in the absence of a grave. So he goes to the whale man's chapel there in New Bedford. And you know like Frederick Douglass reproducing his past and his marriage certificate, he attempts to reproduce for us the cenotaphs. So again, like the boggy, soggy, switchy picture, this a kind of, I don't know, sort of meditictual [assumed spelling] moment, in which we're asked to consider something that in this case not an artwork but something has, that has the same, where we have the same kind of relation to it that Ishmael has to the artwork. In other words, he is also a spectator looking at these things. And he's also looking at the people who are looking at these things. And what would we, what could we find out about them. For one thing if you are about to go on a whaling mission I suppose they should give you pause. Sacred to the memory of John Talbot, who, at the age of eighteen, was lost overboard near the Isle of Desolation, off Patagonia, November first eighteen thirty six. This tablet is erected to his Memory by his sister. Sacred to the memory of Robert Long, Willis Ellery, Nathan Coleman, Walter Canny, Seth Macy, and Samuel Gleig [assumed spelling], forming one of the boats crews of the Ship Eliza, who were towed out of sight by a whale, on the off shore ground in the pacific, December thirty first, eighteen thirty nine. This marble is here placed by their surviving shipmates. Sacred to the memory of the late Captain Ezekiel Hardy, who in the bows of a boat, of his boat, was killed by a sperm whale on the coast of Japan, August third eighteen thirty three. This tablet is erected by his memory, to his memory by his widow. These are men who disappeared at sea. Their stories aren't necessarily incomplete, all we can sort of tell about them, the bare facts, and there put there on the wall. So the novel is inviting us to think about certain things. One of the things that I want to suggest to you as a possibility, is that maybe what this novel is, is in fact one of these things. It's a cenotaph. If you haven't gotten to the end yet, I may have spoiled some part of it for you. It's a cenotaph that does more than a cenotaph possibly could. In other words, it's as if what if we looked at one of these stories and were able to tell it in all of its fullness. So there's a kind of memorial function that this novel has. But the other thing we might say about it is that it may well be a record of a trauma. Think about a cenotaphic function. These are people who have lost love ones at sea, they don't know exactly what happened to them. Somebody was killed by a whale, body disappeared or something. They were towed out of sight. God knows what happened to them. We know about the Essex, we took that type of thing didn't happen to them. We need stories, but more than that we need a place communally to morn them. That's what these things served. There's a kind of communal function that these cenotaphs have. Maybe there's a cenotaphic urge within the novel itself. Its self forming a kind of communal function as a way of dealing with trauma. So one of the things I want to suggest to you is that maybe this is a novel that would benefit very much from using a kind of interpreted lens that today is a, is identified with trauma studies. What does it mean to be a survivor? That's part of what is at stake in this novel. In this chapter I think suggest that to us. Ok, so what, I'm going to try to point out things that I want you to use as tools for interpreting as we go a little bit further on. I want spend time on the pulpit and the sermon today. Instead I would like to look at the chapter that's called A Bosom Friend, this is on chapter ten, this is chapter ten. Now again I suggested to you in some since the novel is kind, this is, is a thought experiment. So it is going to be dramatizing a number of philosophical ideas and asking us to think deeply about that. So one of the things I want to suggest to you, is that it is a novel that poses a lot of what I would call heuristics, or a lot of what ifs? So here is one of them on page fifty five. We're starting with think about Queequeg alright. He returns from The Spouter Inn from the chapel and he finds that Queequeeg is now looking at a book, assuming the bible, and kind of, these things become defamiliarized as if western culture becomes defamiliarized when we see it through Queequeeg's eyes, or at least when we watch Queequeeg consuming it. And this gets Ishmael to thinking. So, this is into the second, first full paragraph on fifty five. Through all his unearthly tattooings, I thought I saw the traces of a simple honest heart. And in his large, deep eyes, fiery black and bold, there seemed tokens of a spirit that would dare a thousand devils. And besides all this, there was a certain lofty bearing about the Pagan, which even his uncouthness could not altogether maim. He looked like a man who had never cringed and never had had a creditor. Whether it was, too, that his head being shaved, his forehead was drawn out in freer and brighter relief, and looked more expansive than it otherwise would, this I will not venture to decide, but certain it was his head was phrenologically [assumed spelling] an excellent one. Right, this is the moment when part of the way of thinking about the relationship between appearance and capabilities, obviously linked to a discourse of race in the nineteenth century. For now it just seems to look at the shape of the heads and the place of indentations in it and think that you can tell something about the capabilities about the person who had that particular shape. It may seem ridiculous, but it reminded me of General Washington's head, as seen in the popular busts of him. It had the same long regularly graded retreating slope from above the brows, which were likewise very projecting. Like two long promontories thickly wooded on top. Queequeg was George Washington cannibalistically developed. Now, again I think this is a little moment when I think it is again an invitation to a thought experiment. What would it mean for George Washington to be developed in a cannibal context? Alright, what would it mean for someone who is a cannibal to be a better example of Christianity than most Christians, who are you know drunken and misbehaving and doing whatever else, right. These are the kinds of little thought experiments that I think the novel is inviting us to consider all the way through. And that's one of the things that I wanted to point out to you here. Now, this chapter is interesting and iconic as well because it gives us another example of Ishmael's religious thinking. And you might say his commitment to toleration. He's trying to understand Queequeg's different practices right, and so he talks to him about them. And then at the top of fifty seven we have this, it's the end of chapter ten. I was a good Christian. Born and bred in the bosom of the infallible Presbyterian Church. And we're going to talk a lot about the Presbyterianism here, but it has, for our purposes it has certain things in common with the period and culture that we look at. And the footnote will tell you why this particular passage was a little bit controversial after the novel was published. How then could I unite with this wild idolater in worshipping his piece of wood? Right, I mean if your cosmopolitan you want to reach out, you want to bridge gaps, you want to. But what is worship? Thought I. Do you suppose now, Ishmael, that the magnanimous God of heaven and earth, pagans and all included, can possibly be jealous of an insignificant piece of black wood, of black wood. But what is worship? To do the word, will of God? That is worship. And what is the will of God? To do to my fellow man what I would have my fellow man to do to me. That is the will of God. Do onto others as you would have them do onto you. That goes by a name. What is that? >> The Golden Rule. >> The Golden Rule. Yes, do onto others as you would have them do onto you. Ok, now Queequeg is my fellow man. And what do I wish that this Queequeg would do onto me, do to me? Why, unite with me in my particular Presbyterian form of worship. Consequently, I must then unite with him in his, ergo, I must turn idolater. So I kindled the shavings, helped prop up the innocent little idol, offered him burnt biscuit with Queequeg. Salaamed before him twice or thrice, kissed his nose, and that done, we undressed and went to bed, at peace with our own consciences and all the world. But we did not go to bed without some little chat. How it is I know not, but there is no place like a bed for confidential disclosures between friends. Man and wife, they say, there open the very bottom of their souls to each other, and some old couples often lie and chat over old times till nearly morning. Thus, then, in our hearts honeymoon, lay Queequeg, laid I and Queequeg a cozy, loving pair. Now that is a very juicy an ripe set of paragraphs which we can think about a lot but I want to ask not about the ending of it, but the beginning of it. What's wrong with the logic that Ishmael implies? Complete with Argo, looks and logistic. What's wrong with it? Golden rule invoked. Golden rule says, do onto others as you will have them do onto me, that's the rule of God. So, he, I want him to be like me, I'm going to be like him. What's wrong? Yes, all the way in the back. >> He's using like syllogistic [inaudible] in order to take one identical [inaudible] and make it [inaudible] against the other one. >> Ok, what's the other one. >> The, isn't that the First Commandment. >> Which is? >> You basically don't worship idols [inaudible]. >> So, yes the First Commandment is, I am the Lord thy God, thou shall have no other God's before me. When Jesus revises the Old Testament and recreates the laws, he doesn't take that one away. Right, you've heard of Jesus would say, you've have heard it say, an eye for an eye a tooth for a tooth, but I say to you, turn the other cheek. The Golden Rule comes out of that. But it's still second, the first is always, I'm the Lord thy God. One of things that you might say is that, that Ishmael here is perhaps having, making a joke, or Melville is making, using Ishmael to make a joke about popular understandings about literature. I mean and a popular understanding of the bible right. What's the most famous thing, The Golden Rule? We talk about the Golden Rule because it's hard to do, but also because maybe we take for granted the First Commandment. Of course no other Gods before me, would never apply the Golden Rule in this context right. So what does it mean to ignore the [inaudible]. I mean this is an example of blasphemous thinking set in a kind of comic way. That should give us a little, we should think about what's at stake here. What does it mean that our narrator is willing to write this, in a since believe this, and try to get us to believe this. Is he pulling our leg, is he egging us on, do we just say, Oh yes on the other hand it's also a very nice statement of tolerance and cosmopolitan principles. Is the comic way and the kind of slightly dodgy logic, does that, does that invalidate the idea of toleration that comes along with it. Is this a sign, maybe that Ishmael and the Devil can quote scriptures for their purposes, should we become more suspicious of Ishmael as a result of this. Again, I think these are the moments in the novel that questions are being opened up. We might link this to the first acquaintance with Queequeg right. There's a similarity in the logic between, a kind of rationalization that's going on with, Better sleep with a silver cannibal than a drunken Christian, and I must turn Idolater. And this is also the moment when Queequeg an Ishmael basically become this cozy loving couple. I mean, they assume the character of an old married couple, and as one of, one of the things to note as, as we embark on a voyage in which they are basically going to be no women that there is a kind of invocation of what we would think of as homo social relations. Relations between men that are complete without women. And we might want to think about that, should that give us pause. Should that be something we understand as a kind of radical suggestion about the future of society. Is there a literary historical way of thinking about it, I mean, maybe this is Melville's way of dramatizing the necessity, to get away from all those damn scribbling women, right? The way Hawthorne talks about it, maybe this is one of the things he's promoting. What would it mean to have a world without women, would it be a better one or worse one? Some of these again, things that we will go on, the homo social train of thought you might say is something that starts here with Queequeg and get continued later on. And these questions about the advocacy of tolerance no matter how you get to it, is there something disturbing about Ishmael modes of thinking, what does it mean to be able to play fast and loose with the bible? All these are questions that the novel continues to explore as it moves forward. Alright, we'll start, we'll end with one more little bit here. This is a chapter that's called, A Ship, here, and this is a chapter that's funny also, but it takes some of the patterns that we've seen already, especially this shifting of ground from one mode of discourse into another. And takes, and has to be taken a little bit more seriously, and part of what's at stake you might say is the cultural uses of religious modes of thought and discourse and speech. So they are in bed again and there concocting their plans for the morrow. But to my surprise and no small concern, Queequeg now gave me to understand, that he had been diligently consulting Yojo, the name of his black little god. And Yojo had told him two or three times over, and strongly insisted upon it everyway, that instead of our going together among the whaling fleet in harbor, and in concert selecting our craft, instead of this, I say, Yojo earnestly enjoined that the selection of the ship should rest wholly with me, in as much as Yojo purposed befriending us. And, in order to do so, had already pitched upon a vessel, which, if left to myself, I, Ishmael, should infallibly light, he repeats the word that he uses to talk about Presbyterianism, infallibly light upon, for all the world as though it had turned out by chance. And in that vessel I must immediately ship myself, for the present irrespective of Queequeg. This is providential logic, what does it mean that comes out of a little block of wood. What do we think about the relationship between faitiveness [assumed spelling]and free will here? These are huge topics for the culture, huge topics for the novel as well. Ishmael has already talked about being part of a larger programs set by the faiths in the first chapter. This is another comic invocation of province. Are we supposed to take it seriously or not, because of the comedy? Anyway he goes and looks at all these ships, and he finally does find one. And this is on page sixty, page seventy of the novel. [ Silence ] He's talking about the Pequad, which he has, I suppose we should go back. On page sixty nine he talks about some other ships that disturb him because of their names, The Devil Dam, The Tit Bit, The Pequad. Devil-dam, I do not know the origin of, Tit-bit is obvious. [ Laughter ] A little humor in that, aromatic actually. Pequot you will no doubt remember, was the name of a celebrated tribe of Massachusetts Indians; now extinct as the ancient Medes. Yes, because the puritans killed them. So what does it mean, you know again, The Spouter Inn, what does it mean to choose the name of this. Ok fine, does name mean something, or do names not mean anything. And when he goes on he decides that, that one is ok, and he goes and he meets Captain Peleg. Top of seventy. Old Captain Peleg, many years her chief-mate, before he commanded another vessel of his own. And now a retired seaman, and one of the principal owners of the Pequot, this old Peleg, during the term of his chief mate ship, had built upon her original grotesqueness, and inlaid it, all over, with a quaintness both of material and device, unmatched by anything except it be Thorkill-Hake's carved buckler or bedstead. This was appareled like any barbaric Ethiopian emperor, his neck heavy with pendants of polished ivory. She was a thing of trophies. This was a kind of barbaric ship, it's all festooned with ivory and whale bits. It almost look liked this kind of, it's something deeply barbaric about the way that it looks. Ok, so he goes up here on the quarter deck, because where the captains are. He goes up there to the quarter deck of the Pequot and he talks about, talks to the two people that are there. This is the top of seventy one. Is this the Captain of the Pequot, said I, advancing to the door of the tent, which was pitched there. Supposing it be the captain of the Pequot, what dost thou want of him, he demanded. I was thinking of shipping. Thou wast, wast thou? I see thou art no Nantucketer [assumed spelling], ever been in a stove boat? No, Sir, I never have. Dost know nothing at all about whaling, I dare say eh? Nothing, Sir, but I have no doubt I shall soon learn. I've been several voyages in the merchant service, and I think that, Merchant service be damned. Talk not that lingo to me. Dost thou see that leg? I'll take that leg away from thy stern, if ever thou talkest [assumed spelling] of the merchant service to me again. Merchant service indeed, I suppose now ye feel comfortable and proud of having served in those merchant ships. But flukes man, what makes thee want to go a whaling, eh? It looks a little suspicious, don't it, eh? Hast not been a pirate, hast thou? Didst not rob thy last Captain, didst thou? Dost not think of murdering the officers when thou get test to sea? I protested my innocence of these things. I saw that under the mask of these half humorous innuendoes, this old seaman, as an insulated Quaker Nantucketer, was full of his insular prejudices, and rather distrustful of all aliens, unless they hailed from Cape Cod or the Vineyard. Now again, in so far as Ishmael is going to be this kind of voice of cosmopolitism hailing from New York. He's immediately in conflict with these Quakers here as [inaudible] to be somewhat insorbed [assumed spelling]. And you'll see that there Quakers that seem to have a lot in common with Puritans. But what takes thee whaling? I want to know that before I think of shipping ye. Well, I want to see what whaling is. I want to see the world, again, a cosmopolitan impulse. Want to see what whaling is, eh? Have ye ever, have ye clapped eye on Captain Ahab? Who is Captain Ahab, sir? Aye, aye, I thought so. Captain Ahab is the Captain of this ship. I am mistaken then. I thought I was speaking to the Captain himself. Thou art speaking to Captain Peleg, that's who ye are speaking to, young man. It belongs to me and Captain Bildad to see the Pequot fitted out for the voyage, and supplied with all her needs, including crew. We are part owners and agents. But as I was going to say, if thou wantest to know what whaling is, as thou tellest ye do, I can put ye in a way of finding it out before ye bind yourself to it, past backing out. Clap eye on Captain Ahab, young man, and thou wilt find that he has only one leg. Ok, so this is the thing we are going to find out about Captain Ahab, he has only one leg, remember that. What do you mean, sir? Was the other one lost by a whale? Lost by a whale. Young man, come nearer to me, it was devoured, chewed up, crunched by the monstrousest parmacetty that ever chipped a boat, ah, ah. [ Laughter ] Right o, [ Laughter ] I was a little alarmed, [inaudible] alarmed by his energy. [ Laughter ] Perhaps also a little touched at the hearty grief in his concluding exclamation. Alright, so he goes on and he says this. Very good, now, art thou the man to pitch a harpoon down a live whale's throat, and then jump after it? Answer quick, I am, sir, if it should be positively indispensable to do so. Not to be got rid of, that is, which I don't take to be the fact. Good again. Now then, thou not only wantest to go a whaling, to find out by experience what whaling is, but ye also want to go in order to see the world? Was not that what ye said? I thought so. Well then, just step forward there, and take a peep over the weather bow, and then back to me and tell me what ye see. So he says go to the back sir, take a look, go to the front, take a look. Ok, well, what's the report, said Peleg when I came back. What did ye see? Not much, I replied, nothing but water, considerable horizon though, and there's a squall coming up, I think. Well, what does thou think then of seeing the world? Do ye wish to go round Cape Horn to see any more of it, eh? Can't ye see the world where you stand? Now this is funny I suppose because something in that right, that's a version of Emerson's idea that traveling is a fool's paradise. It's not a good enough reason says Peleg to want to see the world. The world mostly looks like that. You go on a whaling ship that's what you're going to see mostly. A lot of horizons a lot of open ocean. Why do you really want to go. Well ok he finally lets him sign up and then finally we get this, and this is extensively about Bildad and Peleg but really it should be, were getting a foreshadowing of Ahab himself, this is on page seventy three. Now, Bildad, like Peleg, and indeed many other Nantucketers, was a Quaker, the island having been originally settled by that sect. And to this day its inhabitants in general retain in an uncommon, in an uncommon measure peculiarities of the Quaker, only variously and anomalously modified by things altogether alien and heterogeneous. For some of these same Quakers are the most sanguinary of all sailors and whale-hunters. They are fighting Quakers, they are Quakers with a vengeance. And then again he's punning here right, an almost oxymoronic, fighting Quakers, Quakers are suppose to be pacifists. There are Quakers with a vengeance, which means what, they're really, really, Quaker, or there Quakers who have, who Labarbera [assumed spelling] Chilling [assumed spelling] wrote. One of the things we might say here is what Melville is dramatizing for us is exactly the dynamics of dominant residual in emerging, right. These Quakers have been mutated by their contact with others, with these barbarics [assumed spelling] customs that they have become accustomed too by whaling, by whaling itself, they've changed. So that there are instances among them of men, who, named with Scripture names, a singularly common fashion on the island, and in childhood naturally imbibing the stately dramatic thee and thou of the Quaker idiom. Still, from the audacious, daring, and boundless adventure of their subsequent lives, strangely blend with these un outgrown peculiarities, a thousand bold dashes of character, not unworthy a Scandinavian sea king, or a poetical Pagan Roman. We're invoking Norse mythology, or epics, or perhaps classical tragedy. And when these things unite in a man of greatly superior natural force, with a globular brain and a ponderous heart, who also has by the stillness and seclusion of many long night-watches in the remotest waters, and beneath constellations never seen here at the north, been led to think untraditionally and independently. Again, this might remind us of Hester Prim thinking to herself by her seaside cottage. Thinking by herself of the pressures that may have been done to her, comes to think things she's really not suppose to. Receiving all nature's sweet or savage impressions fresh from her own virgin voluntary and confiding breast, and thereby chiefly, but with some help from accidental advantages, to learn a bold and nervous lofty language. That man makes one in a whole nation's census a mighty pageant creature, formed for noble tragedies. I want you to remember that image, the mighty pageant creature, formed for noble tragedies who speaks a bold and nervous lofty language. That's Ahab, and we're getting a little taste of what Ahab is going to be like. Now, Peleg and Bildad, those are biblical names. Bildad is one of the questioners of Job, one of the self righteous ones who tells Job, oh if he's punishing you, you must have did something wrong, think about it. Peleg a little bit more obscure, Deuteronomy I think or maybe Exodus, he is one of the begets [assumed spelling] his name actually has the derivation, I used to think it meant nothing and then I found out that it actually kind of means a river that divides two lands, or something like that. So in fact there's something going on there about division. Ok these two guys are going to decide Ishmael's salary, and we'll end here with that. Ishmael decides that he's going to have a certain amount of pay. This is on the bottom of seventy five. He talks about the way whales men are paid according to lays. He says that what you get is one fraction of the total net proceeds of the voyage. Right, in which case getting half would be good, getting twenty fifth would be good. He expects something like the two hundred seventy fifth lay. This is at the bottom of seventy five. I made no doubt that from all I had heard, I should be offered at least the two hundred and seventy fifth lay, that is, the two hundred and seventy fifth part of the clear net proceeds of the voyage, whatever that might eventually amount to. And though the two hundred and seventy fifth lay was what they call a rather long lay, yet it was better than nothing. So he goes to these guys expecting to get at least that. What do they offer him? They start to offer him, well let's see, the seven hundred and seventy seven lay. Captain Bildad suggests this, he happened to be reading, oh coincidently, a passage from Matthew. That passage from Matthew is Christ sermon on the mound, he's talking about how to behave and there seems to be a, yes it says, lay not up for yourselves treasures upon earth, where moth, well, Captain Bildad, interrupted Peleg, what ye say? What lay shall we give this young man? Thou knowest best, was the sepulchral reply, the seven hundred and seventy seventh wouldn't be too much, would it, where moth and rust do corrupt, but lay. So he's making a pun, he's reading a passage that says lay, and it's about how you shouldn't want worldly things, but only should lay up treasure up in heaven where they really count and not corrupted by moth and rust. And he uses that as an excuse to say give him this biblically significant number for a lay. Since worldly possessions don't matter, how about the seven hundred and seventy seventh. Lay, indeed, thought I, and such a lay, the seven hundred and seventy seventh. Well, old Bildad, you are determined that I, for one, shall not lay up many lays here below, where moth and rust do corrupt. It was an exceedingly long lay that, indeed, and though from the magnitude of the figure it might at first deceive a landsman, yet the slightest consideration will show that though seven hundred and seventy seven is a pretty large number, yet, when you come to make a teenth of it, a fraction, you will then see, I say, that the seven hundred and seventy seventh part of a forthing is a good deal less than seven hundred and seventy seven gold doubloons; and so I thought at the time. They go on and stage this kind of mock fight. What does Ishmael end up with? What's the final lay that he gets promised? He gets the three hundredth lay. That's worse than what he expected to go in, but he leaves glad to get it. Ok, so as we depart today, ask yourself of what's at stake there. What just happened to Ishmael to make him glad to get the three hundredth lay? How did the dynamics of that conversation work, and how we think might those be implied to what Ahab does when we finally meet him on the quarter deck. And we'll take it up from there when we come back to Moby Dick. |
Open_Ed_Cyrus_Patell_American_Literature | Uncle_Toms_Cabin_I.txt | [ Silence ] >> So if career goes up, you know, it becomes that real estate that was underdeveloped. Critics flock in there. They start thinking about Moby Dick. It becomes very quickly like kind of canonized center of the American novel, which means that nobody reads it so much anymore. Uncle Tom's Cabin had a different career. Many, many, many people read it. It was the best selling novel of the 19th century and it was quickly adopted for the stage. Stowe wasn't so canny as some other people like Irving about her write. So she didn't make any money from the many, many stage adaptations that were made of this. But Uncle Tom's Cabin was quite literally a bona fide cultural phenomenon. And yet you might say because of strategies that it pursues, the novel pursues that we'll talk about. There was a sense in which it kind of outlived its moment, once slavery was abolished, once African-American had increasing rights although there was clearly difficult in the reconstruction era. The idea of the African-American protagonist being patterned on someone like Tom started to seem like not such a good idea or at least not a useful idea. Rather than being the epitome of the good Christian and therefore you might say that the highest form of protagonist. I mean what higher protagonist is there in wester civilization other than Christ. Tom was meant-- came to see sort of the subservient and docile and not exactly the template for what a new African-American person should be. And in part that has to do, I think, with the way this character became stereotyped and the way the novels big scenes became kind of set pieces that were performed on stage. The stage adaptations made Uncle Tom's Cabin into a much more melodramatic story than the novel actually is. It highlighted those things and some of the moral subtleties of the novel were lost in the process. So the novel's career went way down, and you wanna look at the mid 20th century, you'd say, Moby Dick's stock was way up. Uncle Tom's Cabin was probably in an all time low and it took in the aftermath of the '60s and the rise of feminism and you now, people who took a look at the writing that was actually written in red in the middle of the 19th century, writing that was primarily by women and for women. And started to think that maybe there were some kind of masculine is bias in the way the cannon have been construct. I mean was it really just accidental or could it possibly be that they were just better that that cannon was basically Emerson, Thoreau, Whitman, Hawthorne, Melville, Poe and sometimes Dickinson or something else going on there. And I think one of the arguments, one of the powerful arguments that critics made is that Uncle Tom's Cabin is not only antislavery novel but it's also a kind of feminist novel and that's part of what motivates it, that it really is making a kind of analogy, a powerful analogy between slavery, the most pressing problems for the United States in the middle of the 19th century, and a problem that continues on. Again, a problem not solved in the declaration of independence on the constitution, the problem of women's rights, or what Stowe would come to call domestic slavery. And I think one of the things that happens in the '70s and onward is that critics-- feminist critics especially but generally critics would suggest that we forgotten how to read novels like Uncle Tom's Cabin in part because we become so consumed as English majors with text that are hard, with text that are light, you know, they don't seem to have a message. And that there's a certain way in which sentimentality as a genre, has become unavailable for us. And the argument is in fact we are poor readers for it. So it seemed to me in the interest of being, you know, up to date in terms of modern the very-- being the very model of modern literary criticism back whenever that was. Now, if you're gonna do Moby Dick you have to do Uncle Tom's Cabin, too. I chucked about but three weeks or so out of the syllabus. But I think one of the things I want you to understand is that Uncle Tom's Cabin and Moby Dick represent two contemporary novels. They're basically the same time, they are motivated by the same cultural context, they are marked by it in slightly different ways but there are two variant attempts to write a modern major American novel, a national level. I suggest to you that The Scarlet Letter is another way of doing it as well, that it has the same kinds of aims. And we will talk about that although I give it comparatively short shrift in this class because I think many of you have, probably at least been assigned The Scarlet Letter in high school. If that's true and in high school if you skip the Custom House and you find yourself pressed for time for some, who knows what, reason over the next two weeks. I suggest you read the Custom House, hey, this is rare tip. Read the Custom House and skim The Scarlet Letter to re-familiarize yourself of what goes on there. I'll show you some of the major portions of The Scarlet Letter. But one of the things you will understand if you realize that the Custom House is integral to the novel The Scarlet Letter in italics on which The Scarlet Letter that follows the Custom House, Scarlet Letter in quotation marks is simply a kind of a long story. You will understand that one of the things that Hawthorne is trying to do is play off the 17th century against the 19th century. It isn't only a novel about the 17th century. And Hawthorne frames his telling of Hester Prynne's story with ideas that come from the 19th century, alright. So I want you to understand that-- I mean, some-- with any luck, as I said, I don't want you to remember dates and things but by the end of a course I do hope you will realize, it will be firmly implanted in your head that Hawthorne was not a puritan writer. Many students make that mistake. Hawthorne was not. It's one of the reasons I've decided not to ever start this course with Young Goodman Brown which I've thought of doing. He's a 19th century writer. He's writing a critic of Puritanism, okay. So we're gonna back. But he's also writing a critic of 19th century culture. And there's a certain way in which Hawthorne shares that project with Stowe and Melville. They are all in some sense evaluating the culture that they find themselves in from a variety of different standpoints, and in different ways they find it wanting. They have ideas about how it might be improved. And still is more overt about it behind a kind of prescriptive message about how it might be improved. So one of the other things I want you to use is that if Hawthorne is engaged in a kind of critic of Puritanism and is dramatizing some of the shortcomings of typological, allegorical modes of thinking, some of the kinds of way that Calvinism encouraged people to think in the 17th century. If Melville also in some part is drawn to Hawthorne because he is sympathetic to that critic, on the one hand we might say that Stowe is in some sense inheriting many of the kind of impulsives that come from Calvinism. She belongs in some-- in-- you might say, in a kind of long train of what we might think of the sermonic literature that would start for us with Thoreau. So I want you to think about this different trajectories as we are talking about these books, okay. One of the things to say is that and I'll bring back to ask this question of the horizon of expectations that we started about with. And I think I might be even mentioned it to you on the first day. Melville sets himself at odds with the prevailing horizon of expectations in that moment, right, in the 1850s. He is writing a novel that's gonna look weird even to experienced novel readers. And if you'll remember he starts with as-- with etymology section with extracts isn't really get to this personal narrative until many pages in. And even in-- even then it's a kind of dodgy personal narrative. It's one where we should immediately be suspicious of the very chatty narrator that he's presenting to us. It looks weird as a novel. Stowe has a different attitude as I hope you'll see over next couple of days towards the horizons of expectations. She wants to use it. She wants to mobilize it. She knows that one of a things she's trying to get across is something that is deeply controversial at best, perhaps deeply unpopular at worst. So, she wants in some sense to sugar coat that indigestible nugget at the heart of her project with something that will prove to be more digestible that will even make you want to ingest it. And those things are what we called sentimentality, and with them a healthy dollop of Christian doctrine, some melodrama. And you might say, a general idea that what she is trying to do would fall into a category that if it exists at the time we would call realism. Now you'd say that's ridiculous. It's a novel. When you get to the end you'll say, "Wow, that was really so full of coincidence and it's just completely unbelievable story," right. People wouldn't behave that way or, you know, these kinds of things really wouldn't happen except in novels. But what I wanna suggest to you is that Stowe is actually pitching the novel to her readers as realism. And if they read it in that way and that she dramatized the scenes in the novel that are precisely about those kinds of problems of representation. So that's part of where we're going. And again, that would be another thing that separates Stowe's practice from Hawthorne's and Melville's. Today in the 21st century, we would say, "Oh, yeah, Stowe is a sentimental novelist." >> Those guys are doing something more complicated. They're modernist or romantic writers but I would think that a way of capturing the dynamic in the 19th century might be more accurate to say that she is something that is more like realism and less like romantic writing, the kind of romantic writing that they are pioneering. And in the end, you might say of the 19 century when there's a kind of backlash against romantic writing. And genres that we've cope-- when we think of more properly if you take American literature, too, you would start off with the age of what's known as realism and then leading to naturalism. Well, part of realism is an intention to region and regionalist writing as it worked. And one of the major regionalists of the late 19th century-- of the later part of 19th century is Stowe. So you might say that Stowe has-- if you look at her career there's a sense in which she kind of surrounds the romantic writers that are epitomized by Hawthorne and Melville. So I want you to think about that as well. What would it mean to be a reader for whom sentimentality is in fact a form of realism? Okay, now, like Emerson's antislavery lectures, Stowe's novel was motivated by the passage of the Fugitive Slave Law. And in 1851, she wrote to the editor of an antislavery newspaper called the "National Era" that she wanted to write a sketch and this sketch was gonna be called "Uncle Tom's Cabin." And this sketch would run for three or four installments. Maybe some of you are wishing that in fact she'd stuck to her original plan. But once she began her writing, the project took off. It grew to 40 installments. It was later reorganized into 45 chapters for publication as a book in 1852. Alright, so you might see there's a project-- the project gets a way with-- or from her and at the same time which she is not interested in literary form in the way that Melville is. She's interested in literally form, I would suggest to you in the context of course in the way that someone like Phillis Wheatley is. She doesn't want form to be a problem. She wants form that draws you in but she's got something other-- something that's different around. And like Wheatley, one of the things that's thought her in mind is you might say, the faith of Christianity in the new world. Wheatley thinks that Christianity is something that is, you know, eventually going to provide a certain kind of salvation. It's good for Africans to come to the United States if it mean-- even the slaves, if it means that eventually are Christianized. We need to perfect Christianity so the white people will realize that Africans who may be dark has came nevertheless like came can be refined. Stowe also thinks, believes in, you might say, the salvation of-- the idea of Christian salvation, what's gone wrong as far as Stowe is concerned is the institution that supposed to provide-- to help provide that, the church. The church, you might say, has fallen down on the job not only does the church-- not [inaudible]-- the Christian church not necessarily be counted on to oppose slavery. There are many instances and not only in the south of churches and ministers who openly support slavery who find biblical president for. So I think that's a problem. So for her, form is not going to be an issue, and you might say therefore if we were looking to judge the novel in contemporary terms, you might say that actually it's kind of deformed. It probably could have use an editor, although I think that's probably true of most 20th-- 21st century, no, it was not. Everybody here read Steven King, don't you wish Steven King were just a little bit shorter sometimes. I mean, come on, you really need all those words. Probably better when it was shorter. In any case, Stowe's middle section gets away form her you might say. And so, I think you'll notice that as you read over the weekend. There's a sense in which in terms of the story, the narrative, that middle section that sets in New Orleans is too long. And yet there's something about what it is that Stowe is interested in thinking about it that makes how that kind of-- that makes her take all that kind of space. So we'll talk about that, I think, a little bit more next time. One of the things to start by thinking about is couple of things to help you read this. What is that the book has a double plot? It moves geographically north from Kentucky and south from Kentucky. So the northern plot has a certain logic, it's north towards Canada and to freedom. That's the Harris' who escaped from the beginning and moved their way up to Canada. And the logic of south, just as I suggested to you earlier about Huckleberry Finn, the logic of south is the logic of deeper into slavery, down towards Louisiana and the deepest, darkest, most dismal faces of slavery. The early sections of the book are the most tightly plotted. They are the most motivated by the needs to dramatize a critic of Fugitive Slave Law. But as she gets more and more taken with this kind of logic of moving south, you might say it's the southern movement that ends up dominating the book. The northern plot has a kind of climax or they had a central middle climax that was a frequent-- it was frequently the set piece that would close the first act of stage adaptations of Uncle Tom's Cabin. Her people used to go to see how this was going to be performed, Eliza on the ice floes. This is from a French edition of a play. This is an illustration from the 1880's. And again, they do get across that Eliza doesn't look exactly, not necessary look African-American. And this is from an advertisement for production of Uncle Tom's Cabin in the 1880's. How were they gonna do this? How were they gonna dramatize that was typically as these things went on you would have, you know, actual dogs come on the stage and, you know, somebody wonders what they did when the dogs like poop on the stage. Don't ask me that question. I have no idea. [Laughter] But it became spectacle, right. So one of the things you might say about the novel immediately is it it's open itself up to spectacle like that. It contains certain kinds of steps that pieces that draw attention to themselves, that's part of its technique. There is, you might say, an undercurrent of melodrama in this novel. And it's not only in its narrative but even in the voice of the narrator, right. There is a narrative voice her e. It will address you periodically as dear reader. It would comment on what the narrative is doing. And that in some sense also heightens the kind of melodramatic for us, alright. Now, you remember that Eliza after receiving assistance from Senator Bird is reunited with her husband, George. They find a temporary haven in chapter 13 of the novel, in the Quaker Settlement which is run as if it's a kind of matriarchy, right. And you might say that's a kind of Utopian space for Stowe. She's-- It's almost like vision. It's almost like her little furrow thought experiments. What would it look like of women ran stuff and the man didn't mind, if the men were cooperative. What would a matriarchal society look like? It might look like this Quaker Settlement. Interestingly though you can't stay there. It doesn't really for everybody. The Harris's can't stay there. They have to move on. And so that might be one way of thinking about the novels acknowledgment of what is possible especially for people like to Harris's in the middle of the 19th century. Now in the first part of the novel, that novel, that plot of escape alternates with Tom's-- the Tom plot. Tom sailed to a slave owner down South. And it's at the end of chapter 17. So I ask you to cutoff basically where book 1 of the published book, first publication ended off. But that's just the beginning of this New Orleans section at the end of chapter 18. That's where we get more and more of a focus on to the real kind of horrors, both literal and you might say even intellectual horrors of slavery and that part of the novel is less tightly plotted, there's more conversation, there's more thinking especially between Augustine St. Clare and his cousin Miss Ophelia about the kinds of a, you know, problems of slavery, the possible remedies for a slavery. One of the things I want you to immediately see is that it's important that Miss Ophelia is a northerner and it's important that Miss Ophelia is a deeply flawed character. She needs to learn something from the people in the household. And part of that is, you know, there's an insight that Stowe has which is the same insight that motivated Emerson which is that's slavery is a national institution. It isn't that southern problem that the South is part of a union and that's this union is part of a large-- is a larger economy that's built on slavery. You can't have slavery in one part of it and saying that the whole country is into slave holding society. So there's a way in which one of things she's dramatized is northern implication in slavery. The implication of would be do good or is like Miss Ophelia. Notice what happens to her when you found-- when the novel progresses. There's a deep irony about what happens to Miss Ophelia in the course of it. It's subtle but just think about ways in which you would categorize her in relation to slavery as the novel unfolds. That's one thing. The other is that the most-- one of the most vicious villains in all of the American literature is the villain of the last half of this novel, Simon Legree, is a northerner and a capitalist, right. So one of the things we would say is that the worst character in this entire novel is a northerner. Stowe is suggesting that it's a national problem that the south and north are both implicated in this. And there are ways in which she will, you know, almost try-- she would try to address herself to us a sympathetic southern reader at the moment. She doesn't wanna demonize the south that's just too easy an excuse for northern readers. >> Okay, so that's one thing to bear in mind. One of the things we might think about with Uncle Tom's Cabin of course is that it belongs to a model in which of reading and writing and thinking, in which literature was thought to actually have social consequences, to actually have some kind of efficacy. I don't think-- we don't believe that so much in the United States anymore. Do anyone believe that a book can change the world? May even sounds right when you say, "Oh, books will change my life." But there are cultures out there. [Inaudible] with that, there are Americans out there that believed that books can do things, have social effects. Mostly they focus on negative social effects. They think that certain writers are be banned or have death-- you know, death sentences passed on them for certain kinds of sect, religious things that they've written or that certain very, very, very popular books should be burnt because they promote witchcraft and wizardry. [Laughter] Or that no one should read Huckleberry Finn because it contains the word nigger, even though it's one of the most deeply, antiracist books that's ever been written and people would get funny ideas about [inaudible]. Nevertheless, there's one good thing about all those prospectors which is that they seemed to think that literature matters or as you know many-- I don't know well healed liberals are kinda of too bossy about the possibilities for literature. When Stowe went to the White House in 1862 and met Lincoln, finally, he looked at her and you can imagine Abe Lincoln talking. Lincoln at her and probably only half joking said," So, this is the little lady who made this great big war." And one thing again, he's only half joking about that. There was the belief that somehow Uncle Tom's Cabin was related to the civil war. Some would say, he brought it-- it brought it about. Certainly, one of the things we would say is that it kind of galvanized discourse about slavery. To a certain extent, once Uncle Tom's Cabin was published, it was so powerful as a form and so many people read it, that in some sense the slave-- the debate over slavery got turned into literary debates. Was the novel true or not? Was it a true dramatization of slavery? Some people say that's exactly the slavery. See, it's evil. You read the novel. Some people say didn't go far enough. It doesn't show you enough about how horrible slavery is, has pull its punches. Southern writer would appall and say, "No, no, it's completely unfair." That the slavery is actually much better that the kind of wave slavery that you have in the north where people are kinda left with their own devices. The plantation system is like a family. And in a family, there needs to be punishment every now and then, right? Spare the rod, spoil the child. But it's a system in which we care about everybody that's in a family. These were more debates that were mobilized. And so people would say, you know, Uncle Tom's Cabin was true, wasn't true, wasn't true enough. So much so that pass-- Stowe, the year afterwards, publishes a volume what's you called The Key to Uncle Tom's Cabin in which she reveals some of her contemporary sources. And one of the people that's the influence in the story Frederick Douglas, right. So Stowe, herself buys in into this debate over whether the novel is actually true. So then that's the kind of leave the imagination that we have to make. We have to think of a situation we could actually think that a novel could cause a war. Here's an example from later on in the century, this is a Brigadier General who was a confederate general who wrote this in Sewanee Review in 1893. Has Mrs. Stowe ever try to think what her book has been a chief factor of bringing upon the world, have she ever try to weigh those occasional and rare horrors. I'll say that again, the occasional and rare horrors of the old slave day. Hard as they were against the agonies of the million of brave men mutilated and done to death in the ranks of the blue and gray. Has she ever reflected upon the 10, the 20 millions of lives and mothers, sweethearts and daughters who slaughter, whose hearts has been torn up by the roots of the wild slaughter between brothers. Truly the indulgence of sentiment is costly. Again, you can see some things going on here. Right, I mean, there's the apology, the occasional and rare horrors of the old slave days. The family metaphor, the country as a family, brother against brother, with the civil war. He's taking those and he's not actually stupid. He's taking aim at precisely the audience that Stowe's novel was aimed at, you know, women. Here he calls the mothers, sweethearts, and daughter. That's exactly that Stowe's gonna address her book to in end, you'll see. It's like, you know, the men they suck. Women of the America, it's time for you to do something, right? And-- But the idea that truly the indulgence of sentiment is costly is misguided. It wasn't simply indulging sentiments. There wasn't like, "Oh, women, they write sentimental stuff and look what happens." Write about slavery and see what you-- no. Stowe knew exactly what she was doing, right. So that Stowe I would say-- Stowe truly did mean to do harm. I think that was-- but she meant to do harm to this institution that she found to be, you know, a complete disgrace. And you might say a kind of cultural contradiction that was in some sense a sort of very present evil, okay. So that's one of the things I want us to understand that we understand in the 19th century that it was Stowe, that literature can have a certain kind of efficacy and she means it to have a certain kind of efficacy, right? So, here's a-- here's an advertising for the novel, blew that later on. And you can see that it was the greatest hail at this point, it's the greatest book of the age. In addition for the million complete in one volume, people would say, "Oh, you know, she was really successful as a novelist because she had a powerful theme, antislavery," right. She was just the best of the antislavery novels, everybody bought it, right? Wrong. In fact, antislavery was dead at the box office. Everyone knew, including Stowe, that antislavery was a genre that nobody wanted to read. It did not sell well. In effect, Stowe was forced to sell the publication rights to the novel for just a 10 percent royalty and her husband had told her-- he was quoted later on in saying, "I tell my wife that if she can get a good black silk dress or 50 dollars and money for the story, she should take it" which of course was not exactly the right thing to do. And she missed out on a lot of money although I think-- I don't think it really mater. But the success of Uncle Tom's Cabin surprised everybody. Surprised her, her husband, her publishers. You might say therefore more accurately that the novel gained a large audience in spite of rather than because of its antislavery stance. One Stowe scholar put it this way, sometimes critics have assumed that it was the subject of antislavery which made Uncle Tom's Cabin a powerful novel. It is perhaps more exactly through to say the opposite that because Uncle Tom's Cabin was a powerful novel, antislavery became a powerful cause, okay. So that again, as one say you seemed that they-- you could demonstrate and liberate history that this is a novel, a piece of literature that has a certain kind of social efficacy. Stowe knows that she can't just write an antislavery critique that it becomes a [inaudible] or something and nobody wants to read it. How doe she hoodwink the reader? How does she draw the reader in so that finally the reader has to accept this antislavery novel? She does it-- I'd suggest you very candidly by using literary techniques that allow her to appeal to her readers' emotions first and their intellect second. Once she's got the emotional pull then she starts to-- she can bring out the-- try to seek a kind of intellectual change, right? So it is an antislavery polemic. I think that's true. It is also a kind of feminist appeal and you might say that she compelled-- she brings those two things together. It's not incidental by the way. Part of the reason Stowe as a writer is able to imagine what it's like to be a slave is that she feels herself to be what's called a domestic slave. And in some sense, it's not her husband was a bad guy or a thing. It's just that simply the situation of women was such in the 19th century that even if you're relatively well to do you are nevertheless kind of in a situation which your options are limited. You don't live for yourself. You're constantly doing things. Rather, she has large family. And so she has this experience that she's able through what [inaudible] might have called negative capability to generalize out and think about what it might mean to be a slave. So she takes these two things and in priority order, right? Slavery first, domestic labor is second, as the topics of a novel. She wraps them in a technique of sentimental fiction. And what for her is inseparable from the idea of sentimentality. She wraps them in the garb of Christian doctrine, okay. So, I want you to be clear about this. Above all, this is a Christian novel. It is a Christian abolition novel. And it is a Christian abolition novel that takes the opportunity to also offer a kind of feminist dramatization or feminist critique and that's activated by the idea that what Stowe-- you know, that what Stowe experienced herself personally. It's something that she would refer to as domestic slavery, right? And her biography makes this clear that she knows about domestic slavery. She's born in the beginning of the century, 1811, to a very prominent family. Her father, Lyman, is a Presbyterian Minister and he was one of the most famous preachers in the northeast and even in America in that day. >> He was a very strong influence on his children. He had seven children who followed him, some of them into the ministry. One of them, Harriet's younger brother, Henry, became perhaps even more well-known as a preacher than his father. Her older sister in fact, I think the oldest of the children, Catherine, became an influential proponent of education for women and wrote treatises about that. One scholar writing about Uncle Tom's Cabin in a kind of disparaging way in the middle of the 20th century said, that any of the beaches that sat alone on a deserted island would have a church and a missionary society up and running within a couple of days, right. That's kind of activist family. Stowe launches her literary career when she's about 23. 1834, she began publishing a set of stories in a western monthly magazine. On of the stories wins a price of 5 dollars which is more than it is-- oh, excuse me, 50 dollars which is, you know, more than 50 dollars today by quite a bit, but still not a ton of money. But it teaches her this lesson, that you can make money from writing. It can be a form of supplemental income for her family. So she [inaudible] it. I would suggest to you-- one of the least I mentioned is that there's a kind of instrumental idea. Literature is not just there for aesthetic appreciation. It's to achieve things. It's to get things. One of those things you might wanna get at least at the outset of your career is money. In fact, she needed money because in 1836, she married a man who didn't have a lot of money, Calvin Stowe, who was a widower and a professor whose circumstances were not exactly prosperous. He was a classics professor and she said later on after the novel was a success, "I was married when I was 25 years old to a man who is rich in Greek and Hebrew, Latin and Arabic, and alas rich in nothing else." I sympathize. In any case, it becomes impossible to support their growing family on just a professor's salary. So she looks to writing to try to provide some extra money. And in 1842, she was-- she collected enough stuff to actually put a volume together and she was canny about her professional life and a certainly way. She knew where to go. She went to New York to negotiate with the House of Harper which is one of the most prominent publishers. And she-- there's a letter in which she writes back to her husband this, "On the home, my dear, if I choose to be a literary lady, I have I think as good a chance of making profit by, it is anyone I know of." And again this should remind as an earning, right. She's not in this for the love of literature. She's in this to make money. And her husband apparently writes back and says, "My dear, you must be a literary woman." And she writes back to him and says, "If I am to write, I must have a room to myself which shall be my room." [Inaudible] Actually, I don't know if he got that room. I mean this anticipates Virginia Wall, right, a room on its own. But you can kind of see that the situation in which she is writing. Anyway, the result of all these was a volume called the Mayflower that was published by Harper in 1843 to not a lot of notice. And after that, her life was really dominated by trials where in between 1836 and 1850s, so this volume goes about the middle of that. She has birthed to seven children, count them up, the years, 1836 to 1850, about 14 years. Seven children and she suffers at least two miscarriages, that's 9 years [inaudible] so we don't know exactly, right. And she was one of these-- she was not one of these women who could just kinda like have a pregnancy and be up and, you know, jogging the next day. She was frequently frustrated by her pregnancy. So she spent a lot of time in bed and when she was well enough to write, she had to worry about the family. I want you to understand she's not-- we talked about Anne Bradstreet before. It doesn't went with Anne Bradstreet was well to do and had helped and Stowe doesn't have that kind of help. In fact later on, she said this to a friend even-- It's not even that later. It's 1838 before she has a lot of her children. She said, "I am but a mere drudge with few ideas besides babies and housekeeping." And that was before, you know, the drudgery had hardly reached its peak. The following year, she writes this, "I am determined not to be a mere domestic slave without even the leisure to excel in my duties." Alright, so there, early on, you see this connection that's being made in her mind between slavery and a lot of women in the 19th Century. She finally had a nervous breakdown. And in 1846, she had to go for hydrotherapy in Vermont and almost a year of isolation from her family. So that's one of the things to understand about where this novel comes from. In other way, it places novel comes from 1849. There was a cholera epidemic and it killed one of her children, her 1-year-old son, Samuel. And she said this, "It was at his dying bed that I learned what a poor slave mother may feel when her child is torn away from her." She's thinking back about where the genesis of this novel was. "In those depths of sorrow which seemed to be immeasurable, it was my only prayer to God that such anguish might not be suffered in vain. I felt that I could never be consoled for it unless this crushing of my own heart might enable me to work out some great good to others." So, there's a kind of double sense here. Domesticity as a kind of duty on the one hand, domesticity as a kind of slavery. She likes the duty part. She doesn't like the slavery part. She doesn't like the fact that in so far as this drudgery is keeping her from doing the duty particularly. But you can kinda see how this is becoming a kind of complex metaphor for Stowe. It's evolving even in this moment. Finally, the thing that prompts Stowe to write Uncle Tom's Cabin is the passage next year of the compromising 1850 and the Fugitive Slave Law. Let's take a look in the novel now. We've delayed long enough, to page 142 in the Penguin edition, chapter 9, or anybody who's using something separate. Here we find a direct reference to the passage of the Fugitive Slave Law although one of the things to bear in mind is that the law they're talking about is not the national Fugitive Slave Law but a kind of similar law that's being passed at the state level in Ohio. It's about-- So it's about states politics. But this is what-- We have the Senator Bird here talking to his wife. Alright, and he's the man of business and politics, public affairs. She is the little lady who stays at home. Well, said his wife, after the business of the tea table is getting rather slack and what have they been doing in the senate? Now, it was a very unusual thing for gentle little Mrs. Bird ever to trouble her head with what was going on in the house of the state. Very wisely considering that she had enough to do to mind her own. Now I wanted you to see again even in the little thing like that, that's just not a neutral narrative voice. There's a lot of stuff that's going on. In this narrative voice drips with irony much of the time and you should be attuned to it. Mr. Bird therefore opened his eyes in surprise and said, not very much of importance. Well, but is it true that they have been passing a law forbidding people to give meat and drink to those poor colored folks that come along? I heard they were talking of some such law but I don't think any Christian legislature would pass it. Why Mary, you're getting to be a politician all at once. No nonsense. I wouldn't give a fip for all your politics generally. But I think this is something downright cruel and unchristian. I hope my dear no such law has been passed. Alright, so one of the things we're starting to see here as a kind of separation. This is what scholars would later call the separation of steer. There's a male realm of politics and a female realm which is not supposed to be about politics. It's about the home. It's about religions, about education, but not about politics. And there's a certain way in which you should say-- you should see that there's kind of something dismissive about her attitude towards politics. I wouldn't give fip for all your politics. Generally, as if it's all just stuff that men do. But wait a minute, once the men start doing stuff that's unchristian then the women had to take notice. It's all men-- already we see there are two different ways of framing what's going on. The male way is the legalistic way. There has been a law forbidding-- passed forbidding people to help off the slaves that come over from Kentucky my dear so much of that thing has been done by these reckless abolitionist that are brethren in Kentucky are very strongly excited and that seems necessary. And actually she's gonna use the Christian thing back at her, right? And no more than Christian and kind of something should be done by our state to quiet the excitement. And what is that law? It don't forbid us to shelter those poor creatures at night, does it? And to give them something comfortable to eat and a few old clothes and then send them quietly about their business. Well, why yes my dear that would be aiding and abetting, you know. Mrs. Bird was a timid, blushing little woman, of about of 4 feet in height with mild blue eyes and a peach-blow complexion, and the gentlest, sweetest voice in the world. As for courage, a moderate-sized cock-turkey had been known to put her to rout at the very first gobble, and a stout house-dog of moderate capacity would bring her into subjection merely by a show of teeth. And this must be funny guys. Her husband and children were her entire world, and in this she ruled more by entreaty and persuasion than by command or arguments. There was only one thing that was capable of arousing her, and that provocation came in on her side of her unusually gentle and sympathetic nature. Anything in the shape of cruelty would throw her into a passion, which was the more alarming and inexplicable in proportion to the general softness of her nature, right. I want you to see that in this passage, there's a way that we should understand Mrs. Bird as something like a Stowe figure, right. >> Normally she thinks of herself as a wife and mother. Normally she wouldn't interfere in these things. But all of a sudden something is going on in that male realm of politics that forces her to intervene and that is the passage of the Fugitive Slave Law. Her sister in law wrote to her after the fugitive slave law and said, "How do you feel if you use the pen like you can I would actually write something that will make this whole nation feel what in the curse thing slavery is." And still reads that letter aloud to her children apparently and says, "This I will write something. I will if I live." Okay, we're getting closer to passage of Fugitive Slave Law. Finally, this is the story, in February of the following year she's taking communion. She has a vision. This is what she said later on of a slave being flogged to death from the orders of his master and with his very last dying breaths, forgiving his prosecutors for what they have done. And that vision is a thing and supposedly that kicks it all into gear, that brings it all together, and that crystallizes ultimately in Uncle Tom's Cabin. So that later on Stowe says and I think, you know, there's a way which we wouldn't take this ironically. I mean she's tried to mean it ironically. She says that she-- not she but the Lord wrote Uncle Tom's Cabin. I think she is thinking back to that-- the genesis of the novel and that vision. She calls this, she says-- and at this point, she's gotten to be kind of an institution so she started-- she used to write herself in the third person. She says, the Lord himself wrote Uncle Tom's Cabin and she still was but an instrument in his hand. And I wanna understand that we should take that-- to think that that's kind of sincerity, right, that she really means that. So this is God's purpose that she is about. Okay, so that's one of the things that I want us to bear in mind here. There is a way in which one of the things the novel is dramatizing for us is a kind of cultural believe that men and women have different roles to play in society. That's one thing. They have different roles. It's called constructive, caught the separation of spheres. On the other hand-- and therefore you get quotes from Stowe like this, right? Women if they're a writer not suppose to be doing what the men-- think back to Bradstreet. They're not supposed to be doing what the men do. They do it in the different way. She says I had no more thought of style or literary excellence than the mother who rushes into the street and cries for help to save her children from a burning house, thinks of the teachings of the rhetorician or the elocutionist, right. So one of things I want you to see here is that what she's conceiving is writing the novel as an extension of her domestic duties, of her duties as a mother. And again the logic is she's actually always thought about writing this way, right. She wrote for fun at first but then she earned money and then she tried to write to earn money for her family. Again, an extension of her domestic duties. Here, is on a larger stage. The nation if it's a family is really suffering and mothers finally need to, you know, get out there in the street and do something. And in this idea of the teachings of the rhetorician or the elocutionist, you've got to see something like a dig at people, the literati like Ralph Waldo Emerson who are standing at the sidelines and not doing anything and talking about, you know, rhetoric and literature and speech, you know. There's think-- a desire here to say that, you know, the men of the country whether they're be ministers or intellectuals or whatever are falling down on the job. So much so that women have to finally do something about that. Now, again I wanna to suggest to you-- you can't really see it very well. But there's a way in which women are seen as writers, right. But when Stowe says that she hadn't thought about literary style or excellent is because women like Susan Warner or others or Maria Cummins and Fanny Fern although she's a slightly different case, typically these-- this is the best selling novel, the wide, wide world before Uncle Tom's Cabin, right. So people thought of women as writers but they didn't think of them as literary. They were writing the kinds of novels that Charles Brockden Brown in some sense was trying to write again. So it's a continuation about sentimental tradition. They were melodramatic. They were about the family life. They were about-- They have a lot of kind of Christian educative impulses behind them and they were sentimental in this way. They were about, you know, good people dying young or having adversity. So much so that between Warner and Stowe and others, scholars used to refer to this the decade in which this novel was published as the feminine '50s I told you at the beginning of the course about a book that help to set the kinda called American renaissance. You could see the feminine '50s as kind of the counterpart for that. But the feminine '50s is only meant to acknowledge, you know, that's a purely literally historical interest. These women you should know if you wanna know about the literary culture that produce the great writing of Hawthorne and Melville and everybody else. There was this other writing. It was done by women. They were outselling everybody else and in some sense that was another thing that the men have to fight up again, right. So one of the things we would say about all this is that even Stowe accepts that there is this kind of division. Even Stowe would suggest, yes, what people like Susan and Warner and I are doing is not literary per se. It isn't about style or excellence. We leave that to the men. We're doing something else. And therefore this is again the reason to think of this as the feminine '50s 'cause historians later on have talked about writers like Stowe and Warner basically buying into something that was-- that became known as the cult of domesticity, right or sometimes the cult of true womanhood. That women were supposed to do was take care of domestic life that there wasn't kind of separation of spheres and that meant for women what they were suppose to do was write sentimental fiction. That was their genre. And I wanna suggest to you that Stowe buys in to this. Now, that sounds bad. But I want you to understand things from Stowe's perspective. The female sphere is actually an extremely important cultural sphere. It is, you might say, the sphere were Christian values get inculcated and propagated. It's this sphere of the home, of the raising of children, of education, a real religion. This sphere you might say that it's most naturally Christian. And there's one thing that you would say about that I wanna make clear is that Stowe understands the ideal Christian to be the kind of Christian who is willing to turn the other cheek, right? The ideal Christian is someone who is meek and submissive and docile and willing to be educated, who will resist violence, the poor, the outcast, right? Women are naturally like this, right? We all know that. Yeah? Well, it's probably not true but they believed it. I mean, she probably believed it, too. Women are naturally good Christians because they have-- she-- okay, so just to say, the separation of spheres maybe culturally constructive but Stowe's novel seems to believe in certain kind of essential characteristics. Women are naturally this way. They are naturally less aggressive than men. So it's good that men are in politics and women are not, except when the men get too carried away. There's another group or two other groups even that have this qualities that are submissive, and meek, and educable, naturally good Christians. They are Blacks and children. And one of the things that the novel does, you might say, is to make this connection. In fact to have the novel in some sense crucially revolved around this connection. Well, why won't you get that across? So this is an important point that I want to make and I will start again next time by stressing it is that the novel buys into what we would call today essentialism. So some people that don't like it say, it's a racist novel. Because you will find descriptions of it in which African-Americans are characterized as if they have certain natural qualities like good singing voices or a meekness that leads to natural Christianity, right. I would suggest that it is not racist but it is essentialist. It does believe that certain kinds of people have certain kinds of characteristics or at least a tendency towards them because of factors like gender and race. Now, as you go through-- so, okay, that's one thing to bear in mind. It buys into that. And I will say it's not racist simply because it doesn't mean therefore. It doesn't believe that African-American should be enslaved or kept out on the basis of the cause. No! In fact, for a certain-- in a certainly you would say African-Americans become the paragons in the novel. They become the best Christians in the novel. White men like Senator Bird should learn from African-Americans and from women and children to be better Christians because if everybody were a better Christian, we wouldn't have slavery and we wouldn't have most of the problems that we face in the United States in the middle of the 19th century. So there's a certain way in which I would say to you that essentialism is not incidental to this novel. We shouldn't try to apologize for it. It's essential to what the novel is doing it. I suggest next time that comes with certain cause. I've already suggested it to you. I mean, a certain point to say that, you know, African-Americans are natural Christian, yey! Because they're docile and meek, boo! I mean it becomes not useful in the letter part of the 19th century as you try to reconstructed viable African-American culture, right? >> So there cost to this strategy. We'll talk a little bit more about them next time. But I want you to see that they are absolutely central to the meaning of what it is that she's doing. Let's go back to chapter 9. This is page-- Let's go back to chapter-- to 141, right? And look at the title here. In Which It Appears That a Senator Is But a Man, right. This is the kind of title you would see in the novel by Dickinson. Dickinson is one of her inspirations. But what does that title mean when you it got you. What did you think? In Which It Appears That a Senator Is But a Man. I mean, you're gonna you put that in newspaper today I know what we think of that. We think about sexual harassment, right? Men, huh. But look at the category that it sets up. There are two categories of identity here. One of them is senator and one of them is men. And you could say, well, alright one of the things you would say is that the high category of a senator, you know, somehow demeans by the idea of becoming a man. Oh, Senator X proved himself to be just a man. He has do weaknesses. He abused that page, you know. She shouldn't have save that dress all that kind of stuff, right? But in fact, it doesn't work that way. What we expect in other words to be the higher category turns out to be in some sense the lower category. It is better for the senator to be a man. In other words, to be a human being, to not be a senator who's bound by kind of legalistic distinctions but somebody who is a person, a man, someone who feels. And that's the point of this chapter. This is a crucial chapter in the novel to understand what he's doing. Because not only to dramatize what I show you this situation of the separation of spheres and the role that women and mothers can play in, you know, making sure that the country doesn't go radically off course. It is also in some sense about the literally problem that Stowe faces in creating this. Take a look in some of the ways in which she understands herself to have a kind of complicated audience. Take a look at page 155 here. If you're using a different edition, I don't know it's about 12 pages in probably. I'm gonna look at the paragraph that begins what a situation now. Okay, so senator Bird, right, has thought about the Fugitive Slave Law that's been passed by Ohio to help Kentucky out in legalistic terms. And if you thought about what a fugitive slave would look like he thought about it as a caricature perhaps from the newspapers. You know, somebody already went to that kind of stake in this act, been running away and little afford of luck and looking low down and dangerous, never thought that it was gonna be someone like Eliza and her child at the back door. Add that to the fact that this family and again remember the story I told you about Stowe has recently lost a young child. So, middle of 155. What a situation, now, for a patriotic senator, that had been all the week before spurring up the legislature of his native state to pass more stringent resolutions against escaping fugitives, their harborers and abettors. Our good senator in his native state had not been exceeded by any of his brethren at Washington, in the sort of eloquence for which has known for them immortal renown, right. So he's talking about-- remember I told you that the debates over Fugitive Slave Law and the [inaudible] produced a lot of speeches that became very well known, [inaudible]. She refrained to that debate, those senate debates. How sublimely he had sat with his hands in his pockets, and scouted all sentimental weakness of those who would put the welfare of a few miserable fugitives before great state interests, right. So you can see that this course of sentimentality is exactly the same as General Shoup, sentimentally it's beneath noticed. How dare you indulge in sentiment when there are great state interests at stake? He was as bold as a lion about it, and "mightily convinced" not only himself, but everybody that heard him. But then his idea of a fugitive was only an idea of the letters that spell the word, or at the most, the image of a little newspaper picture of a man with a stick and bundle with "Ran away from the subscriber" under it, right. So I want you to understand this. He's a legalistic understanding. He has an abstract understanding of the fugitive slave. A fugitive slave is not part of his own personal experience. And you know what? Stowe understands that for most of her readers, a fugitive slave is not part of their actual experience. They've never met one. They probably won't meet one, right, if they are northern readers. And here is the kicker. The magic of the real presence of distress, the imploring human eye, the frail, trembling human hand, the despairing appeal of helpless agony, these he had never tried. He had never thought that a fugitive might be a hapless mother, a defenseless child, like that one which was now wearing his lost boy's little well-known cap. And I want you to see that the magic of the real presence of distress. When it's there in front of you, when it's real, when it's palpable and you can touch them and hold them, all these abstractions, great state interests must give way. And that is what Stow is trying to do in this novel. She is trying to recreate that situation in words that the senator experiences there when he sees that little boy dresses of his dead son's clothes. The magic of the real present of distress. That's what I mean for you to understand it as realism, right. So it's full of sentimentality. It's full of melodrama but it's meant to provoke that real response of real distress. So it usually palpably feel distress when you read about this. That's what she is trying-- That's what she could see of realism, right. So it's an activist form of sentimentality. It's meant to provoke or I mean activism mainly is politically activist but it's meant to provoke a response from the reader, a gut reaction. And then we'll get to that, the head stuff later on. And you might say that even in that paragraph you see that. This is like referring to a gut reaction and now we're gonna think a little bit more abstractly. And again, you can see here the establishment of men as the higher category than senator. To say a senator is but a man is not destructive but ameliorative you might say. And so, as our poor senator was not stone or steel, as he was a man, and a downright noble-hearted one, too, he was, as everybody must see, in a sad case for his patriotism. And now she's gonna address herself even more widely. And you need not exult over him, good brother of the Southern States; for we have some inklings that many of you, under similar circumstances would not do much better. Now I'm not gonna delay with this. But I want you to think about the kind of inversions that are in placed here. 'Cause remember I told you about the famous one, Huckleberry Finn, does the right thing, gets-- tries to save his slave friend and considers that he's gonna be damned for it. We know him to be assuring his place in heaven by doing that. But the slave system has created this kind of inversion. So look at the inversion here now. She's feeling sorry for the senator, for the southern states because she knows that if they were in Senator Bird's position, they would betray their principles and they do no better than he. They'd save this person, right? So I want you to understand how she's kinda of using-- how she's trying to use this language and this imagery and this situation that comes out of the feminine domestic Christian sphere over against the male political sphere with its legalism and its abstraction. And she is trying to suggest that the South has typically allied itself to that sphere. But it wouldn't do any better in the presence of the real magic of distress. We have reason to know, in Kentucky, as in Mississippi, are noble and generous hearts, to whom never was tale of suffering told in vain. Ah, good brother is it fair for you to expect of us services which your own brave, honorable heart would not allow you to render, were you in our place? What she's talking about? [ Inaudible Remark ] >> Yeah, exactly. Thank you. She's talking about the Fugitive Slave Law, now the National Fugitive Slave Law. You're expecting us to return slaves when we know you wouldn't be able to do it either? So that's-- I mean, to me that is very complicated writing. And I think there's a lot of stuff going on. There's the irony of a narrative voice, the deployment of these different forms, the allusion to the cultural situation. I think anybody that think that Stowe is kind of simplistic writing is missing a lot of what's going on here. But it's not the same kind of complicated, you might say, as it is in Hawthorne or Melville's. It's a part of what we are trying to do is learn how to read it. Stowe sentimentality comes from a couple of her inspirations. [Inaudible] sentimental journey, above all Charles Dickens who gave her a conception of the lowly and that's what its called, life-- the subtitle, life among the lowly, right. And again it's among the lowly that you would find the expression of Christian values. There's a sense in which what she wants to do is return Christianity to its roots among the disenfranchised, the cast out. And so I think-- what I wanna leave you with for today is to understand what Stowe is trying to do. >> What she thinks sentimentality is all about. It's something that becomes an [inaudible] important word in this novel and one that you should bear in mind when you're thinking about it. That word is influence. Women shouldn't be part of the male domestic sphere of politics but they should influence it. The male sphere would probably be better off if it has certain kinds of-- if it were tempered by certain of the aspects of the feminist, particularly Christianity. Women, she doesn't proposing that women should get up there and actually run for senate. She proposes that every woman has a duty like Mrs. Bird to make sure the Senator Bird is a man rather than simply a senator. So women are gonna work through influence. Sentimentality is gonna work through influence, too. It's gonna influence it's readers in this way. So that if what you're looking for by the end of the novel is some kind of program. You could already see at the beginning, you're going to be disappointed. This is a novel that is promoting a model of influence. Now, when you get to the last section of the book which draws on a genre that we've seen before, right, so something happens to sentimentality. It's almost like, this novel is smart enough to know that there are reasons, there are situations in which sentimentality and influence alone will not do the job. There may be people who are so far gone into the logic of slavery and the evil that slavery produces that they can't be saved. So I want you in the last section of the novel withdraw on gothic fiction. Decide for yourself whether you think its hoax gothic or real gothic. Look at what happens to influence in that section. Look for the word. Okay, one last thing. This novel for today, this novel is called Uncle Tom's Cabin. So again, it's a fiction that belongs on a tradition of domestic fiction. So you ought to take all of the houses and domestic situations seriously as alternatives of one another. We start in a household. We go to another household, the Bird's. We find another household, the Quaker Settlement. We find another household, the St. Clare's. And there are a couple of others beyond that. What I want you to understand is that a way to think of the structure of this household as a series of variations on that initial household, right, from which Tom and Eliza-- from which Tom is sold and from which Eliza runs. And it by the way it comes back in at the end. So Uncle Tom's Cabin is at the very beginning. There's a way in which it serves as a kind of alternative right there to the main house and I want you to think of all of these domestic situations. There are variations. So you will see that if the feminine sphere has a set of values associated with it and the masculine sphere has a set of values associated with, in the St. Clare household especially they will become confused in interesting ways. In other words, just being a woman, just having those double X chromosomes is not enough to be an exemplar of the feminine sphere. Alright, we'll leave it there. Enjoy the rest of the novel. Try to open yourself to the experience of maybe shedding a tear or two. |
Open_Ed_Cyrus_Patell_American_Literature | MobyDick_IV.txt | [ Silence ] >> All right. Let's get started, if you will. The first two songs that I've played today actually come from a large or a long performance piece that Laurie Anderson did on Moby Dick, and she performed it at the Brooklyn Academy of Music, back in the day, also, I think, at the Barbican, and these come from the Barbican concerts, which were never officially released but were broadcast on the BBC so these tracks are -- how should we say, generally available or are available on the -- who have -- people who are interested in them. She had mixed feelings, I think, about the way it turned out and some of the material got reused later, a couple of albums of hers, but it's actually -- if you're interested in Moby Dick, it's actually an interesting thing to listen to in its entirety. It does have a certain kind of droning quality about it, perhaps, but I like these two pieces in particular. So our subject today actually is domination, and we will get to that. And I want you to understand, again, that, in some sense, Monday and today are two ways of thinking about a problem that we raised earlier on when we were talking about the enlightenment, which is, that the enlightenment out of which, you know, the US Nation springs, has a lot of ideals that we would approve of, I think, most of us. They are things like life, liberty, and the pursuit of happiness, or the ideas of toleration, freedom, equality, scientific progress, all those things that we associated with Franklin's view of the world. And, on the other hand, we asked is it true that, in fact, these ideals are separable from some of the other things that historically, at least, went along with the enlightenment, right, prominence among these would be slavery and racism and patriarchy and sexism or are those just impurities within enlightenment thought that in the fullness of time get worked out and pared away and so that enlightenment thought realizes its true potential, or are they somehow connected that you can't have freedom without the idea of domination. Freedom doesn't exist without the idea of oppression. Remember I told you that the definition of freedom that most political scientists would say we take for granted in Western liberal culture, in which we all belong, is freedom from oppression, what's called a negative conception of freedom; freedom as conceived as freedom from constraint; freedom as a set of rights that gives us a sphere of immunity from, you might say, the deprivations and constraints and involvement, really, of others. Right. We have certain things that are ours and they can't be taken away from life, liberty, property. These things are supposed to be inherent in every individual. But what I suggested is that, in some sense, conceiving of freedom as freedom from restraint or freedom from constraint or freedom from oppression means you have got to have previously conceived of restraint, constraint, and oppression. That's something that you would want to be free from; right? The opposite view of this is that freedom is not -- that's a very impoverished view of freedom, and that freedom is really -- only exist, you might say, in its exercise; so, then, instead of thinking of freedom as freedom from something or other, we need to think about freedom to do something or other, or freedom for something or other, and that's referred to as political theorists as the positive conception of liberty. All right. But for the most part, I think, when we think about freedom in the West, we think about that former sense; freedom from constraint, freedom from oppression or domination. So if last time was about agency and thinking about the novel of dramatization of some of the problems of agency, you might say that this is, in some sense, continuous with it, but from the other side of the coin thinking about the nature of domination and whether some of these other things that Ahab wants to pursue are inextricably tied to the idea of some people or some things being dominated. One of the things that I want you to think about is the way in which what Ahab proposes on the quarter-deck. And last time, we explored the ways in which the novel itself registers textually; how disruptive Ahab's, you know, change in the ship's mission or rather his revelation of what he conceives to be the true mission of the ship; how radically that disrupts their world; right? The novel itself breaks apart. It has to go to drama. It has to go outside of itself to another genre. We have Ishmael almost fighting to regain control of his own narrative and forcing us to rethink several chapters. I, Ishmael, was one of that crew. I raised my voice as well. I, my oath was theirs. We all swore together. And you can see that the way in which what we have is a kind of textual representation of the phenomenology, we might call it, of the experience of being drawn into an ideological consensus. Ahab very carefully sets out that ideological consensus through us, you know, this appeal to some instincts that they're familiar with. We might think of that as the money instinct to bloom, for example; the natural greed of the sailors, perhaps, or simply their desire to earn more than they expected to be promised -- or that they were promised, changed into something else. From an economic discourse, we saw a slip into a kind of metaphysical discourse, and we suggested that, you know, there are certain ways in which other thinkers in our course, for example, Emerson would probably have approved of some of this; right? Measure a man by money only. No. Money's got to be -- this can't be the only thing according to which we measure man; something royal impoverished about Starbuck's account are why they're there. Maybe there is something greater, more glorious in Ahab's account; not just seeking money, but seeking something else. And what I want you to see is that there are a couple of things that are implicit in the way that Ahab reframes things on the quarter-deck. The first is that he rejects Starbuck's idea that anything could simply be by instinct. That's not acceptable, because, if it's by instinct, then the loss of his leg, his maiming, the loss, you might say, of his bodily integrity is meaningless. It doesn't mean anything. It just happened. It's an accident. It didn't mean anything. Nobody intended anything. Just happened. Accident of the fishery. For Ahab, that becomes unacceptable. It has to mean something. Now, again, you can think about this as -- for anybody who has undergone any kind of loss or trauma, it's almost a kind of natural reflex. It's got to mean something; right? There was a reason that this happened to me, this terrible thing happened to me or my family or that I lost the thing. It's got to mean something; right? We all want meaningfulness. Ahab simply takes that natural instinct and maybe takes it too far. It means not only not nothing, it means everything. And in a way, it becomes a set, you might say, a way of thinking about the affront to Ahab, in some sense, as an affront to humanity as a whole. Think about it this way. Who's at the top of the food chain? By Divine Fiat, if you believe the Bible; right? Man. Adam. Adam is given dominion over the earth, over all the beasts and things of the earth and the sea, and Adam is part of Genesis, actually, names all these things, really, takes control of the earth in that way; right? So there's a sanction for this sort of thing. We eat everything else if we are at the top of the food chain, other stuff is not supposed to eat us. So if your leg becomes lunch for a whale, there's something unnatural about that. In fact, you could say it's against the Divine Order of things. In that sense, you might say Ahab conceives himself maybe as a Divine agent. He's going to reset things the way they're supposed to be. He's going to restore humanity back to the top of the food chain by destroying Moby Dick. Moby Dick's unnatural affront to the natural order of things. It would be one way of thinking about it. But what if God sent the Whale, which is another thing that Ahab doesn't want to exclude. What if that Whale is an agent, maybe it's its own maligned -- maybe it's the principle and the agent at the same time; maybe it was the Whale that thinks -- the Whale that is itself taking issue with human being's right to go and have dominion over the earth and the sea, or what if something else sent -- you know, what if God sent the Whale. That would put Ahab at odds with God. He's willing to be at odds with God. Again, that's not entirely at odds with Emersonian precepts. All right. So remember that moment of self-reliance when he's talking about trust yourself, somebody says, well, what if your impulses come from below; right? From the devil. And Emerson says, I don't think so, but if that's where they come from, that's where they come from. I'm going to play them out. Maybe, in other words, what we're seeing in Ahab is the kind of Emersonian self writ large. Writ is kind of an epic figure that we know from literature. Writ, as an example, you might say, of the energies of American manifest destiny, and, therefore, as an example of American national culture. Maybe one of the things the novel is doing it's saying, what happens if we really put these Emersonian ideas into practice. What does it look like. What if the ship of state is being run by a mega-Emersonian. What might happen then. That's one possibility that we should be thinking about. What I want you to see is that Ahab conceives of the stakes as being very large. It's not just some petty hunt for a whale. This is, in some sense, an idea of restoring balance to the world and almost in the Old Testament way of retribution, and that's one of the things that I think is so disruptive that it gets registered in this way in the text. So that's what the crew has signed on for, you know, this large symbolic mission that Ahab, himself, not just literary critics, Abraham, himself, is making into something symbolic. All right. Now one of the things we might say is that Ishmael tries to understand what's going on here. And I wanted to turn back to that place at the end of the chart. So this is on page 170. All right. He's used some of that same language of agent and principle. He's tried to do what Ahab has done, which is to appropriate this language of economy and make it suitable to philosophy and metaphysics and trying to understand what's going on within Ahab's psychic, and he uses it here. Let's take a look at the -- actually, let's go back to 169. I just want to go over this one more time, all right, because we had to do it somewhat quickly. And, again, you know, another intertext -- I'm not sure -- it's not an actual intertext, but in so far as they are part of a same -- the same kind of web of discourse, you might say, that envelops all of you as literature and culture in the middle of the nineteenth century, we ought to be having Whitman's account of the soul and its relationship to the self and the body and its relationship to the self in mind; right? There's a funny moment you'll remember in Whitman's poem where he imagines the body and the soul, in kind of literal Congress with one another, and he doesn't like an Emersonian who might want to do -- want to disparage the body. He takes it a little far in his metaphor, perhaps, but there is a sense -- if you could see the body and soul, again, if you want the union of body and soul, right, so imagine that scene where he has to [Inaudible] with him in the grass, and they have this kind of -- whatever you want to call it -- orgasmic moment together. It also means conceiving them being brought together, conceiving of them being apart, and so even implicit in Whitman's understanding of union, there's the sense of a possibility of separateness. Look at the way in which union and separateness work here. Union in Whitman is a very good thing. So this is about five years later, Whitman's going to write this and the pressure of the compromise of 1850, he's thinking about joining adhesiveness, sexuality, procreation, creation, union, all this kind of web of imagery. Look at the union that's being described here in this passage and see that what -- one of the things that -- there's something unnatural about the union because something else has been brought in that doesn't belong there. For, at such times, crazy Ahab is scheming unappeasedly steadfast hunter of the White Whale. This Ahab had gone to his hammock. So what we might think about is the conscious self. The self of the enlightenment is interested in him; right? The rationalizing, conscious intending self. He goes to his hammock. It was not the agent that so caused him to burst from it in horror again. All right. So somehow the body is breaking -- is bursting in horror in the middle of the night and that rational self is not the agent, Ishmael says, there's something else. The latter, okay, -- so that latter, we have to map back grammatically to agent, that latter was the eternal living principle or soul and, again, this is principle spelled differently, but I would like to say that there's a pun going on here between principle as in, you know, a precept and principal in the sense of principal and agent. The latter was the eternal living principle or soul in him, and in sleep, being for the time disassociated from the characterizing mind. Right. So in the rational Cartesian self, the soul and the mind are joined together, which at other times, employed it for its outer vehicle or agent, which would seem to suggest that at other times, the characterizing mind employs the soul for its outer vehicle or agent. It's spontaneously sought to escape from the scorching contiguity of the frantic thing, of which, for the time, it was no longer integral. Right. And that's because his idea of revenge has somehow taken on a life of its own. You served way more of Ahab's consciousness that it should; so we see. But as the mind does not exist unless leagued with the soul; therefore, it must have been that. Again, he's speculating. He doesn't know. He's trying to figure it out. He had these principles of how body, soul, and mind must go together. Something's wrong; so he's trying to figure out what's gone wrong. As the mind does not exist unless leagued with the soul; therefore, it must have been that, in Ahab's case, yielding up all his thoughts and fancies to his one supreme purpose, that purpose, by its own sheer inveteracy of will. So it's not his sheer inveteracy. It's the purpose itself. Forced itself against gods and devils into a kind of self-assumed, independent being of its own. Nay, could grimly live and burn, while a common vitality to which it was conjoined, fled horror-stricken from the unbidden and unfathered birth. Right. So we're saying that the soul itself is pleading away from this purpose, and, therefore, at that moment what seems like Ahab is a vacated thing. It's soulless. So one of the things that I suggested to you is this is Ishmael's attempt to think about the psychology of revenge and what revenge does. How does it destroy the self. I mean, again, it's the kind of thing that Hawthorne was investigating in his portrayal of chilling work. And the funny thing about it is it makes Ahab into something like what Ahab conceives the Whale to be, a kind of blank thing; right? A blankness in itself. Now it's -- you know, sometimes I look at this and I think it actually makes sense, and other times I think what it demonstrates is that it doesn't make sense and that there's something about -- because it's part of a chapter which calls into question the possibility of rational explanations of the Whale. Right. Ahab is trying to predict where the Whale is going to show up using these charts and using this sealore and the experiences of others. And one of the things we might say is that maybe what this dramatizes is the way in which the Whale -- if it represents something -- represents what isn't representable or what is somehow beyond our ability to rationalize it. We're just beyond the limits of our fancy and imagination, and, therefore, it resists description, and, therefore, this ultimately is going to be a failure as an attempt to describe it. And if that's true, we might want to think about this, the form of this whole book. Maybe it also is doomed to be a failure. Maybe it set itself an impossible project with the parts we're describing, something that's not describable, representing something and in the end is unrepresentable. And the last thing, I told you last time that the modern Prometheus, right -- so Prometheus -- the Prometheus myth if you're not Rick Reardon -- anybody read Rick Reardon? Percy Jackson? No Percy Jackson in here? I guess you're too old for that now. I have a younger son so -- read all these things. It's really unfortunately not as good. Prometheus shows up as kind of a dapper suit guy who's not exactly on mankind's side, but the idea that Prometheus gave civilization to humankind. He gives him -- he gives humankind fire, right, which allows him, despite what the god's want. So he allows civilization basically to begin in one dominant version of myth but that he's punished. Remember he gets chained to a rock; a boulder comes or an eel comes, I think eats his liver every day but every night it grows back, and the boulder comes again. [Inaudible] I think he's finally freed by Percy or something like that. In any case, you might say, Shelley's rewriting of the Prometheus myth is a lot darker; right? Well, she looks at [Inaudible] Prometheus is the defiance of the natural order of things, and the modern Prometheus is somebody who would -- either you serve the privilege of the god's or you serve the privilege of Prometheus, in any case, attempt to meddle where one shouldn't. Giving life -- giving civilization belongs to something other than humankind. If we serve that, very bad things happen. And what we have is this kind of weird, you know, it's unbidden birth and unfathered, I think, in the sense that the reason it would be unfathered -- let me see if I can find the exact -- creature, and he uses -- makes him -- okay, the idea of God -- the father not being involved in this, I think is part of what Melville is getting at here; right? So let -- I want us to understand that one of the things that's at stake for Ahab, and, therefore, for Ishmael, in so far as he's become part of this oath is, in some sense, a kind of questioning of the order of things that has begun with the Enlightenment; right? Remember the Enlightenment itself is about making the central drama of the West, not the relationship between God and humankind, but human consciousness itself. Right after the cart, we start to become interested in consciousness and anthropocentric, human center vision of the world. Isn't this just an extension of that mode of thinking. I mean, you know, Nietzsche's insight later on in the center will be that God is dead. And what he's dramatizing there is moments like this when we start to question the nature of humankind's relationship to God and even, you know, the importance of God at all. So that's kind of what's at stake here. Okay. That's one thing I want you to think about. Let's get to that other question I asked you about last time. What color is the White Whale really? And how do you know? Anybody? [ Inaudible ] >> Things growing on him? [ Inaudible ] >> You mean, like barnacles? >> Yes. >> That's possible. Can you find it for me? [ Inaudible ] >> It is in Moby Dick. And just so that we're clear, it's in Moby Dick, the Chapter, which refers to Moby Dick, the character, which means there's no hyphen. When we refer to Moby Dick, the novel, we need the hyphen. Mistake not this on your exam. Automatic point deduction every time you do it. [ Pause ] >> What color is the White Whale, really? [ Inaudible ] >> Yeah. [ Inaudible ] >> Transparent? You're going to have to give me textural evidence for this. So you better have a place to show. [ Inaudible ] >> Isn't it a what? [ Inaudible ] >> Yes. It's referred to as the Albino Whale. [ Inaudible ] >> Well, then it would be white. Yes. It would be white. [ Inaudible ] >> Well, she talks about him and the whiteness of the Whale; right? I mean, it's either all color or no color sort of thing. So you're telling me the white -- the Whale is a White Whale? It's Albino, and, therefore, it's either all colors or no colors? I mean, obviously, when you see pictures of the White Whale in the pictures, it's often white. Of course, Ishmael himself has a whole chapter about monstrous and erroneous pictures of Whales so. Are we sure about that? We're willing to stipulate -- we're willing to stake our grades on the course on the idea that this is a White Whale. [ Pause ] >> Any other thoughts? Yeah. [ Inaudible ] >> Very good. Show me where. [ Inaudible ] >> Okay. Read it, please. [ Inaudible ] >> Okay. A name, indeed, literally justified -- this is in the middle of 155 -- by his vivid aspect, when seen gliding at high noon through a dark blue sea, leaving a milky-way wake of creamy foam, all spangled with gold and gleamings. So he's not an all White Whale. He is not a fully Albino Whale. In fact, he's not all that different, it turns out, from most Sperm Whales. I'll show you a picture next time. Most Sperm Whales have white at places around their foreheads, certainly around their mouths. Oceanographers and ocean zoologists think that, in fact, this may have something to do with being able to serve as lures when they sound and go into the depths of dark water of fishes that they're trying to attract and other things they might see. They don't really know. But all whales have a little bit of white on them. It turns out that this one has a lot more white, but it isn't completely white. And I actually think this is one of Melville's telling details. Let's go look up further on the page. And thank you for noticing that. Even stripped of these supernatural surmisings, there was enough in the earthly make and incontestable character of the monster to strike the imagination with unwanted power. For, it was not so much his uncommon bulk that so much distinguished him from other sperm whales, but as was elsewhere thrown out, a peculiar snow-white wrinkled forehead and a high, pyramidical white hump. These were his prominent features; the tokens whereby, even in the limitless, uncharted seas, he revealed his identity, at a long distance, to those who knew him. But the rest of his body was so streaked and spotted and marbled with the same shrouded hue. So the rest of his body is streaked and shrouded with this hue, which is whiteness, that, in the end, he gained his distinctive appellation of the White Whale. So he's a White Whale who's actually a black-and-white whale; right? Most sperm whales have a black body. He too has a black body, but it's streaked and shrouded with this hue and then he has a white hump on the top, right, and a white -- he has a white hump and this white wrinkled forehead. And when does he seem most fully white? What does it say? When is he most fully white? When he's in the dark sea. A name, indeed, literally justified. So previously, not literally justified, but a name then literally justified by his vivid aspect when seen gliding at high noon. So in the light, through a dark blue sea, he becomes whiter, the darker the background around him, the context around him. I want you to think about that for a moment. Melville is writing about, you might say, a White Whale. Here, Ishmael is describing the construction of that whiteness. He's taken to be white by those who see him or have heard of him because of the way he looks in the water when he is surrounded by black and because there is so much white on him, more white than on other whales; nevertheless, he's a black-and-white whale. Think of the context of 1850. I suggest to you that it is not possible to be writing about blackness and whiteness and not have this somewhere in your imagination. Consciously or unconsciously, this is part of the imagination of his text, right, the compromise of 1850; the Fugitive Slave Law; the fact that Melville's father-in-law, the Chief Justice of Massachusetts returned the first fugitive slave. The text is marked by these, you might say, culturally traumatic events. And I think at the heart of the text, this White Whale, it is no accident that it is not just an Albino Whale or that Albino is a kind of shorthand for the actual dynamics of what's going on here; that it's a white whale that seems white because it's more white than other whales; that because in the surrounded by blackness it comes to seem as if it's only white. So there's something about the darkness of the context around that highlights the whiteness. I mean, this is an argument that some scholars and most -- maybe most prominent the Nobel Prize-winning author Toni Morrison makes about all of American literature, and she draws on Melville's novel as an example of a text that's kind of trying to resist this logic. And the logic is that at the deep heart of American literature, lies a guilty conscience about the subject of and the fact of blackness. Her analysis probably could be extended by thinking, as we would know in our course, back to Native American, but there have always -- we might take her point. There have always been dark others. And she wants to say that just as the Enlightenment -- what she calls the Age of Scientific Racism -- construct itself against a background of domination so too does the American liberal self construct itself around a background of domination and, in particular, racism and slavery. That whiteness as a concept is constructed around its difference from blackness and in American historical terms, in fact, there was a huge black population living amidst whiteness. And she says that American -- this is true of American literature even when it isn't apparently true from American literature that when you look at it, there is this kind of awareness of this dark -- where she calls this dark abiding presence at the heart of almost every American literary text for her. And she has a very interesting analysis of Ahab, which probably pictures it too far, but she says, of course, Ahab is crazy, because one of the things that he's doing in resisting the White Whale is resisting precisely this ideology of whiteness. The part of what she -- what's going on is that he is setting himself at odds with the most basic assumption of his society. How could be -- how could he be anything other than crazy if that's the case. All right. I want you to think about this. All Right. Think about the sense -- and one of the things that we've been trying to develop here is a sense of context of American literary text. And I want to suggest to you that one of the ways in which Moby Dick is, in fact, a national novel in the middle of the nineteenth century is because many of these cultural contradictions, conflicts, and energies have worked their way into their text. I think Melville is quite conscious probably about this. I mean, there's a -- I suggested to you that other evidence -- that he knows his father-in-law's cases well comes from his use of the term monomania, which actually was in a case that Shaw presided over. I think it was called Commonwealth versus Rodgers. It was about six years earlier in which Shaw ruled that the Massachusetts state prison inmate named Rogers, who claimed that voices had told him that the warden would kill him, was not guilty by reason of insanity. Specifically, the insanity of monomania. Shaw wrote this: The act was the result of the disease and not of a mind capable of choosing. It was the result of uncontrollable impulse and not of a person acted upon by motives and governed by the will. So that idea of monomania is something that Melville is playing with. But you might say that he's a little bit critical of that idea of monomania or he develops it in a more detailed and dramatic way. Ahab calls himself in his soliloquy, the Sunset Chapter, I am madness maddened. Right. I mean, what does it mean to be madness maddened. It's precisely the kind of madness that comes to interest Poe. The madness that is, in some sense, just this side of rational. That he's able to use rationality as its instrument and appear in many instances to be absolutely rational. Ahab, as you might say, is teetering between these things. In a certain way, it's the Hamlet problem. Is Hamlet mad or not? Is Hamlet play acting or not? Is he play acting sometimes and not play acting at other times, and how do you know? The same thing might be true of Ahab. Is he mad or is he not? Is he completely rational? So a couple of things that I want to show you. I want to go to the -- towards the end of our -- the sections that we read today and look at a chapter that's called Fast Fish and Loose Fish just so you understand a little bit more about these dynamics of freedom and unfreedom and the novel's engagement of what we might call the culture around it. So this is Chapter 89 and it starts on page 307. [ Pause ] >> Does anybody remember it? What's the difference between a Fast Fish and a Loose Fish? Yeah. [ Inaudible ] >> Okay. [ Inaudible ] >> A Loose Fish is a fish that's up for grabs. Thank you. That's right. And there's a little refinement Sue made about that. Having a line attached to it means you're actually holding that line? [ Inaudible ] >> Actually, what it means is that you could be holding the line. In other words, you attach something to mark it as your possession. So if you're fast to it, you start out by hooking your harpoon and holding it, but, then, at a certain point, you can let go as long as you can attach a waif to it. All right. So you hook something else instead of you that acts as your agent, you might say, right, and the only stipulation is you can not go so far away that you can't actually go and retrieve it in a timely fashion. Let's take a look at that on page -- thank you very much. That's right. Let's take a look at page 308. He's developing -- he's trying to talk about the code of the sea. He's developing this. He's talking about these ideas. One, a Fast Fish belongs to the party fast to it. Two, a Loose-Fish is fair game for anybody who can soonest catch it. Right. Up for grabs. But what plays the mischief with this masterly code is the admiral brevity of it which necessitates a vast volume of commentaries to expound it. First: What is a Fast-Fish? Alive or dead a fish is technically fast, when it is connected with an occupied ship or boat, by any medium at all controllable by the occupant or occupants,- a mast, an oar, a nine-inch cable, a telegraph wire, or a strand of cobweb, it is all the same. Likewise a fish is technically fast when it bears a waif, or any other recognized symbol of possession; so long as the party wailing it plainly evince their ability at any time to take it alongside, as well as their intention so to do. All right. So one of the things we've noticed here is that all the questions that we've been talking about having to do with agency, the ability to act, the ability to have intentions are part of whale hunting. They're part of the fabric of whale hunting. So let's talk a little bit more about this. A Fast Fish, we get that. What is a Loose Fish, again? You said it well. Say it again. [ Inaudible ] >> Okay. A Loose Fish is a fish that's up for grabs. If you're -- if you are -- if we think from the standpoint of the whale for a moment, let's [Inaudible]. What's wrong with that way of thinking about things? [ Pause ] >> A Fast Fish is a fish that's caught. A Loose Fish is a fish that's up for grabs. What's wrong with that, from the whale? What's that? [ Inaudible ] >> That's very good. The whale isn't just conceived of as free. It's not a Loose Fish is a free whale. In some sense, it suggested that there's no such thing as a free whale. There's only a Fast Fish and a fish that's waiting to become a Fast Fish, the so-called Loose Fish, because it's up for grabs. Now I think that's an important distinction. And I think it's a distinction that Ishmael is making for us. It's the same idea that I've been talking about before with the negative conception of liberty. Freedom is parasitic on the idea of unfreedom. We can't define freedom without the idea of unfreedom. That's a little weird when you think about it. Likewise, this Loose Fish and Fast Fish business. There's no such thing as a free fish. There's only this conception of whales. This conception in which they are either caught or waiting to be caught, either way they're dominated by humankind. All right. That's interesting enough as far as it goes, but I want you to see what Ishmael does with it later on. All Right. Because he has this kind of anthropia impulse, you might say, to start off with, something that looks material but then to render it abstract and then abstractor, right, as more abstract and as abstract as you possibly can, and more generally applicable. Take a look at the bottom of 309. [ Pause ] >> Is it not a saying in everyone's mouth, possession is half the ball, that is, regardless of how the thing came into possession, but often possession is the whole of the law. What are the sinews and souls of Russian service and Republican slaves but Fast Fish, where a possession is the whole of the law; right? So now he's going to generalize on. Saracen Russia, slaves that we own; right? That context. Their Fast Fish, possession is the whole of the law; right? Remember Frederick Douglass? What right had his masters to take any of his earnings, the right of the grim visaged pirate. That's the right he had. What Irving calls in the history of New York, the right by gunpowder. What's the rapacious landlord is the widow's last might but a Fast Fish. What his yonder undetected villain's marble mansion with a doorplate for a waif. What is that -- by a fast -- but a Fast Fish. What is the ruinous discount which, Mordecai, the bank broker, gets from poor Woebegone, the bankrupt, on loan to keep Woebegone's family from starvation. What is that ruinous discount but a Fast Fish. It's yours because you have the force to take it. And he adds anti-semantic but, you know, this is a nineteenth century text. What is the Archbishop of Savesoul's income of a hundred-thousand pounds -- it sounds like anti-Christian; so equal opportunity -- save from the scant bread and cheese of hundreds of thousands of broken backs, laborers all sure of heaven without any Savesoul's. What is that a globulin or 100,000 but a Fast Fish. What is the Duke of Dunder's hereditary towns and hamlets but Fast Fish. What to that redoubted harpooneer, John bull -- we know who John bull is; right? So a characterization of England -- John bull but Ireland to -- is poor Ireland but a Fast Fish. What to that apostolic Landser brother Jonathan -- United States. Is Texas recently next but a Fast Fish. And concerning all these is not possession the whole of the law. All right. But he says, if that's true of the Fast Fish, think about the Loose Fish, everything else, and think how even more broadly applicable, that is, internationally, he says, and universally applicable. What was American 1492 but a Loose Fish in which Columbus struck the Spanish standard by way of waifing it for his royal master and mistress. What was Poland to the Czar. Greece to the Turk. India to England. What, at last, will Mexico be to the United States, all these fish. Right. I mean, in the middle of the nineteenth century, it sure as hell looked as if the United States, driven by this ideology of manifest destiny was destined in some sense to take over the entire continent. We can say it didn't happen yet. What are the -- so that's the cultural situation, the historical situation. So I'm telling you the novel and Ishmael have these things on their mind, right, slavery, the Mexican War. It's all there. It's in the imagination of the text. What are the rights of man -- still more abstract. What are the rights of man and the liberties of the world but Loose Fish. What does that mean? The rights of man and liberties are up for grabs? Well, maybe it relates back to what I was saying that there is no real conception of freedom. Freedom is always reigned by constraint. What are all men's minds and opinions but Loose Fish. Maybe we're also reigned by constraint in ways we don't see, waiting to be caught. What is the principle of religious beast that believe in them but a Loose Fish. Religion, able to be manipulated as Stowe and Palais and Bildet [Phonetic] and Ishmael all show us. What to the ostentatious smuggling verbalists. Now who might they be? Emerson, maybe. Melville? Hawthorne? Ostentatious smuggling verbalists but a Loose Fish. And here's the kicker. And what are you reader but a Loose Fish and a Fast Fish too. What does that mean? How can you be a Loose Fish and a Fast Fish? Were you loose? I mean, being loose apparently is not that good. And now it turns out that you're fast as well. What's in you reader? What has its tender hooks in you already? Page 310 and Chapter 89 of the novel. Don't say me. I wasn't there when Ishmael wrote this down. All right. I want you to bear that in mind. I mean, I think these are questions that have to do with, you might say, the cultural imagination, but they also have to do with interpretation and your freedom to interpret; right? So they're ultimately questions about reading as well. Now what I want you to see is these kinds of questions that seem like they're separate kinds of questions. Questions about reading and interpretation and audience, on the one hand. Questions about agency and domination, on the other, are entwined in this book. And maybe all of them. Maybe the book's just dramatizing the fact that they're always entwined for us. All right. Video break. I am going to show you what an actual Nantucket Sleighride looks like. This is from a 1922 movie. It's a brief clip called Down to the Sea in Ships. The Nantucket Sleighride is what the name given to -- what happens when you throw a harpoon in a whale and then it takes off. All right. You remember that chapter that's called the Line, there's -- if you have this edition of the book, there's actually a picture of what the Line looks like. It's on page 451. And one of the things that Ishmael then does and then goes on to do in this chapter called the Line is to describe it quite vividly, how this Line works. They're all sitting there in this little boat but you need to have feet and feet and feet and feet of line so that once the thing is caught in the whale, you can let it run out. You can't be right there. You have to let -- give it a lot of room to run itself out. It will tow you along, eventually; right? Because we understand how this works, this whale hunting; right? We understand? They shoot a harpoon. They launch a harpoon into the whale and then they hang on for dear life. And they let the whale run itself -- pissed off, and the whale now trying to get the thing out of it and run itself -- swim itself into exhaustion and then when the whale is really, really tired -- and this might take hours, and it might go for miles and miles away from the ship itself. When it's really tired, they pull themselves up alongside, they take another harpoon and stab it in the heart, sometimes through the eyes, stab it until it's dead, through the blowhole until it's dead, and then they take it back -- they tow it back or the ship comes and finds them to [Inaudible]. They take it back. They stick it on the side of the ship, and they start to peel its skin off to get at the blubber, the fat that's underneath. These are what's described in all of these chapters. So I'm going to show you -- this is a movie that was made almost at the very end of the age of whaling. I mean, I'll talk about it a little more next time. Melville writes this in 1850-51, which is the high point of whaling. By '54, the whaling industry's already started to go in decline, in part, because of the discovery of some oil in New England, and, in part, because of the Gold Rush and, you know, they were quite literally -- in that later period, there are sailors that go out three years of whaling, they bring back full holes, and they find that the price of whale oil has plummeted, and they can't sell the stuff or not sell it to make it worthwhile so. This is an industry that is very short-lived in a certain way. And the way Mel has captured it -- captured something that's almost, we would say, already gone at the time that he's writing about it. And so 1922 -- this is a movie that is well, it's a weird kind of orientalist marriage comedy set around whaling and it also has some kind of documentary footage. All right. So there's that. Then I will show you a little right after a bit of actual footage of bailing the case and the processing of the whale that goes on. That's from the 1930 adaptation. I'm actually going to -- so you can see better, I'm going to turn down the lights, and we'll see if we need to manipulate them at the end to make it lighter. [ Pause ] >> You'll be able to see the Line in there. [ Video Playing ] >> Can I have the sound back. Okay. I want to actually take a quick look at that chapter that's called the Line. This is on -- starts on page 227, and I want to look at the end of the chapter. Now he's described this stuff and you can see how it works; right? Okay. But he's described it in a way that seems like it's just another one of these chapters about whaling that's kind of boring and we should skip it, and they certainly do leave it out of the abridgment that's called Moby Dick, the good parts, of course, to me, these are the good parts. Part of it is I think that one of the things is you avoid these things that you're peril, because they're the moments that Ishmael actually gets the heart of what the novel is really about. It's what makes the novel not just an adventure story about killing whales. So look at the bottom of 229. [ Pause ] >> Or let's do the middle. Perhaps very little thought will now enable you to account for those repeated whaling disasters, some few of which are casually chronicled of this man or that man being taken out of the boat by the Line and lost. I want you to remember these dynamics. They become important. For, when the Line is starting out to be seated, then, in the boat, is like being seated in the midst of the manifold, who is, I think, a steam engine in full play when every flying beam and shaft and wheel is grazing you. It is worse, for you cannot sit motionless in the heart of these perils, because the boat is rocking like a cradle, and you are pitched one way and the other without the slightest warning and only by a certain self-adjusted buoyancy and simultaneously -- simultaneousness of volition and action can you escape being made a zepa of and run away with, where the all-seeing sun himself could never pierce you out. Remember that description over the weekend. Okay. Again, as the profound calm, which only apparently precedes and prophesize of the storm is perhaps more awful than the storm itself, for, indeed, the calm is but the wrapper and the envelope of the storm and contains it in itself as a seemingly harmless rifle holds the fatal power and the ball and the explosion. All Right. So this is a meditation on anticipation and also potential and the hidden things inside of other things that may well kill you. So the graceful repose of the Line as it silently serpentines about the oars and before being brought into actual play, this is the thing that carries more of the true terror than any other aspect of this dangerous affair. And now you should think, I think of Jonathan Edwards in that moment of the spider; right? Remember that. He says, there's no reason that you haven't dropped into hell right now but that God just doesn't will it at this particular moment. All men live enveloped in whale lines. All are born with halters around their necks, but it is only when caught in the swift sudden turn of death that morals realize the silent subtle ever present perils of life. And if you'd be a philosopher, those seated in the whale boat, you would not feel at heart, feel one more Whitmore of terror than those seated before your evening fire with a poker and not a harpoon by her side. He's saying this should not scare you anymore than simply being seated right there with your pen by your side, instead of this harpoon. Or the other way to think about it is that you should be just as afraid sitting there where you are as you would be over there. [ Pause ] >> What do you think about that? Is it true? [ Pause ] >> If it were true, on what assumptions does it depend? If it's not his time to go, then he's not going; right? So he doesn't have to worry about it. As Stowe would say, hey, it's all predestinated. Don't have to worry about it. It's my time, it's my time. Nothing that I'm going to do is going to change it; right? If somebody is sitting right in this room and suddenly it's there time, they'll have a seizure or they'll be injected into space or the ground will open up before them, it will be their time; right? Not likely to happen but who knows. Do we believe it? Or is this -- what is this? Is this a weird kind of rationalizing? Should we be suspicious of this logic here? Is it not the case that if you put yourself here, you are actually more likely to have something terrible happen to you than if you just don't and you sit around and sit, you know, just have a day job and some place that's on land and it's easy and you stay out of harms way and don't run in the road and all that kind of stuff? Yeah. [ Inaudible ] >> Yeah. I guess that's right. If there's something you're saying -- one of the things -- but it does seem -- if you be a philosopher, I mean, that's kind of like the casual excuse well, you know, thinking philosophically or I've got to be philosophical about this. Well, what does that actually mean? Let's be philosophical about this. I mean, we know, even if we haven't taken philosophy courses that there's a bunch of courses in the philosophy department. There's lots of different kinds of philosophy, and they often are at odds with one another; so why -- what is being philosophical -- for what is that shorthand and should we be suspicious of it? Is it not like, you know, there's a certain pattern of logic that's emerging here? Better sleep with a sober canon than a drunken Christian; right? Better to be with, you know, Ahab than somebody who doesn't know what he's doing. Yeah. [ Inaudible ] >> It's possible. [ Inaudible ] >> I think it's possible. I don't know that the -- I don't know that in the moment that Melville is writing just referring to the Line is necessarily in the way that I'm suggesting to you that referring to black and white is going to be charged. I'm not sure, for instance, the Line is going to be as charged. But you know what, that would be a great topic. Well, not for this paper, but, a paper. It would be an interesting thing to think about. I mean, if you were going to make that, and we could say, sure, among the possibilities of the things that might, given all the other possibilities, it could be a reference to that, and, therefore, get another reference to the division of the country and the problems of slavery. But what evidence would you really want to be able to martial from the text in order to be persuasive about that? It's a suggestive thing. I don't have -- I can't say -- I mean, yeah, sure, but I don't know if I actually believe it, but I'm willing to be convinced. Yeah. [ Inaudible ] >> But it isn't arbitrary. It's only arbitrary from maybe your point-of-view. From God's point-of-view, it's fully intentional. That's what Providence is. But you don't know; so you have faith. So one of is -- so is one of the things that Ishmael is saying, that, to do that, you need to have a little faith? What happens when, like Ahab, you lose that faith? What can you substitute for that faith? He seems to be substituting his own revenge maybe or his own force of personality. I don't know. We're only halfway through. We'll have to see how it turns out. But it's kind of, you know, there's certain -- what does it mean to get yourself to go whaling? What do you need to believe? And are you fooling yourself and believing it? [ Inaudible ] >> You could go, I guess, and maybe you don't really care if what you're trying to do is commit suicide by other means. Remember? Right? Cato, you know, falls on his sword, other people take [Inaudible] why go to sea? I go whaling. Is this suicide by other means, then, you don't care? It's like, you know, get it over with please, then, I don't have to work so hard. Yeah. [ Inaudible ] >> I like that idea, although I'm not -- where do you see that in this passage, the idea that somehow being in this position makes you more alive than -- [ Inaudible ] >> Right. Yeah. I can see that's right, but the implication of that to me is that only when you're about to die, do you suddenly realize how -- I don't know [Inaudible] a short life was. [ Inaudible ] >> Yeah. You realize -- I don't know. I think there are other passages where I would go to say that there's something about this that creates a certain kind of intensity of experience and imagination, but it's not incompatible with it. Yeah. [ Inaudible ] >> Yeah. No. I think that's right, that's what he's trying to suggest is that, you know, you're sitting there, you think you're comfortable. You're not in peril but you are. [ Inaudible ] >> That's the other thing he's saying. He's saying both of those things. They're the same, but they're -- what I'm trying to say is they're underwritten by a system of belief and that system of belief is when it's your time, it's your time. What if you don't believe in that system of belief? Or do you have to? Or -- and does he? Does he really? I mean, how are we going to finally decide what he believes about predestination? Does he really believe it in [inaudible]? Or. He makes all these jokes about it. Is he serious here and not serious elsewhere? Is he always serious? Yeah. >> Do you think that if you'd be a philosopher thing also has a kind of ring, like, if you feel like it, like, if you want to be this way, you can? >> Yeah. I think that's right. I think it also there's -- wouldn't you say that there's an implication that, you know, here's one way to look at it is true but also it's something that most people don't; right? Because if you're a philosopher, you would understand it in a slightly deeper way. If you'd be a philosopher, those seated in the whale boat, you would not at heart feel one more Whitmore of terror; right? Why? Because you understand the way it really is. And the way it really is, is that life itself is dangerous. We're always born with a noose around our necks or we have one foot in the grave. We're slipping down towards death. Being philosophical about it means a certain kind of acceptance of this. And when it's our time to -- it could -- it doesn't even mean -- I suppose you could argue it doesn't even mean that. You have to say that -- you have to believe in predestination of any kind, except the predestination of death. We're all dead. We're just waiting to get there. When it comes, it comes. I don't know. All right. I'm going to show you one of the clip. This is what happens after they do this. So this is cutting in and trying out. And this is about 45 seconds long. >> Yum, yum. [ Video Playing ] >> There we go. Is -- what I want to suggest is, is what Ahab doing, something different; right? Or is it, in some sense, just an extension of what it is, that whaling is always about; right? Or is he choosing one whale to pick out? That's a little strange. But insofar as he's suggesting that the mission of the Pequod is going to be the reassertion of humankind's domination over nature. Isn't that what whalers always do? Isn't that part of what's at stake? The domination of nature, the transformation of natural creatures into human products, dead human products. And part of what we see in the chapter, like Stubb's supper is the extent to which, in this moment, the products of the whale are everywhere; right? They come to surround us even in the way that we start to take for granted. So one of the things that I want to suggest to you is that built into the whole business of whaling, and, therefore, coexisting with all the arguments that Ishmael wants to make about the promotion of peace and cosmopolitan relations through whaling -- which we'll say a little bit more about next time. Comes the idea that it all depends on the domination of nature, which is not to say that nature is something that is touchy feeling nice and the kind of, you know, kind of soft environmentalist way. Nature will kill you constantly in this book; right? If it isn't the whale's, it's the sharks that are vicious and all -- I mean, we can take look at any number of places where we see that the nature on the sea is not unlike Bradford's howling wilderness. It will kill you. Everything will kill you in the end. It's maybe one of things that we're starting to realize about this book. Is there any counter weight, therefore, to this? What we might want to think of it is this logic of revenge; this logic of domination; this ostensible logic of freedom, which is always surrounded by unfreedom, is there anything? Well, there's one place we could look. It occupies a place in this book that is somewhat somehow somewhat like the Quaker Settlement in Stowe's book -- and this is Chapter 94, A Squeeze of the Hand. So let's take a look at that. Everybody remember Chapter 94? Now the context is that they've gone and they've gotten this whale, and, as a consequence of it, Pip has fallen into the drink and seeing the eternal and come back slightly nuts. We'll talk about that next time as well. So that's what he means when he says, that whale of Stubb's, so dearly purchased, was duly brought him on the Pequod's side, where all those cuttings and hoisting operations previously detailed, were regularly gone through, even to the baling of the Heidelburgh Tun, or Case. So it all happens. Right. While some were occupied with this latter duty, others were employed in dragging away the larger tubs, so soon as filled with the sperm; and when the proper time arrived, this same sperm was carefully manipulated ere going to the try-works, of which anon. It had cooled and crystallized to such a degree, that when, with several others, I sat down before a large Constantine's bath of it, I found it strangely concreted into lumps, here and there rolling about in the liquid part. Not unlike -- and Hutchinson's afterbirth, I suppose, if you remember that little footnote from John Northrop's journal. If you don't, look it up. You'll find that, that was actually rather a sick joke. It was our business to squeeze these lumps back into fluid. Now as you -- I want you to think about what discourses might -- what kind of language this is. Why all the exclamation points? What language might it be that Ishmael is either invoking or parroting or both? It was our business to squeeze these lumps back into fluid. A sweet and unctuous duty! No wonder that in old times sperm was such a favorite cosmetic. Such a clearer! such a sweetener! such a softener; such a delicious mollifier! After having my hands in it for only a few minutes, my fingers felt like eels, and began, as it were, to serpentine and spiralize. All right. I think it's the -- I think it's some of the language of advertising, even already making its way in here. As I sat there at my ease, cross-legged on the deck; after the bitter exertion at the windlass; under a blue tranquil sky; the ship under indolent sail, and gliding so serenely along; as I bathed my hands among those soft, gentle globules of infiltrated tissues, wove almost within the hour; as they richly broke to my fingers, and discharged all their opulence, like fully ripe grapes their wine; as. I snuffed up that uncontaminated aroma,- literally and truly, like the smell of spring violets; I declare to you, that for the time I lived as in a musky meadow; I forgot all about our horrible oath; in that inexpressible sperm, I washed my hands and my heart of it; I almost began to credit the old Paracelsan superstition that sperm is of rare virtue in allaying the heat of anger; while bathing in that bath, I felt divinely free from all ill-will, or petulance, or malice, of any sort whatsoever. Squeeze! squeeze! squeeze! all the morning long; I squeezed that sperm till I myself almost melted into it; I squeezed that sperm till a strange sort of insanity came over me; and I found myself unwittingly squeezing my co-laborers' hands in it, mistaking their hands for the gentle globules. Such an abounding, affectionate, friendly, loving feeling did this avocation beget; that at last I was continually squeezing their hands, and looking up into their eyes sentimentally; as much as to say,- Oh! my dear fellow beings, why should we longer cherish any social acerbities, or know the slightest ill-humor or envy! Come; let us squeeze hands all round; nay, let us all squeeze ourselves into each other; let us squeeze ourselves universally into the very milk and sperm of kindness. [ Laughter ] Would that I could keep squeezing that sperm for ever! For now -- being the father of a nine-year-old and 5 -- no -- since by many prolonged, repeated experiences, I have perceived that in all cases man must eventually lower, or at least shift, his conceit of attainable felicity; not placing it anywhere in the intellect or the fancy; but in the wife, the heart, the bed, the table, the saddle, the fire-side; the country; now that I have perceived all this, I am ready to squeeze case eternally. In thoughts of the visions of the night, I saw long rows of angels in paradise, each with his hands in a jar of spermaceti. I have been tempted -- I have been very tempted, on occasion -- I suppose I can't do it now that I'm saying this. Too bad. My last chance. I have been very tempted to simply create a final exam that sets that on a piece of paper and says explicate, because I think, in some senses, almost everything that we have talked about this term, is referenced here. There is a way of thinking about this as a commentary on the last 24 some-odd, you know, class days that we've had. And so tell me why? What's going on in there. Anything, by the way, just let's -- we have four minutes left. Let's just name -- we'll start off -- it's so delicious, as it were. We'll start off here on Monday. But tell me some of the things that are going on here, and not just the obvious ones. Okay. You can start with the obvious ones. What's the obvious ones. Yeah. [ Inaudible ] >> Gee, I haven't thought about that. I'm not sure about the wine industry yet, actually. I'll have to think about that. That would be interesting. That is not obvious, and we'll have to look that one up. I think that's interesting. [ Inaudible ] >> Okay. That's fine. The saddle, the fireside -- because there's a certain assumption about what a settler might look like. [ Inaudible ] >> Okay. That's good. That I -- yeah. Okay. That's great. In fact, I think that is like -- that's something that would take me a while to look at after looking at -- so it's good. Moore [Assumed Spelling]. [ Inaudible ] >> Really? I wonder why. >> It's not that it's obvious or anything, but I mean, yeah. >> Why did it remind you of that? >> Squeezing the hand. I don't know. It seems like [Inaudible]. >> All right. Yes. There's homosocial overtones here. Yes, of course. Right. So this -- think of the trajectory of the book. We're going from Queeqeeg, he is cozy, bosom buddies, a loving couple, to this moment where we don't need women. We just have -- we're here and we have this moment of connection. Not only don't we need women, we don't need Harriet Beecher, damn, Stowe. We have sentimentality right here. Isn't that what he's doing again, sort of peeing on that hydrant. We look at each -- I mean, it's certainly invoking the discourse of sentimentality, except it's more complicated than what I am suggesting; right? If you remember Hawthorne in the preface, to the House of the Seven Gables, talking about cooking and using that metaphor, we get that -- so here too; right? Why else would he think of them as woven tissues, that imagery? And we -- there's a kind of validation, you might say, even of the sentimental discourse. But, look, what a falling off there is when you get from this kind of sentimentality to the thing that women actually write about, which he identifies as the wife, the heart, the bed, the table, the saddle, the fireside, the country. Here, on the ship with his mates doing this labor, where you can forget yourself -- have that kind of what, you know, what Young describes as that oceanic feeling. A loss of individuality and all the ideological [Inaudible] that comes with it, including in this context, Ahab's horrible oath. Get rid of all the revenge, all that stuff. Have this moment thinking about heaven and Angel -- and it sure is homosocial, but it's more than just homosocial. What it is, it's suggesting that, in some sense, if you think of it, from the terms of literary history, we, again, can do without that entire tradition. We have it all here within the tradition of American romance. But it doesn't last. You can't stay at sea forever. You can't do this forever. Eventually, you have to realize -- you have to grow up and you have to finally go for, what he calls, attainable felicity. It's not going to be anywhere, he says, in the intellect or fancy; so that division returns. This is almost like a kind of exile and return narrative that you might see some place in Shakespeare in which this is the force of Arden, where transformation takes place, but you don't get to stay. You don't even get to stay here for the length of a chapter. Comment? Question? [ Inaudible ] >> That's good. All right. We're going to stop here. I want you to think about this passage as you finish the book. We'll open up here next time. Let me know if there's anything else that we want to do in that. [ Silence ] |
Open_Ed_Cyrus_Patell_American_Literature | MobyDick_III.txt | >> Teacher: All right, let's get started. So our subject for today is agency, by which I mean the power to act. And one of the things we're going to be thinking about is the ways in which this novel dramatizes what we might think of as model of agency. And in the context of this course, it means the way in which Melville is rethinking some of the issues that have, you might say, motivated writers in our course from at least Winthrop on. The idea of the relationship between fatedness on the one hand, and freedom, the freedom to act, on another. Which is some sense is one of the major trajectories in the course, right? The Puritans had one way of thinking about the relationship between what they called providence or fate, and the idea of freedom. They had to have both, even though they sometimes seemed that they were complement, contradictory ideals, right? But when you think of the idea of total depravity, Adam cannot be held responsible for his disobedience. And his progeny cannot be held responsible for Adam's disobedience if he weren't free to act in some fundamental way. So that even if God had set up a situation in which everything's foretold, and God sees how things will turn out, in the event for the Puritans Adam was always free to obey or not obey. And therefore, free, had to take responsibility for what he did. The fact that God's mind is such that He can always know how somebody is going to choose, does not in fact invalidate the act of choosing itself. When you get to someone like Emerson, you have a radically different idea about the way in which agency is constructed and the way in which it needs to be constructed, right? He's thinking about the sense in which we are too much bound to the past. Our age builds the sepulchers of the fathers, our age is retrospective. The idea that we have in some sense constrained our own agency. That's the point of the fable of the Orphic poet that he tells. In some very deep way Emerson believes we create the world. And if we forget that we do that, we severely limit the possibility of our own agency. So self-reliance becomes a call for human beings to reassert their agency. To let go of the past in certain ways. We've already looked at the ways in which Hawthorne and Melville were skeptical of this, and I want to pursue that a little bit more today. Remember that scene in Hawthorne's Scarlet Letter where Hester says, you know, to Dimmesdale in the forest, Begin all anew. Not possible for some very good reasons. And Melville I think also thinks that there may, you know, that Emersonian swerve might be too quick. We need, as he says in Hawthorne and His Mosses, Something somewhat like Original Sin to strike the uneven balance. So part of what we're thinking of here in Moby Dick, is what is that something somewhat like Original Sin that's being dramatized? What are the constraints on agency here? And who's placed them? What are the models of the agency [inaudible]? What agency does a narrator have in being able to construct his or her narrative? What constraints might be in place there as well? And so those are some of the larger issues that I want to talk about today. Next time I want to talk a little bit about the idea of domination, which is related to the idea of agency. And so I'd like to start next time's lecture with a question. If you know the answer to it now, don't reveal it. But I want to start with a question which I'm going to pose to you right now. And that question is quite simple. What color is the white whale really, okay? Somebody will tell me the answer to that and show me how she or he knows at the beginning of next time, right? So what color is the white whale really? Okay, and I'll even remind you of that in an email later on. Okay. So let's go back to that moment where we ended last time in the chapter that's called The Ship. And remember what was going on there. This is a chapter where Ishmael, it begins with the idea of agency and fatedness being interlinked, right? Ishmael has delegated. Agency, the power to act, can sometimes be delegated. There's a way in which Queequeg, saying that he's actually on behalf of Yojo, has delegated to Ishmael the job of choosing the ship, even though Ishmael is probably not as expert in knowing what the best kind of whaling ship is. Yojo said it'll be okay if you pick it, so Ishmael does. He settles on the ship that's called the Pequod and it's kind of a weird ship. It's all festooned with ivory and whale artifacts. It has a kind of barbaric look to it, which I guess makes it in keeping with the kind of things that we presume that Yojo would like in all of this little blackness, you know, and woodenness. Okay. Then he has a strange conversation with somebody, who's also biblically name, Peleg. And I said that Peleg's name actually refers to a stream that divides different territories. And Bildad, another biblical name. These two are the managing partners of the ship. And Peleg seems to be the real managing partner. He's the one that's constructing the negotiations. Bildad is looking at a book, and periodically he looks up. And what he ostensibly is reading is this chapter from Matthew, right? Chapter 6, verses 19 to 21. Lay not up for yourselves treasure upon earth where moth and rust doth corrupt. And where thieves break through and steal. But lay up for yourselves treasures in heaven, where neither moth nor rust doth corrupt. And where thieves do not break through nor steal. For where your treasure is, there your heart be also. That's what he's ostensibly reading. And what emerges is a kind of interesting pun on the idea of the lay, right? And remember that Ishmael has just told us a little bit about the way in which whalers normally use the term lay. And this is on page 75 of the novel. Here Ishmael is explaining that the way that sailors are customarily is through some portion of the net proceeds of a voyage. You can imagine that everybody has shared in this voyage, and the owners have a certain number. And according to how highly you were rated, and how important you are to the ship, you get a certain fraction of the clear net proceeds. So Ishmael has decided the probably what is appropriate for him to get is something like the 275th lay. Or as he puts it on the bottom of 75, The two hundred seventy-fifth part of the clear net proceeds of the voyage, whatever they might eventually amount to. And though the 275th lay is what they call a rather long lay, yet it was better than nothing. And if we had a lucky voyage would pretty nearly pay for the clothing I would wear out on it, not to speak of my three years beef and board for which I would not have to pay one stiver. All right? So he's thinking he's not going to be paid very well, but he's going to get experience, and he's going to basically break even. Does he end up with the 275th lay? No, he does not. He ends up with something a little bit worse. He ends up with the 300th lay, and he's glad to get it. Why is he glad to get it? Because Peleg and Bildad have put him through a sort of negotiating routine. And it's linked to Bildad's reading of the Bible, right? So Peleg says, What are we going to pay the guy, in the middle of 75. Well, Captain Bildad. What d'ye say, what lay shall we give this young man? And Bildad you can imagine looking up and saying, Thou knowest best. The seven hundred and seventy-seventh wouldn't be too much, would it? And as your footnote tells you it's a biblical number from Genesis. Okay, fine. There are a lot of numbers in Genesis, but that one has a kind of ring to it, so fine. Seven hundred and seventy-seventh, and then this. For where your treasure is, there will your heart be also. Peleg says I'm going to put him down for the three hundredth. Now 300's a lot better than 777. And Ishmael has already [inaudible] on the fact that this 777th lay is a really bad thing. Okay. So Bildad insists a little bit. Captain Peleg, thou hast a generous heart. But thou must consider the duty thou owest to the other owners of this ship, widows and orphans many of them. So there's a kind of Christian logic I suppose that's at stake in 777. I don't know. There's another kind of Christian logic that seems to be at stake here, widows and orphans, right? We have to be Christian. We have to provide charity. We have to provide for those, many of them. And then if we are too abundantly reward the labors of this young man, we may be taking the bread from those widows and those orphan. The seven hundred and seventy-seventh lay, Captain Peleg. Now at this, Peleg, who apparently doesn't like to be contradicted, starts to get a little bit of exercise. Thou Bildad! roared Peleg, starting up and clattering about the cabin. Blast ye, Bildad! If I had followed thy advice in these matters, I would afore now had a conscience to lug about that would be heavy enough to founder the largest ship that ever sailed round Cape Horn. Think of like Jacob Marley and that's the kind of idea. Captain Peleg, said Bildad steadily, thy conscience may be drawing ten inches of water, or ten fathoms, I can't tell. But as thou art still an impenitent man, Captain Peleg, I greatly fear lest thy conscience be but a leaky one. And will in the end sink thee foundering down to the fiery pit, Captain Peleg. All right, them's fighting words apparently, right? Fiery pit! Ye insult me, man. Past all natural bearing, ye insult me. It's an all-fired outrage to tell any human creature that he's bound to hell. Which is of course what every Puritan tells every child that they raise, you know, except for those that are by the grace of God saved. Flukes and flames! Bildad, say that again to me, and start my soul-bolts. But I'll, I'll. They get into almost a kind of fist fight here. And at a certain point it's like okay, fine. I'll take the 300 lay. Now, what is this? I mean what kind of negotiating tactic is this? We give it a name on cop shows. Yes? >> Student: That's [inaudible] to be good cop, bad cop. >> Teacher: Yes, it's a good cop. It's a kind of classic early good cop, bad cop routine, right? Peleg is the good cop. Bildad is the bad cop. But what I want you to see that lies beneath it, is what place does this have in an economic negotiation? You know, okay, we're willing to accept maybe that it's not a bad thing for the owners of a ship to care a little [inaudible] investments for the widows and the orphans. And to be making sure that they are taken care of. Okay, that's a kind of generous capitalism that we don't normally see. But 777th lay because you're reading Matthew? And because lay happens to occur in both your conversation and in text? There's something slightly odd about that. What I want you to see is that there are two discourses that are coming into collision with one another here. One of them is a discourse about the limitations of agency that is also religious and spiritual, biblical. Another is theoretically a discourse about economy, which may or may not be about limitations on agency. But the two collide, and you might say what their strategy is, is to shift the ground of discussion from the realm in which is properly belongs, which is economy and wages. To a realm in which it probably shouldn't belong, which is spirituality and the Bible and biblical sorts of reasonings. And you can say okay, well, maybe they're good Christians and they have a theological reason for that. But then as we see, what happens is later on when they meet Queequeg, they're a little bit concerned about his, you know, his spiritual well-being. But as soon as he can hit the mark with a harpoon it's like pay the man and there's no negotiating. It's like what, what does he get, the 80th lay or something? Something really good, right? So one of the things you can see here is that one of the things that the novel I think is dramatizing here, is that biblical culture is still powerful here. It needs to be contended with. But it can be used for persuasion, and not necessarily only in the arena of religion and spirituality. There are cultural uses for religion, in other words. And one of the uses to which it's put right here is to get Ishmael to take a lower wage than he otherwise would have expected. And so we want to track that. We'll see another use of that. But we want to see where in the novel, you might say, different registers of discourse are combined, juxtaposed, and sometimes put in collision with one another. What is Melville saying about the nature of those discourses when these kinds of things happen? All right, but the chapter isn't quite over yet. He say, you know, I've got a friend. Can I bring him down? Sure, okay. Finally, he's about to leave and on the top of 78 he says, Turning back I accosted Captain Peleg, inquiring where Captain Ahab was to be found. And what dost thou want of Captain Ahab? It's all right enough, thou art shipped. So as you know, I asked you about Ahab before, before you signed up but now you signed up. Sorry, you know it doesn't really matter whether you see him or not. Yes, but I should like to see him, Ishmael says. No, I don't think you'll be able to at present. I don't know exactly what's the matter with him, but he keeps close inside the house, a sort of sick and yet he don't look so. Now we've already been prepared a little bit for Ahab I said, right? I mean this idea of the Quakers that have become Quakers with a vengeance, and they're bloody Quakers and they become pageant creatures. And really if we are, we. We should understand that this is a description, a kind of foreshadowing of Ahab himself, right? He speaks his mighty scripture language, they're born for noble tragedies. So here's another description of Ahab, and in a way it makes him less of an epic figure and more of something like a figure of paradox. A sort of sick, and yet he don't look so. In fact, he ain't sick. But no, he ain't well either. Anyhow, young man, he won't always see me, so I don't suppose he will thee. And then this, which might make you worry if you're a greenhorn who's just sign on to the ship. He's a queer man, Captain Ahab, or so some think, but a good one. Oh, thou'lt like him well enough. No fear, no fear. He's a grand, ungodly, god-like man, Captain Ahab. Doesn't speak much, but when he does speak, then you may well listen. What does that mean, grand? Okay, that's keeping with the ethic of ungodly and yet god-like man? What does that. You know, there's a kind of an apparent paradox there. One of the things that might make you really worry is the fact that what Ahab may be is a kind of figure who's prone to blasphemy, who might well be wanting to set himself up instead of God. Might give you pause. Mark ye, be forewarned, Ahab's above the common. Ahab's been in colleges, as well as 'mong the cannibals. Been used to deeper wonders than the waves. Fixed his fiery lance in mightier, stranger foes than whales. At this point we might wonder what are mightier, stranger foes than whales? His lance! aye, the keenest and the surest that out of all our isle! Oh, he ain't Captain Bildad, no. And he ain't Captain Peleg. He's Ahab, boy, And Ahab of old, thou knowest, was a crowned king! Okay, so we're invoke the Bible. Ahab has authority because why? Because in the Bible Ahab was a crowned king. You might say, well, what's the logic of that? Why does the name of an ancient historical character have anything to do with this present Ahab? But more than that, Ishmael is one of these people who's actually read the Bible and knows his Bible, he's a school teacher. So he knows this. And a very vile one. When that wicked king was slain, the dogs, did they not lick his blood? So you might say Peleg is bluffing. Ishmael calls his bluff, so now Peleg has to change his tactics a little bit. Come hither to me. Hither, hither, said Peleg, with a significance in his eye that almost startled me. Look ye, lad. Never say that on board the Pequod. Never say it anywhere. Captain Ahab did not name himself. All right, so you want to see that he's done a completely 180-degree reversal. At first he says, oh, Ahab authority. Ahab was a king. And then Ishmael says, Ye, he's a wicked king and dogs licked his blood. Okay, never say that. His name doesn't mean anything. He didn't name himself, it's not his fault. 'Twas a foolish, ignorant whim of his crazy, widowed mother who died when he was only a twelve month old. Pause. And yet the old squaw Tistig, at Gayhead, said that the name would somehow prove prophetic. Okay, so we have that other evidence as well. Perhaps other fools like her may tell thee the same. Why bring that up? To be more persuasive? Or because Peleg can't quite get it out of his head. I wish to warn thee. It's a lie. I know Captain Ahab well. I've sailed with him as mate years ago. I know what he is. A good man, not a pious good man like Bildad, but a swearing good man, something like me. Only there's a good deal more of him. Aye, aye, I know that he was never very jolly. And I know that on the passage home pains in his bleeding stump. What? That brought that about, as any one may see. I know, too, that ever since he lost his leg last voyage by that accursed whale he's been a kind of moody, desperate moody, and savage sometimes. Right? So now we're getting a kind of psychological explanation for this. But that will all pass off. And once for all, let me tell thee and assure thee young man. And this formulation should remind you of something that you've heard in the novel already. It's better to sail with a moody good captain than a laughing bad one. Is that reminding anybody of anything? >> Student: That we're cannibals. >> Teacher: Yes, right. So we're cannibals and what do we think about that? What do we think about this? What does it mean that Peleg isn't sometimes using the same kind of rationalizing locution that Ishmael did? So good-bye to thee, and wrong not Captain Ahab, because he happens to have a wicked name. Okay? Naming isn't destiny. Naming doesn't mean anything, right? That's what we take away from this. Oh, one more thing. Besides my boy, he has a wife, not three voyages wedded. A sweet, resigned girl. Think of that. By that sweet girl that old man has a child. Hold ye then there can be any utter, hopeless harm in Ahab? No, no, my lad. Stricken, blasted, if he be, Ahab has his humanities! Okay, fine. So I want to ask you, having, you know, read all the things that you've read, what does it mean if we're going to stake Ahab's humanity on the fact that he has a wife and child? The wife and child he pretty much leaves behind for long periods of time back on land. You might almost say that he goes to sea in part to escape them, or at least that's the effect of it. So if his humanity is rooted back there what do we, what is that image supposed to tell us? Is he leaving behind his humanity? Is that going to be the anchor that keeps him grounded somehow, a thing to which he always returns? Is that what we're supposed to believe? Well, one of them we can go as, you know, students of literary history, we can go meta, if you will. And ask ourselves this. What does it mean that Peleg is invoking, you might say, the Christian domestic tradition of the novel to stake out Ahab's humanities which we already know is precisely the tradition against which Moby Dick is situating itself. Again, these are paradoxes for us to think about. Should, does this ennoble Ahab? Or does it mean. Or is this something. I mean we're going to read a novel in which there are pretty much no women. So what does it mean that one's tenuous tie to a wife and child is going to be the basis of your humanity? Even if we put the best construction on it, we might say that that's a fairly tenuous tie to something that is liable to be fragile, no? As the voyage continues. If that's where we're staking our humanity, then maybe we do have a problem. Of course Ishmael himself doesn't know. Well, at least the narrative does and perhaps if we do. As I walked away, I was full of thoughtfulness. What had been incidentally revealed to me of Captain Ahab, filled me with a certain wild vagueness of painfulness concerning him. And somehow, at that time, I felt a sympathy and a sorrow for him, but I don't know what, unless it was the cruel loss of his leg. And one of the things I want to suggest to you, is there is that idea of a sympathy between Ishmael and Ahab. And I want us to think about that. I mean obviously in a certain way, if we say that Ishmael is constructing this narrative, then Ahab and everybody else, including Ishmael the character in this narrative, is Ishmael's own creation. So of course he presumably has some kind of sympathy or some kind sympathetic, some sort of negative capabilities allowing him to dramatize these characters. Okay. But typically we would say that Ishmael and Ahab are very different kinds of characters. I think I've related this to some of the reading that Melville did before he went away. One of the things that he did in going to Europe was try to steep himself in romantic literature. And one of the people that he read was Goethe. And a couple of things of Goethe's. One, you know, Faust he read, and he probably also Dr. Faustus. Goethe's autobiography, Truth and Poetry. So when he writes to Dante [assumed spelling] later on that, you know, that he's interested in thinking about whaling, but the poetry is hard to comes out. It's like, it doesn't run very well. It's like sap out of a cold tree, but he means to get it up by cooking it up. All that stuff seems to, would indicate that he's got Goethe on his mind a little bit. One other book of Goethe's that he read was Wilhelm Meister's Apprenticeship, thought to be the first bildungsroman. And Wilhelm Meister's Apprenticeship is in part about the young German boy who's trying to bring a production of Hamlet to the stage. And Hamlet becomes an interesting thing to bring to the stage because it allows Goethe, via Wilhelm and his friends, to think about what drama can do and what the novel can do. And they come up with the theory that Melville seems to have somewhat to heart. Which is that drama is all about action and pressing forward. The novel is about consciousness and process and thinking, and therefore resists pressing forward. Hamlet, therefore, becomes the novelistic of dramas. It's got a novelist/protagonist who really doesn't want to do the thing that he's supposed to do. He's in a genre called revenge tragedy. He knows he's in a genre called revenge tragedy. Revenge tragedy requires that he be the revenger, and that he basically kill everybody so that the stage is littered with dead bodies at the end. Preferably not his own, but if it has to be, so be it. And interestingly, if you remember your Hamlet, he gets there by the end. That's exactly what happens, and yet not in the way that would happen in classical revenge tragedy with an actively pressing forward protagonist. Hamlet tries to retard it at everyone's prove, he has to stage a play, he's got to do all this stuff. And finally he comes out almost by accident, or through plots that are not of his devising. This, we might say, is a dramatically inflected novel, and we're going to see today moments where it actually breaks into drama for a couple minutes. So one of the things we might say is that Melville is interested in Hamlet because it's a dramatically, it's a novelistically inflected drama. Or perhaps the most novelistic of dramas. And what he's creating here is a novel that's going to be Shakespearean in several senses, and maybe one of these sense is that it's going to measure these forms against one another. So in Ahab we will find the mighty pageant creature born for epic, born for drama. Pushing forward always. Ahab is the revenger, and in some crucial way this is a revenge tragedy like Hamlet and like its predecessors. In some other ways though, we have the narrator, Ishmael, who is one of these. Who is a very chatty, digressive narrator who tells you things that you really think you don't really need to know. And he's kind of free-associating it with you at times. Wanting to keep us from getting to where it is that we're going. Now I suggested last time that this is a story about trauma. Maybe that's a psychological explanation for what's going on. That in some sense Ishmael also knows where we're ending up, and he's doing everything he can to delay getting there. Or you might say he's giving us as much as we deserve to understand the full weight of the trauma that awaits us. Okay. That would suggest that Ahab and Ishmael are very different figures. And some critics have said that part of the characteristic feeling of Moby Dick is a kind of alternation between their styles. We get these encyclopedic kind of digressive style that's part of Ishmael's narrative when he's interested in the business and the techniques of whaling. And then we get these other very dramatic chapters which are all about Ahab and his performance pieces. And we see this kind of alternation for at least two-thirds of the way through. When you finish the novel we can, you'll see what happens to that set of alternations. So what people would say, at least at the beginning, Ahab and Ishmael are rather different characters. I want us to ask in what ways are they different? And in what crucial ways is there this kind of sympathy between them? Crucial similarities between them all along. That's one of the things that I want to bear in mind. This might be one place where it starts, but it's almost as if as soon as Ishmael thinks about it he drops it. As if perhaps it's almost too traumatic, even in this moment, for him to seriously think about and so he lets it go. Okay, I want to take a look now at the first moment that we see Ahab. This is in the chapter that's called Ahab. And we are prepared for this chapter by a series of chapters that are designed to introduce us to the crew, right? So these are the chapters, Chapter 26 and 27, that are both called Knights and Squires. And so they give us an introduction to the crew, particularly the three mates. Starbuck, Stubb and Flask. All of whom have different characters, and those characters become important as the novel progresses. We're introduced to the three harpooneers at the end of Chapter 27. Not only Queequeg but Tashtego and Daggoo. And remember, Queequeg is a South Seas Islander. Tashtego is a Native American. And Daggoo is an African, so we have a kind of variety of different others who are serving as these harpooneer. And then we get this passage on 107 just before the introduction of Ahab. Let's take about eight lines down from the top of 107. Herein it is the same with the American whale fishery as with the American army and military and merchant navies, and the engineering forces employed in the construction of the American Canals and Railroads. Right? So he's talking here about American military power, and also the power of American progress, right? What's the building the canals and railroads that are enabling U.S., the U.S. government and U.S. culture to take control of a continent. The same, I say, because in all these cases the native American, by which he doesn't mean Indians. He means the white Anglo-Saxon presumably Protestant American. The native American liberally provides the brains, the rest of the world as generously supplying the muscles. Right? And so in this way, you might say, the hierarchy on board the Pequod replicates American culture in the middle of the 19th Century. No small number of these whaling seamen belong to the Azores, where the outward bound Nantucket whalers frequently touch to augment their crews from the hardy peasants of those rocky shores. In like manner, the Greenland whalers sailing out of Hull or London, put in at the Shetland Islands to receive their full complement of crews. Upon the passage homewards, they drop them there again. How it is, there is no telling, but Islanders seem to make the best whalemen. They were nearly all Islanders in the Pequod. Then he gives them a term, a name. Isolatoes too, I call such, not acknowledging the common continent of men, but each Isolato living on a separate continent of his own. And in a way we might think of this as very American. When I think back to Tocqueville's critique of individualism, that it creates a kind of egotism. It creates a kind of atomism. People withdraw from the public society. These guys start out that way. And although they come from all over the world, but maybe they're sort of perfect Americans. They're all isolated, each out for his own game to get his high, you know, his lay and that's about it. But something happens, either on all whalers or certainly on this whaler. Yet now, federated along one keel, what a set these Isolatoes were! An Anacharsis Clootz deputation from all the isles of the sea. And the footnote tells you that this is a kind of cosmopolitan moment when people from different nations of the world come together before the French assembly. And all the ends of the earth, accompanying Old Ahab in the Pequod to lay the world's grievances before that bar from which not very many of them ever come back. And one of the things I want to say about that phrase, is this idea of being federated on one keel. Is a sense in which Ishmael is playing with the old metaphor of the ship of state. And suggesting that there is a sense in which the Pequod may well be replicating the American, you know, national polity. And then one other thing that we should mention. Remember this is 1850. Remember that Melville's father-in-law is the man who sends the first [inaudible] of slaves from New England back down to the South. There was the hope in this moment that the problem, the internal problems of slavery might be deflected, if not, you know, gotten away with, gotten rid of completely by the energies of what became called in this period Manifest Destiny. The idea that the United States would take over the. It was a destiny, the providence, the fate if you will, of the United States to take over the entire continent. If we could be outward thinking, we wouldn't worry about the problems internally that we had. Of course, the whole debate of the Compromise of 1850 shows that there's a problem with that, right? That it's precisely the outcome of the Mexican War that provokes the crisis over slavery in 1850. But there was this hope that somehow Manifest Destiny might take these energies and deflect them outward and keep American coherent. So there's a certain way in which Ishmael seems to be playing with the idea that the Pequod embodies these energies of Manifest Destiny. We'll see how well that works out. Question? >> Student: Do you think it would be like, I don't know, a mystery and also you. [ Question inaudible ] >> Teacher: Yes, I think. I don't think you need to make a, to say that. I mean I don't know how you'd argue that. You say Isolato reminds me of a Mulato that seems. Maybe, it's possible. I think you could make that argument. But certainly the other things that you are saying, and I don't think they depend on that particular point, are true enough, right? That there is this sense of everybody coming together and being. That the nation is all implicated in this larger system. Here he's. He is not at first singling out the south, right, in the way that Stowe is. Stowe is saying love you in the South. We're, you, we understand we're sympathetic with you, and the people in the North are equally guilty. She's putting them together. But look, if you will, where the part of the passage that I didn't get to ends up. Who is this that he focuses on? Black Little Pip, he never did. Poor Alabama boy! On the grim Pequod's forecastle, ye shall ere long see him, beating his tambourine. Preclusive of the eternal time, when sent for, to the great quarter-deck on high. He was bid strike in with angels, and beat his tambourine in glory. Called a coward here, hailed a hero there! So I think that's a whole discourse of rage that's clearly at stake here. Right? It's these South Sea Islanders and others commonly provide the muscle. And then clearly when you bring in Pip, you have that kind of subtext of slavery coming in as well. So I think that it isn't an allegory exactly. But we might say a lot of the elements of the 1850s are being thrown I here, mixed up. And it seems to promote something like [inaudible] we could say. I mean there's a number of possibilities at this point. We could say this is a kind of version of Manifest Destiny, ship of state sailing off, going to go do battle against the white whale, the enemies of the nation. Maybe. But also maybe this is an emblem of a certain kind of cosmopolitanism. And that would seem to be the primary meaning that he's getting at. Now is this a cosmopolitanism that's happening because of the whaling mission? Despite the whaling mission? Is it the captain's intention? It is something that the captain is intending in order to manipulate this crew more effectively? Does it have a different outcome than either we or the captain expect? I think these are some of the elements that are being, you know, proposed here by Ishmael in this moment. And all of this before we've actually seen Ahab. In the next chapter we actually see Ahab. Now remember what Ishmael has heard about him, right. That he had his leg taken off in a previous voyage, and it made him kind of moody and a little bit crazy. And that he might or might not be sick. Take a look at the bottom of 108. Ahab finally comes up, and we see him for the first time. Now I want you to see what it is that Ishmael mentions first about him. So Ahab is standing on the quarter-deck, which is basically the part of the ship that's behind H, right? So that's the captain's province. You go down J to get to his cabin. So he comes up and at the bottom of 108, Captain Ahab stood upon his quarter-deck. He's come out of the cabin and they see him for the first time. There seemed no sign of bodily illness about him, nor of the recovery from any. He looked like a man cut away from the stake, when the fire has overrunningly wasted all the limbs without consuming them, or taking away one particle from their compacted aged robustness. His whole high, broad form seemed made of solid bronze, and shaped in an unalterable mould like Cellini's cast Perseus. Threading its way out from among his grey hairs, and continuing right down one side of his tawny scorched face and neck, till it disappeared in his clothing, you saw a slender rod-like mark, lividly whitish. It resembled that perpendicular seam sometimes made in the straight, lofty trunk of a great tree. When the upper lightning tearingly darts down it. And without wrenching a single twig, peels and grooves out the bark from top to bottom, ere running off into the soil, leaving the tree still greenly alive but branded. Whether that mark was born with him, or whether it was the scar left by some desperate wound, no one could certainly say. By some tacit consent throughout the voyage, little or no allusion was made to it, especially by the mates. But once Tashtego's senior, an old Gay-Head Indian among the crew, superstitiously asserted that not till he was full forty years old did Ahab become that way branded. And then it came upon him, not in the fury of any mortal fray, but in an elemental strife at sea. And remember, Ahab has fixed his lances in stranger things than a while, right? That's what Ishmael has been told. Yet, this wild hint seemed inferentially negatived by what a grey Manxman insinuated. An old sepulchral man, who, having never before sailed out of Nantucket, had never ere this laid eye upon wild Ahab. Nevertheless, the old sea-traditions, the immemorial credulities, popularly invested this old Manxman with preternatural powers of discernment. Right? So we're talking about how stories get passed on. How legends get created. How we believe what we believe. The sailors, by tradition, end up believing one particular person. Does he have more authority really than the others that they choose not to believe? So that no white sailor seriously contradicted him when he said that if ever Captain Ahab should be tranquilly laid out, which might hardly come to pass, so he muttered. Then, whoever should do that last office for the dead, would find a birth-mark on him from crown to sole. So powerfully did the whole grim aspect of Ahab affect me, and the livid brand which streaked it, that for the first few moments I hardly noted that leg upon which he partly. That not a little of this overbearing grimness was owing to the barbaric white leg upon which he partly stood. And now we get to the peg leg. I mean, if you think about Ahab, the next thing you think of after the white whale is the peg leg. I mean, that's the characteristic. What does it mean that it's not the first thing that strikes Ishmael about Ahab? That the first thing he sees is this scar that seems to run down his face, livid white out of his hairline that marks him? What are the associations that are being created here? Why do this? I'll give you one more bit before I ask you. Now this is at the bottom of the end of the last full paragraph. Not a word he spoke, nor did his officers say aught to him. Though by all their minutest gestures and expressions, they plainly showed the uneasy, if not painful, consciousness of being under a troubled master-eye. And not only that, but moody stricken Ahab stood before them with a crucifixion in his face. In all the nameless regal overbearing dignity of some mighty woe. So what's the pattern of imagery that's being created here for us around Ahab from the beginning by Ishmael? What are some of the things that we see here? Anybody? Yes? >> Student: Well, you know, the whole scar thing I think it's biblical. It makes me think of. I mean [inaudible] especially about kings. >> Teacher: Okay. All right. On the one hand, maybe the mark of king, branded from the beginning. And let's go with that branded word. What does branded? Who get, what gets branded? Who gets branded? >> Student: Cattle? >> Teacher: Who? Cattle did somebody say? >> Student: Yes. >> Teacher: Yes, okay . Cattle. >> Student: Slaves. >> Teacher: Slaves. Anything else? Not so much these days but, I mean, you know, they could have done it to Hester but they didn't. >> Student: Prisoners. >> Teacher: Who? >> Student: Prisoners. >> Teacher: Prisoners or criminals, yes. Right, you get that. Anybody ever read the Three Musketeers, one of my favorite books? >> Student: Uh-huh. >> Teacher: Three Musketeers, and the Lady DeWinter, you know, she's got the brand of a criminal which is finally revealed and the whole plot turns on it. Criminals, property, slaves. These get branded. What does it mean? And then you bring up another one, the mark of king. What does that mean, that Ahab has that set of associations? And then at the bottom of 109, Before them with a crucifixion in his face, and some regal overbearing dignity of some mighty woe. What's that? It means now it seems to indicate that he's a kind of Christ figure. Well, okay. I guess that's compatible. I mean Christ was branded, you know. Christ was crucified because he conceived of as a criminal. And so what do we do with this pattern of imagery? Is his, are we seeing someone who is a kind of Avatar or an anti-type of Christ? Therefore, I don't know what, God's agent on earth? That's the imagery that's being created? Or is it the opposite of that? But how would we know? Anything else that see associated with Ahab at this time? Yes? >> Student: Trees. >> Teacher: Trees. What does that do for us? Anything? >> Student: Trees are kind of majestic. >> Teacher: Okay, possibly. Trees are majestic. Nature, maybe. Although again, we're going out on a land, off land so not too many trees. What happens to this tree, by the way? >> Student: It gets hit by lightning. >> Teacher: It gets hit by lightning. And what's the first image at the beginning of the paragraph? He looked like a man? >> Student: Burned at the stake. >> Teacher: Cut away from the stake. Yes, who's been burned at the stake. So a tree struck like lightning. Something majestic has been scarred by lightning, fire. Or somebody that's been burned away, you know, been burned at the stake and cut away and also fire. Another pattern of imagery that's being overlaid, that will be associated with Ahab as we move forward. I want you to track both of these things. Track the kind of, all three of things you might see. Track the imaging, the imagery of branding, whether it's of property or criminality or something else. Track the imagery of Christ-like stuff. Crucifixion and other things. And track the imagery of fire. How do they go along with Ahab? How do they shift as the novel progresses? Okay. So he's up here on the quarter-deck, right, and that's the first time that we see him. And I want to skip to the chapter that's actually called The Quarter-Deck so that we could actually see what it is that Ahab does, right? We've already been told that Ahab doesn't speak much, but when he does you better listen. This is a moment that he speaks. This is Chapter 36, page 136. The Quarter-Deck. And immediately when we get to this chapter we see that this is, there's something a little odd about it. Something a little odd about it. Enter Ahab. Then, all. We get a stage direction, right? Something is going on. It's almost as if what we are immediately clued into is the fact that we're about to see a kind of performance. And it's another way, you might say perhaps with a novel, shifting. It's Shakespearean, it's signaling it's Shakespearean ambitions. So Ahab comes. Now a thing to know about this, the quarter-desk first of all is the province of the officers and especially the captain. So when everybody's out on the quarter-deck, which is in the back part of the ship, if the captain's out there the officers stay to the other side so he can have privacy. And the whole, the ordinary crew doesn't go back. In fact, most of the non-officers are referred to as people before the mast. They're supposed to stay in the front part of the ship. And the officers have the purview of the main, from the main mast on to the back. Bringing more than that, ships operate on watches, right? Not everybody is awake all at once. You need some people to be awake and some people to be asleep. And the ship, some of the ship can be run all the time. A ship like a whaler, by the way, carries a complement of people that's far greater than it actually needs to run the ship. Just because they're, as you'll see later on next time, they, a lot of them have to spend work actually processing the whales that they catch. The shipping in fact becomes a kind of factory on the ocean for a while. But you've got a big crew and most of them are, they're not always in any one place on the ship at any one time. So for Ahab to say, Send everybody aft to the quarter-deck, is a very strange thing to do. This is on page 137. Sir! said the mate, astonished at an order seldom or never given on ship-board except in some extraordinary case. Send everybody aft, repeated Ahab. Mast-heads, there! Come down! It's like we're going to pause, right. Maybe it reminds you of that moment of Bradberg's, you know, but here I must take a pause and look. Everybody's going to get down, no more lookouts. Everybody back here. The captain has something to say. Okay. Vehemently pausing, he cried, What do ye do when ye see a whale, men? Sing out for him! was the impulsive rejoinder from a score of clubbed voices. Good! cried Ahab, with a wild approval in his tones. Observing the hearty animation into which his unexpected question had so magnetically thrown them. I'm going to avoid the temptation to sound like Darth Insidious. Gooood. Unlimited power! Right. What do ye do next, men? Lower away, and after him! And what tune is it ye pull to, men? A dead whale or a stove boat! Okay, so he's working them up, right? Okay. Then top of 138. All ye mast-headers have before now heard me give orders about a White Whale. Look ye! D'ye see this Spanish ounce of gold? Holding up a broad bright coin to the sun. It is a sixteen dollar piece, men. A doubloon. D'ye see it? Mr. Starbuck, hand me yon top-maul. And you can't particularly well here because of the lights. But this is the actual, a representation of the actual doubloon. And if you were to look at it, you would see that there was, I'll put this in the notes so that you can see that there's a sun right here on the top. And a couple of mountains, right? So he takes this doubloon and he nails it to the middle mast, right there. Or to the mast right there, the main mast. Okay. This is not a very good. It's probably better to see it on this one, right? So he's, they're all gathered by, in the quarter-deck and he's going to nail it to F, to the main mast there. And they're all kind of standing in that part of the, rear part of the ship. So he's nailed this thing. What does that suggest? Again, remember we talked about the unacknowledged biblical imagery in the spatter, in the picture scene, right? He's got three masts there. You're going to nail a doubloon to the middle one. That's doing something more with crucifixion imagery, right? Although we have to think what it its we're crucifying. Are we crucifying a. Are we crucifying gold? Are we crucifying the economy? Okay. And then again, these are not allegories. These are symbolic gestures. But not from only the novel, but the characters within the novel are making. Ahab knows how to manipulate. So he wants you to, the first he's doing is he says, look, a good ounce this is, you know. You guys are not making anything on this. Think about how much money this is compared to what you're supposed to make on this voyage. And he says this. This is a couple of paragraphs. Receiving the top-maul from Starbuck, he advanced towards the main-mast with the hammer uplifted in one hand, exhibiting the gold with the other. And with a high raised voice exclaiming, whosoever of ye raises me a white-headed whale with a wrinkled brow and a crooked jaw. Whosoever of ye raises me that white-headed whale, with three holes punctured in his starboard fluke. Look ye, whosoever of ye raises me that same white whale, he shall have this gold ounce, my boys! Hurray! That's a lot of money, and it's going to be there every single day until they see this whale. People are looking at it. So he's created a kind of symbol, and it's got these other overtones that we might notice perhaps. That's one thing that's going on, so he puts that up. He's created this pageant. Everybody's attention is on this, and it seems to be more or less in keeping with what they're supposed be doing. They're supposed to hunt whales, right? Okay. He's interested in a particular one. He's giving a special reward for it. That's fine, right? Maybe not. Captain Ahab, said Tashtego, a little bit further down. That white whale must be the same that some call Moby Dick. Moby Dick? shouted Ahab. Do ye know the white whale then, Tash? Does he fan-tail a little curious, sir, before he goes down? said the Gay-Header deliberately. And has he a curious spout, too, said Daggoo, very bushy, even for a parmacetty, and mighty quick, Captain Ahab? And that's Daggoo. And then our friend, Have he one, two, tree. Oh? Good many iron in him hide, too, Captain, cried Queequeg disjointedly. All twiske-tee betwisk, like him, him. Corkscrew! cried Ahab. Aye, Queequeg. The harpoons lie all twisted and wrenched in him. Aye, Daggoo, his spout is a big one, like a whole shock of wheat. And white as a pile of our Nantucket wool after the great annual sheep-shearing. Aye, Tashtego, and he fan-tails like a split jib in a squall. Death and devils! Men, it is Moby Dick ye have seen. Moby Dick. Moby Dick! Right? Okay. Moby Dick. They're not the only ones who have heard of Moby Dick. Starbuck, the first mate, has heard about him too. Captain Ahab, said Starbuck who, with Stubb and Flask, had thus far been eyeing his superior with increasing surprise. But at last seemed struck with a thought which somewhat explained all the wonder. Captain Ahab, I have heard of Moby Dick. But was it not Moby Dick that took off thy leg? Who told you that? Said Ahab, then pausing. Aye, Starbuck. Aye, and my hearties all round. It was Moby Dick that dismasted me. Moby Dick that brought me to this dead stump I stand on now. Aye, aye! he shouted with a terrific, loud, animal sob, like that of a heart-stricken moose. Aye, aye! it was that accursed white whale that razeed me. Made a poor pegging lubber of me for ever and a day! Then tossing both arms, with measureless imprecations he shouted out, Aye, aye! And I'll chase him round Good Hope, and round the horn, and round the Norway maelstrom. And round perdition's flames before I give him up. And this is what ye have shipped for, men! To chase that white whale on both sides of land, and over all sides of earth, till he spouts black blood and rolls fin out. What say ye, men, will ye splice hands on it, now? I think ye do look brave. Aye, aye! shouted everybody. Okay, so. All right. So the men are all psyched, but what do they know, right? Dumb heathens, right? Starbuck, who clearly starts to serve as a kind of conscience of the voyage. I am game for his crooked jaw, and for the jaws of Death too, Captain Ahab, if it fairly comes in the way of the business we follow. But I came here to hunt whales, not my commander's vengeance. How many barrels will thy vengeance yield thee even if thou gettest it, Captain Ahab? It will not fetch thee much in our Nantucket market. Okay. This is where our experience with difference discourses, coming against one another, comes, it will be helpful to us. He is invoking the discourse of business and economy. What they've signed up for, right? They are the designated agents of the owners of the Pequod. They each are going to receive a share of the proceeds. They need to catch whales, and they need to catch a lot of them. They stay out on the sea for two, three years until their holds are full of whale oil. And then they go back and they sell their oil, and they all make their money. Assuming the price of oil does not precipitously drop, which in a few years it actually does. But that's not for here. Looking for one whale out of a whole sea? That doesn't seem very profitable. Won't fetch thee much in your Nantucket market, right? Ahab has a rejoinder. Nantucket market! Hoot! But come closer, Starbuck. Thou requirest a little lower layer. If money's to be the measurer, man, and the accountants have computed their great counting-house the globe, by girdling it with guineas, one to every three parts of an inch. Then, let me tell thee, that my vengeance will fetch a great premium here! He smites his chest, whispered Stubb. What's that for? Methinks it rings most vast, but hollow. Now I want you to think about Emerson for a moment, among other people. Think about what Emerson says about joint stock companies, and what economy does to people. It gives them this sense of false goods. He wants them to wake up and spring to the truth. There's a sense in which Ahab is sampling rephrasing what Emerson has already told us. Is money supposed to be the measure of a man? But Starbuck won't let it go, because there's another way of thinking about it. Vengeance on a dumb brute! cried Starbuck, that simply smote thee from blindest instinct! Madness! To be enraged with a dumb thing, Captain Ahab, seems blasphemous. Right? Okay. It's just an animal. It struck you because you were chasing it. It didn't mean anything. It was an accident of the fishery. This is another affront to Ahab, perhaps an even worse one. And it's something he can't abide. And so look at the long speech that he gives on the next, top of the next page. Hark ye yet again, the little lower layer. And now he's going into something that we might call a kind of metaphysical key. Certainly this resonates with platonic philosophy on the one hand, you know. The idea that ideas are the real reality, rather than particular manifestations. I think we've talked about this with the Puritans as well. Something about the pneumenal world, the world of spirit rather than the phenomenal world, the world of matter. That's what's the real thing, the world up there. Hark ye yet again, the little lower layer. All visible objects, man, are but as pasteboard masks. But in each event, in the living act, the undoubted deed there, some unknown but still reasoning thing puts forth the mouldings of its features from behind the unreasoning mask. All right, think of the signals he's sending. Visible objects is just a mask. The true meaning, the true reality is somewhere behind what we see. Behind the material world. Think of the number of writers in our course with whom that would resonate positively. If man will strike, strike through the mask! How can the prisoner reach outside except by thrusting through the wall? To me, the white whale is that wall, shoved near to me. Sometimes I think there's naught beyond. But 'tis enough. He tasks me, he heaps me. I see in him outrageous strength, with an inscrutable malice sinewing it. That inscrutable thing. And remember where the word inscrutable comes up. It comes up in Puritan discourse all the time, right, inscrutable. God is inscrutable. What does it mean if the whale is inscrutable, or the thing behind the whale is inscrutable? And this is the sentence I want you to keep in mind. That inscrutable thing is chiefly what I hate. And be the white whale agent, or be the white whale principal, I will wreak that hate upon him. Talk not to me of blasphemy, man. I'd strike the sun if it insulted me. For could the sun do that, then could I do the other. Since there is ever a sort of fair play herein, jealousy presiding over all creations. Principal and agent again is mostly economic language, right? I mean the owners of the Pequod are the principals. The sailors are agents. Ahab is in a somewhat ambiguous position since he's both. He's both a co-owner and one of the chief agents executing the intention of the owners. And that's what agents do, they execute intentions. Is the white whale an agent for something else? Executing some other intention for some other being? If so, what? Is the white whale a principal working on its own intention? Whatever it is, it's that intentional thing that Ahab wants to give to. So if it's the white whale itself, fine. Kill it, we got rid of the intending thing. If the white whale is working on behalf of something else, no other access to the intending thing than through the white whale. What I want you to see is that however you construe it, it construes that there is intention. He is refuting with, he cannot stand the idea that Starbuck has given us on the previous page. That it was just instinct. That there was no meaning in it at all. I want you to think about this logic. We've seen it before, right? Who is that looks at every little thing, and some big things, and thinks there's meaning behind it? That it's part of a larger plan. That there's intention. That there's providence, right? This is a weird kind of Puritan-like thinking. Ahab shares with the Puritans a certain kind of haunt to the imagination. So that even if he is a Quaker ostensibly, you say it's a mutated form of Quakers and it has a lot of seeming fundamentalism built into it. This idea of intentionality, of fatedness, of things meaning things. Except in his case, it's become kind of inverted. And again, there's a kind of epic motif here as well, right? Where is that we would see the sun actually come down in a battlefield and content with a human being, if not on the pages of Homer, right? When Apollo comes and fights on the side of the Trojans, among many different examples. Ahab, therefore, figures himself as in fact what we've heard earlier. As this ungodly, god-like man. He's willing to be what Starbuck thinks of as blasphemous. [ Silence ] And he understands that he has a certain kind of persuasive power, right? What has he done, in other words? He has taken an economic discourse. He's appropriated the terms of that economic discourse, agent and principal, and turned them into kind of a philosophical or metaphysical key so that they come to mean something different. It's almost a reverse, you might say, of what Peleg and Bildad have done to Ishmael on the ship. But he isn't done yet. He needs to seal the deal. So at the top of 141. The measure! The measure! cried Ahab. Receiving the brimming pewter, and turning to the harpooneers, he ordered them to produce their weapons. Then ranging them before him near the capstan, with their harpoons in their hands, while his three mates stood at his side with their lances, and the rest of the ship's company formed a circle round the group. Right? So they're all at the center, everybody's in a circle. There's clearly some kind of ritual about to take place. He stood for an instant searchingly eyeing every man of his crew. Right? He's the boss, but he's going to make a kind of personal connection to all of them. He knows how to manipulate. You can see what this is, is a scene in which, of ideological persuasion which he is bending them from one mission to another. Or perhaps revealing the true measure, the true mission that he thinks they signed up for. But he's got to persuade them. He's only one guy. If they all ban against him in mutiny he can't do anything. So he has a certain position of authority, but he needs to seal the deal. He needs to get them to believe that his mission is their mission. First thing to do, drink together. That always is good, right? Drink and pass! And drink in a ritual way. The crew alone now drink. Round with it, round! Short draughts, long swallows, men. Tis hot as Satan's hoof. So, so, it goes round excellently. It spiralizes in ye. Forks out at the serpent-snapping eye. Well done, almost drained. Steward, refill! Okay. It's clearly a scene of communion, right? So we have a lot of religious imagery here, but it's being manipulated. It's hot as Satan's hoof. We're going to drink together. We're going to have this kind of communal moment. It is a kind of Satanic communion. And remember what I said, right? Melville reverses his own voyage. He sends the Pequod out east where he went west. He goes around. Melville himself goes around South American and Cape Horn. The Pequod goes around the Cape of Good Hope and Africa. What else is it a reversal of? It's also a reversal of the Puritans coming from Europe, sailing west to the New World. These guys sail east. And as they leave the New World, they have this kind of devil communion here. There's again a kind of weird playing with it, as if Ahab is part of a kind of new. He's part of a tradition that's, in which the terms are set by New England fundamentalism, but he's reversed them in strange ways for his own particular purposes. He's not done yet. Advance, ye mates! Cross your lances full before me, at the bottom of 141. Well done! Let me touch the axis. So saying, with extended arm, he grasped the three level, radiating lances at their crossed centre. While so doing, suddenly and nervously twitched them. Meanwhile, glancing intently from Starbuck to Stubb, from Stubb to Flask, it seemed as though, by some nameless interior volition, he would fain, have shocked into them the same fiery emotion accumulated within the Leyden jar of his own magnetic life. And then what does he do? He asks the three harpooners to detach the iron part of their harpoons, turning those into chalices. He fills those and forces the mates, who are basically the masters, each one, of a harpooner, to become the cup bearers. So this is the middle of 142. Stab me not with that keen steel! Cant them, cant them over! Know ye not the goblet end? Turn up the socket! So, so, now, ye cup-bearers, advance. The irons, take them. Hold them while I fill! Now three to three, ye stand. Commend the murderous chalices! Bestow them, ye who are now made parties to this indissoluble league. This is the oath that they all swear together over against what Starbuck has asked them to do, right? And it's done through a mixture of ritual that is a blend of kind of Christian ritual and pagan ritual. And it has a lot of booze. It's ideological persuasion in action, right? What happens? Melville wants, or Ishmael wants, one of the two of them, wants to register how radical a gesture this has been. And so what happens is that Ishmael disappears from the narrative for a number of chapters. And these chapters turn instead to about to be dramatic chapters. In fact, they're soliloquys. The first one, the Sunset chapter, is Ahab's soliloquy. And there are people who have actually said that it's Shakespearean in his language. Somebody's actually rearranged this into blank verse lines and it works pretty well, so it's got that kind of Shakespearean cadence. I won't read it to you, but I'll point out one interesting image at the end of 143. He's talking about people who are fighting against by, they're kind of, they have rifles. They're behind cotton bags. Ahab says, Come forth from behind your cotton bags! I have no long gun to reach ye. Come, Ahab's compliments to ye. Come and see if ye can swerve me. Swerve me? Ye cannot swerve me, else ye swerve yourselves! Man has ye there. Swerve me? Look at this one. The path to my fixed purpose is laid with iron rails, whereon my soul is grooved to run. Over unsounded gorges, through the rifled hearts of mountains, under torrents' beds, unerringly I rush! Naught's an obstacle, naught's an angle to the iron way! Of what is that an image? What's he evoking there? How does he metaphorize himself? >> Student: It's a trade. >> Teacher: Yes, it's a trade, right? So he is linking himself to the very emblem of American progress, right? Capturing that imagery of, you know, the Americans taking over the continent through canals and rail building. But it's an image of purpose. And he says, you know, my purpose is fixed. I can't be served. So think about that as an image of agency. What agency does the railroad engine have? It goes from its starting point to its destination on these unbending rails. But can it deviate at all? It has a fixed purpose. Does it have agency? Is it simply not acting under orders that have been given to it? The place on a rail, it's been sent, you go forward. There's a limited amount of shifting to do. And even when a train shifts it's not even the engineer who can do it, right? The train rails need to be shifted by someone else. It's a kind of paradoxical image of power. Ishmael has Ahab evoking this as an image of his fixed purpose and his power. But I want you to see there's a kind of ambivalent image in which the dynamics of agency are very much constrained. Couple of other things to know. So each of the other mates get their chapter. Starbuck gets his. Again, realizing he is a testimony in some sense. He sees what's going on, but he's almost powerless to do anything about it, right? Take a look at the top of 144. My soul is more than matched. She's overmanned and by a madman! He drilled deep down, and blasted all my reason out of me! I think I see his impious end; but feel that I must help him to it. Will I, nill I, right there, where's his agency there? The ineffable thing has tied me to him. Tows me with a cable I have no knife to cut. Horrible old man! Who's over him, he cries. Aye, he would be a democrat to all above. Namely he says I can, you know, God has to come down to my life, and go to God so I can fight the sun. Look how he lords it over all below. Oh! I plainly see my miserable office, to obey, rebelling. And worse yet, to hate with touch of pity! We'll come back to this, but there's a sense again of a sympathy between Starbuck and Ahab, as if Ahab seems to Starbuck a thing that he himself, Starbuck, could easily become and with whom he has sympathy. The next mate, jolly Stubb. Again these are all versions of Ahab, you might say, and possibly of Ishmael as well. But look at this line here. So Stubb is the one who is the comic force. Ha! ha! ha! Clear my throat! I've been thinking over it ever since, and ha, that's the final consequence. Why so? Because a laugh's the wisest, easiest answer to all that's queer. And come what will, one comfort always left, that unfailing comfort is, it's all predestinated. So that might remind us in this course of Edward Taylor, right? I mean taking a kind of comic view of this idea of providence and predestination, and a potential lack of agency. Who bolds the sun, right? It's kind of funny at the beginning of God's determinations. [ Student sneezes ] Bless you. But notice how the thing that gives Stubb comfort here is precisely the thing that drives Ahab mad. The fact that it's all predestinated. Well, which is it? Is predestinated something that should drive us crazy and feel tragic? Provoke kind of war-like epic responses? Or should it just allow us to, you know, take it as it comes. Enjoy our life. Do what we need to do, and not worry about the larger meanings of it all? The point is, someone like Stubb can do that. Ahab can't. So again, we have a collision of perspectives. Both of them believe in predestination, but there are radically different ways to do it. Which way in the end will win out? Then Chapter 40 gives us a kind of mad Walpurgisnacht, as in Goethe's Faust. Kind of, you know, a night where seemingly spirits come out. Won't go through it all, but there's lots of different voices. Kind of weird racist thing going on with Daggoo. I'm getting into a fight in the center. It kind of, you might say, it takes the whole dramatic portion of this to a climax. And then we get to the top of 152. The chapter that's called Moby Dick, and Ishmael is back. [ Silence ] And again, what we've had is a text that was disrupted, textually, right? Ahab's disruption of the voyage is signaled textually by disruption of the stopalistic [assumed spelling] form of the text. It's almost now as if Ishmael asks us to come back to personal narrative, but we have to go back and rethink everything. We have to go back at least to the quarter-deck and rethink what Ahab's role was and what Ishmael's role was. Because I, Ishmael, was one of that crew. My shouts had gone up with the rest. My oath had been welded with theirs. And stronger I shouted, and more did I hammer and clinch my oath, because of the dread in my soul. A wild, mystical, sympathetical feeling was in me. Now remember we've seen the seeds of that sympathy planted as soon as he heard Ahab's name. Ahab's quenchless feud seemed mine. With greedy ears I learned the history of that murderous monster against whom I and all the others had taken our oaths of violence and revenge. Right? So what I said before was, what Ahab needs to do is he can't just order it. He needs to get them to believe. This paragraph here indicates the extent to which he's gotten them to believe. So much so that to register, Ishmael has to basically lose himself in the oath and the events that follow from it. And only then manage retrospectively to reassert himself. Right? So it's almost as if the narrative happens with him, and then he has to go back and reinject him. And we have to try to reinject him ourselves back into the narrative. That's how effective, you might say, it's been. Ahab has completely taken over them. Their identities have become completely linked to this idea of the mission. Now I want to show you, I'll end today with one other chapter. It's called The Chart in which Ishmael tries to account for Ahab, using that same language of agent and principal. This is on page 166. It's Chapter 44. And it's one of these strange split chapters. It starts off one way and ends another. It's about trying to chart the progress of the whale. Ahab has all these whale charts. I meant to bring one together. I'll start next time with a whale chart so that you can see it. I mean you think this is kind of crazy. In a sense it is, but in a sense it isn't. Though whale ships all tend to follow a similar track. I mean they know from experience where the populations of whales go to at different times of the year. They know where they're going to be birthing, where they're going to be hunting. Where they're going to be doing what. So they all fall a similar track. That's how come whale ships can run into each other on the ocean, and we'll talk about the Gam chapters next time. Ahab is trying to map. He's trying to pursue a route that will give him the greatest chance of finding Moby Dick. He has an idea of where he will eventually find him. Back where in fact he had that first confrontation with him. But he's hoping to go in such a route that he might encounter him along the way. And there's a suggestion with that, that stuff about the spirit spout. And that in fact Moby Dick may be playing with them and being not too far away from them all along. But one of the things that the chapter here suggests is that rational belief and scientific methods and empiricism will only take you so far. That maybe where Moby Dick is concerned, the rules don't tend to apply. And that's what Ishmael tries to get at at the end of this chapter. Take a look on page 169. [ Silence ] This is into the first full paragraph on 169. Ahab is asking himself, And have I not tallied the whale, Ahab would mutter to himself, as after poring over his charts till long after midnight he would throw himself back in reveries, tallied him. And shall he escape? His broad fins are bored, and scalloped out like a lost sheep's ear! Ishmael pulls back, Ah, God! What trances of torments does that man endure who is consumed with one unachieved revengeful desire. He sleeps with clenched hands, and wakes with his own bloody nails in his palms. Another image of crucifixion. And we might think of again part of what Melville is exploring is what Hawthorne explored in the Scarlet Letter with Chillingworth, a kind of psychology, the demented obsession of revenge. And then Ishmael tries to get into Ahab's head, right? And this is another one of these chapters where Ishmael is clearly trying to look at things. He's looking at things that he can't possibly have seen, so he's describing things that he's only imagined. So we need to take this all with a grain of salt. Often, when forced from his hammock by exhausting and intolerably vivid dreams of the night. Which, resuming his own intense thoughts through the day, carried them on amid a clashing of phrensies, and whirled them round and round in his blazing brain, till the very throbbing of his life-spot became insufferable anguish. And when, as was sometimes the case, these spiritual throes in him heaved his being up from its base, and a chasm seemed opening in him. Now remember, he thought that what he figured himself, Ahab was, as a train crossing gorges. Here we have a chasm opening in himself from which forked flames and lightnings shot up. Again, imagery of hell and fire and lightning. When this hell in himself yawned beneath him, a wild cry would be heard through the ship. And with glaring eyes Ahab would burst from his state room, as though escaping from a bed that was on fire. And I think there's more than a little overtones of Milton's Satan here, right? A hell in himself. What Satan realizes in Paradise Lost is that hell is not a particular place. Hell is wherever Satan is, because he's been cast out of the sight of God. Now it's the insight that Satan has that Melville seems to think suggests that we should have about Ahab as well. Now listen to the language of agency. Yet these, perhaps, instead of being the unsuppressable symptoms of some latent weakness, or fright at his own resolve, were but the plainest tokens of its intensity. For, at such times crazy Ahab, the scheming, unappeasedly steadfast hunter of the White Whale, this Ahab that had gone to his hammock was not the agent that so caused him to burst from it in horror again. The latter was the eternal, living principle or soul in him which at other times employed it for its outer vehicle or agent. It spontaneously sought escape from the scorching contiguity of the frantic thing of which, for the time, it was no longer an integral. But as the mind does not exist unless leagued with the soul, therefore it must have been that, in Ahab's case, yielding up all his thoughts and fancies to his one supreme purpose. That purpose, by its own sheer inveteracy of will, forced itself against gods and devils into a kind of self-assumed, independent being of its own. Right? What we have here is a fracturing of personality, a fracturing of agency. And Ishmael uses all this language. But ask yourself whether it really all makes sense. Nay, could grimly live and burn, while the common vitality to which it was conjoined, fled horror-stricken from the unbidden and unfathered birth. Right? The revenge is so powerful that it takes on a life of its own. It gets Ahab soul fleeing from it, and then when Ahab jumps out of bed he's this kind of formless. Thinking of Edgar Huntley's somnambulistic being. A ray of living light, to be sure, but without an object to color, and therefore a blankness in itself. A whiteness, therefore not unlike a certain other whiteness that is in fact its obsession. One last thing. God help thee, old man, thy thoughts have created a creature in thee. And he whose intense thinking thus makes him a Prometheus. A vulture feeds upon that heart for ever, that vulture the very creature he creates. We all know the Prometheus myth. What's the name of the modern Prometheus? It's a book that Melville read shortly before writing Moby Dick. It's what? >> Student: I'll say Frankenstein. >> Teacher: Frankenstein. The unfathered and unbiddened birth. Let's take it up from there next time. |
Open_Ed_Cyrus_Patell_American_Literature | Introduction.txt | >> I'm Cyrus Patell. This is American Literature 1, From the Beginnings to the Civil War, V 410230. And I will be your drill Sargent for the term. I'm not kidding. This is boot camp for English majors, you may have heard. And we are going to read a lot of stuff, we're going to be doing some serious analytical writing, and by the end of the term, with any luck, your literary scholar's chops will be a lot stronger than they are right now. So it is, I will say right at the outset, historically speaking, it's been the kind of course where you put more effort into it, you are rewarded. Perhaps more than in someone else's course. And you're used to getting a B plus, and you put more effort in, identify expect you to get an A or an A minus. If you're used to, however, cruising and kind of getting a B, students like that have tended to get Cs. So I'm not really supposed to say something like if you have to cut a corner in a class because, you know, life is busy and everything, many things going on, cut it in somebody else's class. So I didn't actually say that. That's actually a literary device, and there will be a special prize for anybody who e-mails me afterwards and tells me what that literary device was, that I just used. But in any case, I'm serious about that. We -- this is a course that requires a lot from you. I'm not going to kid you, the reading load is comparatively heavier, probably is slightly heavier than Brit Lit 1 or Brit Lit 2. I have more expectations of you, perhaps. But you will be rewarded if you do the work. So if anybody would like to run screaming out the door and take it in a different term when somebody else is up here, now would be the time. No takers? All right, then let's get started. So it's the first anniversary of Barack Obama's inauguration. So it seemed to be a moment when it would make sense to talk about some of the principles that he embodies. He recently received the Nobel Prize for peace, the Nobel Peace Prize. And I think he deserved it, and I think he deserved it because of the ways in which he has set a particular agenda for how we should all conduct ourselves as individuals, citizens, and indeed as nations. Right? And that way of conducting ourselves is based on the idea of -- fundamentally, I think, of conversation and dialogue. And so that's one of the things that I want to be thinking about in the course of the term. This is what he said. We remain a young nation, but in the words of scripture, the time has come to set aside childish things, the time has come to reaffirm our enduring spirit, to choose our better history carry forward that precious gift, that noble idea passed on from generation to generation, the God-given promise that all are equal, all are free, and all deserve a chance to pursue their full measure of happiness. Right? So one of the things I'm going to want you to understand in the course of the term is the tradition of rhetoric and writing that words like this come out of. The invocation of scripture, the invocation of a reference to the Bible, right? The whole idea of pursuing happiness. Obama is inserting himself in the speech into a rhetorical tradition, and it's one I hope you will come to understand, because it's a rhetorical tradition that works not only through sermons and then political speeches, but also deeply marks what we might think of as the purely literary tradition, what we tend to call American literature. And we'll be talking in the course of the hour what those words American and literature should be taken to mean. One of the ideas I want to put out right on the table is the idea of cosmopolitanism. Because I think that's one of the things that Obama and his approach to politics and diplomacy, one of the things he embodies. Now can somebody tell me what they think cosmopolitanism means, and if you're in my Con West [Assumed spelling] class, forgo for just a minute. Anybody else? What does cosmopolitanism means? It's a word that we sling around a lot in New York City, and here at NYU. So what does it mean? Sure. [ Inaudible audience comment ] >> Members of all nations. Okay, so let's keep that in mind. The idea of all nations. Yeah. >> Diversity. >> Diversity. Sure. Yeah. >> [Inaudible] citizen of a the world. >> Being a citizen of the world. Yes. That in fact is the derivation of the term, cosmo politas, citizen of the cosmos. So it's beyond -- no, I didn't pay him. But there's nice timing there, right? Okay, society idea of being a citizen of the world as opposed to primarily the citizen of a nation. So when we're thinking about nations, we're thinking about it in a kind of plural sense. You might say that cosmopolitanism arose, whether you believe it arose among the Greeks, so say as a rejoiner to the idea of the polis or the city-state. So if you were in ancient Greece, perhaps your first identity if you were a citizen was as a citizen of Sparta or Athens. Maybe later on during the Persian wars you thought of yourself as something like a Greek. The stoic philosophers and others who talked about cosmopolitanism wanted to think in bigger terms. In the 18th century with the rise of the nation-state, cosmopolitanism becomes an alternative to the idea that your primary allegiance is owed to the nation. Somebody who happens to teach in a little school up town has written a little bit about cosmopolitanism. And Bruce Robins [Assumed spelling] suggests that cosmopolitanism should be understood as a fundamental devotion to the interests of humanity as a whole. That's one way to think about it. And he points out again that cosmopolitanism has seemed to claim universality by virtue of its independence, its detachments from the bonds, commitments, and affiliations that constrain ordinary nation-bound lives. Right? So nations in this concept are things that might keep us apart. Right? Nations are borders, boundaries, they keep people from one another, they are separate identities. Cosmopolitanism breaks down those boundaries, creates something like what we might think of as universality. Joins all people together, humanity. These are all the words that are associated with cosmopolitanism. But it isn't quite so simple. In the 18th century, and I just put up Conte as an example of one of the thinkers who's working through some of these ideas. There are a number of different ways proposed to be cosmopolitan. Perhaps if you are a citizen of the world, there shouldn't be any nations. Conte in his earlier pieces starts to think about the idea of a world government that would be beyond nations. By the time he gets to the perpetual peace, he started thinking in slightly different terms. Because more like what we just mentioned earlier, all nations. Are the idea that the nation is somehow still valuable. My colleague in sociology, [Inaudible] Calhoun has made a powerful argument about the continuing usefulness of the idea of the nation. But maybe that's not the last word. In other words, we need to think of perhaps, Conte was suggesting, about a federation of nations. In which -- something that's distinctive about a national tradition would be preserved, but something larger that could bind people together would also be created. And I think that is a kind of conceptual leap that starts to open the door for more contemporary -- by that I mean some of the ways which people are thinking about cosmopolitanism today. Which move beyond simply this notion of an alternative to the nation and really start to take on this idea of universality. So David Holinger, who is an intellectual historian, who teaches at Berkeley, has written a book called Post Ethnic America, which he talks about multiculturalism an cosmopolitanism. He writes that cosmopolitanism shared with all varieties of universalism a profound suspicion of enclosures, but it's defined by an additional element which is not essential to universalism itself. And he calls this the recognition, acceptance, and eager exploration of diversity. Cosmopolitanism, Holinger says, urges each individual and collective unit to absorb as much varied experience as it can, while retaining its capacity to advance it's gains effectively. For cosmopolitanism, the diversity of human kind is a fact, for universalists it's a potential problem. Now what does that mean? Think of it this way. If a universal -- universalist thinker. You're interested in making generalizations about human kind, about men and women, and the ways in which they share certain attributes. Right? You might want to do philosophy that's talking about the soul, for example, or about rights or something like that. Something that everyone shares. So you have to figure out a way, conceptual, to get the beyond the idea of difference. You need to figure out a way to minimize difference, perhaps you might say you need to find a lower common denominator, or at least a common denominator. So difference is a problem that you want to solve. So that then you can make generalizations that apply to everybody. That's the kind of universalist practice. Cosmopolitans don't think of difference as a problem. Cosmopolitans think of it, I would say, as an opportunity. So I'd go even beyond Holinger. Holinger suggests that cosmopolitans see diversity as a fact, I'd say for the actual -- the true cosmopolitan, diversity, difference are opportunities that we should embrace, not problems that we need to solve. If you go to some foreign country, go from New York, go to Seoul or Shanghai or Abu Dhabi. You want it to be a little different, don't you? You don't want -- I mean, get off at airport in Abu Dhabi, you'll see a Starbuck's right away. That's true. And -- but then there will be people dressed radically differently, ordering at that Starbuck's. That will be kind of a trivial example of the interplay of what I would call and what -- Anthony Appiah, a theorist of cosmopolitanism called the idea of cosmopolitanism is universality plus difference. Cosmopolitanism certainly is a link to the idea of universality, right? As Robins has, quote, suggests. It's about -- it is about how in part we are the same. But cosmopolitanism is not afraid of difference in diversity. So in the slogan form that [Inaudible] presents here, it's universality plus difference. We want Seoul as a city to be different so that we have that kind of experience of seeing new things, finding practices that are other than -- hearing stories, accounts of the world that are different from our own. We grow as people, whatever you want to say. There's something about going some place and finding it to be different that's exciting. And yet if it's completely alien you wouldn't be able to make that connection. You need some shared basis to have that cosmopolitan experience. So you go and you find that the people who live in Seoul, Korea, are all people too. Wow! And they have certain ideas that you have at home. That's our kind of shared basis. The universal thinker might want to thing collapse of gulf of difference that exists between New York and Seoul. Right? Stress the ways in which those two cities [Inaudible] cities are the same. The cosmopolitan wants to maintain the gap and then bridge it. So we maintain the gap, we bridge it, or you might say we have conversations across the boundaries of difference without wanting to get rid of the boundaries of difference. So that's a crucial thing. Now one thing else to say about this is that cosmopolitanism is not the same as multiculturalism. You know, which has become a byword in the U.S. academy, in the aftermath of what we called the cultural wars in the mid 1980s. Multiculturalism is a pretty good thing. It respects the diversity of different cultural traditions, right? It's been very important in terms of allowing people who come from minority traditions to feel that they have a voice within U.S. culture. But multiculturalism has ties less to universality or universalism than it does to pluralism. Right? Separate, perhaps separate but equal traditions. Now pluralism, as we'll come to understand, is a very important part of the American intellectual tradition. In multiculturalism, it tends to breakdown into something like this. If you're a multiculturalist, you recognize the dignity of, the importance of many other cultural traditions. But you also say you understand the pool of a cultural [Inaudible] for the person who's in it. So the logic would go something like this. I like my culture because it's mine. You like your culture because it's yours. I respect your culture, because I'm a good multiculturalist. I want you to respect my culture. I'm not going say too much about your culture, you know, I don't walk in your shoes, I don't know what your culture is like. I feel like I should respect those boundary difference s, live and let live, separate but equally, the dignity of all different cultural traditions. Now the cosmopolitans would say that's fine, as far as it goes. But there's a problem. You're a multiculturist, and you want to respect a long-standing cultural tradition. Okay, that's good. That's a good principle. But what if that cultural tradition is less than -- than what we want it to be. Let's say there's a long-standing cultural tradition in another part of the world, it's had an unbroken culture for 2,000 years, it's very well established, it seems to work for the people who live there. It's based on slavery. Do we want, as cosmopolitans, to be able to say that's just okay, you know, they're different. Should respect their -- do we want to have an idea of human rights that we want to promote and say you know what, human beings should never be enslaved, that we should get over it. A multiculturalist would have a hard time sticking to her principles, and then making that argument. The cosmopolitan, on the other hand, she might say look, what we need to do is engage in a constructive conversation with that other culture. And you know what, we should open up our own selves to being convinces that maybe the way they do it is better. In other words, you need to have deep conversations, conversations that put cherished values up for grabs, all right? I think that is behind some of the thinking of Barack Obama. We need to engage in conversations, and not just in the sense that we're the teachers and we have a better story to tell. The cosmopolitan realizes that in a way, part of the importance of conversation comes from the fact that as human beings, we aren't perfect. Right? And that it may well be that other cultures, other people, have better accounts of the world than we do. We ought to listen. We ought to be engaging in these conversations in a way that makes us want -- you know, at least able to be convinced. Real conversations about non trivial matters. All right? So to sum it up, cosmopolitanism starts off as a critique of nationalism, ends up in current theory as being a kind of critique of universalism. And I want to link it to the words that Barack Obama has tended to us in the past, which is the idea of deliberative Democracy. I think what -- he goes through a series, a line of political theory that calls itself deliberative Democracy theory. But if you were to read it you would find that it has a lot in common with a kind of Bruce Robins, Anthony Appiah strain of cosmopolitan thinking that I've been out lining. And one final thing, one of the things that seems to be linked to cosmopolitanism in the American mind is the idea of urbanism. That the city is a place where cosmopolitan interaction really happens. That leads to some interesting ideas. Right? One of them will be that we live in the paradigmatic American city, perhaps. New York. So what about New York. Is New York the most American place in the country? Or is it the least American place in the country? What you think about that question will have something to do with your take on the American ideological tradition. That ideological tradition is one of the things that we'll be talking about this term. My colleague in history, Tom Bender, has talked about the rise of two great cultural mythologies. And this course will be taking on one of those more deeply than the other to show how an ideological tradition takes place. In part it takes place through writing and later through what we call the literary. And to how it makes us think about an idea like the idea of cosmopolitanism. So one of the things that Bender suggests is that there's two main stream American cultural traditions. If people talk about an American identity, they're thinking about one of these two things, he would say. One of them has to do with Massachusetts, where I spent a lot of time and used to like very much. [ Laughter ] >> Has to do with Puritanism and sacred culture, and urban culture, town-based culture. The Puritan origins of the American self. That has been the story of American literature one, for many, many years, and it starting to be undone, you might say, in the last part of the 20th century and now. So we'll be talking about that story and trying to understand what are the strength of that account of American intellectual history and also what some of its weaknesses are. There's another story that Bender points to, and that's the kind of Virginia story. We'll be touching on that. But that suggests that the real American identity comes out of -- not towns, but the country. The pastoral, not sacred experience, but secular experience. Hector Saint John Revicur [Assumed spelling] writes about the American farmer as the kind of prototypical America. That's a powerful tradition too. So you might think of these two versions of the American self probably intermingling. What Bender points out is they seem like they're different. But they both reject the idea of difference. Neither, he says, can give positive cultural or political value to heterogeneity or conflict. Each in its own way is xenophobic, and that distances both of them from the conditions of modern life, especially as represented by the historical cosmopolitanism of New York and increasingly other cities in the United States. Okay? So one of the things we're asking is to what extent does New York, if it is indeed linked with cosmopolitanism, offer a third possibility for an ideological tradition. One that perhaps hasn't been sufficiently taken up or that maybe remains to be taken up. And then we'll think about what the relation of our literary tradition is to all of these things. Will there be moments that we will find in our survey of American literature from the beginnings to the eve of the Civil War that belong strongly to one tradition or the other. And other moments, perhaps, that offer a kind of invitation to cosmopolitanism. These are some of the issues that we're going to be taking up. One outgrowth of the idea of cosmopolitanism that comes from Appiah's work is the idea that cosmopolitan traditions are not pure. All right, think about the multiculturalist, for a second. Multiculturalist says you know what, better have your departments of African American studies, Asian American studies and women's studies, you know, because everybody wants -- those are good important stories, and we should keep them separate, we should keep those departments and maybe we don't want to mix things up and keep disciplinary boundaries. Cosmopolitan theorist think that you know what, cultures don't want to remain pure. Cultures want to mix and miscegenate and fertilize one another and inseminate one another, and produce new forms, and they're very Whitmanian, as you'll come to see. Appiah recruits the word contamination for this. Cultures want to contaminate one another, they want to mix. So one of the things we'll be working with is a model of culture that pre-supposes that. That what culture is about is about change. The cultural models need to be dynamic. And yet at the same time we will often find within any cultural formation that there will be forces at work that want to create pure forms or maintain pure forms or maintain traditions, want to conserve the past. All right? And you might call these the kind of cultural plays, or I don't know what, French people, French linguists wanted to maintain the French language remains pure and free of any Americanisms, right? You can think of any number, I'm sure, of cultural traditions in the world where certain people are legislating about what their people should be thinking and trying to keep outside influences outside. Appiah would say this is not the way cultures want to behave, if left to their own devices. They want to mix and miscegenate and contaminate one another. So we'll be working with a model of culture that's drawn from the neo-Marxist thinker Raymond William, right? And one of the things to say about, you know, Marxist literary criticism is most Marxists today are probably no longer subscribing to historical materialism in the same way that they used to, or that most Marxist culturism is not necessarily about the overthrow of the capitalist system. That one of the things to say is that Marxism has had a broad influence on the way contemporary literary and studies conduct themselves, in part because Marxist had certain insights into the way cultures work. One of those insights, I think, comes from Williams. And it's this model of culture, in almost any cultural formation, as the interplay of three forms which he refers to as dominant, residual, and emergent, okay? And that's one of the things that we'll be wanting to test. Does the literary and cultural history of the United States in the period that we're looking at seem to bear out this model of culture. Are there dominant forms that give way or maybe have taken over, we might say, from residual form. Right, so if we go back to this, dominant, residual, and emergent. It's pretty clear what dominant is, right? It's whatever we take to be at the center of any cultural formation. Residual and emergent cultures. Now think of this as a kind of gravidic center. These are on the periphery. But they're in orbit around that dominant center. In some sense you might say the definition of what's residual and what's emergent absolutely depends on the existence of a dominant culture, because what these forms are about is conversation with that dominant center or negotiation with it. So residual culture, according to Williams, consists of those practices that are based on the residue of some previous formation but continue to play a role in the present. All right? So they're part of the past, but they're not simply archaic. They have a powerful role to play in the present. The present dominant culture will often have to take these forms and practices into account. Here's an example from later on in our course. Journal entry from Ralph Waldo Emerson. He writes in all my lectures I have taught one doctrine, namely the infinitude of the private man. This, the people accept readily enough. And even with loud commendations, as long as I call the lecture art or politics or literature or the household. But the moment I call it religion they are shocked. Though it only be the application of the same truth which they receive everywhere else to a new class of facts. So one of the things you might say about Emerson, he's trying to push what we will come to see as a new doctrine that grows out of the enlightenment into the context of a larger biblical culture that we're starting to investigate next week. And he finds that in many ways people that belong to that still biblical culture are willing to take his ideas and go with them, except when he gets to one particular arena of thought. And there the residual is still powerful. Right? Emerson, as a sign of an emerging set of ideas that are becoming dominant have to take them into account. Residual culture is still powerful culture. Emergent, according to Williams, is on the other end of the spectrum. If residual is linked to the past emergent is linked to the future or the new, or what's new from the stand point of the dominant culture. So it's about new meanings, he says, new values, practices, relationships and kinds of relationships are continually being created by emergent culture. But it's important to understand that both of these forms exist only in relation to the dominant. You need to understand the canonical tradition, in other words, to understand the challenges from the past, from the present, and the future of that canonical tradition. So that's part of what we're up to. We're trying to understand how something called an American canon was created, and we're also at the same time trying to link about what the limitations of that canon-making process are. Okay, so there's a lot of things that I think will be of use to you as you go on in your career as English majors. Okay, first concept I want to talk about for the moment is something called the horizon of expectations. So I'll begin by asking you to tell me where you think the meaning of a text is. If a text has a meaning, where is it? Yes? [ Inaudible audience comment ] >> How you want to relate to the text. Okay. That's a start. Yes? [ Inaudible audience comment ] >> Good. So the comment was that it's a conversation or collision between the text and ideas that surround the text, and the reader and ideas that surround the reader. I think that's good, that's a good way to start thinking about it. The horizon of expectations comes from a branch of critical theory that we might call the aesthetics of reception, or broadly speaking, reception theory. In the olden days we used to think that the meaning of a literary text was in the text, right? So if you in the earlier part of the 20th century, you would say okay, I'm going read a poem, and basically everything I need to know about the poem is pretty much in the poem. We called this the new criticism. It was a theory of the way great works of art worked; they were self-contained. And the best ones were complicated and had symbols and you know, they were really -- they gave you different kinds of readings that you can have, but they were still self-contained. Biography, that was kind of extraneous. Literary history, what we tend to call this course, that was all extra stuff, context. Text was the most important thing. And that was -- you can imagine, that was great for high school teachers of English, right? Didn't really have to prepare, all you have to do is find a good poem, bring it in, and you can talk for your 40 minutes about this poem, it works pretty well. But in part, I think due to a number of critical traditions and in part due to the, you know, certainly the advances that come around because of multi culturalism, we've been to see that the new criticism was underwritten by what we might call an interpretive community. A bunch of readers who share the same ideas about how the text work, what's important about text. You know, a set of shared values. What happens if you're a reader who comes from a radically different tradition and doesn't share those values. Is that text going to mean the same thing to you? Probably not. Is the meaning that you're going to take out of that text invalid? Today we would say probably not. We would say that every text, when it's created, greets what we might call a horizon of expectations. That horizon of expectations is the sum total -- you might say the cultural and social milieu around -- in which a text is coded and in which it is received. We would also say that the author probably has some sense of this. May not -- certainly wouldn't theorize it or think about it openly in the [Inaudible] but they have a sense of what they might call writing for an audience, perhaps. The sense that the audience might expect things. And that is part of the horizon of expectations. The horizon of expectations is the sum total of the historical moment, the moment in the history of artistic forms, all right? And it's personal too, the reader's own personal experience of reading. All of this will go into the horizon of expectations that the reader will have when he or she greets the text. And an author intuits that there are going to be these horizons of expectations out there, right? So you might say the fact that you're going to read Moby Dick, is going to be -- and when you read Moby Dick, for you, the meaning of Moby Dick is going to be profoundly effected by the fact that you know it's a novel. Well, not expected to do the same things that a lyric poem or epic would do. Going to be effected by the fact that you know it's a classic novel. Right? A classic, oh! So that's going to give you a certain set of attitudes towards it. Okay, we're going to have to work on those. That's important too, right? It's going to be effected by the fact that you're reading it under the pressure of a course and knowing that you're going to have to be examined on it, and maybe even write on it. All of these things will effect the meaning of Moby Dick for you. And if you come back to it in twenty years, as I hope you will, it will probably mean something different to you then, because you will have had twenty years of life experience and reading experience between those two encounters with the text. All of this is part of the horizon of expectations. And it also has to do -- something with the notion of genre, as I suggested. It's a novel, not a poem. And a notion of particular forms that are current or not current at the moment the author writes. Author can choose to have a number of relations to the horizon of expectations. You could say you know what, I want to sell a book. So I'm going to give the audience exactly what they want. Dan Brown's thinking to himself they bought my other books, they'll buy this one. I'll use the same device. I'll have a character who's actually another character, but I won't tell them until about two-thirds of the way through. How many of you have read Dan Brown? I read all of Dan Brown. I wanted to figure out, you know, I'm like, poor underpaid English professor, how do you do it. This guy taught at [Inaudible] he's an English professor. How does he do it. I resisted The Lost Symbol, I must say. Then I finally read it. Not as good as the DaVinci Code. How many of you have read Angels and Demons? Okay, and the DaVinci Code? Same book, right? I mean -- literally, even the same -- [Inaudible] a 2 and he's underneath. When I read Angels and Demons, I went oh my God, he wrote this book, not enough people read it, so he rewrote it again with a slightly different template. And I guess nobody noticed. Anyway, it's fine, it's all fine. But you see, that's what we call genre fiction. In a sense, he's making his own genre. Audiences, apparently, are not put off by the fact that it's the same formula over and over again. That's one way to approach the horizon of expectations. And most genre fiction, as we call it, detective fiction, some science fiction, other things. They just cue to those conventions. There are conventions for the literary novel too. The literary novel is supposed to be complicated, or you know, formally challenging or whatever. You cue to those too, if you're going to do a literary novel. So you're not Dan Brown, you're I don't know, pick your favorite literary novelist, Philip Roth [Assumed spelling], you're going to be writing in a way that signals that what you're doing is the literary novel. In the case of Roth, you're also going to be writing knowing your audience presumably has a set of expectations that are based on what you've written before. You could decide, if you're Roth, to contradict those things, to do something radically different. Or you could decide not to. Sometimes a horizonal change takes population well after the production of a text or the writing of a text. And that's, you'll see, is the case with Moby Dick. Moby Dick is written in the middle of the 19th century. And it's laden with clearly literary ambitions. You'll see in sections this week why. Melville clearly signaling that this is not the novel as usually. This is not a personal narrative of the sea, like I used to write, as usual. This is something different. Yeah, it was so different that the audiences went ah, and didn't want to read it. Or only a few people understood it. Melville got a little bumped out, wrote another book in which we actually took time out in this book called Pierre, to excoriate the literary publishing world and then got headlines from reviewers, Herman Melville, crazy. And basically his writing career was, you know, in the tubes. It -- for the most part of Melville's life, he gave up writing, he became a clerk in the custom house and for a long time lived in New York not writing fiction, writing a little bit of poetry. And when he died he was forgotten. People -- it was, you know, the old joke. People were surprised to read his obituary, because they thought he was dead already. I mean, what happened to the Herman Melville. In the 1920s, something happens. One piece is found and published posthumously, the wonderful short piece Billy Bud. People start looking at Melville once again. There's something that begins to be called the Melville revival that takes place. People start reading Moby Dick again. And in the after math of World War II when literary critics and other scholars are trying to prove that the United States, which is now a global power, has a literature, and indigenous literature that stands up there with the big boys and girls. Just as good as the Germans and the French and the English, right? They look around. They're doing this in the aftermath of modernism, which taught us texts should be hard if they're going to be literary, right? Joyce. Right? And they say guess what, we have a modernist novel before there was even modernism, and that novel is called Moby Dick. And Moby Dick got set at the center of the American canon as a result of that. Its meaning changed. It has a horizonal shift which had nothing to do with the writer, you might say, and had everything to do with a very specialized set of readers who could then convey their understandings and their readings to more standardized sets of readers and all that is in the genealogy of this moment, as I'm standing here talking to you about Moby Dick. Okay? So that's one of the things that I want you to understand. The meaning of a text is part of a negotiation, or to use a term that we've brought up earlier, a conversation. And it's important to remember, therefore, that the meaning is -- there are limits. Moby Dick is not a book about a pink elephant. And if you wrote Moby Dick is a book about a pink elephant, that would actually be wrong. It would be one of these rare occasions when people reading a paper on literary criticism could say that's wrong. So you're bound by certain conventions of the language, right? But within that, there's a lot of play. And we might say that one of the things that -- take this as a hypothesis. One of the things that makes a great text great is it allows for that kind of free play of meaning. It leaves space for the reader to create meanings of that text. We'll test that as the -- as the course continues. All right, just to recap, F. O. Matthiessen was the guy who wrote a big book that's called American Renaissance. It came out in the middle of the 1940s, and that really helps to establish the center of the U.S. canon, which is still Emerson, Thoreau, Whitman, Hawthorne, Melville, and then we would add to that Dickinson, who Matthiessen wrote about in a separate place, and sometimes Poe. And there are some others. Right? That's still thought to be the center of the American canon. What you'll get to do is have experience with those writers and you'll decide if in fact that canon is trumped up for all kind of reasons we can't really respect any more, or if there's something that remains valuable within that tradition. For Matthiessen, it was a tradition that embodied the values of Democracy. And that's what made it valuable and what made it American. We can test those as well. That book, and therefore the name of that period, were American Renaissance. Okay, let's see. Let's talk about -- well, let's talk about that first. Literature. What is literature. Everybody took literary -- who took literary interpretation. Okay, good. So you all remember everything you all learned there, right? And what is literature, didn't they tell you? What did they tell you it was? Yes? [ Inaudible audience comment ] >> Any written words. Dan Brown is literature. The New York Times is literature. Your syllabus is literature. That might be a little too far on the promiscuous side, but we'll keep that as a possibility. What else? [ Inaudible audience comment ] >> Okay, so I'll stop you. So the -- it's being suggested that there's capital L literature, lower case L literature, and that within the literary, there's actually a hierarchy of literary forms. What does that do with other kinds of writing, then? Is Dan Brown bad literature or lower case literature, or is literature going to have to be just L with a -- capital L literature, does that mean it's associated with some big tradition? All right, well keep that as a possibility, the L, the capital lower case thing, and see if we want to keep that. Yeah? >> I would say literature often [Inaudible] of the human condition. >> Literature conveys aspects of the human condition. Doesn't history-writing or sociology or philosophy or religion -- I didn't say -- okay, one of the things you might say about that is yeah, but therefore it has things in common with all those things. So that's fine. Except we tend to think of literature as separate or doing something that's different from those. Or let's put it another way. In the course of the years that we're going to be looking through there are people who are going to -- writers -- who are going to have a vested interest in trying to define the literary as not like those other things. So it's going, you might say it's going to convey aspects of the human condition in a particular way or maybe get at aspects those other stupid disciplines don't get at. Okay, we can work with that. Anything else? Yeah. >> Maybe it's kind of like the umbrella term for [Inaudible] encompasses a lot of different [Inaudible] I guess. >> Okay. We would -- >> -- the way that we speak about a classic, the way that we would -- [ Inaudible audience comment ] >> Good. That's good. There are many different sub genres, and there's the idea of the classic built into literary. But let's work on this. What's the difference between literature, if we want to say there's a difference, what's the difference between literature and all writing? I suggest that we might want to make that distinction. So how do you draw that distinction and who is going to draw it. Yeah? [ Inaudible audience comment ] >> Would it can be okay? I don't know, with me, you mean? I'm happy to talk. Artistic aspirations. Well that goes back to the horizon of expectations, right? We might say that the literary has a set of aspirations that we would call the literary. People are always -- why are we worried about this? Because there's something that we've all heard about called the intentional fallacy. You've probably all heard of this. How many people have heard of the intentional fallacy? Anybody ever say that to you? Intentional fallacy was part of that whole new criticism thing. Basically boils down to this. You shouldn't judge the greatness or success of a literary work depending on its author's intentions. In part because you can't always know the author's intentions, and also because the authors aren't completely in control of his or her intentions, right? You don't even need to go to, say, freudian psychology or psychoanalysis to suggest that there are going to be things that occur in the act of writing that aren't exactly planned, and only a certain kind of writer who is absolutely in control of absolutely in control of every single thing that goes on when he or she sits down a particular configuration of words. All right? On the other hand, we don't want to discount intention totally. There's intention when you pick up something that looks like a novel, you say okay, they intended to write a novel. There's something to be done with that. Intention lies -- and we might say we can look and say hmm, we know enough to say that that person decided to write a literary novel. Okay, great. Does that mean it's literature? You know, person X, Dan Brown might have said I want to write a literary novel. And maybe he thinks he did. Would we agree? Some of you might agree, it's okay. How about this. Is Stephen King -- Stephen King novel, your average Stephen King novel literature or not literature? How many say literature? Oh, come on. More than you think -- how many of you say not literature. Oh, come on, no wishy-washy. Start again. Literature. Hands up. All right, that's better. Better showing. Not literature. Hands up. Third category, I didn't tell you there was going to be a third category. Literature in some books but not others. Bag of Bones, that's literature, Scribners, Carrie, that was back in the great days. King, by the way, is a remarkably good writer, I think. And if you want to learn about writing, you should read his book about writing, especially his screed against adverbs. It's brilliant. In fact, I think I'll post it to Blackboard so you can have it. Yes? [ Inaudible audience comment ] >> Okay, lower case and capital again. Yes? [ Inaudible audience comment ] >> Wait, novels are lower case and poetry is upper case? I work on prose, you know. [ Inaudible audience comment ] >> Okay, that's a possibility. We could think -- you know, we certainly could think about whether it's useful to think -- let's talk about this, and you can talk about it in section meetings. Is it useful to make a distinction between something that we might call literature with a capital L and small literature, with a lower case L. But might we also want to think about it, you know, in terms of proper nouns versus other things. I mean, one of the things that American literature would suggest to us, one of the things we mean when we say American literature is a kind of institution the culture, right? American literature connotes a set of books, textbooks, anthologies, syllabi, tests, you know, all this stuff. It's part of a large institution that has to do with publishing and universities. And it's a big thing. And maybe lower case literature is something that give -- let's us get an aspect of text or reading or writing that are separate from that institutionalized set of practices. Yeah? [ Inaudible audience comment ] >> So literature is very well put, something that a particular culture has decided it worrying and should be preserved and read and studied and carried forward. You know, extrapolating from January 19, 2010 forward, yeah, Dan Brown will be on the syllabi in 100 years. You know it. Yes? [ Inaudible audience comment ] >> Yeah, that's good. Literature grows out of what a society decides it good. So one of the things we need to think about is how does a society decide anything? Because I think you're right. But part of what we're going to be investigating is how does cultural change happen. In a word like society, your description of it gives that agency, as if the society could do something. But clearly a society is also -- doesn't -- the actions of a society perhaps only can be understood in retrospect. In the present moment, it looks like the actions or some total of actions of individuals. So how does you know, the horizon of expectations actually function as you might say, the summation of all of the collection of different horizons of expectations. All of you are going to have your own individual horizons of expectations. They are again going to be based on, you know, your experience, historical moment, but your particular experience is going to make them slightly different from one another. Most likely, I'm guessing, they're going to fundamentally overlap in some key ways, but they're not necessarily always going be the same. Some people might think something is literary and something is not, and there would be two -- those two judgments would rise out of different -- you might say horizons of expectations, conditioned by different personal experiences. So we want to think about it. That's a sum total. Just as we might say when a society acts it's somehow the sum total of individual actions. So we want to think about how cultural change happens, using as a prism the acts of individuals, which are the particular writing acts of people that we're going be studied. One of the things I think we can suggest, at least as a hypothesis now, is that literature is something that's constructed by a society, it tends to be an expression of a certain set of values that that society might take to be important or worth preserving. But it is constructed. And what happens is it becomes a kind of institution of culture. What do you suppose literature means to the Puritans that we're going start reading next week. Does it mean the novel, does it mean drama, does it mean lyric poetry? No, what do you think it means? If they don't use it -- if they use the term, and they tended not to. Yeah. Religion. So the -- the highest work of literature, pretty much the only one you needed, was a certain one book. The Bible. Yeah. Everything else is kind of inundations to the Bible. So what the Puritans would have considered worthy, if they were thinking of literary, they would have thought of the Bible, they would have thought of sermons, histories, biographies, fiction? Doesn't that mean lies, doesn't that mean untruths, isn't that story-telling? Something happens in the course of the period that we're looking at to change our understanding of what the literary is. We have a post romantic notion of literary. Romantic writers in Britain, France, Germany, and the United States, are actively engaged in a process of redefining what the literary means, linking it to an aesthetic experience, living it on the imagination of the inward life. And suggesting that it is a discipline unto its own, separate from all those other ones, from religion and history and philosophy and all these things. And some of them would claim that in fact it's the highest discipline, and they wouldn't have been the first. I mean, Philip Sydney [Assumed spelling] was talking about poetry being the queen of all of the disciplines, right? So I want you to get a sense of that. We need to historize in this course our understanding of what literature and the literary are. They mean something to us today and that factors into our horizon of expectations. They meant something different in the 1600s into the 1700s, and we need to remember that as we read those texts. Okay? All right, let's talk about America and American. What does that mean? I -- you might -- if you've been listening closely, you've noticed that I've slipped periodically from saying U.S. to -- what's the difference between American and U.S.? [ Inaudible audience comment ] >> America has to refer to both North America and South America, doesn't it? Well, probably, if we were being -- >> -- I'm American, I mean, they'll probably know what you're saying, but it's not true. >> They'll know what you're saying, but it's not true. >> It's no so distinctive -- >> So if you were in Paris and you're saying oh, I'm going to America next week, they probably wouldn't expect [Inaudible], right? Okay, that's good. So let's think about what's in stake in that. U.S. and American aren't exactly the same. There's a sense in which America is alive. You say if you take America to mean North America only or even the U.S., in a sense, that's metaphorical speech. On the other end, you say but people understand. So we're all skittish about using the term America, and yet it has kind of cultural currency. There's a certain way in which America is constructed both in the United States and abroad. And there are certain agreement about its meanings. Yes? [ Inaudible audience comment ] >> U.S.M? [ Inaudible audience comment ] >> So what does she want to say? So she doesn't want to say American, probably, and she doesn't want to say -- that's a pickle. [ Inaudible audience comment ] >> Okay, so we might say maybe -- I mean, you know, certainly in the literature of the period, America, you're talking about this large kind of continent that's not fully explored. That's part of the, you know, the preenlightenment era, the era of settlement and discovery. And after that we should maybe be saying something else? Yeah? [ Inaudible audience comment ] >> So you think -- so you think if you say, somebody asked you where you're from, I'm an American, does that mean -- you're making a patriotic statement? >> I don't know if I would, but I think that's kind of -- >> What else would you say? I guess you could say I come from the United States? I probably would say I'm a New Yorker. >> I guess it depends [Inaudible] -- [ Inaudible audience comment ] >> Okay, we might say that it has validity, because it does precisely that. As you say. It conveys the sense of a shared experience which transcends many different kinds of boundaries. It's a certain kind of consensus. But it also -- you know, it isn't the same as the political entity known as the United States of America. It upon possibly is something larger. It's possibly a kind of mythical place, that every now and then overlaps and not as often as we like, we might say, overlaps with that actual political entity we call the United States of America. Yeah. [ Inaudible audience comment ] >> It's easy, right? Easier to say American than U.S., U.S. sounds kind of -- can't say United States. Okay, it's easier, and I think it's fine. And it's part of our conical. So you know what I want you to do? I want you to inwardly cringe every time you use the word, just to be a little self conscious about it. Because what I want you to understand is that America, American, all that, the way we use it and the way we use it and it gets understood, so people understand what we mean, all of that is metaphorical. Or we might say that America fundamentally is a trope. It's figurative language. And we need to keep that in mind. We're going to see a whole lot of unself-consciouses of it, but we want to be self conscious about it. Just as we want to be self conscious about every act of meaning-making that we witness in the course of our reading and that we engage in, in the course of our thinking and writing this term, all right? It's a trope. Now it can be a trope that signifies inclusion. I'm going to put up a wonderful sonnet that actually really buys into this idea of America as something that means more than just the United States, that does mean a set of shared values, it means this set of shared values. Would somebody like to read this for us? Yes, loudly. Stand up. Please. Really. [ Inaudible audience comment ] >> Thank you. Let's give her a round. [ Applause ] >> Hey, it's not easy to stand up in the middle of everybody and do that. And I'm going to be asking people to do that in the course of the term. So, thank you very much. Is that familiar to anybody, any of it? Yeah, where, why? Statue of Liberty. Yes, the Bartholdi pedestal. This was written in part to try to raise funds for it. Keep ancient lands in story pomp, cries she with silent lips. Give me your tired, your poor, your huddled masses yearning to be free. The wretched refuse of your teaming shore. Send these homeless tempest-tossed to me. I lift my lamp beside the golden door. Come, welcome. Is that what we say in this country? Is that what they said yesterday in Massachusetts? Inclusion is a nice idea. And many people came to the United States in the late 19th century and you know, in the time that Lazarus [Assumed spelling] is writing, with that dream of inclusion, and they found of it, some of them. And some of them didn't, right? American is a trope for inclusion. It's also a trope for exclusion. At the same time. And that's one of the things about figurative language. Figurative language can embody paradox. And it's almost always more interesting when it does. That's one of the things that we're going to be looking at. So one of the things we might say is that a guy named William Prescott writes a book in the 19th century called The Conquest of Mexico. A lot of people read it. A man named George Bancroft writes a book called The History of the United States. And when Prescott reviews George Bancroft's history of the United States, he doesn't see any connection between the idea of conquest that he's written about in the Mexican context and the history of the United States. Rather, he sees in Bancroft's account the idea that the history of the United States of America is somehow providential. What does that mean, do you know in we will know more about that in a couple of weeks -- yeah. It's the will of God, it's God's providence. Pure -- big word for the Puritans. So you can see that history-writing somehow is part of this larger rhetoric of the providential. This is the same moment that the term manifest destiny starts to be coined, right? Middle of the 1840s. Okay, so you might say that there's certain kinds of exclusion that are based on the United States versus the rest of the world. And that's part of what we're going to talk about. There are certain kinds of other exclusion which we might talk about. There was a young historian named Fredrick Jackson Turner who in 1893 gave an address on the significance of the frontier in American history at the Chicago exposition. Fascinating cultural thing, if you are ever interested in thinking about cultural sites. There was a big architecture -- there were pavilions, stuff was built, it was called the White City because so many of the buildings were white buildings that were temporary structures, but designed to enshrine neo-classical ideas. That was the vision of America that was being put forward. Turner writes about the fact that the west has officially been closed, right? There's no more westward expansion. And he says one of the things that accounts for the American character, the way it is, is the existence of the frontier. The frontier has created certain kinds of values, ruggedness, inventiveness, individualism. And now the challenge will be how to maintain those values with the closing of the frontier. That was incredibly -- that was incredibly influential. Today we would say that it's kind of more like myth-making than real history-writing. But it set the pattern, you might say, for a lot of historical analysis. Became one of the founding ideas in American studies. One of the founding books in the discipline that's known as American studies is a book called Virgin Land, Myth and Symbol in American Literature. Virgin land. What does that mean? Yeah? Untouched land. Meaning the American continent, right? The Europeans came, they found virgin land, they were able to have this frontier. It formed their manually ruggedness, and we're Americans because of that. So that was taken to be history, right? What's the problem with that? They were kind of people here. [ Laughter ] >> But we exclude those from that conception. That particular myth of America excludes those, right? This is what Turner actually said, that coarseness and strength combined with acuteness and inquisitiveness, that practical and inventive turn of mind, quite to find expedience, that masterful grasp of material things, lacking in the artistic, but powerful to effect great ends, that restless, nervous energy, that dominant individualism working for good and for evil. And with all that buoyancy and exuberantism that comes with freedom, these are the traits of the frontier or traits called out elsewhere because of the existence of the frontier. This is exactly the kind of rhetoric that you know, Reagan and Bush, too, all these people draw on this rhetoric of what a true America is. And as we can see, it's predicated on a hidden kind of exclusion that we all -- that we don't want to talk about. So individualism is one of the hallmarks you might say of the American self. According to a large number of commentators. What does individualism exclude is what our little analyst Turner is writing might lead us to ask. Tony Morrison has an idea about that. Tony Morrison about written and talked -- there's a famous moment from an interview that she gave in Time Magazine, where she talks about the engine of American senses. What makes American. Some people say individualism, the Turner frontier, all that kind of stuff, right? She says it's a different thing. Something else that makes most Americans feel like they're American. She said, in 1989, I feel personally sorrowful about black-white relations a lot of time, because black people has always been used as a buffer in this country between powers to prevent class war, to prevent other kinds of real conflagrations. If there were no black people here in this country it could have been Balkanized. The immigrants would have torn each other's throats out as they've done everywhere else. But in becoming an American, from Europe, what one has in common with that other immigrant, so again immigrants, think of Lazarus, immigrant, you know, new colossus kind of image. What that has in common with the other immigrant is contempt for me. It's nothing else but color. Where they were from, they would stand together. Wherever they were from they would stand together. They could all say I am not that. So in that sense, becoming an American, she says, is based on an attitude of exclusion of me. Not inclusiveness, not individualism. Exclusion of a particular type, set of people. It wasn't negative to them, she says, it was unifying. When they got off the boat the second word they learned was nigger. Ask them, I grew up with them. I remember in the fifth grade a smart little boy who just arrived [Inaudible] speak English. He sat next to me, I read well. I taught him to read just by doing it. I remember the moment he found out I was black. A nigger. It took him six months. He was told. And that's the moment when he belonged. That was his entrance. Every immigrant knew he would not come as the very bottom. He had to come above at least one group, and that was us. And of course one of the things we see here among the things that are cultural constructed is that notion of blackness. It's one of the other things we're going to be talking about. To one extent, what is one of the things that American literature that is trying to contend with is the presence of the people that the Turner hypothesis excluded. That are excluded, you know, that are excluded legally as well. The preference of people of color, whether they be Native Americans or African Americans or later on Mexican Americans. Any number of people that don't fit a certain kind of Euro-American paradigm. To what extent is that, you might say, the big problem with which American literature is trying to contend, sometimes to paper over. Sometimes to actually engage with. We'll come up with both of those versions in the course of the term. Again, what I want to stress is that America is a trope, it signifies inclusion, and exclusion both. It signifies providence, individualism, and racism too. And a number of other forms of discrimination that we will be talking about later course of the term. All of this is part of America, and therefore all of this is part of American literature. Okay. We hold these truths to be self-evident, that all men are created equal, that they are endowed by their creator with certain unalienable rights that among these are life, liberty, and the pursuit of happiness. This is from where? Declaration of Independence. Statement of universal principles, right? The basis for American intellectual culture, the basis for our country. And there are people -- you will find text books that will say well, it's kind of written in the language of the 18th century a little bit, you know, that all men thing, they meant people. They would say well, they transcended their moment, they created a set of principles that could evolve and adapt and move forward as the country did. That's all true. But only in a deeply racist and patriarchal culture could you say that all men are created equal means that all people are created equal. They meant men. Did women vote? No. Believe me, Abigail gave John shit about this, he really -- [ Laughter ] >> Not happy about it. You know, when do women vote? In the beginning of the 20th century, okay? They didn't mean all men are created equal. Or if they did, they had a very metaphorical understanding of what man was. You know, or [Inaudible] but they had a very literal understanding of what man was, and also a very metaphorical one. Because it didn't mean all men, did it? No. Not Native Americans, not African Americans, [Inaudible] basically meant white, property-owning European and derived males. So I want you to look at this and see that this too is figurative language. Figurative language is all over the place, and it's part of our job as literary critics to understand it and decode it and understand what its power is. And these guys, people like Jefferson, were men of the enlightenment. They understood the power of the written word. And so did the people that settled the United States. The age of discovery is in part the age of writing. Okay? Columbus sails not too long after, it's roughly contemporary with the Guttenberg Bible, all right? Text is about to explode across the European continent. And discovery, the age of discovery, is all part of that. Melville writing a sea novel in the middle of the 19th century is part of a long history that associates the sea and text and imperialism and con conquest and race. All of these things become kind of a nexus of associations. That's part of what we're going to be trying to untangle in the course of the term. This guy, Christopher Columbus, he knew the importance of writing. He wrote letters back to his -- his patrons in Spain. You will read a couple of them. A diary of his is preserved. The Diario Christopher Columbus. We know that he wrote a lot when he was trying to find the Americas. And Jefferson too knew the importance of writing. He told this to Lewis and Clark as they were doing their scientific explorations. Your observations are to be taken with great pains and accuracy to be devoted to enter distinctly and intelligibility for others, as well as yourself. So these guys are tromping through unknown woods, and periodically, they have to sit down and write. And that's one of them , all of them. They're all writing. Thousands of pages are produced by Lewis and Clark expedition. With the aid of the usual tables to fix the latitude and the longitude of the places at which they were taken, and are to be rendered to the State Department -- I mean the precursor of the State Department, they are to be rendered to the war office for the purpose of having the calculations made concurrently by the proper persons within the U.S.. Is this scientific exploration? To take possession of a continent, really, you need to write yourself across it. That's what Jefferson knows. Writing is powerful. Several companies of these as well as your other notes should be made at leisure times and put into the care of the most trustworthy of your attendants to guard by multiplying them against the accidental losses to which they would be exposed. This is my favorite bit. Further guard would be that one of these copies with written on the paper of the Birch. As less liable to injury from damp than common paper. They wanted that writing preserved and sent back there. Okay, so one of the things I want you to understand right away is the importance of writing to the age of discovery and the age of imperialism. And one thing more. You know those people that didn't exist in the virgin land? You know why, one of the reasons they weren't thought to be people at all, or worthy of notice? They didn't write. North American Indians didn't have a written tradition. They had literature, yes. It was oral. For the Europeans, that didn't rate. Look for those moments when you start to read Columbus or some of the other early settlement narrative excerpts that we have. When they talk about what they're looking for, Columbus is looking for kings and cities. He didn't find them where he looks in North America. He finds, you know, all kinds of resources, and people without number, he says. But nothing of importance. Okay. Last things. One of the things -- so this is what we're going to be doing over the weekend. We're going to be looking at, you might say, the land chapters of Moby Dick. And we're going to use those as a kind of overture for the course. We're going to use those to frame the matter of the course from the early settlement narratives all the way down through some of the concerns of American romanticism. And they will therefore frame the course with Moby Dick. So you're going to get your feet wet by reading the land chapters, and then we'll come back to the sea chapters at the end of the term. That's one thing you're going be doing over the weekend. You're also going to be reading a wonderful essay by Steven Greenblat, this is an excerpt from it that talks about what cultural analysis when literary people do it, and why cultural analysis is necessarily rooted in formal analysis. In textual analysis. Close reading turns out to be about culture too, and in Greenblat's conception, a master piece, a powerful work of art encodes much of its culture within it. To understand the culture, read texts. But to understand the texts, you need to read the culture as well. So this is kind of a reciprocal relationship, what we might say is a more fluid relationship between text and context than you might have been led to expect earlier. That's one of the things that we're going to be doing as well over the weekend. For section meetings which meet this week, please bring Moby Dick. You don't need to read any of it, you'll be looking at bits of it in class. If you do feel like reading it, read it from the beginning. Read the title page, the dedication, and some of the -- just look at the early pages. Does that look like a novel to you? What the hell was this guy doing? Okay, that's part of what you're going to understand. You should understand the practice of back in the old days. And you can still do this on a Kindle, right? Kindle let's you beam a few pages to see if you want to buy the book or back when we used to go to bookstores, we might browse and look at the first few pages, decide if we wanted to read the book or not. I'm here to tell you that that's actually a valid way of thinking. Because what books do in their first few pages is set the ground rules for interpretation. So what you'll be looking at in section this week is what kind of ground rules for interpretation are there. All right, before you go, last couple of things. The lectures do a certain kind of work. We might think of it as kind of literary historical, and I will be doing some close readings of moments within the text. But the section meetings are crucial to this course. And if you have to pick something to miss, miss me, do not miss your section. We have wonderful, brilliant section leaders. They are sitting up there, I'm going to quickly introduce them to you. In reverse alphabetical order, it's Kara Zaverilla, give it up for Kara. [ Applause ] >> Stephanie West. [ Applause ] >> And our token male, Brendan Burn. Okay, there's been a slight change on the syllabus. Kara will be taking the Thursday sections and not the Friday sections. Now there are wait lists for the Thursday sections. There are also issues with the space in the room of those Thursday sections. If you are on the wait list for a Thursday section you need to e-mail me today and tell me why you have to be in that section and cannot be in one of the Friday ones. If you have a good reason, we will do our very best to accommodate you. Okay? That's one thing to note. You must go to sections. We take attendance at lecture, we take attendance at section, there's a big portion of the grade which is participation in section. Go to section. Okay? Am I forgetting anything else, guys? All right, we're off on our great adventure together. |
Open_Ed_Cyrus_Patell_American_Literature | American_Neoclassicism.txt | [ Silence ] >> Teacher: All right. We're going to talk about Jonathan Edwards today as somebody who is a good example. You might say, his life is a kind of case study in the interplay of what Raymond Williams has called dominant, residual, and emergent cultures. Which, if you remember, is one of the ways in which we tried to frame the course. To think about how the patterns of literary and intellectual change that we'll be tracking might well be understood by invoking this framework. So I want us to see Edwards as somebody who belongs to a dominant cultural consensus that is being strongly challenged by a new and emergent form. That dominant cultural consensus we might link to Puritanism and Calvinism in New England. The thing that's challenging it, the emergent cultural forms, are the thinking of the Enlightenments. And Edwards has a kind of personal relationship to that that we'll talk about. So in a way I want to give us again the full sense of where Edwards is coming from. And then think about where it is that he's going. I'm going to go back a little bit and evoke Edward Taylor, the poet, again for us. Because he seems to me to, in certain ways, have the same kind of technical and formal problems that he's wrestling with in his poetry that Edwards wrestles with in his writing. And that's something that I suggested to you a couple of weeks ago, was this. How do you use, if you're a Puritan and a Puritan writer. How do you use something that you conceive of as debased, worldly and therefore untrustworthy? By which I mean human language. How do you use that to convey things that are divine? To try to get at a sense of what it might mean to have grace. To try to get at a sense of what the divine mind might be like. This idea that you have the divine mind is completely incommensurate to you. That what looks like free will to you at any given moment of your life, is actually all foreordained and predestined because the mind of God is able to see past, present and future in a way that human beings simply cannot. Right? So how do you convey all of that using this debased form that we call language? And remember the context for Taylor, right? We talked a little bit about it. Taylor is a kind of American version of English metaphysical poetry. And like people like Dunne and Herbert, he has a kind of religious impulse behind his poetry. But for him, you might say, the appeal of the kind of writing that metaphysical poets do is that it dramatizes the difficulty of precisely the project in which he's engaged, which is writing about things that are unearthly in earthly language. And also dramatizes the experience of a life of the individual sinner. The life of the individual sinner is hard. Reading Taylor's poetry is hard. The life of the individual sinner should all be about kind of abjection and humbling yourself before God. So what is Taylor's poetry, other than a kind of series of ways. And again, you remember the preparatory meditations or poems that he used to prepare himself to give sermons. Or that he wrote while he was preparing to give sermons. And some like Meditation 8 actually will have a kind of biblical text, like the one there from John. I am the bread of life. And one of the things that Taylor does is to actually really think about that. Part of what he's trying to do is get beyond some of the kind of formulaic ways in which his listeners might have started to understand a biblical reading and sermonizing. And therefore, what he's trying to do is create new ways of thinking about these, and the poem tells him to do that. So he takes what would have been a dead metaphor, Christ is the everlasting bread or something like that, and reimagines it quite literally. What would it mean if you ate Christ? What would happen to him? Where would the streams of grace come from? All that kind of stuff. And, you know, there's a way in which what he's doing is trying to find new and inventive ways. What the metaphysical poets might think of as trying to use with to find new ways of expressing old thoughts, or thoughts that have never been completely expressed because of, you might say, the limitations of human language. So one of the reasons the poetry is hard, and hard to read and hard to say, is that it's straining against the limitations of human language. Now all of that makes it sound as if it's all, you know, difficult and might lead you to despair. And in fact, that's the wrong way to think about Taylor. I mean Taylor looks at this predicament that you might say that human beings have. We have this world in which we are looking at signs. We have a sense of being, some of are elect. We don't know when we're elect. The divine mind is just so different from ours. And how do we talk about that? How do we live? For him it's kind of a fundamentally predicament, rather than a tragic one or one that should lead you to despair. And when you, when we go back to reading Moby Dick I think we'll see some affinities between Taylor's point of view and the view of one of the mates, the jolly Stubb. Who says okay, it's all predestinated. Well, that's a comfort then. I don't have to worry about this. It's predestinated. Whereas, for someone like Ahab he takes the other kind of Puritan view which is the more grim view of worries about agency and what does that actually mean for human beings if something is controlling their fates completely? Taylor adopts a slightly more comic point of view. And I want to just give you a brief taste of this to get you, to give you a sense of how he does, he creates these poetic effects. By looking at one of his most poems which is on page 278 of your anthology. It's the Preface to God's Determinations. Touching his elect, and the elect's combat in their conversion. Coming up to God and Christ, together with a comfortable effect thereof, as the footnote tells you. Could I ask somebody to. You know what, I'll do it because this really is hard to read and I'm going to stumble but that's okay. All right. So I'll read you the first few lines of this. Actually you know what, I think it's worth doing the whole poem. It's not that long. It's only about 40 lines. So as you are looking at it, and this will be a wonderful poem actually for doing close reading work on for practicing. Not so much meter and scansion as looking at the way in which he makes these figures of rhetoric and other kinds of figures of speech here. So look for. I'll ask you if you notice some of these things. But one of the things to think about, and this is good in terms of the context of Edwards. Because Edwards will, at first, look like he's doing something different. Then it says what Edwards looks like he's doing is, instead of making it more complicated the way Taylor seems to, he seems to want to strip it down, the language. Right? But I think if you look at certain words in this poem, you will see that when Taylor repeats those words they take on slightly different meanings through the repetitions. Or rather, he is sort of playing on what are almost puns in the ways that these words are put. Okay. Infinity, when all things it beheld in Nothing, and of Nothing all did build, upon what Base was fixt the Lath wherein he turn'd this Globe, and riggalld it so trim? Who blew the Bellows of His Furnace Vast? Or held the Mould wherein the world was Cast? Who laid its Corner Stone? Or whose Command? Where stand the Pillars upon which it stands? Who Lac'de and Fillitted the earth so fine, with Rivers like green Ribbons Smaragdine? Who made the Sea's its Selvedge, and it locks like a Quilt Ball within a Silver Box? Who Spread its Canopy? Or Curtains Spun? Who in this Bowling Alley bowld the Sun? Who made it always when it rises set, to go at once both down, and up to get? Who th' Curtain rods made for this Tapistry? Who hung the twinckling Lanthorns in the Sky? Who? Who did this? Or who is he? Why, know it's Onely Might Almighty this did doe. His hand hath made this noble worke which Stands His Glorious Handywork not made by hands. Who spake all things from nothing, and with ease can speake all things to nothing, if he please. Whose Little finger at his pleasure can out mete ten thousand worlds with halfe a Span. Whose Might Almighty can by half a looks root up the rocks and rock the hills by th' roots. Can take this mighty World up in his hande, and shake it like a Squitchen or a Wand. Whose single Frown will make the Heavens shake like as an aspen leafe the Winde makes quake. Oh! what a might is this Whose single frown doth shake the world as it would shake it down? Which All from Nothing fet, from Nothing, All. Hath All on Nothing set, lets Nothing fall. Gave All to nothing Man indeed, whereby through nothing man all might him Glorify. In Nothing then embosst the brightest Gem more pretious than all pretiousness in them. But Nothing man did throw down all by Sin. And darkened that lightsom Gem in him. That now his Brightest Diamond is grown darker by far than any Coalpit Stone. All right. Let's talk about how it works. Let's take about the first 12 lines or so. How does it work? What's he doing? What are the attribute of this poem that you would recognize or want to point out if you were going to be collecting data for a close reading? Yes? >> Student: The first 12 lines outlines the sentences, and kind of outlines the first [inaudible]. >> Teacher: Okay, good. That's right. So this is another account of Creation. Note that he doesn't feel that he needs to write, you know, Gen 1. There's no. We know the story and he's giving us a telling of the story. Now if you read Genesis you realize that there's at least two Genesis stories kind of smack right on top of one other, you know. If you don't know what I'm talking about, take a look at it and see where is it that Eve comes from, and when is it that she's made? There are two different accounts. That's because the Bible has many different sources that are put together, and some are reconciled and some are not. So this is a Creation story and he's adding to it. Yes? >> Student: [Inaudible] a Job story? >> Teacher: Job? Okay. How about. How's that? >> Student: In the Book of Job when God is just like you have great [inaudible]. >> Teacher: Very good. So remember that, right, when we talked a little bit about the Book of Job. Job is the perfect servant of God. He is tested, tested, tested. All these terrible things happen to him. At the end you'd think God would give him some satisfaction to know that there was a reason behind this. It was not purely whimsical. Satan was, you know, Satan had issued challenge, it had to be met. Did He tell him? No. And what you might say is the Book of Job is a big text for the Puritans and for someone like Taylor. Because it exactly a demonstration of the incommensability of the divine and human. God basically says who are you to ask me anything? And God, there's also a language problem in the Book of Job, right? Job earlier on says, Well, you know when God speaks He speaks in a whirlwind. I can't really understand. And then God comes down and dains to speak, not exactly in a whirlwind. Although He's basically reminding Job that that's, you know, the way he speaks. So again, you can see where the language problem is coming from. It's a very good, these are both very good things to bring up. These are, those are clearly inter-texts for this poem, even though the poem is not announcing hey, here's an inter-text, right? So that's good. What would we say more about this particular act of Creation or narrative of that? Yes? >> Student: I have a question. I know it's [inaudible] right now. But there's [inaudible]. And I just, I think using the capital letters. I don't know if they matter? Or if it's like. >> Teacher: Why would he capitalize things? >> Student: [Inaudible] certain like all those caps? >> Teacher: Well, certain things get capitalized in talking about biblical text. Certain things get capitalized because it is customary to do so. It's either names or it's qualities, right? So there's a kind of precedence there. This is, that's a good question to ask because people often ask that about Franklin who seems like he's doing it in a kind of weirdly archaic way. Why would you capitalize qualities? And there's a way in which some of the commentary therefore is linked to what you might call allegorical writing, right? So I'll talk a little bit later on either today or later on today about Bunion's Pilgrim's Progress. And there's a way in which Bunion writing in the 17th Century is using that same kind of practice, right? And you can see that there's a reason for that. Because he's telling an allegory of a Christian life, so his character is a Christian with a capital C. And he meets all these characters. Their names are Hope, Despair. So that gives you a kind of allegorical cast. Why is it that Taylor does it? He never writes anywhere why, as far as I know, why he does it. So we have to look at it and think about it in terms of these other practices of capitalizing certain words to call out either the fact that they are properties, that there are certain qualities that have almost a kind of. We're going to treat it in almost an allegorical way. Having said that, Taylor is probably playing with that idea. So that certain things are going to be capitalized here because they're really important. And certain things are going to be capitalized because they're not really important, but may they are really important if we think about them again. So why is Bellows of His Furnace Vast all capitalized? I would suggest that that's in fact to create a kind of comic effect, right? I mean take a look at what, you know. He's taken this. He's doing a Creation story, right? It's a Creation story. And he's using this kind of archaic, almost now archaic practice of capitalizing certain qualities and certain things, certain things that give of a kind. Certainly things that refer to God would normally be capitalized. And yet, what has he written about in terms of writing this Creation story? Surely he's invoked Job, but is he talking about creating the Leviathan and the great creatures of the air and the water? No. What are. What is the abiding metaphor? Upon what Base was fixt the Lath wherein he turn'd this Globe, and riggalld it so trim? And you get the footnote, riggalld is an archaic word for group. What's that metaphor? What's a Lath? What's he? Yes? >> Student: It's carpentry. >> Teacher: Yes, it's God and the woodwork or the Carpenter. Okay. So we have some associations in biblical history between the divine and the Carpenter. Okay. But again, this is Taylor doing, making God the Father into the Carpenter. But that's not all he is because he's, you know, multifaceted. What else does he do? Who blew the Bellows of His Furnace Vast, right? Something like a blacksmith who works with bellows, right? Yes? >> Student: I was thinking a blacksmith because he says, Or held the Mould wherein the world was Cast. >> Teacher: Okay, good. So that could be more a black. That could be more blacksmithry. It could be sculpting. >> Student: Or maybe it's hard. >> Teacher: It could be that. Who laid its Corner Stone? God as architect. Or whose Command? Where stand the Pillars upon which it stands? Slightly different one. Who Lac'de and Fillitted the earth so fine. God is a sewer or the maker of cloth. We do on and on and on. And so we're getting a different version of the Creation story, right? I mean we're all, it's all pointing to. In a way it's almost like, less like Genesis and more like the beginning of the Gospel of St. John which is all about the word. Here it's about God the artisan making. It's not about specific acts of making. It's about God figured as maker but in very human terms. Daily activities. This is another way in which, you might say, there's a link between Taylor and Edwards. Because theoretically, right? I mean we're taught, we're using examples from the worldly, from daily life to talk about the divine. There should a kind of lack of fit between those things. Why would you use examples from the debased world in order to do that? Remember that Taylor didn't create these poems for public consumption in the same way that his sermons were created for public consumption. So finally, you get all the way down to like a Quilt Ball within a Silver Box? Who Spread its Canopy? Or Curtains Spun? Who in this Bowling Alley bowld the Sun? And all of a sudden the comic states are raised even further. It's fun to think of God as a kind of artisan dude. But then God is the bowler? It's almost like he takes this premise and then, this is the kind of metaphysical whip part of it, twists it one more time to give it another kind of comic edge to it. Right? So I think that's a part, immediately what he's done is he's given you a Creation story. But it's a Creation story that is not emphasizing or, that's not quite correct. Even as it is emphasizing the magnitude of the deity, God actually can bowl the sun, right? It cuts the deity down to size. Or makes him more, dare I say human or at least approachable in a way that he is never to Job, by giving him this kind of comic thing. And giving him kind of human occupations. You might say this is a just a heuristic. It allows us as abject human beings to be able to conceive of God, and none of them are going to be quite right. But if what we're getting across is that kind of comic idea, that's a road in the right direction. Because ultimately it's a kind of set-up, right? Because where this poem ends is where the Book of, the first Book of Genesis ends with a fall, right? There's a kind of oblique reference to that at the end. Let's take a look at the way one particular word works, and then we'll be done with this. Okay. Infinity, when all things it beheld in Nothing, and of Nothing all did build. That's the way we start. And Nothing comes back late in the poem, and I want to look at that. This is about Line 25, 35. Okay? Most, if you remember from the Defense Report with Henry Wright, the first stanza is questions. Most of this poem is questions too. And then we get answers at 35. All from Nothing fet, but made again an archaic word, from Nothing, All. Hath All on Nothing set, lets Nothing fall. Gave All to nothing Man indeed, whereby through nothing man all might him Glorify. In Nothing then embosst the brightest Gem more pretious than all pretiousness in them. So if we were going to comment on Nothing, what would we say about Nothing? Nothing from nothing leaves nothing. What? >> Student: [Inaudible]. >> Teacher: Yes, anyone? Take it from the appearance. Which from Nothing fet, from Nothing, All. Any little devices and tricks lurking in those lines? Come on, you look like you want to say something. >> Student: Is it an antithesis? >> Teacher: Antithesis? Where would you see the one and not the other? I mean yes, so let's talk about it. >> Student: Is that [inaudible]? >> Teacher: I don't know. >> Student: Isn't that like when you. >> Teacher: Antithesis would set. >> Student: That something is something, and then it kind of merges it? >> Teacher: Right. >> Student: Like an act. So I guess it could say all of nothing and nothing was. >> Teacher: Okay, that's one way. There's something anti. There's certainly something antithetical about this, although I don't think it's classically set up in the form of antithesis. >> Student: All that can be nothing? Anyway, but nothing. Can nothing be all or nothing? >> Teacher: Well, what's he getting at? Which may, which All from Nothing made from Nothing, All. All, Nothing. Nothing, All. Is that structures. Yes, in the back? >> Student: Chiasmus? >> Teacher: That's right. It's chiasmus, which is what? >> Student: [Inaudible]. [Inaudible] AD/DA. >> Teacher: Right. So it's a structure of. It's not parallel, it's crossing which comes from the Greek word, the Greek letter Chi which is the X, right? So there's the AB/BA. Typically we would say you use chiastic structures in order to create a sense of boundedness. It tightens up the line. It makes it seem constrained, in part because you usually are repeating words as well. So there's something the middle that's being framed by something on the outside, is another way to think about it. So here, All is framing Nothing. Or at the heart of All is Nothing. So in a sense this is paradox maybe, or even almost oxymoron, right? All on Nothing set lets Nothing fall. So I guess what I want to ask you, are these all the same Nothing's? Do they change at all? >> Student: It seems they are multifaceted [inaudible]. >> Teacher: Okay. >> Student: It's never, Nothing ever ceases to. >> Teacher: Nothing ever stays? >> Student: Quoting the word Nothing. But that's like the meaning of Nothing ever ceases. >> Teacher: Show me. Can you pick up a couple of instances where the meaning of Nothing seems to change? >> Student: Well, that line where All from Nothing fet, from Nothing, All. And then, Gave All to nothing Man, when Man is capitalized. >> Teacher: Okay. >> Student: Man has Nothing because he can't combine, like he. It's very, it's like it puts Man on a lower scale than God. >> Teacher: So Nothing Man, what part of speech is Nothing then in that? Let's move from a noun to an adjective, right? >> Student: Yes. >> Teacher: Becomes a thing that modifies Man. So we've been talking about the mystery of Creation, the beginning was Word and the Word was God. Then so maybe it was Nothing, All comes out of Nothing? Right? From Nothing All is made, and that seems paradoxical. But again we're. We don't. These are the only words we have. We've got to repeat them because we really don't have better words to talk about this. Have All therefore on Nothing set. Now is it starting to change? Lets Nothing fall? Is that a different Nothing, the one that's not being allowed to fall, than the Nothing on which everything is set? But then it certainly does change. Gave All to Nothing Man. In that sense, it's the idea that man is nothing. I mean man not only comes from nothing, but compared to God man doesn't rate. He doesn't get to be super-humble for really basically nothing. Gave all to nothing man indeed whereby. Nothing Man is repeated. >> Student: But without the capital. >> Teacher: Without the capital, so you'd have to want to interpret that. Maybe Nothing Man is supposed to be a title. Or maybe nothing man, is the lack of capitalization might be a way of delineation that there's now going to be a break. That Nothing Man is not to be taken as a unified phrase. But in fact, nothing now becomes not an adjective, but it is now a noun, object of proposition. Through nothing man where. Gave All to nothing Man indeed, whereby through nothing man all might him Glorify. Now what does that mean? There's nothing we can do to glorify him? Or through the nothing which is everything, that's how we glorify him? In Nothing then embosst the brightest Gem more pretious than all pretiousness in them. And the brightest Gem is what? It's the soul, right? I mean it's the divine light that's in everybody, but it's surrounded by nothingness because. >> Student: I think first the nothing that [inaudible]. [Inaudible] is like [inaudible] Ball is related to [inaudible]. [Inaudible] nothing Ball. And then it's really through nothing man all might him Glorify, it's a scene. It feels like the same Nothing. It's the everything that happens, that is that belongs. >> Teacher: Right. >> Student: It's the [inaudible]. >> Teacher: Yes, I think you're right about that. But overall when you read it, so you get the point, right? I mean we all, it's that he's retelling a familiar story. That man is created out of dust, I am this crumb of dust is another way that he puts it in another poem, right? God creates everything out of nothing, in a way you return to nothing. Therefore, God is [inaudible]. But he's getting at the paradoxical nature, and he's doing it by repeating these words over and over, setting them into different syntactical relations with one another. And then somehow by doing that, it's the relationality amongst the words that he can actually make them mean more than they can actually mean. That's what I mean by straining against the limitations of language. He's using these words in such a. He's using. That's why you do literary devices, figurative language. That's why you would make use of oxymoron and chiasmus and these kinds of things. Why? To get somehow the form in which the words are set, to make the words do more heavy lifting than they're able to do just simply by themselves. Does that make sense? All right, so that's part of what poets are up to. Trying to make meaning beyond literal meaning, and that's part of what his problem is here. And I think that it sheds interesting light on some of the things that we see in Jonathan Edwards. So let's turn to Edwards now, and see. Take a look at some well-known passages in the personal narrative. Take a look maybe on page 387, and we'll start with this, then come back it a little bit later. [ Silence ] The middle of the page. From my childhood up, my mind had been want to be full of objections against the doctrine of God's sovereignty, in choosing whom He would to eternal life. And rejecting whom He pleased. Leaving them eternally to perish, and be everlastingly tormented in hell. And so he's talking about the idea of total depravity. Let me give you a picture of Edwards up there. Now again, the idea of total depravity doesn't seem to bother Taylor. It becomes an opportunity for poem-making. It becomes an opportunity for him to celebrate God's grander and also his own poetic art and trying to do something to capture that. He isn't full of objections to it in the same way. Edwards is a more [inaudible]. It used to appear like a horrible doctrine to me. But I remember the time very well when I seemed to be convinced, and fully satisfied, as to this sovereignty of God. And His justice in thus eternally disposing of men, according to His sovereign pleasure. But never could give an account how, or by what means, I was thus convinced. Right? So immediately a language problem, and a problem with thought. How do we give an account of this? He suddenly is convinced that if you're suddenly convinced by fate, or you have a revelation, how do you actually put the revelation into words? This is the kind of thing that my, you know, my son who's in fourth grade constantly hates when he's doing, say, math problems. Because he knows, he just sees the answer. Then they say but show your work. That's, the showing of work seems to be hard. How do you get at that intuitive process? That's part of the problem that Edwards gives, tries to give here. It's a problem of translation, a problem of translating the divine into the human into language, right? But never could give an account how, or by what means, I was thus convinced. Not in the least imagining at the time, nor a long time after, that there was any extraordinary influence of God's Spirit in it. But only that now I saw further, and my reason apprehended the justice and reasonableness of it. However, my mind rested in it, and it put an end to all those cavils and objections. And there has been a wonderful alteration in my mind, in respect to the doctrine of God's sovereignty, from that day to this. So that I scarce ever have found so much as the rising of an objection against God's sovereignty, in the most absolute sense, in showing mercy on whom he will show mercy, and hardening and eternally damning whom he will. Just listen to the repetition of the language. God's absolute sovereignty and justice, with respect to salvation and damnation, is what my mind seems to rest assured of, as much as of any thing that I see with my eyes. At least it is so at times. But I have often, since that first conviction, had quite another kind of sense of God's sovereignty than I had then. I have often since had not only a conviction, but a delightful conviction. The doctrine of sovereignty has very often appeared an exceeding pleasant, bright, and sweet doctrine to me. And absolute sovereignty is what I love to ascribe to God. But my first conviction was not with this. Now it's a form of writing, please don't do this, will you. I mean it's kind of wordy. It seems to sidle around its subject. And its punchline, the doctrine of God's sovereignty has very often appeared an exceeding pleasant, bright, and sweet doctrine. Is that descriptive? What does that mean? A sweet doctrine? Part of that, then we'll come back to the idea of sweetness. But part of what he's trying to do is use words that we kind of know and think we know the meaning of. And try to get at something that we don't know the meaning of. And it gets even more repetitious than this. I just wanted to give you a quick sense of his problem is a version of Taylor's problem. How do we make words signify more than they can signify? I should probably tell you a little about Edwards. Edwards is someone who was called to the pulpit about 50 years after Taylor's life, right? So we're talking early 18th Century now, 1726. He's born in 1703 at the beginning of the new century, the 18th Century. He goes to Yale College at the age of 13 in 1716, and Yale at that time is a school for ministers, right? So he's precocious, he's very smart, and he's destined to be a kind of Calvinist minister. But the thing about him was it seemed that the most decisive part of his intellectual development occurred not in the classroom. I mean he was already convinced he was a Calvinist. It's kind of what like I tell students when they're thinking about should I minor in this, or what courses should I take? I say take something out of your normal intellectual box that might have the opportunity to change your life. For me it was I always knew I was going to be an English major, so no specific English course particularly changed my life. But that Art History course that I took as a pure elective senior year completely changed the way I think about, thought about many things. Reorganized the way I spent my next year. Exploration, that's what Edwards did. He started reading in the library. The college had a business agent unfortunately named Jeremiah Dummer. But actually Dummer's hope was to try to make the undergraduates smarter. He was sending books from England, and sort of the latest books. And among those books were books by John Locke. And so Edwards read Locke, particularly the thing that I put up an excerpt front yesterday concerning human understanding. And one of Edwards' disciples, Samuel Taylor, Samuel Hawkins, later said he compared in an interesting metaphor. He said Edwards got more satisfaction out of reading John Locke than the most greedy miser gets in gathering up handfuls of silver and gold from some new discovered treasure, right? So he compares Edwards to a miser who's just kind of. I mean again, it's a very vivid and not entirely positive image. And that gives you a clue to the kind of teaching that Edwards did later on. And I gave you this excerpt from the, from Locke to look at. Because I wanted you to get a sense of what it meant to be an empirical thinker, right? So Locke is a materialist thinker. He looks at the world and from that he wants to deduce principles. He isn't an idealist thinker who decides that there are principles first. So you would. You would make a contrast between Locke and someone like Kant, right, who's trying to think about principles that exist from before, a priori as it were. Category, later it's called, you know, the categorical imperatives. What are the first principles? And then we think about how the world reflects those things. Locke is interested in looking around. He's interested in observing, experimenting. And his rationale is this. He believes that human beings are divine. I think I mentioned this when we started talking about the Enlightenment. But he believes that revelation is not necessarily the most reliable or the most frequent mode of obtaining knowledge. If you get it, great. Don't question it. If you get a revelation from God, it's the real. It's the good stuff. Otherwise, we have to do what, we have to use what God gave us. And if God gave us our minds and God gave reason, then those are divine too and we should use them. And we're doing God's work by using them. So he was able to square his belief in God with this idea that you could also be an empirical thinker. Obviously it means you have to give something up, and what you give up is the idea of the total depravity of humankind, and the debased nature of the world. The world has not all become tainted. Human beings have not all become tainted as a result of the fall. And so he feels licensed to be able to use the world to understand larger, many principles. And perhaps even to think about God Himself, so that's a big shift. And you might say it's the newest idea. It's a new, it's a revolution in intellectual technology. It's what's emergent in this period. And Edwards is trying to figure out a way to have it make sense in terms of his own religious beliefs, right? So one of the things to say about Edwards, you know, he gets this and he reads in this book collection. He comes from a tradition of ministers who are already more liberal. Samuel Stoddard is a preach, a minister who has a large congregation in Western Massachusetts who's pushing the limits of the old-time Puritan religion. I mean pushing it so far that he is almost on the verge of saying that the sacraments have a certain kind of efficacy. That they can bring about bring safe. He never really says that, but he's trying to reconcile what, in early periods we've talked about, the contradiction or the lack of fit between justification, right? Being saved. And sanctification, all the holy and moral and yet worldly things that you do. He's more a liberal version of that in his preaching. It becomes, even if you look. I'm told that if you listen to Stoddard you would almost think that, in contemporary terms, you were watching some kind of Baptist minister, right? He's very active trying to save, almost as if the minister could be an agent of being saved. But if you, but when push comes to shove, no. But still, pushing the boundaries of that. Again, another one of these contradictions within Puritanism. Edwards recoils from that a little bit coming, you know, I'm sure, you know. Sometimes people who have very liberal parents themselves become a little bit more conservative. Edwards want to pursue a slightly more conservative vision of Puritanism or of Calvinism. But he reads these books. He reads about Locke. He reads, you know, the idea of, about empiricism. And he believes, you know, he becomes very persuaded by this idea of the mind, as what Locke calls a tabula rasa, a blank slate that's being writing on. Now people who believe in revelations say yes, you know, human beings are blank slates. A soul is blank and God writes on it, the Bible writes on it. That's what gets written on it. And the other writing is not the kind of writing you want. Locke doesn't believe that. Locke believes that what writes on the blankness that is the mind or the soul is experience, the experience that we have in living our daily lives. And that gets written on it. And what we use then is that divine faculty that's called reason to interpret it, what we've experienced. So that means sensory data is reliable. Or as far as it goes, it's not completely unreliable. We need to know how to think about it. But he wants to. I mean how else do we experience the world? Through the senses that God gave us, so we use that. We make use of it. And we use the reason to do that as well. That's what Edwards is trying to have make sense to him. How do you reconcile the old-time Calvinism which is based on those principles. TULIP. Total depravity. Unconditional election. Limited atonement. Irresistible grace. The Perseverance of saints. How do you get all that squared with this new Enlightenment intellectual technology, right? This is what Locke says. The first capacity of human intellect is that the mind is fitted to receive the impressions made on it. Either through the senses by outward objects, or by its own operations when it reflects on them. You might say that the senses and then reason. This is a first step a man makes towards the discovery of anything. And the groundwork we're on to build all those notions which he ever, whichever he shall have naturally in this world. Right? So this is a really. It's a different way of thinking about it. It's not necessarily incompatible with belief in the divine. But it does require you to give up certain things. How is Edwards going to harness this stuff? He can see the threat. This might undo it all, and in fact probably you would say it does at some point. But what he is attempting to do, as a representative of what is a dominant consensus in New England, trying to stave off the challenges that this emerging technology of thinking is posing. How do we make use of it, but retrofit it into the way that he wants us to think about things? And the way that he does that, you might say, is to open up his preaching a little bit too, as Taylor starts to do. And as I think you can see in the personal narrative, he starts to decide that okay, if we are still going to believe in all these things, nevertheless we're going to allow ourselves some license to look at the world and use that, the world in some sense, as a set of exemplar, right? A set of ways of thinking about God that are drawn from the world. And even drawn from not just nature although, you know, the use of nature is somewhat unprecedented. Think about Winthrop. Winthrop would never talk about nature as his example of how to think about God. Think about what nature was for Bradford. What was nature? A howling wilderness, right? Terrible. It's all, you know, nature if the Devil's province. It's here to threaten us and all this kind of stuff. We need to get beyond nature, conquer nature in order to realize God's providence. We need to transform the howling wilderness now into this garden which it doesn't start out being. Edwards has a really different way of thinking about it. And that idea of delight and sweetness and all that stuff is part of it, right? Let's take a look at another moment here in the personal narrative. Take a look at page 390. [ Silence ] This is at the bottom of the page. Holiness, as I then wrote down some of my contemplations on it, appeared to me to be of a sweet, pleasant, charming, serene, calm nature. Again, you know, when you write you probably not overuse adjectives in that way, especially not ones that seems like synonyms from one another. People often read this stuff and say it almost sounds like it's Hemingway. I mean, right? That he's anticipating some kind of weird stripped-down Modernist writing in which we're just going to, you know, we're going to get down to basics. Get the sense of causality out of it, right? Hemingway is known for what's called his paratactic style. You just lay things side-by-side without any kind of causation. The opposite hypotactic. Let's see. Because I go to NYU I will get a very good job. To do it the other way would be, I go to NYU and I will get a very good job, and there's no necessarily causal relation. This is, by the way, none of this is very true in any of that either. But one can, we hope. No. That's not a good thing to say. So that's. So he mentioned that Edwards is trying to wrestle between that. He can't get at the idea of causes so much, or a cause is always attributed to God. So he's going to lay things out. And there's almost a sense that by putting these words, that we think we know what they mean, next to one another, we start to make them mean something other than what we think we already know. Holiness, as I then wrote down some of my contemplations on it, appeared to me to be of a sweet, pleasant, charming, serene, calm nature. It seemed to me it brought an expressible purity, right? A purity that I can't actually express, although I'm trying. Brightness, peacefulness, and ravishment to the soul. And that it made the soul like, and here is the metaphor, like a field or garden of God with all manner of pleasant flowers. So the idea of the garden is kind of an almost dead Puritan metaphor. Like Taylor a little bit, he's going to try to revivify it by being detailed about it. All pleasant, delightful, and undisturbed. Enjoying a sweet calm and gently vivifying the beams of the sun. Now I want you to look at this metaphor here because I think it's very important. And I think it's, you know, a way of understanding what Edwards is up to. The soul is of a true Christian as I then wrote in my meditations, appeared like such a little white flower as we see in the spring of the year. Low and humble on the ground, opening its bosom to receive the pleasant beams of the sun's glory. Rejoicing, as it were, in a calm rapture, diffusing around a sweet fragrance. Standing peacefully and lovingly in the midst of other flowers round about. All in like manner opening their bosoms, to drink in the light of the sun. I think that's a kind of extraordinary passage. What would we say about it? What do you notice about it right away compared to other Puritan rhetoric or just other things that we've been looking at lately? What's Edwards up to there? [ Silence ] The soul of a true Christian is like what? [ Silence ] Like a flower. Okay. So automatically that's kind of nature. Not the soul of a true Christian is like Job, it's drawn from nature. We're taking the garden metaphor and making it come alive a little bit more by being very specific about it. But picture in your head what he says. If you need to, close your eyes. The soul of a true Christian appeared like such a little white flower as we see in the spring of the years. Low and humble on the ground, opening its bosom to receive the pleasant beams of the sun's glory, rejoicing as it were in a calm rapture. Yes? >> Student: The flower opened its bosom? >> Teacher: Opened its bosom. >> Student: So it's like. >> Teacher: And what's it receiving? >> Student: Well, it's receiving the sunlight. But maybe the importance is placed on the action of the flower opening up. >> Teacher: Opening up, right. >> Student: [Inaudible]. >> Teacher: So again this is a simile, so it's kind of. It's almost like an allegory. It's, we're meant to understand that it's the soul of a true Christian but it's figured as a flower. In the back, did you want to add something? >> Student: Yes. It's almost as if [inaudible] relationship to God. >> Teacher: Certainly. We've been, and that's. That would be in keeping with it. I mean we need to open ourselves up and receive what the flower receives, which is sunlight and therefore nourishment. What it needs to live. Yes? >> Student: Opening of the [inaudible] kind of like, you know, like the saving, like the [inaudible]. >> Teacher: Sure. Right. Maybe isn't this the moment of what he's trying to get at, is the moment of conversation, of grace. You receive grace it's kind of like getting sunlight. Yes? >> Student: Well, [inaudible] think of the flower I thought of blooming in church. >> Teacher: Okay. >> Student: Okay, [inaudible]. >> Teacher: That's right, if you're following the metaphor for it's we're part of the earth. But we can't live only on the earth. We need something that comes from the heavens to make us complete. But literally what is this a process of? >> Student: [Inaudible]. >> Teacher: Well, that would be more literal than Edwards would be able to be. But yes. So many a little less literal, but more literal than this. >> Student: With spring maybe? >> Teacher: Okay, sure. The spring. Light. >> Student: [Inaudible]. >> Teacher: Yes? It is literally a process of Enlightenment. I mean, right? I mean he is. In other words, this idea of light, light, light everywhere. We saw it already when we talked about some of the rhetoric of the Enlightenment, right? The light of this, the light of [inaudible], Henry's all about light. Light was a kind of abiding metaphor. That's why they called it the Enlightenment. He's drawing on it too. But for him you see how he wants to say it's not the spread of knowledge, content, you know. You've got a spread of knowledge, you've got to dare to be wise. No, this is the opposite of that. Don't dare to be. Open yourself up. Passively receive. But what you're receiving is literally Enlightenment, right? Take a. Let's take a look at another place so that you can see how he does this is in a slightly different vane. This is in the Divine and Supernatural Light. It's on page 409. He does another version of the same idea which, you know, ordinarily I would use this to prefigure the defense of Fort McHenry. But you can see that. You can see it the other way around now. The bottom of 409. He's talking about this Divine and Supernatural Light, right? So the whole thing is about light. It not only removes the hindrances of reason, but positively helps reason. It makes even the speculative notions the more lively. That's kind of a bonus added benefit. I mean that can't be our real point. But look, you can see how he's trying to talk about some of the same things that someone like Locke would talk about. But talk about them in these religious terms. It engages the attention of the mind, with the fixedness and intenseness to that kind of objects. Which causes it to have a clearer view of them, and enables it more clearly to see their mutual relations, and occasions it to take more notice of them. The ideas themselves that otherwise are dim and obscure, are by this means impressed with the greater strength, and have a light cast upon them. So that the mind can better judge of them. As he that beholds the objects on the face of the earth, when the light of the sun is cast upon them is under greater advantage to discern them in their true forms and mutual relations, than he that sees them in a dim twilight. That's the difference, right? When you have received the Divine and Supernatural Light, you emerge, right? You no longer see as if through a glass darkly. You see everything clearly. Suddenly the world moves from black and white to Technicolor, right? It's just a completely different. Or, you know, the metaphor that he uses is another one that has to do with light. It's the same question that Key is asking, you know. Is the rocket's red glare our own flashes? In the morning we see the full light. When you are a saved person, you move from living in the twilight all the time to living in the clarity of sunlight. So it's the same metaphor used in a slightly different way. Let me show you one that's a little bit different. And this will also show you a further opening up, right? Especially when we remember of the Puritans' hostility to the theater. Puritans don't the theater in all the forms. They don't, there are many things they don't like about it. Not only its subject matter, but the fact that it's kind of, they think it's sort of like. It involves impersonation and fixation on personality. They just don't like the theater. But on top of 408, all of a sudden the theater becomes our legitimate metaphor for Edwards. This is section 4 at the top of 408. It is not every affecting view that men have of religious things that is this spiritual and divine light. So one of the things he's invested in is using reason. He's not going to deny that reason is a good thing, but he wants to put reason in its place. Reason is only a starting point for Edwards. Whereas the development of the reason is partly, almost the whole ballgame for Locke. For him it's going to be the starting point. It's necessary but not sufficient. You need that extra thing, and that extra thing is fate. And once you have that, then there's grace. Men by mere principles of nature are capable of being affected with things that have a special relation to religion as well as other things. A person by mere nature, for instance, may be liable to be affected with the story of Jesus Christ, and the sufferings he underwent, as well as by any other tragical story. Right? So it isn't enough just to think of Christ as a kind of tragic hero. You have to understand the absolute unique nature of the story of Christ beyond any other kind of template into which it might be fit. He may be the more. Then he's, look at the process of reasoning that he's using here to get the point across. He may be the more affected with it from the interest he conceives mankind to have in it. A lot of people, this matters to a lot of people. I ought to be interested in it. Yea, he may be affected with it without believing it, as well as a man may be affected with what he reads in a romance, or sees acted in a stage play. Right? So a stage play is still going to be something that is false. It's not sufficient. And yet, the idea. It's not completely denigrated here. It is used as a legitimate example as a way of talking about something that he's approving of. That you're affected by the story of Christ, but it's not enough to be affected in that way. That's a real different I think from a lot of the kind of Puritan rhetoric that has gone before Edwards. And again, let me just stress he is a very, very late modern Puritan, okay. The heyday of Puritanism is the, you know, 17th Century. All the people, you know, the Puritans who come in 1620 are already having problems by the '50s and '60s. The Jeremiah period is the 1667 or so. So that's a lot later when he lived. And there's in which what we might be seeing here is either the last gasp of the Puritanism, or with the Great Awakening, which I'll talk about in just a second. That kind of final reassertion of Puritan principles before they finally yield to the Enlightenment. So there's a sense of inevitability that Edwards has, and he's tried to push it off. He's tried to push that off a little bit. Now one of the things that happens here is that there is a period of awakening that occurs. And it occurs partly in his pulpit. Edwards apparently wasn't the most vivid speaker. He used very vivid language but he was kind of, apparently kind of dull and spoke in a monotone. So it took people a while to get what he was talking about. But when they did, it sparked this period of rivals. Now there are different ways to date the Great Awakening. I think that Norton does it this way so it gives it a kind of wider period. Other people do it this way, just really think about the Great Awakening period as very, as ending when Edwards himself is removed from the pulpit. But take a look on page 417 here. At the letter to the Reverend Dr. Benjamin Coleman which tells us a little bit about what the Great Awakening was like. Right? So this is 1735, right after you might say this period. So this is, for me this is my preferred dating of it. He explains it over the course of the last few years he's noticed that the town has gradually been reforming their contentious disposition has quieted down. Young people have left off, they're frolicking. Everybody is a little bit more serious about things. Let's take a look on 418 in the middle. There began to be a remarkable religious concern among some farm houses at a place called Pascommuck, five or six that I hoped were savingly wrought upon there. And in April, 1734, there was a very sudden and awful death of a young man in town in the very bloom of his youth, who was violently seized with a pleurisy and taken immediately out of his head, and died in two days. Which much affected many young people in the town. This was followed with another death of a young married woman, who was in great distress in the beginning of her illness, but was hopefully converted before her death so that she died full of comfort. And in a most earnest and moving manner warning and counseling others, which I believe much contributed to the solemnizing of the spirits of the young people in the town. Right? Again the sense of affliction, but there can be benefits from it. In the fall of the year I moved to the young people that they should set up religious meetings, on evenings after lectures, which they complied with. This was followed with the death of an elderly person in the town, which was attended with very unusual circumstances, which much affected many people. About that time began the great noise that there was in this part of the country about Arminianism, which seemed strangely to be overruled for the promoting of religion. People seemed to be put by it upon inquiring, with concern and engagedness of mind, what was the way of salvation, and what were the terms of our acceptance with God. And what was said publicly on that occasion, however found fault with by many elsewhere, and ridiculed by some, was most evidently attended with a very remarkable blessing of heaven. And if you map this onto what we've just been looking at, you can say that this is reason gearing up. People are interested in the kind of intellectual questions that have to do with Arminianism. And then things start in earnest at the beginning of 1735. So a few lines down on 419. All seemed to be seized with a deep concern about their eternal salvation. All the talk in all companies, and upon occasions was upon the things of religion, and no other talk was anywhere relished. Scarcely a person in the whole town was left unconcerned about the great things of the eternal world. Those that were wont to be the vainest and loosest persons in town seemed in general to be seized with strong convictions. And again, this is something that goes beyond reason. It's almost like a kind of weird viral thing, it's sort of contagious. Those that were most disposed to contemn vital and experimental religion, and those that had the greatest conceit of their own reason, the highest families in the town, and the oldest persons in the town, and many little children were affected remarkably. No one family that I know of, and scarcely a person, has been exempt. And the Spirit of God went on in his saving influences to the appearance of all human reason and charity, in a truly wonderful and astonishing manner. The news of it filled the neighboring towns with talk, and there were many in them that scoffed and made a ridicule of the religion that appeared in Northampton. Right? Immediately you can see that we're at a moment where religion is ebbing in its influences. It's this kind of notion of Revivalism can be ridiculed. It means that there's a sense at which we are at the end of the dominance of Puritan thinking in the Northeast. Take a look on page 421, and again you'll hear some of the same language that he's talked about. This is the end of the full paragraph that [inaudible] the page. I never saw the Christian spirit in love to enemies so exemplified in all my life as I have seen it within this half year. They commonly express a great concern for others' salvation. Some say that they think they are far more concerned for others' conversion, after they themselves have been converted, than ever they were for their own. Several have thought, though perhaps they might be deceived in it, that they could freely die for the salvation of any soul, of the meanest of mankind, of any Indian in the woods. And you wonder what it is that makes them think that they couldn't possibly go that far. This town never was so full of love, nor so full of joy, nor so full of distress as it has lately been. Some people, some persons have had those longing desires after Jesus Christ, that have been to that degree as to take away their strength, and very much to weaken them and make them faint. Right? I mean this is what we call enthusiasm. In a certain moment directed a certain way, it results in the Salem Witch Trials. Directed a different way it's this period of Revivalism. Notice, and then it says, Many have been even overcome with a sense of the dying love of Christ, so that the home of the body has been ready to fail under it. There was once three pious young persons in this town talking together of the dying love of Christ, till they all fainted away. Though 'tis probable the fainting of the two latter was much promoted by the fainting of the first. That's a joke. Edwards is making a joke in the middle of his sermon, right? Anybody ever see a film called The Goonies? >> Students: Yes. >> Teacher: Remember the balconies like. It talked about vomiting, that they're vomiting and then everyone's vomiting. It's kind of like that kind of. I can't believe you've seen that movie. Okay. Did it just come out on Blu-ray or something? Anyway, never mind. >> Students: [Inaudible]. >> Teacher: What? The Goonies is a classic. Okay. Who directed The Goonies? >> Student: [Inaudible]. >> Teacher: No, no, no. He sponsored but it wasn't Chris Columbus, was it? >> Student: Yeah, it was. >> Teacher: Was it? >> Student: It was Richard Donner. >> Teacher: Richard Donner, yes! It was Richard Donner. Excellent. Good, excellent. Actually that bears rewatching I think. Should, I think [inaudible] yes, okay. >> Student: [Inaudible]. >> Teacher: Anyway, if you think about it then, think about fainting instead of vomiting, that gives you the idea here. It's contagious. It's fact if you do it because other people are doing it. Now there's a downside to all of this, right? If everybody's having conversions around you, you really want them too. What if you don't get it? That's not so good. What if you feel like you converted, you faint away, you find [inaudible] dying over Christ? That's all good. The next day you wake up and you really want to have a drink or you really want to fornicate. You want to do whatever it is you want to do. Huh! Sinful impulses, you've perjured yourself. Oh, my gosh! Right? So this actually happens. Take a look at the postscript to the letter. This is in June of 1735. Since I wrote the foregoing letter, there has happened a thing of a very awful nature in the town. My Uncle Hawley, the last Sabbath-day morning, June 1, laid violent hands on himself, and put end to his life by cutting his own throat. He had been for a considerable time greatly concerned about the condition of his soul. Till by the ordering of a sovereign providence he was suffered to fall into deep melancholy, a distemper that the family are very prone to. He was much overpowered by it. The devil took the advantage and drove him into despairing thoughts. He was kept very much awake anights, so that he had but very little sleep for two months, till he seemed not to have his faculties in his own power. He was in a great measure past a capacity of receiving advice, or being reasoned with. The coroner's inquest judged him delirious. Satan seems to be in a great rage at this extraordinary breaking forth of the work of God. And it was not only despair, you know, that this. The flipside of enthusiasm, right, is a sense of despair. And even worse when you feel like you've gotten the true calling, and then you find yourself to have simple feelings at the same time. One of the things that we might say about Edwards' personal narrative, is he seems to understand conversion as a process that takes a little bit of time. If you actually go read it, there seems to be a couple of times in which he has had these kind of breakthroughs. So the revival ebbs with the suicide of Hawley. And it kicks up again very shortly afterwards when this guy, George Whitfield, an itinerant preacher from England, comes to the East Coast of the United States. This is about 1739. And this guy is like a rock star. I mean literally. He draws incredible crowds. He goes from parish to parish, and people come up. And he's extremely vivid in the way that he speaks. And he speaks in a way that's designed to pull on the emotions. He talks about hell fire and damnation, right? And that same kind of rhetoric that we saw in Wigglesworth, Whitfield uses. Up and down the East Coast he goes, you know, to various parishes. You can imagine that the ministers who are residents in these towns have a kind of mixed feeling about here's this kind of guy coming in and stirring up our flock. Or, you know, what authority does he have? What are we supposed to do about it? But there's, it becomes a force that is too much to be reckoned with. Edwards himself succumbs to this in probably what is ironically his most famous sermon. Now I've tried to suggest to you that Edwards is like Taylor thinking about, you know. The light and sweetness and the personal narrative is all about that experience of Enlightenment, Divine and Supernatural Light is, you know. There's a, I haven't shown it to you but you can look at it. There's a crucial moment in Divine and Supernatural Light where he talks about sweetness, right? And he says, you can understand you can have a rational understanding of grace without having experiences. Just like you can know that sugar is sweet because people have told you without ever actually tasting it. But once you've tasted honey, then you know in a radically different way than you did just by hearing about it. You understand sweetness in a way that you couldn't possibly have before you tasted anything that was sweet. And so that's what he stresses. That's the mental thing he does, and that's the way he stresses. But this one is different. Sinners in the hands of an angry God, on page 425, which takes its text from Deuteronomy 32-35. Their foot shall slide in due time. Shows all of the influence of the Great Awakening, and gives you a sense of what the Great Awakening must have been like. Take a look on 426 and then I'll read out to you a passage just so that you get it right. The middle of 426 after section 4 he says this. The observation, so this is the part that would be, you know, there's the [inaudible] that's starting to be the doctrine. The observation from the words that I would now insist upon is this. There is nothing that keeps wicked men at any one moment out of hell but the mere pleasure of God. By the mere pleasure of God I mean his sovereign pleasure, his arbitrary will restrained by no obligation. Hindered by no manner of difficulty any more than if nothing else but God's mere will had in the least degree, or in any respect whatsoever, any hand in the preservation of wicked men one moment. And then he goes on, right. The reasons and proposition section is long and takes a long time. And it's what people remember about this. I'll read you in the Application, let me read you one of my favorite bits. This is on page 431. [ Flipping pages ] The God that holds you over the pit of hell, much as one holds a spider, or some loathsome insect, over the fire, abhors you, and is dreadfully provoked. His wrath towards you burns like fire. He looks upon you as worthy of nothing else, but to be cast into the fire. He is of purer eyes than to bear to have you in his sight. You are ten thousand times more abominable in his eyes, than the most hateful venomous serpent is in ours. You have offended him infinitely more than ever a stubborn rebel did his prince. And yet it is nothing but his hand that holds you from falling into the fire every moment. It is to be ascribed to nothing else, that you did not go to hell the last night. That you was suffered to awake again in this world after you closed your eyes to sleep. And there is no other reason to be given why you have not dropped into hell since you arose in the morning, but that God's hand has held you up. There is no other reason to be given why you have not gone to hell, since you have sat here in this lecture hall, provoking his pure eyes by your sinful wicked manner of attending his solemn worship. Yea, there is nothing else that is to be given as a reason why you do not this very moment drop down into hell. O sinner! Consider the fearful danger you are in. It is a great furnace of wrath, a wide and bottomless pit full of the fire of wrath that you are held over in the hand of that God, whose wrath is provoked and incensed as much against you, as against many of the damned in hell. You hang by a slender thread with the flames of divine wrath flashing about it, and ready every moment to singe it and burn it asunder. And you have no interest in any Mediator, and nothing to lay hold of to save yourself, nothing to keep off the flames of wrath, nothing of your own, nothing that you ever have done, nothing that you can do, to induce God to spare you one moment. And consider here more particularly. And he goes on and on and on, right? That is the imagery of hell fire and damnation. That is a complete commitment to total depravity, unconditional election, right? The power of God. Edwards pulls back away from this. I mean I want you to see. I want you to really think of this as uncharacteristic. And to give you a sense of the power of the Great Awakening. It becomes a kind of, I don't know how you would want to put it in terms of dominant, residual and emergent, right? It probably shows you the power of the residual. Even if some places you could make fun of Revivalism, there were other people who were wanting to be revived as it were. And I think it's important to put Edwards in his context. So one of the things to say about Edwards, is that he is the last great Puritan thinker, right? But he's also clearly a man of the Enlightenment. He is almost, and we'll talk about this in about 20-some odd minutes. He is almost exactly contemporary with Benjamin Franklin, right? Edwards was born in 1703, Franklin was born in 1706. We tend to think of Edwards as a Puritan. We tend to think of Franklin as a man of the Enlightenment. I want you to both see that they are recognizing the changes afoot intellectually. And they are making their peace with that change and attempting to use that moment to change in different ways. They pick different solutions. Edwards tries to prop up the old-time religion, harnessing this new intellectual technology. Franklin wants to push the new intellectual technology while recognizing some of the residual power of the old. Yes? >> Student: So he wrote [inaudible] sermon after the other one? Or was. >> Teacher: Yes, there mostly. It's mostly, it's late. But then he goes back on when he writes his big treatises. After things don't go so well for him he is, he goes back to thinking about, you know, the idea that there's something sweet about the idea of divine [inaudible]. I mean the big philosophical treatises that Edwards writes are basically about how to understand the relationship between God's sovereignty and free will. And to try to philosophically make those things sense. His great treatises is called The Freedom of the Will. He has a kind of tragic life. I mean he gets, he has a. He runs afoul of people in his parish. Some of the well-to-do people are, their children are caught reading a birthing manual and he calls them out. And he basically gets kicked out. He goes to Western Massachusetts for a while. He ends up becoming the president of the College of New Jersey, it has a different name now. >> Student: You've seen it. >> Teacher: It's in Princeton. And he gets inoculated for smallpox, it's a thing to promote, and dies of it. So he dies sort of young. So Edwards has a kind of tragic career I suppose. One of the things to say though is that there's three ways in which I want you to think about him. So he's the last great Puritan. He's also a man of the Enlightenment. I mean that's the moment in which he's living. And insofar as he is in fact pushing the idea of Enlightenment towards thinking about nature and thinking about. I mean he's full of kind of natural. And thinking about beauty. There are other things that he has written that which are really about aesthetics more than anything else. I would say he is one of the first early American romantic thinkers, so he's a really important kind of cusp figure for us. He ties the early part of the course to the later part of the course. And I think we'll leave it there and you can take a break for a few minutes, and me too. And when we come back we will think again about the conjunction of these two, Jonathan Edwards and Benjamin Franklin. |
Open_Ed_Cyrus_Patell_American_Literature | MobyDick_V.txt | >> Couple of business items before we get started. Let's see, final exam is a week from Monday, a week from today, right? It's late. I'm sorry about that. I think it's what, 2:00? Does that sound right? Good. I will send out guidelines for the exams that you all will know what it is you're getting yourselves into, but it will in some sense mirror the style of the exam that we had for the midterm. It will be an opening section of names, definitions, terms, concepts. All of them will be drawn from "Moby Dick." There will be a second section that will be identifications, and then there-- but the point is not many identifications. It's few identifications on which you will be asked to write about the passages that are there, and there should not be any doubt about which authors are the authors of which-- identification is not going to be the big deal. It's more-- it's going to be very much what you write about it. And this goes for the second part and the third part, as well, which is these are the places where the exam is cumulative. You are not going to be held responsible for the stuff before the midterm in quite the same way that you were for the midterm. But each of the questions in parts two and three will ask you to compare the object that you are analyzing to another object that comes from earlier in the midterm-- earlier before the midterm. So for example, if you're looking at a passage by Stowe, what you'll be asked to do is comment on the-- sort of the techniques, the form, the style of the passage to say-- to talk about how the thematic or other content resonates with, or the larger piece from which this comes from Stowe's work generally, and then you're going to be asked to compare Stowe's handling of that idea or theme to its handling in the work of one author from before the midterm. And I mean for you to do a little bit more than say, well, like Stowe, Phyllis Wheatley was interested in Christianity. Need to have a little bit more. I mean, we need to understand that Stowe will help you to read this other author, and the other author will help you to read Stowe. You don't have to say that in that way, but we want you to be able to term the analytical screws a couple of notches of when you're doing-- when you're talking about the other author, right? So, for example, you might well say that-- if you're doing a piece on Stowe, and you wanted to compare her to Frederick Douglass, for example, you might say that Stowe is less-- Douglass is more concerned with Stowe to show that he belongs with certain kind of literary history, and therefore-- and you might even point out-- refer to one salient moment in the Douglass narrative that'll clinch all the points for you. The rhetoric of exemplarity that we've been using all term is going to have its payoff on the exam. In other words, what I want you to do is think in terms of exemplary moments. All right, so the last part of the exam will be an essay that's basically on "Moby Dick." You'll be asked to talk about "Moby Dick," and then in comparison to two other texts, one from after the midterm and one from before, around one central theme, and it will be a major idea within the course. I mean, you can just think about the things that we've talked about, and there shouldn't be any surprises. I'm more interested in seeing what you-- how you can synthesize things, how you can put things together. So part of the exam will be-- we want to see the breadth of your learning and understanding. You should not repeat arguments that you made in your papers, particularly, not in your final paper. And you should again think in terms of this exemplary way, so that if you are thinking about how the best way to study for this exam would be, I would suggest find a moment in each of the authors, especially after the midterm, but even before the midterms, find a moment that for you sums it up. The best moments-- you could refer to something interesting stylistically, and also something interesting systematically. These will serve as pegs for you to hang your analyses on, right? We don't want you to quote from the text. We don't expect a lot. What we do expect is that you will be able to speak with a certain amount of specificity of reference, right? So that if you are trying to build a case that, you know, Melville's treatment of nature is just as savage as Bradford's, you would want to point to that moment in Bradford's narrative where he pauses, and he brings in the Indians, and he refers to the barbarians, and all that stuff. You know, Brendan will be really impressed if you can-- and so will I, if you can point to that specific moment. You don't have to quote it even, just so that we know that you-- if you had the text with you, you could go to that place and do something interesting with it. In other words, the exam is a certain kind of shorthand. So I want you to think with the idea of exemplarity. Think, if you will, synecdocally [phonetic]. You're thinking about parts that have larger significance. All right, that principal should serve you well on your papers, but I think it also will serve you well on the exam. I will send out a set of instructions and guidelines. Make sure, please, that your email accounts are not over quota. I've had a number of message bouncing back. So I need to be able to get in touch with you between now and the exam, certainly, to send you this set of guidelines if nothing else, but also that timely reminder of when the exam is going to be. Okay. Last thing, I offer graduating seniors the opportunity to take an exam early on Thursday afternoon at 2:00. I need to hear from you so I know what kind of room to get. So I will extend the deadline. You can tell me up until 9:00 tonight by email. All right, after that, you're committed to taking the exam on Monday with everybody else if you're a graduating senior. Okay, any other business questions? Any other logistical questions? All right, when you get these guidelines and instructions, if you have any questions, email me back and ask, okay? I will-- if there are errors or things that need clarification, I will send them out to everybody. So don't hesitate to email me and ask. All right, now let's get started with things-- with the end of things. So I want to take us back on our last day together to our first day together. It's muggy, and warm, and humid out. On that day I believe it was, you know, cold and in the dead of winter. And I want to think a little bit about some of the stuff that we talked about on that day, because I suggested to you that we were in part going to frame the course with "Moby Dick" and with a certain set of ideas. And I want to revisit some of those ideas today and think about where-- what we think about them now having read all of these things together. So I started off by quoting from the President, his idea that we are a young nation. It's time to grow. The time, he says, has come to reaffirm our enduring spirit, to choose our better history, to carry forward that precious gift, that noble idea passed on from generation to generation, a God given promise that all are equal, all are free, all deserve to pursue their full measure of happiness. This is, you know, a statement of what we have taken to be a set of abiding ideals in the United States. One of the things that people said when they first started thinking about American literature as a serious field is that distinguished American literature from, say, British literature was commitment, primarily, to that set of ideas, to the idea of democracy, to the idea of equality, freedom, right? Ethel Matheson, when he wrote that big tome, American Renaissance, identified a kind of Democratic poetics as being at the heart of the canon of literature that he had a large hand in creating, a canon of literature that has come down to us as something like Emerson, Thoreau, Whitman, Hawthorne, and Melville as a kind of shorthand. And one of the things I think we've been investigating is the way in which, you might say-- is it the case that the writers that formed the mainstream of American tradition have found themselves engaged with this set of democratic ideas? Have they found them wanting? What does the literary tradition tell us, in other words, about both the power of these ideas and about our abilities, and perhaps our failures, to live up to them? We started, also, by suggesting the idea of cosmopolitanism, right, as something that, in fact, may not be a particularly American idea. There's been a suspicion throughout US intellectual history of the idea of cosmopolitanism. Remember, I told you it was the idea of individuals as citizens of the world owing their primary obligations not to their local organizations, or their hometown, or even their country, but to humanity as a whole, right? So it emerges as a kind of critique of nationalism, and one of the things we suggested is that perhaps, you know, the mainstream tradition of American literature as this course has constructed it, moving from settlement narrative from the puritans on down might well be hostile to this idea of cosmopolitanism defined now as not only in contradistinction to nationalism, but as-- and this is the way in which it was refined in the enlightenment by Emanuel Conn [phonetic], not only in contradistinction to nationalism, but really in contradistinction to something else that we might call universalism, right? So cosmopolitanism is all about the appreciation of difference. And if you look at some of the core texts in this course, you'll see that many of them actually are interested in engaging various forms of difference. Some of them are petrified of difference. Some of them want to stamp out difference. Some, like Emerson, are interested in certain kinds of differences, but are really interested, primarily, in something that we might call universalism, the way in which we're all alike, rather than the ways in which we're different. I wanted to suggest to you that some of the other writers, and I would count Melville among these, are more profoundly interested in the ways in which we are different and don't necessarily think that the ways in which we are different are simply incidental. In other words, maybe for Melville, the most important thing about us is not that we have a soul. Maybe that's an important thing, but another thing that might be important, exactly, our cultural context, our particular mental and physical characteristics. Maybe all of those qualities are not simply contingent. And I suggested to you that one of the current theorists of cosmopolitanism, Anthony Appiah, a philosopher over at Princeton, offers a very useful way of thinking about cosmopolitan theory has evolved now. It's interested in thinking about the interplay of universality and difference. He talks about a slogan form of cosmopolitanism would simply be universality plus difference, right? So in contemporary theory, cosmopolitanism emerges as a critique of nationalism. It starts to become a critique of universalism, in favor of difference. Difference, as I said to you at the time, is conceived not as a problem to be solved, but rather as an opportunity to be embraced. Appiah and others are starting to think that maybe we need a little of the universalism back, or that the universalism can never leave entirely. It's about bridge building, and we might think again of certain of the writers on our syllabus as engaging in what me might think of as the anticipation of a certain kind of cosmopolitan poetics, rather than simply democratic poetics, right? So cosmopolitanism, nationalism, universalism, these are all key terms for us, and I just want to-- remember, we linked them back to a set of things, right? Cosmopolitanism seemed to be linked to urban experience, and it was-- it seemed to be linked to what our President calls the idea of deliberative democracy, that somehow the fundamentally important thing about democracy is that it enables us to engage in conversations, productive conversations in which we deliberate. Another way to put it might be we are willing to engage in conversations in which we will put some of our crucial values up for grabs and be willing to consider an alternative, something that we hold dear. And I want to suggest to you that, in fact, this may be what great literature asks us to do, to engage in these kinds of thought experiments, to engage in conversations over time through the medium of a text with authors and characters, people who have other ways of being in the world than our own, so that literature might be said to be a space of conversation, and at its best, it gets us out of ourselves, gives us a kind of experience of otherness. I mean, think about that. When you read, if you have the time to read it with any kind of-- without, you know, the extreme haste a course like this demands, but when you read "Moby Dick" and let yourself, you know, let the text flow into you, you kind of get Ishmael in your head. It's a kind of weird thing to have in your head. It's almost like you lose track of your subjectivity and allow Ishmael-- or occupy Ishmael's subjectivity. To me, one of the brilliant thins about "Moby Dick" is that it seems to be aware of this process happening. I think that's part of what's at stake in the dramatization of Ishmael's loss of self in those chapters that follow the quarter deck and move into, finally, that chapter called "Moby Dick," in which he sort of reasserts himself. That same kind of loss of self that Ishmael the narrator experienced is something like, I think, our experience as readers in the face of powerful literature. There is a certain kind of loss of self, and then a recouping of self, and then we think back-- perhaps we recollected in tranquility, we think back to what it is we've experienced and measure our own experience against that. So this idea of urban experience that Tom Bender talks about. He suggested that one of the things about New York, the place where we live, and work, and study, and learn together is actually a kind of cosmopolitan space in contradistinction to the spaces of Massachusetts and Virginia, at least in the cultural imagination, right? So when I think about the ways in which Massachusetts and the puritan tradition are in some sense anti-cosmopolitan, and for Virginia, we don't do very much with Virginia in the course, but you can see that in so far as he identifies the idea of Virginia with Jeffersonians [phonetic], we have had a chance to look at some Jefferson, and we can see that there's a kind of funny interplay between sameness and difference in Jefferson's own writing, just the little bit of it that we have, right? There are certain kinds of difference for Jefferson that do not seem to be bridgeable, but he does-- even though he believes in freedom and equality, he also believes that Africans are different in some essential way and simply do not have the set of talents that Europeans do. So that's a kind of gulf of difference that Jefferson is unable to bridge. And one of the things I suggested at the outset is that maybe one of the reasons that "Moby Dick" begins in New York is to signal an affinity with this historic cosmopolitanism. You could begin the story someplace else, in New Bedford, in Nantucket, below decks of the Pequod itself, as the rather brilliant adaptation of "Moby Dick," in opera form that I was lucky enough to see on Friday in Dallas, does. It's [inaudible] transferred to the-- below decks of a quarter deck were there, and the quarter deck scene comes up right away. You know, the New York setting is lost. We might ask ourselves-- by the way, it's very powerful even without that, but we might ask ourselves what does it mean to begin in New York, right? And part of, I think, what it suggests is that this term-- another useful term from Apia of cosmopolitan contamination becomes something, you might say, that the New York opening does to the text. There's a sense in which New England, the place to which Ishmael goes, and then the ocean, the place that he ends up, are in some sense contaminated by the opening in New York. I wanted you to think about this as a kind of thought experiment. You might think of this as a kind of Hawthorne-like move, in which Hawthorne will put something out there and shift your attention away from it, but that's always going to be in the back of your mind. You know, it's not-- it's like-- reminds you of the virgin child, of course, only by opposite, but both things are in your mind. So to what extent, you might say, is there a kind of carry through of the New York cosmopolitanism into Melville's book. One last thing that I talked about on those opening days was the whole interplay of different kinds of culture, right? And we invoke the new [inaudible] theorist Raymond Williams talks about cultures as being the interplay of dominant residual and emergent forms. Dominant I think we understand. Residual means something that is from the past no longer dominant, most likely once dominant, still exerting a force in the present. And I gave you as an example-- here's his definition of that, but I gave you as an example this from Emerson. In all my lectures, I've taught one doctrine, namely, the infinitude of the private man. This, the people accept readily enough and allow commendation as long as I call the lecture art, or politics, or literature, or the household. But the moment I call it religion, they are shocked. That would be only the application of the same truth that they receive everywhere else to a new class of fact. This was on the first day of class, I think. I think we have-- we should have a firmer understanding now of what is at stake as we see the kind of long residue of Puritanism all the way through into the 19th century, into the pages of Melville's novel. This wouldn't surprise Melville at all, I don't think, the fact that you can't talk about religion in the same way. So Melville has to find a different way to talk about religion, and that's one of the things that I want to talk about today. You might say that the opposite of residual is emergent, a set of places where new practices are emerging, and I think that there's a certain way in which we can think of some of the literary practices that Melville is using as a forum of the promotion of certain emergent ideas, or certain emergent cultures. So again, culture is the interplay of dominant residual and emergent forms always. Culture is always dynamic. It's always changing. And in the course of our course, I think you can see that. At a certain point, Puritanism is dominant. Then there is an emergent set of ideas. We call it the enlightenment. They take over, and yet, Puritanism remains a powerful residue within enlightenment thought. Powerful figures like Edwards and Jefferson show that interplay of the old and the new that's at stake there, and we see the power of the residual even when, theoretically, enlightenment thinking has taken hold in the 19th century. So that's part of what I want us to be thinking again. One other concept that we had that I think is very important when we're thinking about Melville is this idea of the horizon of expectations, right? Remember we talked about where meaning resides. I asked if our text means anything if nobody reads it, like that tree in the woods, and one of the things we suggested is that maybe what we need to understand about meaning is that it's a cooperative venture. The author has a lot to do with the creation of meaning, but doesn't control it entirely, and not only because there are things within the author's unconscious that his or her control doesn't completely cover, also because readers are always bringing their own experience to the text. I don't only mean your life experience, or your biography, but even the set of reading practices that you have come to expect, the institution of literary culture that exists when you actually turn to a text, the history of a novel has gotten to a certain place by 1851. Melville's novel tries to insert itself into that history. Stowe's novel tries to do the same thing. It's the same, you might say, horizon of expectations, perhaps, the two authors are construing, yet slightly different from one another, but they're meeting the same horizon. How are they going to meet it? One way to think about that might be to go to the first definition of the idea of the great American novel, which comes from John William Deforest, I guess now considered a minor novelist. He wrote a pretty good civil war novel called, "Miss Ravanale's [phonetic] Conversion." But he coined, as far as we know, the phrase. The great American novel, he said, the picture of the ordinary emotions and manners of American existence. Hawthorne, the greatest of American imaginations, staggered under the load of the American novel. In, "The Scarlet Letter," "The House of the Seven Gables," and "The Blithedale Romance," Deforest writes, "We have three delightful romance full of acute spiritual analysis of the light of other worlds, but also characterized by only a vague consciousness of this life." But he's kind of getting at that kind of weird other worldliness, although I think he maybe overstates is the case. He maybe suggests that, you know, Pearl would be the dominant figure if we had to think of who's exemplary with Hawthorne, rather than someone like Hester. Nevertheless, his argument is that Hawthorne only has a little-- a vague consciousness of this life, and by grasping as a catch little, but the subjective of humanity. Such personages that Hawthorne creates belong to the wide realm of art, rather than to our nationality. He wants an art that's more grounded, in other words, in the local. He says there's something either universal or abstract at Hawthorne. Surprise, surprise, the desired phenomenon is "Uncle Tom's Cabin," 1868. There were very noticeable faults in that story. There was a very faulty plot. There was [inaudible] be a fault, a black man painted whiter than the angels, and a girl, such as "Girls are to Be, Perhaps, But Are Not Yet." But there was also a national breadth to the picture, truthful outlining a character, natural speaking, and plenty of strong feeling. Though cleanliness of form was lacking, the material of work was in many respects admirable. Closest thing, 1868, to a great American novel, "Uncle Tom's Cabin." Seems counterintuitive to us today, but you can see how one of the things that happened was Stowe wrote what she thought was a national text. It was designed to confront a national problem. It was designed to create characters that were drawn from all regions of the nation, at least north and south, ignoring the west somewhat, and you can see that she did the job, right? I mean, she hit that horizon of expectations. Nobody doubted that it was a novel. In fact, people said it was a powerful novel. They were moved by it. To a certain extent, as I said, it's not that antislavery made the novel powerful, but that the novel made an antislavery a powerful problem-- or powerful cause. She hit the horizon of expectations, not just willy-nilly. I think if you look at what she does, you can see a very careful merging of different elements, sentimental fiction, domestic fiction, Christianity, all as the kind of delivery mechanism for a [inaudible] first and foremost, antislavery, but then also anti-domestic slavery [inaudible]. Melville takes a different [inaudible] and in a way, one of the things you might say is that he is writing, as did Hawthorne, over against the tradition that Hawthorne represent-- that Stowe represented, that domestic tradition, and he took his lumps for it. Novel was not appreciated in its day. Melville was bitterly disappointed in the reception of "Moby Dick." He wrote a novel called "Pierre" that had a long section in the middle where he kind of went off about the publishing industry, and editors, and people wrote things like, "Herman Melville crazy," and he died in obscurity having given up novel writing, working for years in a New York custom house writing a little bit of poetry, and he was finally rediscovered well after his death by a set of critics who rehabilitated his reputation. Anybody see the Demi Moore "Scarlet Letter?" Well, that's actually comforting. But if you happen to want, like-- if you happen to want to see a really bad adaptation with lots of, you know, sexy bits, the people that made "The Scarlet Letter" with Demi Moore thought that, oh, it's a Victorian novel that just needs to have its bodice, you know, untied a little bit, let it out. So she lets it out. There's a bathtub scene, as I remember, yes? Okay, so shortly after that, please, never see that movie and then think you can talk about the novel afterwards. You really can't. That had a certain kind of earthiness. Maybe Deforest would have liked it, I don't know, but this came out in The New Yorker shortly afterwards. That's not a very good print. I'm sorry about that. But if you were able to see it better, you would see that here is a guy with a peg leg, and a lance, and a rather buxom lass, bit of cleavage right there. In fact, I think it's described on The New Yorker site as, you know, Ahab standing next to a buxom lass, actually. And you can see here on the [inaudible] there is "Moby Dick" with the requisite cartoon X's, "Caught," and it's "Moby Dick," the Demi Moore version. Okay, it has a happy ending. It has a girl. It has sexy bits, cool. Actually, this version was made. It was, in fact, the first version that was made of "Moby Dick" for screen, really. It existed in two versions. One was a-- I think it was 1922, silent version called, "The Sea Beast," completely silent, and then it was revised in 1929 again starring John [inaudible] as a talkie called now "Moby Dick," because something called the Melville revival was underway. People knew that "Moby Dick" was a book. Hollywood producers knew that it was a book, which meant that many people knew that it was a book. But they didn't have to be too faithful to that book. So what I'm going to do now is show you some clips from this 1930s version. As you're looking at it, I want you to see the irony of what's at stake here. Melville has written over against a sentimental domestic marriage tradition. Hollywood takes his whale hunting novel and puts it right firmly back into the sentimental domestic marriage tradition. There is a character called Faith. There is a brother called Derrick, and there is a dog. [ Silence ] [ Music ] >> I want you to be thinking about the sentimentality of the-- [ Music ] >> Lucas later redid that moment in the Empire Strikes back. [laughter] One of the points of showing that to you is, again, to give us a sense of meanings circulate, right, how "Moby Dick" becomes, you might say, something more than simply a novel. The film adaptations play a role in that, but we also get some sense of an index about the status of the novel in the 1920s, right, when that film was made. We get a sense that, in fact, it was-- you know, all you needed was Ahab, and a whale, and you could do a lot of other stuff with the story and still extensively be telling the story of "Moby Dick." If you ever have a chance to see that, and you probably won't, because as far as I know it is not available. I happened to run into it on TNT years and years ago, I think, and it's not on videotape. "The Sea Beast" is available in a bad archival version from Canada, I think. But if anybody really wants to watch the 1930s version, it is actually quite amusing, let me know, and we can make-- I can get it to you, but you have to promise to actually watch it and send me a comment back about it. But I want you to see that one of the things that's going on precisely in this period is the Melville revival, right? So from "The Sea Beast" to "Moby Dick," the fact of the book, and yet the book is not yet [inaudible]. One of the things that happens during the Melville revival is that Billy Bud is discovered, and Melville starts to have a different kind of reputation. Paul Lauder, who studied the way in which Melville's reputation changes from the 1920s on, suggests that Melville was construct. Now he's talking about Melville. The idea of Melville was constructed during the 1920s as part of an ideological conflict which linked advocates of modernism-- right, we're English majors, modernism, Faulkner, Joiful [phonetic], and a traditional high cultural values often connected to the academy against a social and cultural other, generally, if ambiguously, portrayed as feminine genteel, exotic, dark, foreign, and numerous, a good thing about different kinds of representation in this period. What is modernism taking aim at? It's a certain set of things. It has to do with sentimental writing. It has to do with realist ethnic writings. It also has to do with a certain kind of, you know, drippy romanticism that TS Elliott was very disparaging of. What goes on in this context, a distinctively masculine angle of sex. An image of Melville was deployed as a lone and powerful artistic beacon against the dangers presented by the masses. In other words, modernism constructing itself as elite culture can find a predecessor and an exemplar in Melville. Creating such an image entailed overlooking issues of race [inaudible] democracy and the like, which have been commonplace as a contemporary criticism, indeed, the kinds of things that have interested me, and I think I've tried to bring to the fore in talking about "Moby Dick." So, Melville and "Moby Dick" get constructed as, you might say, the great white father, so much so that when-- has anyone ever read Maxine Hunt Kingston? Maybe you've read "The Woman Warrior." She's one of the first Asian-American novelists to kind of crack university syllabi. People don't tend to read her great novel [inaudible] as much, but one of the things you would see very early on in "Trip Master Monkey" is an artist figure who's an Asian-American, who's thinking about what it means to be an Asian-American artist figure. And at one point, he says, "Okay, when do I say, you know, what my ethnicity is?" Does he announce now that the author is Chinese, or rather Chinese-American, and be forced into autobiographical confession? Stop the music. I have to butt in and introduce and my race. Dear reader, all these characters who you've identified with, Bill, Brooke, and any-- are Chinese and I am, too. The fiction's spoiled. This is what the character is arguing. You who read have been suckered along, identifying like hell, only to find out that you've been getting a peculiar colored slant eyed POV. And then he goes on to say this, "Call me Ishmael." See you pictured a white guy, didn't you? To me, that's a misreading of Melville's novel in many ways, but I think that's one of the things to understand about the meaning of the novel for a writer like Kingston, who finds herself inspired by the American literary tradition, and somehow also antagonistic towards it, feeling like the American canon hasn't left a space, perhaps, for Asian-American writing. You know, Melville, in some sense, becomes one of the fathers that needs to be slain. "Call me Ishmael." See you pictured a white guy. But as Lauder suggests, I think one of the reasons that Melville's novel continues to hold the fascination of critics these days is not simply because it's been constructed in a certain way, but because when you go back to it, it repays reading. I mean, for one thing, it's pretty funny. It has lots of stuff going on that if you are interested in, you know, delving deeply into books, it repays re-reading. But I think when you go back and look at now, you see that it's very attuned to certain kinds of dynamics of otherness that have come to be interesting to us now in the early part of the 21st century, and I think I want to argue for you, finally, that Melville is aware of this. He doesn't have the language of dominant residual and emergent to draw on, but look at this image at the very end of the book. "It's so chanced that after the Parsees' [phonetic] disappearance, I was he whom the fates ordained to take the place of Ahab's bowsman when that bowsman is soon to vacant post." So this is another one of those moments that should remind you when you get to it of that chapter called "Moby Dick," when Ishmael actually said, "By the way, I was there. I did the oath. I participated in this whole thing." Now we have to rethink the chapters of the chase third day to think about where Ishmael was in this. The same who when on the last day the three men were tossed from out of the rocking boat [inaudible]. So, and this is the phrase that I want to highlight for you, "Floating on the margin of the ensuing scene and in full sight of it when the half spent suction of the sunk ship reached me, I was then, but slowly drawn towards the closing vortex. Round and round, then, and ever contracting towards the button-like black bubble at the axis of that slowly wheeling circle, like another ixion I did revolve." So picture the image. Apparently, when a ship does go down, it actually does create a kind of vortex that sucks everything in around it. Ishmael has been dropped at the margin of the scene, and because he is at the margin of the scene and not at the center of it, he is saved. His marginal status, in other words, is what has saved him, okay, symbolically. And then when we think back about the role that Ishmael has played in the course of the novel, we see that he has also constructed himself as a kind of marginal person. He's on the outskirts of things. He doesn't ever, per se, say that he's part of the central action. He has, more than even most narrators, a kind of weird observer of function-- a participant observer of function, and I think part of that idea is that Melville is recognizing the power of what we might think of as the margins of culture. At the site, emergent practiced ideas and values can arise. One other thing, symbolically speaking, what is it that saves Ishmael? What is he hugging that allows him to float at the margin of the scene? It is Queequeg's [phonetic] coffin transformed into Queequeg's body by-- you know, once he no longer is dying, puts versions of his tattoos all over this thing. So it's kind of like, you know, a wooden Queequeg and transformed into a life buoy. So out of death there is life, and the life, symbolically, come from Ishmael's embrace of his friend, Queequeg, that embrace of otherness with which Melville begins. Remember I told you the story of the Essex. Instead of telling the story of the Essex again, we have the confrontation of the whale. We go-- we try not to become eaten by the cannibals. We become the cannibals. Melville reverses the story. We confront the cannibal first, and then we have the cannibal motif to use throughout the novel. Go to Gutenberg.org and search for cannibal. Every time you'll see that in crucial places Ishmael is making comparisons between the cannibal and everyone else. Who ain't a cannibal? Everything is cannibal. That's part of culture. Culture, as I suggested the other day, is about domination. We are all cannibalizing one another. Ishmael embraces the cannibal. "Moby Dick," the novel, embraces otherness, and that's part of what the resolution is about. I want to take one other motif very briefly and show you how it works, okay, and from beginning to end. This is that motif of the scar that Ahab has when we first see him, right? Remember that the first thing that Ishmael has heard about Ahab from Captain Peleg is that his leg was taken off on his last voyage by this whale, right, and so it's supposed to-- puts a strike of fear of whales into Ishmael. On page 108 of our edition, you'll remember that Ishmael doesn't notice the peg leg first. What he notices, instead, is this, "Threading its way out from among his gray hairs and continuing right down one side of his tawny, scorched face and neck until it disappeared in his clothing you saw a slender, rod-like mark, lividly whitish. It resembled that perpendicular seam sometimes made in the straight, lofty trunk of a great tree when the upper lightning tearingly darts through, down it, and without wrenching a single twig, peels and grooves out the bark from top to bottom are running off into the soil, leaving the tree still greenly alive, but branded." Right, and we talked about that image of branding. We talked a little bit later on about the legends that arose. Was it a birthmark? Did it happen at sea? And it's even liken to a kind of crucifixion. Ahab is somebody who has a crucifixion in his face, and we-- you know, at one point I suggested to you that this novel takes the form of a kind of novel-- of a narration by an apostle, of someone who is a kind of Christ-like figure, perhaps. There's a lot of language throughout that would identify Ahab with Christ and with the crucifixion, although, perhaps, in a Hawthornian way may be the opposite, right? He's somebody who challenges God, rather than carries out God's will. But I want you to see where this imagery goes, right? If you think about the tri-works, the association between Ahab and fire is carried out in the tri-works. There's the image, finally, at the end of that section of the Pequod burning a corpse, right, becoming in some part-- in that way an emblem of its monomania commander's soul. But where the imagery comes to a head, finally, is in the chapter that's called "The Candles." And one of the things that we need to know in order to get-- to understand what's at stake in "The Candles" is to think about a character whom I haven't had occasion to talk much about yet, and that is Fidalla [phonetic]. Fidalla is a Parsee, which means that he is someone who has come-- whose ancestors probably have come from-- if we're taking the strict meaning of the term, have come from Persia and migrated to the Indian subcontinent. In Melville's day, Parsee was also a term that was used for Persians more generally, but what's known about Parsees even then is the idea that they are Zoroastrians. They worship the prophet Zarathustra, who is, in fact, the founder of what is taken to be the oldest still practiced monotheistic religion in the world, however, there was a-- one of the symbols of Zoroastrianism is the fire, because it's something Zoroaster-- takes the fire worshipping practices, which were dominant in Persia, and creates an emergent monotheism that still recognizes the residual power of some of these old practices, and therefore, transforms fire into a symbol of purity and light. And it becomes-- it's a dualistic religion in which the powers of God are wholly separate from the powers of darkness and evil, and human beings are enlisted along with-- created by God and then enlisted by him to combat powers of darkness and chaos, which don't arise from God himself. Now, Melville read a lot about this in Pierre Bale's encyclopedia, right, and very drawn, we think, to the kind of dualistic thinking that's embodied there, that there are certain ways in which you look at the way in which the-- if you look, for example, at the chapter on the whale's head, you'll see there's something approving about the idea that the whale manages to keep [inaudible] in its mind at the same time, right? It sees where its ears are-- where our ears are, or where its eyes would be. So you might say it sees what's on the side, doesn't see what's in front, and has to synthesize to opposite kinds of perspective. I mean, think back to your Emerson. You remember that thinking about contradiction is a mark of genius. Being able to hold two things in the mind at once is perhaps beyond what most human beings are capable of, but apparently, it's what the whale has to do every waking moment. So, Melville and Ishmael are drawn to loads of binary thinking. You might say that for-- you know, for someone who is thinking about what's wrong with Puritanism and its account of evil and depravity, that it all has to originate with God-- Adam is, you know, sort of set up to fall. This provides an interesting possible solution. If you were to pursue this ending, you'd see that what Melville does with all of this Persian imagery that's in there is to create an alternative to Christianity, a way of getting outside of the straight jacket that sometimes Christianity seems to be, you know, in this novel. So, finally, we get to "The Candle." That's right, you'll remember this chapter. This is a chapter where they are very near the whale's ground. They've gone through a storm. Ahab has turned them right into the storm, and as a result of this electrical storm, they have this phenomenon that more commonly, I think, is known as St. Elmo's Fire, but it's referred to in the novel as a corpasance [phonetic]. It's when the lightning-- electrical and discharge from lightning works its way up on the top of the masts, right? So you can imagine here, we again have a certain kind of what looks like Christian imagery, masts topped by fire. It might be a kind of light version of the boggy, soggy, squitchy [phonetic] picture. Take a look at page 382, Ahab here. Stub says in the middle of 382, "The corpasance have mercy on us all. At the base of the main mast full beneath the deblune [phonetic] and the flame, the Parsee was kneeling in Ahab's front, but with his head bowed away from it, while nearby from the arched and overhanging rigging where they had just been engaged securing a spar [inaudible] arrested by the glare, now cohered together and hung pendulous like a knot of numbed wasps from a drooping orchard twig. In various [inaudible] like the standing, or stepping, or running skeletons in Herculaneum. Others remained rooted to the deck, but all their eyes up cast. 'Aye aye,' cried Ahab. He recognizes the opportunity for another ritual. 'Look up at it. Mark it well. The white flame but lights the way to the white whale. Hand me those main mast links there. I would fain feel this pulse and let mine beat against it, blood against fire.'" And then look what he says. "Oh, thou clear spirit of clear fire, who on these seas I as Persian once did worship, 'til in the sacramental act so burned by thee that to this hour I bear the scar." And now we have his example, at least filtered through Ishmael's report, of where that scar comes from. It comes from worshipping outside the bounds of Christianity. It goes farther barbarous shores, right? Remember, Peleg said Ahab has fixed his lance and things more strange than whales. He's gone outside the bounds of western culture to worship as a Persian. What happens? "I now know thee, thou clear spirit, and I now know that thy right worship is defiance." One of the things we might say is that Ishmael is a cosmopolitan figure. I suggested this at the outset, right? He embraces Queequeg. He embraces difference in others, but so is Ahab. Ahab had actually gone out, tried to get outside of Christianity. He's gone to these strange seas. He's worshipped as a Persian. He's given himself over to otherness, but there's something wrong with Ahab. Perhaps you might say that Ishmael's cosmopolitanism is finally validated and empowered by a sense of outwardness, a sense that he is not always turning inward, that he's more interested in other people in narrating-- in opening himself up to others. So he becomes subsumed into his own narrative and disappears [inaudible]. Ahab is always about Ahab, and ultimately, there's a certain kind of selfishness or egotism that short circuits, quite literally, this cosmopolitan impulse. It becomes about Ahab. It becomes about Ahab's revenge. It becomes about Ahab fighting against the divine, rather than working with it. "To neither love nor reverence will thou be kind, and even for hate, thou can but kill, and all are killed. No fearless fool now fronts thee. I own thy speechless, placeless power, but to the last gasp of my earthquake life will dispute its unconditional un-integral mastery in me." Right, and so he goes through another ritual here where he allows-- where he basically has a crew re-consecrate its oath, right? This is a chapter that you should look at. I think it's one of the important places where much of the imagery of the novel comes together, and we start to see what it is that-- in some sense, if Ahab, as I suggested to you, is sort of branded by Calvinism, even if he's a Quaker, there's a kind of mutated form of Calvinist fundamentalism that structures his engagement with the world and with God. You might say he's never fully able to get outside of that box, perhaps. And in the end, he can react only, in some sense, as a fundamentalist would. Think of him as a version in the end of Roger Chillingworth [phonetic], perhaps. It's like all one thing or another, and therefore, it can only be this kind of contentious relationship with God. Another chapter that you should pay attention to as you're thinking about this novel is chapter 132, "The Symphony." It's a moment where Ahab and Starbuck, in short, have a moment. And one of the things you should see is this is the place where some of that domestic imagery is tied up and tied off. Remember, Peleg's saying, "Oh, Ahab has his humanities. He has a wife and child." And I said, oh, that's kind of flimsy ground. If we're good readers and we know our literary history, we know that this novel is, in some sense, designed to shoo away that tradition, or to minimize its impact. Here, Starbuck is evoking that same kind of tradition. This is, in fact, a sentimental moment that Ahab almost gives in to. Page 405, "Oh, Starbuck, it is a mild, mild wind and a mild looking sky. On such a day, very much such a sweetness as this, I struck my first whale, a boy harpooner of 18. 40, 40, 40 years ago, 40 years of continual whaling, 40 years of privation." He starts to think about what might have been. It's almost a little thought experiment here. Can he give up the cherished value of whaling, really be what we would think of now as a cosmopolitan, open himself up to something else. Starbuck sees his opening, right? He's going to invoke all of this domestic experience, try to make a connection to Ahab. He wants nothing better than to-- nothing more than to turn the boat around and go home to wife and child. Forget the logic of the marketplace or business. It's the logic of sentimentality and domesticity that Starbuck wants at the end. Ahab gets close, and then no. Bottom of 406, "What is it? What nameless inscrutable, unearthly thing is it? What causing hidden lord and master and cruel, remorseless emperor commands me that against all natural lovings and longings I so keep pushing, and crowding, and jamming myself on all the time, recklessly making me ready to do what in my own proper, natural heart I durst not so much as dare?" And then the crucial sentences, is Ahab, Ahab? And think about what that means. What does that mean? Why the repetition? Is Ahab what, the Ahab of old? Is Ahab himself? Who is Ahab? "Is it I, God, or who that lifts this arm?" Now, you'll have to compare this soliloquy to what happens in the quarter deck and afterwards. Ahab seems to come around to a certain final fatalism. "If the great sun move not of himself, but is an errand boy in heaven," again, the language of agency, "nor one single star can revolve but by some invisible power, how then, can this one small heartbeat, this one small brain think thoughts, unless God does that beating, does that thinking, does that living, and not I. By heaven, man, we are turned round and round in the world like yonder winless, and fate is the hand [inaudible]." It's done. Now Starbuck realizes that it's done. Ahab has locked himself into this vision of fadedness, and later on, when there is one possible last moment in chase, the third day, Ahab talks about being-- or chase-- I think it's the second day. Ahab talks about being the fate's lieutenant. This is on page 418 at the very bottom. He says, "Starbuck, of late I've felt strangely moved to thee ever since that hour we both saw," you know, that sentimental thing, he can't even bring it up, "thou knows what," in one another's eyes, "but in this matter of the whale be the front of thy faith to me, at the palm of his hand a lipless un-featured blank. Ahab is forever Ahab, man. [inaudible] which was rehearsed by thee and me a billion years before this ocean rolled. Fool, I am the fate's lieutenant." That's Ahab's final self-revelation. Once that happens [inaudible] is ready to happen. Moby Dick comes. It's everything that we've been led to believe that it is. It breaches. It's majestic. It's amazing. It looks as if [inaudible] agency, and in the end, it drags everybody but Ishmael down to the bottom of the ocean with it, along with all the answers that we would want to have. Ahab's ending, you might say, is closed. Ishmael's ending, as we've seen already, by being at the margin of the scene, is open. And I think that's one of the things that have drawn people to Moby Dick over and over again, is the fact that there are these continual thought experiments, and beyond that there is a kind of openness in the novel that allows you to find new things in it every time you look at it. It's very difficult for me to lecture on it, actually, with a book open, because then I kind of notice things that I want to bring to your attention, and it kind of derails my train of thought. I'm trying to be very disciplined today. So I'm going to take you to the one last place that I want you to see before we leave each other. It's in the chapter that's called "Queequeg in His Coffin," and I think what it does is it gives you a figure for the novel itself, and for Ishmael, the practice of romance. This is the bottom of 366, "With a wild whimsiness, he now uses coffin for a sea chest, and emptying into it his canvas bag of clothes, set them in order there. Many spare hours he spent in carving the lid with all manner of grotesque figures and drawings, and it seemed thereby-- that hereby he was striving in his rude way to copy parts of the twisted tattooing on his body. And this tattooing, those hieroglyphic marks had written out on his body a complete theory of the heavens and the earth and a mystical treatise on the art of attaining truth, so that Queequeg, in his own proper person, was a riddle to unfold, a wondrous work in one volume, but whose mysteries not even himself could read, though his own live heart beat against them. And these mysteries were therefore destined in the end to molder away with the living parchment where on they were inscribed, and so be unsolved to the last. And this thought, it must have [inaudible] to Ahab that wild exclamation of his when one morning turning away from surveying poor Queequeg, oh, devilish tantalization of the gods." That image of the wondrous work in one volume, I think, is an image of the book, but what you see happens to that coffin is that it has another life. Ishmael embraces it, and out of that embrace comes this novel. I've been teaching this novel now for probably 20 years, and every time I look at it I see more stuff in it. I hope you will come back to it at some point in your future, not just on Wednesday-- or Monday of next week, but at some point beyond, and I hope it will look different to you. So, thank you very much for listening, and I'll see you in a week. [applause] |
Open_Ed_Cyrus_Patell_American_Literature | The_American_Enlightenment.txt | >> Lecturer: All right, let's get started. I want to thank those of you who were able to come during for the last session for coming. It would have been a little odd to be here and talking just to the chairs. And not only that, everyone who was here had good things to say. So I'm very grateful for you for making the time. Those of you who had a conflict or weren't able to attend, we are going to try to do something for you. As you know, the class is being taped, and so we're going to attempt to stream it from Blackboard sometime later this week for ten days or two weeks. So those of you who weren't able to see it will probably be able to see it if you wish. Personally, I think since I said it was about Edwards and he was a crucial figure for the course and he tied together the first part of the course and the second part of the course, I'd watch it. But in any case, we'll let you know as soon as that's available. And it will be for a limited time only. So you should strike while the iron is hot, as it were. Okay, so I'll let you know about that later on in the week as soon as we sort out the tech things. Okay, I wanted to remind us we're talking about the Enlightenment. If it's 2:00 o'clock, this must be the Enlightenment. Now we're back in the Enlightenment. And these are some of the things we laid out as principles of the Enlightenment. During the last hour, I was talking about Edwards as somebody who's caught on the cusp of the Enlightenment. He's trying to preserve the principles of old-time Calvinism, but he's very drawn to the kind of new intellectual technology I said that Locke is using -- John Locke -- and thinking about empirical philosophy and the importance of reason. Edwards is trying to understand the appeal of that. He's trying to figure out a way to harness its power without giving up everything that he believes is important in religious terms. So some of the doctrines that come along with the Enlightenment, which seem to be antithetical to any kind of Calvinism, starting with that top one -- the natural goodness of human beings, right? At the end of the hour before we looked at that sermon, "Sinners in the Hand of an Angry God," which basically is making absolutely the counter argument: human beings are naturally good or if they were, they weren't for very long after the fall. Everyone is damned to hell and is only hanging by a slender thread with flames licking up all around it. It's only by God's sufferance that you don't drop into hell right now. And who knows? You fall asleep, you may not wake up in a good place. Perfection is the idea. The Enlightenment believes in the perfectibility of the human race and in part is because they say human beings have souls, they have divine reason, God gave us a lot of good stuff and we should use it. And as a result of that, if we all have some of God in us, the logic would go, we should all be equal. We're equal before the law. We have the right to liberty. There should be various things that would flow from that, the ideas of toleration brotherhood, and an emphasis on progress. Human beings' ability to make progress by applying reason and therefore an emphasis on science. All of these things get associated with this guy, with Benjamin Franklin, who is often is pointed to as the absolute embodiment of Enlightenment principles in the Early National Period. And something I said last time, we really ought to remember that this country is founded in a moment of enlightenment, of the Enlightenment. It comes out of the Enlightenment, as I think we will see a little bit maybe toward the end of hour, there are some downsides to that as well. These are the good things that are supposed to come with enlightenment. There are some less good things. Toni Morrison refers to the Enlightenment as the "age of scientific racism," for example. And that's only one of the things we'll talk about, in which there may be some limitations to Enlightenment thought. And that will become important to some of the writers that we're talking about. Franklin mostly lives in the light side of the Enlightenment, or at least presents himself that way. But again, I want to stress that he and Edwards are almost exact contemporaries. Edwards would be a senior and Franklin would be a freshman if they were in college together. But basically once you get out of college, such differences make not so much difference. So they're really contemporaries. Edwards dies young as a result of failed smallpox inoculation or an inoculation that caused him to get it and die of it. Franklin lives a long life, and his life basically spans the 18th century. So they both are men who are caught in, you might say, the interplay of larger cultural forces. And I suggested in the last hour and will suggest again that now I'll say the pairing of these two thinkers is really an excellent way of understanding the interplay of dominant, residual, and emergent cultures. There was a dominant consensus in the religious intellectual life of the Americas in the north, in and around Massachusetts, Boston, even down toward New York, and beyond. Which oriented itself around Calvinism -- that's the story of the Puritan origins of the American self. Edwards wants to preserve that. He comes from a very orthodox family. He's even more orthodox than his grandfather, who was a preacher. And he's trying to figure out a way to diffuse the threat that the Enlightenment poses, although you've got to imagine given the way in he writes and the way he's so clearly drawn to the principles of the Enlightenment and to what almost looked to us like proto-Romantic aesthetics. You got to imagine that he's thinking that this is a kind of inevitability to the triumph of Enlightenment thought, this kind of thinking that will place human beings at the center of what matters, rather than spiritual life or God. The drama of the West becomes the drama of the individual consciousness, rather than man's and woman's relation to God. Franklin's got a different way of mixing these things into a balance. He's interested -- drawn to -- the principles of Enlightenment. But he understands that what is becoming residual, the principles of Calvinism and religion, still exert a powerful force. So he wants to find a way to diffuse those, appropriate those, channel the energies that might be associated with those towards of the direction of Enlightenment. There was a moment in the letter to Benjamin Coleman, the letter that Edwards writes to another minister, describing the revivals in North Hampton that indicates something of the way in the religion. He talks about this period of revival and says that in some sense, "people in other towns kind of ridiculed us." And so before there was a big period of revival afterwards. And so you see that there's a sense in which the Enlightenment is starting to give sway to something else. So as we think about Franklin, I want us to -- and as you look at his prose, I want you to ask yourself these questions: In what ways does Franklin show himself in the way that he writes to be a man of the Enlightenment? If the two of them are contemporaries, roughly speaking, what is it that he shares with Edwards? What strategies of representation even might he share with Edwards? But then also, how is he different? And I think we would want to locate the difference in his at attitudes towards Christian religion. There's a certain way which in which for Franklin the use of Christianity is not deeply felt, but is almost a rhetorical engagement. He needs to show himself in certain moments to perform religion. At one point that we'll look at he talks about the importance of appearance even more so than reality. So there's a certain way in which he has to give a religious performance. But how does he make use of that? We'll look at some particular lines from the autobiography that show us the way in which he actually attempts, through language, destabilize a religious consensus. And then one of the abiding themes we've had has been the relationship between the individual and community or society, and the individual and God. And we might think about "individualism" as a word that is not even coined yet. Individualism [inaudible] Europe right in around the time of the end of Franklin's life. We'll talk about this again later on. But it doesn't even get used by Emerson -- Emerson, who's supposed to be the great prophet of American Individualism doesn't have the term to use. He talks about self-reliance. It's only later after that famous essay is published that it's in enough currency that he actually refers to it in a piece called "New England Reformers." It comes into the American parlance probably through the translation of de Tocqueville's Democracy in America, where the translator has to apologize for it. He says it's an ugly word, but we don't have another word that expresses exactly that idea. So individualism is a new idea and it accompanies the Enlightenment. Again, that shifting the drama of the West, if we could put it in those terms, onto the individual away from God or the church or other larger communal forms. So remember the balance that Winthrop was trying to strike. He understands that there are energies that we later called individualism, energies around the individual, and economic imperatives, and the desire to have certain kind of material prosperity, economic opportunity, as well religious freedom. He tries to harness those, to subordinate those to a community. And remember, we talked about the ways in which the symbol that he chooses, "The City on the Hill" eventually gets recycled later on by Ronald Reagan and the meanings, the relationship between the individual and the community, are flipped around. You can't control how your symbols are going to work later on in culture. And that's one of the things that happened. Reagan reverses that attitude towards individual. Where does Reagan get it? A lot of it has roots in Franklinian thought, Franklin's idea about prosperity. And so I'll try to get at some of those. So we and to think about the ways in which, you might say as one sign of the change from Calvinist modes of thinking to Enlightenment modes of thinking, we can locate a set of attitudes about the place that the individual holds, whether individualism itself as a kind of new idea is something that's being denigrated or celebrated. All right. There's a way in which we might think of Franklin's autobiography as a secular version of a very famous text in early America, which is John Bunyan's Pilgrims' Progress, his allegory. Pilgrim's Progress. This is from the ninth edition. That's actually Bunyan himself figured as the sleeper. Some people often mistake this for a medieval text. It's not a medieval text. It's a 17th century text that draws on the medieval trope of the dream vision. So it starts off as a dream vision -- I think I brought some, yeah. "As I walked through the wilderness of this world, I lighted on a certain place where was a den , and I laid me down in that place to sleep: and, as I slept, I dreamed a dream. I dreamed, and behold, I saw a man clothed with rags, standing in a certain place, with his face from his own house, a book in his hand, and a great burden upon his back." And all of the biblical citations. Should remind you of Wigglesworth or even Winthrop. "I looked, and saw him open the book, and read therein; and, as he read, he wept, and trembled; and, not being able longer to contain, he brake out with a lamentable cry, saying, What shall I do?" And of course as this goes on, this guy, the dreamer, the guy that he sees turns out to be the protagonist of this Pilgrim's Progress. His name is Christian, with a capital "C." Anybody have a sense of what the great burden on his back might be? What's the name of the backpack? That would be sin, the burden of sin on your back. He's probably reading the Bible and looking at it and thinking, "Not good, not good, not good. What am I going to do to be saved?" And he meets another guy who has a name that begins with a capital "E," Evangelist. And Evangelist says go out into the world and go seek the celestial city, which he does. And along the way to the celestial city -- we'll talk about this more when we get to Hawthorne -- it's one of the most famous allegories in the English language and he meets all these people. They have various names like "Help" or "Despair" or "Sloth" and "Anger." And he meets all these people. And then eventually it's an allegory of the Christian life. It's really a sermon by other means. This, however, is a kind of precursor for Franklin. This book, Pilgrim's Progress was in almost every household in New England by the time that Franklin is writing. And so there's a certain way in which his whole career, and particularly the autobiography, is designed to resonate with this, to provide almost a kind of secular version of Bunyan's prose allegory, Pilgrim's Progress. Pilgrim makes a difficult journey. He has doubts, he's propped up, he has help, he finally makes it to the celestial city. Franklin also is recounting for us a progress, his own progress. But I think you would see, if you compare the two texts, not only are they very stylistically different, there's a way in which Franklin's writing is not an allegory per se. But I want you to understand that it has some affinities with allegory. If an allegory comes from Greek words that mean "that which speaks other than openly," remember how allegory works. I mean, it's the story of a guy named Christian who's looking for the celestial city. So you can read it as kind of an adventure story, but really what it is is a sermon about the progress of the Christian life. So the characters map onto ideas and values. Franklin isn't doing that, but he does present himself as a representative person. So he's writing an autobiography. And you think about why it is that you write autobiographies. And in the pattern of autobiography in the West perhaps comes from before this back to maybe St. Augustine. So when you read Augustine's autobiography, his conversion narrative, you'd say that in some sense sets the pattern for autobiographical writing in the West. And therefore, an autobiography is going to be a form of conversion narrative. Now, it doesn't mean you have to have a religious conversion necessarily and Franklin actually doesn't. It does mean that at least one act of conversion has to take place. You have to go from being -- you have to turn into author self and you have to re-render yourself as character self. So you have to have that conversion from where you're living your story to being able to talk about it. When you talk about it, you have to recreate yourself as a character. And I think you can see that Franklin very consciously does that in the course of it. So it does have affinities with a kind of spiritual tradition. It does have affinities with the idea of the representative nature of autobiography. I'm telling you this why? Well, why did Mary Rowlandson tell her story? So that you could learn something from it. Although you might say what Franklin would have you learn from his life is very different than what Rowlandson would have you learn. Or if you want to think about it in a slightly different way, you might say that Franklin's entire autobiography picks up on something that we thought of as a kind of subtext -- an almost elicit subtext in Rowlandson's narrative. You remember we talked about the way in which the natives start to have names and almost personalities once she figures out she can barter with them. Once they become economic agents, once she can engage in relations of contract with them, all of a sudden, they become people -- briefly, and then of course when she's [inaudible], shuts down and she has to go back to the doctrinaire of explanations of the things. So Franklin understands the power of economy to make a person. And that's one of the things that animates his autobiography. So Franklin's autobiography is a kind of Pilgrim's Progress, but what it really is is a kind of [inaudible] perfectionism, the idea of being able to perfect yourself. And he goes, he tells you what programs that he has in the first couple of books of the autobiography that he has for this. But really, there's almost a kind of process of trial and error through which he engages in this perfectionism. Now, to give you a sense of the way his autobiography works, I want you to take a look at one little passage here. This is on the bottom of page 509, part one of the autobiography. Now you'll notice that -- I mean, he uses many of the same kind of devices that we would see in Taylor and Edwards, even in Bunyan. This isn't a really good paragraph for that. But the use of capital letters to highlight words is something that Franklin also is making use of. But he doesn't have the same kind of religious investment in them. Bottom of 509: "I grew convinced that truth, sincerity, and integrity" -- and don't ask me why they're capitalized and italicized. I don't know. Super-important. "Truth, sincerity, and integrity." It sounds like the Superman motto. "In dealings between man and man were of the utmost importance to the felicity of life. And I formed written resolutions which still remain in my journal book to practice them ever while I live." And here's a sentence I want you to pay attention to: "Revelation had indeed no weight with me as such." Okay, so we're talking about what I said with Locke, that revelation is one way the getting the truth. Franklin downgrades it. "Revelation had indeed no weight with me as such, but I entertained an opinion" -- putting himself front and center -- "that those certain actions might not be bad because they were forbidden by it or good because it commanded them" -- revelation, that is -- "yet probably those actions might be forbidden because they were bad for us or commanded because they were beneficial to us in their own natures all the circumstances of things considered." Now again, if you read this in tandem with "Sinners in the Hands of an Angry God" you'll see that that sermon is making the opposite case. It's "God's sovereignty, God's sovereignty, God's sovereignty, stupid. Only God's sovereignty." God can will whatever He wants and that's the way it is. That would be the same line of argument that would say, "actually there's nothing particular about the truth, the tree of the knowledge of good and evil. God just picked that one." It could have been some other tree, a tree of the knowledge of 3D special effects that you weren't allowed to do. But no, he picked that one. Other people like Franklin would say, "No, I don't think so. I think there was something special about good and evil, and that in fact, there's a reason for it being that particular one." So it depends on how far you want to push the God's sovereignty argument. Franklin wants to undo that argument. So revelation has no weight with him as such. But he's not going to throw out the baby with the bathwater. Again, you might say he sees that if something has a long-standing tradition, it may have started out as "Fiat: Revelation do it because we say so" or it says so, or he says so, or whatever says so. He said, "But maybe there actually is some good common sense behind that." So he first destabilizes the authority of revelation, and then look what he does here. He says, "And this persuasion, with the kind hand of Providence, or some guardian angel, or accidental favorable circumstances and situations or all together preserve me through this dangerous time of youth and the hazardous situations I was sometimes in among strangers, remote from the eye in advice from my father without any willful gross immorality or injustice that might have been expected from my want of religion. I say willful because the circumstances I have mentioned had something of necessity in them from my youth, inexperience and the knavery of others. I had therefore a tolerable character to begin the world with; I valued it properly, and determined to preserve it." I want you to look at that sentence. "This persuasion with the kind hand of Providence, or some guardian angel, or accidental favorable circumstances in situations are all together preserved me without any willful gross immorality or injustice that might be expected from my want of religion." So what is it that preserves him from the "willful gross immorality that might have been expected" from his want of religion? What does he say preserves him? >> Persuasion. >> Lecturer: What's that? >> Persuasion. >> Lecturer: Well, the persuasion that he has is from the previous sentence. It's the idea that revelation -- he's persuaded that his opinion is the same thing. His idea that revelation didn't have any weight, but it might have some beneficial -- if you think about what it's telling you to do, maybe it is a good reason it's telling it. It's kind of like when your mom says, "Because I said so," but actually she probably has your best interest at heart. So you think, "Okay, Mom really is being kind of a pain, but nevertheless she's probably got my best interest at heart and there's a good reason for this." Not always, but sometimes. I'm just asking you to repeat what he says, and then I'm going to ask you to think about how he says what he says. So what does he say? It's like multiple choice. Yeah? >> [Inaudible] Providence and guardian angels, that kind of -- >> Lecturer: Okay. And the third thing? >> Favorable circumstances. >> Lecturer: What kind of favorable circumstances? >> Oh -- accidental. [Inaudible] circumstances. >> Lecturer: And what's choice D? We love choice D, right? It's all of the above. Okay. Now if you are this guy, what are you going to say about that? >> That it's only got Providence that would be guiding you through life. >> Lecturer: Exactly. It's only going to be God's Providence that's guiding you through life. What do you need the other two things for? Or the other three choices? Just God's Providence, right? That's how he would write that sentence. "The kind hand of Providence preserve me without any willful gross immorality or injustice." End of story. What's the effect of adding the other two things, even if we want to include the third choice, the three things? Yeah? >> [ Inaudible ] >> Lecturer: Is it individualistic? What does he actually say? I mean, where's the agency in there? So if you're saying it's individualistic, it's like, "yes, you make your own luck." He doesn't quite say that, although he says it in other places, but he doesn't quite say that here. No. He says "Providence, or some guardian angel, or accidental favorable circumstances and situations." Now, how compatible is "accidental favorable circumstances and situations" with the idea of Providence? >> Is he saying fate as opposed to Providence? >> Lecturer: I don't know, did he say fate? >> I don't know. >> Lecturer: "Accidental" means what? >> Not because of Providence. >> Lecturer: Not because of Providence. Accidental means not by intention, not planned. Providence means it's all planned, all intention. He's gone. He has a triptych of three phrases, and the first and the third are absolutely opposite to one another and shouldn't be in the same sentence together -- not if you had any strong conviction about the first thing. How does he get to it syntactically? He puts in a middle term, which is somewhat compatible with Providence. "Providence or guardian angel." Now think about that. My guardian angel. Angel, okay that's good. We're down with angel and the Providence thing, that's good. But my guardian angel? What's that? >> That's individualistic. >> Lecturer: That's sort of individualistic in so far as you might say, "Okay, you have a particular guardian angel looking over you," but -- so there are actions the guardian angel is protecting you. Think about It's a Wonderful Life. Clarence comes down, has to make this guy not commit suicide. Yes. But think about that: that's already in this moment something from pop culture. I mean, it's not religion reference to talk about a guardian angel in that way. But it's compatible with Providence. So you go from Providence, you slide over to guardian angel, and then from guardian angel it's just a hop skip and a jump to "or accidental favorable circumstances." So we've moved very quickly from Providence or not Providence at all. And to say "or all of the above." See what he's done, he's given something for everybody in a kind of common sense, low style that you find it hard to disagree with and then he says, "or whatever." But the effect of that "or whatever" is to radically undermine the first term. So there's a sense in which you can see in this passage all of Franklin's technique: he kowtows to religious belief; he attempts to be compatible with it; but by the end, in this case it's through simple syntax and the creation of association he has completely undone the reasoning underneath it, right? To say "Providence or this or that" as if all things were equal means that somehow Providence is just as culturally weighty or as religiously weighty as accidental favorable circumstances? Not what Edwards would do. So I want you to see that Franklin is actually a very careful stylist. This autobiography is a rhetorical performance. And he knows he is performing for us. And I think that's one of the things that we want to bear in mind. In terms of Franklin's own religious beliefs, he is, you might say the religious equivalent of someone like John Locke. The kind of belief that he has is usually identified with what's called "deism" -- I don't think I brought it today -- which is basically a belief in God but established by reason and by evidence, most notably the evidence is usually the argument according to design, that there are too many things about the world that seem to be designed for there not to have been a maker, but not on the basis of any special information, not on the basis of revelation. The revealed religions -- Judaism, Christianity, Islam, they all are based on a scripture that's revealed from God to a prophet. He doesn't believe in the efficacy or the importance of revelation, but he does believe there's a God and he believes you can see the workings of God out there in the world. Deism is that broad position; it has lots of different philosophical forms. It's almost always rationalistic you could say. It depends on the use of reason, but it can veer very close to atheism to think there's a kind of weak principle of -- I don't know. If you believed in The Force as opposed to God, you'd probably be very close to one of the positions that's out there that was called deist. The archetypal deist is probably Voltaire. Voltaire believed that God's evidence could, in fact, be proved by arguments about cosmology and the design of the universe. But he didn't believe in the idea of Providence. So in this he squares with. There's no plan, but there seems to be a kinds of design and you can see it in what Voltaire would have called "natural religion." And as a result of that, Voltaire was very committed to a lot of these principles here: toleration, brotherhood, progress, equality. He thought that religious impulses were served best if they were directed towards that. So that's where Franklin -- Franklin is a deist, and you can see it even in that little passage, the way in which he is destabilizing the idea of revelation. Now he's also a printer, right? So you have to understand that in comparison to Thomas Jefferson, whom I'm praying we're going to get to, Thomas Jefferson was an aristocrat or the closest thing we had to it in the Early National Period. I mean, he came a wealthy family, he was a gentleman farmer, college was his birthright just like John Adams, too. They were patricians. Not Franklin. Franklin had humble origins, although you can see at the beginning of the autobiography is -- and this will become important to us later on -- it's addressed to his son. It's about the importance of those humble origins as a kind of pattern. So at the very beginning, this is on page 473, he talks about the way in which he has "emerged from poverty and obscurity in which I was born and bred." But he celebrates that because by the time he's writing this, he's a celebrity -- a diplomat, a man of science, a member of the Royal Academy. He's the ultimate self-made man and seen as that. So it's a story about material success, paving the way for other kinds of success. And yet he can point to his family. His family is a little bit obscure, but it's still there for him, not always in ways that he likes, but it's there. This will be for us contrasted to experience of Frederick Douglass, who in some sense out-Franklins Franklin because he can't even point to origins as humble as these. So Franklin in some sense bears out the kind of argument that Jefferson makes about merit. Remember this quote from last week? "The mass of mankind has not been born with saddles on their backs, nor a favored few booted and spurred ready to ride them legitimately by the grace of God. These are grounds of hopes for others." Franklin's autobiography was also meant to be the ground of hope for others. It showed you that you could take humble origins and transform them into something that's far from humble because the early republic was going to be based primarily on the concept of merit. So a lot of people who were poor took heart from reading Franklin's stuff. And he writes explicitly about the idea of achieving wealth. There's one pamphlet that's given to you in the Norton, which is called The Way to Wealth. Let's take a look at it. It's on 451. It's a preface to one -- it's separate but it's published 1757. It's a very successful thing. It's kind of addendum to his Poor Richard's Almanac in which Franklin adopts the persona of an elderly minister, Poor Richard, and then produces this stuff. This is widely translated. By the end of the century, by the end of Franklin's life, it's been translated into French, German, Dutch, Swedish, Greek, Chinese, Hungarian, Russian, Welsh, Gaelic, and Catalan. And there are ten printings in Italian alone. So a lot of people are reading this. It's about 100 maxims or so delivered by this elderly speaker named Father Abraham. It resembles a sermon. So I want you to see if you look at this, you will see that there are ways in which he is drawing on the sermonic form. And yet, he's giving a rather anti-Calvinist lesson. For example, what would John Winthrop or Jonathan Edwards say about this on the bottom of 453? He's talking about maxims. "And again, the eye of master will do more work than both his hands; and again, want of care does us more damage than want of knowledge; and again, not to oversee workmen is to leave them your purse open." And then he says this, "Trusting too much to others' care is the ruin of many; for, as the Almanac says, in the affairs of this world men are saved, not by faith, but by the want of it." I mean, think about that. That's an even more open and slightly jokey way of talking about his difference from Calvinism. "Men are saved not by faith, but by the want of it." I mean, it's a pun on faith. We're not talking about divine faith; we're talking about faith in other human beings. But even then, compare that sentiment to John Winthrop at the end of A Model of Christian Charity, "We must be knit together in this work as one, make others' cares our own," right? That vision of community? Not so much for Franklin. Or how about this one? Bottom of 452. "Industry need not wish, as poor Richard says, that he that lives upon hope will die fasting. There are no gains without pains; then help hands for I have no lands, or if I have, they are smartly taxed." I mean, it's kind of witty common sensical joking thing. He's trying to write prose that will get you to agree, even though he's giving you a kind of mock sermon that in many senses is turning a lot of well-received religious wisdom on its head. Or this one: "God helps them that help themselves." Famous maxim. Some of you who have been in one of my conwest courses might remember a piece by the environmentalist and Christian, Bill McKibben, who talks about the fate of Bible religion in the United States. And it's called the Christian paradox. And it asks why the United States is by profession the most Christian nation in the world, so how come it's the least among the least Christian by its actions, if you look at things like giving to charity, and providing healthcare, and doing all these other things. And he starts the article by asking -- I think he cites a poll in which people are asked: Is this in the Bible? And the majority say yes. It's not. It's from Franklin. So that has a larger point. I mean, again you think about what happens in culture, something like this. Franklin makes use of the sermonic form. He gives you this maxim, which is really fairly anti-Christian in a sense. And it somehow becomes associated with mainstream Christianity in the United States. I guess be careful what you wish for. I don't know, maybe Franklin would actually say that was a poison pill that will bear fruit later on. In any case, this is an example of the way in which Franklin is using the sermonic form for these kinds of -- to basically produce a set of meanings that are other than -- strictly speaking -- Calvinist. All right, let's take a look at couple of other things because I want to show you just some key moments in this, so that you can understand how it works as a whole. I talked a little bit about it as a rhetorical performance. And he actually does talk about performance here. Take a look at the middle of 515. So okay, so he's had to apprentice himself, but he manages to get out of his apprenticeship and he eventually opens a stationer's shop. He says here, "I had in it blanks of all sorts, the correctest that ever appeared among us, being assisted in that by my friend Breintnal. I had also paper, parchment, etc. I now began gradually to pay off the debt I was under for the printing-house. In order to secure my credit and character as a tradesman, I took care not only to be in reality industrious and frugal, but to avoid all appearances of the contrary. I dressed plainly; I was seen at no places of idle diversion. I never went out a fishing or shooting; a book, indeed, sometimes debauched me from my work, but that was seldom, snug, and gave no scandal; and, to show that I was not above my business, I sometimes brought home the paper I purchased at the stores thro' the streets on a wheelbarrow. Thus being esteemed an industrious, thriving young man, and paying duly for what I bought, the merchants who imported stationery solicited my custom; others proposed supplying me with books, and I went on swimmingly." Look at the prose, a kind of nice neo-Classical [inaudible] balanced prose and then "I went on swimmingly." Franklin is always in some sense performing. He gives you sort of what you expect and then he brings you up short. But think about it here: His commitment is to what? The reality of all these things? Not so much, although that's nice but it's to the appearance of it. He needs to cultivate a reputation. And one of the things to say about that is he is aware, therefore, that he is performing for people in his life. And that's the way he represents it. But the other thing I want to suggest to you is that he is aware that he is performing for you, the reader or putatively, his son. And therefore he is able to step back at certain moments and think about the story as almost a critic would or in this particular case, as a printer would. And so he has a metaphor that's linked to the idea of perfectionism that comes from the printing trade. And that's the metaphor of the erratum, the defective font of type. If you go to the library, and I don't know how late this would be, you might see bound into it there's a slip of paper that says "errata" on it. This is because they had found some things that were wrong with it and they couldn't reprint that printing, so they slip in a sheet of errors. "Erratum" is Latin singular for "error," "errata" is the plural. [ Inaudible ] You still find that in books at the library. So printers would do that, they would come up with a list of those things. And then when they reset the plate later on, they would pull out the defective font of type or errors and plug new ones back in and to create a new edition. So this idea of the erratum becomes for Franklin a kind of governing metaphor for his life. Let's take a look at the middle of 485. I think that's the first time that it comes up. He's talking about the printing house. And at the bottom, about six lines up from the bottom of the first paragraph on 485. He says, "At length a fresh difference arising between my brother and me, I took upon me to assert my freedom, presuming that he would not venture to produce new indentures. It was not fair in me to take this advantage, and this I therefore reckon one of the first errata of my life; but the unfairness of it weighed little with me, when under the impressions of resentment for the blows his passion too often urged him to bestow upon me, though he was otherwise not an ill-natured man. Perhaps I was too saucy and provoking." So that's the first time he talked about the erratum. Take a little bit further on and you'll see that this recurs as a motif. Page 494 he talks about he had some care of money from Vernon and he misuses it. First full paragraph on 494. "The breaking into this money of Vernon's was one of the first great errata of my life; and this affair showed that my father was not much out in his judgment when he supposed me too young to manage business of importance." Or turn the page. The first paragraph on 496 tells us, "I had made some courtship during this time to Miss Read. I had great respect and affection for her and had some reason to believe she had the same for me; but, as I was about to take a long voyage, and we were both very young, only a little above eighteen, it was thought most prudent by her mother to prevent our going out too far at present, as a marriage, if it was to take place, would be more convenient after my return, when I should be, as I expected, set up in my business." But a few pages later it doesn't turn out that way. Take a look at the bottom of 499. He's with his friend Ralph. And it's kind of like a bad buddy movie, right? "I immediately got into work at Palmer's, then a famous printing-house in Bartholomew Close, and here I continued near a year. I was pretty diligent, but spent with Ralph a good deal of my earnings in going to plays and other places of amusement. We had together consumed all my pistoles, and now just rubbed on from hand to mouth. He seemed quite to forget his wife and child, and I, by degrees, my engagements with Miss Read, to whom I never wrote more than one letter, and that was to let her know I was not likely soon to return. This was another of the great errata of my life, which I should wish to correct if I were to live it over again. In fact, by our expenses, I was constantly kept unable to pay my passage." You see the next paragraph there's another errata. It continues for a while. The courtship with Miss Read is one of the errata that he is able to correct, as is the repaying of Vernon. He repays Vernon on page 513. And on page 517 we find that when he comes back, he does get together with Miss Read again. So there is a way in which he is able to correct some of these errors that he's made actually in his life. But I want to suggest to you is that in writing the autobiography, he is able to correct all of the errors because in the act of writing them down, and owning up to the mistake, and pointing them out as errors, he has done the equivalent of slipping in that piece of paper that would be an error slip, the errata slip. He's having his cake and eating it, too, by stepping back and saying, "Character Ben Franklin made these mistakes and now, I, author Ben Franklin wish to change them," he's able to suggest to you the way that you should properly behave. And you know, in fact, that his life has worked out okay. So he reaffirms the entire process of being able to correct error in your life. You don't have to be perfect, in other words, you just have to aspire to be perfect or you aspire to what we might call "perfectionism." And so this metaphor of the erratum becomes his way of talking about how you can, if it's possible at any time to identify these faults, you can remedy them. Later on in the second part, he does a little bit more to talk about some of his actual attempts to promote this idea of perfectionism. And I just wanted to show you one example of this. This is on page 526. He talks about what he calls "the bold and arduous project of arriving at moral perfection." He says, "I wish to live without committing any fault at any time. I would conquer all that either natural inclination, custom, or company might lead me into. As I knew or thought I knew what was right and wrong, I did not see why I might not always do the one and avoid the other." This, by the way, is his alternative to going to church. He goes to church and he's not satisfied with what he hears. So he's individualistic, he says, "I'll make up my own precepts. I'll make up my own conduct manual. It will serve me better." And so you can look at what the virtues and precepts are. You can see that there is some affinity to the Puritan's idea of self-denial, or abnegation, of even a kind of calling. But his calling is almost entirely material. There's a sense in which if he perfects his material life and is successful, he will be able to raise a family, he will be able to then even think beyond the family, to the good of human kind, to the good of his country, all of that stuff. So the 12 virtues that he gives us here plus the baker's dozen, the 13th, are derived from classical and Christian traditions both. And again, there's a certain kind of common sense or practically that he tries to get across. Oh, I don't know. My favorite one I suppose is Chastity, number 12: "Rarely use venery but for health or offspring, never to dullness, weakness or the injury of your own or another's peace or reputation." I mean, that's not what the Puritans would say. There's other reasons not to do that. So what I want to suggest to you is there are certain ways in which one of the things he's really doing is kind of reversing the Puritan ethos. And I think that's an important way in which he's sort of using religious forms against themselves to reverse the generally larger Puritan ethos behind it. One other thing about Franklin -- this comes from a piece called "Information for Those Who Would Remove." It's from 1784, so I think it's around the same time as that Jefferson quote that I showed you. It's in 465 of your text. But if you look at it, you can see the logic here taken out of Franklin's own life and applied to kind of larger national terms. "Tolerably good workmen in any of those mechanic arts are sure to find employ," -- here in the United States -- "and to be well paid for their work, there being no restraints preventing strangers from exercising any art they understand, nor any permission necessary. If they are poor, they begin first as servants or journeymen; -- as he did, as a kind of apprentice -- "if they are sober, industrious, and frugal, they soon become masters," -- as he did, he made himself sober, industrious, and frugal -- "establish themselves in business, marry, raise families, and become respectable citizens." [Inaudible], but back to Reagan quote where you start with the individual, then you move out families, neighborhoods, communities, our nation. It's the same kind of logic here. You radiate outwards. "Also, persons of moderate fortunes and capitals, who, having a large number of children to provide for as desirous of bringing them up to industry and so secure states for their posterity have opportunities of doing it in American, which Europe does not afford." So the idea the Franklinian story becomes known not only in America, but in Europe as one of the myths of America very early on. This Franklin story becomes one of the things that Americans consider to be distinctive about their country and it comes about because there's no aristocracy, because theoretically, this is supposed to be a place where merit and industry will be rewarded. And that's the kind of Franklinian mythology. This is where it comes from. And I think you can you can see it has long legs and we're still a part of it. Jefferson is another person that's often identified with the American Enlightenment. And his autobiography is briefer. And you can see that it's quite different. I mean, it really is a text that makes you -- that presents him as a public person from the getgo and that makes an argument not about primarily material success, but always the idea of himself as a statesman, someone who has the best interest of the nation at heart, right? And people would argue perhaps that some of the principles that Franklin is able to take for granted are established in some of the founding documents and perhaps even particularly in the Declaration of Independence that Jefferson wrote the first draft for. And he includes his draft, as you saw, in the autobiography. He shows you exactly what he wrote and what changes were made to the document by Congress. Yes? Did you want to say anything? No. Okay. So I wanted you to see the way in which that document works in that context. And in a way, I want you to get a sense of the way the document had to be altered in order to get consensus in that moment. I mean, the kind of compromises that Obama has to make over healthcare -- you always have to compromise in a democratic system. Jefferson wanted to condemn slavery. Being a slave owner, he knew about it firsthand. He wanted to condemn it, and couldn't get the South to sign on. I'll have some more to say about Jefferson and slavery a little bit later on. I think I was hard on Jefferson earlier in course, but today I really want to talk to you about the way in which the Declaration of Independence actually works brilliantly as a piece of rhetoric. So one, I've talked about Franklin's autobiography as a rhetorical performance. Clearly Jefferson's is, too. All right, he's performing this statesman's role. The body of Jefferson and the body of the nation become almost the same thing in this autobiography, which comes across in the text. But I want to suggest to you that the Declaration of Independence is a conscious performance as well and that it's a brilliant document because it creates a sense of inevitability. With Franklin, you might say you were almost cajoled into agreeing with him. He presents his things in a kind of diction that seems like it's common sense, how would you argue with that? How do you argue? Oh, it's Providence, or a guardian angel, or some accidental favorable circumstances. Sure, why not? So he presents it as common sense. Jefferson wants the Declaration of Independence also to embody common sense. But he presents it not in that kind of offhand way. Franklin never appears to be arguing with you. Jefferson wants to make a kind of -- give the appearance of a kind of rigorous argument that will be so simple and elegant that it will seem to be inevitable. So he's promoting the document in a sense of rhetorical inevitability. And one of the things we might say is that it is thought to have come in part from John Locke's Second Treatise of Government. Locke is the one that I think I've already said in the Second Treatise of Government, he comes up with a defense of individual property in which he says that in the state of nature, we are all born with property, which is ourselves. So for him, the big triple is life, liberty, and property. That's not what it is in the Declaration of Independence. What is it in the Declaration of Independence? >> Life, liberty, and the pursuit of happiness. >> Lecturer: Life, liberty, and the pursuit of happiness. Now you might want to think about what the relation is between property on the one hand and the pursuit of happiness on the other. Is it a more idealized version, Jefferson's version? Is it in some sense bad faith because it's covering up what we're really thinking about? We're really thinking about property, but we're going to call it the "pursuit of happiness"? There's a kind of complicated rhetoric around that. But one of the things he would say is even that revision is not Jefferson's own. People now have suggested, I think Garry Wills most famously in a wonderful book about where all of these texts of this documents come from called Inventing America that in fact, Jefferson owes a lot to Scottish common sense philosophy in various forms of more communally-oriented philosophies in making that revision. But one of the things that he does, so he brings together lots of different philosophical traditions but he gives it this form: it's a syllogism. Can anybody tell me what a "syllogism" is? What is a syllogism? It comes from logic. No one has taken philosophy? Syllogism has a major premise and a minor premise. So it goes something like this: All A is C. All A is C. Minor premise. All B is A. What's the conclusion? All B is C. It will be easier if you see it. A equals C, B equals A. But equals isn't quite right, so B equals C. What it basically says is this is a larger principle. This is a manifestation of that larger principle that leads you to conclude something about B, right? So in the Declaration of Independence, the major premise is the opening proclamation of a people's right to overthrow a tyrannical government. This is on 652. "When in the course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another and to assume among the powers of the earth the separate and equal station to which the Laws of Nature and the Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to separation." That's the Preamble. Then, "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their creator with certain inalienable rights, that among these are life, liberty, and the pursuit of happiness. That to secure these rights, governments are instituted among men deriving their just powers from the consent of the governed, that whenever any form of government becomes destructive of these ends, it is the right of the people to alter or to abolish it and to institute new government, laying its foundation on such principles and organizing its powers in such form as to them shall see most likely to effect their safety and happiness." That is the major premise. Governments are instituted among men to preserve rights and happiness and a government that does not do that can be overthrown. The minor premise, which is most of the declaration itself, most of you what read afterwards is the minor premise, takes the form of accumulated evidence that British rule in the Americas has been destructive. A long train of usurpations, right? And a conclusion, therefore, is that the British government is exactly this kind of government that's destructive and therefore that the colonies have a right to free themselves from this destructive rule. So it takes that form of inevitability: we assume that we have the right to overthrow a destructive government, we prove that the British government is a destructive government, therefore, we have the right to overthrow that destructive government. Now the reason to use the syllogistic form, again, is to give it a sense of rhetorical inevitability. And again, we might say that Jefferson is drawing on what he takes to be common sense arguments. And most of the arguments in the declaration are not original with him. In fact, afterwards he wrote this: "The object of the Declaration of Independence was not to find out new principles or new arguments never before thought of, but to place before mankind the common sense of the subject in terms so plain and firm as to command their assent." He wrote that, "it was intended to be an expression of the American mind and to give that occasion the proper tone and spirit called for." This is close to the end of his life, 18-something. I forget when it is. That's too late. So that's what he's remembering, that he was trying to give it this sense of common sense. Now there's a couple of other things that he does that are quite brilliant. How is it that he goes about proving that the British government is a destructive government? What does he actually do in the language on pages 653, 654? How does he actually go and list all of these things? It's almost if it were a poem, it would be kind of anaphora. Yeah? >> He uses [inaudible]. >> Lecturer: So that procession of "he's" -- he has refused, he has forbidden, he has refused, he has called together legislative bodies, he has [inaudible] gives it that stately sense of rhetoric and a sense of inevitability. That's certainly true. But who is the "he"? Who is the he? Oh, come on. Who is the he? >> [ Inaudible ] >> Lecturer: Yes, it's the King of England. Did the King of England do all this stuff actually all by himself? Exactly, right? "He" is standing in for the British government. And you have to imagine that the people in the Second Continental Congress have ties to people back in Britain. You don't really want to get in the business of necessarily, you know, criticizing Parliament too much. But everybody can get behind criticizing the king, who was thought at the time to be mad. So the king serves as a kind of synecdoche for the larger British government. If he lays the charges of the British's government being destructive onto the footsteps of the king, you might say, that has the effect of getting everybody behind him. We can all get behind this. It's easier to criticize the king. It in some sense compels a certain kind of inevitability. That's one thing. The other thing is: Why is it called a declaration? Well, a "declaration" is a legal document. The English jurist, William Blackstone, describes it as the "foremost form of pleading." So this is a legal document of a plaintiff against the defendant. So who is the defendant? Who is the defendant, if that's what this is? It's King George. And if King George is the defendant, who is the plaintiff? Yeah, all the American colonists. And what's just happened if you are suddenly on equal legal standing with the king? That's ennobling. It's a radical assertion of self-confidence, you might say. And one of the things to suggest about this is that the document works brilliantly in that way. It has a sense of rhetorical inevitability. The language is beautiful. I mean, it's like a play by Shakespeare. It has many sources. You could look at other things. I brought the [inaudible] along. The preamble to the have a Virginia Constitution, which he had worked on, George Mason's Declarations of Rights from the previous year, even the English Petition of Right -- all of these things have echoes in the Declaration of Independence. We don't tend to remember their language because somehow the language of the Declaration of Independence is not only better, but it's had a certain kind of cultural weight. It's again, exactly the way that we read Shakespeare's plays and forget that there are sources for them. We don't care about those sources. We care about Shakespeare. But we care about this document. That's one of the things to remember. And I think it has something to do with that sense of inevitability. And it works through the creation of syllogistic logic, drawing on all these phrases that are in the air, drawing on different kinds of philosophies that are in the air. It appeals to many of the people who were the founders because they were all lawyers themselves. So they understood the symbolism of being able to create a declaration and charge the king with this long train of usurpations and abuses. And in the end, the document itself almost stands in. I mean, this brings us almost full circle from where we started out. Again, with Jefferson I'm saying the importance of writing. We told you about Jefferson telling Lewis and Clark to go off what write and when you're off looking for the Northwest Passage. It's almost like a nation can be born, or deserves to be born, or deserves to be created if it can produce a document like this one, a document that is so brilliant at compelling assent. And you might even say people who give US culture more of the benefit of the doubt than somebody like Toni Morrison would, would say, "Look, this is a document that is so brilliant that it even manages to transcend aspects of its ideological moment." "All men are created equal, we hold these truths that all men are created equal." On the first day of class I said, "Okay, come on. They really meant men." They didn't let women participate fully. They didn't even mean all men. They didn't allow slaves. But people say, "Okay, look. That's true." And yet there's a way in which the formulation with just with a little adjustment can accommodate all those people, that there are certain basic principles that are being laid down here that can outlive the limitations of the ideological moment that produced them. You'll have to think about whether you think that is true or not. But that's what people say who think about these documents, this continuing cultural power. What is July 4th, 1776? That's our nation's birthday, right? We all celebrate July 4th. Well, what happened on July 4th? What happened on July 4th? >> They signed -- >> Lecturer: They signed this version of the document. It wasn't when they actually voted for independence, it wasn't when they actually approved the document, it's when they actually got up there and signed this text and made it the official text. And again, it's kind of a weird symbol about how important texts were in the period leading from colonization to the moment when the early nation comes into being. We can think of the Declaration of Independence as a kind of emblem of that, of the Enlightenment in many ways, and also as an emblem of the continuing importance of writing to this culture in a way that maybe writing is never going to matter again. I should say something about Jefferson's shortcomings. I mean, people have often asked, "Well, you're saying all these great things about Jefferson and he was a slaveholder. So how do you square the wanting to condemn slavery in the Declaration of Independence and actually being a slaveholder and fathering children from slaves and all of that?" And there's two things to say about that: one is that Jefferson, having had firsthand knowledge of slavery, understood or believed he understood that you couldn't simply abolish slavery, that the system of slavery had turned into a paternalistic structure in which the slaves were kept as if they were children. To release them with no further help into the world would be doing them a disservice. And he felt that a free population of blacks that migrated to the north would be disastrous socially. Many people believed that. Wheatley's own career, as I told you, bears this out. Her life was disaster after she was freed because she didn't have protection or patronage and because her writing was appreciated in London, which with the Americans were at war, she wasn't able to support herself. She was an inspiration to many people but not to Jefferson. And this is one of the things Jefferson writes in Notes on the State of Virginia: "Never yet could I find that a black had uttered a thought above the level of plain narration. Never seen an elementary trade of painting or sculpture. In music there are more generally gifted than whites with accurate ears for tune and time, and they've been found of capable of imagining a small catch. Whether they will be equal to the composition of a more extensive run of melody or of complicated harmonies is yet to be proved. Misery is often the parent of the most affecting touches in poetry. Among the blacks is misery enough? God knows, but no poetry. Love is the peculiar oestrum" -- madness -- "of the poet. Their love is ardent but it kindles the senses only, not the imagination. Religion indeed has produced a Phyllis Whately" -- he doesn't get it right on both counts -- "but it could not produce a poet. The compositions published under her name are below the dignity of criticism, the heroes of the Dunciad are to her as Hercules is to the author of that poem." What do we say about this? Well, again, it's why Jefferson is an excellent example of the Enlightenment as a whole. He is the author of that document which embodies all those wonderful principles that I put on this screen at the outset. He is also quite clearly someone who thinks in a sense what we call "essentialist terms," as if people have certain characteristics according to race. And he's pretty much a racist. I mean, he does believe that blacks have certain limitations. It doesn't mean that he can't care for individual blacks or even love someone who happens to be a slave of his, it just means that when he thinks about human characteristics, he thinks that some people are less capable and he divides them up according to race. That makes him exactly a man of the Enlightenment. I mean, all of those things go together. The Enlightenment is about all of those wonderful principles and it's also about the denial of the benefits of those principles to large segments of the population. The Enlightenment strains against its ideological and cultural moment. It's pushing against aristocracy. But there are certain ways in which it remains unable to transcend those moments. Arguably, we still haven't. If this nation is the child of the Enlightenment, the whole slavery thing -- that had to take a while to get worked out and it didn't work out very well. And some would say it's still not quite working out. You know, equal rights for women? Yeah, that took even longer. But there are those would say we're making progress of various kinds. But what I wanted you to see is the roots of contemporary political and intellectual problems run deep. They run back into the very founding moments of the United States. All right. I am supposed to get to Joel Barlow. Do I really want to do this? Let me give you a little bit on Joel Barlow, just so that it makes sense that I can play my last song. So Joel Barlow -- when you read the Hasty Pudding, one of the things I want you to look at is the way in which he embodies many of these kind of neoclassical principles and principles of the Enlightenment that he's talking about. Like Franklin, Barlow is very interested in economy, particularly in the possibility of trade as a way of promoting peace. Interestingly, he goes to Yale. He starts off as a kind of doctrinaire Calvinist in the Edwards [inaudible], but then he gets converted. He's really moved by the French Revolution. He ends up spending a large period of time in France. And one of the things that he writes is this famous mock epic poem called the Hasty Pudding. And I think we'll take a look at that next time, but I just wanted to get you to thinking about this because Barlow's career is another way -- he's another one of these people that seems to exemplify all of the opportunities and also the contradictions of Enlightenment. The Hasty Pudding is very much about the possibility -- not even the possibility -- but the opportunity for producing poetry and culture in this new land, in the new world. Columbus said there were nightingales. There are no nightingales. Many poets would say, "How can we write without nightingales? How can we write without aristocracy? How can we write without these kinds of long cultural histories that exist in Europe?" And Barlow makes an argument as the trope of the Hasty Pudding for saying that, "Guess what? Neoclassical poetry has pretty much exhausted itself. It needs a new subject. It needs kind of new inspiration. And we can find it here in the new world with Hasty Pudding." So in some sense, it's a rewrite of the Rape of the Lock. It's showing how neoclassical poetic devices are perfectly well-suited for thinking about the new world and the particular materials that we have here. He begins the poem much as Bradstreet begins her first prologue poem by disavowing the epic tradition, even as he sort of invokes it. And we'll take a look at that next time. But the thing I wanted to say to you is that in the course of his career, Barlow becomes disenchanted with all of these things that he believed. I'll talk about Windsor Forest next time. Barlow ends up writing a poem called Advice to a Raven in Russia. He's been sent off as a diplomat. So like Franklin he has a diplomat -- he has been sent off to negotiate with Napoleon. Napoleon is in a bad way militarily. He wants to put off the negotiations as long as possible. So he is sent off to find Napoleon and go through Poland into Russia. Can't catch up to Napoleon -- in fact, never does -- sees the remnants of Napoleon's battles, which are all of these corpses strewn across Russia and Poland. I think he writes the poem Advice to a Raven in Russian, which is a really horrific poem about ravens eating the dead off the battlefield. It's kind of horrifyingly brilliant in the imagery that it produces. And we'll look at it next time. But one of the things I wanted you to see is that Barlow also comes to realize that the Enlightenment may not be everything that it's cracked up to be. And so when we look at that poem and the beginnings of Romanticism, one of the things I want you to ask yourself is: What are the limitations of Enlightenment thinking, even beyond the racism and sexism? What happens if human consciousness, if human reason and intellect are not all that they are cracked up to be? All right, thanks a lot and we'll continue there on Wednesday. |
Open_Ed_Cyrus_Patell_American_Literature | American_Gothic_I.txt | >> Today, we are going to talk about the move out of the Enlightenment to Romanticism. And as I suggested at the end of last time, the Enlightenment and Neoclassical account of human consciousness, the stress on humanism had a kind of sunny disposition that you see in many of the principles of the Enlightenment that we've talked about. You know, the idea of liberty and equality, and brotherhood, the stress on progress, I would say is part of the re-centering of philosophical and intellectual interest on human beings, what we might call humanism, away from thinking about human being's relationship to the divine as kind of a central act, both of individual life and of culture more generally. So there are many good things that come with the idea of enlightenment, and I think there are real ways in which many of the ideas that were spawned by the enlightenment are, in fact, ideas that represent progress in human thinking, thinking. Things that today we would still want to maintain, things like the dignity of the individual, human rights, things like that, but as I suggested last time when I was talking about Jefferson and his, you know, questionable ideas about African Americans, Phyllis Wheatley in particular. I suggested that there was possibly a link between some of those nice ideas, the conception of freedom for example, that we might have from the enlightenment, and things that are not so nice. You might say enlightenment is all about light and sunshine. It also casts some shadows. And when you look at those shadows, you look at what's under the rocks of the Enlightenment; you start to find some things that aren't so nice. One of them I pointed out. Tony Morrison calls the Enlightenment, "The age of scientific racism," in which scientific arguments were made to justify slavery because blacks and other people of color were thought to be somehow inferior to whites. And there are other things as well. You know, the Enlightenment doesn't give equal time or consideration to women. That's something that needs to get worked out. And even beyond that we might say this, if we are betting everything now on human consciousness, if we are relying less on providential outcomes, what happens if human beings and human consciousness are not all they are cracked up to be? right away, when things went bad for the Puritans, they knew, "Okay wait a minute; this is part of God's plan. It's kind of a hiccup on the road to the Second Coming, or we're being punished, but we're still God's chosen. So we understand that. Our place is secure." History is secure, and it has an endpoint. But with the rise of deism and other kinds of enlightenment approaches to religion, you might say that assured outcome is no longer there or what the endpoint is, is that people are no longer convinced about it. All right. If Revelation is only one way of having truth, you might say there are a lot of other possibilities for understanding how progress might unfold. Progress becomes increasingly secular in conception, rather than sacred in the way it was to the Puritans. So what if human beings and their consciousness are not all they're cracked up to be, all right. I mean we already know that the conscious mind - we can - we know that now post-Freud in a certain way. But even then, people would think the conscious mind isn't always in control. What happens when you dream? What happens when people go mad? What happens when you dream and go mad as you'll see in the weekend with Edgar Huntly. All right. So that's part of what we want to be thinking about now and part of what romanticism addresses. The part of romanticism that we will call gothic addresses those negative things, those dark things, the idea of madness and criminality, the kind of demonic sides of consciousness, directly. But even a romantic poet such as Wadsworth or Coleridge or in our context Freneau or Bryant are thinking about the account of the minds that the enlightenment gives and finding it a little bit thin or impoverished. Enlightenment, in other words, is staking a lot on the idea of reason. Well again, what if reason is not all it's cracked up to be. More than that though, even if reason is all it's cracked up to be, isn't there something dry about reason or doesn't it miss something that is at the heart of creativity. So as the songs that I played at the beginning of the hour might suggest, there is another idea that the romantic thinkers come up with. And that is the idea of imagination. It goes, sometimes, under the name of fancy. Some romantic thinkers like Holdridge [assumed spelling] will try to make distinction between fancy and imagination, but we might think of them as roughly synonymous. Fancy, imagination as trying to understand a faculty of human thinking that is linked to creativity that you might say, for them, goes further than reason, gets at things about humanity that reason doesn't cover completely. So that's part of the critique of the enlightenment that the romantics are offering. So it's kind of a double-pronged critique. One is reason alone isn't enough because it doesn't account for things that inspire human creativity and poetry, and the other is reason alone is really not enough because it's flawed. It doesn't control as much as we would hope it does. So to stake everything on the primacy of reason is to make a really big mistake. Okay. Let's start with Barlow because Barlow is an interesting figure for us. Again, we were talking about certain figures who span these intellectual developments. All right, we talked about Edwards as both a Puritan and a man of the enlightenment and also as a kind of proto-romantic thinker. Barlow's career follows something of that trajectory as well. Barlow, as I think I mentioned quickly last time, was someone who had originally been drawn to the thought of Jonathan Edwards. He thought he was, you know, going to follow Edwards in his Calvinist thinking. He went to Yale, as Edwards did. He wrote the early commencement poem. One of his early poems is a commencement poem written in, yes, 1778 for Yale, and it was called "The Prospect of Peace." But then he changes. Like Edwards, he comes under the sway of the Enlightenment. He renounces the kind of form of congregationalism that he subscribed to before for a form of deism. Remember I said, deism thinking about God being manifest in the world through what we can observe, not primarily though scripture. And in tuning to deism, he turns to a set of other ideas as well that have to do with many of the principles that I laid out as being central to the Enlightenment, the ideas of liberty and fraternity and particularly, you might say, a conception of the free market as a way of guaranteeing both individual rights and, through a sense of mutual obligation, the possibility of peace. One of the main inspirations for Barlow, as for both so sweetly, was Alexander Pope, again who is kind of a grandfather of neo-classicism, I suppose. And in particular, Barlow was drawn to one of Pope's poems which was called "Windsor Source." It's quite a long poem, but this little excerpt, I think, will give you a sense of what lies at the heart of the poem. Pope imagines the Themes, the River Themes, because of its connection to the oceans as something that can tie England to the rest of the world and through England's preeminence in navies and in shipping, would make England a force for peace, right, primarily through creations of systems of economic obligation. That would mean that countries that are trading with one another wouldn't want to be warring with one another. So this is a passage from Pope: "The time shall come when free as Caesar wind and bounded Themes shall flow for all mankind. Whole nations enter with each swelling tide and seize but join the regions they divide. Earth's distant ends our glory shall behold, and the New World launch forth to seek the old. Oh stretch thy reign fair peace from shore to shore, 'til conquests cease and slavery be no more." And I think in this context we would say that the New World, in his conception, is actually England compared to the Old World of the east and the ancients. Barlow will see the New World in rather different terms, right. For one thing, he gets really taken by the ideas of the French Revolution and ends up spending time in France and becoming a diplomat in France. And one of the things he realizes the French Revolution does is transform the United States. Instead of being the newest nation in the world, it's the oldest practicing democracy, right. So it becomes a way to use the United States as a kind of template for the French Revolution. And with that, he writes this poem, "The Hasty Pudding." And "The Hasty Pudding" really is, you might say, a way of thinking about the relationship between Old World, so for him Europe is the Old World not the new, Old World poetic forms and the possibilities of the New World. What does the New World present to the poet? I said last time that, you know, people complain about this. Keats can't write "Ode to a Nightingale" in the New World because there aren't nightingales. Later on, you'll find Charles Brockton Brown in the preface to "Edgar Huntly" saying we don't have this old tradition of castles and aristocracy and ghosts, you know, all that kind of. The things that would seem to be the prerequisites for gothic fiction, they're not here in the United States. So how are we supposed to write gothic fiction? And that becomes a larger project. How are we supposed to do poetry in this New World, when all of the familiar poetic forms, all the stock devices, the long heritage that we have are here. For people like Barlow and Brown, this actually becomes a kind of opportunity, right. We don't have to be bound as much by the old. So what Barlow does is he takes a template, let's call it neoclassicism. Let's call it further the kind of mock epic, the mock epic that is most famously embodied in the English tradition by Pope's "Rape the Lock" about a lock of hair. He combines that, you might say, with a sense of the pastoral, which comes from Dryden's translation of the Georgics. He puts this together and takes up a New World theme, and this is what he starts with in "The Hasty Pudding." He has a preface here in which he tells you the general setting for it. It's written in 1793 in the Savoy, and he eats something in this restaurant, and it's like an early version of Pruce Madeline [phonetic]. It all of a sudden recalls home for him. And this happens to be the hasty pudding. But look at the way he begins it. Okay, this is the very beginning of "The Hasty Pudding." "Ye out salacious through the heavens that rise to cramp the day and hide me from the skies. Ye Gallic slags that o'er their heights unfurled bear death to kings and freedom to the world. I sing not you. A softer theme I choose, a virgin theme unconscious of the muse, but fruitful rich while suited to inspire, the purest frenzy of poetic fire." Okay. Let's put on our close readers hats for a minute. What do we notice about just these lines? First thing we might want to track is line length, rhyme scheme, some of the easy stuff, and then beyond that. So stanchion, anything to note? [ Inaudible audience comment ] >> All right, but before you get to that since that's even harder than the thing I'm asking. Tell me about the form. Are these - anything interesting about the form or not? >> How - >> I'll come back. If you don't want to do it, I'll let somebody else, and I'll come back to you. [ Inaudible audience comment ] >> Okay, go ahead. [ Inaudible audience comment ] >> Yeah, it's basically standard stuff, right. Rise, skies, furled, world, choose, muse, inspire, fire, okay. Anything else? So the form of the poem is not gonna be an issue. Because it's mock epic, it's gonna take place in basically heroic couplets. You'll notice that mostly they're end-stopped. Not the first line, which is doing something slightly different. But otherwise, furled has a comma, world has a comma, choose has a comma, muse has a comma, and again, not the last line of this. But for the most part, you'll see that he's writing in this familiar. So form is not going to be the issue here. Well, take the form for granted. We don't have to worry about it. See that it works, okay. Now what were you gonna say? What do you see going on in here? [ Inaudible audience comment ] >> Okay. So we see allusions to what we [inaudible] what we might call it, Europe's imperial past, right. But also, "Ye Gaelic flags that o'er their heights unfurled bear death to kings and freedom the world," to what is that an allusion? It's 1793, right? Yeah. >> French Revolution. >> Yeah, so it's the French Revolution. So it's not really the imperial past, but it's the recent political events of the French Revolution. Those are set out for us in the first four lines, and then there's a turnabout. What's this device called in the context of this class? Yes. [ Inaudible audience comment ] >> That's right. So "I sing not you," he lays out what he's not going to say. You would argue about whether it's actually a para-ellipsis because it's not the same structure as I don't need to tell you that the midterm is coming up soon so you better catch up on your reading, that kind of thing. But it has the same effect, right. All of this stuff is laid out for you and then "not," right. But think about the effect of that. You've spent - again, you can think about this in the same way that I suggested to you, you read the "Day of Doom" by Wigglesworth. You spend 200-some odd lines talking about hellfire and damnation and punishment, and you get about six stanzas afterwards saying, oh but you know nice, peace, heaven, right hand, all that kind of stuff. What are you going to remember? So "Ye out salacious," right. Politics, politics, politics, not but you remember the politics. This is kind of a way of framing this poem as I'm not a political poem, right. I mean the first four lines are about politics. He says, "I sing not you," but you know it's a way of, especially when you're reading and you can go back and reread. The poet can't just take it back. If the poet just didn't want to talk about it, he wouldn't talk about it. So there's a sense in which he's putting it up there, taking it back rhetorically, but the impression is left. So you might say the poem, despite is protestations, is framed by the political. Okay. There are other allusions too, though. I mean what else is he signaling with those lines. I mean, why would - you can say - he might argue, 'Well come on, I don't buy all that. That's literary critic stuff. I think that I didn't mean to say not political. I just had to start this way because it sets me in a certain tradition.' That tradition would be? "Arma virumque cano?" does that ring a bell for anybody? Anybody study Latin in high school or - so what is it? >> Can you repeat the phrase? >> "Arma virumque cano," I sing of arms and the man or of arms and the man I sing or - what is it? [ Inaudible audience comment ] >> It's what? [ Inaudible audience comment ] >> Well yeah, I guess except the "Iliad's" is Greek and that's Latin. But who inherits the Iliad, yes. It's the beginning of the Aeneid, right. So that's exactly what he's - I mean this already becomes that. The beginning of that is "Sing muse of the raphekilis," right. So it's the same idea. We're all singing here, but the particular, I sing, I think is more invocation of Virgil, but in any case, it is the invocation of the epic tradition except not. Which means that it's also the invocation of the mock epic tradition as we see in Pope, right. So this is doing a bunch of heavy lifting. It's setting up the genera of the poem, which is going to be mock epic. And it's setting up a way of thinking about the poem. The poem is in fact, I'd suggest to you, actually going to have a political subtext or a way of being read politically even though it's ostensibly about cooking. "A softer theme I choose, a virgin theme unconscious of the muse," and again think back to Bradstreet, right. I'm not writing poetry. I'm not writing epic. I'm doing what I do, and I should get, you know, thyme leaves for my crown if I do this well. Parsley, my domestic things. "That fruitful rich while suited to inspire, the purest frenzy of poetic fire," so I think what he's trying to suggest here is that there is something new here. It's a virgin theme. He doesn't know all the stuff about the muse, but that doesn't mean it's unrelated to poetic fire. There's even a sense that, you know, all this muse business has kept us from thinking. We're so preoccupied by the whole discourse of the muse that we actually don't do real poetry anymore. Maybe you come to the New World, you find something that is fruitful, rich, well suited to inspire. The purest frenzy as if there was something impure about this whole Old World tradition that's being invoked there. So this is the way that Barlow does it. Now that doesn't mean - I mean this is one of the poems by Barlow that we still read. The other one we're going to read in a few minutes. Because he wrote some other stuff, that frankly, you don't want to read. In the sense that, it isn't as playful this way. He writes this as a mock epic, but he actually wrote epics. He wrote something called "The vision of Columbus," and then as if that weren't stately enough, he transformed it into "The Columbiad," and you really don't want to read. It's just a lot of this without the kind of wit. There's a certain way in which it's straight-up neoclassicism and quite pious even in its adoption of the neoclassical machinery to do the work of creating a public poetry that celebrates the founding of the United States, all this kind of stuff. There's a certain way in which we like this better as critics because it has this more playful feeling and it doesn't take itself quite as seriously. And therefore, it rises to a level of self-consciousness that those more overtly epic poems don't. and there's a sense in which this humbleness in this political context is also a political statement, right. It's a statement in favor of democracy as opposed to the kings. Freedom to the world is going to be stressed but not through the violence of the French Revolution, through something else, right. Through, you might say, the honesty of the Yankee. Yankee food is good food 'cause it's not, well as he says here, vicious. Okay, so if we have here like kind of the European poetic tradition. This is the European culinary tradition in his account. "To mix the food by viscous rules of art, to kill the stomach and to sink the heart." Maybe he's thinking about English food, could even be French food, you know, with all that heavy cream and sauces. "To kill the stomach and to sink the heart to make mankind to social virtues sour cream o'er each dish and be what they devour, for this the kitchen muse first framed her book, commanding sweat to stream from every cook, children no more their antic gambles tried, and friends to physic wonder why they died. Not so the Yankee, his abundant feast with simples furnished and with plainness dressed, a numerous offspring gathers 'round the board, and cheers alike the servant and the lord," right, no this isn't political at all. "Whose well bought hunger prompts the joyous taste, and health attends them from the short repast." Okay. So I see a lot of rhymes and it's unclear whether some of them were actually pronounced differently back in the day. You can see here that this is not really about cooking and dishes. It's really about a number of things. It's about democracy as opposed to European forms of aristocratic and royal organization. It's also about art, right. Viscous rules of art in the Old World, nice abundant feasts, simple, plain. Although again, this is anything but plain, right. So what you can see is he's taking this kind of Old World poetic machinery and running the kind of New World materials through it and in a kind of jokey way. So, you know, fine. It's not - it's unconscious of the muse, but okay, we'll play along. We'll invoke the muse. "Assist me," he says, "first with pious toil to trace through wrecks of time, thy lineage and thy race," all right. He's talking to that hasty pudding as if it's the muse. "Declare what lovely squaw in days of yore e're great Columbus sought thy native shore, first gave thee to the world, her works of fame, have live indeed but live without a name, some tawny series, goddess of her days, first learned with stones to crack the well-dried maize." Now that's a small thing, you might say, but there is a kind of invocation of a pre-Columbian, pre-European tradition. And I think in the context of the poem, it's suggesting that there is something about the New World that we should celebrate that doesn't come out of the things that the Europeans brought to it. This is a little bit later on in the poem, right. You might say Europe may be first in poetry, for now, but America is first in all this lovely, well, corn. And you therefore give, the corn has a lot of different names for it here. And there's a certain - well let me just read it to you, "But man were fickle the bold license claims, in different realms to give thee different names, thee the soft nations 'round the warm lament, polentacal [phonetic]," the French of course polenta. "Even in thy native regions how I blush to hear the Pennsylvanians call thee mush, on Hudson's banks while men of bilge expawn insult and eat thee by the name suppon, ausperious Appalachians void of truth, I've better known thee from my earliest youth. Thy name is hasty pudding." So again, we have some of the idea of naming that comes along with discovery narratives, right. And that's part of what Barlow is invoking for us as well, this idea of a kind of truthfulness in American forms of naming as opposed to all of these other less-truthful names. So one of the things I want to suggest to you is that Barlow is very carefully thinking about language and about naming and about the uses of language. He's even picking, you might say, neoclassical devices that are suited for this particular theme, right. And again, I suggested to you that it's drawn from, in part, not only Pope's mock epic, "The Rape of the Lock," but Virgil's "Georgics," which had been recently translated by Dryden and was well known. So there are moments in the poem where you can say if the poem takes itself seriously it's not really in the political moments. It's more in the moments that seem to come out of a straight-up kind of pastoral tradition, and it's those moments that give a kind of gravity to the whole of the poem, so that it's not simply just a mock epic, right. So these lines could well come out of Dryden's translation of the "Georgics." "Slow springs the blade while checked by chilling rains. E'er yet the sun the seed of cancer gains, but when his fiercest fire emblazed the land, then start the juices then the roots expand, then like a column of Corinthian mold, the stalk struts upward and the leaves unfold. The busy branches all the ridges fill, entwine their arms and kiss from hill to hill." So one of the things I want us to see is, again, it's not a complete rejection of the European. It's a kind of appropriation of the European and a sort of fitting it to American models. Even to suggest that there's something revivifying about the American context. Neoclassiscm won't be dead if it can take American matters as a subject, right. So again, you can see there's a kind of symbiotic relationship here between the matter and the form. And the poetic tradition is not entirely being repudiated. It's just being put to a new purpose, we might say. And in the end, the whole thing is kind of an affectionate joke, but yet, we take it seriously in part because of moments like this which strike us as kind of real pastoral poetry. This is, you know, most of Barlow looks like this. His last poem is written in 1812, which is the last year of his life. And it's, therefore, almost roughly contemporary with the defense of Fort McHenry. But it's rather different in its approach to the Enlightenment. I said that part of what inspired Barlow was a sense of possibilities through economic interdependence, right, peace through trade. But that's not what happens to the French Revolution, and Barlow like many romantic thinkers later on - people like Wordsworth and Coleridge had been inspired by the French revolution, only to be disappointed to find that it quickly turns into something else. It quickly turns into the kind of tyranny they thought of Napoleon, and Barlow experienced the same thing. And so he writes his last poem "Advice to a Raven in Russia" when he's on a diplomatic mission to talk to Napoleon after he's been appointed Minister to France by James Madison the previous year. And he's sort of chasing after Napoleon in Europe. Napoleon's war effort isn't going so well. He's planning his invasion of Russia. Napoleon wants to stall negotiations with America. So he puts Barlow off, finally lets Barlow come in 1812. But he says, I'm going to meet you in Poland. And before he could get to Poland in November of 1812, he finds out that the Russian invasion hasn't gone well and that Napoleon is already beating a retreat to Poland. So he imagines what the battlefield looks like after Napoleon has left it. And if Barlow is talking to the hasty pudding in "The Hasty Pudding" here he's addressing another part of nature, and it's far more savage, right. It's the raven. "Black fool why winter here, these frozen skies worn by your wings and deafened by your cries should warn you hence where milder suns invite and day alternates with his mother night. You fear perhaps your food will fail you there, your human carnage, that delicious fare, that lured you hither following still your friend, the great Napoleon to the world's bleak end." And again, the style is fairly standard iambic pentameter in rhyming couplets, but the tone is really different. "Fear not," a few lines later, "my screamer, call your greedy train, sweep over Europe hurry back to Spain. You'll find his legions there, the valiant crew, please best their master when they toil for you," right in other words when they're producing dead bodies. The more you kill the happier Napoleon is and the more food there is for the raven. "Abundant there," see that word abundant again, right. But it's a radically different context here. "Abundant there they spread the country o'er, and taint the breeze with every nation's gore." And again, read this back against the earlier poem, that other passage I put up where hasty pudding has all these names and there's a kind of list. Here, there's a list, but it's put to a different kind of purpose. "And taint the breeze with every nation's gore, Iberian, Lucian, British widely strewn, but still more wide and copious flows their own," right. There's a kind of savagery to the imagery here, and it's the side, you might say, of real disillusionment. And this is really - this is kind of at the heart of the poem. This, you might say, is a moment of self consciousness in which Barlow comes very close to repudiating everything that he previously thought about the possibility of peace through mutual economic obligation because what he comes up here is with an image of mutuality. People serving one another's interests except this Napoleon the butcher serving the interests of the raven scavengers. "Fear nothing then, hedge fast your ravenous brood," little pun, "teach them to cry to Bonaparte for food. They'll be like you of all his suppliant train, the only class that never cries in vain," right. The only class. "Foresee what mutual benefits you lend, the surest way to fix the mutual friend. While on his slaughtered troops your tribes are fed, you cleanse his camp and carry off the dead." That's mutual obligation for you, but it's a rather dark kind of mutual obligation as if Napoleon only cares about killing and not at all about the other ideals that supposedly motivated the enlightenment. And then there is the kind of wonderful imagery that Barlow comes up with to kind of seal the deal and fix it in your memory. "Imperial scavenger but now you know, you work is vain amid these hills of snow. His tentless troops are marbled through with frost and changed to crystal when the breath is lost. Mere trunks of ice, though limbs like human framed and lately warmed with life's endearing flames." Does anybody remember what comes next, what the next image is? "They cannot taint the air, the world impest, nor can you tear one fiber from their breast. No, from their visual sockets as they lie, with beak and claws you cannot pluck an eye. The frozen orb preserving still its form, defies your talons as it braves the storm. But stands and stares to God as if to know, in what cursed hands he leaves his world below." Close your eyes. Think about the image. Corpse, lying, looking up with eyes wide open to God, frozen solid. The raven on his face, plucking at the eye with claws and beak and talons and can't get the eye out. That's the image. So it's a radically different kind of image of the relationship between human beings and nature. The only way, Barlow says at the end of the poem, for this situation to change is this, "'til men resume their soles and dare to shed Earth's total vengeance on the monster's head. Hurl from his blood-built throne, this king of woes. Dash him to dust and let the world repose." Barlow doesn't live to see this, actually. I think he catches pneumonia on the battlefield and ends up dying before he can actually meet Napoleon. So one of the things we might say is that Barlow explores what's under the rocks of the Enlightenment and of Neoclassicism. There's a kind of optimism in "The Hasty Pudding," but politics and other kinds of context interfere with the achievement of his vision. The promise of the French Revolution is dashed. And that has a profound effect on Romanticism, all right. And I think we want to bear that in mind. Barlow, in other words, starts to explore the dark side of Enlightenment thought, and you should keep this image in mind, especially maybe, tearing fibers, yeah, tearing fibers when you read Edgar Huntly. [Inaudible] to bear in mind. Okay. One of the things that we might say then is that Barlow in this final poem, imagining all these bodies there and the raven trying to clean the bodies of flesh and being unable to, as if these bodies have become kind of marble monuments, right. He uses that phrase marbleized. Is to think of this poem as kind of a larger grouping of poems that's well known in the English tradition as the graveyard school of poetry. There was a fascination in the later part of the 18th century with graves and churchyards and castles and basically the gothic. People used to build little gardens that had grottos and things that had these kind of morbid sensibility behind it. But this was inspiring to the romantics in part because these places became kind of scenes where you can imagine contemplation and where you could think self-consciously about the purposes of your life because you're contemplating the end of your life. Graveyard school of poetry, here are some famous poems in the graveyard tradition. Maybe this one is the one that gets in to Brit Lit, maybe 2, beginning of Brit Lit 2. Anybody read Gray's Elegy? There's the first four lines of Gray's Elegy. "The curfew tolls the knell of parting day, blowing herd wind slowly o'er the lay. The plowman homeward plods his weary way and leaves the world to darkness and to me. Now fades the glimmering landscape of the sight and all the air of solemn stillness holds. Say where the beetle wheels his droning flight and drowsy tinklings lull the distant folds." What's going on in those lines? He's creating a certain set of poetic effects. What might they be? I guess I didn't read it with enough emphasis. Let's see. Okay. So you know rhyme, we get the rhyme, right, AB, AB. Okay. So again it's gonna be, for the most part, fairly standard rhyme. But look at all the L sounds. Tolls and knell, lowing herd, lay, there's a kind of liquidity to it. There's a sense of lulling you. I mean part of the way in which he creates the feeling of silence and quiet, the elegiac feeling is created in part through the consonants that he uses and repeats throughout these first few lines. And then finally, "Beneath those rugged elms that you trees shade where heaves the turf in many a moldering keep, each in his narrow self forever laid the rude forefathers of the hamlet sleep." Okay, I don't want to do a lot with this particular poem other than to suggest that it is a pattern for the poem by Phillip Freneau that I asked you to look at for this time, which is called "The Indian Burying Ground." I think I put a slide up. Yeah. Let's just - how long is this thing? Yeah, all right. We'll just read it. It's in your book. It's page 742. >> 745. >> Yeah, so take a look at it there on 745 or up here, as you prefer. "In spite of all the learned have said, I still my old opinion keep; the posture that we give the dead, points out the soul's eternal sleep. Not so the ancients of these lands - The Indian, when from life released, again is seated with his friends, and shares again the joyous feast. His imaged birds, and painted bowl, and venison, for a journey dressed, bespeak the nature of the soul, activity, that knows no rest. His bow, for action ready bent, and arrows, with a head of stone, can only mean that life is spent, and not the old ideas gone. Thou, stranger, that shalt come this way, no fraud upon the dead commit, observe the swelling turf, and say, they do not lie, but here they sit. Here, still a lofty rock remains, on which the curious eye may trace, now wasted half by wearing rains, the fancies of a ruder race. Here, still an aged elm aspires, beneath whose far-projecting shade and which the shepherd still admires, the children of the forest played. There oft a restless Indian queen, pale Marian, with her braided hair and many a barbarous form is seen to chide the man that lingers there. By midnight moons, o'er moistening dews inhabit for the chase arrayed, the hunter still the deer pursues, the hunter and the deer, a shade. And long shall timorous fancy see the painted chief and pointed spear, and reason's self shall bow the knee to shadows and delusions here." All right. What do we make of this? I mean if you look back at this, right, in Gray, "the rude forefathers of the hamlets sleep," all right. So we're thinking about the past of this particular place, this hamlet. "Each in his narrow cell forever laid." And that's immediately what's being evoked Freneau's poem by contrast, right. "The posture that we give the dead, here figured as a narrow cell forever laid, points out the soul's eternal sleep. The ancients of this land," so like Barlow, he's thinking about the possibilities for, you might say, poetic invention that might come from an acknowledgement of the culture that was here before the Europeans. "Not so the ancients of this land, would form from life's roots is seated with his mutual friends and shares again the joyous feast. His imaged birds and painted bowl and venison for all eternity dressed bespeak the nature of the soul, activity that knows no rest." So this is a kind of, again in a slightly different way than Barlow, it's more contemplative and in some sense it's quieter and less showy, less use of poetic forms. Like "The Hasty Pudding" it's making a plea, you might say, on behalf of American materials over against the European tradition, and I'd suggest to you, over against the Enlightenment. Right. I mean you might see echoes of Keats later poem in here, right. [Inaudible] of the "Ode in a Grecian Urn" it's that same idea of freezing something in place and thinking about it, thinking about it and thinking about how it lasts for eternity. Here it's not an artwork that's lasting for eternity, but you might say - or you might say the whole effect, the whole burial, becomes a kind of aesthetic effect for him. But here, look at these words, "Long shall timorous fancy see the painted chief and pointed spear and reason's self shall bow the knee to shadows of delusions here." Right. So one of the reasons that you're attracted to the graveyard, to the burying ground, is because it's not in the city. It's not in normal life, you might say. It's not in the world of politics and economics. It's something else, and it's a place where reason does not hold sway. In the same way that you would say part of the reason that we're trying to develop something that will later be called romanticism is because it points out the limitations of reason. Here, in the burying ground, poetry takes root because reasoned self has to bow the knee to something else. Maybe shadows and delusions aren't so bad. I mean I started pitching those things to you as problems with enlightenment thought, right. Shadows, all the things on the negative side, what the sunshine of enlightenment thinking creates as its kind of residue. Delusions, madness, yeah, but maybe there's something freeing about that. If we're tyrannized by reason, maybe we're damming up creativity, and that's exactly what he means by this phrase "timorous fancy," fancy that's been afraid to assert itself. In "The Indian Burying Ground," and I would suggest in the Americas more generally, fancy can create a new space. It becomes a new place where poetry can take root. So that this poem belongs to this graveyard school, but again, it's taking the principles of the graveyard school and applying them to American materials. William Cowen Bryant writes perhaps the most famous of these graveyard poems in the American context. And he is deliberately drawing on the work of William Wordsworth, right. So Bryant, and again this is all roughly the same time. This is Wordsworth. You can see that Wordsworth is a slightly older poet. And his work is known to Bryant when Bryant is a teenager. Wordsworth writes this. People have read that preface to the "Second Edition of Lyrical Ballads"? I mean it's taken to be one of the great statements of English Romantic poetic principles. And there he talks about what it was he was trying to do in his poetry, all right. He says, "The principle object proposed in these poems," which the collection that he put together with Samuel Taylor Coleridge, "was to choose incidents and situations from common life and so were later describe them throughout in far as possible in a selection of language really used by men. And at the same time to throw over to them a certain coloring of imagination whereby ordinary things should be presented to the mind in an unusual aspect." Again, this is Wordsworth programs. Coleridge's program is a little bit different. But people take this to be the statement of standard English romantic poetics. Take a look at these lines, right. "The language really used by men," as opposed to what? The artifice of neoclassical poetry or of the kind of fancy writing that's meant to be read rather than led aroud [phonetic] that you would see in someone like Johnson or maybe in the essayists Addison and Steele, right. Something really common, what we really would hear as language and yet, of course, it's not gonna be just transcribed. We're gonna do something to it because of course we're poets and we need a reason for being. So we're going to throw to them a certain color of the imagination, right. The thing that Freneau evokes, fancy, that's what Wordsworth is evoking as well, imagination. "And further above all to make these incidents and situations by tracing in them truly, though not ostentatiously, the primary laws of our nature." So they're meant to be representative as well. So he says, "the language too of these men has been adopted, purified indeed from what appeared to be its real defect from all lasting and rational causes of dislike or disgust because such men hourly communicate with the best of objects from which the best part of language is originally derived," right. Again, think of the resonances back to Barlow. There's something honest about the way we name things here in the America. There's something honest about our feast compared to all that fancy stuff that's gonna give you a stomachache from Europe, right. We, these men - you might say that what Barlow says America can do, Wordsworth is saying by looking at common people. Stuff that is not necessarily thought to be poetic stuff, so we can do that same sort of thing. It's a kind of common project. Wordsworth is trying to do it back in England. It's again, the idea of, he wouldn't call it democracy in the English context, but it's the idea of looking at the people that are not high born for inspiration. He says, "I had wished to keep the reader in the company of flesh and blood, persuaded there by so doing I shall interest him. Others who pursue a different tact will interest him likewise. I do not interfere with their claim, but wish to proffer a claim of my own." All right. I'll give you these quotes to remind you. But that's the idea behind Wordsworth, right. There wills be found in these lines little of what is usually called poetic diction, although clearly it's, again, not just transcribed. So there is poetic diction there. It's just not poetic diction as normal. He's gonna take this language, run it through the poet's imagination and come up with a poetic language that's never - gonna give the appearance of being somehow more natural and less artificial. Bryant takes Wordsworth's principles to heart. In fact when Oliver Wendell Holmes heard this poem, he said, "That's never been written on this side of the Atlantic," as if to suggest that this is a new thing. And in America, romanticism comes a little bit later. It starts later on. I mean it's well underway by the time Bryant writes this, well underway in England. So one of the things that Bryant does here immediately is to start to do some different stuff. Rhyme scheme? What's the rhyme scheme? There is no freakin' rhyme scheme; it's blankworth, but it's still iambic pentameter. What is it? Can somebody read the first two lines for me? Come on. Read those lines. Yes. [ Inaudible audience comment ] >> Very good. Now scan them. [ Inaudible audience comment ] >> Okay. Wait a minute. So what is that? I heard it in your - to him who in the love of na-ture holds. How many feet? To him who in the love of na... >> Five. >> Five feet so it's pentameter, and what are they, duh-duh, uh-uh... >> Iambic. >> Okay good. Next line. [ Inaudible audience comment ] >> Okay, hold on. Com-mu where would you put the stress? Co-mu, that's what you said. So foot there. Ion-with... [Inaudible]. Okay. So where would the second foot be? That was a hint? [ Inaudible audience comment ] >> Okay, there's a problem in this line, right. If it were Gray doing this, he would do this "He de-lie the extra eye." Communion with her visible form she speaks. I mean that scans into standard iambic pentameter. This doesn't work quite so well. All right, one trips over it. So to him who in the love of nature holds. Gray would do it this way. Communion with her vis'ble forms she speaks, standard iambic pentameter. First line, standard iambic pentameter. Second line, not so much. Now, you know, the professor is reading in again, right. No. This is a trisyllabic foot. Communion with her visible forms she speaks. And later Bryant writes that - if you think I'm just joking, Bryant later writes an essay that's called "On the use of trisyllabic feet in English meter," in which he says the poet should be free to break the strictures of iambic pentameter if he helps him to either create an effect of naturalness or to create an effect of - to say things that he wouldn't be able to say, right. So it's almost as if you imagine it this way. He's writing this poem. It's word worthy and it's in blank verse. First line says I know how to do it. Second line says I'm not always gonna do it that way. And I think that's deliberately there in the second line of this poem. So one of the things we might say about Bryant is that in that early poem he is trying to, in some sense, create a new program for an American poetry, one that's gonna be based in Wordsworth to a certain extent. One that is going to use language that is more free. It's not gonna be bound by rhyme scheme. It's not even gonna be bound by the strict necessity of neoclassical metrical regularity. It will break decorum periodically. And if you remember what the poem is about, it's also about creating a kind of thinking about a kind of communal experience, right. It's about death. "Thanatopsis" is a meditation on death. So the idea is to think about communal experience but to use that form of communal experience to develop a kind of more individualized idiosyncratic, poetic voice. So you might say the syntax and the diction are going to be more individualized. The theme is communal, and that's one way in which Bryant solved the problem of how do you do what Samuel Johnson called "getting at the species as well as the individual," right. Individualized voice talking about a larger theme that's common to all of us and telling us not to worry about death. So that's his solution to it. Now as I said to you, Wordsworth is only one half of the big two of the first generation of English Romantic Poetics, and Samuel Taylor Coleridge is the other one. So if Bryant comes from the Wordsworth line, the Coleridge line in the United States might be said to spawn Edgar Allen Poe. And here's what my once - well, one colleague of mine - people know who Harold Bloom is? Harold Bloom, okay. So Harold Bloom mostly associated with Yale University, writes this about Poe. [Inaudible] he writes the western cannon and all those volumes of essays taken [inaudible] places telling you what to think about things and how to rank them. And he's kind of interested in ranking. So 19th century American poetry is considerably better than it is acknowledged to be. There are no figures comparable to Whitman and Dickinson, but at least a following are clearly preferable to Poe. Oh, I think this is from the "New York Review of Books" essay that I think was called "Woe to Poe." In chronological order, Bryant, Emerson, Longfellow, Whittier, Jones, Berry, Thoreau, Melville, Timrod, and Tuckerman. Poe scrambles for twelfth place with Sidney Lanier, whom we don't read anymore. I do remember Sidney Lanier though because he was on a stamp, back in the day when I was collecting stamps. God knows when that was, many years ago now. Yeah. So he doesn't like Poe. Why? If this judgment seems too harsh or too arithmetical, it is prompted by the continued French overvaluation of Poe as a lyrist. No reader who cares deeply for the best poetry written in English can care greatly for Poe's verse. Period. Glove thrown down. You think you care about poetry, you can't like Poe. You're a serious student of film. You can't like "Avatar." Vote for "The Hurt Locker." Now Coleridge, right, and I want to suggest to you that this is wrong, actually, that Poe is doing interesting things with verse. And a lot of it comes from the same inspiration that comes with Coleridge. Right. So if Coleridge is Wordsworth, in the buddy-movie that's called 'English Romantic Poetry, The early years," - yeah, maybe he'd be like, you know, Eddie Murphy to Nick Nolte, Wordsworth's Nick Nolte. Or I don't know what are other - I'm trying to think what that other new one is, Bruce Willis and Tracy Morgan. Is that right? >> Yeah. [ Inaudible audience comment ] >> What is that? >> John Bell. >> All right. Anyway, Coleridge says this, "My endeavor should be directed to persons and characters supernatural." All right, so if Wordsworth is trying to take the ordinary and see what's interesting or extraordinary about it, Coleridge in some sense is trying to look for extraordinary experiences, moments that seem to break out of normal experience and find what is ordinary within them or bring them down to Earth or make them comprehensible. Mr. Wordsworth on the other hand wants to pose himself as his object to give the term of novelty to the things of every day. I mean you can just see it in the syntax there. That charm of novelty that he thinks his project is kind of the more interesting one. All right, so here's Poe, character, and I think that's from that same year the "Review of Books Article" actually. Whoa. Oh, all right. Yeah. So "The Raven," let's talk a little bit about "The Raven." "The Raven" is an interesting poem because it sounds so different from a poem like "Thanatopsis." Let me just read you a little bit of it, and then I think you'll hear it right away, right. It's in the typical Poe form. This is in volume two, I think. So if you didn't bring it, just listen along. I'm not gonna do a lot with it, but once because I was a showoff, in like sixth grade, I memorized this whole damn poem. We were supposed to memorize poetries, and I actually didn't know that it was gonna be performed. We were supposed to do this particular reciting on parent's day. But it was, and I did, and it actually worked out well, but I have this memory of in the middle of the week trying to remember the silk and sad and certain rustling of each purple curtain, in one of the rooms in my parents' house that had a curtain in it, very vivid memory. Okay. "Once, upon a midnight dreary, while I pondered weak and weary, over many a quaint and curious volume of forgotten lore, while I nodded, nearly napping, suddenly there came a tapping, as if someone gently rapping, rapping at my chamber door. 'Tis some visitor I muttered, tapping at my chamber door. Only this and nothing more. Ah, distinctly I remember, it was in the bleak December, and each separate dying ember wrought its ghost upon the floor. Eagerly, I wished the morrow; vainly I had tried to borrow from my books, for cease of sorrow, sorrow for the lost Lenore. For the rare and radiant maiden, whom the angels named Lenore, nameless here forevermore. And the silken sad uncertain rustling of each purple curtain thrilled me, filled me with fantastic terrors never felt before. So that now, to still the beating of my heart, I stood repeating, 'tis some visitor entreating entrance at my chamber door, some late visitor entreating entrance at my chamber door. This it is and nothing more." So you can hear the deliberate artifice of the rhyme. There's a kind of cunning internal rhyme here with stanzaic form is lengthened. It sounds deliberately artificial. It's everything you might say that Wordsworth says you shouldn't do, everything that you might say "Thanatopsis" with its trisyllabic foot is setting itself against. This is another possibility for poetic practice in this period. And I want to say that I think this is deliberate. This is what Poe is about. Poe is about using language in ways that, in some sense, in our context, we might think, go back to Edward Taylor, right. Edward Taylor is using language that's difficult and sounds odd in order to get at this thing that is difficult, representing the divine or representing graves or representing the incommensurability of the human mind and the divine. Poe was trying to get at stuff that resists representation too. Madness, how do you represent madness with language? One of the things that's great about a typical Poe story. We don't do it this year. [Inaudible] is a pity, but like "The Imp of the Perverse," is barely a story. All the action that's in that story has already happened. This guy has committed the perfect murder. The only way that he can possibly be caught, and you just stipulate that. You don't have to worry about that. It's like the McGuffey. Don't worry about it. Perfect murder, only way that he can be caught is to confess. No sooner does he think that then what does he want to do? He wants to tell somebody. He's dying to tell somebody. He can't keep himself from telling anybody. How do you get that across, right? How do you get across that sense of madness? The thing about Poe is that he uses deliberately artificial language. He uses language that is kind of heightened language of the enlightenment precisely to show you what's wrong with the language of the enlightenment. You read a Poe thing, it's full of philosophical terms or scientific terms at the very beginning and a few paragraphs in, maybe even a few pages in, you start to realize this narrator is barking mad. Because now, he's matter of factly, told us how he's just put a hammer in his wife's head and buried her in the wall, and you know. We'll get to that, okay. So one of the things that I want to say is that Poe is not original. He claimed, in some sense - or his originality is of a different kind. He claimed in a piece that's in "The Norton" called "The Philosophy of Composition," that no one had ever written anything like "The Raven's" verse form before. But well, "with a murmurous stir uncertain, in the air the purple curtain swelleth in and swelleth out around her motionless pale brows. While the gliding of the river sends a rippling noise forever through the open casement whitened by the moon's slant repose." It's not as good, in a certain way. It's also [inaudible]. But it's, you know, it's Elizabeth Barrette before she married Robert Browning. So Poe has his sources, and there's a certain way in which Poe is a big shyster, and he loves to perpetrate certain kinds of literary and other hoaxes. But he's also a serious critic, and part of what he was trying to do in his writings as a critic is to try to push this project that we're calling American Romanticism. All right, so there is Poe the way he's more normally seen. So I want to suggest that part of the artificiality that we see in "The Raven" is what makes it so memorable. I mean it's probably one of the most memorable poems. When people hear it, they don't forget it. It's one of the most well-known poems from the middle of the 19th century, and it's precisely because of that sense of artificiality trying to get at something else. I mean it's an interesting exercise to compare that to Jonathan Edwards and think of their use of repetition and personal narratives. I had a student do that once. He decided finally that Edwards had to have been on drugs of a certain kind. And I said, you know, actually I think that's kind of right. Although, he didn't inject anything into himself or swallow anything. It was a different kind of drugs. This is Bloom on Poe. Oh, by the way, I think he says, Bloom says, that you know the French like Poe because they read him in translation. "Poe's survival raises perpetually the issue whether literary merit and economical status necessarily go together. I can think of no other American writer down to this moment" this is the late '80, "at once so inescapable and so dubious. Mark Twain catalog Fennimore Cooper's literary offenses, but all that he exuberantly listed are minor compared to Poe's. Allen Tate proclaiming Poe 'our cousin' in 1949 at the centenary of Poe's death remarked, 'He has several styles and it is not possible to damn them all at once.' Uncritical admirers of Poe should be asked to read his stories aloud but only to themselves." Okay, he can write. It's - "The association between the acting style of Vincent Price," does that mean anything to anybody? Yes? How - throw what is it - is it "Throne of Blood"? Not "Throne of Blood" the one where he's the actor. He kills all the critics. Oh, I'll put it in the notes when I write the - I can't remember the name of it. It's really great. There's all these critics. He's a terrible actor, right. There's all these critics who have written terrible things about him. So he takes revenge on all of them by killing them in ways that are drawn from Shakespeare's play. Oh, it's priceless. And no doubt, streamable from Netflix. Anyway, "The association between the active celebrants in Price and styles of Poe is alas not gratuitous and indeed is an instance of deep crying out unto deep," which is not very deep. All right. "Lest I be considered unfair," Bloom continues, "by those devoted to Poe, I hasten to quote him at his strongest as a storyteller. Here is the opening paragraph of 'William Wilson" a tale admired by Dostoyevsky and still central to the great western [inaudible]." And part of the why I asked you to read it. Get a sense of the Poe style but also because it introduces the idea of a double or doppelganger, right. In this case, a figure who seems to be an emanation of the conscious. And that, I think [phone rings] - I'm having one of those days. That, I think, is a way that you ought to think about Edgar Huntly, right. Edgar Huntly becomes the story of a doppelganger. It's before Poe, but if you read Wilson, which is a simpler version of it, I think you'll understand what's going on in Edgar Huntly better. Okay. So here is "William Wilson" on the "Topes of the Devil." Okay, and this is the first paragraph, right. "Let me call myself, for the present, "William Wilson". The fair page lying before me need not be sullied with my real appellation. This has already been too much an object for the scorn, for the horror, for the detestation on my ranks. To the uttermost regions of the globe have not indignant winds brooded its unparalleled infamy, oh outcasts of all outcasts, most abandoned. To the earth art thout not forever dead. To its honors, to its flowers, to its golden aspirations, and a cloud, dismal, dense, and limitless, does not it hang eternally between thy hopes and heaven?" All right. Bloom says, "This rhetoric including the rhetorical questions is British gothic rather than German gothic [inaudible] Lewis rather [inaudible]. Its palpable squalors require no commentary. Its palatable squalors [inaudible]. The critical question surely must be how does "William Wilson" survive its bad writing. Poe's awful diction, whether here or in the 'Fall of the House of Usher' or the 'Purloined Letter' seems to demand the decent masking of a competent French translation." There you go. "The tale somehow is stronger than its telling, which is to say that Poe's actual text does not matter." Again, I say this is completely wrong. It's precisely - I mean there is something about Poe's story, but it's exactly in the way that he tells it that he creates the particular effects that he does, right. Bloom wants to read Poe as if he's Oedipus or he's Sophocles and Oedipus that the story somehow transcends the language. I don't think that's exactly true. And I think - he says, "What survives as Poe's writing are the psychological dynamics and mythic reverberations," blah, blah, blah. "Poe can only gain by a good translation, scarcely [inaudible] fully retells the stories to one another." So he wants to make Poe back into the oral tradition. I think Odin [phonetic] had it more right on Poe. "Poe is sometimes attacked," he says, "for the operatic quality and decor in his tale." And you can see that here right. "Oh, to the earth art thou not forever dead. To its honors, to its" - well no wonder this is William Wilson's head. Poe is trying to get across William Wilson's consciousness. And I think for [inaudible] operatic is just right. His heroes cannot exist except operatically. And then he says, "Take for example this sentence from "William Wilson"," right. "Let it suffice that among [inaudible] out Heralded Herod, and that giving name to any multitude of novel follies I added no brief appendix to the long catalog of vices than usual in the most dissolute university of Europe, right." Bloom would say that's terrible wordy - it's peripherousous. It's wordy. There is grandiosity. And Odin would say exactly. That is the way that you capture this kind of character. This kind of character is captured by this language, and it's irrational, and it's not reasonable language precisely because what we're trying to get at is the irrational and the not reasonable. And again, this thinking about that will help you to read Edgar Huntly over the weekend. And so, Odin says, "In isolation is a prose sentence. It is terrible, vague, verbose, the sense at the mercy of rhetorical wisdom. But dramatically, how right, how well it reveals the William Wilson who narrates the story in its real colors, as the fantastic self who hates and refuses contact with reality." So from William Wilson, we will take away the prose style, but even more from Edgar Huntly the doppelganger and the double, and I think I've left myself about six minutes, which is a good thing. |
Open_Ed_Cyrus_Patell_American_Literature | American_Transcendentalism_V.txt | >> Alright, let's get started please. I am going to be filing midterm grades later today. Sorry for the delay. I'll be contacting some of you personally about your grades. In some cases to say congratulations on fine work. In unfortunately more cases to ask what's going wrong. But one thing I do want to you to understand is that most of the work of the course in terms of evaluation is yet to be done. You a short paper coming up. You have a long paper coming up, and you have the final exam. Now, I think by my calculation roughly speaking, the exams in this course count a total of about 35%, right? 15% for the midterm and 20% for the final that's because at NYU final exams don't last that much longer than midterms as opposed to other places where there's a big, where the final is sometimes three times longer. So, in those places the final counts like 50% of your grade. Here it's about 20. But I'll make you this deal. If you improve your grade on the final exam, I will drop how much that midterm grade counted down to about 5%. So it'll count, the final will count a lot more. And if you absolutely blow away your performance, I mean if you do so much better on the final exam than you did on the midterms. So say you get an A on the final having gotten a D on the midterm, I will simply think that you had a bad day at the midterm exam and discount it entirely. Or even more, even better perhaps, I will think that you adopted a kind of Franklinian perspective, [ Laughter ] >> identified your errata and fixed them. So you have a significant incentive now to not to despair. This is not cowardive depravity we're talking about, at least not in the cases of most of you. Not to despair and start to mail it in just because your final, your midterm grade isn't what you and I had hoped it would be. No, this is a time to pull yourself up by the bootstraps and do better. We are looking to reward upward progression. We are looking to espouse perfectionism rather than the idea that we're all doomed and depraved. So I want you to take that seriously, alright? There are in certain cases, I will be asking you to come in to see me because there's certain levels of performance where I think that something, there's a crucial thing that's missing in the way that you're approaching your work. I don't actually care if you've been blowing off, if you tell me look sorry, I just had a play that I was in so I blow off your course. I will actually not worry about you as much, because you're making a choice. You're allowed to make a choice, right? You can choose to not do well in this course. That's fine. I'm more concerned with people who expected to being doing better and who haven't, who don't know why things aren't working out either on the papers or the exams. If you find that I have not contacted you but you still feel like you're in that boat. Like you got a B minus and you really thought you were going to get an A minus, then come and see either me or your TA and we can talk to you about. I think in many cases this is about fixing your strategies of reading and understanding what's going on in the text. Alright, any questions about that? Paper assignment will go out by email tonight. Remember it's not due Friday but a week from Friday. Very soon, and I think actually I'm just going to put the prompt for the final paper on there as well so you can start thinking about it. You should think about the final paper basically as an attempt to build on what you've been doing in the earlier two papers. Think of those as kind of building blocks as the final paper might be two or three put together pieces of analysis like the ones that you've been doing but assembled into a kind of larger argument. In this case, an argument that you will propose to us. So we're going to ask you for topic statements. We'll take a quick look at them and let you know if you're on the right track of the wrong track. And when you do those topic statements, we'll be asking you to not only give us a sort of hypothesis about what you think you'll argue but also give us a kind of catalogue, appropriate in talking about Whitman to be talking about catalogues, a catalogue of evidence that seems to you likely to be important to you. And in general, we would like you to find more evidence than you can possibly use. We'll ask you for a few things, but you should have, be in the position of needing to pick the best evidence to make the case that you want to make and simply feeling that you need to use every single thing that you thought of, okay? So, you can talk about those things in section this week. Alright, Whitman, let's look at some more Whitman. Let's turn to the beginning of Song of Myself actually. This is on 2210 of the anthology. And then we'll move on to talk about Emerson and think about what I suggested before, about the ways in which that we might want to temper our optimism about Transcendentalism now as we approach the unit of the course that's really devoted to slavery. Alright, so Song of Myself, which is given the title late, later in its career, begins this way. I celebrate myself and sing myself. And what I assume you assume for every atom belonging to me as good belongs to you. I just want to stop and pause and think about those three lines a little bit more closely and think about the ways in which they may or may not encapsulate Whitman's project, in Song of Myself and in his writing as a whole. I celebrate myself and sing myself and what I assume you shall assume. For every atom belonging to me as good belongs. You can think about there's any number of ways to say this. Let's go around and have people different people from the class say it in different ways, and I want to know what's at stake in saying it in one or more of those particular ways. So, somebody tell me where you would place the stresses on those words if you were the one up here reading it aloud. And close the door while you think for a moment. Anyone want to volunteer because I do have the attendance sheets still up here and I can call on people. Yeah? >> [inaudible] >> Okay, I want, so say it out loud. >> So, I celebrate myself and sing myself >> Okay. >> I think that, I don't know, I guess drawing on >> I celebrate myself and sing myself, and what does that do. >> I feel like if Whitman is trying to draw on past poets and past poets always speaking about God. And he's kind of, he's borrowing this I guess the theme of self-divinity >> Okay. >> And he's trying, yeah. >> So self-divinity, thinking about someone in contrast to somebody like Edward Taylor for example, also formally experimentive, but would not say I celebrate myself and sing myself. He starts thing with, I am this humble crumb of dust. I am this miniscule speck that you should walk on. Right? This is quite different from that. >> And he's not as humble towards I guess, if he was trying to, if he was going to try to mention a higher being, he's not to humble in his opening line. >> Okay. >> He's kind of placing himself on a pedestal. >> Okay so he's not humble. Would we tie that to anybody else that we've read? Where's this coming from? Yeah? >> Thoreau. >> To who? >> Thoreau. >> Thoreau, how so? >> [inaudible] conceited I think that emphasizes self-reliance and having >> You mean Thoreau or Emerson? You could mean both. >> I mean both. >>Okay. Right, because I think Thoreau is right, because he's interested in himself and in his particular observations. It's Emerson that says, all mean egotism vanishes in that moment, right? Although he is trying to talk about a connection between himself, but it's interesting again to renote that phrase in Emerson. It's not that all egotism vanishes and I become like Taylor, this crumb of dust and the speck, this particle amongst the divine current. We keep a certain amount of egotism, a certain amount of egotism is necessary for self-reliance. It's the mean egotism that we want to get at. It's almost that there's a sense of a way of being self-reliant or if you want egotistical that nevertheless has a kind of outward flow to it. Maybe that's part of what Emerson, what Whitman is picking up from Emerson. Yeah? >> I feel like you could put the emphasis on the word myself, like that kind of a emphasize the whole self-reliant part, like it's almost like he's saying that he's doing it alone like. Kind of by myself whereas if he put it on the words celebrating [inaudible] it's more about praising the sacredness of the individual. >> Okay, so we can think about that dynamic as well. There could be, you could say I am so, you could say if you celebrate, if you stress yourself you are, he's celebrating himself, but there is a sense of being by myself, right, while you're celebrating. And it might be that if you don't want that you might choose another. I celebrate myself and sing myself. Not with other people, he doesn't play nicely with the other children. >> Like he's the only person he can count on to celebrate himself. >> I think that's very good, I think there's a tension in the poem between those different visions of what it means to celebrate yourself. There's a sense in which he is doing something that is quite different if we think about it from the kind of, some of the past histories of poetic forms. He's not afraid to put himself front and center, right, I mean if you think about the progression of forms that we've looked at. Puritan poetry is supposed to be about venerating God. Public poetry in the Revolutionary era is supposed to be about venerating your country or celebrating the lives of famous people. It's not supposed to be about the self. We start to move to lyric experience when we get to somebody like Bryant, right, but even then Bryant is describing, he's creating a somewhat idiosyncratic voice but really stressing a kind of communal theme. The voice comes quietly idiosyncratic. It's not upfront about itself, right, it's meant to be idiosyncratic in a way of making its kind of connection. It's meant to be a more personal kind of voice and you might say the impersonal marching rhythm that you might find in so much neo-classical poetry. And it's meant to make a connection to the reader on the subject of death. It's a meditation on death. This is a meditation on life in all of its fullness and messiness, right, and part of what he does is he celebrates himself. But I think there is a tension. Is he alone doing this. Emerson talks about meeting somebody with a tyrannous eye. Well maybe it's a kind of lonely place to be if you're going to have that tyrannous eye. What about the second line. What I assume you shall assume. Yeah? >> I'm having a little difficulty. When I first read it like my brain puts a comma after a [inaudible] even though there isn't one. So it comes off as a very demanding like what I assume you shall assume, but instead when I look at it that there is no comma there, what I assume you shall assume, so he's guessing what someone else is going to interpret? >> I think that's probable. I think it's possible. What I assume you shall assume. What I assume you shall assume. >> Like he's assuming that they will >> Say that three times fast. Okay. It's pos, I would say that's right. The lack of a comma does make it possible to think of, you shall assume as the object of the verb, what I assume you shall assume. >> It's hard to get a grasp because there isn't a rhythm because it is free verse. It's hard to see what [inaudible] >> How else might we think about that, yeah. >> Well I guess this is a kind of different point, but first when I heard the say, that it seems like it doesn't match because celebrating and singing aren't necessarily interpretative or analytical. And then like every [inaudible] is very material and it doesn't really have much to do with assumptions as, I don't know I think there are two ways that you can, maybe I'm wrong and need to look up the definitions that I didn't, but it seems that he could also mean rather than using the verb >> What, okay, let's think about assume. What might assume mean? Yeah? >> Assume as in to making an assumption or like making like an approximation. [inaudible] I think people mean now but could also assume a form. >> Okay that's good. So what we take for granted, what I assume, but what I take up. What I bear. I assume your burden. What I assume, you shall assume. My poetic project shall be yours. Yeah. >> I think you have to read that line directly with the one from the one from Self-reliance where Emerson says, to believe your own thought, to believe what is true for you and your private part is true for all men. That is genius. Or he also brings up the same kind of nature in chapter five, every universal truth [inaudible] to every other truth. >> That's good. I mean, I think one way to think about it is that it's a poetic statement precisely those insights from Emerson. That there's a kind of, there's something universal about our nature, right. Emerson says most people are afraid to speak out. They don't raise their hands in section, and then they find that someone else said exactly what they were going to say and maybe didn't even say it quite so well. Our own thoughts were turned to us, he says, with a certain kind of alienated majesty. There's a way in which Whitman is plugging right into that idea. Anybody get bothered by this, feel like it was a bit pushy? What I assume you shall assume. >> I don't read it that way. I also read it as assuming as him taking on but not necessarily as taking on a form. I feel like the first stanza is his mission overall. Like he talks about, the way the rest of the poem falls out with all of the visual stimulus and then he keeps picking on and appropriating. I think it's his mission of almost removing the shame from subjectivity. That's the universal element that we all have, it's an awareness of self as representation almost like Franklin. Like he's talking about every atom of me belongs to you because we all perceive. That's just what it seems to me. >> Why as good? >> As good? >> What does it mean, for every atom belonging to me as good belongs to you. >> I think that's the universal principle that he's arguing. He's using, his poetic mission then is to use all of these images to necessarily represent these qualities as in everyone's experience is just as good. There's no lesser qualities, like, which is why he argues the essential unity of everything. >> Okay that's good. I think that's right. I think there's a way in which he's arguing that sometimes we're consubstantial. It can seem a little pushy or even imperialistic if you will to say what I assume you assume. It's like you don't have a choice reader, I'm making meaning and you're going to take it up. But then it's qualified, why does he say for every atom belonging to me as good belongs to you. That's a statement about consubstantiality or maybe even contingency or chance. The atoms in me are quite literally could be in you. They are, we're all made of the same stuff. Did you want to add something? >> Yeah. Another kind of way that I was looking at it was kind of in acknowledgement of the relationship between the writer and the reader. As I go along, you're following me. What I assume, you're going to read it and assume as well. So there's all these kind of [inaudible] that he asks question that he asks throughout the poem. There's other lines that kind of point to this, >> Yeah I've talked to you about the ways in which I think we ought to think about texts as collaborations between writers and readers. And so there's a sense in which we'd suggest that the meaning of a text doesn't exist until somebody takes it up takes it up and reads it or speaks it and engages with the author and constructs that meaning. People that are, that find themselves a little perturbed thinks that there's a certain way in which if that's true Whitman is taking up a lot of the oxygen in the room. That he's taking up, he's not leaving a lot of room for you in there. That, some people would argue that there's a kind of perfunctoriness to the way in which he constructs a you. That really it's just a, one of these people who just talks at you without leaving much space to do your own constructing. I just want you to bear it. I'm not saying that's what I think you should believe or even what I believe, but there are people that read this and find it a little bit disturbing and that would be the basis of arguing that there's something that should disturb us about Whitman's poetry. Yeah. >> When I saw this, I kind of saw it as he's setting himself up almost in the same way as Thoreau and Emerson use nature as an instrument to explain the world. He's kind of just saying that he's kind of going to be the instrument to explain the world. >> Okay that's good. >> Making a representation, like using himself. >> So then there's a funny split, right. I suggested to you that maybe Emerson or Thoreau finely are using nature instrumentally right. It's an object for them. Something that gets them someplace. It's funny then to be Whitman, if you're using the body and yourself in that same way, you're sort of objectifying yourself. Or you're even, you're containing within you that kind of subject object split that Descartes writes about. So that there's a secret kind of way in which he writes that maintains his subjectivity but part of the way in which he constructs himself as a subject, is to construct himself as an object. But remember that actually shouldn't seem very strange. Again, pointed it out to you before. It's a strategy of personal narrative. What's Franklin do in order to write his autobiography? He has to transform himself into two things. One is Franklin author and what does Franklin author write about. Franklin author writes about this thing called Franklin character so that there's a sense in which Franklin has to objectify his own life in order to settle it down and turn it into a story and talk about himself even if he talks of himself in the third, first person there's a sense that he constructed that kind of third person version of himself. So that's one of the things I think that Whitman's poetry brings out. In that sense it really is a kind of personal narrative. Anybody else find themselves disturbed by assume or anything that goes with it? Yeah. >> Well, I think that it seems pushy because it's very much like a disclaimer. It's like this [inaudible] that you have to buy into in order to find the rest of the poem, like, because obviously Whitman is not the reader but he's making this comparison, and he's making this argument that you have to believe in order to like buy into the fact that Song of Myself is not some of what Whitman is. Some of everyone. >> Good I think that's right. I mean he asserts and establishes the premise. It is going to be, he's going to have us buy it's going to be about himself. But it's also going to be about everyone else, and there's certain ways in which he's trying to establish, well I just want to point out to you that there's a certain kind of materiality here that he's talking about. Emerson would maybe use in these first three lines the word that Whitman deserves for the fourth line which is the word soul. I mean, Emerson thinks that what connects all of us together and what connects us to the divine is the idea that we have this divine soul. Whitman wants to make that a little more problematic because he thinks that gives short shrift something that he thinks is very important or integral to his self, namely the body. So the first way, you might say the first way in which he asserts our commonality is not by going the soul route but rather the body route. By literally talking about atoms. We are all made of the same matter and stuff. You can say that's his first premise. He's going to get to the soul and then he's going to make the whole question of the soul problematic by suggesting that the soul is something with which he is in dialogue. We get that in the fourth line. I loaf and invite my soul. I lean and loaf at my ease observing a spear of summer grass. Which would suggest to us that the soul is somehow not part of the I or there's some part of the I that's not including the soul or, it's an odd locution, and you should think of it in relation to Emerson. This is one way in which fundamentally he's deviating from Emerson. Emerson thinks that who you are is your soul, everything else is contingent, right. Everything else, even your own body belongs to that not-me. There's a certain way in which Whitman is turning it around at least for the start and relegating the soul to the not-me. At least in terms of the subjectivity of the soul as it's first laid out here. Did you have a, did you want to say something? >> Yeah. I saw that as kind of acknowledging good to me what good is to you. So as you're saying the commonality, like is he saying that the good also belongs to you as well or is he just saying that, >> Well I think that once you start to pull these lines apart, they start to mean not exactly only what you thought they meant. Every atom belonging as good belongs to you. It just might as well belong to you or it's could be, but then if you start to think about it. Every atom belonging to me as good, belongs to you. That would seem a little artificial but is it excluded. The idea that, well he doesn't say might as well belong to you. He sticks that word good in there which creates certain kinds of syntactical resonances. That's part of what we have to look at. I was just talking in office hours today to somebody, an economics person in one of my other classes, completely baffled by the reading of poetry, so just of just talked to him by the way. I mean if you come to Whitman without thinking about the other stuff that we've been thinking about, it can look baffling. You might not understand why is it that this is poetry and not prose. What if you just ran it all together, wouldn't it look like a piece of prose. And maybe you could do that. Not all of it would work that way, but I think part of what we need to understand is that Whitman is trying to express something. That, as Emerson says, expresses the kind of, that encapsulates the entire country. The experience of the country. He's trying to get it all down on paper you might say. So that forces him to explode previous forms. All the other poets have not done a good job of capturing what is distinctive about the United States. Some of them complain that it's an unpoetical country. Some of them are just flabbergasted by what they see. Emerson says the same thing. We're looking for the poet. Where's the poet. Part of the problem, as he suggested in the American Scholar, is that we're too sycophantic when it comes Europe. We've listened too long to the courtly muses of Europe. But we don't have courts. We don't have King's courts heres. We have law courts. We have other kinds of things. We have other forms and Emerson wants to say that those are poetical. Banks and tarrifs and business and all this other stuff is part of the poetry of this country. Whitman understands that as well. And a part of what he's doing, you might say, is exploding forms, but once you start to understand that and realize that. I really want to stress something that almost was a throwaway last time and I think is really true. When we look at every other poet that we've looked at up until now, we're interested in what they do with metrical feet. We think about how long their lines are. Are they pentameter lines, tetrameter lines. Was it anapestic tetrameter or was it iambic pentameter as in Wheatley or what is it that Taylor is doing to these things and how come it doesn't scan so well. Ask yourself about scanning Whitman. What would it mean to scan a line of Whitman. What would it get you. If I asked you to do a close reading of Whitman, which of the, I mean I sort of said before do a kind of checklist. Look for stanzaic form, look for line scheme, look for meter, are those things going to be of use to you when you're reading Whitman. Maybe not. So what is going to be of use to you. Maybe some of the other things we were looking for. Larger rhetorical form. And also moments when you can just isolate the fact that certain words are placed in kind of ambiguous relationship to one another. So that there's a kind of ebb and flow of a line which almost even in a line it seems to shift its meaning depending on how you read it. I think that's one of the things that you must understand about Whitman. The poetry is designed, his metaphor is the leaf of grass, but the poetry itself is designed to mimic water. It ebbs and flows. It has big bursting places and times when it's quiet. And he does, there is a lot of imagery of water and rivers and other kinds of things going on in the poetry. So it has different styles and they're all encompassed. So part of what I think you need to do when you read his poetry to really get decided is to think about the larger project, think about how he got here from where other people were. I mean why is this not, why would you, if we put this on the exam you'll know it right? You're not going to mistake this one. Oh by the way, I should mention that in terms of knowing it there will be passages on the final, but being able to ID them is no longer the point. Because it's very distinctive, I mean, all of these writers are except for possibly where we could seek to confuse you between Emerson and Thoreau and promise you we won't do that. So, Whitman is very distinctive. In some sense in this part of the course, he's by himself as a poet. And in some sense we want to say he is both summing up a poetic tradition and also contradicting it. And that's a way that a lot of poetic traditions work. Poets often repudiate what's gone right before. Sometimes trying to create something new but sometimes openly looking back to earlier forms. You might want to think is Whitman only repudiating what's gone before or is there any way in which he's looking back to something. Can you think of any other poetic forms that you know about, not necessarily just from within the confines of our syllabus, that Whitman might be invoking in this poetry? Yeah. >> Free verse. >> Well, yes free verse is what he's doing alright. There's a sense in which free verse is part of what Whitman is helping to create. Poetry in the United States doesn't look the same after Whitman and in part because he become, he creates this thing called free verse. So that's of the moment, but within the free verse. I guess what I'm trying to point out to you is that it looks like free verse. And you could just say, well anything goes. In the same way that people who look at modern art think, well my three year old sister could've done that one. Oh what does it take to just draw a bunch of lines. What does that mean, that painting that's just purely white. But it means something different if you look at it just as an object than if you look at it as the last in a series of objects to which it refers and which it contextualizes. It's, I think that both of them are valid responses. I see a white painting on the wall. Looks like a white painting on a wall, but then if I see it has a title and refers back to something else, I get another response. And if I know things about the things to which it refers, I have perhaps a richer meaning than I am able to construct. I don't think the first meaning is wrong. It's just not as complex. Just like if you're reading Moby Dick and you don't know that the book called the Bible exists, your meaning is going to be a little bit rich as somebody who does know that a book like, called the Bible exists. And it's going to be a little less rich who actually knows what's in the Bible and can get all the dirty little jokes that Melville has implanted, because he doesn't believe that people are actually going to look stuff up. So, okay let's talk a little about other forms that are invoked. Yeah. >> Virgil's Aeneid is the first first line. >> Sure why not. >> Why not? >> Why not. Sure, absolutely. [ Laughter ] I sing of arms and a man. Interestingly, he's talking about himself, but why not sure. We could even do that. Yes, I would that isn't necessarily, that's probably not the first thing you thought of though right when you read it. That's the first thing you thought of? It could be. >> Yeah it was. >> Okay. Good, that's fine. I think that if it weren't the first thing that you thought of, it might be something that you might think of later as you start to realize what's going on in the poem. I mean, you could think of it first if you think, okay we know this is a poem. It's meant to encapsulate an entire culture. And gee isn't that exactly what the form of epic does. It's meant to encapsulate something about a culture. Now Virgil is really different right. I mean there's a sense in which Virgil is kind of narrative. It's full of inset stories but it's pushing a particular narrative together. It's about, the Aeneid is about, you find yourself in the middle of a story but the story really begins with the sack of Troy and moving forward to eventually found what's going to turn out to be Rome. So it's a kind of narrative but a national thing. Whitman is doing a national thing too. So I think one of the things we would say is, Whitman is trying, one of the things he's trying to do is, one of the way in which he's looking to older poetic forms is, he's leap frogging all of these forms and if he finds an American example it's not going to one that's going to be to his taste. If he even knew Barlow's Dunciad, it's exactly the kind of poetry that he would not be want to try, but he would want to write an epic, that's in some sense is a new world epic not a sycophantic neo-classical version of an epic. So yes, there's probably an echo of [inaudible] in these lines. But think about the cataloging that goes on inside the poem. All of those different catalogs of things, that he sees people, that he sees, it's a little less remarkable than Virgil, although Virgil does it as an echo of Homer. There's also this epic cataloguing that goes on in the classical epics by Homer and Virgil. I mean, that's part of the technique to show you who's out there in the battlefield. What they're wearing. Just a catalogue of stuff. And that's one of the ways in which epic seeks to get its entire culture into the poem. So I think one of the things we would immediately say is that what Whitman is doing is signaling a kind of democratic project, but it's a project that has certain reference points and epic would certainly be one of them. Both Homeric I would suggest and Virgilian. Anything else? Are there any other constraints that we might find that Whitman is trying to put on himself? Yeah. >> I don't know if it's a constraint, but I guess the conventions of classical music is something. I get the, like you said before, the motions of water and their arising and swells and use of punctuation established, like, pace in multiple ways. >> I think you're absolutely right. Music is one of the things Whitman is trying to do. To rethink his project. I mean, he was a big fan of the opera. And you would say there's something operatic about what Whitman is trying to do in terms of big gestures. There's almost like, it has a structure of an opera where we have moments that are big showy set pieces, the kind of opera that he would've been listening to in the middle of the 19th century. Just, you know, not quite going to be Wagnarian. It's going to be something else, more like operas that have kind of set pieces and then moments of recitative. I mean there's definitely a model that he's using. So you have the kind of different moments in this thing, where you have different cataloguing moments. Those are on the one hand maybe epic on the other may function as a kind of recitative. You have other very kind of lyrical and loud moments that are lyrical soft moments. You have moments of narrative, dynamic things that are going, all these are part of whatever metaphor you want to use. As part of the ebb and flow of it or as different kinds of set pieces within a larger poem that tries to do something beyond what literary normally does. Epic invocation is one of the, music is definitely another one. Thanks to the both of you. Anything else that we want to say about this? Yeah. >> I think it's interesting that I noticed that there was no stanzas or sections at first. It was almost like he put his constraints on himself after he had written the poem. [inaudible] like structure. >> I think that's very, it's hard to know exactly why he breaks it up into these set stanzas. If you were going to go and compare, I mean I showed you one little moment where the word Manhattan is interpolated into this version of it, but yeah. There's a sense that one of the things he does is he possibly reigns in his verse a little bit. He makes it look a little bit more conventional. He takes out some of the phrasing that is a little bit, I don't know marked by youthful exuberance but people think. I mean I already told you about the scholar that writes a gay life of Whitman and in order to find the poems that illustrate, he has to go to kind of not even, not this one, sort of the versions before this. So there's a certain way in which Whitman himself is editing his own canon. That's one of the things that's kind of remarkable about him as a poet. He takes his set of poems, enlarges it over his career, but keeps working on them. Little bit like George Lucas, yes. >> I guess is it kind of like a bloated soliloquy? >> Well yeah, sure. I think that's another good thing. We've talked a little about, remember Melville earlier in the course, we'll come back to it again. But Melville thought of him as having kind of Shakespearean ambitions and I think Whitman doesn't tend to talk about Shakespeare as often, but certainly there's something dramatic. I mean, Whitman was a fan of the theatre, and he used to go and when he was young he would go to the old Bowery theatre down there, the working glass theatre. He writes about it later on as if it, kind of romanticizing all those young muscly men on the stage and everybody kind of, there's this democratic exuberance of the audience. So he knows about theatre and there is something theatrical about this. There is a sense that this is a kind of soliloquy writ large. And it has some of that kind, so a series of soliloquys, so I think that's good. I think Whitman whether you think of it as epic or music, opera, or theatre, there is the performative aspect of it right. Epics that were meant to be performed. The written version of the Odyssey is one version that we've gotten. Virgil's is different because he's evoking the for written context. But likewise, theatre and music both of these I think there's this aspect of performance that's definitely part of what Whitman's project. Even more than what we would say in some of the other poetry. I mean, you do, don't you get the sense that you're reading Bryant's Thanatopsis. It's not really meant to be performed. It's a kind of quiet meditation that you probably read to yourself. And certainly Taylor's poetry are all personal private meditations that weren't meant to even be seen by anybody else. I think those are three very good things to bear in mind. Anything else that we might like to say about Whitman? One of the things, last things that I would suggest to you is that like both Emerson and Thoreau, Whitman is interested in a largeness that includes the possibility of self-contradiction. So I just wanted to point out one passage to you. This is line 1323 towards the end of the poem. Well we can even go back to the beginning of that whole section there. Section 321. The past and present wilt I have filled them, emptied them, and proceed to fill my next fold of the future. And again there's a kind of weird thing that's going on there. I mean, Emerson says we got to tyrannize the past, make use of it, but what does it mean to make the past wilt and to be filling up the fold of the future. Listen all up there, what have you to confide in me. Look in my eyes while I snuff the sidle of evening. Talk honestly. No one else hears you. And I stay only a minute longer. It's clearly he's constructing readers and listeners out there, with which whom he is in dialogue. Do I contradict myself. And this is the line I wanted you to see. Very well then. I contradict myself. I am large. I contain multitudes. Many things in me. But you could also read it as, I contain multitudes. I keep them pinned up, penned in. Again there's that one word, there's the kind of, the kind of productive ambiguity that you find in Whitman. There's something tyrannical about being the tyrannizing poetic eye and yet maybe what we need is the tyrannizing poetic eye. Yeah. >> When there's this coming at the end of this poem, the idea of him creating a naturalidge [assumed spelling] for America. It's sort of like, he's conflicting himself because he's talking about himself when referring to an entire country of people and the words multitudes there could convey the sense that it is America that conveys, that contains the multitudes, but it still is one. >> That's right. >> At the same time, people [inaudible] individually. So I think there's that contradiction. >> I think that's great. I mean there's, one of the things we say about Whitman is that, at least this is the way that I tend to read Whitman, is that unlike Emerson, he takes up the kind of cosmopolitan opportunity that's there in the country. I said that Whitman liked to walk around the Lower East Side. He didn't find himself distressed by all the immigrants and the people who were coming to this country. He works them into his poetry. Now there's a sense in which you could think about what the dynamics of this are. What did I say about the melting pot before, everybody goes in whatever they are, and they come out Presbyterian. Well everybody, all the voices go into here and they come out Whitman, which you might say is true of Emerson too, he's very eclectic in his rhetoric and it all comes out sounding like Emerson. But I think for me, there's a greater attention to difference and to bridging gaps and to the energies you might say of the city that kind of work their way into even the lines of the poetry that aren't about the city, that I think of as in some sense deeply cosmopolitan in nature. And again let me remind you, well let me let you hear this. >> Centre of equal daughters, equal sons. All, all alike endeared, grown, ungrown, young or old. Strong, ample, fair, enduring, capable, rich. Perennial with the Earth, with Freedom, Law and Love. >> That's from a wax cylinder recording and it's believed by most scholars to be the only recording of Whitman that actually exists. So that's Whitman's voice when he's an older man in 1888. But again there's that idea of being equal, equal daughters and equal sons, all, all alike, endeared, grown, ungrown, young or old. Strong, ample, fair, enduring, capable, rich, perennial with the Earth. There's a sense in what Whitman wants to be is a kind of a couple things I think. One is a kind of cosmopolitan presence that's able to engage difference and appreciate people that are different from one another and yet he's also I think a poet of union. And sometimes he wants to bring all these people together. For me, the difference between Emerson and Whitman is that, Emerson wants to, Emerson is not interested in the details of other peoples' lives, in the details in which people experiences are different. He's not even interested in the details of his own bodily experience at least not rhetorically. Whitman is. He's interested in all the things that go into life and he's trying to make them all part of experience that we can, we can appreciate. I mean, late in the poem he talks about all these secret thoughts and unvoiced things people are afraid to say, and he wants them to come out in the open. So for me, Whitman is a lot, adopt a kind of perspective that we might really think of as cosmopolitan. This really comes from David Hollinger, intellectual historian from Berkeley, who talks about cosmopolitanism in opposition to multi-culturalism. Multi-culturalism is this idea of very separate traditions. African-American, Asian American, women's writing, all these things separate. We say that they all count for something. They all have dignity. And we keep them separate. We don't want to make inroads from one discipline from another. We don't certainly want to tell somebody that we don't like their cultural practices. Cosmopolitans want to engage in conversation among other things. They appreciate difference. Difference is not a problem for them. For someone like Emerson who I would call a universalist, difference is a problem. He solves it through the question of the soul. For multi-culturalists, difference is also kind of a problem. We extensively appreciate difference but we want to keep the people who are different, different. We don't like mixing if we're multi-culturalists. We need to keep those African American syllabi pure. We need to keep that Asian American department running. Whitman might say, let culture do what cultures going to do. Which is going to be a lot of creating and groping and miscegenating, and I think Hollinger gets into some of that too. Cosmopolitanism urges each individual and collective unit to absorb as much varied experience as it can while retaining its capacity to advance its aim effectively. I think that's a very good description of what Whitman is trying to do. His aims are democratic and ultimately you might say, his aim is to promote the idea of union. Both literally in terms of the United States and metaphorically. Emerson is aware of the difference, the differences of people. He doesn't write about it so much in his own pieces, but in his journal he does. In his [inaudible] he writes in 1845, asylum of all nations. The energy of Irish, Germans, Swedes, Poles, and the Cossacks, and all the European tribes and the Africans, the Polynesians, we'll construct a new race, a new religion, a new state, a new literature, which will be as vigorous as the new Europe which came out of the old smelting pot of the dark ages, and that which earlier emerged from the Pelasgic and Etruscan barbarism. But this is hard for him. There's a kind of, there's a way in which at other moments, Emerson is bothered by what he thinks of as the kind of barbarism of some of these races which he's not sure they can overcome. You can look for moments in that in Whitman when Whitman seems to fall down on the job and is not as cosmopolitan, but I think overall Whitman is somebody who's pushing the envelope of what it is possible to think in the middle of the 19th century. And so, he really is a poet. I think it's not accidental that much of his experience comes from the streets of New York. A poet who is able to appreciate differences and take different people on their own terms, but I do want to suggest that Emerson is interested in this kind of commonality. He overstresses commonality whereas I think Whitman is, I think this idea of universal mind, whereas I think Whitman is much more interested in a sense of diversity than that. We are a set of minds and he's trying to bring them all together. Emerson's interested in creating something called universal history. And I would ask you to think finally about the end of this poem and think about how this statement about the generalizable nature of all private facts, what does that tell us about how to read Whitman if anything. Is Whitman at the end of Songs of Myself deviating from this project. He's interested in timelessness right, he's interested in trying to capture moments of local particular experience that are going to resonate. If you read Crossing Brooklyn Ferry, he articulates something that's clearly wrong, I mean we don't have the same experience that he has. We don't cross the East River on the ferry very much anymore. We have other ways of going, subways and bridges and other things. But Whitman is certain that there's something timeless about that experience. That he can connect to you because you're having essentially the same kind of experience even though it's going to differ in its local details. So look what he says here, the end of the poem. The spotted hawk swoops by and accuses me. He complains of my gab and into my loitering. He can poke fun at himself at the end of this large project. I too am not a bit tamed. I too am untranslatable. I sound my barbaric yawp over the roofs of the world. And I think that's a wonderful figure for what this poem is. The cry of a hawk, the barbaric yawp. Think about barbaric there in relation to this quote of Emerson. We want to emerge from barbarism, that's the point for Emerson. Whitman wants to in some sense to delight in barbarism. I want to stress that in a way what Whitman is interested in is in the kind of barbaric nature of city experience and in what Tom Bender from the history department is called the historic cosmopolitanism of New York, part of urban experience. So you see, think about what happens at the end of the poem as Whitman decides that he's finally, in so far as he's embodied the nation or represented the nation, he's finally sort of gone into the very dirt and soil of a nation at the very end. I bequeath myself to the dirt to grow from the grass I love. And the grass for him is this great democratic figure. The leaf of grass, each one is special. Each one seems to be alike but put them all together, you get a, you step back and you see what a field looks like. But that doesn't stop him from appreciating a single leaf of grass either. I bequeath myself to the dirt to grow from the grass I love. If you want me again, look for me under your boot soles. And that's maybe a kind of, I don't know if it is, it's a kind of nod to Edward Taylor. Edward Taylor's talking about how you're a crumb of dust. Well, Whitman by the end recedes into this kind of crumb stuff. Dust is going to be under your boot soles in the Earth itself. You will hardly know who I am or what I mean but I shall be good health to you nonetheless. And filter and fiber your blood. Failing to fetch me at first keep encouraged. Missing me one place, search another. I stop somewhere waiting for you. So there's a sense of time but it's not quite the same as this universal time. You should think for yourself about what it is. What's the difference between Emerson's universal history and this notion of history that Whitman is trying to evoke. Now, thinking about union in the moment that he's writing this at first, 1885 is five years after the fugitive slave law. So you cannot think about union without thinking about the problem of slavery in 1850, in New York and anywhere in the country at that moment. So that, you might say that if I suggested to you that one of the subtexts or one of the cultural contexts that we need to keep in mind for a full understanding of Whitman's poetry is a situation in the New York streets, the immigration and the aftermath of the Irish famine, the crowding on the Lowest East side, the question of what it is that immigrants are going to do to this country and I've said to you that Whitman embraces that change rather than resists it. Another crucial cultural context is the fugitive slave law and its aftermath. So the fugitive slave law is part of a larger pattern of acts, well you might say of Congressional debates, that finally brings the slavery question to a head. It had sorted started to become a problem in the national imagination with the onset of the Mexican American war. And the fugitive slave law becomes a part of this larger package of legislation that becomes known as the compromise of 1850 that was meant to basically keep the union together. That was the design. It was to keep the nation together from splitting off, to keep the south from seceding. And as I said, part of the problem that arose with the Mexican war which ended in 1848 by the treaty of Guadalupe, Hidalgo. And had a set of interesting consequences, as a result of, well let's think back before the Mexican war what we have is a proposal in Congress from David Wilmot who's a representative called the Wilmot Proviso which said that any territory that was to be gained from a conflict with Mexico, which was already looming, would be free, period, no slavery in them. And this was, it caused a lot of heated debate in the course of the beginning of the war, during the war, and finally after the war itself. It was never passed, but one of the things you can see is that as a result of the Mexican war, a ton of new territory becomes part of the United States which had previously been Mexico is now part of the United States. So all this stuff over here. This is Mexico here, all this stuff here is ceded to the United States from Mexico. So all of a sudden the people living here are part of the United States and many of them previously had thought of themselves as Mexicans. And of course they are promised equal rights as Americans blah blah blah. That doesn't really happen. Gadsden Purchase brings this. Texas has already been annexed by the United States in 1845. It's a whole bunch of new territory out here. And so the question is, is this stuff going to be slave or free, and it causes all these debates in the United States Congress. The President at the time of all of this is Zachary Taylor who is a hero of the Mexican war. And Taylor basically is someone who wants to have both of California and New Mexico admitted to the Union. That's one of the things he wants, but he wants it to be admitted as free states. So this causes a big problem. The aging Whig party leader Henry Clay offers a series of compromises. So the Whigs, the political landscape is a little bit different. There is a Democratic party, the Conservative party tends to be the Whigs, Republicans are just forming. And in the end, Republicans become the main anti-slavery party with Lincoln. At this moment, it's the Whigs are sort of the conservatives and they are the, Henry Clay is interested in a series of compromise resolutions that can be a kind of alternative to the Wilmot Proviso. So he proposes that California be admitted as a free state, but, he says, there should be no restriction on any of these other territories that are gained from Mexico. And he also proposes that a more stringent fugitive slave law be passed. Now there's been a book, on the books, there's been a fugitive slave law that's been in effect since 1793 but it's a national law that supposed to be enforced by the states. So it doesn't have teeth. The states are supposed to enforce it, but some of the states have regulations prohibiting some of the, especially in the North, prohibiting any of their law enforcement people from enforcing that law. So Clay calls for a new law, one that's going to have federal marshals be the ones that are enforcing it. And this creates a series of debates which are, for students of Congressional history, one of the prime moments for speechifying. John Calhoun, this old guy, he is the aging I don't know what he's kind of like a 19th century version of Strom Thurman. Does anyone remember Strom Thurman? But he's a southerner and he speaks against the compromise, and this is what he's worried about. He's worried about the fact that if these states are allowed, any states are allowed to come in as free, what will happen is that there will be a numerical majority of states that are free in the Senate and because the South's population is bounded by its territory and will not grow, there will also be a majority in the House of Representatives which is based on population. As a result, he believes that the inevitable tide is going to turn against the south. There will be a tyrannical northern majority and eventually, he thinks it's inevitable that, slavery will be abolished and therefore the South's way of life will be completely destroyed. So he says, if these measures pass, the South will in order to preserve itself, its civilization, will have to secede from the union. There can be no compromise without secession. Into this fray steps Daniel Webster who features, who's featured in Emerson's address on the fugitive slave law. Webster is a senator from Massachusetts which is a state that's opposed to slavery, and he gives a famous reply to Calhoun in which he says, there is no such thing as a peaceable secession. You secede, we go to war. Webster doesn't want that. Pretty much nobody wants that. So, Webster had opposed the Mexican war. He wasn't an imperialist. He had supported the Wilmot Proviso, but he feared the possibility of disunion even more than he disliked slavery. He really feared civil war. So he sides with Clay and pleads for the compromise of 1850 and for, what he calls, a charitable spirit towards the south. Because he does agree with certain southern complaints that they have about the way abolitionists have been portraying their society. He also supports Clay's demand for a stringent fugitive slave law, but there's a kind of pragmatic bent to his thinking. He thinks look, the Western territories are radically different in climate from the South. The South's climate is conducive to crops like tobacco and cotton that need kind of workers like slaves to pick them and produce those raw materials. Not going to be true in the West, he says, not going to be true in California either. It's basically a moot point. Those will never become slave cultures in the way that the south has. So why would we break up the union now over what is practically a theoretical point. In the midst of all this, Taylor dies. He doesn't stay in office very long. And he's succeeded by. He's succeeded by. He's succeeded by. >> [inaudible] >> Yeah. >> [inaudible] Fillmore. >> Never never good to be 13th, they always forget you. He's a buddy of Clay's and he sides with Clay and the compromise passes. So that is what Emerson is writing about. And in its final form, the compromise of 1850 contains four provisions that should concern us because they're related to slavery. It's a big ominous bill. We're familiar with those these days. We've always been. First one is, California is admitted as a free state. The rest of the Mexican cession is organized into two territories which are called New Mexico and Utah with no federal restrictions on slavery. They can do what they want later on. The slave trade, but not slavery, is prohibited in the nation's capital. And, there is a stringent fugitive slave law in addition to requiring that the northern states capture and return slaves to their owners in the south. The law even goes further and deprives blacks of jury trial or the right to testify in their own defense. It really sucks. And it gets people in the north absolutely outraged. What they start to realize is they can't sit by any longer. Now, Massachusetts is party to slavery. Of course this is something that's always been true. It's part of what Harriet Beecher Stowe will dramatize for us. That it's a national economy. The south was never exempted from benefiting from the slave trade in so far as it bought raw materials, it was even part of the same national system. But now what's come home to these people is that they are by law required to abet the slave catchers. Everyone in the north now becomes a slave catcher. This and there are other things. I mean yeah the slave trade goes on in District of Columbia and even California has slavery. Indians are enslaved in California. So it's full of problems. It doesn't actually solve anything, and you might argue that the compromise of 1850 makes civil war inevitable rather than preventing it, which just takes a little bit of time. It creates a kind of veneer of peace but one that isn't going to last. The fugitive slave law is tested right away in Massachusetts. A slave named Thomas Simms is there, and he's captured and then there's a restraining order and it goes to trial, and the chief justice of Massachusetts returns Simms to his owners in the south. Does anybody happen to know who the chief justice of Massachusetts was in that moment? This guy, Lemuel Shaw. Anti-slavery guy, but he supports the Constitution. Fugutive slave law is the law of the land. He has to find it, he doesn't find it unconstitutional. Do you know who this guy is? He has a famous son-in-law. >> George Bernard Shaw. >> No. His son-in-law has a different name. It's Herman Melville. >> Oh. >> Wow. >> We'll talk about this again, but in so far as context, everything contexts, slavery is not something that simply an abstract thing for Melville. His father-in-law out rules in what is arguably the biggest slave case to date, and Melville is somebody who is aware of his father-in-law's cases. The term monomania which figures largely in Melville's Ahab or Ishmael's descriptions of Ahab comes from one of Shaw's cases. We'll get to that. I just want to strike that note now. Don't forget it. Emerson is particularly bitter about this, and we go back to thinking about the American scholar. Remember what he says there that men in history are bugs, are spawn, all of them behold the hero or the poet their own greed and crude being and are willing to be less, are content to be less so that may attain its full stature. Later on, he goes on in his writing he goes on to develop a concept of what he calls the representative man. Somebody who embodies self-reliance, a kind of hero. He wishes we were all representative men. One of these representative men is Daniel Webster. Webster you might say is one of Webster's culture heroes which is why it's particular disappointing for Emerson to see Webster support this compromise and this fugitive slave law. And if you have a copy of the essay, you might probably bring it now and I'll put some of it on the screen. And I want you to look at the way it begins. This is the second version of the address, shortly after 1850, I mean I think the first of these addresses is in 1850 when Emerson decides he has to speak out on this question. So, Emerson wanted to be aloof from particular public questions. Political questions. He wants to write a philosophy that's universal in some way. Find that he can't do that in good conscience anymore. Slavery is something different and the fugitive slave law has implicated everyone and he has a moral duty, he believes, to speak out against it. I do not often speak to public questions. They are odious and hurtful, and it seems like meddling or leaving your work. I have my own spirits in prison, pirits in deeper prisons, whom no man visits, if I do not. And then I see what havoc it makes with any good mind. This dissipated philanthropy. But he has to do it. Anyway, let's turn the page a little further on, page 76 when he actually gets into the swing of things and starts talking about Webster. This is about the quote that's on the board here. Here's thinking about an appearance where he saw Webster speaking at Bunker Hill. He says, there was the Monument and here was Webster. He knew well that a little more or less of rhetoric signified nothing. He was only to say plain and equal things, grand things if he had them. And, if he had them not, only to abstain from saying unfit things, and the whole occasion was answered by his presence. It was a place for behavior much more than for speech, and Webster walked through his part with entire success. Webster, culture hero. And he goes, he's a good speaker right. His wonderful organization, Emerson writes, the perfection of his eloction and all that thereto belongs, voice, accent, intonation, attitude, manner, we shall not soon find again. Then he was so thoroughly simple and wise in his rhetoric. He saw through his matter, hugged his fact so close, went to the principle or essential, and never indulged in a weak flourish, though he knew perfectly well how to make such exordiums, episodes, and perorations as might give perspective to his harangues without in the least embarrassing his march or confounding his transitions. In his statement things lay in daylight. We saw them in order as they were. And think about the things that Emerson has said in the American Scholar about man thinking, right, Webster is man thinking. We're watching, thinking, in action in contrast to the cynic dopey command. The partial man in the divided or social state. Or think about Thoreau's talking about little statesmen and divines who can't get back and see the larger picture. Webster was not that. Webster was a big statesman. He was able to see things. If you think about Emerson's belief that a true theory will be its own evidence, it'll explain all things, there's something of a resonance of that here. We saw things in order as they were, he says, though he knew very well on occasion how to present his own personal claims yet in his argument he was intellectual. It's no mean egotism that's going to be here. Stated as that pure of all personality so that his splendid wrath when his eyes became lamps with the wrath of the fact and the cause he stood for. His power of that like all great masters was not in excellent parts. Again think about what Emerson says in the American Scholar. But total. He's a total guy. All the parts are coming together. He had a great and everywhere equal propriety. He worked with that closeness, that hesion to the matter in hand which a joiner or chemist uses. And the same quiet and sure feeling of right to his place that an oak or a mountain have to theirs. Webster is almost a kind of force of nature. Think about that. The goal of nature, defining a true theory that's its own evidence. Emerson says that Emerson seems to have that kind of rhetorical power. He can make his argument seem self-evident. And Emerson, I don't know how Emerson is at this, but we criticized Emerson frequently for being nevertheless, despite what he says, a kind of fragmentary thinker. Somebody who's assembled things but maybe they don't all go together. There's all that kind of leaping thought and those contradictory moments. That's not what we find here in Webster. Webster creates a sum total which has a certain kind of propriety. So far so good, but it turns out, and this is what Emerson is going to argue here, is that Webster has a fatal flaw despite all of this. A flaw that we might think of as his moral sensibility, and as the essay goes on a little bit, you might say Webster seems like somebody who, well Webster seems like somebody who emerges as a kind of anti-Emerson. Or he lacks certain things that Emerson has. He seemed, so he goes, he seemed born for the bar, born for the senate, and took very naturally a leading part in large private and in public affairs. For his head distributed things in their right places, and what he saw so well he compelled other people to see also. Great is the privilege of eloquence. There's something of that tyrannous eye as well. But the flaw comes in, and Emerson goes on to say that the history of this country has given a disastrous important to the defects of this great man's mind, and we're going to talk about those. Whether evil influences and the corruption of politics, or whether original infirmity, it was this misfortune of this country that with this large understanding he had not what is better than intellect, and the essential source of its health. It is the office of the moral nature to give sanity in right direction of the mind, to give centrality and uni, and I want you to go back and think again. To map this back onto the end of nature. The ideal philosophy, however smart it might make us, is not enough. It leaves us in the labyrinth of our own perceptions. We need something else. There it's kind of a spirituality. Spirit is the thing we are after not just idealism. There's a sense in which what Webster is lacking is a certain kind of spirituality. That's one thing. Another thing is what Emerson goes on to call, a kind of sterility of thought. So he says like, though the whole thing is nice and has an equal right, it's almost like Emerson says when I think about it, he didn't say anything that was actually that great. No aphorisms. The sterility of thought, the want of generalization in his speech and the curious fact that with a general ability that impresses all the world, there is not a single general mark. Not an observation on life and manners that can, not a single valuable aphorism that can pass into literature from his writings. And who of course is the master of the aphorism of maxim, if not Emerson, just go back to that Reebok's commercial, just lay them all out there. Who's so a man must a non-conformist. Speak related thought and prove blah blah, just that's what Emerson is really good at. Webster isn't. And I think the essay is making a kind of connection. There's a way that we kind of understand the flaw in the moral nature by understanding this inability to synthesize or generalize and distill things down to their essence. And you might say that's what Emerson's philosophy is all about in the end. Distilling things down to their essence and finding in that essence self-reliance. So that will be the way that Emerson will think about what I call his universalism. Webster is unable to do that and therefore, in the crucial moment when his moral sensibility is needed most, it fails him. If any man, Emerson says, had in that hour possessed the weight with the country which he had acquired, he could've brought the whole country to its senses, but he doesn't. So one of the things we might say about the fugitive slave law address is that it really is in a certain way a lot like, and this is Webster later on, looked like a colleague of mine in the English department. Sorry I didn't say that. He has a certain kind of, you might say that Webster has a certain kind of flaw which if we follow the logic of Emerson had thought of him as a kind of representative man. Somebody who's sums up the country becomes a kind of national flaw. We have a morally defective nature as our country. So you might say, what I want to suggest to you therefore, is that there are two different moments in Emerson's writing that we've looked at where he's testing his philosophy of self-reliance. I've already talked to you about one of them which is experience. Can we maintain our belief in the need for self-reliance in the aftermath of the most terrible grief. And I've suggested that what Emerson discovers to his chagrin, maybe even to his horror is, yes we can. We lose our son to a certain extent it's a tragedy but we are left fundamentally unchanged. And he pulls himself up by his bootstraps, said that even among the most bleak of these walks, there's God there and it gives him hope for the future. This you might say is a testing on the largest cultural grounds, and what we might say is that Emerson finds at the end of this episode, that the country really should listen to him. That the country is lacking in self-reliance, at least in so far as it is embodied in somebody like Webster. Does Webster go for what he knows to be right. Is he self-reliant. No. Webster goes for compromise and for Emerson that is a cultural disaster. Okay. Next time we will start to explore what the dimensions of that cultural disaster are. That thing that's left unsolved from the Declaration of Independence, that thing called slavery. Alright, thanks a lot. |
Open_Ed_Cyrus_Patell_American_Literature | American_Puritanism_I.txt | >> Alright, let's get started today. I wanted to start by reviewing some of the stuff that we talked about at the end of last time, which the piece by Bruce Kuklick should have helped you to understand and to put into context. The concept of type and anti-type is sometimes confusing to people. Remember I said last time that the type should be considered something like the dye that produces a coin or the stamper that you ink and produces the stamped image. It's almost like a reverse of the thing that is going to be produced. And it has no meaning really in and of itself. You don't care about either the dye that produces the coin or the stamper. You care about what's produced. In that sense, the type is not what we're interested in. It's the anti-type that we're interested in. The thing that the type produces. The thing you might say is the fulfillment of the potential within the type. So here's a little bit about the etymology, which comes from the Oxford English dictionary. And you can see that the definition is that which is shadow forth or represented by the type or symbol. And they in fact use the idea of the dye, and they talk about the way in which that's part of the etymology of the term. So once you get those things start, type and anti-type. Type, when you're thinking about the way in which the term typological human hermeneutics arose, it's a way of reading the Bible. A form of Biblical exegesis in which the Old Testament is full of types which are fulfilled by the anti-types which are present in the New Testament, and of course the anti-type of all anti-types if Christ himself. Later on, I suggested to you when the Puritans come to the New World, they start to get away from what you might think of as strict or of conventional notions of typological reading and start to use it as a method of interpreting their entire world. So that is, and in which they think the Bible as a whole now becomes the type, and they and their experiences in some sense are now the anti-types that the types of the Bible have foreshadowed and which can be interpreted in that way. Let me give you a quick example of this that comes from some reading that actually isn't I don't think for today, but we'll take a look at it. It's in the Norton anthology. It's from the journal of John Winthrop, and this is on page 159 of your text. And you can see how even the littlest thing can be subjected to a typological reading, although this I guess is somewhat unusual event that therefore begs to be interpreted typology. It's the little section of Winthrop's journal on 159 that's called overcoming Satan. July 5th, 1632, at Watertown there was, in the view of diverse witnesses, a great combat between a mouse and a sick. And after a long fight, the mouse prevailed and killed the snake. The pastor of Boston, Mr. Wilson, a very sincere holy man hearing of it gave this interpretation. That the snake was the devil. The mouse was a poor contemptible people, which God had brought hither which should overcome Satan here and dispossess him of his kingdom. Upon the same occasion, he told the governor that before he was resolved to come into this country, he dreamed he was here and that he saw a church arise out of the earth, which grew up and became a marvelous goodly church. Right, it's a strange little thing. How does the, we don't really know how the mouse defeats the snake, but you can see how something like that immediately what they'll do is, they'll go and think of a way to relate that to a kind of Biblical reading and then to take that Biblical reading and apply it to their own situation. You might say that in fact this little journal entry has the structure of a sermon as we'll see in a little bit, but in this case, the text comes not from the Bible but from this little anecdote of the mouse and the snake. It is then read and interpreted by means of the Bible and then applied to the situation of the Puritans themselves in the New World, which is exactly what Winthrop does in his sermon as we'll see in a little while. So, just want you to see the ways in which typological thinking can work, and part of what we'll do is investigate typology at work both in Bradford's history and in Winthrop's sermon. But first, let's make sure we've got some of these basic principles down. So John Calvin's institutes of the Christian religion is a founding text for the Puritans who we might say are one variant of Calvinism that arose in the aftermath of Calvin's life and teaching. Calvin places particular emphasis on God's sovereignty and therefore on the idea of fatedness, of providence, on the lack of human free will. And that's again something that we should keep thinking about, the way that the Puritans and others interpreted this is that in fact free will does exist in one sense. In the sort of earthly sense, the sense of individuals making choices, at any moment you're given a choice. That for you is the exercise of your free will. The only catch is that God always already knows how you're going to choose in that moment. So in some sense, it's already destined or providential. Calvin wants salvation not at all to rest on good works, which are not pendable, but on God's eternal and unwavering will. So, remember I talked to you last time about the covenant of works and the covenant of grace and the way in which as a result of the fall, evil comes into the world, or at least the knowledge of evil comes into the world. This original sin is something for which Adam and his progeny are all responsible. It creates a debt to God through disobedience that can never be fully repaid. Except that God sends down Jesus Christ to repay that debt at least for some people. So, that is the only way that salvation can occur, through the agency of Christ for a few chosen people. So this Calvinist to a doctrine of what we call election in which God has chosen some people for salvation and others are not chosen for salvation. And the Puritans believed that they are those who are elect. They are the ones who are chosen for salvation. So, the principles that are discussed by Calvin, in a philosophical way and not a schematic way, are codified into this variant, which is created in a meeting of church elders, Synod, which takes place in Dort in Holland from 1618 to 1619, which is the year before the Bradford, and the pilgrims go from Leiden to the New World. And, the Synod of Dort is directly addressing a heresy, an anti-Calvinist heresy, that they are worried about which is called Arminianism, which his named after the Swedish philosopher Arminius who emphasized the ability of sinners to respond to do good or evil as they chose. And therefore, he said, they would earn their way into heaven through good works, and this is something akin to other doctrines you would find in other versions of Christianity such as Catholicism. Good works have a certain kind of efficacy, not so for the Puritans. There is no way to earn your way into heaven, and that is a result of the total depravity of human kind. So remember we came up with this acronym tulip last time to help you remember these five different principles that come out of the Synod of Dort. The idea that after original sin, human beings are all damned, they are totally depraved. Their election is unconditional. There's no strings on it. You might say, there's no way of human intervention into the process of election. God has already decided, and there are no strings attached. It is limited. It's for some people and not for others. It's irresistible in the sense that you don't get to choose the time or the place when you receive grace, and when you receive, you really receive it. So that there's no resisting it at all, and once you have it, you have it. That's what they mean by the perseverance of the saints. Of course, what they also mean is that who the saints are is already set. God has already foreseen who the saints are going to be. So the elect already you might say have a place in heaven, the problem is they don't know. Or they can't be sure. No one can be sure that he or she is among the elect. That wouldn't be so bad except for the Puritans were also trying to create a polity, a social organization, and a politics that was based on these principles in which they wanted people who were full of church members were the ones who were running society. So you need to figure out a way to make the earthly church, what they called the visible church, resemble as closely as possible the invisible church. So this is part of the Puritan project in the New World. Today we'll be talking a little bit about the startup or the setup of this project. Next time, we'll be talking about the ways in which it starts to go awry. And, in which compromises need to be, but if you hold on to that paradox, how can free will and fatedness exist at the same time for individual human beings, and what kind of coded conduct can come out of this. I mean, if you're elect and you don't have to do anything good, why should you do anything good? Why don't you just get drunk all day, secure the notion that you're going to be elect in the time comes, when the time comes, you'll be converted and you'll get your one way to the big, to heaven. Why wouldn't you want to act that way if you were a Puritan? Sure. >> Maybe because the type of person that God would choose to be elected wouldn't have the desire to be that way. >> There you go. If he says, the kind of person that God would choose to be among the elect wouldn't have the desire to do that. That's right. You would sort of be calibrating what you wanted to do versus what you've been told the elect person actually does, so if you find yourself tending toward sinfulness and drunkenness, you would say oh boy that's not a good sign is it. I'd better mend my ways maybe the signs will be changing at that point. Or maybe my desires to mend my ways is a sign that I'm among the elect. People sometimes ask, well if you think that heaven is so great and things are really tough here on Earth, why don't you just kill yourself and get up to heaven that much faster? Well what's the problem with that? Yeah you'll be committing a mortal sin and therefore obviously you weren't among the elect to begin with. The thing you have to understand about these people, that I will try to get across today, is that they are fundamentalists and they really believe this stuff. They believe all of this. They want to believe. It's not even a matter of wanting, they believe it. The Puritans among the pilgrims, and they want it to work. So it's a problem for them when they come across paradoxes and contradictions and they try to figure out ways to work for, the idea that always is that humans are fallible compared to God, but it doesn't lead them to a kind of cosmopolitan understanding of fallibility. In other words, they have faith about certain things. That faith is predicated on the idea that they are fallible. That only God is infallible, but there's no questioning the faith itself. So, the people wouldn't want to make false confessions of conversion. They want real conversions to happen. They want to be among the elect, and really most of them believe that they will be among the elect. But, we'll see next time that there are problems that occur in this. Again, I'm setting all this up. I want to refer you back to again where the endpoint of the course is going to be with Moby Dick. That one of the things that Melville sees in Hawthorne's writing is a continuing engagement with these Puritanic ideas. He calls it a touch of Puritanic gloom. And when we read Hawthorne, you'll remember maybe. How many of you said you read The Scarlet Letter in high school? Okay. How many of you read The Custom House along with short story that's called The Scarlet Letter? Do you even know what I'm talking about? The Scarlet Letter in italics is a book that contains two things. One of them is a sketch called The Custom House, a long sketch called The Custom House, which is introductory to a long tale which in quotation marks is called Scarlet Letter which intended to be only the first of a number of tales that were to be included in this volume, but it got so long that it became the volume itself. So there's the novel The Scarlet Letter has two parts. In the first part, which I'm actually, going to read more closely than you're probably used to. In fact in certain ways more important to me than the long short story itself. Hawthorne has his moment of thinking back about what his ancestors are thinking about him as a writer. He thinks about the beetle browed Puritans who are looking over him. Like his descendants are, what is he a writer of stories? Why he might as well be a fiddler. Writing doesn't rate, and that's part of the dilemma for the writer like Hawthorne and Melville. Is there a sense in which there's something frivolous about writing. There's a larger sense in which the culture, as we talked about in the first day, the culture is inclined to believe that certain kinds of writing are better than others, and imaginative writing, what we now consider the literary, is not among those. So there's a kind of weird guilt that Hawthorne and Melville are working thorough, but they're also trying to change the status of writing, to make arguments on behalf of both the important and the worth, the moral worth, of the kind of writing that they want to do. Certain it is, Melville writes, that this great power of blackness in Hawthorne derives its force from its appeals to that Calvinistic sense of innate depravity and original sin. And now I think we're getting a sense of what that means, where it comes from. How it's embedded in a larger cultural logic. From whose visitations, in some shape or other, no deeply thinking mind is always and wholly free. And remember I pointed out all the kind of weird hedging that's on in there. But one of the things you might say is, that in terms of that model of dominant, residual, and emergent in the moment that we're looking at, in the 17th century. When a new culture is brought to the shores of the New World, it quickly becomes the dominant culture. Puritan New England dominates what is around it, and ultimately dominates the line of American literary history that Hawthorne becomes part of. So what we see here, you might say, is the continuing residue of Puritanism in a time when Puritanism should have been pretty much left behind in the wake of enlightenment. Still, there's something. Puritans were on to something. And now in the modern 19th century, we don't call it original sin, but we can't get away from it either. Something, some shape or other, has to be there in that place occupying original sin. Keeping us honest, making us sure of an understanding that we are limited beings. We no man can weigh this world without throwing in something like original sin to strike the uneven balance, so we're working our way towards that. So let's talk about Bradford now. What I'm hoping to show you in some sense is how Bradford's text is example of that typological way of looking at the world. And last time, we were talking about that excerpt from a pamphlet that's called Mourt's Relation that was prepared in 1620 or so just after the Plymouth Puritans had settled. It was thought to be co-written by Bradford and someone named Edward Winslow, and is named Mourt's Relation after a guy named George Mourton who brought it back to England saw it through the press. Winslow would later publish his own pamphlet that was called Good News from New England that was four years later in 1624. And so, it's a tract that takes the form of a history, but as I suggested last time, it may perhaps be presenting an overly optimistic reading of the circumstances that they're encountering. But it's really not too much different than the promotional tracts that are famously written by Captain John Smith trying to encourage immigration from England and Europe into the New World. If you compare Mourt's Relation to Smith's writing, many scholars believe that Mourt's Relation provides a more matter of fact, slightly more trustworthy account of things than Smith's does. One thing to know about Bradford was that he was a great linguist. He became interested enough to learn Hebrew in his old age. He knew Greek and Latin, but he wasn't at all interested in native languages and cultures as we will soon see. So that's one of the paradoxes you might say about Bradford. And I think when you read the history of Plymouth plantation, one of the things you see is where this idea of virgin land starts to come from. You get the sense that the wilderness is pretty much deserted except for a bunch of savages. That really all the people that there are in the New World who matter are simply the small group of Puritans, and of course that is a consequence of the way in which he's written the thing up. So, his thought has often been described as writing in something we might call the Puritan plain style. It seems to be just matter of fact. And that's supposed to be one of the hallmarks of Puritanism. As you'll see next week when we'll get to Puritan poetry, the Puritans actually rewrite the book of Psalms. They retranslate them in trying to get away from the kind of poetical translation they've brought with them from England. To try to get to something that's closer. They go back to the Old Testament passage that suggests that God tells the Israelites to create and alter for him and it should not be of hune or graven stone. They don't want anything carved. Richard Mather writes the preface to this new translation and says, because God's alter needs not our polishings. It's enough by itself. So we don't want figurative language. We just want a plain style, but of course, one of the things to say about that is that it's not exactly true or rather, their language is very figurative. The thing is that just it depends on a whole symbolic and figurative system that we're calling typology. So it's not a language that's full of rhetorical flourishes and metaphors, but it depends on a sign system, a system of symbols which means that really it's anything other than simply plain. Alright, let's take a look at the passage in Mourt's Relation. Again, and I wanted you to keep track of the dates, and while you're at it you should probably turn back now to the other thing I asked you to look at which is on page 114 of Plymouth plantation. And that's the corresponding passage, so what we basically see is that Mourt's Relation turns out to be a kind of draft for the history. Their retelling the same events. One of the co-authors of Mourt's Relation is the person who's writing this history of Plymouth plantation, and at the time that he's writing this, he is, the time that he's recounting, Bradford is the governor of Plymouth plantation and he's thinking back and retelling the story that's told here. So again, let's just take a look at it again. Wednesday the 6th of September, the winds coming east northeast, a fine small gale, we loosed from Plymouth. The appearance of much comforted us especially seeing so goodly a land and wooded to the brink of the sea. It caused us to rejoice together and praise God that had given us once again to see land. And thus we made our course south south west, purposing to go to a river ten leagues to the south of the Cape, but at night the wind being contrary, we put round again for the bay of Cape Cod; and upon the 11th of November we came to an anchor in the bay, which is a good harbor and pleasant bay. Right and we see all the stuff here. It's got all these different kinds of trees, which are individually named. It's a big harbor where you can bring in a thousand sail of ships. You have wood and water. The greatest store of foul that we ever saw. And he goes on. As soon as we could, we set ashore 15 or 16 men well armed fetch wood. We had none. They also go to explore. He repeats again he excellent it is. Like the downs in Holland but much better. The crust of the earth a spit's depth black earth wooded with oaks, pines, sassafras, juniper, blah blah. At night our people returned, but found not any person, nor habitation, and laded their boat with juniper, which smelled very sweet and strong and of which we burnt the most part of the time we lay there. So it's a place where they see it looks like a kind of virgin land at least at the start. It's got all these natural resources. It's wonderful. Its part, in other words Mourt's Relation takes part in that discourse of wonder that we were talking about last time. But they didn't see anybody unlike Columbus, they don't find people innumerable, and it takes them a while to meet up with the natives. For a long time, if you read into Mourt's Relation, one of the things that you see is they find little kind of remnants of things that people would've left, but they don't meet people themselves. Now, let's take a look in the Norton here, chapter 9 of their voyage and how they passed the sea and of their safe arrival at Cape Cod. So we see the date is the same. It's September 6th, these troubles being blown over and now being all-compact in one ship. They put to sea again with a prosperous wind, which continued to first days together which was encouragement under them, yet according to the usual manner, many were afflicted with seasickness, and I may not omit here a special work of God's providence. So, immediately you're getting this idea that there's something providential, good fate, that God has seen. There was a proud and very profane man, one of the seamen of a lusty able body, which made him the more haughty. He would always be condemning the poor people in their sickness and cursing them daily with grievous execrations. And did not let to tell them that he hoped to cast off half of them overboard before they had come to the journey's end and to make merry with what they had. And he would by gently reproved, he would curse and swear most bitterly, but it pleased God before they came half sea's over to smite this young man with a grievous disease from which he died in a desperate manner. And so was himself the first that was thrown overboard. We call that what cosmic irony or something like that. And you can see in that, that's God's providence, but we can see a little bit of vindictiveness in it. And that's something that we're going to be thinking about. What's the interplay of the charity that they're supposed to be pursuing, and some of the other impulses that come along with having in your mind that you are a chosen people. Let's take a look at the middle of 115 here, and let's take a look at what we find. Being thus arrived in a good harbor and brought safe to land, this is the first full paragraph on 115, they fell upon their knees and blessed the God of heaven who had brought them over the vast and furious ocean and delivered them from all perils and miseries thereof. Again to set their feet on the firm and stable earth, their proper element, and no marvel if they were thus joyful seeing why Seneca was so affected with sailing a few miles on the coast of his own Italy as he affirmed that he had rather remain 20 years on his way by land than pass by sea to any place in the short times so tedious and dreadful was the same onto him. So this isn't typology. This isn't citing the Bible, but it does have something in common with that. Again, it's that same kind of comparison that you see here. It's like the downs in Holland but much better. This is like the experience of Seneca but much worse, and that's the kind of comparison that characterized the history of Plymouth plantation. There's a sense in which what Bradford does is look back to the past as a way of showing how much worse the current chosen people have it. You think it was bad for them in the Bible? So much worse for us. Seneca he was a wise revered Stoic philosopher, he complained about just a little bit of seasickness so much around, just sailing around that Italy that never wanted to get in a boat again. But look what we did. We sailed all the way across the Atlantic. So much the worse for us. And then, there's kind of a moment that Bradford takes here. Right here after that. And it's a signal moment. A moment that in fact asked you to highlight it. And he's pausing rhetorically and he asks us to pause, and it's worth looking at. But here I cannot stay but make a pause and stay half amazed at this poor people's present condition. And so I think will the reader too when he well considers the same. One of the things you can see is there's a kind of awareness of a readership here. And that's kind of in part because Bradford is writing this in 1630 when Winthrop's group of Puritans is about to arrive, as we'll see that group of Puritans doesn't have exactly the same understanding of Calvinism that this group of Puritans does. There's no guarantee at this moment that the Puritan mission or the Puritan civilization here in Plymouth is going to survive. So Bradford is both describing and writing a work that's clearly of advocacy with a future reader in mind. Some people would say that future reader is his own people's progeny. Thinking about ways in which they are going to be justifying what they've done to future generations and using that justification as a way of inspiring those future generations to continue that project on. So he's aware of a reader, and here he actually addresses the reader. I think you're going to be amazed reader. If you pause, as I'm doing, to take stock and think about the situation. Being thus passed the vast ocean, and a sea of troubles before in their preparation as may be remembered by that which went before, they had now no friends to welcome them or inns to refresh or entertain their weather beaten bodies. No houses or much less towns to repair to, to seek for sucker. And one of the things to say right here is that this is taking place in the aftermath of the third chapter, which talks about the Holland experience, and some of those chapters that talk about it after that. I gave you a tiny little excerpt from that. It's on the black board site. If you haven't taken a look at it, take a look at it. It's a couple paragraphs long, but one of the things it does is it makes a sense of comparisons within Holland where there are towns extensively for sucker. But one of things you find is that Holland is just as treacherous in many ways. It's a hospitable place, it seems civilized, it is no good for the Puritans. People are against them. They are being persecuted even there. So you might say that's rationing up the stakes again, even the towns that were helping them weren't such great towns. Here don't even have that. It is recorded in scripture as a mercy to the apostle and his shipwrecked companies that the barbarians showed them no small kindness and refreshing them. And you'll see here that this comes in the Acts of the Apostles. That book of the New Testament that's written by Luke which talks about the immediate missionary work that goes on in the aftermath of Christ's crucifixion. So, the apostles go out as these current saints are doing and they go out and meet a bunch of barbarians and try to convert them, but guess what those barbarians gave them refreshments. These barbarians when they met them as, oh we haven't met the barbarians. He's talking on and saying, look, our situation is really terrible and then there's these barbarians. Oh, you haven't met the barbarians yet. Well, you will see that, now ask yourself why does he break the chronology right there? It's not there in Mourt's Relation. It took them a while to find these people. They would see signs, but they don't find them for quite a while. What's the point of it? One of the things you can see is again, it's a rhetorical moment. He's stopping and taking stock. He's addressing the reader, and how he's going to break chronology. He's going to foreshadow their future meetings with the Indians, and he's going to foreshadow them in such a way that you already know how to interpret those Indians when you see them. What are they? They're barbarians, and they're worse barbarians than Biblical barbarians because the Biblical barbarians gave the apostles sucker. And these savage barbarians, when they met with them as after will appear, were ready to fill their sides full of arrows than otherwise. So again, you can see that one of the things that Bradford is doing is subtly manipulating the history too here and it doesn't stop at that. If you go back to this, you'll see what the land looked like. It seems like a pretty good place full of natural resources. It's better than Holland. Like it but much better. The earth is a spit's deep, excellent black earth. You can plant stuff here. Ah well, but for the season, he tells us here in the history, it was winter and they didn't know the winters of that country know them to be sharp and violent and subject to cruel and fierce storms. Dangerous to travel to known places much more to search an unknown coast. And again look at this constant comparative logic. Bad enough if you have a map or you know where you're going but look what we had to do. We had no idea where we were going. And besides, what could they see but a hideous and desolate wilderness full of wild beasts and wild men. Again, on the date that he's talking about, he didn't know anything about the wild men. They hadn't really seen beasts, and he wasn't interested before with beasts. He was interested in all this good stuff. What's happened? What multitudes there might be of them he knew not, but it's here we're going to get another moment of typology. We're going to get a Biblical story. He'll be compared to the current situation. The current situation will be not only the fulfillment of that story, but it'll be a lot worse. Neither could they as it were go up to the top of Pisgah view of this wilderness a more goodly country to feed their hopes, and the footnote tells you that's the mountain where Moses could see the promised land. So he had some sense that the promises were to be fulfilled. These guys only had faith. For which so ever way they turned their eyes, telling a parenthetical save upward to heavens, that's the only sucker you're going to get. Right up there, can't look down here. The Earth, forget it. Only God. Which so ever way they turned their eyes, save upward to the heavens, they could have little solace or content in respect of any outward objects. For summer being done, all things stand upon them with a weather beaten face and the whole country full of woods and thickets represented a wild and savage hue. If they looked behind them, there was the mighty ocean, which they had passed. And now as a main bar and gulf which separates them from the civil parts of the world. If it be said that they had a ship to succor them which is true, but what heard they daily from the master and company but that with speed they should look out a place with their shallop where they would be at some near distance for the season was such as he would not stir from then until a safe harbor was discovered by them where they would be. And he might go without danger. And that victuals consumed a place but he must and would keep the fishing for themselves in return. So, don't look for a ship to help you. Got to find your own stuff. We're definitely leaving ourselves enough to make the ocean voyage back. We're not staying here. You guys are staying on your own really soon, the captain is telling them. Yea, it was muttered by some that if they got not a place in time, they would turn them and their goods ashore and leave them. Let it also be considered what weak hopes of supply and succor they left behind them, that might bear up their minds in this sad condition and trials they were under and they could not but be very small. And again going back to the conditions at Holland. It is true, indeed, the affections and love of their brethren in Holland was cordial and entire towards them, but they had little power to help them or themselves; and how the case stood between them and the merchants at their coming away hath already been declared. What could now sustain them but the spirit of God and His grace? May not and ought not the children of these fathers rightly say. In other words, you who are reading this book. Our fathers were Englishmen, which came over this great ocean, and were ready to perish in this wilderness, but they cried unto the Lord, and He heard their voice and looked on their adversity. Let them therefore praise the Lord, because He is good and his mercies endure forever. And then he ends this with this idea that the wonderful works of God. So you can see the logic of this. This is very Puritan logic in its typological thinking in action. This new-ish kind of typology. It's what you do as you look back to the Bible for precedent and then you think of your own situation in terms of that precedent. It gives you some hope, but you also understanding, and you might say, well gee what is he doing. He's saying, it's so much worse for us than it was for them, but again with the logic of the Puritans, you would see that's the cause in a funny way for even more hope because God afflicts those worst whom he loves best. He gave the Israelites a hard time. He's giving us a worse time. He really took care of the Israelites. He's really going to take care of us. Why, because we're living in New Testament time. Not only that, we're living in the fulfillment of New Testament time hence the final emphasis on God's grace, God's mercy. So that's Puritan logic for you. It's the same logic that goes from the covenant of works to the covenant of grace. Covenant of works, big fall, then risen up to grace end up in a higher place. So that's the logic. It's worse for us but better for us in the end. Just a couple of other things then. This is an example of the way in which one of the things that's going on is a kind of heightened level of abstraction. If you go back here, you'll see that he's quite interested in certain details of the coastline. By the time you get to Plymouth plantation, he doesn't care about those details anymore. It's all a hideous and howling wilderness. It's almost like everything that's actually there has got to be erased so that the Puritans can rewrite themselves onto the landscape. So here's just a little moment, but again it gives you this sense of it. This is from Mourt's Relation. It's about a battle when they meet the Indians. One of our company, being abroad, came running in and cried, they are men, Indians, Indians, and with all their arrows came flying amongst us. Our men ran out with all speed to recover their arms, as by the good providence of God they did. In the meantime, Captain Miles Standish, having a snaphance ready, made a shot, and after him another. After they two had shot, other two of us were ready, but he wished us not to shoot till we could take aim. Okay so it's a battle is going on. And then we find all of this. We heard three of their pieces go off, and the rest called for a firebrand to light their matches. One took a log out of the fire on his shoulder and went and carried it unto them, which was thought did not a little discourage our enemies. The cry of our enemies was dreadful, especially when our men ran out to recover their arms. Their note was after this manner. Woach woach ha ha hach woach. Our men were no sooner come to their arms, but the enemy was ready to assault them. Let's look at the corresponding passage of Plymouth plantation. This is on page 119. So from the cry of our enemies was dreadful. Here we get this. This is about 12 lines down from 119. Men, Indians, Indians, and with all their arrows came flying amongst us. Okay so we got that. Their men ran with all speed to recover their arms, as by the good providence of God they did. In the meantime, of those that were there ready, two muskets were discharged at them, and two more stood ready in the entrance of their rendezvous. I don't think Standish gets a shout out in this one. He's here, but we're too busy for that. We got to make it more abstract here. The cry of the Indians was dreadful, especially when they saw their men run out of the rendezvous toward the shallop to recover their arms. The Indians wheeling about upon them. But some running out with coats of mail on, and cutlasses in their hands, they soon got their arms and let fly amongst them and quickly stopped their violence. Now look at the slight difference in that passage alone. The cry of the Indians was dreadful. No sense that they had language, instead they are simply crying out. They're kind of wheeling about creating what seems to be a kind of chaos. And I told you Bradford was a linguist, but he wasn't interested in the native languages, and rhetorically he becomes less interested when he comes to write the history of Plymouth plantation. So, that little phrase there is excised, and all the Indians do is get to have a kind of crying. No sense that they were able to speak or communicate in any way. What's at stake here is creation of the Indians as a set of barbarians. And more than that we might argue, a set of Biblical type barbarians. Worse than the Biblical type barbarians, and you know what happens to barbarians in the Bible. You can get rid of them. God takes care of them for you or he licenses you to take care of them. And that's exactly what happens. Ultimately, the Pequot tribe is wiped out by these Puritans. And even their minister John Robison who's back in Holland writes to them and says, you know you might have converted a few before you killed them all. Or you might have used that kind of time honored method of killing their leaders and not everybody. And they basically write back and say, you had to be there. [ Laughter ] >> Right? If you'd been there, you would've realized those were not options, just massacre. So they're not, they don't see themselves as missionaries. They're done with that. What they see themselves as, that's in some sense different from the Spanish in South America who do have a sense of mission as well as a sense of murder, theft, and repine, but there's no missionary impulse really among the Puritans where it's really kind of submerged. You see that here. They just simply are caught up in their own Biblical drama. And they write the history of the New World as a continuation of the history of the people of Israel and the Christians thereafter. So these are the things I want you to see about Bradford. How he uses this set of rhetorical devices, they have to do with typology. They have to do with a heightening of the abstraction of the New World. The transformation of the world of Mourt's Relation, which is a world of wonder still, into a world of no wonder at all. A world of only savagery, barbarism, a wilderness that is howling and inhospitable. In some sense you might say, they erased what's there, sketched it all over in black so that their own light can shine out more brightly. That's the rhetorical thing that he's doing here, and it's very much in keeping with the kind. It's almost like a more hardhearted version of what we see Winthrop trying to do. There's a sense in what Bradford, in what comes across in Bradford in these particular passages is the darkness of the New World. Whereas Winthrop in some sense in a model of Christian charity is trying to concentrate on the light. And the image that he comes up with at the end is an image that has everything to do with this idea of creating light in the New World. So let's take a look now at Plymouth plantation, but there are a few things I want to tell you about Winthrop and his Puritans as well. I think you'll get a sense of this in that Berkavitch article which is called the Puritan vision of the New World. It's worth saying a few things more about it. The Purtaisn who came with Winthrop were more kind of middle of the road Puritans. They weren't quite as doctrinaire as the Puritans who were part of the pilgrims. And remember the thing about Plymouth is that they actually tried an experiment in communal property holding. When they started out, the land was held in common and everybody was kind of shareholders in this, but property was going to be held. They thought it was a way of knitting people together more effectively. That is a kind of radical version that these joint stock companies that they belonged to might be organized and Winthrop's Puritans don't do that. They are much more interested in as what we might think of as individual, the problems and rights of the individual, and that's one of the things that Winthrop himself has to combat as he's trying to give this sermon. So there's some things to know demographically about these people. Winthrop starts what's called the great migration. It starts in 1630 and this migration to the New World takes about ten years. And over that ten-year period, you have quite a few coming across. I think the number is something like ten thousand, no twenty thousand follow Winthrop's group. And there have been demographic studies of what the people are like in this great migration. It's interesting to think about it. 10% of the people were poor servants. I'll give you these figures in the post lecture notes, which I'll get up today. 10% of them were unskilled laborers and therefore lower class. The combination of aristocrats, children of aristocrats like second and third sons of aristocrats, and complete underclass riff raff, together they make up only 1%. So that's 21% accounted for. The rest of them, 79%, the bulk of these people, were what were referred to as middling sorts. You might think of them as middle class. They were artisans, tradesmen, shopkeepers, independent farmers. Not everyone who came with Bradford was a Puritan, but even those people who were Puritans, weren't only rebels against a state of religious persecution. They were also seeking a kind of economic opportunity in the New World as well. There was a study recently of the Puritans called profits in the wilderness. It was a pun because most people think if you say that title, you would assume they meant Biblical prophets, but its profits with an 'f.' It's about economics. And one of the things they say is, the Puritans who came were interested in both things. They were interested in getting ahead spiritually, or not being persecuted, and they were also interested in getting themselves to have a better economic future. So, they belonged to what was called joint stock companies. That means they were shareholders in this enterprise. They had to raise money also. It's not cheap to send boats across the Atlantic with supplies. So the idea was they created these joint stock companies. They were shareholders back in England. They were shareholders amongst the company themselves. They would come. They would farm. They would do everything else in the New World. They would send back stuff to England and profits would be made, and these profits would be shared. So that's a sense in which they were part of an economic enterprise. It's how they fund their way across the Atlantic. And I think that's important to remember as a kind of context for everything that we're thinking about. Certainly, it's the context of Winthrop's sermon. It's not just a sermon that's supposed to promote certain Biblical ideals, he's speaking to a very particular audience that has a demographic make-up, and he's aware of both their concerns, and their tendencies. Now one thing to say about sermons generally. The Puritan sermon will generally take this form. It will start out with a Biblical text, often very short Biblical text, and then you'll get a section that's called the explication. You'll get a quick gloss on this Biblical text. A quick interpretation of this Biblical text, and then you will get a longer section that's called the doctrine in which a larger doctrine behind the text and its explication is laid out for you. And then you will get what's called propositions and reasons. Sometimes it takes the form of questions and answer session in which different facets of the doctrine are explored, questions and answers might be raised and then gotten rid of, and then finally you will get a section that's called application in which you're made to understand why it is you've heard this particular sermon. Why the message has been given to you and that is the form of the typical sermon as it would be preacher by a member of the clergy. Now, it may well be that the most famous sermon that comes out of Puritan America, which we read for today, is in fact atypical because it's not a church. It's not preached by a clergyman, it's in fact by a member of the laity. And it's therefore called the lay sermon. And one of the things we would say is that prominent people like John Winthrop were permitted to give sermons on certain events. And so Winthrop takes, who becomes the governor of Massachusetts Bay colony, takes advantages of this and gives this sermon. And, I want to say a little bit more about the way in which this sermon works, because it isn't the same as other sermons. Let's take a look at it therefore. It takes place in your book it's page 147. It's called the model of Christian charity, and it starts off in this way. God almighty in His most holy and wise providence, hath so disposed of the condition of mankind, as in all times some must be rich, some poor, some high and eminent in power and dignity, others mean and in subjection. Now, what immediately do you notice about that as a starting point? You can flip the page if you want. Where, how does this structure that's given to you in the Norton anthology map on this structure that I just told you about. What part is that that I just read? Yes? >> It takes the place of a Biblical text. >> That's right. It takes the place of a Biblical text. There's no Biblical text here. I mean there is a Biblical text. It comes out of Saint Paul. It's a very famous one actually. It's where he talks about giving up childish things, and it's about charity in the original King James translation. Now call it Paul's Hymn to Love. I'll give you an excerpt from it in the notes that you can see it, but in the original King James it's charity. So that's the text. He doesn't cite the text. He could've, he's done something different. He's given you in lieu of a Biblical text, he gives you a model. Now it's being called a model of Christian charity. His audience probably would've thought, well if we're going to be talking about charity, we're going to be clearly going to Paul. That's the place that you'd go. Fine, so why begin this way. God almighty in His most holy and wise providence, hath so disposed of the condition of mankind, as in all times some must be rich, some poor, some high and eminent in power and dignity, others mean and in subjection. Now if you take a moment to look at the piece that I assigned to you from this book, which is this brand new literary history of America. It's kind of like one of Entertainment Weekly's top books of the year. It's gotten a lot of place for an academic book, but in a way it's interesting because each of these essays that are in here, and I've given you a few to read in the course of the term, are about 2,500 pages long, which is a pretty short length for an academic essay. In fact, in a panel discussion, I've kind of joked the first kind of academic reader, this book makes good bathroom reading if that's what you do. You can pretty much polish off 2,500 words very quickly. And they're meant to be sort of invitations to think about a text again. So this piece that I asked you to look at, the city on a hill subtitle is John Winthrop explains the bonds of community. It's written by one of his descendants, Elizabeth Winthrop, and if you look at it, in some sense it's making an argument on behalf of Winthrop. Winthrop, the Puritans, the sermon have gotten a bad rep. Their meanings have been misrepresented. By the end of the hour, you'll see one prime person who's done some misrepresenting of the meanings of this sermon, and she really wants to bring back this idea of, the radical idea, of a community that's formed in the bonds of love. I would say to you actually that's still pretty much a radical idea just presented that way. Emerson would later say that a state that's based on the power of love hasn't been tried yet. And if you look at our current state, around the United States, and we don't love each other very much do we. So, maybe if we did it would be better. Of course, there's a lot of other things that that interpretation of the sermon and the Puritan is sweeping aside. I want to give you one example of that. So, when she talks about this on page 29. She says, she's speaking, I think it's good and gives you a vivid sense of the sermon and where it was preached. She says, we don't know really, where it was, but I think most scholars tend to think that this sermon was preached when they're on the verge of reaching land. So preached on the boat, which is called the Arbela, and he's about to, he's telling them we're about to get there so we need to talk and this is what I'm going to say. He says, speaking directly to the diverse members of the expedition. Winthrop began his sermon by attempting to explain why God made all men different. And from these reasons, he argued stemmed important implications for their new community. True enough. The first reason according to Winthrop was to hold conformity with the rest of his works, being delighted to show forth the glory of his wisdom in the variety and difference of the creatures. Okay then. Diversity then is inherently superior to uniformity as a reflection of all of God's parts. The second reason for diversity, Winthrop continued, was so that God quote might have more occasion to manifest the work of his spirit. First upon the wicked and moderating and restraining them so that the rich and mighty should not eat up the poor, nor the poor and despised rise up against their superiors and shake off their yoke. Let's stop there and see if there's a kind of trick in the argument that she's making there. And since we're being self-conscious this term, we want to keep it, we want to see works of advocacy and persuasion. What's the trick that, there's one word that she's using here that's in some sense the argument she presents turns on it, but there's something slightly dodgy about it. Anybody? I'll read it again. The second reason for diversity, Winthrop continued, was so that God might have more occasion to manifest the work of his spirit. First upon the wicked and moderating and restraining them so that the rich and mighty should not eat up the poor, nor the poor and despised rise up against their superiors and shake off their yoke. Yeah? >> Manifest. >> He's what? >> Manifest. >> What's manifest? >> [inaudible] >> So why would manifest be the trick word? Have more occasion to manifest the work of his spirit. >> Thinks he's doing the work of God. >> Okay, to me that doesn't seem entirely contradictory. I mean, part of what Winthrop does want people to do is he wants to show how our work should manifest God's providence. So this idea of manifesting is sort of making clear, so that doesn't make it quite as problematic as other things. Yeah? >> Yoke. >> Yoke. Yoke's a good word. >> What's the definition of the word in that passage? >> Of yoke? >> Yeah. >> It's what oxen have. You throw it off. In this case, the poor have it. And we don't want them to throw it off. >> I just got the sense of yoke as an egg. >> It's not yoke with an lk, yoke with a ke. >> Ah, okay. >> Anybody else? >> If he's talking about God being manifest through his work on Earth then he's not making sense [inaudible] it's like a common humanity as opposed to slavery >> Okay, now we're starting to get at something. We have this idea of stressing the common humanity instead of, it's not quite slavery but it's poor. Some people are definitely going to be mean and that doesn't mean nasty. That means low and in subjection. So you're not exactly enslaved, but you're not free. So there is a sense of oppression. Yeah? >> It just seems kind of strange that the rich would not oppress the poor, yet the poor still have a yoke, which would kind of be like, >> It's a comfy yoke, you can put a little velvet on it or pad it. It's not so bad. [ Laughter ] >> But then they should not throw off that yoke >> Well you need the yoke. Somebody's got to work. Who's going to plow the fields? With Winthrop has done you might say, he has a sermon that's called a model of Christian charity, and he begins it with a defense of hierarchy. Some were born rich, and some were born poor, some were born mean and in subjection, some were born to rule. And that is not accidental, in fact, that's part of God's plan. Okay the trick from my perspective is the way that she, Elizabeth Winthrop, describes what John Winthrop does. John Winthrop talks a little bit about difference here. Differences among people, and he's thinking about differences in degree and rank. She uses a word that we all love these days if we're good multiculturalists. What is that word but diversity. She says this is about diversity. Diversity is inherently superior to uniformity as a reflection of all of God's parts, and it helps her to make the argument that there's something good and worth reconsidering in Winthrop's sermon, because we all love diversity. Diversity's great. Look at us all around here. Look at your professor, he's brown, isn't that great diversity. [ Laughter ] But he doesn't mean that kind of diversity. For him that might've even been a radical idea, but the difference here is not about cultural diversity. It's about economic difference. It's about social inequality. I'm sounding like Walter Ben Michaels now. There's a famous argument that Walter Ben Michaels makes. At least one of you heard him make it ad nauseam the other day. In which he says, look we all feel that we're good progressive lefties if we support multiculturalism but that does nothing to address social inequality and the real social injustice. If we're more diverse that just means that proportionally there are more African Americans and Asian Americans in the top tier of society than there used to be, so great. 20% African Americans would mean 20% among the rich, 20% among the middle, and 20% among the abject poor, but you still have the abject poor. You just feel better about them now. And what she's doing is in some sense getting away from the fact that the primary kind of diversity that he is defending is economic inequality. He's defending hierarchy. He's defending the organization of human culture in rich and poor. Again, in the context of a communal experiment that they knew to have happened in Plymouth where there wasn't the same kind of economic diversity or inequality because people were engaged in the kind of communal property experiment, which didn't work. Why would you begin a sermon like this, which is supposed to be about charity, with a defense of hierarchy and inequality. A Biblical, a divine defense, why would you do that. Any thoughts? Yeah. >> [inaudible] why should I give charity to someone else, we're all on the same page, as opposed to a hierarchal system. If you accept the fact that you're upper class, or someone else is upper class, you embrace it and realize some people are lower class. And that opens up the possibility of charity. Charity to someone, the one in need, one less fortunate. So when hierarchy is supported. It's not a bad thing, you shouldn't be afraid of it, you should embrace it and then doing that, you should welcome in charity. >> I think that's right. I think that's part of what he's trying to get at. He says in some sense, charity is good and it's a good that we need to promote. It's a form of divine love, and it is more clearly necessary because of the fact of inequality. It means that the, it also, the rich realize that they have an obligation to be charitable because they're rich, because there are poor people who depend on them. There is a system of obligations in which the rich's obligation to the poor is clear. The poor also have a system of obligation. They understand that the owe something. They owe labor, they need to work hard, so one of the things you might say is that inequality creates a kind of hierarchy that has a place of binding people together in a way that they wouldn't be bound together if they were all equal and didn't owe anybody anything. So what he's defending you might say is hierarchy because it's a system of obligation. Yes? >> I was just going to say that it seems like the second point he makes is a rhetorical move to placate his audience. Yes, I am creating this radical idea of caring, but the status quo is something >> Well it wouldn't be such a radical idea in that sense. It would've been familiar to them from Paul's Hymn to Charity. They would understand that charity is an expression of divine love. One of the things he wants to talk about theologically is how this works. Theologically you shouldn't try to do anything about hierarchy or be upset about it because God ordained it. It's the way God created the world. There are hierarchies of animals. There's a lot of diversity in nature. Human kind should necessarily mirror that and also it creates as we see this system of obligation. He actually what he is doing is taking a familiar even by now metaphor from political science or political philosophy, which would be the body politic, and rethinking of it in Christian terms. In which the body politic of the Puritans is knit together, and he uses exactly this language, through the ligaments of Christ's love. It's a body that's literally going to be knit together. What knits it together, Christ through love. What promotes Christly love? Inequality. That's the theological, the official version of the narrative. The unofficial version of the narrative or the one that goes hand in hand below, is that it's a better way for this society to actually do which is to generate profits if everybody is not upwardly mobile looking to change their class position, looking to much out for themselves, and not looking for the common good enough. So one of the things you might say is that Winthrop is trying to do is harness the energies of what we might call a kind of incipient individualism. He wants to keep those energies because that will create an economic dynamism. The people these days talk about the need to have a vibrant economy or making the belief on behalf of getting government out of the way and letting individual and individual businesses do their own thing. The kind of laissez faire Capitalist model that Adam Smith will later on go to write the great philosophical statement about. Winthrop is in some sense wanting to maintain those energies, but he wants them strictly reigned in. So one of the things that's at stake in this sermon is a particular notion that he's trying to create about the relationship between individual and community. And in his case, it's got to be community first individual second. The individual has to subordinate himself or herself for the good of the community. The individual energies that we're going to pay attention to those but they always have to be recognized as part of this larger body. We are knit together in a system of obligation, and that works theologically but it also has practical consequences. We don't want people to be worrying about making too much money or being upwardly mobile. We want to preserve things as they are. It's a message of conservatism, and you might say, to keep. Immediately they start, it's not a fresh start in other words. You don't come to the New World if you were a servant in the old world; you get to be a lord here and vice versa. You bring in your baggage with you, and we're just going to set it up here and make it all work. We're not trying to radicalize here in the New World is part of the message that he's sending across. If you look at the beginning of the sermon on page 148, he talks about two rules. He says two rules about the fourth paragraph. Two rules, this is after he's talked a little bit about the system of obligation. Justice and mercy. These are always distinguished in their act and in their object, yet may they both concur in the same subject in each respect. Sometimes there may be an occasion of showing mercy to a rich man in some sudden danger or distress, and also doing of mere justice to a poor man in regard of some particular contract, etc. What's that? And then there's a second one. A double law by which we are regulated in our conversation towards another. In both the former respects, the law of nature and the law of grace. So, two things. Justice and mercy, nature and grace, they're mapped onto what. Old Testament and New Testament, right. Justice, eye for an eyetooth for tooth, Old Testament. Mercy, turn the other cheek. Love thy brother thy neighbor as thy self. Christ in revising the Old Testament keeps the top commandment. I am Lord thy God there shall have no other God before me, but changes several crucial things particularly about the relationship between justice and mercy. Puritans don't believe in, there's no such thing as justice when you're talking about your relation to God. You don't deserve anything. You get everything you get because God is merciful. Therefore, mercy is a higher value than justice. Justice somehow goes along with the state of nature. Mercy goes along with the state of grace and the New Testament and the Puritan mission. Anything you can do therefore to produce mercy, the need to be merciful, is good. It's Christly. It's Godly. So that's one of the things I want you to see that he's setting up. He's setting up sort of these interlinked things. He's mapping them on to the way in which the Puritans typically think about the Old Testament, the New Testament. He's mapping them onto the ways that people think about ant-type and anti-type, and he's creating these interlinked ideas. Individual and community, we're going to put community first. Another one would be materialism and idealism, and we might think of those in a double sense. The low sense of materialism is greed. You're greedy, you're materialistic. The low sense of being idealistic is you want to do good works. That's part of it I suppose. But really, there's a way in which this is also an attitude that we might call philosophical materialism and philosophical idealism. It's philosophically idealist. That means, it believes that the real truths in the world are not in the world at all and cannot be discerned from the world, but are only to be found above. And we'll go on and talk more about this as the term continues, but for now let's just say philosophical materialism takes a look at the world and tries to reason from it. Tries to find evidence in the world of various things and uses the world as its evidence for making larger statements about the nature of the world, the nature of the mind, whatever. You might say, for those of you who know any philosophy, it's Aristotle. Looking around and seeing how things work. How do we do the poetics, how do we figure out how to do a good play? We see a shitload of plays and then we write about it. Socrates would have a wholly other way of going about it. He would believe there were certain first principles and we would try to discern what those should be by logic and intuition. In the Christian context, we would say the real world is undependable. Why? Well, what do we know about the real world or this world, the earthly world. I shouldn't use that term real. It's all depraved. As a result of the fall, the Earth is depraved. You couldn't possibly derive truth from it. You need to look out there. Bradford, we couldn't see you in getting those sucker from here or straight or down, got to look up. Same thing for Winthrop. So therefore what you're saying is, he wants to harness the energies of the individual to promote the communal good. He wants, in some sense, to start to think about materialism in both of its senses, but ultimately use any of those as a vehicle for certain kinds of philosophical idealism. So finally, we get at the end to the application of this, and I think it's worth looking at. The first part, which is longer, is full of references to the New Testament. The second part, the application, this starts on page 156. Suddenly starts to get a little bit more preoccupied by the Old Testament. So up until this point it's been very Pauline in its approach. It's about love to others. Saint Paul the apostle goes out and preaches a doctrine in which both the Jews and the Gentiles can be converted and saved. Those who were circumcised and uncircumcised can find salvation so long as they come to the word of the lord Jesus Christ. Paul is also famous for emphasizing Christ's sacrifice on the cross, but he does that because he sees it as the ultimate act of love. It's not a form of discipline that he's interested in. He's interested in Christ was willing to suffer that because he loved us so much. That's the measure of it. He suffered so much, we can't even understand it. It's boundless and that's why it can wipe out the debts of everybody else who would come to see Christ. The Puritans should believe in a doctrine therefore in which the Jews and the Gentiles, the circumcised and the uncircumcised, they and the Indians, everybody can be saved. Doesn't quite happen that way and part of the reason for that, I think you start to see here, they get fixated on the idea of themselves as the chosen people. So in the last part of Winthrop's sermon there are many more references to the Old Testament. Take a look here, 157, he's talking commission. He uses a language that seems somewhat Old Testament. He uses the language of covenant and somewhat 17th century or more modern commission and contract. Those two were put together here. So he's talking about Saul being given a commission. He indented with him upon certain articles, okay. Middle of 157. Famous passage. Thus stands the cause between God and us. We are entered into covenant with Him for this work. We have taken out a commission. So the Biblical language, 17th century language. We've taken out a commission, the Lord hath given us leave to draw our own articles. We have professed to enterprise these actions upon these and those ends. We have hereupon besought Him of favor and blessing. Now if the Lord shall please to hear us, and bring us in peace to the place we desire. If he gets us to the New World, he is ratifying this contract. He ratified this covenant and sealed our commission, and will expect a strict performance of the articles contained in it; but if we neglect the observation of these articles which are the ends we have propounded, and prosecute our carnal intentions. That doesn't only mean sexual. It even has a bodily, material, earthly intentions. Seeking great things for ourselves and our posterity, the Lord will surely break out in wrath against us. Be revenged of such a people, and make us know the price of the breach of such a covenant. Now the only way to avoid this shipwreck, and to provide for our posterity, is to follow the counsel of Micah. Again, going back to the Old Testament. To do justly, to love mercy, to walk humbly with our God. For this end, and here we get all the language coming together. This idea of knitting together and you can look at the way the rhetoric quickens up. He starts to omit the subject of these senses as he goes on. For this end, we must be knit together in this work as one man. We must entertain each other in brotherly affection. We must be willing to abridge ourselves of our superfluities, for the supply of others' necessities. We must uphold a familiar commerce together in all meekness, gentleness, patience and liberality. We must delight in each other; make others' conditions our own; rejoice together, mourn together, labor and suffer together, always having before our eyes and community in the work. Our community as members of the same body. If we do this, if we buy into this kind of idea of the ligaments of Christly love, something really good is going to happen. And that is this. We will become the glory of the Christian world. That's the idea of shedding light. When He shall make us a praise and glory that men shall say of succeeding plantations, the Lord make it like that of New England. For we must consider, now he goes to a moment on the Sermon of the Mount, we must consider that we shall be as a city upon a hill. The eyes of all people are upon us. So that if we shall deal falsely with our God in this work we have undertaken, and so cause Him to withdraw His present help from us, we shall be made a story and a by-word through the world. Right, the stakes are higher, we are setting ourselves as this beacon for everyone looking, and if we screw it up, we will be that much worse off. We will be perjured. We will be a laughing stock. Worse than that, we will make Christianity a laughing stock. We will as he puts it, open the mouths of enemies to speak evil of the many ways of God and all professors for God's sake. So that's what's at stake here. It's again that same logic. It is harder for us because more is at stake, but in the end, we become this idea of the shining city on the hill. And that's why this sermon is thought in some sense to be a kind of blueprint for the community that they are trying to create. He's trying to get them to see how they need to behave in their social, their religious, their economic lives in order to make themselves keep their covenant and avoid being perjured. So one of the things you would say here is that the first part of the sermon draws heavily on Matthew and the Pauline sections of the New Testament that are all about love. Paul is a great missionary and these are missionary texts, but in the end, we get the city on the hill image from Matthew but heavily contextualized by the language of the chosen people from the Old Testament, and it's that interplay that makes Winthrop and the Puritans reign in the possibilities of love. Love yes but for us. We are not turning the other cheek. Now, one other interesting thing to say about the city on the hill is that it became very famous in the late part of the 20th century. It was revived as an image, and it was revived by this man. Does anybody know who he is? [ Laughter ] Good I'm glad to hear it. The great communicator, the guy who was the populist. It's morning in America again. In 1980, everybody was just really, America was humiliated abroad. There was a terrible economy. Does this sound familiar? Reagan comes in and he says this, this is in 1977 after they've lost the White House, the preservation and the enhancement of the values that strengthen and protect individual freedom family life, communities, and neighborhoods and the liberty of our beloved nation should be at the heart of any legislator or political program presented to the American people. This is how the Republicans will revitalize themselves. Liberty can be measured by how much freedom Americans have to make their own decisions, even their own mistakes. The Republican party, he said, must be the party of the individual. So he's not like Winthrop putting the group first. It must not cater to the group, that's Democratic party politics. No greater challenge faces our society today than insuring that each one of us can maintain his dignity and his identity in an increasingly complex centralized society. Then with God's help, we shall indeed be as a city upon a hill with the eyes of all people upon us. So here's the symbol. He takes it from Winthrop, although for most of his career, he doesn't actually credit Winthrop, but he uses it and it's powerful. People are like, yes the city on the hill, and what does it mean the city on the hill? It's a city of free enterprise. Can't sell out the individual to cater to the group. And there's a certain logic that he has in which, you might say, if you pursue individual goods, you ultimately have this kind of ripple effect. When you start to care about the family's good, the neighborhood's good, the church's good, the community, the state, the national society. It all kind of builds on the idea of the individual. I don't have time to show you the speech that he would give, maybe I'll do it next time. It's worth looking at. In his final speech, 1980 farewell address, people are watching this all over the country, people are weeping that this great president is leaving the public stage. He says this, what Winthrop imagined was important because he was an early pilgrim. An early freedom man, he journeyed here on what today we'd call a little wooden boat and like the other pilgrims, he was looking for a home that would be free. So far from taking up Winthrop's sort of subordination of the individual, Winthrop is turned into a cowboy, a rugged individualist, a freedom man, a frontiersmen, by Reagan, and I want you to bear this in mind. It's what happens to symbols as they circulate in a culture. Once you let it out, you can't control its meanings anymore. Alright we'll take it up from there next time. |
Open_Ed_Cyrus_Patell_American_Literature | Nathaniel_Hawthorne_II.txt | [ Silence ] >> Alright. Thanks, everybody, for coming. It's hard for me to do this in a-- to an empty room. So let's-- [ Pause ] >> If you wouldn't mind. [ Pause ] >> Alright. So last time, we were talking a little bit about allegory. And I suggested to you that Young Goodman Brown was a kind of manipulation of the allegorical mode by Hawthorne. And you can see that it's quite a bit earlier than the Scarlet Letter. But one of the things I suggested was that in moving from the Celestial Railroad to Young Goodman Brown, Hawthorne is making less use for-- less use of allegorical techniques. Alright, I mean, in the Celestial Railroad, he really do-- does want you to think that Mr. Smooth-it-away represents a kind of tendency of intellectuals to smooth away problems. And here, we might think of Emerson's perhaps undervaluing or underestimating the power of evil, which is one of the critiques that have often been launched at Emerson. And in Young Goodman Brown, it's almost as if they're pulling back, the allegorical dreamer is now being observed, and what we're looking at is a group of people who seem to see the world in allegorical terms, mapping one thing on to another and therefore, following a logic that we might think of as being very much marked by either/or. And so, the Young Goodman Brown can believe one of two things: Either his wife and his neighbors are good virtuous puritans or at the other end of the scale, what the dark man in the forests says, that evil is the nature of mankind. Alright, there's no in between space there. It's kind of either or. And Goodman Brown, thinking as an allegorist, has trained-- has been trained to think of the worst, right? Or you might say it's this, is that the-- that this logic of either or works in a particular way, which is that once you've thought of the thing to which one level points-- so you say outward behavior points to the fact that what these people are actually doing in their real lives is hanging out and being the devil's disciples, there's no going back. And what we tend to have is a kind of-- a coloration of the entire system by the idea that evil is the nature of mankind. So that, in some sense, is the way that allegory works. Once we realize that Christian story in Pilgrim's Progress is really about the progress of the Christian soul, it's hard to go back and simply enjoy it for the plot. That secondary level turns out to be the primary level and takes over. That's what happens to Young Goodman Brown. But what I suggested to you is that the story doesn't really want us to come away, I don't think, believing that evil is the nature of mankind. It's really a kind of dramatization of what it's like to be amongst a group of people who are inclined to believe that evil is the nature of mankind, and who, in some sense, when push comes to shove, find themselves unable to be redeemed. I mean, Young Goodman Brown cannot redeem himself from that kind of thinking. So that even though outwardly, he seems to have a full and happy life, he's much for love and he has many neighbors, people come to his funeral, he has a big family, his-- you know, his final days were all gloom. And that's the idea that behind it-- that there's something wrong with living in this way. And I wanna suggest to you that the Scarlet Letter is actually a further exploration of this idea, and it's a text that is very interested in what we might think of as the idea of the liminal, being in between one state and another. Liminal comes from the Latin word "limin" which means threshold. And it's a novel that's very interested in what we might think of as threshold states, states where you're about to crossover from one state into another. That almost seems like a kind of possibility. So I would say to you that Hawthorne in some respect is very much interested in and in sympathy with that portion of the Emersonian project that is all about crossing and power being-- ceasing in the instant of repose and dark-- and being in the-- darting to an aim, the shooting of a golf. He's interested in those in between states, which are states of potential, states of possible becoming. But I think he is a little skeptical about how possible it is for us to break out of the kind of retrospective thinking that Emerson points out and then suggest that we move beyond. There's a moment you could probably remember in The Scarlet Letter where Hester urges Dimmesdale to begin all a new, let's start again. But it doesn't turn out to be that simple. And I think Hawthorne is interested in some of the constraints that are in place, right. So there's a sense in which having a logic of both end, which I'm suggesting is the logic of Hawthorne's romance is a kind of hybrid logic that means-- it gets us out of this logic of either or but it means we can't get rid of either possibility. It's therefore a logic that's built of certain kind of compromise. And we might remember that this book in being written in 1850 which is again the same time of-- that The Compromise of 1850 is being passed. So I think there is a connection between the kind of cultural energies that are seeking to preserve the union and seeking to find forms of compromise in the decade beginning in 1850 and Hawthorne's romance project. I mean, in his own life there are certain things and certain ways in which Hawthorne like-- the country decides to defer certain issues. For example, he writes a campaign biography for his friend Franklin Pierce, who's running for president and in it he talks about slavery. And he finally decides that slavery is not something that we can deal with now, that it will be dealt with by God in the fullness of time. So, you might say like the Founders he understands that slavery is a problem but unlike Stowe he is not suggesting that there is anything that we can do about it at the present moment. There's a kind of logic of deferral and compromise even in Hawthorne's writing that isn't about fiction. And I guess, you know, scholars have suggested that in fact that they form part of a web of discourse. And that some of the cultural energies of compromise work their way into Hawthorne's romances and that Hawthorne's romances enable us to see that there is a kind of larger cultural logic compromise that people are attempting to promote in this period, it doesn't work as we know. But that's one of the things that seem to be going on. In other words, if Emerson is a force for unbridled individualism it is not possible in this novel to be an unbridled individualist, attractive as that may seem at times. There's a name that Hawthorne gives to that kind of unbridled individualism. It's antinomianism which still has a kind of cultural resonance. And remember that Emerson himself suggest that we need be aware of antinomianism, right. He may be more in sympathy with antinomian principles than he would like to let on but he wants to avoid that label. Hawthorne understands that there needs to be a certain kind of give and take. So you might think that there are certain ways in which-- what for Emerson are almost intolerable bonds. Society is just unnecessary evil. Hawthorne understands that some ways the social constraints can be enabling constraints and that I think is part of what he is dramatizing in The Scarlet Letter, right. Now, that's one thing to bear in mind as the overall-- as one of the overall framing ideas of The Scarlet Letter. The other is something that takes us back to Irving. The idea that we are still trying to create a form of writing that we will think of as distinct from those genres of history and biography and criticism and philosophy. We're still looking to create something that now we call the literary and Hawthorne is part of the-- what we know call American romanticism. He is part of a project that we refer back in this course to Irving at least and perhaps even back to Brown. But remember what Irving is trying to do in the history of New York. He is writing something that is gonna be a blend of history, local knowledge which may be wouldn't normally be dignified by the name of history and out the out imaginative thinking. And he created in such a way that it has this logic of both end, right? So that when you bring together the imaginative materials with the historical materials you have the effect of privileging the imaginative material because now you can't tell what's real and what's imaginative. There's a kind of shift of authority that's going on within Irving's text, away from facts and historical objectivity towards something else. In Hawthorne's case it would be called romance. But you might remember that gesture that Irving makes at the end of book one of the history when he talks about the task of a historian being not unlike the task of the knight in shining armor who has to defeat a number of enemies in order to proceed on with his history. And remember he uses that word threshold, right. He's on the threshold of his history. But he has to take care of those things. >> So he is already invoking the world, in that case, of chivalric romance. Hawthorne is gonna take the idea of romance and push it even further to what we now think of as the literary. And he is doing this very consciously. As we said last time, knowing that the novel has a particular meaning in this time, its linked do domestic experience, it's linked to writing of a kind of sentimentality that Stowe does. He wants to move writing away from that direction. So he doesn't-- novel for him is a debased term. He promotes this term romance. And you can see in The Scarlet Letter which is a much longer version of that preface to The House of the Seven Gables that we looked at, that some of the same things are going on in this document. The Scarlet Letter I guess was intended really to be only the story proper. So in like-- in quotes rather than italics, it was intended to be simply one story within a collection and there's a reference to that, the longest of the tales included here in this Custom House preface which seems a little bit anachronistic, and it is. It's because that was set before Hawthorne decided to enlarge The Scarlet Letter story into something approaching a novel itself and he couldn't go back and change the original text so he was stuck with it. But the-- and the other stories weren't ended up being written. So there's something about this. It does a little bit of the Stowe idea of Hawthorne getting kind of drawn into this story and almost carried away with it. Although you can see that unlike Stowe's Uncle Tom's Cabin the Scarlet Letter is actually fairly tightly structured. And there are many ways in which it's a quite economical narrative, even though a lot of its syntax seems to be expansive in the way that it has a habit of kind of laying out a possibility, considering the possibility, perhaps withdrawing the possibility and again that syntax itself, we'll look at some examples, is an example of both end. You know, is Hester Prynne like the Virgin and Child? Well, she might remind you of that, but not really, right? She's the opposite of the Virgin and Child. But just couching-in in those terms means that you can't get Virgin and Child out of your head. So a connection is made. It isn't fully erased verbally. Once he's done with saying, oh, but it's the opposite, okay. And that's Hawthorne's-- there's something paraleptic about Hawthorne's general technique and I think it's something that's worth bearing in mind. So The Custom House preface has some of that Irving like effect. It's meant to create a sense of authority. It means it's linked to Hawthorne's personal life supposedly. And it creates this idea that what we are seeing is a story that he has discovered rather than invented. Take a look on page 1353 at the beginning of The Custom House if you've got your anthology with you and you will see that he starts talking about what he's doing here right away. This is how its self-consciousness about. And one of the things that we realized when we enter the Scarlet Letter through the doorway that is The Custom House is that we are in the 19th Century not in the 17th. And one of the things that you might say marks the volume as a whole is a sense of in betweenness. We start off in the 19th Century. We go to the 17th Century but I think we have the sense having read The Custom House preface that in fact we never really leave the 19th century behind. That there's a certain way in which for one thing the whole thing is marked by the 19th century context in which Hawthorne is writing, as students of literary history would think this. But even that-- that there's maybe a sense in which Hawthorne is again inviting us to allegory in one certain way. He might well be asking us to think of his long story of the 17th century as something like a kind of allegory of the 19th. Although I would suggest that's it's more than that-- it's-- he's talking about it both at the same time. There's a critique of the 17th century, there's a critique of the 19th century and finally they seem to exist on similar terms. Both provide certain kinds of constraints on the individual and on the artist. Some of those are gonna be disabling and a few of those are gonna be enabling, right. So again there's that sense of in betweenness, both contexts are being evoked and that's part of the work that The Custom House preface does. In the first full paragraph on 1353 he talks a little bit about what he's doing. It will be seen likewise, that this Custom-House sketch has a certain propriety of a kind always recognized in literature, as explaining how a large portion of the following pages came into my possession and is offering proofs of the authenticity of the narrative therein contained, right. Now think about that. Always recognizing literature and that will show you a little bit about the instability of the term. And we no longer think that literature demands these kinds of proofs. But Hawthorne is arising out of a novelistic context in which in fact its something that were gonna be thought of as literature it had to have a closer relation to truth than you might say, we customarily think it needs to. So the frequently, in the early republic, you know, say even 50 years before Hawthorne's writing, novels are not only published anonymously but they're often-- they include this sort of claims about relationship to the truth, you know, based on a true story. We still see this periodically. But then it was very important to say this is based on a true story. Or it was based on a series of facts that had become widely known. And so there's a way in which Hawthorne is trying to move outside of that while still drawing on it. So we have a little bit of the sense of attestation that was necessary for people like Whitley and for Rowlandson and even for Bradstreet and we suggest well, why is Hawthorne a white guy after all, needing to have this kind of attestation? Well, notice that he is able to give it himself. So he is posed in the position of sort of you might say master or authority figure and outsider. But it's precisely as-- in so far as he is an artist and a writer that he is figuring himself as an outsider, right. So similar things that we have said were very true about people like-- literary true of the people like Whitley and Rowlandson and Douglas, right, that they are outsiders; they need to be authorized to speak. Even you might say the people that we now think of as insiders. All the canonized white male writers still have this kind of funny relationship to literary culture and to literary culture in its relationship to business, right. Irving worries, Hawthorne worries about what kind of work writing might be said to be. Can it be said to me manly and masculine if you are a writer? And in fact, Hawthorne's first sort of novelistic fiction called Fanshawe which he later wanted people not to read which is about-- exactly about somebody who is a kind of neurosthenic is sickly person protagonist whose masculinity is very much of question. So here is Hawthorne working with a variety of these different things here. It will be seen likewise that this Custom House sketch has a certain propriety of a kind always recognized in literature as explaining how a large portion of the following pages came into my possession and is offering proofs of the authenticity of a narrative therein contained. This, in fact, a desire to put myself in my true position as editor or very little more, alright, so again that's-- I just want you to notice this little hallmarks of Hawthorne's writing. As editor, he could have stopped there or very little more, well how much more? And what does it mean to be slightly more than an editor? Doesn't that open the door to, I mean if we say editor objective, anything that we add to that category has the effect of eroding the category in much the same way that adds something imaginative to the history of New York and are we still doing history anymore. That's the kind of thing that Hawthorne is kind of evoking here. Or very little more of the most prolix among the tales that make up my volume. This and no other is my true reason for assuming a personal relation to the public. In accomplishing the main purpose, it has appeared allowable, by a few extra touches. And again think about what the sudden use of the impersonal does. It has appeared allowable. What's the difference between I have fought it, meet and fit, or I have decided that it's a good idea. It has appeared allowable, has the effect of creating a veneer of authenticity and authority but it also distances Hawthorne a little bit, right. There's this kind of weird distancing game that he's playing between himself, his text, and his text and his reader. By a few extra touches, to give a faint representation of a mode of life not heretofore described, together with some of the characters that move in it, among whom the author happened to make one, right. So we want to see that one of the things we are wondering about is how much authority really should we be attributing to supposed fact? And in some sense there's a pleasant pun that's available to Hawthorne in the title of the Custom House. I mean who works in a Custom House? But we might be wondering how much authority should we give simply to custom? Is custom going to be a good thing or something-- something that's enabling or is it something that's going to be constraining for the characters in the novel that we are about to read. So he claims that this thing is actually real. Take a look on page 1369. He talks about kind of opening up this package. [Pages Flipping] It's the second full paragraph. The object that most drew my attention in the mysterious package was a certain affair of fine red cloth, much worn and faded. >> There were traces about it of gold embroidery, which, however, was greatly frayed and defaced; so that none, or very little, of the glitter was left. It had been wrought, as was easy to perceive, with wonderful skill of needlework. And the stitch, as I am assured by ladies conversant with such mysteries, gives evidence of a now forgotten art, not to be recovered even by the process of picking out the threads. So immediately this is a kind of art object. It belongs to the past. It's something that we need to-- that contains a certain kind of mystery. Point up to close the door. [ Noise ] >> And its part of that mystery that Hawthorne is trying to get to suggest is part of the romancer's art here. This rag of scarlet cloth for time and wear, and a sacrilegious moth, had reduced it to little other than a rag,-- on careful examination, assumed the shape of a letter. It was the capital letter A. By an accurate measurement, each limb proved to be precisely three inches and a quarter in length, right. So even in that little phrase he is invoking the idea of the empirical, right. This is in the kind of investigation, he's an editor. He's got an artifact. He's a historian. He gotta measure the damn thing. It had been intended, there could be no doubt, as an ornamental article of dress. But how it was to be worn, or what rank, honor, and dignity, in the past times were signified by it, was a riddle which, so evanescent are the fashions of the world in these particulars, I saw little hope of solving. And yet it's strangely interested me. My eyes fastened themselves upon the old scarlet letter and would not be turned aside. Certainly, there was some deep meaning in it, most worthy of interpretation, and which, as it were, streams forth from the mystic symbol, subtly communicating itself to my sensibilities, but evading the analysis of my mind. Now again when I look at the categories at stake there, right, there is a sense in which this is a symbol. It has a certain kind of archeological interest. A historian would be interested in this. Somebody who is recovering the past will be interested in this. You would subject it to measurement. You would subject it to analysis. You wouldn't get it all. The analytical mind can only take you so far. This should remind us a little bit of Edgar Huntly, right. I mean there's-- there's some place that we need to go and that's why you need that little extra. Why you can't simply be an editor. While thus perplexed, and cogitating, among other hypotheses, whether the letter might not have been one of those decorations which the white men used to contrive in order to take the eyes of Indians, I happened to place it on my breast. It seemed to me, the reader may smile, but must not doubt my word. It seemed to me, then, that I experienced a sensation not altogether physical, yet almost so, as of burning heat. And as if the letter were not a red cloth, but red-hot iron. I shuddered and involuntarily let it fall upon the floor, right? So there's a kind this, you know, obviously now when you read The Scarlet Letter and you go back to this you kind of-- you understand that it was kinda of joke that his making-- he's kinda preparing you for what's going. But think about-- then again, I want you to think about, having said that, what residences are being taken, right. If he puts it on his own, unknowingly, about its history, yes. He puts it on his own breast. He feels there's a kind of mystery. So the thing is calling to him. To whom does the letter call in the course of the novel? Who feels the kind of hot red iron on his breast that's like the aye? And what does that mean that those associations between the writer or editor are bing set up now. A little bit further on 1370 he says this, it had been her habit from an almost immemorial date to go about the country as a kind of voluntary nurse, and doing whatever miscellaneous good she might. Taking upon herself, likewise, to give advice in all matters, especially those of the heart. By which means, as a person of such propensities inevitably must, she gained from many people the reverence due to an angel, but, I should imagine, was looked upon by others as an intruder and a nuisance. I mean, that almost again is a kind of funny joke. It's a proleptic commentary on the light. And one of the thing we're gonna see is when he give us his little account, what we realize by the end of a longer narrative is how impoverished that account seems to be. We need something more. Prying further into the manuscript, I found the record of other doings and sufferings of this singular woman, for most of which the reader is referred to the story entitled "The Scarlet Letter". And it should be borne carefully in mind, that the main facts of that story are authorized and authenticated by the document of Mr. Surveyor Pue. He sources yeah, you know, you come over and look it up, come over, come by look at the stuff. The original papers, together with the scarlet letter itself, a most curious relic, are still in my possession. And shall be freely exhibited to whomsoever, introduced by the great interest of the narrative, may desire a sight of them. I mean it's a joke. Everybody knows that he is making this up, right? But it sounds like [inaudible]. It's like you can look it up, you could come over. Come over and see The Scarlet Letter. And then the disclaimer, I must not be understood as affirming that, in the dressing up of the tale, and imagining the motives and modes of passion that influenced the characters who figure in it, I have invariably confined myself within the limits of the old Surveyor's half a dozen sheets of foolscap. Again, think about that whole cooking and dish metaphor and the later preface to the House of Seven Gables. Here we have the dressing up metaphor, right. There's a little bit of a hint of, you know, appropriating the space of a domestic novel to do something else. On the contrary, I have allowed myself, as to such points, nearly or altogether as much license as if the facts had been entirely of my own invention. What I contend for is the authenticity of the outline. So again authenticity here has shifted its meaning. What was supposed to attest to the authenticity of this thing? The presence of this manuscript, the presence of this relic now, there's a sense of authenticity. It's the authenticity of the outline. But really the guarantor of authenticity is going to be something else, what he calls in the later preface the truth of the human heart. What makes this an authentic document that we're going to read is the fact that it evokes things that otherwise we lose and in the course of history get lost. We need the imaginative writer to bring these things back. Take a look at the bottom of 1371, right. So he talks a little bit about in the-- the last full paragraph here, he talks about wretched numbness. It was not merely during the three hours and a half which Uncle Sam claimed as his share of my daily life, that this wretched numbness held possession of me. So the work is debilitating. It creates a certain kind of numbness. But it's every where in the 19th century it seems. It went with me on my sea-shore walks and rambles into the country, whenever, which was seldom and reluctantly, I bestirred myself to seek that invigorating charm of Nature, which used to give me such freshness and activity of thought, the moment that I stepped across the threshold of the Old Manse. The same torpor, as regarded the capacity for intellectual effort, accompanied me home, and weighed upon me in the chamber which I most absurdly termed my study. Nor did it quit me when, late at night, I sat in the deserted parlor, lighted only by the glimmering coal-fire and the moon, striving to picture forth imaginary scenes, which, the next day, might flow out on the brightening page in many-hued description. So this is how deadening the 19th century is. It seems actively hostile to the production of the romance. And then he talks about the kind of grounds where romance might well be produced. And again, I want you to see how he is transforming what we might think of as domestic imagery. There's a sentence in which domesticity here now figured to be kind of daily life. It creates this wretched numbness which is very hostile to romance. If the imaginative faculty refused to act at such an hour, it might well be deemed a hopeless case. Moonlight, in a familiar room, falling so white upon the carpet, and showing all its figures so distinctly, making every object so minutely visible, yet so unlike a morning or noontide visibility, is a medium the most suitable for a romance-writer to get acquainted with his illusive guests. There is the little domestic scenery of the well-known ; the chairs, with each its separate individuality; the centre-table, sustaining a work-basket, a volume or two, and an extinguished lamp; the sofa; the book-case; the picture on the wall; all these details, so completely seen, are so spiritualized by the unusual light, that they seem to lose their actual substance, and become things of intellect. So here he's making a-- you might say a divide between the actual and the intellectual although we see what happens to intellectual, itself as a term as we move forward. Nothing is too small or too trifling to undergo this change, and acquire dignity thereby, right? So all these things about, yeah, I mean, again they're mostly child's things, their domestic items but they-- so they seem to lack dignity. Turn on the moonlight and by implication turn on a little of the imagination and everything acquires dignity. A child's shoe; the doll, seated in her little wicker carriage; the hobby-horse; whatever, in a word, has been used or played with, during the day, is now invested with a quality of strangeness and remoteness, though still almost as vividly present as by daylight. Think about Jonathan Edwards, the example that he give in a divine and supernatural life of trying to understand the meaning of grace. >> It's as if you saw only in darkness and then you had light switch on and you get enlightened, you received grace and you see in technicolor now. Maybe technicolor is not always-- it's cracked up to be. There's something about daylight, it's too bright. And you start to miss shades and shadows and you miss something crucial. Hawthorne once had not only turned down the lights but bring in a different kind of light. Moonlight instead of daylight transforms the subject of domesticity into something else. Something that he uses word has dignity. Thus, therefore, the floor of our familiar room and again, see how this idea of liminality or in betweenness comes in to play here. The floor of our familiar room has become a neutral territory, somewhere between the real world and fairy-land, where the actual and the imaginary may meet. So see what's happened to intellect from earlier in the sentence. Earlier-- I mean earlier in the paragraph. Earlier in the paragraph is they seem to lose their actual substance and become things of intellect. Here the divide is between actual and imaginary, even in that little syntactical shift we see the work that he is doing. He is moving us away from intellect which is again gonna be very associated with the enlightenment, with rationalism, with empirical philosophy, touch something else. Reason is not gonna be the highest faculty for the romancer. Imagination is. The actual and the imaginary may meet, and each imbues itself with the nature of the other. Ghosts might enter here, without affrighting us. It would be too much in keeping with the scene to excite surprise, were we to look about us and discover a form, beloved, but gone hence, now sitting quietly in a streak of this magic moonshine, with an aspect that would make us doubt whether it had returned from afar, or had never once stirred from our fireside, right? So these are very good-- I think exemplary moment for capturing what Hawthorne's romance art is about, this idea of the neutral territory where the actual and the imaginary meet in moonlight. The Custom House therefore is evoking this in betweenness. Its very existence in this book creates a sense of in betweenness. We mediate between the 17th century and the 19th century and therefore you might say it is one of the threshold through which we might have to pass in order to get to the main tail of the Scarlet Letter. Now, I think I've told you before, right, that a novel tend-- some-- many novels tend to set their ground rules in their opening chapters. Some of them like this book or like Moby Dick if you remember create a set of almost antechambers that you have to walkthrough before you get to the main room, which is the narrative. This is one of these antechambers. It's kind of a big one. It's decorated in a certain way, call of the 19th century. But then when it ends we get to some place else. A different kind of opening, a second opening and this is on page 1377. It's the first chapter of The Scarlet Letter, right. And it's a short chapter which again has this feeling of being a kind of introduction although we already had a kind of introduction. And it focuses also on an object on the prison door. A throng of bearded men, in sad-colored garments and gray, steeple-crowned hats, intermixed with women, some wearing hoods, others bareheaded, was assembled in front of a wooden edifice, the door of which was heavily timbered with oak, and studded with iron spikes. And a concrete object to look at and it's a doorway, right. So again this-- the idea of the threshold is being carried over. The founders of a new colony, whatever Utopia of human virtue and happiness they might originally project, have invariably recognized it among their earliest practical necessities to allot a portion of the virgin soil as a cemetery, and another portion as the site of a prison. So you have Utopian hopes but death is a fact of life and so is criminality. In accordance with this rule, it may safely be assumed that the forefathers of Boston had built the first prison-house somewhere in the vicinity of Cornhill, almost as seasonably as they marked out the first burial-ground, on Isaac Johnson's lot, and round about his grave, which subsequently became the nucleus of all the congregated sepulchres in the old church-yard of King's Chapel. Certain it is that, some fifteen or twenty years after the settlement of the town, the wooden jail was already marked with weather-stains indications of age, which gave a yet darker aspect to the beetle-browed and gloomy front. The rust on the ponderous iron-work of its oaken door looked more antique than any thing else in the new world, right. So we're focusing on this object and I think there's the invitation for us to think about it allegorically, right. This door looks like it's ageless. It's become old and weather beaten just as much say this colony though young has already taken on some of that sense of being old and weather beaten. Like all that pertains to crime, it seemed never to have known a youthful era. Before this ugly edifice, and between it and the wheel-track of the street, was a grass plot, much overgrown with burdock pig-weed, apple peru, and such unsightly vegetation, which evidently found something congenial in the soil that had so early borne the black flower of civilized society, a prison. Okay. So again, look at the allegorical gesture that's kind of being setup for it. We have this black flower, these weeds amongst these weeds we have what? On one side of the portal and rooted almost on the threshold, almost on the threshold was a wide rose bush covered in this month of June with its delicate gems which might be imagined to offer the fragrance and fragile beauty to the prisoner as he went in and to condemn criminals he came forth to his doom and token that the deep part of nature could pity and be kind to him. I just almost-- we've got a lot of concrete details but there's something a little bit other worldly, maybe almost allegorical about this. This rose bush and if that's not enough, he's gonna connect it to this business of-- in history, we have this further affect a rendering in allegorical. This rose bush by a strange chance had been kept alive in history but whether it had merely survived after the stern old wilderness so long after the fall of the gigantic pines and oaks that originally overshadowed it, or whether as there is fair authority for believing it has sprung up under the footsteps of the sainted Ann Hutchinson, as she entered the prison door, we shall not take upon us to determine. Finding it so directly on the threshold of our narrative, which is now about to issue from the inauspicious portal, that inauspicious portal, we could hardly do otherwise than pluck one of its flowers, and present it to the reader. It may serve, let us hope, to symbolize some sweet moral blossom that may be found among the track, or relieve the darkening close of a tale of human fragility and sorrow. That's good sentence. I think that one of it, so what we have is gestures-- it's gonna be almost allegorical, you think, but there's a kind of direct address to the reader, right? So it's kind of hiding and self-conscious. We're aware that this is a performance that this narrator is giving. And what we're about to see is get another performance. So this is a narrative that is clearly marked by a sense of drama and performance. It's marked by thresholds. And what is that-- I mean that little gesture that always is related to Ann Hutchinson? She goes into prison. Something comes out? What comes out? Hester Prynne and her baby but also the narrative comes out of that. He says that we're on the threshold of a narrative. The narrative is about to come out. What comes out is Hester. So Hester is the narrative and, you know, The Scarlet Letter, you might say that she is wearing is the narrative. He setup this antechamber for us and he set certain terms of engagement. There is a certain kind of allegory and yet we're being a little bit self conscious about it. We have a relation to the past. Let's think now, let's investigate what these relations are gonna be. We start again. This is beginning number three, Chapter II, The Market-Place. The grass-plot before the jail, in Prison Lane, on a certain summer morning, not less than two centuries ago, was occupied by a pretty large number of the inhabitants of Boston. So you see that it's the same scene now, now, we're gonna make it specific. It's gonna be that particular day. Amongst any other population, or at a later period in the history of New England, the grim rigidity that petrified the bearded physiognomies of these good people would have augured some awful business in hand. So look at the way this is set up. Why go this way? Amongst any other population but we're talking about this one, or any later period in the history of New England but we're talking about this one, their grim rigidity would have augured something else, but why talk about something else when we're taking about what's going on now? In the early severity of the Puritan character, an inference of this kind could not be so indubitably drawn, right? That it was gonna be a death sentence basically. It might be that a sluggish bond-servant, or an undutiful child, whom his parents had given over to the civil authority, was to be corrected by the whipping-post. It might be, that an Antinomian, so here's Hutchinson being vogue for us. A Quaker, or other heterodox religionist, was to be scourged out of the town, or an idle and vagrant Indian, whom the white man's fire-water had made riotous about the streets, was to be driven with stripes into the shadow of the forest. It might be, too, that a witch, like old Mistress Hibbins, the bitter-tempered widow of the magistrate, was to die upon the gallows. In either case, there was very much the same solemnity of demeanor on the part of the spectators; as befitted a people amongst whom religion and law were almost identical, and whose characters both were so thoroughly interfused, that the mildest and the severest acts of public discipline were alike made venerable and awful. >> This is an evocation of this culture, right. I mean there's a sense in which we get all of these little details, we get all of these possibilities, all of these possibilities laid out. These are not what are happening here. So again, this is typical of Hawthorne. It's how the novel proceeds. We lay many possibilities out. We choose among the ones that we lay out even later, the other possibilities sort of float there in your mind. They are not fully erased by all of this, right? Take a look on page 1382 and you'll have the example that I referred to a little bit later on, right. So she comes out and she is holding her child. And he says this at the bottom of 1382 on the second to last paragraph. Had there been a Papist among the crowd of Puritans, he might have seen in this beautiful woman, so picturesque in her attire and mien, and with the infant at her bosom, an object to remind him of the image of Divine Maternity, which so many illustrious painters have vied with one another to represent. That's five lines before the semi colon. Something which, which should remind him indeed, but only by contrast of that sacred image of sinless motherhood, whose infant was to redeem the world, that's shorter. So, not that, but the other thing. So, look at what's going on here, right? We get virgin and child. We erase it but it doesn't fully get erased, I'd suggest it was still there as a kind of mental image but why evoke a Papist here? I mean, there's not had been a Papist here. 'Cause that's a context from outside that's being evoked which is then linked to the perspective of the narrator and also linked to Hester Prynne. That's how Hawthorne's narrative is kind of working here. And what we realize here is it's a culture of spectatorship and surveillance. And what they have designed is a kind of allegorical drama in which Hester Prynne and her child are supposed to play a role. That's what the A on the breast is supposed to symbolize. A, we label her. She plays a role as if in an old mystery play, the adulteress. And perhaps, you know, they thought of it as a [inaudible] thing. They think of it as a stroke of genius, as part of her own punishment, the beginning of her penance like Christ carrying the cross across the stations up to Golgotha. She is gonna sow herself, this A, and put it on her breast. But as I suggest, that's probably their first mistake. 1380 at the bottom, we see again, we've already been prepared for this, right? Hawthorne is just looking at this thing-- this thing is in tatters. Now, he is evoking its formal splendor when it was first created. If your eye is drawn to it then-- I don't really need it. If his eye was drawn to it then, then we-- imagine what's it's gonna be like when-- if you are evoking it in the day when it's born? Let me see if I can plug in-- pause. So, we get this. On the breast of her gown, in fine red cloth, surrounded with an elaborate embroidery and fantastic flourishes of gold thread, appeared the letter A. So here we have the beginnings of the erosion of the official meaning of the A, from the very start. She is supposed to be adulterous artist is already starting to be at least in the readers minds here. It was so artistically done, with so much fertility and gorgeous luxuriance of fancy. Again, that technical term in the 90th century for imagination that it had all the effect of a last and fitting decoration to the apparel which she wore; and which was of a splendor in accordance with the taste of the age, but greatly beyond what was allowed by the sumptuary regulations of the colony. She is using her needle work to immediately, you know, put her thumb in the eye of the men who have sentenced her to play this role. And this needle work becomes very important. I mean, there's a certain limitation of Hawthorne's imagination or may be there's a certain, you know, he knows that women are writing and publishing things, right? That quote about the damn scribbling woman indicates that. But he makes suggestion later on that in fact, this is on page 1396 in the chapter that's called Hester and Her Needle that in fact, there's something, there's a particular relation between women and needle work. In the middle of-- about five lines into the first full paragraph on 1396. Lonely as was Hester's situation, without a friend on earth who dared to show himself, she, however, incurred no risk of want. She possessed an art that sufficed, even in a land that afforded comparatively little scope for its exercise, to supply food for her thriving infant and herself. It was the art, and here's the limitation of Hawthorne's feminism, we might say, then as now, almost the only one within a woman's grasp of needle-work. I suppose you could say that could be taken as a critique of the 19th century which doesn't give woman enough of a role. But what one of the things he's thinking of is that she doesn't-- she has limited means at her disposal. She makes use of the limited means and needle work is one of them. It enables her to transform this but it also enables her to earn a kind of living. Again, we might think later on of what Stowe would go through. Stowe was trying to earn money by writing but still ends up creating something else as a result of this. So that's has one thing to bear in mind about this letter, it's transformed right away. Other thing to bear in mind about the letter, where is it on her? Where is it on her? Right around her breast and it's like Time Square on her breast, right? Boom, boom, boom, A, look at my breasts! [ Laughter ] >> So how everyone sees it, is it sexuality? Is it maternality? It's like look at my breast. Well, that in some sense, the novel-- you think I'm making a joke but in fact the novel is playing with this idea, right? We've said this already before. What's the first thing that Adam and Eve know when they know? And know they know that they're naked and that there's two of them and sexuality is all-- so for the Puritans, right, knowledge and sexuality especially women's sexuality since it was Eve who was tempted and who tempted Adam are intricately interrelated with one another. The A works on this simple. Right, it becomes, you might say, it becomes a sign of precisely the things that the Puritans are worried about. Sexuality isn't the only thing that Hester commits. The other, you might say they are afraid of but they don't fully articulate it but they create her punishment in such a way that the second sin that she commits, she commits while she is theoretically doing her penance. She is doing her penance but she is never really fully penitent, alright. Take a look at the chapter that's called Another View of Hester. It starts on page 1438. This is a crucial chapter in this book. Hester and her needle is one. Another view of chapter, it gives her like check on Hester. Okay, Hester and her needle, a little bit after the scaffolding scene. Check on her again. This is about seven years later, 1439 you find out a little bit more about Hester. This is about eight lines from the top from the bottom of the paragraph that starts 1439. Her breast, with its badge of shame, was but the softer pillow for the head that needed one. She was self-ordained a Sister of Mercy; or, we may rather say, the world's heavy hand had so ordained her, when neither the world nor she looked forward to this result. The letter was the symbol of her calling. Look again how its meaning has changed. Now, it's not exactly the artist, now it's-- this is-- there's an almost kind of social component to it. Her individuality seems to have been tempered a little bit, right? The first that Hawthorne uses that word individuality, when he talks about the letter it's one of the things that the letter does is enables her to express her individuality despite their attempts to clamp it down, right? They will try to make her into a type adulteress. She's-- embroiders the letter in such a way that she resists being typed. But now you might say she types herself in a different way. And it becomes, quite literally, enabling. T he letter was a symbol of her calling. Such helpfulness was found in her, so much power to do, and power to sympathize, that many people refused to interpret The Scarlet Letter by its original signification. They said that it meant able; so strong was Hester Prynne, with a woman's strength. Okay, so this is changing, right? Outwardly, even people are beginning to see that Hester behaves in such a way that adulteress may no longer be the most accurate description of what she was. But all of the change Hawthorne wants to suggest is not for the better. Turn the page on 1440 and we find at the beginning of the first full paragraph that the effect of the symbol or rather, of the position in respect to society that was indicated by it on the mind of Hester Prynne itself, was powerful and peculiar. All the light and graceful foliage of her character had been withered up by this red-hot brand, now she feels the brand too, and had long ago fallen away, leaving a bare and harsh outline, which might have been repulsive, had she possessed friends or companions to be repelled by it. >> Something has happened to Hester. As she transforms herself into a Sister of Mercy, she somehow becomes a little bit less womanly perhaps. A little bit further on, it might be partly owing to the studied austerity of her dress, and partly to the lack of demonstration in her manners. It was a sad transformation, too, that her rich and luxuriant hair had either been cut off, or was so completely hidden by a cap, that not a shining lock of it ever once gushed into the sunshine. And you should ask your self why it is that the narrator does not know which it is. What perspective or point of view is he taking up? Bottom of the page-- bottom of the paragraph, such as frequently-- or just a little bit further on, such is frequently the fate, and such the stern development of the feminine character and person, when the woman has encountered, and lived through, an experience of peculiar severity. If she be all tenderness, she will die. If she survived, the tenderness will either be crushed out of her, or and the outward semblance is the same, crushed so deeply into her heart that it can never show itself once more. The latter is perhaps the truest theory. She who has once been woman, and ceased to be so, might at any moment become a woman again, if there were only the magic touch to effect the transfiguration. We shall see whether Hester Prynne was ever afterwards so touched, and so transfigured. Okay. So something is going on with her and it's not all good from the perspective of the narrator. And if they but knew it, the Puritan fathers would also realize that not all is good. I mean this is the second sin that Hawthorne is getting out. Bottom of the page, second to last time, the world's law was no law for her mind. It was an age in which the human intellect, newly emancipated, again think about back to Edwards, the beginnings of the enlightenment, had taken a more active and wider range than for many centuries before. Men of the sword had overthrown nobles and kings, right. So here, you see that this is about English Civil War being referred to. Men bolder than these had overthrown and rearrange, not actually, but within the sphere of theory, which was their most real abode, the whole system of ancient prejudice, wherewith was linked much of ancient principle. Hester Prynne imbibed this spirit. She assumed a freedom of speculation, then common enough on the other side of the Atlantic, but which our forefathers, had they known of it, would have held to be a deadlier crime than that stigmatized by The Scarlet Letter. So sexuality, knowledge are linked. There's a funny way in which the Puritan fathers may well have produced the very thing that they feared. In punishing her for her sexual sin, they have led her to what they would have thought of as even more serious sin, an intellectual sin. And so, on the next page, we get a kind of stunning one sentence paragraph. In a few months, in some sense is the crocks of this, the Scarlet Letter had not done its office. The rest of the novel, you might say is a discussion of how it is that the Scarlet Letter in fact comes to do its office. Now, we might think of the novel as being structured around the three scaffolding scenes. This is another way in which that novel would [inaudible]. The first scaffold scene when Hester and her child are trotted out, it meant to do performance, right, and we get the sense that she is supposed to play a role in an allegorical pageant, right. In the middle there's a night time, so may be this is the romancer's time. There's a kind of night time invocation of a scaffold where Dimmesdale was up there and Hester and Pearl come and Hester-- and Pearl is wondering, you know, trying to force them to doing what she wants them to do. But Dimmesdale is private-- it's a private thing. And Dimmesdale is not ready to do anything. That's-- there's another invocation of the A there, right up in the meteor, if people think they might have seen. Okay, last scaffolding scene when they're all up there again and this time it's transformed, alright. And you know the ending, Dimmesdale, you know, Pearl has been urging and then Dimmesdale finally admits it. He preached his election sermon, he admits what's happened. It's almost like a magic spell breaks from Pearl. She becomes like a normal kid, having to run around as kind of like the most weirdly allegorical figure in the novel. The flattest, she's dressed in red all the time. She is quite literally, thought by-- suggested by the narrative, thought by Hester, thought by everybody to be the kind of Scarlet Letter embodied, in a certain way she is. Right, I mean, she is the product of the sin. So she is the Scarlet Letter. It's like the skull is broken. She is able to-- she becomes a normal person again. Dimmesdale does to just or unjust reward. He may or may not have a Scarlet Letter on his breast, nobody really knows for sure, they don't remember. They don't wanna say. They think they've seen it. Again a nice, you know ambiguities there. Boom! Pearl goes to Europe, to hell with this place. She goes to Europe. What does Hester do? Hester Prynne comes back. Some years later, Hester Prynne comes back. Why does Hester Prynne come back? And one of the things I think that we need to think about is this idea of unbridled individualism is something that the novel is interested in exploring, right? And to understand some of the problems here, you might, well think about three characters who in some sense are versions of Hester as well, like Chillingworth. Chillingworth is in some sense an extension of the system of justice. He has an under but-- but there is an interesting term that's used for him especially laid in the last chapter. He's called the necromancer. He is like the dark side of romance, right. He is Darth Vader of romanticizing. He, no-- but he really-- he liked the romancer who appears into the truth of the human heart but what he is interested in is revenge. One of the things that-- that the novel points out, it's a kind of brilliant psychological study of revenge, is revenge is never gonna be enough. Revenge will never give you back what it is you've lost and the more he gets part of the cycle of revenge, this kind of weird sadomasochistic thing that he gets into with Dimmesdale, the more he ends up destroying himself, right. So he is what we don't want Hester to become. We don't want her to become so bitter that she gets caught up in this cycle event. So he is a bad possibility. But Dimmesdale is no better. You know, if Chillingworth is a sadist, Dimmesdale is the masochist. They kind of deserve each other and there's a funny kind of thing. If we say with Chillingworth, the more he pursues revenge, the less he can be satisfied by what he gets, the more he ends up destroying himself. Think about Dimmesdale. Okay, it's a kind of Puritan-- it's supposed to be a Puritan trope. Think about retailer. I am this humble crumb of dust, you know, I am unworthy, I am unworthy [inaudible]. I am unworthy-- that's what Puritans are supposed to do. I have sinned. Now, if you're the minister, you get up there and you say, I have sinned, I have sinned, and the congregation is like look, he has sinned. What about the rest of us? He's such a kind of an exemplar for us but he hasn't really-- we all know he hasn't really sinned. He is a kind of typification of the entire human condition that saintly as he might be he is still totally deprived. But Dimmesdale kinda actually is-- if not totally deprived, he is certainly sinful, and he has done things that would have been thought of as deprived by appearance. So the more he says, I've sinned without actually giving the specifics, you might say, the more he compounds his sin. The more he compounds his sin, the more worried he is about it. The more worried he is about it, the more effective he is as a preacher and the more effective he is as preacher, the more he compounds his sin. You can imagine every time he preachers this kind of thing goes on and on and on until we finally gets to this election of servant. So here, also is a version of the romancer. Think of what happens to him in the woods when Hester gets to him. They're out there in the woods. The woods that we all know liminal space can't stay there. You think about Shakespeare. Any Shakespeare play where they go in the woods, transformation happens. Couples sort themselves out. Fairies do this and that but eventually, you've got to leave the woods, right. Hester goes into the woods and all of a sudden it's like woo! Magical space! She takes off her letter and then, oh what the-- hey! She takes off her cap and it turns out all the hair is there and woo! It's still nice looking hair, right? [ Laughter ] >> All of a sudden there's like sunshine and Dimmesdale is like whoa, now I remember why. [ Laughter ] >> But-- and she-- what is she urging him to? She's not saying lets do it right here on the floor, no, something worst than that. She's like chuck it all! Leave it all behind. Begin all anew. She says please right, let's leave. We'll go! We start again. But again, look at the economy that way this is setup. You know, it would have been fine if she wanted another, you know, to be reminded of why they fell in love to begin with or-- well, except the kids there. But still-- but even worse is this idea of leaving everything behind, beginning again, doing the Emersonian thing, you can't do that. Dimmesdale can't do that and so he leaves. Do you remember what happens to him? He's almost kinda of like having one of these Young Goodman Brown moments, it's like every-- he is so inflamed by all this that he sees people and he's like he has to keep himself from doing what was like Ismael, knocking people's hats off in the street or like cursing at people or doing kind of things that are basically evidence of his sinful nature, right? So he goes and has this kind of-- and then what did he do right after that? >> That's the context in which he writes his final sermon that he preaches. Does that seem like it's the kinda nice writerly grounds for producing a prophetic religious Puritan sermon? I don't think so. Something else is going on, right. And we get that because Hester, you'll remember she's outside of the church, she starts to hear it. And Hawthorne talks about this kind of low expression of anguish that she detects just in the sound of Dimmesdale preaching that you can't quite understand. She doesn't hear his words but she understand the subtext and she understands what's going. Dimmesdale of course thinks he's been redeemed. He uses that Puritan logic of suffering saying, you know, then will all suffer therefore I'm surely going to heaven except you're not-- if you're a preacher you're not really supposed to predict that you're elected and you're not surely supposed to say it in public and you are certainly not supposed to, you know, believe it yourself. So there's a way in which Dimmesdale is a another failed version of the romancer. He is not the kind of romancer that we-- 'cause it seems to be some type of unbound, unbridled, self-aggrandizing romance. It doesn't end up really having a kind of integrated function. Which leaves us Pearl, now Pearl I've already said is the Scarlet Letter, right? But think about what happens in the woods. So Dimmesdale has his moment and he goes running off and he writes his lecture and sermon and we know what happens. What happens when Pearl sees her mother take off the Scarlet Letter? She says, put it back on. Thank you. Why would she say put it back on? Yeah? >> Whom she doesn't recognize it as her own. >> Exactly, there's a psychological reason. This is a psych-- you know, from the moment that Pearl has, you know, is awakened she sees her mother. She's held right, sees the Scarlet Letter. Scarlet Letter equals mommy. Scarlet Letter equals mommy. That's what she understands. Okay. But think of it in-- now, we think about it in romance or symbolic terms. Pearl is the force within the novel that acts as-- she is the Scarlet Letter embodied which means she is both the vengeance of the community embodied but also the text itself that you were reading embodied. And she agrees wit the text. The Scarlet Letter hasn't done its office yet. Mommy, you have to put it back on until the Scarlet Letter has done its office. Now we would think that by the end of the novel it has. You know, the family is reunited so they're brought together. Dimmesdale has confessed. Pearl's bale of enchantment is free. She is off to go off and have her life, fine and good. Why can't her mother accompany her? And one of the things that we would say about the scarlet, the end of the Scarlet Letter is that finally it's the forces-- the romance serves as its force for kind of compromise and integration. But you might say the impulses of the Puritan followers were not entirely wrong. It's just they go about it in the wrong way. There's a sense in which in order to be complete Hester has to internalize the meanings of the Scarlet Letter. The Scarlet Letter finally becomes all of those things at the end. Adultress, and able, and artist, she becomes this kind of figure for the community-- looking forward, thinking forward to the day when women might, you know, have be emancipated in ways that she couldn't possibly be. But she comes back. And we said there's a psychological realism too. I mean, it's where she knows, it's where she is from. She feels that's her home. That's where she comes back but you could say oh, well, but maybe somebody who had suffered so much in a place would wanna leave it behind. She has internalized the values and that's finally what-- the way in which the romance, you might say, is integrative. This is 1493, towards the very end. Earlier in life, Hester had vainly imagined that she herself might be the destined prophetess, but had long since recognized the impossibility that any mission of divine and mysterious truth should be confided to a woman stained with sin, bowed down with shame, or even burdened with a life-long sorrow, right. I mean, you have to see that it's one of the things she has done now has started to internalize some of the terms of engagement. Begin all anew is not a possibility she comes to realize even for her. The angel and apostle of the coming revelation must be a woman, indeed, but lofty, pure, and beautiful; and wise, moreover, not through dusky grief, but the ethereal medium of joy; and showing how sacred love should make us happy, by the truest test of a life successful to such an end. You think that's the narrator, no. It's Hester. It's what she has come to believe. So said Hester Prynne, and glanced her sad eyes downward at the Scarlet Letter which she has put on again. It's almost as if, like Pearl, she doesn't recognize herself that or she has come to embrace all the things that it has come to mean. And after many, many years, a new grave was delved, near an old and sunken one, in that burial-ground beside which King's Chapel had been laid since built. It was near that old and sunken grave, but tellingly symbolically right, yet with a space between even in death she and Dimmesdale are not gonna be exactly together as if the dust of the two sleepers had no right to mingle. Yet one tombstone served for both. This is a funny image of both ends, right. Think about what that's-- as an image of both ends think what this one means. All around, there were monuments carved with armorial bearings; and on this simple slab of slate-- as the curious investigator may still discern, and perplex himself with the purport there appeared the semblance of an engraved escutcheon. It bore a device, a herald's wording of which might serve for a motto and brief description of our now concluded lesson. We end with an image from chivalric romance as it were so somber is it and relieved only by one ever-glowing point of light gloomier than the shadow on a field, sable, the letter A, gules. Okay, we'll leave it there and I'll pick up in a few minutes with Moby Dick. |
Open_Ed_Cyrus_Patell_American_Literature | The_Literature_of_Settlement.txt | >> Alright let's get started. I wanted to remind you of something that I mentioned on the first day of the class. We used last time the discussion of Moby Dick in some sense to give you a sense of where we were going in the course for the sense of where, to get you invested in some of the issues now that are going to become important later on. In the past students have wondered why it was that we were slogging on a lot of the different, you know puritan forms and what the payoff was and I wanted you to see right away that some of the ideas that the puritans bring to the new world and that haunt them continue to haunt writers all the way up through Herman Melville. A writer like Emerson perhaps we'll see tries to swerve away in the aftermath of enlightenment and the beginning of romanticism away from this sense of puritan, what Melville calls, "The sense of innate depravity", right that Puritanic glue. But writers like Hawthorne and Melville think that the swerve away from these things, that Emerson, perhaps Thoreau and Whitman take as quick perhaps, a little too easy; that what we need to do is to contend with whatever the residue of Puritanism has become by the time we get to the middle of the 19th century. So we're going to circle back now and think about the very earliest moments of settlement and do a kind of quick sketch of the way that settlement worked and then specifically talk a little bit about Puritanism to prepare you for your reading for the weekend. So Christopher Columbus, 1492 is his first voyage. That's drilled into us when we are growing up. But I want to emphasize again a conjunction that I mentioned the first day, which is that the Guttenberg bible, basically the first printed book in Europe is the same area as Columbus right. Columbus was born three years before the first Guttenberg bible is printed. In fact, it's probably in preparation in about 1450. So they are contemporaries and I don't think that's an accident. The creation of the printing press so that manuscripts don't have to be copied by hand anymore enables -- it's a brand new technology that in some sense revolutionizes the flow of information. More people now have access to text and it has an incredible ripple effect through western culture. It makes writing crucial to the whole process of settlement. So I think I mentioned the first day all of these sailors are also writers. They're constantly keeping track of things. They're sending letters back to their patrons. And what we will start to see is the growth of something like a reading public in the year that they are talking about. So I want you to understand, this is the great so-called age of discovery. It's also the great age of text. There's some who think we might be on some other great age of something else; the transformation of print to something else may herald the kind of information revolution, that's possible. We'll have to see how that plays out, although I'm interested in conjunctions of digital medial and textuality. Does the word iPad mean anything to anybody? As of 1 o'clock it apparently exists and it's -- you know it's the latest cutting edge Apple device and it is all about textuality. It's about re-presenting text in a way that will enable it in a way to be more modern and give us a greater opportunity to interact with it. People say that English professors are a bit worried about the, whatever you want to call it, the Googlizaton or the Kindelizaton of the world. I don't think so. I think there's going to be more need for people to study the way that literature intends text because there's going to be more people with access to text, and many different kinds of text then there used to be. So we're going to go back to the great age of the beginning of textuality and this is one conjunction that I wanted to remind you of. Another conjunction is this one, Shakespeare right. Shakespeare is writing say 100 or so years after this, but the English are very slow to become involved in the business of American colonization right. So Shakespeare writes the Tempest from 1611, you know one of his last plays, the last great romance, and it's inspired the story of a [Sound effects] wreck that actually took place in the Bermudas. So that you might say the very end of Shakespeare's career coincides with the start of the age of colonization. So that's another echo that we want to bear in mind. Shakespeare in some sense also hovers our course. For this reason and also because of what you see, part of what Melville thinks he is doing in writing Moby Dick is to bring a Shakespearean project finally to American culture, a modern Shakespearean project. Not one for the early 17th century but one that befits the modern age in another words the middle of the 19th century and therefore he's going to use a new kind, a different literary kind of technology, the novel. And he's going to be thinking about the relationship between the novel and drama as you will discover. So I want us to keep this in mind as well. The English as I said were slow to become involved in the business of American colonization. A couple of brothers named John and Sebastian Cabot had sailed for English merchants in the reign of Henry the 7th and Henry the 8th, but it didn't go well for them. John was lost at sea in 1948 and Sebastian went to work for Spain, they paid better I guess in 1512. It was really until the 1570's that there was real English interest in the new world and again things didn't go very well. Martin Frobisher, Humphrey Dilbert explored the north of America with very little success. Sir Walter Raleigh oversaw the famous colony of Roanoke in 1584 and Arthur Barlow who was one of the men that Raleigh dispatched gave this account of what they found. He said, "The 2nd of July we found Shoalwater, where we smelled so sweet and so strong a smell as if we had been in the midst of some delicate garden abounding with all kinds of odoriferous flowers by which we were assured that the land could not be far distant. Now the Europeans bring things with them to the new world. You know you've all heard -- disease would be one of them. I suppose Christian ideology might be another, but they also brought what we might think of as rhetoric of wonder. They had a kind of template in their mind for what they were going to find. Some of thought the might find the fountain of youth. Some of them thought they might find the Garden of Eden, but they expected to be amazed. So, a lot of the discourse of settlement that you would find in all of the different European traditions, partake some of this discourse of wonder, the marvelous and that's part of it right. We get to Shoalwater, we can't quite see the land but we smell this incredibly sweet smell, so we think the new world must be nearby. So Raleigh and Barlow take possession of Roanoke for Elizabeth the first. They spend about six weeks exploring the shore and then they return to England. The next year they come back and plant a colony. It's Governor, Richard Genvalen has a way of alienating the native inhabitants. And there's an expedition famously to Roanoke that's led by a man named John White in 1590. What does he discover when he gets to Roanoke? Did you study this in high -- yeah? >> It's totally abandoned. >> It's gone. It's still a -- people say it's still a mystery exactly what happened to them. Among the missing people were White's own daughter and her family and in fact, White wrote an account. It used to be in the Norton, but I don't think it's there anymore in which he describes his discovery of the ruined colony and includes a kind of pointed account of finding three of his own storage chests torn apart. This was the Barlow quote. I think I brought the White. He says, "Many of my things laid spoiled and broken, my books torn from the covers. The frames of some my pictures and maps are rotten and spoiled with rain and my armor almost eaten through with rust." That's the biggest thing of this description. And then he says this, "At my departure I willed them that if they should happen to be distressed at any of those places, then they should carve over the letters or make a cross in this form, but we found no such sign of distress. It was kind of a mystery. Having well considered this we passed towards the place where they were left in sundry houses but we found the houses taken down and the place very strongly enclosed with a high palisade of great posts, curtains and flankers", which are defensive walls. "Very fort like and one of the cheap trees or posts at the right side of the entrance had the bark taken off. And five feet from the ground in fair capital letters was graven, Croatoan, without any cross or sign of distress. Many of my things" and this is the passage I had just read to you, "Laid spoiled and broken, my books torn from their covers. The frames of some my pictures and maps are rotten and spoiled with rain and my armor almost eaten through with rust. This could be nothing but the work of our enemies at Dasa Moon Kapuk [Assumed spelling] who must have watched the departure of our men to Croatoan and soon as they were departed dug up any place where they suspected anything was buried. White searches around but the bad weather prevents him from doing too much to look for his family and he never finds out what actually happens to them. In 1606 is a second Virginia colony which is set up and then the first permanent settlement is established at Jamestown in Virginia in 1607 and that becomes sort of the start of that Virginia trajectory that was one of the ones that Thomas Bender. A later voyage in 1609 becomes famous when its flagship the Sea Adventure is wrecked before reaching Virginia and that is the voyage and the wreck that inspires Shakespeare's Tempest okay. So that's the story you might say of the English in North America, but of course the colonization of the north and south begins with Columbus. And so I wanted to take a look at the writing that we have for Columbus. If you have your first volume of the Norton open it up and take out to page 32, which is the letter to Luis De Sant Angel on how -- regarding the first voyage. So this is written basically back to his patron's agent. De Sant Angel is a Spanish treasurer and Columbus wants to impress him with the success of the voyage right. So this is basically a report from his -- to his employer. "Sir, as I know that you will be pleased with great victory with which our lord has crowned my voyage I write this to you from which you will learn how to in 33 days I pass from the Canary Islands to the Indies with a fleet with the most illustrious kind and queen our sovereigns gave to me. And there I found very many islands with people too innumerable and of them all I have taken possession for their heinouses and proclamation made with the royal standard unfurled and no opposition was offered to me. And then he talks about naming. What do you immediately notice about the language of this? "As you know I will be pleased of the great victory." What do we say about this? I mean I'm calling this the literature of settlement. Sound good to you. What is the language that he is using here? How would you characterize it if you had to? Yes? >> Language of appeasement. >> Language of appeasement. How -- in what way appeasement? >> It's a lot of like -- like you can kind of detect like pressure under like the officials and stuff to like -- >> So he's sucking up a bit? >> Yeah, basically. >> Okay yeah he wants to -- again it's a letter to his employer and he wants to impress him. He is perhaps trying to appease his employers, make sure that he has fulfilled his employer's wishes? Yes? >> He's trying to like keep their wishes but you can also sense sort of his responsibility. He gets to the point where he's like taken possession of their heinouses. >> Okay. >> Like he know his role there. He knows what he needs to do. >> Very good. Very good. He says he knows his role. It's self-promoting right. I have taken possession for their royal heinouses. >> [Inaudible background question] >> Right. That's good. Anything else? Yes? >> It describes a conquest but just with passive language. >> Very good. It's passive but you're right. It's conquest. It's marshal language. At the first sentence, we're please at the great victory. I went there. I took possession. I unfurled the royal standard and nobody made any opposition. Let's try for a moment to think of it from the standpoint of the people that are watching this happen. You know a guy comes out, trudges. He's dressed in a way they've never seen before. He takes out this thing, sticks it on the beach, says some words in a barbaric language. [Laughter] The beginning of the end, if they could only have seen what was going to happen, they'd have killed him right there. But that's not what happened. Look what he sees. He sees people innumerable okay. And one of the things to say about Columbus's letters is that he really is a -- portrays himself as a primary kind of actor. This is in some sense a drama of his discovery and it's his discovery. So you might -- there's a certain way he's substantiating here a whole genre of personal narrative that we're going to be seeing throughout the course. It's going to finally culminate for us in Kalmi Ishmael. Let's take look at the end of the passage and see -- well no next paragraph. He says, "When I reached Juana, I followed its coast to the westward and I found it to be so extensive that I thought it must be the mainland, the province of Kotaio." And you can look at your footnote and see what that means. He thinks he's in Kafe or China. They were looking for another way to get to China. China had been discovered. Marco Polo and others had brought things back to Europe from China like spaghetti. So they were looking for another way to get to China. They had no idea at first that there was this continent. There's a wonderful thing, I should have brought a picture of it. Maybe I'll do it next time. It's called the Christopher Columbus Chart and it's -- I think it's in the [Inaudible] in Paris now. But it's a weird hybrid thing of an actual -- we call it an actual sea chart, something that would look recognizably to us like a map on one side, and I think it's on the right side. But then on the left side kind of joined to it is what they call these portolan charts, which are kind of much more about mythical places and they have kind of sea beasts sort of there, the edge of the world kind of stuff. And it's really interesting to look at it. I'll definitely bring it see these things kind of literally joined as a glued together to make this think. It's not even regular in shape. You can see that what they're on the verge of is a kind of paradigm shift in the way that they understand the world, not flat but round. All the things you know of sun at the center of the universe, not so much. And early on people were burned at the stake for thinking these things. We're at the great age of discovery. That doesn't only mean looking for land. People are thinking of different things and paradigms are shifting and that chart is a wonderful way of thinking of Columbus as that sort of guy who's right in the middle of a sort of shift in understanding and conceiving the world, much more so actually than he first understands here. So he says, "Since there were neither towns nor villages on the seashore but only small hamlets of the people of which I could not have speech, because they all fled immediately." I mean what would you do? I went forward on the same course thinking I should not fail to find great cities and towns." Again, he thinks he's in China. "And at the end of many leagues, seeing that there was no change and that the coast was bearing me northward, which I wished to avoid since winter was already beginning and I proposed to make for much of the south and as moreover the wind was carrying me forward, I determined not wait for the change in the weather and retrace my path as far as a certain harbor known to me. And from that point I sent to men inland to learn if there were a king or great cities. They traveled three days journey and found an infinity of small hamlet's and people without number but nothing of importance." Okay that's too obvious. What do we say about that? What has he also brought with him from Europe, what conception is clear here? Yeah? >> The idea of civilization that doesn't account for anything that's not the western. It doesn't account for anything. It doesn't really make sense in this topic, so more western. >> They thought they were going into the east. >> So maybe he thinks he's in the east but yes. >> This idea of European civilization. It doesn't exist within that distinction. It doesn't exist at all. >> That's very good. In other words he has a conception of western civilization that he's brought with him. To be civilized you can see some of the things he's expected to find. If you're a civilization you've got a king. If you're a civilization you have to have great cities. Presumably you have many of the other things that are going along with that. He has a certain amount of social organization and writing will be one of the things that Europeans are expecting to have if you're going to call yourself a civilized person or civilized society. Did you want to add something? >> I was just going to add the ultimate area of pride that's universal, like in the writings of Smith. >> Yeah, yeah sure. I mean all this people have a certain kind of hubris -- and Smith is even more Hubristic than most. I mean he's really a self-promoter. Columbus looks very humble compared to him, but I think there's a Hubris that they don't even understand. It's the moment that we would call it of first contact, and they have no idea that the people that they are encountering should count as people. We called some people here -- people without number but not of importance, not worth reckoning with. Yes? >> Even from the very beginning when they have the early saga of these people of their civilization -- about their civilization is that mean they are not important, or they already see them as the same species, and that becomes a big problem. >> Yes, right. It's almost like they don't see them as these people enumerable as the same species and later on the subtext is that he sees them as something else. Let's gone on to the very end oh about -- he's starting to describe what it's like. So let's go on to about the third paragraph at the top of 33. " -The island and all the others are very fertile to a limitless degree and this island is extremely so." So again, it's a kind of progress report. He wants to prove that everything was worthwhile, all the expense of sending these ships out there; in it there are many harbors on the coast of the sea beyond comparison with others, which I know and christened them and many rivers good and large, which is marvelous" right. So he's using what he knows. It's predictable that you would do this, christened them as it was in your benchmark. And you're going to compare what you find to that and he thinks what he's found is better. Again that word, marvelous, it's all marvelous. "Again its lands are high and there are in many sierras and many lofty mountains beyond comparison with [Inaudible] All are beautiful of a thousand shapes and all are accessible and filled with trees of a thousand kinds and tall and they seem to touch the sky. And I am told that they never lose their foliage as I can understand for I saw them as green and lovely as they are in Spain in May. And some of them are flowering, some bearing fruit and some in another stage according to their nature. And a nightingale was singing and other birds of a thousand kinds in November there where I went. There are six or eight kinds of palm which are a wonder to behold on account of their beautiful variety, but so are the other trees and fruits and plants." What's wrong with that account? It says he hears a nightingale and it's wonderful. Yeah? >> Well I think that the map that you forgot to bring in [Laughter] where it's just like the clash of kind of strict like [Inaudible background discussion] I forgot my question now. I'm sorry. >> I think that's an example of what goes around comes around. [Laughter] Raise your hand when you think of it. But I was asking what's wrong with that account? In the back? >> It's placing more importance on fruits and animals and the people. >> Well that's true. That's really true, although we'll get to that in slightly later sentences. Is there anything else that's a little dodgy about this? Yes? >> I got it. >> You got it good. Like the literature of wondering off, like meaning the [Laughter] just like the practicality. The rivers are really marvelous, yes because of their beauty but also because there's kind of a sense of utility you know. Like we'll be able to use these rivers. >> That's very -- the point was worth waiting for. Yes. [Laughter] He's looking at them all as commodities right. This is resources we've discovered here. It's amazing, it's better than what we have at home. Now again I'm still looking for what's dodgy about the account though, yeah? >> [Inaudible background question] >> Ah yeah, see they tricked you because they stick the footnote a couple sentences later to talk about the hummingbird. But there's no nightingales. That's one of the big we don't keeps, Ode of the Nightingale. Ode to a Nightingale, everybody read that? Do they still do that? That's one way in a nutshell of talking about a problem that we're going to encounter later on. You know, how the hell are you supposed to write a literature here in this continent where there are no nightingales? What the heck are we going to write about? [Laughter] How are we going to have a gothic literature when there's no castle, there's no ghosts and vampires and things like that in the new world. What are we supposed to do? So Columbus doesn't actually notice that. He figures it must be. So I want you to sort of see a template in place for understanding. And part of that template is being used to create a sense of awe and wonder. This place is different. It's unlike what we have, but he's not attuned to the differences. He's just saying it's different because it's more. It's better. We can use it. And when he has an opportunity to note something, it's got to be a different kind of bird, no. A certain part of his brain just simply maps the old world on to the new. And one of the issues we're going to be discovering is that can be a kind of dangerous thing to do, that are certain ways -- how many of you have now seen the top grossing movie in all of history -- Avatar? None of you have seen Avatar? Oh come on. [Background sound effects] I should make it an assignment. You go see Avatar. You go see Avatar. You think I'm joking. You go see Avatar in 3D Imax. You'll get a sense of wonder. You'll get an understanding of Columbus by seeing that movie. You go to a -- I mean what is that movie except for settlement to discovery and dances with Smurfs. [Laughter] Actually it was a cheap shot because I loved that movie. I think the movie is brilliant. I have colleagues who think oh it's not progressive enough. They should have done more to with like an echo this and echo that and hybridity. And I'm thinking for a piece of popular art it's pretty progressive. You know you go away thinking don't wreck the trees [Laughter] you know be sympathetic to your animals. I mean that's all pretty good stuff. I mean who has seen it come on? You've not come on, you mean you all just saw it in the last minute? [Laughter] You weren't willing to confess because you didn't want to -- you clearly have not heard enough about me. [Laughter] So those of you who have seen it -- I'm not going to spoil it for you for those of you haven't. I'm serious that you should go see it though because it partakes in the same discourse of wonder and then it's wonder that if you don't understand it in the right way it will kill you. That's part of what they discover here, you know that planet. That tough Marine colonel who is Pandora, the place will kill ya! The battle scar veteran right, the scars he got are from this first day on the new world. But the sense of wonder is captured in that film where the crippled protagonist suddenly gets his Avatar body and starts to run again. And I think that's a -- just that whole sequence where he starts to understand the joy of using his legs again, in this kind of new context. That's part of this whole thing. I mean the camera is actually drawing on the same discourse of wonder that marks these texts and that's a -- for my vision -- for my money it's a better account of first contact and finding or just the aftermath of first contact and what it's like to be a new world. And that really arty movie that was called the New World that just went on about Pocahontas and it just went on and on, okay. That's my little editorializing. Hey, but I like pop art. I'm very serious though about going to see Avatar. If were feeling like it was not worth your time or your 12 or 16 bucks or however it was just say, "I'm going because it's my American Lit I assignment", seriously. But take a look again and again the comparison is the go to -- and this is a joke -- they go -- it's a movies joke. They go to this place to find some Magoffin resource that's called unobtanium. [Laughter] But you know they are unable to see the wonder of that world. Really what blocks them from truly understanding the wonder of the world is that they see it really as resources, many of the people -- the reason that they are there. And that's what Columbus does to with this nightingales business, with singing a thousand birds, their eight kinds of palm, which are a wonder to behold on account of their beautiful variety with several other trees and fruits and plants and there are marvelous pine groves, and there are very large tracks of cultivatable lands and there is honey and there are birds of many kinds of fruits of great diversity. Did I say there were birds, like he says you know? He's getting it across in the anterior of our mind and the meadows and the population is without number. Espanola, the last thing he mentions there is minds of metals and of course we're going to need people to get those mines of metals out, right. So luckily there are people without number. You know there's a kind of sinister side we say to this document the drama of Columbus's life is that he actually comes to understand what you might say is the dark underside of this conception of civilization. The first voyage -- let me see did I bring the first voyage -- yes so he makes four voyages. He raises money for a second voyage in 1493 but he's racked with doubts when he discovers that the small settlement that he's left back in this place that's been marveled is a massacre. His third voyage in 1498 is marked by his own in ill health and by increasingly chaotic conditions back on Espanola. In fact, at the end of this third voyage he is stripped of all of his properties and sent back to Spain in chains. I bet you didn't know that about the Columbus story. He finally -- you know he finally gets his reputation back and has a fourth voyage in 1602 that is in fact a complete disaster and it sees him finally stranded in Jamaica and that's where he writes this letter directly now to the King Ferdinand and Isabella regarding his fourth voyage on the bottom of 33. "Of Espanola, Paria and the other lands I never thing without weeping", he writes. "I believe that there example would have been to the profit of others. On the contrary they are in an exhausted state. Although they are not dead, the infirmity is incurable or very extensive." Okay so how many years is this, eleven years later? "Let him who brought them to this state come now with a remedy if he can or if he knows it. In destruction everyone is inept." It was always a custom to give thanks and promotion to him who is a person. Now he is again his own situation. He's talking about the injustice done to him. But he's also talking about the cultural situation. "It is not just that he who has been so hostile to this undertaking should enjoy its fruits or that his children should. Those who left the Indies flying from toils and speaking from evil of the matter in me have returned with official employment. So it has now been ordained in the case of Oragua [Assumed spelling] is an ill-example and without profit for the business and for the justice of the world" and then he goes on. So you can see that Columbus learns first hand to see what it means to put your face in things like Kings and great cities and there's a way in which Columbus is emerging out of these letters as the first of a kind of type, the first kind of alienated American or the first American exile perhaps. Now the guy who prepared a summary of Columbus' first voyage it survives today as the diario of Christopher Columbus was a sailor on the first voyage who later became a monk and we might say the kind of first new world activist on behalf of native Americans and that's the next writer that's featured in the Norton, Bartolome de las Casas. And I ask you to take a look at this. On the bottom of 36 you get his very brief relation of the devastation of the Indies and you can see you know how quickly Europeans have altered the way the new world is. This was the first land of the new world to be destroyed and depopulated by the Christians. And you've got to remember by this time he's a monk right, he is a Christian. "And here they began their subjection of the women and children taking away -- taking them away from the Indians to use them and ill-use them, eating the food they provided with sweat and toil. The Spaniards did not content themselves with what the Indians gave them of their own free will according to their ability, which was always too little to satisfy enormous appetites. For a Christian eats and consumes in one day the amount of food that would suffice to feed three houses inhabited by ten Indians for one month. A bit of an exaggeration, but you see the point he's trying to make. "And they committed other acts of force and violence and depression which made the Indians realize that these men had not come from heaven. Some of the Indians concealed their food while others concealed their wives and children and still others fled to the mountain to avoid their terrible transactions with Christians and the Christians attacked them with buffets and beatings until finally they laid their hands on the nobles of the villages. Then they behaved with such temerity and shamelessness that the most powerful ruler of the islands had to see his own wife raped by a Christian officer." Alright so that gives you a sense of settlement and discovery which really are misnomers perhaps for conquest. And from this time on, from 1493 onward Europe maintains a permanent presence in the West Indies. Columbus finds the mainland of South America. During the 1498 voyage he finds Central America. During 1502 the Italian and Portuguese and at that point we're exploring the coast of both South and North America beginning in 1515 under the Charles the fifth, the grandson of Charles and Isabella. The Spanish enter Mexico, Florida, the Isthmus of Panama, Cortez is conquering the Aztecs 20 years after this, only 50 years after 1492 the Europeans have managed to explore the east coast almost completely. They've made major inroads into the continent and they've defeated the most American civilizations which were the ones in the south, the Aztecs and the Incas. Fifty years after Columbus discovered first the new world the Europeans are there to stay. And in some sense the history that we are now talking about begins. Now part of the problem I've mentioned is that the Indians weren't thought to have a civilization in part because they didn't have writing. They didn't have a written literature but they did have an oral literature. And I give you to read, I ask you take a look at the two pieces that the Norton reprints for us, the Iroquois Creation Story and the Pima Creation Story just to give you the sense that there was something here before the Europeans, and it was a culture. There wasn't just a bunch of barbarians who were better than animals, right. They had a culture. But the way they expressed their culture was oral. And therefore the Europeans were unable to understand as a culture. Some anthologies of cultural America chose instead to present you the gap. They don't present any of these texts because these texts are problematic. For one thing anytime you get a written version of an oral text, you're getting one performance of it. So you've lost something about the essential nature, the orality of the text, only because you don't hear it spoken, but because an oral text lives with variations and it's passed on. Any single rendering of it is just one performance, as if you -- I mean I suppose we're used to doing that as what a theater critic does. He goes or she goes to one performance and makes a judgment about the way the entire is play, wondering whether it's a particularly good night or a particularly bad night. So we need to keep that with a grain of salt. The other thing of course is that these are transcriptions of oral presentations and therefore they are mediated. There's somebody in between the oral presenter and the audience who is the reader, even you might say if that oral presenter is himself the writer or transcriber. Somebody who writes down an oral story is also mediating it for us. And I think the Norton introducer and I disagree about the extent to which it seems likely that the second of these Pima stories is actually mediated in that way. There are ways in which you might say a European audience would expect to see certain hallmarks of creation in the creation story. There should be a creator. If you are a believer in the literal truth of the bible you would say there would have to be a flood so these things work their way in. It's unclear whether there really were part of or the extent to which they are part of the original story. So what you might say is what you're getting in some sense is a damaged, a very damaged version of the original story that was here. Nevertheless, I think for our purposes it's worth having even that damaged version to call attention to the way in which it's damaged to bring it out of chronology. If we were going to read these in chronology in terms of the time they were printed, these are mid 19th century texts. They don't belong at the beginning of the course. But we have them here to again give us a sense of the justice that's being done when we talk about something as virgin land. So I think it's important to remember that these Native American creation stories we should consider to be literary but they belong to an oral rather than written literary tradition. And that jester that Columbus has in his first letter of naming, showing us the names that he's giving to the island is actually an important thing. I mean one of the things that you would say that the Europeans do is they go and name everything and take possession of it. Sure you can stick a stand in the sand and unfurl your banner. You can bring in soldiers but it's really when you start to rename everything and bring in your culture that you are actually taking possession of it. And so, one of the things that we might say is that this has become a kind of understanding among many contemporary Native American novelists and artists about the way that the conquest worked. This is a wonderful novel, which if any of you like 20th century literature I would imagine that you should read this one. It's one of the brilliant novels I think of the late 20th century. It's Leslie Mormon's Silk of Ceremony which is about a Native American who has gone off to fight in World War II and comes back kind of shell-shocked and tries to reintegrate himself into his community. It looks at first glance like a kind of wonderful, modernist text but one of the things that she is doing is trying to incorporate the oral tradition of the Laguna Pueblo Indians into a kind of western novelistic tradition. This is one moment from that novel and I think it's worth thinking about just for a second. This is described in the Christianized Indian called -- she's the aunt of the protagonist so she's called Auntie. And the narrator tells us this, "An old sensitivity had descended in her surviving thousands of years from the oldest times when the people shared a single clan name and they told each other who they were. They recounted the actions and words each of their clan and taken and would take from before they were born and long after they died. The people shared the same consciousness. The people had known with a simple certainty of the world they saw how everything should be." Pre-columbian, when people say pre-columbian that means before Columbus' discovery. So that's in some sense the pre-columbian vision, the first four worlds. But the fifth world had become entangled with European names. The names of the rivers, the hills, the names of the animals and plants, all creations suddenly had two names, an Indian name and a white name. Christianity separated the people from themselves. They tried to crush the single clan name encouraging each person to stand alone because Jesus Christ would save only the individual soul. Jesus Christ was not like the mother who loved and cared for them as their children, as her family. And you get a sense of that mother figure in one of the stories, right. In the Iroquois story, which is really very different from the account of creation that we would get in Genesis, and we get in Genesis right. I mean the Pima story is a little more like that, although again it's not quite certain why. In the Iroquois story we sort of start in the middle. There isn't like this moment of creation. There's a greater emphasis on motherhood, on process on collaboration, on community. Again in contrast to the kind of radical individualism that certainly from a Native American standpoint we would see in Christianity and I think it's worth remembering this idea of individualism because it will become important as we go on for much of U.S. ideology is predicated on the idea that that individualism is a good thing that's created many good ideas like natural rights and other things like that and we'll get to the flowering of it in Emerson and we'll talk about self-reliance as the way to develop not only a culture but a person. So you might say that our liberal system is based on the idea of individualism. It's a strange idea from another cultural perspective. Solko gets at that and I think some of these stories will suggest that as well. A different kind of culture another words is going to come out of a creation story like the Iroquois then out of a creation story like the one that we find in Genesis. Compare the Iroquois mother of the world in that story therefore to the you know male God figure in the Christian tradition. The monsters in the dark are not evil in the way that Satan later on and his devils are evil. They belong you might say to a different way of thinking about the world and they come together and they collaborate in the creation. So when the good twin begins the work of creation it can't be completed until the bad twin is able to partake in that. So I think that's a really quick of sketching you might say some of the limits of the ideological tradition that comes along to the new world with Christianity. So I want you to look at those accounts and think about the ways in which -- you know even the Pima account is different in certain ways. Joworta Makai becomes a kind of trickster figure. He makes mistakes, not that there aren't mistakes that are made. You know human beings aren't acting so well, let's wipe everybody out except for a single family and start again. So there's some of that in the Christian tradition as well. But you get the sense that there's more of a kind of trial and error process, sort of the creator figure as a kind of trickster even in the Pima account and he makes the world four times until he is satisfied, which scholars think corresponds to the emphasis that's placed on the number four in many native cosmologies including the Pima which would correspond say to the four directions as a kind of significant number. So I wanted just to put those out there for you as a way of indicating something like this was here and a lot more of it and we can't every really know what it was like. That's what cultural theaters would call a situation of cultural damage. The cultural damage is profound. Some tribes are completely wiped out. You know the Puritans completely wipe out the Pequots later on. That will become important to our friend Ishmael. So again I want to just emphasize the contrast between the oral and literary traditions. Now I want to talk a little bit -- okay we'll do it this way. I wanted to talk to you a little bit about the ways in which the Puritans interpret the bible that will help you to read some of the stuff -- to think about some of the stuff that you've read already and to read the stuff that you're going to start to read over the weekend, which include John Winthrop's very famous sermon, A Model of Christian Charity and then later on the account of the captivity of Mary Rowlandson. So one thing to understand is that the Puritan's have a particular -- and you will have a piece which you definitely should read carefully by Bruce Kuklick which will go over the same material. So I'm going to give it to you now, you can read it and then it all -- you'll start to understand. Because I think you will find in a way that it's counter-intuitive or at least paradoxical. One thing to understand about the Puritans I talked a lot about cosmopolitanism in the first couple of classes. The Puritans are what we would call counter-cosmopolitans. They are fundamentalists and whatever it is you think of fundamentalism you should think about the puritans. I mean they are people who believe that they have the one true way. Do you remember a little bit of your English history there's a whole big reformation that's going on in Europe. The English are a little bit late to the party and it's not for the best reasons. Henry the eighth decides he what needs a male heir. He's tired of his catholic Spanish wife so he decides to divorce her. Slight problem with that, Catholics can't divorce. So what's the solution? Let's not be catholic anymore. So Henry the 8th founds the Anglican church, becomes the head of the church, grants himself his own divorce and marries Ann Berlin and he keeps going on until he finally gets a male heir who doesn't last very long and is succeeded by his eldest daughter with Catherine of Aragon, Mary the First. She has another name, a nickname. We drink it. [Laughter] Some of us drink it. >> Bloody Mary. >> Bloody Mary. Why is she called Bloody Mary? Actually she should be called something like Roasty Mary, because what she did was actually burn a lot of Puritans at the stake. And then Elizabeth who is a Protestant succeeds here and then things switch around again. But Elizabeth -- the Puritans don't like Elizabeth much more either. Elizabeth is a great politician so she is trying to mediate between the different religious constituencies that she has. So you have to imagine that in this period it's the Catholics who are the right-wingers. They represent the conservatives, the long traditions of the church. The Puritans are big left-wingers. That's what I mean by counter-intuitive because the way the cultural system is turned around if you found a puritan in front of you today you would think of them as right-wing in comparison to our current ideological alignment. And there are the lefties and the Anglican's are somewhere in the center right. Some people say that when Henry the eighth changed the church around all he did was basically translate the liturgy out of Latin and into English and left it there. But you were still going to find a lot of incense and all kinds of other rituals in high Episcopal services. The Puritans don't line any of that. They think it's all kind of graven images. They think the church has become -- and rightly so - they think it's become this bloated institution which has gotten away from the true faith. When was the church great, in the early years of the first apostles and martyrs, when the saints were walking among us. They think of themselves as return to those days. That's what they are trying to do. They are trying to create small congregations that are going to mirror the early church and luckily for them in fact the have a Catholic persecuting monarch who's creating new martyrs and new saints. One of their revered books in this period is called Fox's Book of Martyrs that talks about all this. So Puritans come to create a theocracy, quite literally. A separation of church and state, they would find that idea ludicrous. For them church is state, it's the only reason to have a state. Now they bring with them a particular interpretation of the old and new testaments and the relationship between the old and new testaments and you might say a part of this -- there's some key books for them. Certainly Genesis and the Account of the Fall are key books. >> The Gospels. >> The Gospels. The -- Some of the Epistles of Saint Paul talk about it a little bit with Winthrop, because there's a certain kind -- certain part of Paul's message that they want to adopt and a certain other part that they want to leave aside and then the Book of Revelation. Why the Book of Revelation? Again think of the Puritans, the Berkovich article on Puritan Vision of the New World is very good on this. They have a different sense of history than we have. We live in what they think of as a secular history or debates history. They live in the sense of sacred history and it's comforting to live in sacred history in a certain way because you know what, there's a roadmap in sacred history. What is that roadmap? Yeah it's the Bible. It starts in Genesis, has a few bumps along the way but eventually it leads to the day of judgment and they like the day of judgment. Why? Because they think they are living close to the end times and they think they are God's chosen people re-created. In fact, you could say they think they are really God's chosen people. The previous version of God's chosen people was just a warm-up for them. So they think of themselves as living in the end of days and they're looking forward to that second coming of Christ and all that comes with it. So they go back, and under the influence of John Calvin they start to interpret the Bible in a certain way. They think of the Bible as in Genesis establishing a covenant. God establishes a covenant between himself and human kind, between himself and Adam. They regard this as the covenant. It's called the Covenant of Works. And it's a kind of a strange title but what it basically means is that given the nature of that covenant all of Adam's works were going to be good. Adam didn't know the difference between good and evil. There was no distinction between good and evil. So, all of Adam's works were guaranteed to be good, so long as Adam obeyed God. And Adam pretty much said he could have all these beasts and depending on which version you pay more attention to -- has anybody -- how many of you have actually read Genesis? You ever notice that there is certain kinds of repetition in Genesis. It's like there's one creation of the world in which Eve has a certain role and gets created in a certain time and then somehow a few verses later there's another one and she gets created out of the rib. Have you ever read the story of Noah? Everybody remember the story of the dove and Noah and how many days, forty days and forty nights? That's the one you remember? Who remembers the raven in Noah? There are two different versions of the Noah story and the Bible, if you do sources studies of the Bible which they start to do in the 19th century, you find that there are different sources and there is thought to be an editor, a redactor figure who brought these things together and sometimes the seams show. It's kind of a wonderful exercise. It's kind of beyond the point here. People who are in my Con West class may have seen it. But if you're interested I'll put up a little piece that you can read about this. But the Noah story is wonderful because you can almost pull them apart, almost perfectly and read one entire account written by one source that tells the story that features a dove. An entire other account that works in its own logic features a raven instead. One of them has forty days and forty nights, the other has a slightly different chronology. The two of them however are intertwined with one another in the actual text. There have been in fact attempts to say that they aren't separate, they go together and that in fact you could make a kind of chronological sense to all of this. I would suggest that you just read it and take a look and see what you think yourself. In any case there was at least this one idea, and at least one story was that Adam is basically supposed to go and he's God's agent on the ground. He's going to name things. He's going to take possession and the world is created for his dominion so long as he obeys one little rule, "Do not touch the fruit of that tree over there." That tree over there happens to be the -- >> Tree of knowledge. >> Yeah it could go by the tree of knowledge but it also has a longer name, "The tree of the knowledge of good and evil." Puritans, diehard Catholics would probably say, "You know what, God could have picked any tree." These are logical implications because you could say if it's the tree of knowledge of good and evil that God doesn't want to people to eat from is because he specifically doesn't want them to know the difference between good and evil so that there presumably wouldn't be evil. Others could say, "You know what, the thing that's important is just God's commandment." It could have been the tree of the recipe of how to make sugar cookies [Laughter] and he could have decided that was it. So, basically it was obedience that was fundamentally at stake, not the knowledge of good and evil. Okay, either way Covenant of Works. So you know the story right? The serpent is that right, not exactly right. Satan, but he's not the serpent yet, he's some other form that we don't know. He talks to Eve. He had a little chat with her. "This fruit really tastes pretty good. It actually does, why don't you have it." [Laughter] "It's good stuff." So she has it and then she goes to her husband and either because he's seen what she's done and he realizes that he's got to take part in it or just because he's convinced that it's good stuff, he eats it too. What happens next? >> They're chased from the garden. >> Okay, before they're chased from the garden what's the first thing they know? >> What? >> They realize they're naked. >> They realize they're naked. So they cover themselves. [Laughter] I want you to remember that conjunction. Especially when we get to The Scarlet Letter, which I hope will look radically different to you with me than it does -- by the time we get to it -- then it did in high school. But there is something about -- look at the connection that is being made there. If you assume that the knowledge of good and evil is important the Puritans are going to say -- what's the first bit of knowledge that's evil that they know, stuff about sex. [Laughter] It's the woman's fault. [Laughter] I mean just think about it. The Catholic tradition -- I'm being a little irreverent but not much -- the Catholic tradition reveres the Virgin Mary. There is no kind of feminist counter-weight, equivalent in the Puritan tradition. It's much more patriarchal, much more difficult. And I think that will give you -- and if you keep that in mind you'll get a real sense of the achievement of Mary Rowlandson and Bradstreet as writers. So we'll get to that next week and the week after. But they know the knowledge, the have the knowledge of good and evil and all of a sudden and it has everything to do with good and evil; so sexuality and knowledge, very important. And Hawthorne gets this and that's why he writes the story that he does and when you get to it, or if you've read it you'll remember that she is being punished for a sexual sin that she has been proven to have committed. But in the course of what looks like her penance she is sinning a lot more -- the sins of intellect. And there's a connection that is being made between those two things. Okay so covenant of words broken, chased out of the garden of evil, Satan takes the form of serpent and now which is taking the form that we know it has, which it's forced to wriggle on its belly and it has an enemy forever with man and woman. Human beings have to toil for their labor. Instead of getting nice fruit of the tree you have to work, you've got to plant stuff. You've got to kill stuff. Women [Sound effects] Child birth, this doesn't mean anything to most of you. I'll presume most of you yet. But, child birth -- I've seen child birth way up close and I haven't experienced it myself, but I've seen it. Painful! [Laughter] I mean when you look at it you say, "Who made up this system." [Laughter] But then if you say, "Oh, but it was punishment." But the thing about God though however -- the God of the Old Testament is a loving God. He's very severe. But the Israelites are always the chosen people and he is chastising them, but he always cares about them. That's one thing, even when they're in captivity and prison you know. They know that they are the chosen people and that it will work out. They have that promise. So that's one of the things you've got to understand. The New Testament is a different story. From the Old Testament we get the doctorate of original sin. The doctorate of original sin is a bit problematic because why should all of human kind be punished for one guy's mistake. And you might say -- and I think I mentioned this -- that God knows, that whole bit about providence at the end of the first chapter of Moby Dick. God knows that I'm going to do this. So was it really Adam's fault? Didn't he kind of set up the situation. Like using reverse psychology on my four year old. "Don't eat the tricky fruit." [Laughter] "Susie you can't possibly dress yourself before I come into the room, can you? I'm sure you can't." So is it really -- I mean come on is it really Adam's fault? Fine, and all that stuff that is going on is happening pretty quick as far as we can tell. So, Adam hasn't learned very much. But God is merciful. So the doctorate of original sin is really bad. The doctorate of original sin means not only that you have work and you have to bear life birth and all that messy stuff, but you're also going to hell at the end of that. Yes, human beings are now eternally damned. Really I mean it, the hot place. You're going to hell. That is the meaning of the doctorate of original sin. It will have a name and it will be called total depravity. But God is merciful. Human beings deserve nothing, nothing. But God does still love them. So he creates a new deal. The new deal is another covenant. It's called by the Puritan's the covenant of grace. Anybody have an idea who seals this bargain? You've all heard it. Yes? >> Jesus Christ. >> Jesus Christ that's right, God's only begotten son comes down to the world to extend God's mercy. So what does Jesus do? He sacrifices himself. There's a certain way of which the Old Testament is still partaking of a certain kind of old and logical sacrifice. And remember Jesus is Jewish. He found Christianity, but he's Jewish. He sacrifices himself on the cross as the supreme act of love. That's the interpretation that they get from Paul. Paul is the one. If you think about why -- if you're skeptical of Christianity for any reason you say why do Christians revere that kind of bloody crucifix? It's because they don't see it that way. They see it a supreme symbol of love, somebody that loved other people so much that he was willing to undergo that and you might say that kind of wipes out the books. Human beings owed God more then they could possibly repay because of the doctorate of original sin. But Christ suffers so much that he wipes out the books. [Sound effects] and that is the new covenant and it's the covenant of grace. And according to Puritan logic, the covenant of grace is actually better. The covenant of words is fine. It's in the Garden of Eden. It's scenery, good food, but is God above. Covenant of grace, where did those who received grace get to be -- Garden of Eden, no -- at God's right hand with the angels, up there. It's better so there's a certain logic that's in place there. This was good, and we broke it and we suffered but we got back, which is better. It's through suffering that we achieve something greater. This mode of thinking is called typology. And the larger mode of thinking is typological hermeneutic. So hermeneutic -- hermeneutic is a way of interpreting and hermeneutics pleural is you might say the science of interpretations. When you put it together it means a way of interpreting through typology. A typology -- and it's a way of interpreting first the Bible. Now typology depends on the existence of types and anti-types. And they don't mean exactly what you think they're going to mean. And type is the first thing. When I don't know. On the day of the iPad this seems radically inaccurate to be saying this. But it's like a font of type. Maybe I should say like a stamp pad. Maybe like the dye that you use to create, maybe like a reverse image. So you take your stamp pad, you ink it and what is that you care about the stamp itself? No you care about the image that you create. The image is the anti-type. The type is the kind of reversal of the anti-type. The type prepares the way for the anti-type. The type's meaning only comes clear when you encounter the anti-type. You don't care about the stamper. You care about the image that's produced. You don't care about the dye that produces the coin. That's the relationship. Now in the Puritan understanding the Old Testament is full of types. That's what they are. Like the recurrence of forty, forty days and forty nights, [Inaudible] at forty days all pre-figures Christ out in the desert struggling with Satan and his conscious for forty days and forty nights. The meaning of forty days and forty nights only comes clear through the life of Christ. And you pick any number of things. And if you actually go back and read the gospel according to Saint Matthew especially you will see that he's very concerned to show that some of things that Christ does fulfills scripture. Christ is the fulfillment of what has been predicted or foreshadowed in the Old Testament. And so it has that relationship. It's a way of reading the Bible in other words that gives of pride of place in the New Testament over the Old Testament and it says that the Old Testament is kind of like John the Baptist, it has a preparatory relationship for the New Testament. This all really comes out of their understanding, comes out of Calvin's Institute of the Christian's religion. The Puritans, so this is on the eve of the Bradford's and the other Puritan's coming to the new world in 1620. There's a big meeting of the church elders in Holland called the Synod of Dort. And they agree on a kind of official interpretation of Calvin's Institute and that's the one that they start to put into practice with the new world. So this is the idea that comes out of original sin, the total depravity of human kind. And I mean total, right. You're totally depraved right? You're born. You're going to hell. However because God is mercifully and there is a thing called unconditional election that takes place. It doesn't mean you vote. This means that you become among the elect. It means that you are saved and you receive grace. It's unconditional because there's no strings attached to it, not on God's end and not on yours. There's nothing you can do to earn it. This is the point that I have to stress. For the Puritans there is no way to do enough good works to balance -- to pay off your debt. Only Christ can pay off your debt. So there is no way that good works can earn your way into heaven and if you think that's true for them it's a heresy. They call it the Arminian heresy after the Dutch thinking Jacobus Arminius who propounded it. So any chance good works getting you into heaven? No, no, no, you could be the worst sinner in the world, but if you're converted and you receive grace boom you're in. The best person in the world, not received grace, sorry the gates barred to you. But there's another hitch I forgot to mention -- did I mention Christ died for not quite everybody's sins. He died for those who were already going to be elect. So Christ's atonement for these sins is limited. Christ died for the chosen people and who are the chosen people? Funny how that works right? The Puritans are the chosen people. But good thing is there's -- grace is nice and irresistible. I mean when you read accounts a little bit, which we will, it's like receiving grace, whoa. And guess what once you have it you always have it, perseverance of the saints. It's probably more correct to use the French theory who say you always already had it. Because God always already knew who was going to receive grace and who wasn't. So these are five principles that I would like you to remember. They will help you as read the Puritans. Can anybody thing of a way? No Con westies. >> TULIP. >> Yes, TULIP -- total hereditary depravity, unconditional election, limited atonement, irresistible grace and perseverance of the saints, TULIP. Are there any questions about it? No [Laughter] we're not going to play that one yet. We are almost as you can tell at the end. But I want to know if there's any questions about it this? Yes? >> [Inaudible background question] >> Well we'll talk about this. I mean the goal is the Puritans believed -- hope that all of them are going to have been saved. But the goal is here in their theocracy here in the new world is they want to try to create a church that is close to what they will call the invisible church. So it's actually God's church that is actually real and exists in heaven and God's mind. And they want to mirror that on earth. So they really want only the chosen to be there. Than there's a kind of an epistemologic kind of problem, how do we know who's chosen and who isn't? I mean it goes without saying that John Winthrop or William Bradford, they're chosen right. And what about their kids -- kids don't seem to have the greatest experience, that proves to be a problem later on and they have to figure out ways to deal with it. So there's a kind of -- there's a couple weird paradoxes that I want you to be thinking about. One is if God has already chosen all of this, how can there by anything like free will? How can that work? And we have an idea of providence and what's called pre-destination and also have free well at the same time. Don't those constitute mutually exclusive ideas? So that's one thing that the Puritans are going to wrestle with. And how do you know if you have the signs of grace? And it's going to be really important if you're trying to create a society or even a politics that's based on this. You gotta now who's in and who's out. But only God knows really who's in or who's out. So you've to figure out ways of guessing. That's one of the upshots of this, but what I want you to see is the way in which what we have here is a kind of haunted imagination. Everything means something. Nothing is neutral. Typological hermeneutics starts as a way of reading the Bible but becomes a way of history and their own daily experience. In other words, if strictly speaking typological hermeneutics is a way of reading the New Testament, or reading the Old Testament in the light of the new or the way of reading New Testament that says that's the fulfillment of the Bible, for the Puritans typological hermeneutics starts as that but it radically becomes something else. It becomes a way of reading their own history and experience and seeing the entire Bible as a type that they are fulfilling or full of types which they are fulfilling. They are they say, "The latter day Israelites." That means the previous Israelites only mean something with the appearance of the Puritans. It's only with the appearance of the Puritans who are the anti-type, the meaning of the Israelites that it finally becomes clear and fulfilled. That's you might say the ultimate hubris of their way of thinking. But it's comforting in a certain way because when things start to get bad here in the new world, and like Avatar the new world kills a lot of them, they have comfort because they know it's for a purpose. They know that God cares about them and when things go really bad they blame themselves and say God is punishing us. But it's only because he wants us to get back on the straight and narrow. It's not unlike we break the covenant with them and Winthrop will use this language of covenant but we can always re-establish it just because there's a precedent for that -- the covenant of words, the covenant of grace. We establish that we are still God's chosen people. That's comforting for them. But it means, go back under this point under this point they're always trying to figure out ways of understanding what things mean. So the littlest thing can be read typologically and these things are. People look at the tiniest events and try to understand them. But understand, they've got this kind of template. It's another template. Columbus has the template of wonder; these guys have the template of typological hermeneutics. Let me give you one instance of this and then we can be done for the day. Take a look -- if you have it with you -- take a look at the piece that's called Mourt's relation and you can see -- you've got this thing printed out, which I hope you do, take that out and then at the same time go to the first volume of the anthology and turn to page 116. [ Sound effects ] >> Now this Mourt's relation is a pamphlet. It was published in England in 1622. It's thought to have been written by William Bradford and Edward Winslow in the colonies and brought back by this guy named George Mourt to be printed. And it's -- not unlike Columbus' letter it's kind of like a pitch. It's almost like prospectus for further colonization and it's kind of a justification. So when you read it you will see that in some sense it partakes of that same kind of discourse of wonder. Okay they get to -- "On Wednesday the 6th of September the wind, coming east northeast, a fine small gale, we lose from Plymouth. Having been entertained kindly and courteously by diverse friends we had their dwelling and many difficulties in boisterous storms that landed by God's providence. Upon the 9th of November, falling at the break of day, we spied land upon which we deemed to be Cape Cod and so afterward it proved. And the appearance comforted us, especially feeling so goodly at land and would it to the brink of the sea cause us to rejoice together and praise God that had given us once again to see land." And what you -- if you read through it you see that they just can't believe, again like Columbus they're comparing it to what they know and they can't believe how lush it is. "And later on circle on the entrance which is about four miles over from land to land, compassed from the very sea with oaks, pines, junipers, sassafras and other sweet wood. It is a harbor with a thousand sail of ships, may safely ride." Good to know for the future right, if we wanted people to come here. And then at the end they start exploring the shore a little in the shallop, which is a little ship. And the very last paragraph we have. "As soon as we could we set ashore, 15 or 16 men, well armed with some to fetch wood as we had none left so as to see what the land was and inhabitants they could meet with. They found it to be a small neck of land and the side lay the bay and the furthest side the sea and the ground or earth, the sand hills much like the downs in Holland, but much better. The carse of the earth a spit's deep, excellent back earth all wooded with oaks, pine, sassafras, juniper, birch, holly, vines some ash, walnut. The wood for the most part open and underwood, fit either to go or ride in. At night our people returned but found not any person." Unlike Columbus they don't see anybody at first. "Not any person nor habitation and laden their boat with juniper that smelled very sweet and strong and which we burned many of the time we laid there." Alright again this pamphlet partakes in the discourse of wonder. Go ten years into the future and you get Bradford writing the history now of Plymouth Plantation. And if you look on the bottom of page 116 at chapter 10, you will see an interesting date. "Being thus arrived at Cape Cod the 11th of November and necessity calling them to look at a place for habitation as well as the masters and mariners, they having brought a large shallop with the [Inaudible] stood on shores of the ship they now got her out and took their carpenters to trim her up. But being much bruised in the ship with foul weather they saw she would be long in mending." Okay we've got the same dates. This is another account of the same event and they talk about -- he goes on and talks about all of this stuff [Sound effects] that's going on here. One of the things I want you to see is the way in which Bradford is re-writing. From the time that he gets Mourt's relation to this he is re-writing. And the way to understand how the re-writing works is through typology. Alright so what I want you to do over the weekend is to go back right before the place that I've just brought you, which is chapter 9, which starts off September 6th, which is the same place of the excerpt from Mourt's Relation. And what I want you to think about is what is the difference between this earlier account and the account that we see in Mourt's Relation? What has Bradford done to filter his account through the idea of typological hermeneutics? Where would you find moments of typological thinking? You should be looking for moments where he's comparing the Puritans to the saints earlier on? What is the logical of those comparisons? Who had it worse, the apostles being shot at or these guys? And remember this idea of the lush, wonderful wilderness that they've come to in Mourt's relation, how is it portrayed here? Is it the same kind of wilderness or is it something else? And if it's something else, why portray it in that way? One last thing and this you would find in the -- probably the single place to look at the exemplary place to look at would probably be in the middle of 115. He says that they didn't find anybody but in the Plymouth Plantation he brings those people that they didn't find into his account right here in a particular way. Why do that? What's the point? Okay, this is one of the earliest books we might say -- Plymouth Plantation is one of the earliest histories of the Americas -- of North America. And the think to understand is that at the moment you might say that American history writing is being created. It's revisionist history. It's re-writing. Why? That's where we'll start when we start next week. [Background sound effects] Thank you. [Music] |
Open_Ed_Cyrus_Patell_American_Literature | MobyDick_I.txt | >> Okay, I asked last time about a device, rhetorical device, that is the name of the rhetorical expression that I used, I think was I'm not going to tell you that you shouldn't cut corners in my class. And thereby in saying I'm not going tell you, I told you. And I had a few e-mails about this. Somebody said oh, it's an idiom. Which is true, cutting corners is probably an idiom. But that doesn't get at what was unique about that statement. And I had a few others. Somebody came close. In fact, it's theoretically correct, I suppose. In suggesting that this was called apophysis. And that is one term, name, that is sometimes given to this rhetorical figure. And I don't tend to use that one simply because it also is -- it refers to a type of reasoning as well as a rhetorical figure. The type of reasoning one that's close to being Socratic, where you would determine what is true by eliminating what is false. Right? So you affirm by negating. But basically, apaphasia is thought now to not only cover that but a large group of devices that basically share in common the idea of affirming by negating. The one I used to like was acre la tad o as a name for this. But people have suggested to me, aha you know, there are those who prefer that acre la tad o be reserved for certain kinds of dramatic scenes and you know, then there are a whole bunch of names. One of the things to know is that many of these rhetorical figures have double -- I mean, they sometimes have triple names. Personification, right? You've heard about in literary interpretation, probably, also gets called proslapia, and there's a Latin version of it too. So the name that we're going to give to this figure, we're not going to call it apophysis, we're not going call it oclatado although you wouldn't be wrong, I suppose, to do that. No, the one that we're going to use and that's going to appear on the scavenger hunt that we're going to give you in a little while is this paralypsis. If you really want to be fancy pants, you can also say that a particular version of that is prolepsis. In which you give a ton of detail while you're saying that you're not going talk about it. Right? But this is -- paralypsis is one of Cicero's favorite devices. He'll begin by saying I'm not going talk about how terrible Katline has been, blah, blah, blah. So one of the things to remember is that when we identify a figure of speech or a figure of rhetoric, write paralypsis. That's only the beginning of the work that we're supposed to be doing. In other words, I say what is that, you say paralypsis, you're not done. Because the next question I'm going to ask you in the context of this course is so what. What work does having that figure in that place do. All right? And that's what the point of the scavenger hunt is going to be. We're going to ask you to look for an example of a metrical foot, a couple of figures of speech, a couple of figures of rhetoric. You'll have a list from which to choose. In the reading that you're doing you should be sort of tracking these things. And it will be due shortly before the midterm. The idea is not only for you to identify that this is, I don't know what, cesura in a line of poetry, but then to be able to say what the effect is that the cesura creates. Why would the poet use a cesura, a pause, in the middle of a line in that particular place, or a figure like paralypsis. What did it buy Phyllis Wheatly to create that structure at the beginning of her poem instead of just speaking openly, right? So we're going to be wanting from just identification to something like interpretation. And that's really part of what the point of close reading is for us. Close reading is going to be -- we might say we as English majors is interested in how texts work. We're also interested in a number of other questions, but one of the things you might imagine that we're going to take a text and we're going to read it in a really strange way. We're not going read it the way other people read it who are in different majors or who are general readers. They tend to read one time through and figure they've got the meaning of it or don't, and then they're done. We reread. We often reread and reread and reread. Not only that, but we read in a particular self conscious way. Last time I started to try to get you to think about the ways in which meaning are being constructed. Not simply because the author has put some set of marks down and created meaning in text. But in a sense, those marks are the guidelines for you, the reader, to be able to construct the meaning of a text within certain guidelines. It's like the tree falling in the forest. The text that is not open has no meaning. It only has meaning if somebody has read it, only continues to have meaning if more people read it. And it only continues to have meaning after that if people talk about it, and it becomes kind of a living document, right? So we're very interested in the ways in which meaning is constructed and part of that means to understand how those marks work when they're on the page. If you're a good reader, you will be able to, as it were, take the text, put it up on the blocks, look under it, look under the hood, take it apart, put it back together again. You want to figure out, in other words, how the text creates certain possible meanings, certain kinds of effects by putting certain words together, creating certain kinds of images. Making use of ambiguities, contradictions, paradoxes. Those are going to be the most interesting things for us, right? So we're reading in a strange and artificial way. And one of the ways I think that it's helpful to get used to reading in this way is to breakdown the text into what I will be calling exemplary moments. And when I say exemplary, I don't mean like the best, what I mean is coming from the Latin exemplum, something that is a representative example of the way the text works. Or of something that is extremely important to that text. I will try in lecture to bring out certain exemplary moments. But I want you to be looking for these things. So you are going to get a midterm exam. And the midterm exam is to a certain extent going to be a reading check. But it's not only going to be a check of have you been reading, it's even more importantly a check on how you've been reading. And we want you to read in a way that allows you to notice these exemplary moments. Now again, you're all different readers with different horizons of expectations, you're likely to think that different moments are exemplary. Therefore, we also want you to be able to say why you think a moment is exemplary. Therefore, the teaching staff and I have agreed that we are going to try to promote this form of reading by asking you to do it while you're reading and in preparation for section. Okay? So this is what we're going to do starting this week before Wednesday's lecture. We will ask each of you to e-mail your section leader, we'll do this just -- we're going set up separate Gmail accounts where these things go, so they're all segregated in one place. We want you to e-mail two sentences. These two sentences -- the first isn't even really a sentence, it's a sentence fragment. It's going to be an identification of your exemplary moment by author, text, page, in the Norton anthology or Moby Dick or whatever it is, the text that we're using, and delimited. You don't have to copy the whole passage, if it's a passage. But we want you to give the beginning and the ending. So it's kind of like the bracketing words. So your TA and I can take a look at this and see immediately what the passage is. Now they shouldn't be whole chapters of Moby Dick, unless it's a really short chapter, and there are some of those. You need to think about why what you've identified constitutes a moment. Could be a moment as short as a sentence or even a phrase. Then we'll want you to say something about why that moment is exemplary. So one more sentence about why you think that moment is exemplary. Of what is it exemplary. It could be exemplary of a number of things. Could be the style that the poet uses is captured by this passage, right? Probably be a long sentence in which you explain what that style is, then, so don't just say this is stylistically characteristic. We want to know why. This is stylistically characteristic because it -- right? It could be thematically exemplary. This is thematically exemplary because it, you know, it shows Melville's interest in the dynamics of freedom and fate or whatever. The best ones will probably be both, stylistically and thematically exemplary. And here's the fun part. You should come to section prepared to talk about your moment. You'll have your moment. Each of you will have at least one moment to talk about your moment in class, and you'll want to have picked a good one, and you'll want to be able to talk about why you think it's exemplary. . And you'll be doing this in front of your peers. So if you pick a particularly lame moment and give it no thought and you picked a particularly lame moment and you're unlucky enough to be called on that week, well, you can do the math. You know, you're going to be there in front of everybody and they're going to -- well, maybe you don't care. But they're going to think that you're kind of lame. So we don't really want that. We want to -- we want to promote anti-lame behavior. So we really want you to start thinking in ways that are not from an English major's point of view, lame. We want to be interesting. Okay? Are there questions about that? So what I'm going to do is I'm going to send you an e-mail, I'm going to remind you of these instructions and I will give you the three addresses. One of them is going to be the one to which you should send your moment before this time on Wednesday. Yes? >> Is it one [Inaudible] or is it -- >> No, no, no. Just one a week. Let's not go crazy. Just find me one good moment that's worth talking about. That should be easy, right? But the idea is then you have to do a little bit -- you don't have to spend a ton of time. Just think, it will get easier as you start to recognize -- and these are the kinds of things that are -- I don't know, you might call them highlighter moments too. If you're a highlighter type of person -- I'm not. If you're a highlighter type of person, these are things like -- that scream out highlight me. There are certain ones that do. Might be more interesting to find the ones that only certain kinds of readers will see as highlightable, or something you recognize as highlightable. Try to explain to everybody else why they should have highlight tide. Come up with a really good one, you'll feel good about having done it. Okay? More questions about that? But again, one of the -- so, the larger lesson that's in place here, what we're trying to do is get -- if you don't want to use the rhetoric of exemplarity, think of the rhetoric of synecdochally. We're going to try to be thinking synecdochally. Look at this term. By which I mean what, what doe synecdochally mean? Yeah? [ Inaudible audience comment ] >> That's right. Part -- stick to part represents a whole. So all hands on deck. what's the difference between synecdochally and metonymy, while we're at it. Some people say there's not a real difference [Inaudible] there's a real difference. So what were the difference -- what's a metonymy? [ Inaudible audience comment ] >> Yeah. [ Inaudible audience comment ] >> Hmm, I wouldn't say it that way. Yeah? >> A related object represents another object. >> Okay, give me an example. >> If a waiter is holding a glass of champagne, he would say the champagne is moving through the crowd or whatever. Because the champagne isn't actually -- it's not -- >> That's -- would I call that a metonymy. I don't know, I might have called that a synecdoche, because it's a part for the whole. But I take your point. Yes. There's a common one. They use it in the newspaper every day. >> The crown. >> Good one. Why, the crown for the queen, the White House for the president. Well, the newspaper, is that already dating me? Anybody have any other examples? Yeah? >> The law? [ Inaudible audience comment ] >> Okay, but the thing about it is what characteristic of a metonymy -- it's going to be a substitution of one thing or another from -- to which it is contiguous in our experience. To which it's connected, right? So the White House is the place where Obama lives, and it's the place that we locate the presidency. So when we talk about the White House, we're talking about something with which its associated. So it's a kind of a trope, being next to one another. Whereas synecdoche we're going to use a part for the whole. So it is a trope substitution in which a smaller part stands in for the larger. One of the things I want you to understand, and this leads me to thinking about Stephen Greenblatt a little bit, is that there aren't actually -- for the most part there are, you know, most synecdoches are not just conveniences. They're actually coded with values and meanings and in fact, ideology. Now I think that's part of what Greenblatt is getting at in his article on culture. I wanted you to read that, because it gets you to understand why in a course that's called literary history we're actually going to be doing quite a bit of close reading. He makes a powerful argument, I think, on behalf of the fact that text -- well, in his case probably great text -- encode a lot of their cultural meanings, context, the ideological milieu from which they spring, they get encoded into the text. To understand those things we need to read the text really closely so the -- we read the text to get a kind of window into say the Melvillean world, the world of the 19th century, for the world of Shakespeare, in Greenblatt's case. But again, as I said last time, there's a kind of a reciprocal relation. So we read the text to get at the culture, but the culture also helps us to get at the text. Knowing something about the culture in which MacBeth was written -- there was an issue about succession and possibly the play it miswritten, you know, as the first of the plays in which Shakespeare is the king's men, the Lord Chamberlain's men, might be seen as a cautionary tale. All of those things help to illuminate the play. So we can read the play and the culture in a kind of reciprocal relationship. That that's what we're going to be trying to do, and I think Greenblatt makes a powerful argument about that. So how does synecdoche, as an example, encode ideology. If I say all hands on deck, that's kind of become a dead expression, I suppose. But it starts off as a synecdoche. All hands on deck. Not all men, not all sailors, all hands on deck. Tell me about that? What's at stake in that, yeah? [ Inaudible audience comment ] >> Very good. Exactly. So what's important to you about a deck hand? His hands, his ability to labor. The language encodes that. All right? Now what happens to us, as these things become used, they become kind of dead metaphors, and all of these are a species of metaphor metonymy, synecdoche. Part of our job as good readers or as English majory-type readers, literary scholars, is to revivify dead metaphors to understand what was at steak and what might continue to be at steak in the language that we use. That goes back to what I was saying about the term America last time. America is a figure -- a piece of figurative language. I wanted to argue that it was a trope, and it was a trope that signified paradoxically, think Lazarus, and exclusion, right? Think imperialism, colonialism, slavery. Right? Racism of any kind. So part of what our goal is in this course is to understand the complex ways in which language works. So we're going to be paying attention to figures like paralypsis. But we're going to be doing more than playing the English major game of naming them. We want to understand why they're there or to try to have an interpretive guess as to why the poet puts it there, or what effect it is, that's created by doing that. Okay? So that's part of why we'll be mentioning things like this, and we have some assignments that are devoted to this. And that's part of why I asked you to read the Greenblatt. It's making the argument about the importance of close reading for cultural reading, and reciprocally, how culture can help us do close reading. If you'll remember, one of the things he talks about in -- in this, is to -- to suggest this, right, that a full cultural analysis needs to push beyond the boundaries of the text, to establish links, he says, between the text and values, institutions, practices, elsewhere in the culture. But these aren't a substitute for close reading. Right? And you know, just -- since you're English majors, you might care about this. Greenblatt is identified with a School of thinking that he helped pioneer that's called the new historicism. And the new historicism in part took aim at the kind of literary thinking that's exemplified by the piece that I asked you to read, by Andy Delbanco [Phonetic], which came from the New York Times Book Review some years ago, but is also excerpted from a very good book of his, a little book, called The Real American Dream, which is like a short account of American literature, which you might say embodies a kind of humanistic approach for lack of a better word, a humanistic approach to the story of American literature. Delbanco is telling one story of American literature, it has to do with a certain set of values, with a kind of canonical tradition. It -- it -- in some sense, it positions literature as part of the history of ideas. It's -- compatible, I think, with -- for example, Harold Bloom's account of literary history as great minds contending with one another over time through text, reading and misreading one another. Greenblatt and the new historists were interested in something else. Right? And for somebody like Delbanco, and this might be a little bit of a caricature, you would say he gives primacy to the text and allows it -- the context to appear as a kind of background against which the text is staged or that might illuminate certain aspects of the text. It becomes a kind of scenery for the term. Greenblatt is interested in this reciprocal relationship that we've been talking about. When people didn't like what they did, they were parodied. And in deed, some new historists practice is quite parodyable. The typical practice was to say that a text is part of something larger that we might call discourse. This comes out of the French thinker Michele Foucault. We would say part of a larger thing called discourse. And you know what, lots of other texts and lots of other practices, lots of other things that we encounter in culture are also part of this discourse. And the discourse is ultimately all about different kinds of power relations. So you might imagine this discourse as a kind of cloth. And the text is a thread within it. And another text is another thread, and an event in culture is another thread. And if you pull on one you start to pull at the weave. Something else moves somewhere else. So if you wiggle this story about a hermaphrodite over here, from something like As You Like It starts to move over there. Right? That's in some sense the way new historians practice. Obviously, that can -- when that works, it works very powerfully. You can see things in a play by putting it together with something that might seem remote from it in experience. [Inaudible] something that is not most nominal in relationship to it. But also if you pick the wrong thing it becomes kind of ludicrous. Who's to say what is right or wrong. The proof might be in the pudding, if it works, it works. But what people used to say about this is they don't -- new historians didn't believe in writers and they didn't believe in genius, so the parody was Greenblatt thinks that Elizabethan England wrote Shakespeare's plays or the culture wrote the plays. And isn't that ludicrous, ha, ha, ha, Greenblatt is clearly addressing that in the culture article. And I think it's clear that he believes in something called genius. Shakespeare for him is a better writer than others. But the way in which Shakespeare is original is not by thinking of things out of the providence of his own imagination, as if out of whole cloth, rather, Shakespeare is a collaborator with his culture. He takes the material of the everyday and transforms it into something else. He takes his sources, he takes history, he plays with it. He makes prince howl and hot spur, foil for one another, in Henry IV, Part I, even though in actual history they were separated I think by 20 years in age, right? But it doesn't work as well, dramatically. He gets at a larger truth by knowing what details to change. And that's part of the genius of Shakespeare, and that's part of what Greenblatt is getting at. But in so doing you might say he illuminates his culture. So the thing that's -- be interested in is how is a Shakespearean play timeless precisely because it's time-bound. We're going to ask the same questions of all these texts, particularly Moby Dick. If Moby Dick is a text that repays reading long after the time when the kinds of industries and the people that it describes are dead and gone, why is that? How come this is -- if you believe it, maybe it's an open question that we should answer at the end of the term -- if you believe that this is more than just simply a historical artifact, what is it that allows it to keep living. And we might actually say that it might not be something intrinsic to the text itself. It may be the way the text is constructed. As a center of a cannon, as I told you last time in a way the American cannon was constructed precisely so scholars could prove to other scholars that America has a literature that befits a great nation that's a world power. We already had it. It's not like we're going have it soon because we became this great nation, we already had it. It's here. And maybe people keep saying that Moby Dick is a great book because people like me keep assigning it. You'll have to tell me at the end of the term what you think about it. If I were [Inaudible] I'd probably dart a harpoon right now. Okay, so in other words, to -- so Greenblatt is making this argument, right? So he basically says in part we need to read contextually, to recover the meaning of texts. Some of which are incomprehensible when they're removed from the surroundings. We need to reconstruct the situation in which they're produced. But he's making an argument about the great text is going to be one that actually enables us not simply to have to reconstruct in that way. Works of art, he says, contain directly or by implication much of this cultural situation within themselves, and it's this sustained absorption that enables many literary works to survive the collapse of the conditions that led to their production. So maybe that's one model -- if I was going say what makes a text great and maybe, you know, as people who are majoring in a profoundly -- I don't know what we would say, people who are majoring in a thing that other people think is not so economically wise, you might want to have an argument for why it is you do what you do, and what it is that makes text great, and why we should continue to read them. We're going to help you marshall arguments like that in the course of the term. All right, so then finally on Greenblatt. Cultural analysis is not by definition an intrinsic analysis the way it used to be, in other words, thought of, as opposed to an internal formal analysis. At the same time, cultural analysis must be opposed on principle to the rigid distinction between that which is within a text and that which is outside. So part of what he's trying to do is reconfigure what we typically thought of as text and context as inside and outside. Things that we used to think of as extrinsic to the text, such as ideology, we would say now are part of the text, they're encoded in the text. We use close reading to tease them out, to understand the way that they work. Ideology works precisely through words, through the ways in which to use a different kind of language. Signs are created. And if you're a derivation [Phonetic], you'd say there's a slippage between the sign, in the sign, between a signifier and the signified. How many of you have any idea what I'm talking about, did you do this in literally interpretation? We'll get to it later on. Don't worry about it for now. But it's in that slippage that you might say ideology seeps itself in. A good close reader undoes that. And is able to pull those things out. Any questions on any of that so far? Good, we're all on the same page, you understood -- you bought into why we need to read closely now? Okay, good. So one more word O'Dell bank o. This is a story about American literature. It's actually a pretty good story, I like it. I have a few bones to pick with it, perhaps. And one of the things I want you to be able to do by the end of the course is to have your own understanding of what is good and maybe what needs inundation in this account, which isn't necessarily a brief account. More than that, I want you by the end of the term to be able to have your own opinion and be able to make an argument about what is good, what is powerful, and what needs inundation in a story that I'm telling you about U.S. literary history. Right? Because any literary history is going to be one way of doing that literary history. We're going to be looking at -- in some sense, I've giving you my construction about this, thinking about the horizon of expectations that I see in front of me, horizon of expectations would also include the way that I've been trained, the things that I think about. I want you to be able to start to interrogate what it is we're doing here. To be able to understand why this is one story among many that could be told, and in part you might decide that there are other ways in which if you were doing it, you would tell the story. Anybody that goes on to write an honors thesis or something like that will want to be able to evaluate the ways in which he or she has been taught, precisely so they can carve out a space for their own original modes of thinking. Okay, so that's part of again, self conscious thinking. All right, New York in 1817. I show you this because this is the way the city looked, kind of this part of it. And Herman Melville is born down here. Down on Pearl Street. He's born shortly thereafter in 1819. And one of the things that I want us to think about is whether it makes a difference to think of Melville as a New Yorker. I think I mentioned this last time. But insofar as one of the stories that's going to be a main line for us is again something that we might call the Puritan origins of the American self. So starting next time we're going to be talking about settlement narratives and Puritans and a whole bunch of people that lived in New England. Well, Melville was a sometime-New Englander, but his life is framed by New York. He's born he and he comes back here when he's no longer a practicing novelist, and works in the custom house, and dies here. So there's a kind of New York experience that's framing Melville's writing. What difference does that make, or should that make, to our account of Melville's career. Again, one of the things we're going to be doing today is to use these opening chapters of Moby Dick to frame some of the larger issues that are at stake in the course of the part of the argument, therefore, I think I'm making implicitly is that Moby Dick sums up a lot of things. It sums up literary history up to the point of which it's written in 1850 and 1851. It sums up the state you might say of American culture, as well in that moment, basically, on the eve of the Civil War. That's a claim I think I want you to be able to test and evaluate before we get to the end of the term. Melville's parents were rather different from one another. The father was -- they both -- on both sides of the family, and this is a very good little biography of Melville that you could look at, at the beginning of the supplementary materials in this Norton. But Melville's father and his mother on both sides, he's descended from, you know, families that were prominent in the Revolutionary War. That is not a misprint. That is the way the family name was originally spelled. The mother changed it later on after the early and untimely death of Alan Melville, in part to distinguish them from this past that she considered to be somewhat problematic and possibly to help them evade creditors. You see, Alan was not much of a very good businessman. He came from a family from which it was expected he would live kind of a practice Trishant life, but he found it difficult to maintain that life. And so you might say that Melville's childhood was marked by economic difficulty. A kind of economic status that was below their actual class status or what they assumed should be their class status. And involved a lot of moving around in the lower part of the city. Alan was secular for the most part, but Maria wasn't. She was raised in a kind of Calvinist way. And transmitted that to her son, Herman. Right? So one of the things we might say about Herman is he was steeped growing up in a kind of biblical culture that his mother was very invested in, and that his father sort of tolerated, perhaps for appearance's sake or not to have a rift in his marriage. So this biographical information is interesting to us simply because we see evidence in the text in a kind of ambivalence towards this Christian inheritance. One of the things I want us to see in Moby Dick is the way in which Christianity is an inspiration and a provocation, and also an antagonist for Melville, as he puts this novel together. And I want to say that there's a certain way in which that's exemplary of certain kinds of developments within the larger literary and cultural history of the United States. Right? So a religious up bringing, a failed economic situation, there's a famous story in which he and his father, the father had sent the family up state. He and his father had to take a steamer in the middle of the night up the Hudson, they didn't have a cabin, they were huddled together in the rain. All of this marks Melville's up bringing. And at a certain point later on he had to become basically a -- he had to leave school, he was a school teacher briefly, but then he went to sea, in part because he didn't have other prospects, and he needed to figure out a way to -- if not send money back, not to be a burden on the family. There's a couple of things. This is another picture of Alan Melville. That's Maria again. Pearl Street is down here. It was right by the water front. And this is a nice little thing. I don't know if you can actually see it. I'll post it to the web site so you can see it. But right here, close to the front, I don't know if you can see it in the back. There's Alan Melville. This is a jury census from 1819. Alan Melville is recorded there. And the number of people in the household is there. And I think there's -- no [Inaudible] how many, four, three Melville males there. So that's Herman Melville, New Yorker, born on 6 Pearl Street in 1819. And this is from an introduction to one of Melville's earlier novels. It's in fact generically ambiguous. Should it be called a novel, should it be called a personal narrative, Typee. And what John Bouyant tells us is that much of the area that is now park is built on land fill, but in those days Pearl Street was right on the water front. This was perhaps slightly extravagant description, but it gets -- it let's the story, it gets the point across. Melville's home stood right at the confluence of Hudson and East River, so that in the summer of his first year Melville learned to walk on the edges of New York harbor. Today, iron railings gird those edges, allowing tourists to lean safely and observe the Statue of Liberty, but the infant Melville toddled the area, unfenced in search of the sea shells that gave the street its name. Thirty years later in the voice of Ishmael, the author would describe his old back yard as a magnet for all manner of seekers fixed in ocean reveries. His birth place was a spot where meditation and water and wedded forever, Melville new the sea from birth. And the passage actually points to a problem that Melville biographers often have, which is there are portions of his life that we don't really have a lot of independent verification of. So they typically go to the personal narratives that Melville wrote, like Typee and Omoo and Redburn, as if they constituted kind of facts that could be useful to the biographer. One of the things you might say about Melville is that he's one of those authors who invites us to take a kind of approach to his novels that is biographical or autobiographical. But especially in Moby Dick. I say we do that at our peril. If you choose to write about Melville later on and you choose to write about Moby Dick, I think you're going to make -- need to make a distinction in your paper. Are you going be talking about Melville all the time, Melville does this, Melville dramatizes this, Melville writes. Or are you going to talk about Ishmael. Ishmael does this, start to think about why it is you do one or the other. And also is there any reason that you would ever find to use both. Is it possible to have a rational for saying in certain sentences I will write Ishmael dramatizes such as such-and-such a relationship with Queequeg but then have Melville elsewhere? Let's just say for the time being as our hypothesis, that Moby Dick, with the hyphen in the title but not the name of the character, Moby Dick is a novel written by Herman Melville that takes the form of a personal narrative written by Ishmael. So that's our convention. Now, in other words, what it is, is an incredibly tall fish -- tall sea tale. It's a yarn. The biggest fish story you're ever going to encounter. And one of the things that we imagine about Ishmael is he knows that. He knows he's working in a genre. Or Melville's working in a genre. Take your pick. There are some people who would say okay, Melville is writing a novel that takes the form of a piece of writing by Ishmael that may be a novel masquerading as a personal narrative. That might fit too many layers. Let's just say it's a novel masquerading as a personal narrative. So that points out a question, a kind of technical question that we might want to ask, which is this. Is it ever possible for a novel to know more than its first person narrator. Is there a way in which a novel can somehow convey the limitations of its first person narrator, even if the convention is that the first person narrator is writing every single word down. How many of you guys have read the Great Gatsby. Great Gatsby. Okay, first person narration, right? Every single thing we think as a result of reading that text we get because of the character of Nick Caraway who's our narrator. Why is the Gatsby great? Because Nick says so, right? He created this kind of romantic character out of this bootlegging gangster, who when he talks is not particularly articulate. I say old sport. It's not -- Gatsby is not much of a wordsmith, but Nick is. And sometimes may be over the top. He kissed daisy and -- whatever it is. Some people like that, and other people think it's just really bad purple [Inaudible] prose. So that's the question. Are there -- start with the Great Gatsby, because it's a simpler case. Is it possible to think of the Great Gatsby as a text, as a novel, knowing something beyond what Nick Caraway is representing to us. Are there ways in which a novel can be configured to point out the limitations of its own first person narrator, to create a sense of unreliability of that narrator, and how would that work. Then generalize out from there. Is it possible that in some way or other, every first person narrator is an unreliable narrator. We'll get to that. And I think Moby Dick is a good vehicle for talking about these things. Is your head hurting yet? My head's hurting just thinking about it. Okay, so the sea. And the problem of Melville's biography, and the invitation to biography. In a word, I think we should not confuse Melville and Ishmael. I think we should keep them rigorously separated. And my own advice would be use Ishmael and use Melville rarely. If you went down to Pearl and State Street, you would see this. A little exhibition called New York Unearthed, an archeological excavation. The plaque on the wall says on this site, Number 6 Pearl Street, Herman Melville was born, August 1, 1819, author of Moby Dick, [Inaudible] the Scribner, Pierre, Philly Bud and many other American classics. Okay, so Melville goes to sea. And he comes back. And he has an interesting experience when he's at sea. Unlike Ishmael, as you will discover, he isn't faithful to his captain. He jumps ships a couple of times, he leaves his ship, he deserts from the ship that he's on in the Marquesas where he spends a few weeks among supposed cannibal tribes, and he writes this up in Typee. All right? And presents this as a kind of personal narrative. Then he goes off from Typee, he makes his way to another island, he writes it up in Omoo, eventually he ends up in Honolulu, he's in prison for a little bit. He finally ends up on another whale ship, and after that he ends up on a military brig. All of these things go into his novel. Typee and Omoo, about the time in the Marquesas, the military ship gets written about in White Jacket. The time on the whaler becomes Moby Dick. Now the thing -- couple of things to note. That Melville was already playing on the boundaries of what is fact and what is fiction. So that's one of the things that I mentioned last time that we're going want to track in the course of the term. What is literary, and what is literary's relationship to fact and to fiction, all right, so the Puritans that we will start reading next time in the next week, fiction is a dangerous category. It's akin to lying. By the time we get -- and history is something that we would respect, as well as biblical poetry and sermons and that sort of thing. By the time we start to get to the enlightenment, people are starting to get slightly away from this religious imagination and think about the ways in which there may be higher faculties that we need to think about, that make us human. The imagination. The reason. The story of enlightenment is the beginning -- people beginning to understand that knowledge may not only take place as a result of revelation from God. That maybe if you believe in God and maybe if you're religious, you say what did God give everybody. God gave everybody a soul, okay. But God gave everybody reason and the ability to think. That's God-given. We should use it. Don't always have to sit around waiting for revelation or reading the Bible. We can use our own reason and that's a divine faculty. Romantic thinkers start to push beyond that. Maybe reason is overrated. Maybe there are things that reason doesn't cover, the sub conscious, the unconscious, the dreaming life. We'll encounter this in a wonderful novel called Edgar Huntly. Right? And we see some of it at work here as we move on through Moby Dick. The imagination, then, because a fact that romantic writers start to develop. That's where we get to when we get to Melville, right? He's starting to be one of those writers whom we would call a writer of romantic literature. And by that doesn't mean he's interested in, you know, kissy-face between men and women or women and women -- whatever -- it's not Hollywood romance, right? We're talking about romance as opposed to what the novel has already come to mean by the middle of the 19th century. The novel has tended to mean writing about seduction or writing about domestic situations or religious forms, that's what's selling in the middle of the 19th century. Not the kind of stuff that Hawthorne and Melville are writing. And one of the things that Melville is doing, along with Hawthorne and other writes, is try to create a form of the novel that can have higher aspirations than they think the typical novel does. So Melville writes to his publisher in 1848. He's already known as the writer of some successful sea tales, based mostly on his personal life, although again he gets into trouble with Typee when people say wait a minute, some of the dates don't add up, was this guy really there. Later on the companion that he has in Typee, a guy named Toby whose name Melville actually used comes back and writes an annotation that's bound into the second edition and says I was actually there and this really happened. So Melville is interested in pushing the boundaries. If personal narrative is what's going to sell, fine, we're going to bill it as personal narrative. Get people to read it by calling personal. There's some recent scandals along those lines, the same, you know, literary history replays itself. Anyway, in 1848 Melville tells his British publisher my instinct is out with the romance, and let me say that instincts are prophetic and better than acquired wisdom. So you see the key terms here, and we'll get back to this. I'm trying to set these as seeds in your imaginations that will germinate as we read. To out with the romance. Romance is somehow here being a counterweight to acquired wisdom, right? This is a code for saying I'm interested in what we would call romanticism as opposed to the kinds of thinking that went along with the enlightenment and with neo classism. Right? So who writes romance? Well, one more thing. In 1850, about the whaling voyage, he writes another novelist who's written about the sea, I am halfway in the work. It will be a strange sort of book though, I fear, blubber is blubber, you know, though you may get oil out of it the poetry runs as hard as sap from a frozen maple tree, and to cook the thing up one would need to throw in a little fancy, which from the nature of the thing must be as ungainly as the gambles of the whales themselves. Yet I mean to give the truth of the thing in spite of this. Who writes romantic writing? Well, one of them is a German named Goethe. And one of the things that Melville has done on the eve of writing Moby Dick is take a trip to the continent. People think in part because he's looking for a kind of intellectual community that he's not finding in the United States, as we can see. People talk about the United States culture in this moment as being young, psycho-fanatic. Too reliant on British and European models. Melville wants to go to the source. He reads Goethe's autobiography, which is called Truth and Poetry. And he starts to think a little bit about what romantic writing is going to be like. This term fancy is a kind of code word for the imagination. In the romantic era, fancy means imagination , someone like Coleridge in the British context would try to separate it out as a different faculty, fancy is one kind of imagination, imagination is another kind of image nation. It doesn't really work. It takes -- so for our purposes, we might say that they are -- this is a kind of technical term from the imagination, right? But there's one other thing to note that's going on here, it's a strange sort of book, right? Blubber is blubber, you know. The poetry runs as hard as sap from a maple tree. But look at the metaphor that he uses. To cook the thing up. That's a meta for that refers to domestic life. And there's a way in which both Hawthorne and Melville are doing is trying to appropriate the territory that's occupied the best seller list, if there were best seller lists, novels that are selling are these domestic novels written by people like Susan Warner and Maria Cummings. And in some senses say we can do that, and we can do it better, right? Our kind of cooking is harder, our kind of cooking is ultimately more rewarding. Now Hawthorne complains about precisely this genre of the domestic novel written by women in this famous quote. And this is after he's already started to publish his own book-length romances. America is now wholly given over to a damned mob of scribbling women. I should have no chance of success while the public taste is occupied with their trash. And I should be ashamed of myself if I did succeed. There's something a bit petulant about it. I mean, he wants to sell books. But the marketplace is not interested so much in the kinds of things that Hawthorne and Melville are writing. So that's one of the things I want you to understand about the way the cannon was constructed. The literary historians didn't go back to see what people were reading. They went back and said this is what people should have read if they were smart, they were literary. This is what we think from now on you should read that represents the American literary tradition. Hawthorne calls his novels romances. And these are the book-length ones that he completed. So as we move forward, we will see that Hawthorne is part of what Melville draws in separation from is precisely Hawthorne's mode of writing. If you -- when I said you should open up this book and read it, take a look at it from the title page on. One of the things to note is the dedication. In token of my admiration for my genius, this book is inscribed to Nathaniel Hawthorne. And there's a famous story about this. Melville begins writing Moby Dick when he's in New York. And in that moment he moves to Massachusetts, into the Berkshires. So the time when he's actually writing this, he has one, I think, conception of the book in place. And then, so the story goes, he meets this guy Nathaniel Hawthorne, at a picnic. Hawthorne by this time is an older writer, he's just written the Scarlet Letter, he's got these other things going on. He's known as a -- an excellent writer of short stories and tales. Melville's imagination is fired up by meeting the older man. He goes and reads a short story collection [Inaudible] from the old [Inaudible] and immediately gets to thinking. He very quickly writes the piece that I asked you to read for today, which is called Hawthorne and His Mosses. It appears in two parts, anonymously. Hawthorne is a little bit embarrassed by the extravagant praise that he receives in it. But I thought it was worth looking at, at the outset of both our reading of Moby Dick and the course precisely because of the way in which it pitches not only the project of Melville's own writing but the project of American literature. Okay? This is one of a number, probably chronologically the latest, but probably a one of a number of pieces that we'll encounter in the course of the term that are kind of manifestos for an American literature. If you have your Moby Dick, take it out and take a look at Page 521. All right, he's been talking about Hawthorne's writing. And what he calls the Indian summer sunlight of one aspect of it. But that's the side of Hawthorne's writing that really draws Melville to it. This is in the middle of the page. For despite all of the Indian summer sunlight on the hither side of Hawthorne's soul, the other side, like the dark half of the physical sphere, is shrouded in a blackness ten times black. But this darkness but gives more effect to the ever-moving dawn that forever advances through it, and circumnavigates his world. Whether Hawthorne has simply availed himself of this mystical blackness as a means to the wondrous effects he makes it to produce in his lights and shades, or whether there really lurks in him a touch of Puritanic gloom. This, I cannot all together tell. And part of our project for the next couple of weeks is going to be to try to understand what that phrase Puritanic gloom means, right? He gives us a little gloss here. Certain it is, however, that this great power of blackness in him derives its force from its appeals to that Calvinistic sense of innate depravity and original sin from whose visitations in some shape or other, no deeply thinking mind is always and wholly free. For certain moods no man can [Inaudible] this world without throwing in something somehow like original sin to track the uneven balance. I want you to go back to the model of culture I offered up last time, of dominant, residual, and emergent. Calvinist culture in Melville's conception would be residual. It's part of the past. It has an ongoing hold on the present. No deeply thinking mind is always and wholly free from it. I want you to look at that and spend some time with it. Look at the way the sentence is constructed. It's a marvelous Hawthornean sentence that's full of all kind of hedging and negative statements. No deeply thinking mind is always and wholly free. So how connected is that deeply thinking mind? I guess some minds that aren't deeply thinking can be wholly free of what is it? Original sin. Calvinist depravity. From whose [Inaudible] in some shape or another, there's wiggle room there. That's why it's residual. It's changing. Maybe by the time of Melville, it isn't so much actual Calvinism that's lurking over American culture, but something, something like it. Something else that's going to be needing to take its place, right? So this is an example I think of the interplay of residual and dominant cultures, this is after the enlightenment. Calvinism, which we're going to study in the next couple of weeks, has started to recede into the background, yet it still has its hold over Melville, it still has its hold over this book Moby Dick. All right? Then Melville does this. He goes on and he compares Hawthorne to Shakespeare. This is on Page 522. Now it is that blackness in Hawthorne of which I've spoken that so fixes and fascinates me. It's the first full paragraph. It may be, nevertheless, that it is too largely developed in him. Perhaps he does not give us a ray of his light for every shade of his dark. But however this may be, this blackness that is, that furnishing the infinite be secure of his background, that background against which Shakespeare plays his grandest conceits, the things that have made for Shakespeare his loftiest but most circumscribed renown as the foundest of thinkers. One of the things we might say about Shakespeare is you know, at this moment, when Melville is writing, perhaps the cheer writer in the English tradition because of the writings of a number of people, including Samuel Johnson, have made us see how important Shakespeare is. And yet he isn't quite sacrosanct in the same way he might be thought of as today. I mean, today when you take liberties with a Shakespeare play, you adapt it, you do all kinds of things, you cast Leonardo DiCaprio, oh, that's fine. But do you give Romeo and Juliet a happy ending when you put Leo in the play? No, you don't. They did, in the 19th century. They felt free to tamper with Shakespeare's meaning. They played up the melodramatic side of Shakespeare. And that's what Melville is alluding to here. But he sees something greater in Shakespeare, Shakespeare as a kind of philosophical writer. We'll talk about this more when we get back -- when we get back to Melville. But take a look at the bottom of 523. I mean, Hawthorne was one of those who Melville's about to describe here. Some may start to read of Shakespeare and Hawthorne on the same page. They may say that if an illustration were needed some lesser light might have sufficed to illustrate this Hawthorne, this small man of yesterday. But I am not willingly one of those who is touching Shakespeare, at least exemplify the maxim of [Inaudible] that we exalt the reputation of some in order to press that of others. Who to teach all noble-souled aspirants that there is no hope for them, pronounce Shakespeare absolutely unapproachable. But here's the rub. Shakespeare has been approached. There are minds that have gone as far as Shakespeare into the universe, and hardly a mortal man who at some time or other has not felt as great thoughts in him as any he will find in Hamlet. You will see later on that this is a very Emersonian moment, right? We have to be cowed by the previous achievements of England. More than that, Melville wants to say, in the middle of 525. This too, I mean, that Shakespeare has not been equalled. He is sure to be surpassed, and surpassed by an American born now or yet to be born. And, since you're English majors you should look at the footnote. And the footnote tells you with all the manuscripts, not the text as it was printed. Because Dikinky [Phonetic] the editor almost certainly was the one who toned the passage down to read if Shakespeare has not been equalled give the world time and he is sure to be surpassed in one hemisphere or the other. I'm going to stop there, but you can see why this is a program piece on behalf of an American literature. And I think that Herman Melville has a pretty good idea of which American it's going to be, that's going to surpass Shakespeare. You'll have to let us know at the end of the term what you think, how extravagant a claim you think that is. Okay? So this -- this is what we want to see here, right? That there's a sense in which the Puritanism that we're going look at is hanging over American culture, American writers, this writer, this book. So we study it now in order to understand in some sense what it means to Melville and what, perhaps, it might still mean to us today. Okay? So that's part of what our goal is in this course, to think about the ongoing residual effects of the fact of the Puritan origins or at least part of the American self. Now I want to go back to one other thing. This New York business, right? So Melville has written sea tales before. He's taken liberty with a few of the facts. But he's never taken liberty with as many of the facts as he does in Moby Dick. In Moby Dick, he takes his own personal narrative and changes it almost utterly, right? I mean, Melville was never on a ship that has happened to it what happens to this particular ship. And since some of you may not know, I won't tell you yet. His ship sails west. It goes down, it sails around South America to the west. Melville sends the Pequad east. It goes across the Atlantic, it sails around Africa to the east. You end up in the same place, it's just two different ways to go. He sends his fictional ship in the opposite trajectory from the one that he has come to, okay? The one he has done himself. So immediately, you can see Melville is playing with his narrative of his own experience in a way that he's never done before. So the we question remains why start the book with that first chapter in New York? Why start there at all. In fact, why start the book the way that he does. I said last time a novel often will begin with a kind of beginning that's sort of an ante chamber, that sort of sets the ground rules for interpretation. Let's you know what kind of book it is that you're reading. Take a look on Page 7. This is the beginning of our novel. It starts with a section called Entomology. Supplied with a late consumptive usher in a grammar school. And then in funny brackets the pale usher, thread barren coat, hard body and brain, I see him now. He was ever dusting his old lexicons and grammars with a clear handkerchief, mocking the embellished with all the gay flags of all the known nations of the world. He loved to dust his old grammars. It somehow reminded him of his mortality. Already, we're thinking what kind of novel is this? And then we get to entomology, we get three quotes, and we get well, the word whale and basically I don't know, looks like a history of western culture from Hebrew, interesting that Hebrew gets pride of place. Through Greek, Latin, Danish, Dutch, all the way down to Aaron Mangoin. So what do we make of this list? Do we take is seriously? Is that really Aaron Mangoin, did he make that up? I think he didn't make it up. I think that's actually it. This is a history of what, the world, the west, colonialism. Is it cosmopolitan. It is says that Aaron Mangoin has as much standing for entomologists as Hebrew, Greek, Latin, or Anglo Saxon. In any case, it isn't business as usual for a novel. And we turn the page thinking we're going to get the start of our book now, right? That was maybe the first page. No! The extracts. And the extracts have an event longer bracketed thing. And then all these extracts. Again, beginning with the Hebrew. God created great whales. Or Job, leviathan maketh a path to shine after him, one would think the deep to be horrid. And we go on. Down through Roman writers, Rabole, all the way down to oh, I don't know, we got Hobbes in there, we've got Burke in there, Blackstone, oh my God, this thing is going on forever and ever. Got pages and pages, got a missionary journal, and the final things -- a Nantucket song. So be cheery, my lads, that your hearts never fail while the bold harpooneers striking the whale. Or oh, the old whale mounts storm and gale, and his ocean home will be a giant in might where might is right and king of the boundless sea. What do these things all have to do with one another. Why are they here in the beginning of our novel. What signals are they sending. You can imagine why some people might look at this and just say okay, another book. You don't have that luxury. So tell me what signals is that sending to you. What's it do, when you encounter that -- yeah? [ Inaudible audience comment ] >> Very good. It -- well, okay. Yes. It is places human -- placing [Inaudible] within a history of human understands, and then you add in the whale, which is correct. But it's even without of the whale, right? It is placing it within a genealogy of test. Maybe we should do it the other way. It is placing it within a genealogy of text that go all the way back to the Old Testament. As it's doing that, and inserting -- one of the things it's doing is sort of demonstrating whaleness throughout all those texts. You might say it's making a kind of crypto argument, a tacit argument more the whale already. See, the whale's here, the whale's there, the whale's -- you didn't think you were going see it. It's creating a kind of intellectual genealogy more, you might say. And it's going back to sacred books. The question arises is this in some sense thinking of itself as a kind of sacred book. And it's also a little bit funny. It's mixing high and low. It's mixing the Bible are philosophy, with scurrilous things and whale songs and pop culture. There's a kind of encyclopedic impulse here. And Ishmael, we find out, is a former school teacher, he's a bit pedantic. He's interested in these kinds -- believe me, he's going to talk and talk. He's gone -- he's done a lot of research. There's a certain way in which -- and maybe, you know, if you had gone and talked to these sub-sub librarians and God knows who else, you'd want to show everybody the benefits of your research too, having spent all this time doing all this kind of tedious stuff. So it's out there for you to see. There are pages and pages itself. And then finally -- finally, after all of that, we get to something called Chapter One Lumies. And three of the most famous words in the American literary tradition. Call me Ishmael. Tell me about that. Call me Ishmael. What signals is that sending? [ Inaudible audience comment ] >> So it's casual. He's being conversational. Call me Ishmael. Okay, that's very possibly true, and yes, it's true. Yes? [ Inaudible audience comment ] >> Ah, but what's this call me Ishmael business? Looks like it's all friendly and stuff. Why didn't he just say my name is Ishmael. What's the difference between those two. Yeah? Go ahead. [ Inaudible audience comment ] >> Okay, that's fine. That could be, maybe it's not his real name. Maybe he's making a statement about somehow being an outcast. And I think it was Carlise who wrote around the same period that the writer is an Ishmaelite. You know, people don't want to read literary writing, so we feel like Ishmaels. Okay, we're an outcast. Then if you read the rest of the footnote you'll see that he's actually evoking a particular person from the Bible. Did you want to add more to that? [ Inaudible audience comment ] >> And a contested figure. Let's not forget that Ishmael has a different status in Christianity than he has in Muslim thinking, right? Ishmael is a big hero. It's Ishmael who comes back to Abraham in the Quran, not Isaac. So it's the out cast, possibly somebody who has found this great alternative tradition, immediately in three words, we've got a very complicated kind of textual literary dynamic going on. And maybe it's a little bit coercive. You know, we think he's being all friendly, call me Ishmael. But it's an imperative. Syntactically, it's an order. Call me Ishmael. Or else. Some years ago, never mind how long ago precisely -- why not? Already maybe we should be having our little English major bristling spines in our head, you know, going like -- if we were porcupines, they should go spring -- like that. Whoa, let's be on our defense. Never mind how long precisely. Having little or no money in my purse and nothing particularly interesting me on shore, I thought I would sail a little and see the watery part of the world. It's a way I have of driving off the spleen and regulating the circulation. Whenever I find myself growing grim about the mouth, whenever it is a damp grisly November in my soul, whenever I find myself involuntary pausing before coffin warehouses and bringing up the rear of every funeral I meet, and especially whenever my hypos get such an upper hand of me that it requires a strong moral principle from me to prevent me from deliberately stepping into the street and methodically knocking people's hats off -- then I account it high time to get to sea as soon as I can. This is my substitute for pistol and ball, with a philosophical flourish Kato throws himself upon his sword. I quietly take to the ship. There is nothing surprising in this, [Inaudible] knew it almost all men in their degree some time or another, cherish [Inaudible] the same feelings towards the ocean with me. Put it up on the blocks, take it apart. What's going on here. What images are these? First of all, serious or funny? Funny. Both. How come both. What's serious about it. He's talking about suicide. Yes, he is. Which leads you to believe, okay, stay on land, commit suicide or go to sea. Or maybe going to sea is suicide by other means? In this kind of joking voice, but already call me Ishmael. Is that friendly or coercive, or maybe a little of both. Is this funny or serious, or maybe a little bit of both. Is this death-obsessed? We have a suicidal narrator here? Maybe we already -- we have the signals of unreliability laid out for us, right? But he wants to suggest that this is kind of a universal thing. If they but knew it, almost all men in their degree cherish fair [Inaudible] same feelings towards the ocean with me. And now we get to the question I'm asking. There is your insular city of Manhattan built round by war, Indian isles, by corral reefs, commerce surrounds it with her surf, right and left the streets take you water-ward. And you can see that. One of the things that's interesting about the city is people often think about the way Manhattan is laid out is a kind of north south city, right? We have these broad avenues. But when it evolved, the thing that was really interesting about lower Manhattan and would have been true in Melville's day is what was remarkable were the big east west streets, that could take you from one set of wharfs to the other. And you can see from this picture in and around the same time that Moby Dick is published how the whole city is ringed with these wharfs that are full of ships. You can very much see why Ishmael would think of this as a kind of watery city. New York became a hub precisely because it was in this amazing harbor, where things could -- it could accommodate many ships. It became even more of a hub when the Erie Canal about twenty years before this opened up the whole middle of the country. Right? You can take stuff up the Hudson, and then through this canal system, all the way to the great lakes. It made New York temporarily, you know, the port of ports in the United States. Right? So it -- you can see what it is, that Ishmael is talking about, when he talks about this. But why start here. Because he spends about a chapter here. It's a chapter that functions as a kind of overture. But then as soon as Chapter Two starts, he stuffs a shirt or two on my old carpet bag, stuffed it under my arm and start for Cape Horn in the Pacific, [Inaudible] the good city of old Manhattan I duly arrived in New Bedford. He goes to New Bedford, ends up in Nantucket, and then out to sea. Why? Why start here? The hypothesis I want to give you, and it has something to do were the reading from Thomas Bender about this alternative mythology that New York might represent is this. That maybe one of the things that Melville is trying to do in this overture to the book is signal an engagement with what Bender calls the historic cosmopolitanism that has been associated with New York City over against things like the Puritan tradition that Ishmael seems to be invoking at the outset, or that's going to hang over this book. So one of the things we might want to ask is to what extent is Moby Dick the novel an attempt to draw inspiration from and also be antagonistic to precisely the kinds of things we're going to be reading over the next two weeks. We could go even further. To what extent does this novel going to be a way of making sense of and appreciating and amending the entire tradition that leads up to, starting with the Puritans and moving on through the enlightenment and up into the romantic period. Right? So that's what I want to suggest to you as a hypothesis. That maybe one of the things about these canonical American novels is that from the out set it is setting itself against what people take to be the main stream American tradition. Whether it be the traditional novel writing exemplified by the damn scribbling women in an art course, Harriet Beecher Stowe, or whether it be the kind of larger New England tradition represented by people that go from the Puritans all the way down to Emerson, to try to offer something else, something that is more cosmopolitan in its orientation. More interested in the strange, the wondrous, the other. So when Melville goes whaling, he gets on the ship, he goes into the south Pacific. He meets a guy who is I think the nephew of Owen Chase. Owen Chase was the first man on the ship called the Essex. About 1820s, I think the Essex is sunk by a white whale. People who reported what happened to the Essex say that it looks like the whale turned on the ship and actually stove it as if it meant to do that. It was a famous case. There were -- so the boat goes down, the sailors are all in their whale boats, and they're thinking like, shit, what do we do now. We're not meant to be out here on the open ocean. And you'll see, I mean, long boats have a sail, but they're small. They're not meant to be on the open ocean for very long. So the thought is, you know, we're near the Marquesas. We could go to the south sea islands and probably hit land pretty easily. Down side to that is we've all heard that there are cannibals there. Don't want to do that. So instead, I should have brought a map, we will sail to the western shore of South America. Okay, that's only about 2, 3, depending on how you go about it, say 2,000 miles of open ocean with not too many provisions. No, we're not going to go to the cannibals. We're too afraid of them. We're going to go to the western shore. Some of them make it. Some of them do make it. They come back. In fact, two separate groups make it. But here's what we might call the kind of cosmic irony. Cosmic irony is that form of irony that some people say isn't irony. But it's when the gods seem to be laughing at you and using you as a play thing. Guess what happens to them in their desire to avoid meeting up with cannibals? They become cannibals. They have to. I mean, when some of them die. They don't -- I think there's only one case in which somebody is actually killed. But they do -- once somebody dies of starvation, they do it to keep themselves alive. So you know, that's the story. Melville encounters this story. He gets a copy of this, this becomes an account that's written. Melville gets a copy of this account on there. And he reads it. And it's sitting there in his brain, germinating and becoming Moby Dick. So what does he do when he writes Moby Dick? He reverses the story of the Essex. Just as I said that he reverses his only personal experience and has the ship go out east where he went west. The Essex had an encounter with a whale and then an encounter with cannibalism. What happens in Moby Dick? We get our cannibals out on the table right away. We embrace our cannibal. We become a cozy, loving pair with our cannibal. And then we're going to go off and find our whale. But see, I want you to understand, if you get that cultural context you understand what a profound gesture that is. And when we come back to Moby Dick we'll spend some time with just how it is that Ishmael gets to know Queequeg. But I want you to think of that as a kind of radical gesture. Ishmael's friendship with Queequeg is [Inaudible] and not only because it has all these homo-social relations and they talk about themselves as bosom buddies, you know, as if they're an old married couple. Yeah, yeah, yeah. But it's that embrace of the other, right? The other -- cannibal is a signal gesture that this novel makes right on the outset. Okay, one last thing. In the aftermath of 9/11, alt.paranormal went wild on the internet. When people looked at what is your Page 22. Again, it's one of these things that sounds like it's, you know, just funny. And doubtless, my going on this whaling voyage formed part of the great program of Providence that was drawn up a long time ago. And you'll understand better what Providence means in this context in the next couple of weeks. It came as a sort of brief interlude and solo between more extensive performances. I take it that this part of the bill must have run something like this. Okay? So think about back then, I know you were younger. But remember what happened? Here's what Ishmael writes. Grand, contested elections for the presidency of the United States, which [Inaudible] one Ishmael. Bloody batted in Afghanistan. Okay? Bush V Gore, 9/11, the bombing of Afghanistan, the beginning of the war that we're still fighting. People looked at this and went whoa, and started to wonder whether Melville's text wasn't in fact something like spookily predictive. A kind of Nostradamus in the American context. It is -- it was a little uncanny, teaching this text in those days. So I just point this out, right? Ishmael is talking -- and I don't know what to say about that, that kind of strange mirroring. But there was actually a contestable explanation, there was actually a battle in which a bunch of British soldiers were bushwhacked in Afghanistan. But Ishmael goes to say though I cannot tell why it was exactly that those stage managers, the Fates, put me down for the shabby part of a whaling voyage when others were set down for magnificent parts in high tragedies and short and easy parts in comedies and jolly parts in farces. So I cannot tell why this was exactly. Yet now that I recall all the circumstances, I think I can see a little into the springs and motives which so -- being comely presented to me under various disguises, induced me to set about performing the part that I did. Besides cajoling me to the delusion that it was choice resulting from my own unbiased free will and discriminating judgment. I like you to think about that, because comic as it may be, that is a statement about radical limitations on human agency. And that's something that we're going to be exploring all term. The Puritans wonder how can it be that we have free will but that there's also something called God's providence, in which everything is predestined. How can we be held responsible for Adam's sin if God knew that was going to happen all along. That is a paradox that the Puritans wrestle with. You can see that Melville is wrestling with it too, or maybe Ishmael is wrestling because Melville is acting the part of the stage manager, having him do that. The last thing for today. Take a look in the next paragraph. Why does he go on the whaling voyage? With other men, perhaps such things would not have been inducements. But as for me I am tormented with an ever-lasting for things remote. I love to sail forbidden seas and land on barbarous coasts. Not ignoring what is good, I am quick to perceive a horror and could still be social with it, would they let me, since it is but well to be on friendly terms with all the inmates of the place one lodges in. I take that to be a statement of cosmopolitanism. So we will test and see how that kind of cosmopolitanism fares in the literary and cultural tradition that leads up to this. All right, thanks, that's all for today. Settlement narratives for Wednesday. |
Open_Ed_Cyrus_Patell_American_Literature | American_Transcendentalism_III.txt | >> Alright, let's get started. I'd like to say just say a few last words about Emerson. At least last words for now by taking one last look at the essay experience, which I wanted to suggest last time after the, the death of Emerson's son becomes a way of him to kind of do a gut check, you might say, or head check. And see if the theories about the nature of the individual and the soul, and the way the way the self works. That division between the me and the not me can really work under the pressure of some kind of a trauma, or a grief, like the one prompted by the death of his child. So, again I wanted to point out to the place where we were at the end of last time. It was at the top of 1207. It's a kind of dramatic crux I suppose for the essay. And, you really ought to compare it to that moment in nature; that moment of revelation that is the transparent eyeball. You remember that moment where he talks about the currents of the universal being flowing through him. Becoming part and particle of God, am nothing, I see all. Compare that as a moment of vision to this one. And, I'm going to read it again. It is very unhappy, but too late to be helped. The discovery we have made that we exist. That discovery is called the fall of man. Alright, so this is his rewriting of the book of Genesis you might say. And, it's in terms of human consciousness and human vision. Ever afterwards we suspect our instruments. We have learned that we do not see directly, but immediately. And, that we have no means of correcting these colored and distorted lenses, which we are, or of computing the amount of the errors, right? So that means we don't see directly. Instead of that vision of transparency we have a vision of mediation. Between us, and what's out there there's some mediating force, and that mediating force turns out to be ourselves. We have no means of correcting these colored and distorting lenses, which we are. Once we lived in what we saw now the rapaciousness of this new power, which threatens to absorb all things, engages us. Nature, art, persons, letters, religions, objects, successively tumble in, and God is but one of the ideas. So, this is, I mean one of the things you might say is he's taking aim at here is that sense of the Cartesian split between mind and body which he wants to uphold. But, even the Cartesians split between subject and object. These things are no longer separable, he thinks. And, therefore he suggests he suggests you know that either subjectivity whether it's in the form of something like a scientist's instruments, or in the form of an individual's way of thinking. His way of life, ideology always colors the vision of what you're looking at. Even for someone as acutely observant as Emerson, right? And, I suggested last time that this is actually a fairly modern thought. I mean it anticipates something like Carl Monhon's ideology principle in which he talks about the fact that there's no outside for example of ideology. Even perhaps Verna Heisenberg's uncertainty principle where the very fact of observing changes in nature of what is being observed, or you know definitions of ideology from Marx down to Altizer. All these things I think are built in here. And, one of the things we would say is that Emerson is looking for some kind of compensation for this insight, the inescapability of subjectivity. What are we supposed to do about that? The truth that we say we might have hope to find in reality, or remember that whole business of study thyself, study nature, becoming one thing, he's looking out there in nature to try to find out truths about himself, that may not work. Or, rather it may be exactly what he has said all along. That in fact that nature was always already only instrumental. That really what we were looking at when we thought we were looking at nature was in the self. And, now we're sort of cutting to the chase. We realize it's all self. So, Emerson puts it this way. He's looking for a way out of this problem you might say, but I'd suggest to you that it's a way that he's already looked at in the earlier essay nature. When he talks about spirit letting him out of the labyrinth of his own mind, remember when he talks about the ideal philosophy, and if it disputes the, denies the existence of matter that's not enough, right? Because, otherwise you might say you are, you don't have any guarantees outside of this self. What is it that provides those guarantees, spirit? He comes much more gloomily than in the earlier piece, but to the same realization. This is at the top of 1209. It is true that all the muses of love and religion hate these developments, and will find a way to punish the chemist who publishes in the parlor the secrets of the laboratory. And, we cannot say too little of our constitutional necessity of seeing things under private aspects, or saturated with our humors. Again, he's thinking about the inability perhaps to split mind and body; the fact that what he's been asserting is in some sense always difficult to do, but then he goes on. And, yet is the God, the native of these bleak rocks. That need makes immoral the capital virtue of self-trust. We must hold hard to this poverty, however scandalous and by more vigorous self-recoveries after the sallies of action posses our acts, or axis more firmly. It's almost as if having gone through this kind of crucible of grief, Emerson realizes what he thought before is even more true. He realizes the truth of it. That's the force of the insight that the death of his son has left him unchanged somehow, and that is a kind of terrible insight to have, but he has it. We must hold hard to this poverty, however scandalous. The life of truth is cold, and so far mournful, but it is not the slave of tears, contrition and perturbations. It does not attempt another's work nor adopt another's facts. And, from this moment this is a kind of turning point where you might say the, the Emerson is going to come to a kind of optimistic close, but I want you to see that despite the fact that Emerson is no puritan thinker. We already talked about the way in which if he comes out of a kind of Unitarian framework, which is a real liberalization of New England congregationalism, right. So, if the Puritans, and later the Congregationalists who inherit from them believe that, believe in the total depravity of human kind after the fall, and was said that the Unitarians actually believe in a model of perfectionism. They stress the life of Christ rather than death. Christ's life as a kind of model. They believe in the perfectibility of human kind. Emerson shares in all of this. In fact he finds Unitarianism still to be a little bit too restrictive. Nevertheless I want you to see that there's a certain kind of residual almost Calvinist logic at play here, alright. Remember what happened to the Calvinists. They believe the fall of man is ultimately a good thing. God tests those whom he loves. You fall, but what you get in the end after you receive God's grace is something that's even better than the Garden of Eden. You get to sit at God's right hand in heaven. And, that kind of logic of things are going to get worse, so that they can get that much better seems I think to be operative a little bit here in this essay as well. He comes, he's tested, his belief himself, what he calls self-trust is tested, and in the end he comes back to self-trust. You might say chastened, but he comes back there nonetheless. Take a look at the very end of the essay. You almost get rhetorically as if it has to happen for almost a kind of act of just will itself. Let's take about ten lines up from the bottom of the page on 1210. Patients and patients we shall win at last, at the last. We must be very suspicious of the deceptions of the element of time. It takes a good deal of time to eat, or to sleep or to earn $100 in a very little time, to entertain a hope and an insight, which becomes the light of our life. So, little a time that we might actually forget to do it, right? We dress our guard, we eat our dinners, discuss the households with our wives, and these things make no impression are forgotten next week, but in the solitude to which ever man is always returning, he has a sanity, and revelations, which in his passage into new worlds he will carry with him. Never mind the ridicule, never mind the defeat. Up again old heart it seems to say. There is victory yet for all justice, and the true romance, which the world exists to realize, will be the transformation of genius into practical power. And, again you should go back and compare this to the end of Nature when he talks about the kingdom of man over nature which cometh without observation will be beyond his present dream of God, right. I mean there's a sense in which finally genius is going to converted into practical power, but only for whom might say the supreme act of will power, which is to go back to self-trust, finally. You might say that in the American scholar and self-reliance, Emerson is giving us a ringing exhortation to trust itself. Self-trust, self-trust, self-trust, right. Later in the essay, in the essay self-reliance it's called self-reliance. It's a little bit different by the time we get to the end of that experience. You might say that in the aftermath of disillusionment, skepticism, doubt, grief even, Emerson comes to realize that it isn't just the necessity of self-trust, but it may well be that there isn't anything that you can trust besides the self. That's a hard place to have to come to, but I think it's the logical extrapolation for him, of the kinds of things that he's been thinking all long. What he calls in other places the infinitude of the private man, but what finally, what finally underwrites that idea of self-trust is the idea that it's based in the soul, which is a link to the Godhead, right. We have some of the divine in each of us, therefore that emphasis finally on revelation; the solitude to which every man is always returning. And, what do we find there? Sanity, and revelation, and that's why, that's why those two things are linked I think. So, I want you to see that this is a kind of shift for Emerson, a kind of shift into a minor key. And, it is a moment of testing, but like the Puritans before me comes out you might say stronger for having had to go through the fire. The other thing that I wanted to point out about the end of this is that it's a kind of Thoreauvian [assumed spelling] moment that he has at the end of this essay experience, particularly in this moment when he thinks about the ways in which the everyday tend to, to create experiences that might lead us to over look what we find in solitude, that sanity, and revelation, right. We dress our garden, eat our dinners, discuss the household with our wives. These things make no impression are forgotten next week. That sounds a little bit like Thoreau. I want you to understand that in a way Thoreau is possibly the closest thing that Emerson has to a real disciple in his own time. Quite literally Walden is built on a foundation laid by Emerson. It's built on a piece of property that Emerson owned and lent to Thoreau, and it's also built on a foundation of the kind of belief in self-reliance, and the idea of investigating nature that Emerson lays down. So, at this moment I want us to think a little bit about the ways in which we might say there a links among these three thinkers. Emerson and Thoreau I think it will become clear, but again I want you to see that there are ways in which there are links between what they are doing, as kind of romantic writers writing in the early part of the 1800's compared to what Winthrop who is 200 years ahead of them in the history that we're talking about. They have a similar kind of idea. Winthrop is his model of Christian charity is designed to set forth a kind of template. Life create this idea of the city on the hill, a template for a new kind of society. That society runs 200 years old by the time it gets to Emerson and Thoreau. They're thinking about the necessity of maybe rebuilding or renovating that, right? A greater self-reliance will lead to a kind of renovation of the social state Emerson says. And, there's a way in which I want you to think of what Thoreau is attempting at Walden is a kind of thought experiment. Fundamentally, it has a lot, tells us a lot about building, and measuring, but ultimately it's a thought experiment that suggests what would it take to rebuild our civilization from the ground up? To simplify, simplify everything so that we can get away from all of the kind of accumulation of stuff that we've [inaudible] from the time that the Puritans, and even from before, and get back to basics, and find life rewarding once again. Additionally, again there's that idea that there's this lurking somewhere in Emerson. I'm not sure it's true in Thoreau, but working somewhere in Emerson there is the kind of residue of Puritan logic, particularly if you think of the shift from nature through self-reliance down to experience. Okay, so, that's one thing to bear in mind. Now Thoreau graduated from Harvard in the same year, 1837, that Emerson gives the Phi Beta address that's called, the Phi Beta Kappa address that's called the American Scholar. We don't actually know if Thoreau was present on that day, but as they say, he might as well have been, in the sense that exactly the things that Emerson is talking about there, become the kind of foundations for Thoreau's own philosophy. And, I want to, I suggested last time that we should think of the two pieces that we have looked at, the shorter resistance to civil government, and the longer Walden as in something's taken their cue from Emerson. So, I'd like to suggest to you the resistance to civil government which was written in 1849 to protest the aftermath the Mexican War which we'll have more occasion to talk about when we get to Harriet Beecher Stowe, and also the Institution of American Slavery which we'll also talk about when we get to Stowe. It's written to protest those things. We might see it as Thoreau's version of the American Scholar. I mean like the American Scholar it's built on a foundation of what we would call individualism, what we might even call ontological individualism, right? The idea that the self has a primary reality and that society itself is a second order construct. It's derived out of the necessity of protecting the majority of our freedoms from the state of nature. And, it's almost as if society is a necessary evil, and for Thoreau an evil that he hopes eventually will kind of, you know, to quote someone else in a different context that will eventually wither away. So, Thoreau like Lennon thinks, hopes that the state will eventually wither away. Take a look at page 18, yes let's look at 1857, earlier on in the very beginning of the essay, and listen to how he begins. I hardly accept the motto that government is best which governs least. And, I should like to see it acted up to more rapidly and systematically, carried out it finally amounts to this which I also believe, that a government is best which governs not at all. And, when men have prepared, are prepared for it that will be kind of government which they will have. Government is at best but an expedient, but most governments are usually, and all governments are sometimes inexpedient. The objections which have been brought against a standing army, and they are many, and weighty and deserve to prevail may also at last be brought against a standing government. Alright, so then you get it right there. This government is a kind of necessary evil that's necessitated by the current low stage of society at which we're at. And, you might think about Emerson's fable of man thinking from the American scholar, which describe you remember men as partial. Men as beings to whom senectity [assumed spelling] has happened. We walk around on a walking [inaudible], cut off from the [inaudible] a finger, a nose, nothing, but never the whole man, or to which metonymy has happened. We have become linked to things, and we have gotten away from process. So, even someone as exalted as a thinker is kind of reified and static. That's why Emerson would rather see the scholar described not as a thinker, but as man thinking to emphasize the kind of dynamic nature of what's going on there. Thoreau has a similar kind of critique to offer here when he talks about the mass of men serving the state as machines, right? So, it's a kind of thought experiment, this essay. He recalls the night that he spent in jail after refusing to pay his poll tax, and protest to the way in which he thinks the government is likely to use the poll tax. Take a look at the, a little further on. This is the middle of page 1864. And, this is in some sense harkening back to the Declaration of Independence, which we looked at earlier on, right. That idea of, remember Jefferson's syllogism, and that the people have a right to overthrow destructive government. And then he goes on to prove throughout most of the document that the British government particularly is typified or exemplified, or embodied by the king is that kind of government. Therefore we have the right to overthrow that. Thoreau is taking his cue from that here. Look at the first, second full paragraph on 1864. Under a government, which imprisons any unjustly, the true place for a just man is also a prison. The proper place today, the only place which Massachusetts has provided for her freer and less desponding spirits is in her prisons to be put out, and locked out of the state by her own act as they have already put themselves out by their principles. It is there that the fugitive slave and the Mexican prisoner on parole and the Indian come to plead the wrongs of his race [inaudible] find them on that separate, but more free and honorable ground where the state places those who are not with her, but against her, the only house in a slave state in which a free man can abide with honor. And, one of the insights here is an insight that other people have had. We'll talk about it a little bit with Stowe. People have read Huckleberry Finn? Didn't you read Huckleberry Finn in high school? Yes, good book, huh? Huckleberry Finn is an interesting book, because it's preceded by a book called Tom Sawyer. Tom Sawyer belongs to a certain genre. We're going to call it the boy's book. It's thought to be a kind of adventure book. It's about the search for gold. [Inaudible] treasure hunt kind of book. So, you might say that Huck Finn promises to be something in the same kind of vein. It also has a boy's name. It does something different. First of all it takes the first person narrator, and then it takes the first person narrator from the lower or even underclass, and lets him create the kind of vernacular voice that lets him speak. But, if you remember the moment that everyone points to as a kind of signal moment for supposedly Huck's transformation in that book is the moment after when they've gone on the raft. They've missed the turnoff to Ohio. Alright, they're supposed to get off the river and go into free country in Ohio. If you don't get off the river, what happens, at the right time what happens? Well, the Mississippi keeps flowing south. The further south you float the deeper into slavery you float. You'll see that again when you get to Stowe, right? In Stowe's novel there's a kind of double plot in which one group of slaves moves north towards freedom, and another group moves south deeper and deeper to the darkest parts of slavery which turn out to be in Louisiana in the swamps near New Orleans. And, so Huck and Jim missed this. If any of you remembers what happens, Jim gets taken off, and he's basically brought back into slavery. And, Huck has this moment where he thinks, what am I supposed to do? I should go free my friend Jim, I should go try to get him back, but he's been taught that slavery is good, and that good Christian people support slavery. He's also been taught that he's bad, but there's a certain kind of, what the novel does is manage to make us understand the kind of ideological inversions that slavery is creating. Somebody who is morally and naturally good like Huck is placed on the outside of this society, and can only believe that he's bad, because he supports a set of values that we as the readers are being taught to understand is, are good. So, do you remember what it is that Huck says? He has this kind of moment. He says then alright I'll go to hell. He'll go to hell for his friend to save him out of slavery. And, that becomes this kind of single moment, which we'll say yes if a kind of morally good nature despite all the inversions of values that society, a slave society is creating. Huck somehow innately knows to do the thing that's right, and then the novel proceeds from there to the part that Ernest Hemingway said was cheating. Because, of course the logic of Huckleberry Finn is you're going down the river, the river only flows one way, you're flowing to tragedy, and death and slavery. There's no other way is now what happens in Huckleberry Finn, and it's almost like through a kind of, well people have said, Hemingway said it's cheating. Other people you know, Twain thought long and hard. He got to a point in the narrative where couldn't continue and he realized what he had done. Twain's novels are very interesting from that standpoint. He gets to a point often where he's like shit, what did I do? Where am I, and how do I continue? Connecticut Yankee also breaks down in that same sort of way, and then needs to go on from there. The way I like to read Huckleberry Finn, and if you're interested in going back to it sometime you might think about this, is that what it does is graft onto a, graft on a happy ending, right. It brings back Tom Sawyer. It brings back the whole feel of the boy's book from the Tom Sawyer novel that precedes it. People say that's terrible. That moment that I just told you about that Jim has, you know that moment of revelation it's all thrown out the wayside. It's all made trivial, right? What I would suggest is [inaudible] these brilliant books that actually asked us to think a little bit self-consciously about what we're reading. So, it grabs onto a happy ending that the un-astute reader will be happy with. The astute reader will find there's a little bit of a betrayal or something, and the most astute reader will probably realize that that sense of betrayal is inevitable, and is designed to be there. That what we realized is we graft on a happy ending that is openly, showily, extravagantly unsatisfactory. Give us an experience of something that we might call ideological contradiction. So, we understand that precisely we get our own feeling of precisely the thing that Huck is feeling which is that he's caught between untenable positions or the only way to do good is to be bad. I think you should think about that. That's Twain's solution to this. We've got to give everybody a happy ending, but it's going to be a really unsatisfactory happy ending, or one that really doesn't work. One that seems grafted on, and by that we're going to bring out the nature of ideological contradiction. I think Thoreau is pointing out something like that, too. In a slave state the only place you can be free is in a jail. That's what he suggests. Now, Thoreau's an interesting thing. I mean this is a thought experiment, right? His aunt pays his poll tax, and gets him out the next day, and he knows that's going to happen. Just like he doesn't actually go and live in the woods. I mean he comes back to town. He just doesn't write about that. There are stories about him stealing pies from people's windowsills. So, there's a way in which these are both kind of constructive narratives. They're both thought experiments, and that's kind of what I want, want to get out for us to think about here today, right. The jail cell for him becomes a kind of place of simplicity where you can get back to basics. It's almost like getting that lock-in tabula rasa, right? That blank slate and he allow, he is able to then rewrite what's on there so he creates his own new idea of what society should be. Or, rather you could say he's able to see things from the simplicity of the jail cell that he wouldn't have been able to, that he isn't able to see before. Here's a figure for that. Let's take a look on, let's see if I can find it. Yes, let's do in, page 1867. There's a place where it's indented. It's about eight lines down from that indented place when he's talking about the night in prison. The rooms he says were white washed once a month, and this one at least was the whitest most simply furnished, and probably the neatest apartment in town. And then he [inaudible] he naturally wants to know where I came from and what brought me here, and when I told him I asked him in my turn how he came there, presuming him to be an honest man of course, and as the world goes I believe he was. Why said he, they accuse me of burning a barn, but I never did it. As near as I could discover he had probably gone to bed in a barn when drunk, and smoked his pipe there, and so a barn was burnt. He had the reputation of being a clever man. Had been there some three months waiting for his trial to come on. I would have to wait much longer, but he was quite domesticated and contented since he got his board for nothing, and thought that he was well treated. That again the paradoxes of being in jail, but take a look a little bit further on. One of the things we realize is that in, let's see, this is about three lines down. Yes, look at the top of 1868 where he's talking about the kind of circulation of gossip in the, in the jail. It says that I found that even here there was a history and a gossip that never circulated beyond the walls of the jail. Probably this is the only house in the town, he writes, where verses are composed which are afterward printed in a circular form, but not published. I was shown quite a long list of verses that where, which were composed by some young men who had been detected in an attempt to escape, who avenged themselves by singing them. Now he's a little bit tongue and cheek, right? But one other thing I want you to suggest here is that, that the jail itself is also a kind of cultural site too. It's a place where poetry is happening. Not a kind of self-interested market driven poetry, but something else altogether, right? In other words being in jail gives Thoreau new insights into the nature of the culture outside of the jail. Take a look at the next two paragraphs later. It was like traveling into a far country such as I had never expected to behold. To lie there for one night. It seemed to me that I never had heard the town clock strike before, nor the evening sounds of the village. If we slept with the windows open which were inside the grating. It was to see my native village in the middle ages and our concord was turned into a Rhine stream, and visions of knights and castles passed before me, right? So, has a kind of literary kind of view that he's bringing. Again, what I want you to say, see is that this is a kind of thought experiment. And, it's therefore I would suggest to you less a personal narrative than a it is an actually kind of piece of political theory. And, so finally at the end he ends the essay with a kind of ringing defense of Emersonian individualism where there was self-reliance. Last paragraph on 1872, the authority of the government even such as I'm willing to submit to for I will cheerfully obey those who know and can do better than I, and in many things even those who know neither know nor can do so well is still an impure one. To be strictly just it must have the sanction and consent of the governed, right. So, again that language of the Declaration of Independence. It could have no pure right over my personal property, but which I concede to it. I mean again this is in kind of main line lock-in Jeffersonian political theory. The progress from an absolute to a limited monarchy from a limited monarchy to a democracy is a progress toward a true respect for the individual. And this sounds a bit like Emerson. Is a democracy such as we know it the last improvement possible in government? Is it not possible to take a step further towards recognizing and organizing the rights of man? There will never be a really free and enlightened state until the state comes to recognize the individual as a higher and independent power from which all its own power and authority are derived and treats them accordingly. I please myself with imagining the state at last which can afford to be a just to all men, and to treat the individual with as a neighbor which even would not think it inconsistent with its own repose of a few, and now he's talking about himself, right? Because, he and other people who thought of themselves as transcendentalists were criticized for holding themselves aloof from society, for not paying their taxes, not being contributors. Not meddling with it, not embraced by it, who fulfilled all the duties of neighbors and fellow men. A state which bore this kind of fruit and suffered it to drop off as fast as it ripened will prepare the way for a still more perfect and glorious state which also I have imagined, but not anywhere seen. Alright, so what he's thinking about is again a new kind of state, one that he can first formulate paradoxically in jail. Although I would suggest to you that again one of the places where he's formulated it is, you know, is in the pages of Emerson himself. In thinking about Emerson, the kind of Emersonian project of exalting the individual, what he does here, I suggested last time that Emerson's individualism should be thought of as a kind of social philosophy even though he's, he never really makes statements about democracy in this kind of bald way in the essays that we've read. So, you might say that Thoreau is translating Emerson's ideas here into a more overtly political key, or a key that belongs more overtly to the realm of philosophy that we would call political theory. And, I think Walden does that, too. That's the row. I think Walden does that as well. Alright, I think it's a lard, In some sense it's an even bigger thought experiment, and it's a thought experiment that resists you might say being a thought experiment, because it's masquerading as a lot of other kinds of writing; its masquerade as a kind of personal narrative and also perhaps as a kind of natural history tract. So, we might say that if resistance to civil government is Thoreau's version of the American Scholar, Walden is going to be his version of Nature. And, as I suggested to you all it's both literally and figuratively built on Emerson's land, on Emerson's foundation. So, if in the American Scholar Emerson says that the old maxim know thyself, and the new maxim, study nature are at last the same thing I think Thoreau is building on that insight. So, fundamentally he's, I would suggest to you again using nature as Emerson does instrumentally as a way of understanding the self, and also understanding the nature of society, except that he's willing to get dirty more than Emerson is. I mean he's willing to actually investigate actual nature, to go and get his hands dirty, to build something, to play in the mud and look at stuff. I mean you get a sense of Emerson as a little bit I don't know what, standoffish, or refined. He's like kind of one of these Boston Brahmas. Thoreau is just grubbier, and although you also get the sense, I get the sense that Thoreau doesn't really like people all that much. He's more at home with the bugs and the slime than with the, with the neighbors. But, remember the other thing, the other thing that I pointed out Emerson says like you know men are sleepwalking. Wake them, and they'll quit the false [inaudible] and aspire to the true. I think Thoreau agrees with that. Take a look at the beginning of Walden. Let's take a look at 1875 maybe. [ Silence ] I mean he's kind of, he begins with this long part that's called, because of this long section that's called Economy, and he's really interested in the idea of what it might mean to rethink the very nature of economy. So, take a look at, take a look at this towards the bottom of the page. Most men, even in this comparatively free country, through mere ignorance and mistake, are so occupied with the factitious cares, and superfluously course labors of life that its finer fruits cannot be plucked by them. Their fingers from excessive toil are too clumsy and tremble too much for that. Actually the laboring man has not leisure for a true integrity day by day. He cannot afford to sustain the manliest relations to men. His labor will be depreciated in the market. He has no time to be anything but a machine, right? Remember that moment in the American Scholar where the farmer is just the same as the cart with which he works? How can he remember while his ignorance with his growth, which his growth requires who has so often to use his knowledge? We should feed and clothe and gratuitously sometimes and recruit him our cordials before we judge of him. The finest qualities of our nature like the bloom on fruits can be preserved only by the most delicate handling. Yet we do not treat ourselves nor one another thus. Take a look further on now. So, we get this structure of this is strange, right? You kind of get plunged in. You get 80 pages almost in the original of this chapter that's called The Economy. It's really big. And, then finally you get to a second chapter that's called Where I Lived, and What I Lived For. And this is on, it starts on page 1914. And, even then it's a little bit abstract at the start before finally on page 1920 near the top of the page we get this statement of the project of Walden. So, this is quite a way in. It's almost as if he's wanted you to kind of discern the project of Walden for yourself before he's going to tell you what it is. Or, you might say watch him in action. Be thinking the idea of the economy before he tells you what his larger project is, so he says this. I went to the woods, because I wished to live deliberately. To front only the essential facts of life, and see if I could not learn what it had to teach, and not when I came to die discover that I had not lived. I did not wish to live what was not life. Living is so dear. Nor did I wish to practice resignation unless it was quite necessary. I wanted to live deep, and suck out all the marrow of life. To live so sturdily and Spartan like as to put to rout all that was not life. To cut broad a swath and shave close, to drive life into a corner, and reduce it to its lowest terms. And, if it proved be mean why then to get the whole and genuine meanness out of it, and publish its meanness to the world. Or, if it were sublime to know it by experience, and be able to give a true account of it in my next excursion. For most men it appears to me are in a strange uncertainty about it. Whether it is of the devil or of God, and have somewhat hastily concluded that it is the chief end of men here to glorify God, and enjoy him forever. Alright, so we should see echoes of Franklin and Emerson here. Alright, remember Franklin's common sense idea. He's not going to do things from precept, but he's going to imagine that behind the precepts there might be some useful advice. So, he's not going to do it, because he should, but he's going to test whether or not he should do it. Same with Thoreau. He wants to test. He wants to experience for himself. And, it's like that moment in Emerson's self-reliance too when he talks about writing whim on the [inaudible] post. And, somebody asks him how do you know these impulses don't come from below? And, he says well, if it comes from the devil I'll be the devil's child. I have to do what's true to me. He thinks that's not going to be the case, but he's willing to go with it. Same with Thoreau. If life be mean he wants to really know what it means to be mean. If life is sublime he doesn't just want to hear about it in some other person's poetry, and reading about it. He wants to go and experience it for himself. And, he comes up with a metaphor about this. And, this metaphor is very appropriate given that a lot of his attention is going to be spent on a very deep lake. He wants to get to the bottom of things. He even to this question of what the purpose of man is with his relation to God. Somewhat hastily concluded that it is the chief end of man here to glorify God, and enjoy him forever. He's not saying that we might not get to that conclusion eventually, but we won't want to get that conclusion too fast. So, I want to suggest to you that Walden is all about getting to the bottom of things. Take a look on page 1923. This is a long passage, long paragraph. Well many of the paragraphs are long paragraphs, but this one is at the bottom of 1923. And, he says this. Let us spend one day as deliberately as nature, and not be thrown off the track by every nutshell and mosquito's wing that falls on the rails. Let us rise early, and fast, or breakfast gently, and without perturbation. Let company come, and let company go. Let the bells ring, and the children cry, determined to make a day of it. Why should we knock under and go with the stream? Let us not be upset, and overwhelmed in that terrible rapid and whirlpool called a dinner situated in the meridian shallows. Whether this danger and you're safe for the rest of the ways downhill. With unrelaxed nerves, with morning vigor sail by it, looking another way, tied to the mast like Ulysses. If the engine whistles let it whistle to its horse for its pains. If the bell rings why should we run? We will consider what kind of music they are like. Let us settle ourselves and work and wedge our feet downward for the mud and slush of opinion, and prejudice, and tradition, and delusion and appearance that alluvion which covers the globe through Paris and London, from New York and Boston, and Concord through church and state. From poetry, and philosophy and religion till we come to a hard bottom, and rocks in place which we can call reality, and say this is, and no mistake. And, then begin having a point dappui, below freshet and frost and fire. A place where you might found a wall or a state or set a lamppost safely, or perhaps a gauge, not a Nilometer, but a Realometer, that future ages might know how deep a freshet of shams and appearances had gathered from time to time. If you stand right fronting and face to face to a fact you will see the sun glimmer on both its surfaces, as if it were a cimeter, and feel it's sweet edge dividing you through the heart and marrow so you will happily conclude your mortal career. Be it life or death, we crave only reality. If we are really dying let us hear the rattle in our throats, and feel cold in the extremities. If we are alive then let us go about our business, right. I want to spend a little bit of time looking at that. A point d'appui, hard bottom with rock in place. Something you can found wall or a state on, right? Again, he's trying to, he's looking, he's interested in bottom, in foundation. And, he wants to call that search for bottom a search for reality. He wants to know what's real. You need to understand that what he's talking about is for him the definition, the difference between real and what isn't real is the difference between kind of appearance. So for him society is full of appearances. We're meant to put on appearances. We have to speak in ways that seem hospitable. We have to abide by social conventions. We have to be nice to one another. That's bullshit for him. He wants something real. Something he can found a wall or a state on. So, what's at stake in this search for solid bottom? I think it means, and once it's taken this long book that I ask you to read. I mean he's showing you at length the process of looking for what is real. It involves asking the right kind of questions. It involves sometimes pursuing scientific methods, and it also involves moments when scientific methods are not going to be adequate, alright. Many of the things that we thought aren't going to adequate. Take a look at the top of 1924, right. We have the mud and slush of opinion and prejudice. Alright, that's appearances, right, social appearances. Tradition and delusion and appearance. That alluvion which covers the globe through Paris and London, and New York and Boston, and even Concord near where he is, but then he goes after various institutions of culture. Church and state, poetry and philosophy and religion. We've got to sweep all of these things aside till we can come to this idea of hard bottom, right. So, the only way to reach the point d'appui, hard bottom is to keep questioning everything, and so where does Thoreau start? He starts as Emerson I supposed would have him start by looking at nature, but not abstract nature. Going out into the woods, and actually looking at nature. Trying to find something that is inhuman. In other words think back to Emerson's distinction between the me and the not me. He's going to go look at the not me, and he's going to look at the not me extremely seriously, but ultimately as an avenue for getting to the me, right. Here, I think I put [inaudible], yes. Here's that you know, again nature and the soul. Strictly speaking all at a separate from all of us which philosophy distinguishes the not me nature in art. That's Emerson's statement about what the difference is between man, and human beings and nature. Thoreau obviously just adopts the similar conception. Although I have a feeling that at least at the start of Walden, he's giving you a process of discovery, so he stipulates at the start something less than Emerson's faith in the transcendent powers of the me. May well be that Thoreau needs more prompting from nature. More a sense of maybe that the sense that maybe the me is not enough. Unaided to pierce through all of these appearances. It needs something artificial to happen to get thrown into jail, or maybe to go out and build this little house in the woods, right. One of the things that Thoreau criticizes is the statesman and legislatures who never manage to get outside of a larger system in which they are. And, there's a way in which he's appealing to this. People know it. The maxim of Archimedes, give me a place to stand and I will move the world. It's all about leverage. The Archimedean point is that point outside of a system where you can see the system whole and judge it. So, it's obviously an interesting thing, because people would argue there's no such thing as an Archimedean point ever, right. I mean that's Manheim's paradox. You can never get outside ideology. You can never get fully outside of the, the system. Thoreau is testing this. Is it possible to get outside the system? The paradox of resistance to civil government is you can get outside the system by being right in the heart of the system as long as it's the right place, right. The jail cell becomes a place outside that's still inside. But, that's what Emerson, that's what he's looking for. That's what Emerson is thinking nature is. That's what Thoreau is thinking nature is possibly, and Walden. Not just in retreat, but something about where we can approach a kind of Archimedean standpoint. A place where we can stand to gain some find of perspective, right. And, so that's part of what Thoreau discovers in the course of building the house at Walden. Let's see, a couple of pages further off, further back, let's take a look at, 1913 would be a good place. I mean there's a lot in Thoreau's text that recapitulates itself. But, this is a good statement I think of that. You can see the resonance with Emerson. It's the last full paragraph on 1913. Our manners have been corrupted by communication with the saints. Our hymn books resound with melodious cursing of God, and enduring him forever. One would say that even prophets and redeemers had rather consoled the fears than confirm the hopes of man, right. You could understand that. I'm giving you what we said about, and read about Calvinism and Puritanism. There is nowhere recorded a simple and irrepressible satisfaction with the gift of life, and any memorable praise of God. While health and success does me good however far often withdrawn it may appear all disease and failure makes me, helps to make me sad and does me evil, however much sympathy it may have with me or I with it. Okay, forget all the Puritan logic of being tested and afflicted and all the crap. If then we would indeed restore mankind by truly Indian, botanic, magnetic, or natural means this is the crux here, let us first be as simple and well as nature ourselves, dispel the clouds which hang over our own brows, and take up a little life into our pores. Do not stay to be an overseer of the poor, but endeavor to become one of the worthies of the world. And, you could say again there's that kind of the sense of mean to pull yourself up by the bootstraps, and do something that we get at the end of experience. Thoreau's task is to get us out into nature, but it's not quite that simple. It never is. Because, if you look back at this Emersonian statement, right, we looked at it last time, you'd see that one of the things that Emerson does is to class both nature and art as part of the not me. And, he has that statement about that we haven't really done so much to nature. It's all kind of insignificant. And, I think there's something of that, too. That ultimately Thoreau often looks as if he's talking about simply natural facts. And, yet he does it in a funny way that reinforces this idea that everything outside the self is a mixture of both nature and culture. A good place to go to see that is that passage that I read at length. Let's go back to it, 1923. Let's go through it again, but this time I want you to find, and we're going to stop, and think about the logic of what's going on here. Let us spend one day as deliberately as nature. And, not be thrown off the track by every nutshell and mosquito's wings that falls on the rails. Okay, let's stop there. That's a metaphor. What's the metaphor? [ Silence ] What's the metaphor? To spend one day is deliberately nature, and not get thrown off the track by every nutshell and mosquito wings that falls on the rails. What, train? Train. Yes, train, sure; rails, rails. Okay, but now let's look at the coding of value that's taking place there. Let us spend one day as deliberately as nature, okay; down with that. It's Walden, its life in the woods where you're in nature, okay; nature, good. But, to spend on day as deliberately as nature, second part of the sentence, and not be thrown off the track by every nutshell and mosquito's wing that falls on the rails. Coding good, bad, indifferent in the latter part of the sentence? That's good, yes? >> [inaudible] >> Yes, it might be too soon to say mechanical problems, but certainly some sign of the very, you know the various sign you might say of mechanical progress in the 19th century. The train is quoted here with approval. So, we get nature with a capital N in the first part of the sentence. Called that good, but the rails, the tracks, let's not get thrown off the tracks, right? Theoretically, the track that we're on is to live one day as deliberately as nature. And, what's throwing us off? Nature itself, but oddly almost trivial nature, right. Nutshells and mosquito's wings as if those things could derail a train. All right, let us rise early and fast, or breakfast gently and without perturbation. Let company come, and let company go. Let the bells ring and the children cry determined to make a day of it. Okay, so no we're back in thinking nature good. This is all kind of the noise of everyday life in society. Now what? Why should we knock under and go with the stream? How do we coat that? Yes? >> [inaudible]. >> Yes, but what is the stream? If the stream is metaphorical, what is going with the stream? Yes? >> [inaudible] with society? >> Yes, right. It's whatever in the fruit of the sentence before, and all that stuff. If you kind of go with the stream you're doing all that stuff. Why should we? Why should we knock under? Instead of that we should let company come and company go. Okay, let us not be upset and overwhelmed, here we go again, in that terrible rapid and whirlpool called a dinner situated in the meridian shallows. Okay, so we're getting that, right. You know dinner of God. Fancy things, you've got to be on your good behavior, it's all boring. Okay, but why are we using nature to describe that? Terrible rapid and whirlpool called a dinner. Whether this danger, you're safe the rest of the ways downhill. There's a mixed metaphor. With unrelaxed nerves with a morning vigor sail by it looking another way, and now interestingly we get into a slightly different vein. Tied to the mast like Ulysses reference. Footnote tells you I supposed, but it's the Odyssey, right? So, it's Greek history, mythology, culture. Nothing is safe. If the engine whistles let it whistle till it's hoarse for its pains. Now wait a minute, we've seen the train already. The train was good. Now the train is being associated with the things that we're supposed to get away from; the train whistle. If the bell rings why should we run? We will consider what kind of music they're like. Let us settle ourselves at work, and wedge our feet downward. And, again another mixed metaphor for the mud and slush of opinion, and prejudice, and tradition, and delusion and appearance, that alluvion which covers the globe. You have to ask yourself how is this working? Is, you might say he tarring and feathering, or mudding society by using these images from nature that we think to be negative, and murky and yucky? Yes? >> Did you say that he's doing kind of whatever [inaudible] using nature to explain everything in the world? >> That would be one way to think of it. In some sense then he's using, he's feeling free to use nature without value coating it in any particular way. It's not necessarily going to good, it's not necessarily going to be bad. It's going to be used to make whatever point he wants. In other words he's not going to create a kind of binary of nature and culture, or nature even and society in which nature is just going to be coated good. It's going to be the thing that we want to get to reality. Sure it's all those things, but he's also willing to say that ultimately there are, it can be used to make negative points, and there are even negative things about it. There are whirlpools, and shallows, and mud; stuff that will kill you. Ultimately what I would suggest to you is that he's building up a case for all of that being part of the not me. In the end what he's doing is building up a case for the me. This is kind of shifting and ambiguous imagery. Thoreau's aunt Maria, you know the one who bailed him out from, to pay his poll tax, she said that this was part of the transcendentalist zeitgeist. Exactly this kind of writing, and she said it was a problem in the current moment of intellectual history. In fact she said I do love to hear things called by their right names. And, these transcendentalists do so transmogrify their words, and pervert common sense that I have no patience. So, she thought her nephew was a little bit of a pain in the ass, right. And, even Emerson, you know, Emerson, Mr. Contradiction as I've been arguing, say he found contradiction to be unnecessary advice, and braze contradiction, blah, blah, blah, blah, blah. He criticized what he called Henry's old fault of unlimited contradiction. The trick of his rhetoric is soon learned. It consists in substituting for the obvious word, and thought a diametric antagonist. It makes me, Emerson said, wretched and nervous to read it. So, I guess all things in moderation or what's good for the goose isn't good for the gander, I don't know. In any case I want you to see what's going on in Thoreau's prose, right. I mean he's deliberately provocative, deliberately contradictory. And, what he does is, is, you might say that this is part of a larger project of upsetting your system of values. He believes he lives in a country where the system of values is upset, because it's a slave state. He wants to give you that sense of being unsettled that he feels. So, he's not let you become comfortable anywhere. Not in nature, not in culture, and certainly not in society. All right, so the house that he builds looks kind of like that. It's not very big. And, I want to suggest to you that in building this house right, he's doing that thing that he suggests. Founding something that you could find; you're looking for bottom where you could find a wall or a state. So, I want to suggest to you that this another version of rhetoric that's about founding a city on a hill. Something that's going to be an example, so that it shares that with Winthrop's notion. Take a look at this. This is back in the chapter, and it's called Where I Lived and What I Lived For. It's on page 1916. [ Silence ] This is about the founding of his settlement here. It's the last, the beginning of the last paragraph on the page. When first I took up my abode in the woods, that is began to spend my nights as well as days there which by accident was on Independence Day or the Fourth of July 1845, my house was not furnished, finished for winter, but was merely a defense against the rain. Without plastering or chimney the walls being of rough weather stained boards with wide chinks, which made it cool at night. Now again those look like little details of building. Something to interest those of us who would like to build our own houses or have an interest in carpentry or whatever, right, just details. What can we say about that? There's interesting stuff going on there. Let's take the first sentence. When first I took up my abode in the woods, that is, began to spend my days and [inaudible] nights there, let's start there. Anything to note about the syntax of that, or what he's written, or how he's written it? [ Silence ] Yes? >> [inaudible] >> Okay, so he's calling your attention to time, fine. He gives you a date. [ Silence ] Yes? >> [Inaudible] >> I'm sorry, back and then forth. Yes, go ahead. Yes? >> [Inaudible] >> House isn't quite ready, but he's got to move in anyway. Why does he have to move in? >> [Inaudible]. >> Well, does he ever explain why he has to move in? I mean I didn't finish reading it, but does he ever say why I had to move in that day? Why does he have to move in that day? >> Because [inaudible] Independence Day [inaudible] America itself. >> Yes, he had to move in so he could say that he did it on Independence Day, right? Which by accident, yes, sure, right. This might have been an accident that when he decided, or maybe not. He just decided oops look, it's Independence Day. But, it certainly was no accident. I mean think of Franklin and his errata's, no accident, it's the opposite. It's no accident that he's used to mention this to you. When I first took up my abode in the woods, that is, began to spend my nights as well as days there, right, so even then that notion of taking up an abode has to be defined and qualified for you. A founding moment is perhaps not as clear and intentional as we think it is, or maybe it is intentional in a kind of constructed sort of way. Maybe it's telling you something about the arbitrariness of moments that we think of as [inaudible]. Remember what I said about the Declaration of Independence? We commemorate the day they signed the piece of paper. Not the day they thought of it, not they day they approved it, the day they signed that particular piece of paper. Something arbitrary about that as well. Yes? >> [inaudible] going out there during the day to work on it so [inaudible] there at night [inaudible] in reality the way he looked at it [inaudible] specific moment with [inaudible] details like [inaudible] time in the woods and if I feel the way he feels about [inaudible] house is [inaudible] Independence Day. And, the fact that he [inaudible] that probably wasn't actually there in reality, but it makes for a better story. >> Sure. It makes for a good story. It gives you a fixed starting point, but it also lets you know that there's something arbitrary about that starting point. And, go back to what you said about the unfinished nature of the house. The house wasn't' yet finished for winter; wasn't set to keep the cold out. >> [inaudible] in July too. >> So you've got a little bit of time to work on it? >> Yes, so in reality he's probably like okay, well it's warm out. I have all these months to finish it, but [inaudible] moved into an incomplete house [inaudible]. >> So think about this, if the metaphor is the founding of the state, something you build a wall or a state, if his house is a version of re-founding the state, and he's going to found it on the same day as the birthday of the nation, the sense that the house isn't finished yet is a way of talking about the project of the nation, right. From 1776 to 1845 there's still a lot of work to do in the house. And, you know proleptically or looking retrospectively I could say yes, 1845 winter is coming. It comes not too long after. Do you want to add something? >> [Inaudible] government through [inaudible] the government is a byproduct of war, because of the war [inaudible] army you mentioned that the army is the arm of the [inaudible] government, and their connected. Because of [inaudible] government [inaudible] of the war [inaudible] moved into his house. >> Yes, I mean I think a sense of, you might say a sense of war or I mean 1845, the conflict with Mexico is starting to look inevitable. Beyond that conflict over slavery is happening over and over again. It's starting to look inevitable that something is going to happen. That's what I mean by winter is coming. Yes? >> [inaudible] you have [inaudible] house is more representative of Thoreau's [inaudible] state of America. >> And, those two being separate aren't necessarily separate? >> Not necessarily, but I think the idea in itself [inaudible] self-trust [inaudible]. >> I mean I think that's right, but I think it's, with Thoreau nothing is simple, so I think it is a voyage of self-discovery, and self-making. So, it's a personal narrative like other personal narratives that we've seen. But, I think he keeps, you now this is shout forth of a lot of this language. I mean something you can found a wall or a state on is not just an accidental locution. He's really, I think, one of the things I want you to see is this book encompasses many genres. It is a sort of personal narrative. It is a work of natural history. It also is something like a settlement narrative. It should remind us a little bit of Bradford although it's constructed as such. It is a little bit like a template for society like a model of Christian charity. It is a work also of political theory. But, it masquerades as, and I would suggest to you also it's a kind of a work of rhapsodic romantic writing. We'll get to that I hope, but before the end of the term. Yes? >> [Inaudible] that passage is kind of screaming at [inaudible], and that he's relying on [inaudible] in definitely doing [inaudible] in the woods. That's make me think of a howling wilderness and all of that. [Inaudible] America, and the frame is still [inaudible]. He's living in America [inaudible]. European influence and it just seems like he's never [inaudible] down to the cell. >> I think that's right. See, that's good, because that's the way to connect the personal project and the social project. He's a little bit like what I said about Emerson. I said that in Emerson's essays we have this kind of rhetorical reflex, which is to take social questions and recast them as individual questions. And, it you can do that then you can make a generalization about the individual whether it be about the soul, or just an individual self. And, thereby be making generalizations about society or all people. So, if you recast the grounds of social choices and individual choice you can make the declarations about society as a whole. I think that Thoreau is doing the same kind of thing. Instead of rebuilding a whole society he's just building one cabin. It's the simplest society you can possibly make. It's a culture of one person. But, I think it's meant to stand symbolically for culture at large. Take a look. Let's take a look at another one. Take a look at let's see, if I can find you. Take a look at 1879. [ Silence ] He's thinking about necessity. [ Silence ] In fact let's go back further. Let's go to 1877, after the break. Let us consider for a moment when most of the trouble and anxiety I refer to is about, and how much of it is necessary. How much it is necessary that we be troubled or at least careful. It would be some advantage to live a primitive and frontier life though in the midst of an outward civilization if only to learn what are the gross necessaries of life, and what methods have been taken to obtain them; or, even to look over the old day-books of the merchants and see what it was that men commonly bought at the stores, what they stored, that is, the grossest groceries. For the improvements of ages have had but little influence on the essential laws of man's existence: as our skeletons, probably, are not to be distinguished from those of our ancestors, right. There's a sense in which if you owe certain things to Franklidian [assumed spelling] testing, he is a little bit less certain of about progress and science. There's a certain way in which the progress of civilization may not have been progress forward. That there may be sense in which it's better to go back and look at what's essential. He goes on by the words necessary of life. I mean whatever of all that man obtains by his own exertions has been from the first or from long uses, becomes so important to human life that few if any whether from savageness, or poverty, or philosophy, ever attempt to do without it. And, on the next page he talks about wanting to find what, or the next pages he's talking about wanting to find what is indispensable. This is the top of 1879. Most of the luxuries, and many of the so-called comforts of life are not only not indispensable, but positive hindrances to the elevation of mankind. Thoreau was interested in putting together a new kind of economy in other words; a new way of organizing a culture. Later on think about the jail in these terms, right. Strip down the walls. Whitewash them. Get them as simple as possible before you start hanging anything up. Get down absolutely to essentials is what he's talking about. And, he wants to make us rethink the nature of what it is, to reshape the nature of economy. At one point he talks about the cost of the thing, of a thing. The real cost of a thing is how much life you have to get up, give up to get it, right. He wants us to think about economy in ways other than we've been used to thinking about it. So, there's a sense in which he's very much in keeping with the kind of critique of materialist, the kind of critique of materialists that Emerson does. In fact that quote I just referred to I think is at the top of 1888. [ Silence ] How it happens it is that he who has said to enjoy these things is so commonly a poor civilized man, while the savage who has them not is as rich as a savage? If it be asserted, if it is assertive that civilization is a real advance in the condition of man, and I think that it is thought only the wise improve their advantages. It must be shown that it is produced better dwellings without making them more costly; and, the cost of the thing is the amount of what I will call life, which is required to be exchanged for it, alright. So, that's part of what he's interested in. He's thinking about, he's asking, part of the thought of the experiment he's asking us to strip things down to basics. Think about how we would start again if we were going to go back to the state of nature. Rewrite the social contract and begin again how might, this is one you might say, one man's proposal for how we might go about doing it. Again, not literally so; it's a kind of thought experiment that's asking us to rethink many of the things that we've thought. Go back to basics. Think about what it is that we need and why we need it. It becomes a literal project of doing that. Take a look a little further on back in the second chapter. In, it's page 1915 when he thinks about what the house actually represents for him. So, about ten lines down, wherever I sat there I might live, and the landscape radiated from me accordingly. One of the things, I mean going back to this idea of this Archimedean point, he's very aware of perspective. Going the woods gives him a new perspective on things; and walking around gives him a new perspective on things as well. Where I sat, there I might live, and the landscape radiated from me accordingly. What is a house, but a sedes, a seat, better if a countryseat. I discovered many a site for a house, not likely to be soon improved, which some might have thought too far from the village, but to my eyes the village was too far from it. Well, there I might live I said, and there I did live for an hour, a summer, and a winter life. Saw how I could let the years run off, buffet the winter through and see the spring come in. The future inhabitants in this region whatever, wherever they may place their houses, may be sure that they have been anticipated. And, one of the things here that you find, I mean part of what makes him this, what I've said, is a romantic writer is that the house, and the simplicity of the house become springboards for the imagination. Take a look a couple of pages on, maybe 1918. This is an example of how new perspective, can give you, you can gain new perspectives. He's talking about this lake that's nearby him. I'll skip around in here, but about five lines down, the way I look between horizon and over the near green hills to some distant and higher ones in the horizon, tinged with blue. Indeed by standing on tiptoe I could catch a glimpse of some of the peaks of the still bluer and more distant mountain ranges in the northwest. But, in other directions even from this point I could not see over or beyond the woods, which surrounded me. And, then look at this insight to the eyes. It is well to have some water in your neighborhood to give buoyancy to and float the earth. Sounds almost Montvillian. One value even of the smallest well is when you look into it you see that the earth is not continent, but insular. This is as important as that it keeps butter cool. When I looked across the pond from this peak towards the Sudbury meadows which in the time of flood I distinguished elevated perhaps by a mirage in their seething valley, like a coin in a basin, all the earth beyond the pond appeared like a thin crust, insulated and floated even by this small sheet of intervening water, and I was reminded that this on which I dwelt was but dry land. Now think about that for a moment. Dry land is a dead metaphor, dry land. What's the opposite of dry land? I guess wet land. What's wet land? Well for Thoreau that means all of the oceans, right. Most of the globe as we know is covered by water, but we don't think of that as land. We think of it as ocean or water. Thoreau says it gives us a sense of our place. It give us a way of re-contextualizing what we are to be able to stand in this, from this perspective and have this little insight. And, what I wanted to say is that there's kind of like these little local insights that Thoreau has that drives the technique of the book so that later on when he talks about the way he is here, he talks about in the some sense the imagination is let free by the constraints that he imposes on them by coming to the woods. A little bit further on, on 1918, both time, and place in time were changed and I dwelled nearer to those places, parts of the universe, and to those errors in history, which had most attracted me. Where I live was far off as many a region viewed nightly by astronomers. We are wont to imagine rare and delectable places in some remote and more celestial corner of the system behind the constellation of Cassiopeia's Chair, far from noise and disturbance. I discovered that my house actually had its site in such a withdrawn, but forever new and unprofaned part of the universe. Again, he's looking for these points where he can find this idea of hard bottom or sort of new perspective. I think I'm going to leave it there for today. One of the things I want you to think about is this image again. We'll come back, we'll finish up with Thoreau, and go on to Whitman. And, what I want you to do actually if you would is look at the place in the spring chapter where he talks about the leaves. Do I have a picture of it? The way the sand creates patterns of leaves. Look at the passage that he talks about there when he talks about belief and compare it what you're going to read in Whitman. The title of which is Song to Myself comes in a larger book called Leaves of Grass. Okay, let's think about that for next time. |
Open_Ed_Cyrus_Patell_American_Literature | American_Transcendentalism_IV.txt | >> Lecturer: Chapter 17 of Thoreau's Walden, which is entitled "Spring" is a climatic chapter which gives us a very good example of Thoreau's symbolic method. It's a method that allows him to move from materialist observations to idealist conclusions. In a way what Thoreau does is to build on the observation that Emerson makes in the fourth chapter of his little book Nature, that particular natural facts are symbols of particular spiritual facts. Moreover, Thoreau makes use of a rhetoric of what we might call "exemplarity." He takes little pieces of evidence, talks about the ways in which they stand for larger patterns that he sees recurring in nature, and then talks about the ways in which those larger patterns are evidence of what you might call idealist conclusions or principles that he wishes to discuss. So for example, on page 2028 of the text, Thoreau talks about the ways in which the phenomenon of the year take place every day in a pond on small scale. "Every morning, generally speaking," he says at the bottom of the page, "the shallow water is being warmed more rapidly than the deep, though it may not be made so warm after all, and every evening it is being cooled more rapidly until the morning. The day is an epitome of the year. The night is the winter, the morning and evening are the spring and fall, and the noon is the summer. The cracking and booming of the ice indicate a change of temperature." So one of the things I want to suggest to you is that even in a little sentence like that, you can see that Thoreau is mixing actual observation with something that we might think of as a larger set of observations -- more abstract, more idealist in their imaginings, thinking about the larger truths behind these natural facts that he notices. So as he watches the pond start to melt, and he sees the return of spring to the neighborhood, there's a certain kind of wonder that comes into the prose. And that's another thing I wanted to say to you. Again, remember last time I suggested that this narrative should be thought of as encapsulating some of the other forms. And I think if we were to think about some of the wonder that we found in the early settlement narratives, Thoreau has some of that, too. It's a settlement narrative in that sense. But then he goes off and he does some things that you might say most good naturalists in this period wouldn't do. And you could start to see, particularly when he talks about the railroad bank, that he's doing something that is not strictly speaking natural history. Take a look at page 2030. I mean, he recorded lots of signs of nature in his journal. And there were lots of possibilities for a kind of epitome for him of correspondences with various forms of nature and beyond. So it's interesting that he chooses this one: the thawing of sand and clay in the deep cut by the railroads. You can see that to culminate which you might call the revelations of spring in his text. And I wanted to point this out to you because it's a good encapsulation of how his symbolic method works. This is the second full paragraph on 2030. "Few phenomena gave me more delight than to observe the forms of which the falling sand and clay assume in flowing down the sides of a deep cut on the railroad through which I passed on my way to the village, a phenomenon not very common on so large a scale, though the number of freshly exposed banks of the right material must have been greatly multiplied since railroads were invented." We looked at this before. There's a kind of weird conflation of nature and culture going on here. And that passage about the meridian shallows and not being [inaudible] dinner. We saw how Thoreau was strangely mixing images from nature and culture in order to make a larger point about the routineness of life and the need to strip things down to their essentials. So here, again, he's not going to do what's predictable. He's going talk about nature but using as an example man's incursion into nature. So of all the things you could talk about, you go to Walden Pond, you live in nature, you're going to talk about the way in which man has cut through nature to create railroad banks and in particular, he's going to talk about this, what he calls sand foliage. "The material was sand of every degree of fineness and of various rich colors commonly mixed with a little clay. When the frost comes out to the spring and even in a thawing day in the winter, the sand begins to flow down the slopes like lava, sometimes bursting out through the snow and overflowing it where no sand was to be seen before." Now we're going to have very close observation of this. "Innumerable little streams overlap and interlace one with another, exhibiting a sort of hybrid product, which obeys half way the law of currents, and half way that of vegetation. As it flows it takes the forms of sappy leaves or vines, making heaps of pulpy sprays a foot or more in depth, and resembling, as you look down on them, the laciniated, lobed, and imbricated thalluses of some lichens; or you are reminded of coral, of leopard's paws or birds' feet, of brains or lungs or bowels, and excrements of all kinds. It is a truly grotesque vegetation, whose forms and color we see imitated in bronze, a sort of architectural foliage more ancient and typical than acanthus, chicory, ivy, vine, or any vegetable leaves; destined perhaps, under some circumstances, to become a puzzle to future geologists" -- they become fossilized -- "The whole cut impressed me as if it were a cave with its stalactites laid open to the light." So Thoreau was interested in taking a look at this formation. And you can see there's a set of associations that he makes. But again, these are associations that he makes out of his own experience. He kind of sees that these look like other shapes that he's known. But what he wants to do is generalize out from that. So it's a kind of weird version of materialist thinking, right? He's going to look very closely and observe this. Then he's going to apply his own reason to it. But the conclusions he's going to make are in some sense not reasonable; they are marked by something else. A scientist would be afraid to make these conclusions, wouldn't even say they're ridiculous. But Thoreau is trying, you might say, to get at a larger truth than that which science alone can provide. And in that sense, he's kind of making a case for the power of the imagination. And that's in part what makes him a Romantic writer. So he's initially concerned with recording how the sands forms these shapes of what he calls "sappy leaves" or "vines." But one of the things to say is that he is making an argument about certain kinds of correspondences that take place in the visible world in matter itself, as if somehow there were something animating matter. It's a kind of paradox. He knows this is inorganic material, but over and over again he sees it taking organic forms. "Why?" he wants to ask. Take a look at the rest of that paragraph. "When the flowing mass reaches the drain at the foot of the bank it spreads out flatter into strands, the separate streams losing their semi-cylindrical form and gradually becoming more flat and broad, running together as they are more moist, till they form an almost flat sand, still variously and beautifully shaded, but in which you call trace the original forms of vegetation; till at length, in the water itself, they are converted into banks, like those formed off the mouths of rivers, and the forms of vegetation are lost in the ripple-marks on the bottom." What he sees here is a process of change of becoming, but one that seems to that place in an orderly way and that recapitulates in the same way that the pond recapitulates a day or a year or year on the pond recapitulates a day of the year of the whole seasonal cycle. These things we recapitulate other things that we see, the feeding off of streams into water itself. So there's a sense in which he is doing something that looks like what a naturalist would do, kind of dividing his observations out into larger principles that create a kind of progressive idea. But it leaves him finally to a belief that no natural scientists would argue, which is what he says on page 2032 that "the maker of that earth but patented a leaf." That's at the beginning of the first full paragraph there. "The maker of this earth but patented a leaf." Now again, probably a natural scientist wouldn't write that, either, this idea of the "maker" kind of secularized version of the divinity patenting -- very 19th century business language -- a leaf. What does he mean? He means that basically there is one design, one set of principles and it is embodied in the idea of the leaf. The leaf for him, which comes out again in the spring in the same way that it's come out every spring, is a pattern of regeneration. That's what spring means for him. But you might say that what the project of book is from here on out is to link that natural concept of regeneration to a cultural concept, which we might think of something like redemption. And in this way we might say that Thoreau is in line with the kind of thinking that we saw in Emerson: not interested in the total depravity of humankind, interested possibility of perfection, interested in the possibility of redemption, the idea of redemption and perfection are for Thoreau written into nature itself. And that's what he finds there. So if you go back a page in the middle of 2031, you'll find this. It's in the middle of long paragraph on that page. "I feel as if I were nearer to the vitals of the globe, for this sandy overflow is something such a foliaceous mass as the vitals of the animal body. You find thus in the very sands an anticipation of the vegetable leaf. No wonder that the earth expresses itself outwardly in leaves, it so labors with the idea inwardly. The atoms have already learned this law and are pregnant by it." There's one idea here. It's the idea of a leaf. And therefore he says, by the time we get to that sentence that I quoted -- well, if you look at no time middle of the long paragraph that begins 2032, he looks at this. And then in kind of an almost an echo of one of the biblical stories of origins, he says, "What is man but a mass of thawing clay? The ball of a finger is but a drop congealed. The finger and toes flow to their extent from the thawing mass of the body. Who knows what the human body would expand and flow out to under a more genial heaven?" Again, I want you to look at the way that prose works. He looks at the fact that our fingers and toes have these [inaudible] it's almost like we're flowing outward and then we stop. And maybe if we were in a different kind of creation, we would keep flowing and become one with the things that we're separated from. So he finally concludes, "Thus it seemed that this one hillside illustrated the principle of all the operations of nature." Although again, I want you to see that these principles are generated out of human beings' incursion into nature. Now you can think about that in any ways you want. You can say Thoreau underestimates the extent to which the railroads will start a process of the deformation of culture that leads us to the nature that we have or don't have today. You can say that part of what he's thinking is this idea that it's even an extension of the idea that Emerson has that all our operations taken all together don't really affect other nature and are somewhat trivial when we think about the largeness of nature. And Thoreau would say, "Not only that, nature manages to reincorporate all the things that we would do to it." So we make this cut to make a railroad bank, these kind of forms start happening here. So you might say it's the use of an illustrative analogy. But it isn't good science. What it is, really, is you might say it's transcendental philosophy and that's really what the culmination of this is. Thoreau calls it in the middle of 2037, he refers to this as the kind of "inexhaustible vigor of nature" is what he calls it. And it is the chapter that basically ends the narrative proper when he leaves his cabin. Although he ends the chapter on page 2038 in a very strange way: "This was my first year's life in the woods completed. And the second was similar to it. I finally left Walden September 6, 1847." I mean, that's kind of weird when you think about it: we have this incredible detail about the first year; the second was similar to it. What does that mean? I mean, what about all those material details? Why don't we get them for the second year? Surely, it couldn't have been the same thing. Ultimately, this is a kind of case study for him, this first year, as a case study and something larger than simply natural forms. Therefore, you might say that the first year stands in for the second year, and both of the years taken together stand in for something else. I've already told you, of course, that there's a way in which this is an artificial construction. We talked about when I decides to official begin the project. It just happens to be July 4th. And we know that he didn't stay out there all the time. He used to come back in, bother people who were living in Concord. I told you apparently take pies from window stills when they were cooling, that sort of thing. So this is a kind of constructed account. And there's a way in which the conclusion of Walden makes it clear to us that we are part of the constructed nature of this account. And if you looked at it, you might say that the conclusion is a little bit different because in a certain way, he ceases being somebody who's kind grounded in this cultural seat and becomes someone who now starts to walk around and think more broadly. So it's almost as if the foundation that Walden -- the house or the cabin -- laid, has simply been preparatory to this final conclusion in which he will think things that he was unable to think when he first got there. And even more than that, you'll say, he starts to rethink things that he thought when he first got there and things that he presented to us earlier on in the book. Take a look -- he openly starts to use this language of discovery at the top of 2039. And some of antecedents that I've suggested this narrative evokes are evoked literally here. "Is Franklin the only man who was lost that his wife would be so earnest to find him? Does Mr. Grinnell know where he himself is? Be rather the Mungo Park, the Lewis and Clark and Frobisher, of your own streams and oceans" -- these are all explorers, right -- "explore your own higher latitudes -- with shiploads of preserved meats to support you if they be necessary and pile the empty cans sky high for a sign. Were preserved meats invented to preserve meat merely? Nay, be a Columbus to a whole new continent and worlds within you, opening new channels, not of trade but of thought." We won't give you that on any exam because it looks too much like Emerson. This is probably the most Emersonian of these chapters. And it's a chapter that's full of maxims as well. I'll give you an example of one that's fairly well-known. How about 2041? "Why should we be in such desperate haste to succeed and in such desperate enterprises?" This is in greeting cards all over the country. "If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away." There are lots of maxims that are here. And then Thoreau goes on to do a very Emersonian thing. You'll remember how Emerson ended Nature, which was supposed to be again kind of inspired by natural history with a weird parable, his Orphic poet, this figure that he creates to ventriloquize thoughts that he himself has been thinking. So Thoreau gives us a parable as well. He gives us an Emersonian fable about -- and this is the top of 2042 -- "There was an artist in the city of Kouroo who was disposed to strive after perfection. One day it came into his mind to make a staff. Having considered that in an imperfect work time is an ingredient, but into a perfect work time does not enter, he said to himself, It shall be perfect in all respects, though I should do nothing else in my life. He proceeded instantly to the forest for wood, being resolved that it should not be made of unsuitable material; and as he searched for and rejected stick after stick, his friends gradually deserted him." And this becomes a certain kind of parable about time and timelessness, and about the timelessness of the imagination a little bit later on. "As he made no compromise with Time, Time kept out of his way, and only sighed at a distance because he could not overcome him." This artist has a commitment you might say to creating a perfect object. And it finally leads him at the very end of the paragraph to a certain kind of triumph of the imagination. So that what we see here is Thoreau shifting himself away from natural history and observation as evidence of some kind of regeneration or redemption. Here's a different model. It's the not scientist. Finally, it's the artist -- the artist now as the maker of the world. Little bit further on: "When the finishing stroke was put to his work, it suddenly expanded before the eyes of the astonished artist into the fairest of all the creation of Brahma. He had made a new system in making a staff, a world with full and fair proportions in which though the old cities and dynasties had passed away fairer and more glorious ones had taken their places, and now he saw by the heap of shavings still fresh at his feet that for him and his work, the former elapse of time had been an illusion. And that no more time had elapsed than is required for a single scintillation from the brain of Brahma to fall on and enflame the tinder of a mortal brain. The material was pure and his art was pure, how could the result be anything other than wonderful? So what does this mean? At the end of all of this what appears to be natural science and observation, Thoreau is attributing the world around us and the making power of the world, you might say, both to Brahma his figure for God and to the artist. What I would suggest to you is this is another aspect of transcendentalism, right? We saw it in Emerson, this need to conflate the human and the divine. Emerson does it by talking about the soul that we all have that is part the divine mind. Thoreau does it here in some sense by taking himself out of natural observation into, you might say, the life the mind or the imagination. And it suggests to us that Thoreau ends his book this way because he knows that this is going to turn into this. I mean, this we see is a replica across the road if you go to Walden Pond. This is what's left of the cabin today, just these little markers. That stone that you see there on the far side is it marks the chimney foundation. It says "Beneath this stones lies the chimney foundation of Thoreau's cabin 1845-47." So that's what left of Thoreau's project. And what I'm suggesting to you is that the shift now in emphasis, he's done this whole thing -- natural science observation, looking at a whole year, this process of regeneration -- but what's the real regeneration of the world going to be? It's not going to take place in some sense only through natural processes. Maybe this is the point of bringing nature and culture together all the time. It's going to take place through the human imagination. Walden disappears, but this Walden stays, particularly with people like me keep assigning it. But I think there's a sense in the power of textuality that we finally end up with here, right? On September 6th, 1847 Thoreau tells us he left. He leaves the cabin which he had built where he lived for two years, two months, and two days. That of course, is purely accidental math. Emerson then bought the cabin from Thoreau, resold it to his own gardener, who then converted it into a cottage for his family. The guy who bought it from Emerson had drinking problems, prevented him from completing the necessary modifications. The cabin was abandoned in 1849. It was purchased by somebody else who moved it across town to his own farm and used it for grain storage. So the cabin gets practical purposes. The roof was removed in 1868, used as part of a pig sty. 1875, the rest of the cabin's timber was used to patch up the barn. So all that remains is just what we saw. This is the Walden that remains to us. And I think the next part of the conclusion after this artist of Kouroo parable tells us in some sense that art, culture preserved through art, or text is really necessary because the process of building a culture is so difficult, fraught with uncertainty. So one of the things you might say is that at the end of very end of conclusion we have these showy parables -- the one the artist of Kouroo, the very end we have that beautiful bug that's coming out of the trees. But in there, there are bits and pieces that give us pause or that ask us to reconsider one of the places where we began. Do you remember that? That [inaudible]? The hard bottom on which you can build a wall or estate? Well, Thoreau asks us to think about that again as we've come through this long project with him. This is page 2044, about five lines down. "It affords me no satisfaction to commence to spring an arch before I have got a solid foundation." All right, that sounds like it's what we would expect, right? We want to find solid foundations in order to build a wall, estate, or an arch on. That's what the whole project has been about, looking for solid foundations. And then he says, "Let us not play at kittlybenders. There is solid bottom everywhere." And kittlybenders is this game of trying to be on the ice and not have it crack under you. Anybody here like Pink Panther movies? Ever seen the movie called The Pink Panther Strikes Back? Peter Sellers is Inspector Clouseau. He's trying to track down this nefarious super criminal. He ends up going to this inn someplace nearby this guy's castle. I think it's in the south of France someplace. There's this old guy sitting behind a desk and a dog. And the old guy has come there, "Do you have a room?" And Peter Sellers mangles it, "Do you have a room?" "A what?" "A room." "Do you have a room?" "Oh, a room." "That is what I said along, you idiot." "Okay, yes, we have a room." Then he's looking, he goes, "Does your dog bite?" "What?" "Does your dog bite?" "My dog? No." So Clouseau reaches down to pet the dog that's sitting there. "I thought you said your dog does not bite?" "Yes, but that is not my dog." [ Laughter ] All right, that's a version of this. You have to know how to ask the right questions. There is solid bottom everywhere, but maybe that's not the only thing that's going on. We read that the traveler asked the boy if the swamp before him had a hard bottom. The boy replied that he had. But presently the travelers' horse sank to the girth. And he observed to the boy, "I thought you said that this bog had a hard bottom." "So it has," answered the latter, "but you haven't got halfway to it yet." He didn't ask the right question. Is it hard bottom and close enough that I can walk across if with my horse? Sure, it's got a hard bottom somewhere down there. So this is a little bit of joke, right? So it is with the bogs and quicksands of society, but he is an old boy that knows it. "Only what is thought, said, or done at certain rare coincidence is good. I will not be one of those who will foolishly drive a nail into mere lathe and plastering. Such a deed would keep awake at nights. Give me a hammer and let me feel for the furring. Do not depend on the putty. Drive a nail home and clench it so faithfully that you can wake up in the night and think of your work with satisfaction, a work at which you would not be ashamed to invoke the muse." So again, it's a kind of weird conflation now of the kind of carpentry and stuff that he was interested in earlier and this idea of artistic creation. But what I think this retelling of the solid foundation thing is to suggest to you that there's something at stake that's crucial in this search for a hard bottom and it's not necessarily going to be an easy search. In fact, the implication is if you're not careful, if you're this kind of traveler, you may well drown in this bog if you don't understand the right way to ascertain what the hard bottom is. So that one of the things we say here is that this exertation at the beginning of the book to find this foundation, this hard bottom, here becomes a kind of warning. And I think you would understand something central to what Thoreau is doing here if you were to compare this section of the conclusion to that session earlier on that we talked about, about the mosquito's wings on the rail and being tied to the mast like Ulysses. It tells us something more about the quest for the real. In the first version you might say Thoreau recognizes that death is a possibility -- that's the invocation of Ulysses tied to the mast, trying to hear the sirens. So he's searching for knowledge that the siren's song produces for him, but he needs to be tied, he needs to be restrained. That's the image from The Odyssey. But here, something else is going on. We don't hear the end. We don't know what happens to the travelers. Does the boy sort sit there and let him sink? I mean, we know Ulysses makes it through. There's no necessarily guaranteed ending [inaudible] this kind of obscure little thing. When he hits the bottom, he will hit the bottom, but he'll be dead when he does it. I mean, if we want to take this as less of a joke and more of a kind of serious -- you might say, therefore, if that is the new parable for searching for hard bottom, it's an impossibility. You actually set yourselves an impossible task. The bottom is there, but human means will not allow you to find it. So what means do you need? You need something that transcends mere humanity, mere natural observation. In other words, you need something like the artistic imagination. And I think that's why we finally end with this parable that is a kind of folk story, which prophesize the possibility of some kind of redemption or rebirth. But it can only be done it in terms of the story, in terms of the imagination. It can't be done within the realm necessarily of natural history or natural history won't be enough. Take a look on page 2045. "Everyone has heard the story which has gone the rounds of New England of a strong and beautiful bug which came out of the dry leaf of an old table of apple-tree wood, which had stood in a farmer's kitchen for 60 years, first in Connecticut and afterwards in Massachusetts from an egg deposited in the living tree many years earlier still, as appeared by counting the annual layers around it, which was heard gnawing out for several weeks hatched per chance by the heat of an urn. Who does not feel his faith in a resurrection and strength in immorality strengthened by hearing of this? Who knows what beautiful and winged life whose egg has been buried for ages under many concentric layers of woodenness in the dry dead life the society deposited at first in the alburnum of the green and living tree, which has been gradually converted into the semblance of its well-seated tomb, heard per chance gnawing out now for years by the astonished family of man as they sat around the festive board. May unexpectly come for amid society's more trivial and handselled furniture to enjoy its perfect summer at last." So the image of belatedness. We've come late in the world; we don't expect miracles to happen. But maybe this sign of this bug somehow coming out could possibly be a sign that within our larger society, there is some kind of seed or bug or something laid in the foundations years ago that when we strip things away we might be able to find. Thoreau finally says this: "I do not say that John or Jonathan" -- England or the United States -- "will realize all this, but such is the character of the morrow which mere lapse of time can never make the dawn. The light, which puts out our eyes is darkness to us. Only that day which dawns, only that day dawns to which we are awake. There is more day to dawn, the sun is but a morning star." I mean, that's kind of the final image of light. Enlightenment has its source in both a divine and a human consciousness. It should remind us a little bit of some of the rhetoric of the Enlightenment but given this kind of romantic imaginative cast, it shows us finally that Thoreau is not a naturalist, but Thoreau is in sense a Romantic writer and a transcendentalist. So I want you to see that there's a sense in which what Thoreau's project has been is fundamentally a kind of compliment to what Emerson's was in nature and those other. He promotes a certain kind of investigation through nature, he cons you almost into thinking that that's what it is, that it's a piece of science. I mean, if Emerson uses the structure of natural science in his little book Nature, you might say Thoreau kind of pulls an Edward Taylor and really goes and does this writ large in his own experience, but ultimately the aim is the same: to find out something about the self, to find out something about the sense of where American culture is in the middle of the 19th century, and to think about what further exploration of the self, and trusting in the self, and the imagination might do for that culture -- get us out of what Emerson calls the "dry bones of the past" and get us to imagine something new. In that sense, he's a transcendentalist thinker and I would say to you that Walden is full of rhapsodic moments like this that in some sense recapitulate this structure. So the very same thing that Thoreau says about the pond recapitulating the entire season might well be true of particular moments in this, in the text as well. They recapitulate this larger structure. And I think you can therefore see as different as they are, there are real affinities between Thoreau's writing and Whitman's. You get the sense kind of that Thoreau is more comfortable with mud and excrement and stuff than with people. I mean, I always got that sense. With Whitman it's a little bit different. I mean, Whitman seems to be really interested in people and comfortable with people. And what we might say about him is that he extends Emersonian self-reliance and this Thoreau exploration of nature by taking a look at the one province of nature with which Emerson and Thoreau seem to be uncomfortable. That part of the not me that is not nature out there, but is nature here, the body. Whitman is really, really interested in the body. And one of the things we might say about that is that he constructs a kind of larger-than-life image, a kind of poetic persona. And there's a sense in which you could start to read the poem that we read for today, Song of Myself as in part a kind of narrative of the development of a self and a poet, but one that is going to use exploration not only of nature, but of the culture and of the body, and of sexuality in order to be able to encompass the entire country out of which he comes. So Whitman is very interested in constructing images of himself. As the piece by Angus Fletcher suggests to you, Whitman is constantly reworking his poetry. He comes up with a small volume of poems in 1855. He edits them and produces more and more editions, adds to them, changes it. Song of Myself looks different in 1855 from the version that you read, which is the last edition. And with that, he kind reinvents himself all along. In the end he ends up sort of like this -- the American bard, a sage. He starts off kind of like this around the time he writes Leaves of Grass. He's more of a kind of dandy man about town, what Baudelaire would call the "flaneur," somebody that walks around and observes. When he publishes it, he reinvents himself again on the title page of the 1855 edition as "one of the roughs, Walt Whitman." And the nine poems that are in the original edition are untitled. They're just kind of there. And Whitman introduces himself -- about 29 pages into the poem, he finally introduces himself in these lines: "Walt Whitman, an American, one of the roughs, of kosmos, disorderly, fleshy and sensual, eating, drinking, and breeding. No sentimentalist, no stander above men and women or apart from them. No more modest than immodest." So that's the way that Whitman is presenting himself in this time. And one of the things that people actually say about Whitman is that he becomes, for a certain time, more adventurous as a writer, perhaps in response to Emerson's suggestion that he tone things down a little bit. But then, gradually as he becomes well-known or becomes thought of as a kind of bard figure, he becomes the edits that he does and the things [inaudible] become a little bit more culturally conservative. In fact, there's a biographer of Whitman named Gary Schmigdall who wrote A Gay Life of Whitman, which is difficult to do because you have to -- everyone has a sense that Whitman was at least bi-sexual, if not gay, that he was very interested in young men, but he was very interested in things that were associated with gay culture in the middle of the 19th century. But there's not a lot of hard and fast evidence about it. But one of the things that he noticed in the course of doing this is he wanted to put together an anthology of poems to accompany it. And you realizes that the poems that he needed were not in the earliest edition and not in the latest edition, they were somewhere in the middle editions. So one of the things we would say is that Whitman is kind of reinventing himself all the time. There are contexts for thinking about Whitman. So one of the contexts for thinking about Whitman is part of a trajectory of poetry that begins in our course with neoclassicism, goes through Bryant. Remember I talked to you about Bryant's project being a kind of Americanization of Wordsworth's project? You remember this? Bryant is a little bit older. Maybe we should do it that way. So one of the things to think about is that Bryant is somebody who is kind of part of this larger trajectory. And Bryant is thought of in that sense as somebody who's part of a kind of New England story of letters which would then lead to Emerson, right? This is Emerson in 1837. Remember "American scholar. We've listened too long to the courtly muses of Europe? Spirit of the American free man is already suspected to be timid, imitative, and tame?" Now imitative, again is something that we should think it with poetry, right? Remember it in neoclassicism, imitative was a good thing. Poetry was supposed to be precisely following Aristotle mimetic. You were supposed to imitate nature if you were a poet. And if you were a poet like Phillis Wheatley, you were supposed to imitate the masters of poetry. That's how we all knew that we were doing poetry. We could tell. Originality is not something that turns out to be prized by neoclassicism. It starts to be prized later on by people like Bryant, and then Emerson, and then Whitman. So that by this time you would see that imitative is not part of the solution to creating an American poetry, it's part the problem that's preventing American poetry from being created at all. And interestingly, Emerson as I told you before, goes off lecturing. He was a lyceum lecturer. People used to raise funds to let him lecture in their neighborhood. He lectured in New York and Whitman heard him. He gave a lecture in 1842 called "The Nature and Powers of the Poet." This was later collected in the second series of essays and revised into the essay that you read for today. And Whitman has a very famous quote about this. He says he attended this lecture on the poetry of the times, March 7th, 1842. And he said later on describing attending this lecture, "I was simmering, simmering, simmering, and Emerson brought me to a boil." Simmering, simmering, simmering, right? So this is what he heard, if you want to look at in the text, we'll start off with page maybe 1187. But you can just look -- I'm sorry, 1183. You can just look at it up there. Emerson is writing in some sense against the grain. If poetry was supposed to be about decorum and form, Emerson wants something else, not just metres, but a "metre-making argument" he says, "that makes the poem a thought so passionate and alive that, like the spirit of a plant or an animal, it has an architecture of its own and adorns nature with a new thing." I'm not sure that I know whether Emerson knew the poetry that was metaphysical poetry what he said about that. He certainly wouldn't have known Taylor's poetry because it was lost at this point. But you would imagine Emerson would have approved of that poetry and along with it, the idea of wit that Samuel Johnson so disparages. The poet has a new thought. He has a whole new experience to unfold, and he will tell us how it was with him and all men will be richer in his fortune. And he goes on later on in the essay -- this is on 1191 -- to talk about the poet as liberating gods. This is not unlike Shelley in Defence of Poetry talking about the poets as legislators of the world. He says, "The ancient British bards, had for the title of their order those who are free throughout the world. They are free and they make free. An imaginative book renders much more service at first by stimulating us through its troops, then afterward when we arrive at the precise sense of the author." It's the process of reading. Again, think of that moment from Self-Reliance -- "power ceases in the instant of repose consistent the shooting of the gulf, a darting to an aim," same with reading. The end isn't the important thing, it's how you get there and what kind of creative reading it can inspire you to do. "I think nothing is of value in end books, excepting the transcendental and extraordinary. If a man is inflamed and carried away by his thought, let me read his paper and you may have all the arguments and history and criticism." Again, this is just in line with what he says at the beginning of nature, that our age is retrospective, it builds us up [inaudible], it likes history, biography, and criticism. On those old genres. Give me some new thinking and you can have all of the rest. And so Emerson goes onto say, a little bit further down on 1193, that he looks in vain for the poet that he's describing. And there's something poignant a little bit about this because Emerson is a poet also. He writes poetry. And you can read it. But nobody really does compared to reading Whitman. Although there are moments when Emerson seems to anticipate Emily Dickinson of all people. There are certain poems that he has when you would look at them and you would say, "Oh, that's Dickinson," and it isn't. So there's some interesting things going on in Emerson's poetry. But he himself, or maybe you might say he doesn't have the self-aggrandizing personality that we find in Irving or in Whitman. But he says, "I look in vain for the poet whom I describe. We do not with sufficient plainness or sufficient profoundness address ourselves to life. Nor dare we chant our own times and social circumstance. Time and nature yield us many gifts, but not yet the timely man the new religion to reconcile to whom all things await." And he goes and he evokes other people who have made history, you might say, in poetry. But finally, he wants to say this: "Banks and tariffs, the newspaper and caucus, Methodism and Unitarianism are flat and dull to dull people but rest from the same foundations of wonder as the town of Troy and the Temple of Delphos and are as swiftly passing away." He's making a counter argument to those who would say, "Look, sorry about the lack of world poetry, but you know we live in unpoetic times." Remember the kind of Irving critique of economy or even [inaudible] critique of Irving's critique. This is the kind of dull nation. Everybody drinks beer and all they think about is business. Emerson says, "You're thinking about it the wrong way. Even this business life of ours is something. And beyond that, our logrolling, our stumps and their politics, our fisheries, our Negroes and Indians, our boasts and our repudiations, the wrath of rogues, and the pusillanimity of honest men, the northern trade, the southern planting, the western clearing, Oregon and Texas, are yet unsung. Yet America is a poem in our eyes, its ample geography dazzles the imagination and it will not wait long for metres." This essay, if you were to read this essay and then read Whitman's preface to the 1855 Leaves of Grass you would see strong resonances. Whitman basically takes up the invitation that Emerson's lecture had posed to him. This is what he writes in the preface to Leaves of Grass: "Americans of all nations at any time upon the earth have probably the fullest poetical nature. The United States themselves are essentially the greatest poem." So the story goes is that Emerson writes this. It's said to have been published July 4th, 1855. It's basically self-published. Whitman publishes the book himself, he sets part the type himself, he takes care of his distribution, prints about a thousand copies and sells very few of them. The preface appeared with twelve -- not nine, but twelve -- untitled the poems. They eventually get names -- Song of Myself, I Sing the Body Electric, The Sleepers, There Was a Child Went Forth. Whitman sends copies of the first book to the leading literary figures of the day in New England and in New York. It is said that this man, John Greenleaf Whittier, a very well-known poet and politically progressive, antislavery, said he took one look at his and threw his into the fireplace where he used it for kindling. And you can imagine why that is when Whittier thought poetry should look something like this: "Bearer of freedom's holy light, breaker of slavery's chain and rod, the foe of all which pains the light or wounds the generous ear of God. Beautiful yet thy temples rise through their profaning gifts are thrown and fires unkindled of the skies are glaring round thy altar stone." Okay. There's a way in which if you think that's what poetry looks like, you're going to look at what Whitman writes and think "What is this stuff?" But Emerson got it. So probably made up for the lack of response from other people. Emerson got it and his response was more than enthusiastic. In fact, it's probably one of the most famous letters in American intellectual history. He writes this to Whitman: "I am not blind to the worth of a wonderful gift of leaves and grass. I find it the most extraordinary piece of wit and wisdom that America has yet contributed. I'm very happy in reading it. This great power makes us happy. It meets the demand I am always making of what seemed a sterile and stingy nature, as if too much handy work or too much lymph in the temperament were making our western wit fat and mean." And you can see there's an echo of the American scholar in that quotation. "I give you joy of your free and brave thought," he said, "I have great joy in it. I find incomparable things said incomparably well as they must. I find the courage of treatment which so delights us and which large perception only can inspire. I greet you at the beginning of a great career, which must yet have had a long foreground somewhere for such a start." A long foreground somewhere for such a start. And the letter goes on, actually, in this vein. There was own one comparable commentary on the poem that appeared at this time. It said -- it was an anonymous review that said, "An American bard at last." Any idea who might have written that review? It was Whitman, right? Okay. So Whitman is very smart about this. Ever the self-promoter, he actually goes and without asking Emerson's permission, he has the letter printed in the New York Tribune. And he has the words, "I greet you at the beginning of great career, RW Emerson," stamped in gold print along the spine of the second edition of Leaves of Grass, which is basically a rebinding of the first edition. And he actually then goes on in I think the next edition takes out his preface, reprints Emerson's letter and as a kind of long essay-like response to it thereafter. So that you can say that one of the things that Whitman realizes is that he has the opportunity to have the Emersonian stamp put onto his work and he takes that opportunity. Emerson wasn't exactly happy about it for a while because it was a private letter that he didn't really expect to be reprinted. And I think he actually edited it shortly thereafter in an anthology of poems in which he did not include Whitman, but later on they kind of passed that over. One thing that Emerson did say about the poetry that he -- just a little bit friendly of advice, he sort of suggested that maybe you should tone down some of the sexuality. And so Whitman's response to this actually takes issue with this. And he says, and he writes this letter back to Emerson in which he says, "No, this is exactly what I want to do. By silence or obedience to the pens of savants, poets, historians, biographers, and the rest" -- so all those people that Emerson doesn't like -- "have long connived at the filthy law and books enslaved to it that what makes the man of a man, that sex woman [inaudible] desires, lusty animations, organs, acts, are unmentionable." See what he's doing? He's turning the tables on Emerson. Emerson becomes aligned in some sense insofar as Emerson is critiquing Whitman's use of sexuality in his imagery. He suggested that Emerson might well be aligned with all of those old things old things that Emerson himself doesn't like -- "historians, biographers, and the rest are unmentionable and to be ashamed of, to be driven to skulk out of literature with whatever belongs to them. This filthy law has to be repealed. It stands in the way of great reforms. I say that the body of a man or a woman, the main matter is so far quite unexpressed in poem. But that the body is to be expressed and sex [inaudible] for these states if it comes to a question it is whether they shall celebrate in poems the eternal decency of the amativeness of nature, the motherhood of all, or whether they shall be bards at the fashionable delusion of the inherent nastiness of sex and the feeble and querulous modesty of deprivation." One of the things that's a generative metaphor for Whitman is a link between procreation and creation, artistic creation, right? And there's a sense in which the poems themselves kind of embody that. Whitman therefore later on describes Leaves of Grass as the "outcropping of my own emotional and other personal nature and attempt from first to last to put a person, a human being, myself in the latter half the 19th century in America freely, fully, truly on record." And that means everything -- all of his feelings and his desires, even the things that someone who was kind of more decorous thinker might actually choose to omit. So he rejects Emerson's plea to tone down his sexuality and in fact, writes a series of poems called the Calamus Poems for the 1856 edition that are even more frankly sexual in their imagery than before. So one of the things I want to suggest to you is that there is this kind of opening up of the poetry. And in some sense, it comes in part through what he talks about and also how he talks about it. We can come back to Bryant here again and thinking about what Bryant does at the beginning of Thanatopsis. Remember the opening lines, "To him and who the love of nature holds communion with her visible form she speaks." We said, "Oh, it's not rhymed. It's got a blank verse. It does this, it has this fourth foot here in its second line. It's trisyllabic. It's making a point." One of the things I want you see about this is if you're making a point that way, you're asking your readers to notice the importance of metrical feet. Therefore, in some real way you're suggesting that the unit of meaning for a poem is the metrical foot. So I want to suggest to you that one of Whitman's big innovations is to make the unit of meaning not simply the metric foot, but the line, the entire line -- however long or short. So you can scan Whitman's poetry, but it almost seems like it's beside the point. He's doing something other than that. And that's why you might say people who were used to poetry that can scan and it fits itself into rigid bounds don't like and understand what Whitman is doing. So what Bryant is doing is blank verse. What Whitman is doing more blank than that, it's free verse. That's the term that we use for it. And it looks like that. I mean, I have to squish them in order to put them on the screen. But these are all lines. They have weird -- forget caesuras, they have actual ellipses in the middle of that, right? Now, turn to section 29 of your poem. This is -- sorry section 24. It's on page 2227. This is the 1855 version. And if you look at in your book, you'll see that the 81 version is different from it. And that in fact, there are instead of being simply "Walt Whitman, an American one of the roughs of kosmos," he changes it a little bit. "Walt Whitman, a kosmos of Manhattan the sun, turbulent, fleshly, sensual, eating, drinking, and breeding, no sentimentalist, no stander above men or women or apart from them, no more modest than immodest." What I want to suggest to you that religion is important because it's a way in which Whitman is identifying back with another story that we can tell about the roots of his poetry. I mean, if Emerson said that this "long and great career must have had a long foreground somewhere for such a start," where that foreground is is in the streets of Brooklyn in New York, Whitman wandering around the streets of New York, meeting Bryant, who by this time is kind of an older person. So Bryant is not only part of the New England story, he comes and becomes even more famous as an editor than a poet in New York city. And Whitman himself, like Bryant, becomes part of the press. He writes for what's called the Penny Press. Actually, The Aurora was a couple of pennies; it was slightly a cut above. But one of the things that's going on in the beginning of the 19th century is the establishment of very cheap newspapers that sold papers through sensationalism, you might say. And Whitman partakes in that. Later on he writes this about the newspaper: "Whoever does note that our city" -- by which he means New York -- "is the great place of the western continent -- the heart, the brain, the focus, the mainspring, the pinnacle, the extremity, the no more beyond the new world -- whoever does not know this, we say, must have been brought up in a place where they didn't take the paper and where The Aurora in particular had never scattered its [inaudible] light." In other words, Whitman is making argument that New York is now the most American place in the country, that New York should be the seat of culture, not that New England. And that where you're going to find what's distinctive about the United States, you're going to find not in high literature but in the papers, in that democratic form. And Whitman writes in many of his articles that the papers can actually be a force for education and for democracies. He goes, "Among newspapers, the Penny Press is the same as common schools among seminaries of education. They carry light and knowledge in among those who most need it. They disperse the clouds of ignorance and they make the great body of the people intelligent, capable, and worthy of performing the duties of republican free men." One of the things to understand about this is that he's making an argument on behalf of a form that many of the intellectuals of the day would scorn as being just full of sensationalistic writing. And Whitman is, at this stage of his career, interested in a certain kind of sensationalism. He is -- he styles himself as kind of a flaneur, somebody who walks around the city and observes and observes lots of interesting things. This is an example of a guy who was known as a sensationalist writer, George Thompson. And he wrote many of these books about city life were serialized in precisely these papers, the Penny Press. You can look at some of names. Venus in Boston and city crimes. New York life of mysteries of [inaudible] revealed. The Gay Girls of New York. Katherine and Clara or the Double Suicide. There's a kind of sensationalistic side to the Penny Press. Whitman is part of this sensationalist side. For a while, one of his beats was to cover murders off the police blotter. These are the kinds of things that was the frontest piece to one of Thompson's books. This is a kind of discourse, you might say, that Whitman is involved in when he was involved with the papers. This is an ad from one of the papers -- ad for one of these books about the mysteries of Bonham Street; ads for some fancy French stuff; ads for another book called The Confessions of the Sofa; ad for another racy novel; cundoms [phoenetic], whatever those might be; ad for a neat and curious book. This is in Whitman, too. The high fluting New England story of transcendentalism, sure, that's in there. But Whitman is actually a poet of the streets. And one of the things to understand is that he wandered around the streets of New York. He looked at the ships, clearly he writes about those. He looked at the immigrants, people who were desperately poor, especially the immigrants who would come from Ireland in the aftermath of the Irish famine in the middle of the century. They're all moving down into the Lower East Side. The Lower East Side was just kind of teeming hideous slum. You know, the upper crust people were moving uptown in horror, first to Washington Square, then up Fifth Avenue, right? Henry James, at the end of the 19th century writes about Washington Square. You have no idea how close the slums of the Lower East Side are to the place that he described. Upper class culture. Literature. Keeps aloof from all of that. Whitman doesn't. Whitman sees in the streets. This is a scene from the Five Points where I dramatize Scorcese's Gangs of New York. Whitman sees the opportunity for a new culture precisely in these immigrants. I'll say a little bit about it next time, but Whitman talks. He uses a term, "adhesiveness," touching closeness to one another. The people often will say, "Okay, you know what? That's a code word." That means a gay experience. It means people coming together. Sexuality -- that's what adhesiveness is about. And that's fine. And that's revolutionary insofar as it goes, I suppose. But really, it means something else as well. I mean, when you think about bodies touching one another, you think about the slums of a Lower East Side and the Five Points. I mean, those are bodies touching. That's what adhesiveness is -- being cheek by jowl, living on top of one another. It scares the crap out of most intellectuals. Not Whitman. Whitman is fully a part of this culture. He sees in these immigrants the crucible of democracy. So I think "adhesiveness" is even a more powerfully subversive term because it connotes not only the fullest exploration of human sexuality, but also the fullest exploration of the changes that are happening in New York and in the country as a result of the influx of immigrants, first from Italy and then Germany -- I mean, from Ireland, then Italy, then Germany, and then from Eastern Europe at the end of the century. Whitman sees all of this as a kind crucible of democracy. And that's part of the story that's often lost in Whitman's poetry. That's part of story I want you to remember: that Whitman is in some sense a city poet and not just any city, this city and downtown in this city, exactly the places where we now romp around. So I want you to see Whitman as somebody who is exploring themes that the transcendentalists are mostly afraid of exploring. He's using pop cultural forms, mass culture like in the Penny Paper, sensationalism, and linking them to this higher discourse of the soul and the body, and suggesting to us that the body should not be given short shrift, that we ought to explore the body as deeply perhaps as Thoreau explored nature, even if in the end we're going to think of it as instrumental. Take a look on page 2213. A famous passage, section five. "I believe in you my soul, the other I am must not abase itself to you, And you must not be abased to the other. Loaf with me on the grass, loose the stop from your throat, Not words, not music or rhyme I want, not custom or lecture, not even the best, Only the lull I like, the hum of your valved voice. I mind how once we lay such a transparent summer morning, How you settled your head athwart my hips, and gently turned over upon me, And parted the shirt from my bosom bone, and plunged your tongue to my bare-stripped heart, And reached till you felt my beard, and reached till you held my feet. Swiftly arose and spread around me the peace and knowledge that pass all the argument of the earth, And I know that the hand of God is the promise of my own, And I know that the spirit of God is the brother of my own, And that all the men ever born are also my brothers, and the women my sisters and lovers, And that a kelson of the creation is love, And limitless are leaves stiff or drooping in the fields, And brown ants in the little wells beneath them, And mossy scabs of the worm fence, heaped stones, elder, mullein and pokeweed." What's going on in that passage? [ Pause ] >> Lecturer: Yes? Come on. Anyone? What's going on in that passage? Look at it again. Who's doing what to whom? Best response I ever got -- I take it a braver group than you -- was somebody's hand goes up. I'm like, "Yeah?" He said, "I don't know, but I think it turns me on." [ Laughter ] So actually, if that's what's going on, you're a little embarrassed to admit you were just a little bit turned on by reading something in your English class. What's going on? Yeah? >> They're rolling around in the summer, like it's just -- >> Lecturer: Rolling around in the grass. Who's having sex? >> He and "my soul" I guess. [ Laughter ] >> Lecturer: Yeah, right? There's a kind of bifurcation of self, typical body and soul. "I believe in you, my soul" -- he's talking to himself -- "the other that I am must not abase itself to you, the body. You must not be abased the other." And in fact right now, "loaf with me in the grass" -- so he's having this kind of sexual encounter with himself. So it's masturbatory, I suppose or maybe it's just -- think of it as a kind of Edward Taylor moment, right? I mean, you have a split between body and soul, so what if you bring them back together again? That's fun, right? [ Laughter ] And it's kind of -- "my head athwart my hips." Come on. And then look what happens. It's like the best use of anaphora in the entire course. What goes on here? Why all the "and, and, and, and, and" at the end? What just happened there? [ Laughter ] Yes? >> He orgasms. >> Lecturer: Yes, he did. Exactly. And that's exactly the structure of it, right? He has this moment and then there's this moment of kind of procreative orgasmic ecstasy, which is registered formally in the poem by the use of anaphora, right, the repetition of "and" at the beginning of all these lines. That's exactly the structure. And then of course, him being a man, it abates. It doesn't happen again yet and we do something else. In fact we go to child, which is interesting. [ Laughter ] So that's part of what Whitman is doing. That's part of what is going on in the poetry. I mean, there's a kind of frank exploration of this. And this is one of the uses of a poetic technique. So we have to understand that this is poetry. It makes use of a lot of poetic techniques that were on your list; it just makes use of them in a slightly different way. And the arbiter of what is appropriate is it Whitman. Whitman is the one who has to set the constraints on himself and sometimes he will, sometimes he'll decide that he needs to short line, sometimes he needs a long line. Look at the other things. We'll talk about this more next time. There's a kind of cataloging function that goes on here. I mean, the anaphora sometimes work to survey all of these things become part of matter of a poem. It's his body and the United States and sometimes he's trying to bring these two things together. Let's leave it there for now. I was going to play you a little bit of Whitman voice but we'll start with that next time. All right, thanks. |
Open_Ed_Cyrus_Patell_American_Literature | American_Gothic_III.txt | >> All right, let's get started. I'm told that there are some questions about what may or may not be fair game for the scavenger hunt. So if there are questions, ask them. Are there questions about...yeah? >> Is Taylor fair game if you wrote a paper on [inaudible] >> Can you use an example from Taylor? Yes, as long as it's not one that I mentioned in class or one that you used in your paper. [ Inaudible comments from audience ] >> Oh come on! [ Laughter ] Look, the course is designed to, many of the assignments in the course and the finals in the course, all that stuff is designed for you to have the opportunity to demonstrate the breadth of your reading and thinking. So if you're going to reuse something from your paper for another assignment, how lame is that? Don't do it. Take the opportunity to show us more. >> [Inaudible comment from audience] >> Why, is it a really, really good one? [ Inaudible comments from audience ] >> So, like, you've found the only zeugma in the course and you're not allowed to use it? Actually, I know of a zeugma or two and they're not in anything we've talked about. So please don't repeat stuff, ok? I mean, if you do it, we're going to, we'll accept it, we'll just think less of you. [ Laughter ] And that often has actual letter-related consequences. Alright, let's talk a little bit more about Edgar Huntly. We have a lot to get through today, and I want you to understand that Charles Brockden Brown and Washington Irving are both part of this larger project that we might say is moving from enlightenment modes of thinking, and with them, the kinds of genres that had prestige, like biography and history, into what we are going to call 'romantic modes of thinking' that are going to try to promote other faculties than reason, call them fancy or imagination, and other forms. So literature as we commonly think about it, literature as the province of the imagination. It's having something to do with fiction, or lyrical experience, or interiority, right? All of these concepts that we take for granted as being what constitute the literary are actually post-romantic conceptions of literature, of the literary. And I want you to understand that Brown and Irving in the United States context play a role in getting that to happen, right? As we said last time, the way Brown does it, in part, is to take this genre that has been denigrated, right? The novel, associated with certain other kinds of low forms, and certain kinds of leadership. He tries to make it appropriate for pedagogy and for thinking about questions of morality and virtue. So you say, you might say he tries to rehabilitate the novel and by extension, the province of the imagination by making a link back to things that we accept as necessary and authoritative, right? So, history is important because it teaches us something, philosophy is important because it teaches us something, the novel can teach us something. And I think the argument would go with Brown, the novel can in fact teach it to us in a more compelling way than these other forms can. So what we're seeing at work in Edgar Huntly is a kind of critique of enlightenment thinking from a variety of points of view. Brittany [assumed spelling], could you get the door? Thanks. And I wanted to step back and take a look at page 92, which I think I mentioned, but we might as well look at it again. Remember that Edgar thinks of himself as a scholar, and a student, and a hiker as well. So he says at the bottom of 92, 'When Sarsefield came among us, I became his favorite scholar, and the companion of all his pedestrian excursions. He was fond of penetrating into these recesses, partly from the love of picturesque scenes, partly to investigate his botanical and mineral productions, and partly to carry on more effectually that species of instructions which he had adopted with regard to me, and which chiefly consisted in moralizing narratives or synthetical reasonings,' right? So you can see it all kind of laid out for you there, and even the language of that is the language of philosophy, and the language of enlightenment. 'These excursions had familiarized me with its outlines and most accessible parts; but there was much which, perhaps, could never be reached without wings, and much the only paths to which I might forever look, forever overlook.' And that's important. He's seen a part of the woods. He perhaps is a little overconfident about how much of the woods he's seen. What happens when he starts pursuing Clitheroe and when he sleepwalks, is that he goes to portions of the woods that he hasn't mapped before. And in this sense, you might say, Brown draws on the typical motifs of the gothic in suggesting, in creating a landscape that is in fact a psychologized landscape, in which features of that landscape are actually ways of thinking about features of Edgar's mind. You might say that in typical gothic fictions or in revenge tragedies like 'Macbeth' or other things, part of what happens is that there is some kind of major upset at work. 'Something is wrong...' Shakespeare says, .'..in the state of Denmark, or as Marcellus puts it, 'Something is rotten in the state of Denmark,' and because of that, ghosts are walking around, there's a problem with succession, right? You can see this is a trope that carries over into gothic fiction. There was a problem of succession in Walpole's 'The Castle of Otranto.' And if things only were turned to some kind of peacefulness and normalness once that problem of succession is worked out. So things that are wrong in the social world manifest themselves through the ghostly, through an upset in the natural world. Likewise, things that are wrong internally in certain gothic fictions also manifest themselves in the natural world. Both of these kinds of wrong or upset or disorder are present in Edgar Huntly, although it's the second kind: the problems with Edgar's own thinking that seem more obvious at first, and we have to do a little work to recover that other kind, that problem, you might say, that has to do with inheritance and succession, or something like that. Ok, so, what happens to him in the woods? Let's take a look at the panther scene. This is the bottom of page 158. It places Edgar right on the edge of the pit. [ Silence ] 'What impediments and perils remained to be encountered I could not judge. I was now inclined to forebode the worst. The interval of repose, which was necessary to be taken, in order to recruit my strength, would accelerate the ravages of famine, and leave me without the power to proceed. In this state, I once more consoled myself that an instrument of death was at hand. I had drawn up with me the tomahawk, being sensible that this should, that should this impediment be overcome others might remain that would prove insuperable. Before I employed it, however, I cast my eyes wildly and languidly about, around. The darkness was no less intense than in the pit below, and yet two objects were distinctly seen. They resembled a fixed and obscure flame. They were motionless. Though lustrous themselves they created no illumination around them.' And again, whenever you see the language of light now in this book, you know, think about the ways in which the light is being described as a kind of commentary on the project of enlightenment or lack of enlightenment. 'This circumstance, added to others, which reminded me of similar objects, noted on former occasions, immediately explained the nature of what I beheld. These were the eyes of a panther.' Ok, so, he struggled around, he's been in the dark, he's in the dark, he's starving, he's gotten himself into a place where he thought things might be getting better, he might a little bit more safe, he's got a weapon, a tomahawk, and all of a sudden, a panther. 'Thus had I struggled to obtain a post where a savage was lurking, and waited only till my efforts should place me within reach of his fangs. The first impulse was to arm myself against this enemy. The desperateness of my condition was, for a moment, forgotten. The weapon which was so lately lifted against my own bosom, was now raised to defend my life against the assault of another. There was no time for deliberation and delay. In a moment he might spring from his station and tear me to pieces. My utmost speed might not enable me to reach him where he sat, but merely to encounter his assault, I did not reflect how far my strength was adequate to save me. All the force that remained was mustered up and exerted in a throw. No one knows what powers are latent in his constitution. Called forth by imminent dangers, our efforts frequently exceed our most sanguine belief. Though tottering on the verge of dissolution, and apparently unable to crawl from this spot, a force was exerted in this throw, probably greater than I had ever before exerted. It was resistless and unerring. I aimed at the middle space between those glowing orbs. It penetrated the skull, and the animal fell, shrieking, struggling and shrieking, on the ground.' Alright, that's pretty unbelievable, right? Something has happened to him. He's in the woods, he's in the dark, he's got this tomahawk, so what would you notice about the way in which this scene is presented to you? There's some aspects of it that should bear noticing for us. What do you think? Anything about the particular words that are used? Yes? >> Is he getting savage? >> He became a savage. Edgar does. Ok. How would you, if you were to say, Assertion: Edgar becomes a savage. Support that. Why is he a savage? >> Well at first he is very self-conscious and then he describes a moment where he uses all thoughts about his sort of, mental ability and uses his survival instincts. >> Ok, good. So, no more over-thinking, he's got to act. In fact, it probably took him less time to do this than he spends talking about it. And this is, of course, in retrospect, when some of the mind has come back. Ok. So, that's good. What else? What else do we note about savagery in this section? Yeah? >> Well I think there's a parallel between him killing the panther and Clitheroe killing his mistress' brother. >> Ok. >> Because there's this aspect of, you know when he says, 'There was no time for deliberation and delay, something else comes over him and he acts purely on instinct. >> So there's a kind of madness, right? The same kind of madness that comes over Clitheroe, he doesn't know what he's doing, madness seems to come over Edgar. It's, whether we want to call it instinct or even more than that. So it reinforces the parallel, or the doubling between Edgar and Clitheroe. That's good. Anything else of note? Yeah. >> He compares the instrument of death as opposed to simply a weapon... >> Ok. >> [Inaudible]... because if it was merely a weapon [inaudible] an instrument of death, it demonstrates some sort of intent of actually killing. >> Ok. Yeah. I would say that. That's right. I mean you might look at the syntax and say, 'Instrument of death' does mean you know, he's really aware of what the potential is with what he does and he has an intention behind him. You might also think of 'instrument of death, there's a certain way in which, there's almost a kind of rationalizing after the fact of what's going on. Remember he's telling this to somebody who's unlikely to actually believe it in a certain way. I mean, 'Oh come on, you? You did what? To what? Where?' Right? So he's saying there's an awareness and he says this openly at a certain point. I know you're not going to believe how, you know, old mild-mannered me doing this, but. Ok, so good. So there's a way in which, you might say, the prose is still designed to keep what's actually going at bay a little bit as if it's kind of horrifying. Right? I mean it's a little bit wordier than it might be. Anything else? What is it he actually uses to kill this panther? [Inaudible]. Yeah. >> A tomahawk. >> And who uses those normally? >> Native Americans. >> Interesting. White guy using a tomahawk. [ Laughter ] And what are other names that are given to said Native Americans? >> Savages. >> Right. Savages. So where else is savage used in this paragraph? Where's the first time he's using it in what I read to you? 'I had struggled to obtain a post where a [pause] savage was working, right? So, I mean, again, this is the same discourse. He's a man of the enlightenment. It's Bradford, right? There's no difference between the panther and the Indians. Both of them are savages, both of them are enemies. It's almost like the panther is dignified by having human-like qualities, the Indian is denigrated by having panther-like qualities. And it gives, you know, it makes us wonder a little bit about how far the enlightenment has actually taken us from the kinds of these thinking. People of the enlightenment would call them superstitious modes of thinking that would be embodied in Calvinism. The wilderness still seems to be howling here. You might think about that. Is there a kind of lack of fit between Edgar's nature walks and the wilderness that he actually comes up to here. Alright. So this happens to him. Then do you remember what happens next? Take a look, page 160. 'My hunger had arrived at that pitch where all fastidiousness and scruples are at an end. I crept to the spot. I will not shock you by relating the extremes to which dire necessity had driven me. I review this scene with loathing and horror. The whole appears to be some freak of insanity. No alternative was offered, and hunger was capable to be appeased even by a banquet so detestable. If this appetite has sometime subdued the sentiments of nature, and compelled the mother to feed upon the flesh of her offspring, it will not excite amazement that I did not turn from the yet warm blood and reeking fibers of a brute. One evil was now removed, only to give place to another. The first sensation of fullness had scarcely been felt when my stomach...' So he rips the thing apart right, and starts eating it raw, right? Just so we know what he's doing. 'The first sensation of fullness had scarcely been felt when my stomach was seized by pangs, whose acuteness had exceeded all that I ever before experienced. I bitterly lamented my inordinate avidity. The excruciations of famine were better than the agonies which this abhorred meal had produced. Death was now impending with no less proximity and certainty, though in a different form. Death was a sweet relief from my present miseries and I vehemently longed for its arrival. I stretched myself on the ground, I threw myself into every posture that promised me, promised some alleviation of this evil. I rolled along that pavement of the cavern, wholly inattentive to the dangers that environed me. That I did not fall into the pit, where I had, whence I had just emerged must be ascribed to some miraculous chance.' And that might remind us syntactically of Franklin, right? I mean, again, it's kind of like trying to make the enlightenment language fit here. Some chance saved me from, you know, the problems that might have arisen out of my want of religion, that might have arisen out of my falling into the pit. 'How long my miseries endured, it is impossible to tell. I cannot even form a plausible conjecture. Judging by the lingering train of my sensations, I should conjecture that some days elapsed in this deplorable condition, but nature could not have so long sustained a conflict like this.' Right? I mean, his ability to even analyze this situation is completely breaking down. Now, what would we say about that scene, right? Kills a panther, a little bit of discourse of savagery working in, then what? Eats panther. Anything we want to say about that? Yeah... >> [Inaudible] caused his freak of insanity. >> So it's just a freak of insanity. Good. Good phrase to note. What else? Yeah? >> His bouts of insanity seem to be pushed by the upsets as he calls them, his extreme hunger, before and beginning when he's talking about needing to know who killed his friend. All these things push him towards... >> Ok, so he's filled, there are certain necessities and when something is a necessity, you do what you've got to do. It's true. Ok. Anything else? What kind of scene, literally, imagine this: He eats, all of a sudden, ahhhh, he's feeling sick and you know, terrible things are happening and he's doing a Benicio del Toro interpretation, impersonation, and then he falls insensate, and when he gets up, he's like Superman, right? What has happened to him? What does he go on and do right after this? [Pause] I mean, one of the things I want you to see this is a kind of weird version of something like a kind of communion narrative, or a ritual conversion, right? He goes, he adopts the weapons of the savage in nature. He eats the 'reeking fibers of the brute' and consumes them, and as a result, he is kind of transformed. And you might say that the rest of Edgar Huntly are, really draws on one of the forms that we've already encountered, which is the captivity narrative. Remember there's a back-story to Edgar: his parents have been killed in this Indian raid and that's why his sister and he are living with his uncle. Take a look on page 166. He now talks about, you know, how he's gotten out of there. Middle of 166. He says this: 'Most men are haunted by some species of terror or antipathy, which they are, for the most part, able to trace to some incident which befell them in their early years.' Right? And that's a classic gothic setting. And what do you do to a gothic protagonist? You take them and make their biggest fears come true. Ok? So that's part of what's happening here. He thinks, 'You will not be surprised that the fate of my parents, and the sight of the body of one of this savage band, who, in the pursuit that was made after them, was overtaken and killed, should produce lasting and terrific images on my fancy. I never looked upon, or called up the image of a savage without shuddering.' Right? So he has a kind of template in place for behavior. He's programmed to act in a certain way. Now normally, mild-mannered Edgar, the child of the enlightenment is not going to do, be able to do too much. But this Edgar? Sleepwalking Edgar? Slightly insane Edgar? Eaten of the 'reeking fibers of the brute' Edgar? He's been able to do a few other things. Let's skip ahead a little bit to page 193 and you will see this passage. [ Silence ] Ok? I mean, he encounters his band of Indians and is like bang, bang, bang and he like kills them all. It's amazing. I mean, you know, just, you've got to imagine...did you ever see a movie called 'Total Recall'? Anybody ever watch a movie like that? 'Total Recall'? I'm thinking about, so it's Arnold... [ Laughter ] But you have to understand, in the Philip Dick story from which 'Total Recall' comes, it's more like Woody Allen, I mean it's supposed to be a mild-mannered guy who's kind of transformed into something else. So you should imagine this here. I mean, imagine Edgar as this kind of bookworm all of a sudden becoming Rambo. Because that's really what we're talking about here, right? And this is what he's addressing here. He said, so he's killed little old Kudegra [phonetic], he's killed this Indian here in the middle of 193. 'This task of cruel lenity was as last at length finished. I dropped the weapon and threw myself on the ground, overpowered by the horrors of the scene.' And now: 'such are the deeds which perverse nature compels thousands of rational beings to perform and to witness! Such is the spectacle, endlessly prolonged and diversified, which is exhibited in every field of battle; of which, habit and example, the temptations of gain, and the illusions of honor, will make us, not reluctant or indifferent, but zealous and delighted actors and beholders! Thus, by a series of events, impossible to be computed or foreseen...' So they resist the rational examination that enlightenment thinking would produce, .'..was the destruction of a band, selected from their fellows for an arduous enterprise, distinguished by prowess and skill, and equally armed against surprise and force, completed by the hand of a boy, uninured to hostility, unprovided with arms, precipitate and timorous. I have noted men who seemed born for no end but by their achievements to belie experience, and baffle foresight, and outstrip belief. Would to God that I had not deserved to be numbered among these! But what power was it that called me from the sleep of death just in time to escape the merciless knife of this enemy? Had my swoon continued till he had reached the spot, he would have effectuated my death by new wounds and torn away the skin from my brows? Such are the subtle threads on which hang the fate of man and of the universe!' Right, it's a kind of unbelievable story. In fact, we could go back a few pages and take a look at the way in which he addresses Mary. He knows that it's going to be a little bit hard to believe. This is the beginning of that chapter, Chapter 19. He says at the beginning, on page 184, 'Think not that I relate these things with exultation or tranquility. All my education and the habits of my mind, life tended to unfit me for a contest and a scene like this. But I was not governed by the soul which usually regulates my conduct. I had imbibed from the unparalleled events which had lately happened, a spirit vengeful, unrelenting, and ferocious.' Right? And he goes on to say, middle of the next page, 'Thus, I have told thee a bloody and disastrous tale. When thou reflectest on the mildness of my habits, my antipathy to scenes of violence and bloodshed, my unacquaintance with the use of firearms, and the motives of a soldier, thou wilt scarcely allow credit to my story.' In other words, he's protesting, look: 'I'm a man of the enlightenment and not a savage. I know you're not going to believe this,' right? 'But I was able to do these savage things, in spite of the fact that I'm a civilized person.' But I think there's another kind of logic that the book is actually suggesting to us. And you can see it in the words here, this idea of being put in unexpected situations. Forced to do things out of necessity, right? Is it possible that what we're seeing here is not the fact that Edgar is savage despite the fact that he's civilized? Is it possible that Edgar is forced to become savage precisely because he wants to be 'civilized'? In other words, in order to be civilized in the new world, you have to commit acts of barbarity and savagery, which are the equal of the things that you've encountered there. Only then can civilization actually take root. I mean, think about that for a moment. In some senses, it becomes a story of the new world encounter. You come here for whatever reasons. If you're a Puritan, you come to escape religious persecution. You come to have economic, a better economic life. You come to establish the city on the hill, and slowly what happens to you, you find yourself massacring Pequots, right? There's a way in which this is a commentary on the settlement narratives that we've read, the captivity narratives that we've read, and it really becomes a kind of commentary on the nature of European civilization in the new world. Savagery and civilization go hand in hand. In order, eventually, to be civilized, Edgar and all those around him, need in fact to be savage. And I think that's part of what the novel is actually dramatizing for us. That that line between the civilized and the savage is far too porous to stake everything on the primacy of reason, right? Reason's supposed to hold the line. Here we've seen a number of things, a number of ways in which reason is unable to hold the line, right? I mean, you go into nature, you meet panthers, you meet madmen, you're sleepwalking. You've got to do what you've got to do. Except let's go back to the scene a little bit later on in the chapter that I started with before on page 193, after he kills this Indian. I just want you to look at the slight of hand, or the kind of slipperiness of the prose in the middle of that second to last paragraph on 193. 'Such are the deeds which perverse nature compels thousands of rational beings to perform and to witness!' So, where's the agency there? Is he taking responsibility for it? Not exactly. It's 'perverse nature,' it's compelling us, who would otherwise be rational, to do this. Ok. But he goes on, 'Such is the spectacle, endlessly prolonged and diversified, which is exhibited in every field of battle...'Is this nature?'... of which, habit and example...' Nature? '...the temptations of gain...' Nature...and the illusions of honor...Maybe human nature? '...will make us, not reluctant or indifferent, but zealous and delighted actors and beholders!' Right? It's almost like: 'Nature made me do it, sorry mom.' But in fact, it's culture made me do it. Civilization made me do it. And I think that's one of the things that Brown is dramatizing. That's when, it's one of the things that is the project of the American gothic. The things that civilization is trying to keep a lid on, keep covered up, they come out in the American wilderness. And not only in this story, they were coming out of the American wilderness from the moment that Europeans set foot in it. And that's part of what we want...now when I said, when I was talking about Mary Rowlandson, I suggested to you that Rowlandson had a template for thinking about the woods, that's what she was designed to have. It was part of God's providence. It was not supposed to be about land rights or competing claims of culturally equal groups. It wasn't supposed to be about the West Bank kind of situation. It was supposed to be read as part of a larger biblical story. Ok. But we have certain modes of access to that other story, I mean, one is we can contextualize the war. The other is that we can kind of see that there's a kind of economic language that bubbles up in her narrative, despite itself, you might say. The same thing happens in Edgar Huntly. Remember that little whim of sub-plot? I mean, what's all that doing there? There's a notion about inheritance. He has to admit, 'You know, I was going to marry you, but, well that was depending on inheriting from your dead brother, and now, well you know the uncle's son he hates us and...' Let's talk a little bit about the one Indian figure who is not a Bradford-like faceless narrative. The one who gets a name. Who is that? Who? Somebody said it and that's the name that Edgar gives. What was it? >> Queen Mab. >> Queen Mab. Ok. Old Deb is what she's also called. Queen Mab comes from where I gave you an excerpt from Romeo and Juliet to read. She's from a fairy figure from the English poetic tradition, right, and the speech by Mercutio is a wonderful indication of the way in which Queen Mab comes and dreams, and ok. Imagine Barlow taking the old-world forms and running the new world hasty pudding through them and producing the hasty pudding poem, ok? Way cool, neoclassism works in the new world. In fact maybe it works even better. Edgar's going to try to do the same thing. Old Deb. I'm kind of interested in Old Deb. Old Deb is there, she speaks this weird language, she has these dogs around. He wants to think of her as a kind of picturesque figure, a figure of fancy, a figure from the English poetic tradition, so he gives her this name, Queen Mab. And he's interested, so long as he can make her this kind of figure. But she resists being made into that figure because what is Old Deb really? What is Old Deb really? I mean, what has she been doing while she's been out there alone? [Pause]. >> She's been sort of plotting this attack by the Indians. >> She's Osama bin Laden, folks. [ Laughter ] I mean, she's the one who has been planning all this. You know, the Indians are responsible for Waldegrave's death. She's been, why is it by the way? Because where is it that that Huntly farm happens to be located? Her old place of living, right? Her old domicile. They've stolen her land. She's got a beef, and it's a legitimate beef. She's the one that's been organizing all these Indian raids. But Edgar either doesn't know it, or he doesn't let himself know it. But the novel does, right? The novel enables us to see that there's something else that's going on here. And assume as she doesn't fit into his story, he's no longer interested in her, right? She goes off, when they finally catch her, she goes off, proclaiming all these things and he just ceases to be interested in her. So what I'm suggesting to you is that there are two kinds of things at work here. One is a problem in Edgar's psychology, that makes it gothic. The other is more like something that goes on in a play by Shakespeare like 'Macbeth' or a gothic fiction like 'The Castle of Otranto' in which we're talking is a problem with property. There's been a usurpation, and usurpation causes the gothic situation. The usurpation that's taken place here is the Europeans taking the native lands. Edgar keeps all of that at bay, and I want you to see that, that he is in fact trying, the discourse about property and money, and all that kind of stuff is kept at the margin so that you can actually overlook it if you're reading it quickly, but it's there. One of the things to say is, you know, the whole progression of what Edgar wants is not that different from what Clitheroe wants. Clitheroe wants kind of the upward mobility. Edgar wants that too. Think about when Edgar finally emerges from the woods. He goes through a succession of houses. There's Old Deb's rude hut, then there's a kind of farmhouse, and finally he gets to a mansion. I mean, that's exactly the kind of procession in the world that he wants. And there, hoping to provide the kind of [inaudible] is Sarsefield returned with, you know, and the strands of the story come together and this is [inaudible]. Great. Ok. [ Laughter ] So let's talk. We talked, somebody mentioned the term 'bildungsroman' when we first started talking about this novel. And maybe it's time to ask about that. Is this a bildungsroman? A bildungsroman is a novel of development. You go from immaturity to enlightenment perhaps. It's a novel of development. You learn, you grow, it's the novel of education. Does Edgar learn anything in the course of this narrative? He's writing it down, right? Franklin learned, Franklin identified errors. He corrected them in life and in his text. What about Edgar? Yeah? >> I think he's experiencing; he's not learning. >> He's not learning. So if you were going to make that argument, what would you tell me? What's a piece of evidence that I would, that you would use to say, 'Edgar doesn't actually learn anything'? >> Well, just the language of passivity... >> Ok, it's possible. The language of passivity. It's still that kind of weird paraphrastic enlightenment prose. Possibly. >> Over and over again he's saying, 'I was controlled by others.' >> Ok. So language of passivity that goes along with a lack of taking responsibility, right? 'Nature made me do it,' or 'Look at all the things we are led to.' That's good. That's a good start. What else would we marshal as evidence to say Edgar in fact has had no bildung whatsoever. Yeah? >> Well I mean from the very beginning, he kind of keeps getting himself involved in other people's business [inaudible]. >> The father's clemency right? Ok? >> And at the very end, he still gets involved and causes problems. >> You're absolutely right. He makes the same damn mistake at the end of the book that he made in the first pages. Right? He thinks he can fix it. Doesn't work and it has another disastrous consequence. Great. That's good, and you would want to cite that. So there's a kind of, Edgar doesn't learn anything because he still can't, despite everything that's happened, he still believes in the primacy of reason. One other thing, a formal thing that would suggest to us that Edgar is, that we are meant to realize that all along, and we should have realized this early on, that we've been reading an unreliable narrative by an unreliable narrator who doesn't learn much. What happens to the form of the narrative at the very end? Edgar signs off: 'Farewell. E.H. Solebury, November 10.' Then what? Take a look on page 273. We get a letter to Mr. Sarsefield in Philadelphia. Then we get another letter. This is where we're discovering all of the later doings of Clitheroe. E.H. Letter three. This is on page 283: 'To Edgar Huntly.' And from whom is this letter? It's from Sarsefield. And what comes after that in the book? [ Silence ] Nothing. That's the end of the book. Who gets the last word, who gets the last farewell? It's Edgar's book, he doesn't get the last word. That should tell you something, right? And you may well think of, if we're looking for a way of thinking about this...Let me see if I can find you this particular quote. It's the one where, he talks to, where Sarsefield tells, talks to him about consciousness itself. Look on page 267. It's a little bit before the end, but it might serve as a kind of summing up of the way in which this happens to launch a critique of the enlightenment. And it comes again from Sarsefield. It's the second to last full paragraph. Sarsefield is telling Edgar:'He can never be regarded with complacency by my wife. He can never be thought of without shuddering by Clarice. Common ills are not without a cure less than death, but here, all remedies are vain. Consciousness itself is the malady; the pest; of which he only is cured who ceases to think.' You know, it's a little bit like Sayid in Lost. [ Laughter ] Better off dead. Some things are better off dead. There are some things that reason can't cure. Right? That's almost a kind of Poe-like idea. It's the kind of narrators that Poe becomes interested in. So you imagine, Poe would probably be, there's a certain way in which you might say, well Poe is kind of, would most be interested in Clitheroe's story, at the guy who seems rational and then becomes mad, and it's not clear quite when that happens, but you can see the same thing going on with Edgar. I mean, Edgar comes back from actual madness at the end to become a functioning human being, but he has participated in a lot of madness, and he has that same kind of slyness that some of Poe's narrators have. Keeping certain salient details off to the sides. And if he doesn't finally succumb to the perverse in the way that Poe's narrator does in the imp of the perverse, nevertheless, he shows up, he shows us what some of the problems with reason are. So, in the end, this becomes a story about the limitations of enlightenment. It becomes a story about the encounter of the Europeans and the new world. Gothic in America is pressing, because it's an actual political situation. Forget all those stupid [inaudible], and ghosts and goblins and ghostly aristocrats who are bigger than castles, that stuff's not real. Indian hostilities, that's real, and the time in which he's writing, they're still going on. Ok. That was a nice story that I just told you, right? There's one other way to think about it, or maybe it's a complementary way to think about it. And you can ask yourself this: In the end, what is the fit between those two stories? Which is the more pressing of them? The cultural story that I just told you, or the story about Edgar's psychology? Or even better, the link between them, because is this novel actually interested in the Native Americans? Has it not also, like its narrator, used them instrumentally to dramatize something as I've been suggesting to you, about whether it be contact, the limits of enlightenment in terms of colonization, or even just the limits of enlightenment in terms of reason. Has this not, in some sense, then become a kind of allegory of the Western mind in a moment of enlightenment? And if so, hasn't it just, hasn't it, in some sense, recapitulated precisely the thing it's described. It's tromped into the wilderness, used it for its own good purposes and leaves it be. And so I want you to think about that. The question would then be: to what extent is the novel implicated in precisely the kinds of things it seems to be launching a critique of? Alright. Some food for thought. Ok. Any questions about that or observations? Alrighty then. Let's think about the guy who actually made money writing, because Brown didn't. He wrote that series of novels very quickly and then in fact, because they didn't sell very well, he had to write two other novels. And they were called Clara Howard and Jane Talbot. Do those names sound familiar to anybody, I mean, as names? What do we notice about the difference between Wieland, Edgar Huntly, Ormond, Arthur Mervyn, on the one hand and Jane Talbot and Clara Howard? >> [Inaudible comment from audience]. >> Jane Talbot and Clara Howard sound not a lot, not unlike Pamela and Clarissa. Brown wants to make money. Doesn't make it doing these gothic novels, so he goes back and writes precisely in that kind of Richardsonian vein that he was theoretically disavowing. That doesn't work either, and he eventually goes out back and makes a career as a kind of a journalist and pamphleteer. He fails, in other words, to make money as an imaginative writer. It's Irving, Washington Irving, who becomes the first successful American writer. The first person who lives off writing that we might call imaginative. And Irving, you might say, like Brown, maybe even better than Brown, has a sense of what he's up against. Very early on, he writes an essay that's on a poet named Robert Treat Paine, and we don't read him very much. But one of the things that he says is this: 'The writer is unfitting for business in a nation where everyone is busy, devoted to literature where literary leisure is confounded with idleness. The man of letters is almost an insulated being, with few to understand, less to value and scarcely any to encourage his pursuits.' Right? We're living in a culture that is a culture of business already in the early part of the 19th century, and a culture that seems to have little time to, or little, you know, considered interest in promoting a literary culture. And I've already talked to you about the ways the models that we have from England in the United States don't really apply. The model of patronage, for example, isn't there. The model of a gentleman amateur, it isn't there. Instead of patronage, we're getting this growing market place. Irving had a profound ambivalence, and part of what we understand is he does, in the course of his career, a kind of balancing act between two models. One is the man of business, because he's worried about being idle. He comes from a merchant family, he was supposed to be a lawyer like Charles Brockden Brown, he doesn't do it. Is writing just idleness? Ok, so maybe we shouldn't be, you know, a writer of commerce but can we afford to be the gentleman amateur? And will people respect a gentleman amateur in a world where everybody is full, you know, is working on business? So, there's a kind of ambivalence that Irving feels and a kind of ambivalence that he recognizes in his audience as well. You might say that it's between these two poles, writing as business, writing as kind of imagination and leisure, you don't want to sully the imagination with business too much, but you don't want to be so full of leisure that you're thought to be idle. These are the kind of Scylla and Charybdis between which Irving charts his career. And he, too, understands the potential within the copyright law of 1790, but unlike Brown and other writers, he also understands the limitations of it. He knows it's a domestic law, therefore he goes and secures his copyrights abroad. He publishes English editions first, then has them sent back to the United States. And I want you to see that this worry about what kind of business is writing, what kind of labor is it? Is it manly enough?, is a concern that will be part of American writing up until at least Hawthorne. I've already mentioned Hawthorne and the Scarlett Letter. But the opening preface portion, the Custom-House, Hawthorne is worrying in 1850 precisely about the same things. What would my ancestors say about what it is I want to do for a living? And, what are, you know, why am I not able to make money, by the way, off what I'm doing for a living, right? So, Irving is setting in place a set of ideas and a set of problems that will be resonant for later writers as well. So, I guess within the language of conceptualization that we've used in the course, one of the things that we ought to say is that Irving has a kind of canny understanding of what we call the 'horizon of expectations.' He understands that there are certain generic expectations in place, and he's going to play with those, he's going to appropriate those. He understands that there are shifting tastes that an audience might have, and shifting impressions of what an author should do. He's going to make use of those and play with those as well. So, that's part of what Irving is up to. And his first major success was a book that was called 'The History of New York, which has recently been published in a new edition by Penguin. It had its bicentennial just this year, last year. It came out in 1809 in the fall and so this new edition comes along with that. We can say about Irving then, is he's creating a kind of a New York history in the absence of a New York history. The thing that prompts him to write 'The History of New York' is a call by the New York Historical Society, which was created just a few years earlier, for any materials related to Dutch New York. I mean, they were telling people like: 'Look in your attics, look in your basement, look in your trunks, we just don't have documents.' A lot of it had been burned during the Revolutionary War, and they were interested in any material that was possible about the Dutch past. Just before Irving writes this, a polymathic kind of professor named Samuel Latham Mitchill, who's mentioned in the introduction here, had published a book called 'Picture of New-York,' which gave very, very short shrift to the Dutch portion of the city's history. And so, Irving decides that here's an opportunity, and what I want you to see is that Irving is, in some sense, taking up the project of using a form, let's call it history, in the service of the creation of another form, let's call it literature. He tries, in other words, to adopt, to adapt, some of the prestige of the historian and transform it into the prestige of a literary person. And here's a perfect opportunity, because you have an opportunity to write history where a lot of the history has gone lost. There's not a lot of documents. What there could be is a lot of local knowledge, the kind of thing, in fact, you'd get through oral tales or stories that you would listen to, bits of local lore, that even then, would have been beneath the notice of most historians. So, Irving decides that he's going to put these things together, and in fact, he jumbles actual events and personages with made-up things, in such a way that historians still have arguments about what it is that he made up and what are actually bonafide sources that can be trusted. And finally, what we get in history is an awareness that in fact, the history is, I mean this is going to sound banal to you, probably, but history is a story, like anything else. It's a story, right? A historian is an editor, takes so-called facts and assembles them into a certain kind of narrative. Therefore, Irving is quite aware that all histories are partial, and really are almost always written by the victors. Take a look, if you've got it with you, take, bring it, pull it out, if not, just listen. This is the beginning of Chapter 5 and it's page 40 of the excerpt. I want you to listen to the style. 'Chapter 5, in which the author puts a mighty question to the rout, by the assistance of the Man in the Moon, which not only delivers thousands of people from great embarrassment, but likewise concludes this introductory book.' Right? I mean that's grandiloquent, it's also poking fun at exactly the kinds of head notes that you would find in histories or works of biography. But now look what he does at the very beginning. Listen to the style that's grandiloquent. But look at the metaphor that he's adopting. 'The writer of history may, in some respects, be likened unto an adventurous knight, who having undertaken a perilous enterprise, by way of establishing his fame, feels bound in honor and chivalry, to turn back for no difficulty nor hardship, and never to shrink or quail whatever enemy he may encounter. Under this impression, I resolutely draw my pen and fall to, with might and main, at those doughty questions and subtle paradoxes, which, like fiery dragons and bloody giants, beset the entrance to my history and would fain repulse me from the very threshold. And at this moment a gigantic question has started up, which I must take by the beard and utterly subdue, before I can advance another step in my historic undertaking; but I trust this will be the last adversary I shall have to contend with, and that in the next book I shall be enabled to conduct my readers in triumph into the body of my work. The question which has thus suddenly arisen, is, what right had the first discoverers of America to land and take possession of a country, without asking the consent of its inhabitants, or yielding them an adequate compensation for their territory?' The same question I've just suggested to you that lies at the heart of Edgar Huntly. Alright, what do you notice about that? If you were thinking about standard history writing, does this look like standard history writing? I mean, what, rhetorically, what is he doing? Yeah? >> He's mocking the exact thing he's supposed to be doing? >> How's that? How's he mocking the thing that he's supposed to be doing? [ Inaudible comment from audience ] >> Ok, so he's dealing head-on with this question that may be historians have either, you might say, have either ignored or you might say, philosophers have found various justifications for. So I think that's right. There's a sense in which he is exposing to view something that most people, and most historians, would rather not talk about. But think a little bit more about the way in which he introduces this subject. What's the metaphor that he uses? I suppose we should really say it's a simile, because it's something that is likened to something else. What is it? 'Writers of history may be likened unto a...' >> An adventurous knight. >> An adventurous knight. What genre do adventurous knights come from? >> [Inaudible comment from audience] >> What? >> Fairytales. >> Fairytales, what, you know, other things? Chivalric romance, perhaps? What's at stake in saying, if you're a writer of a history, that you are like an adventurous knight? Yeah? >> It's medieval. >> It's medieval, so that would go against a sense of maybe being the very model of a modern major historian. What else? >> He's supposed to be brave and noble in all the chivalrous aspects of the knight. >> Ok, bravery, so do we expect our historians to be brave, noble, and chivalrous? >> No. >> Do we expect them to be conquering stuff? Do we expect them to be marching in triumph through stuff, our historians? And this is kind of weird, again, it's another one of these things. Irving here, would seem to be as a historian, complicit in precisely the kinds of things that he shouldn't be complicit in, right? I mean, you shouldn't be having a triumphant story. But in pointing this out, you might say he is poking holes at what the standard operating practice for historians usually is. He's, in other words, calling attention humorously to the fictionality of most fiction, of most histories by overemphasizing the links between history and fiction here. But it also has another disarming kind of effect, right? If you're making this association between history and romance, ok. But you might say there's a way in which the kind of chatty voice that he has will get you to read along and maybe not object to things that in another way you might object to, if they were told to you in another way. Take a look, for example, I don't know, you can pick any one from the course of this chapter, but take a look on page 45. He's in the midst of talking about the different justifications that white settlers had for controlling the land. In fact, he calls these the right of discovery, the right of cultivation, the right of civilization. And with civilization of course, what's really important is the church and the spread of Christianity. Middle of 45: 'The most important branch of civilization, and which has most strenuously been extolled by the zealous and pious fathers of the Romish Church, is the introduction of the Christian faith.' Interestingly, he is going after the Roman church. So it's not going to be, I don't know what, the Dutch reform Calvinists that you would find in and around the British, the English, you know the new Amsterdam, or even kind of Anglican stuff that you would find as a result of British New York, or even the kind of Calvinism that's so prevalent in Puritanism. He's going at something that would seem to be, you know, a safe target, almost like gothic fiction. We'll put our sort of uncertainties over onto them Catholics in Italy, right? But everybody knows that we're actually talking, worrying about something else. Ask yourself whether what's described here doesn't sound as if it were precisely a critique of Bradford in 'A History of Plymouth Plantation.' 'It was truly a sight that might well inspire horror, to behold these savages stumbling among the dark mountains of paganism, and guilty of the most horrible ignorance of religion. It is true, they neither stole nor defrauded; they were sober, frugal, continent, and faithful to their word; but though they acted right habitually, it was all in vain unless they acted so from precept. The newcomers, therefore, used every method to induce them to embrace and practice the true religion, except indeed that of setting them the example.' Ok, you may or may not think that's funny, but I want to, take a look at it and see how you think it works, right? How does it poke holes in something? How is the style designed to get you to come along. It's almost like he's paying you a little bit of rope and allows you to hang yourself with it at the end as the reader for that little sticking point. It's a mixture of exaggeration, of seemingly rational balanced syntax, but you can see that even, you know, where does he end up here? What's the fourth right after the right of civilization? The one that trumps them all? The middle of 47. 'The last right might be entitled the right by extermination, or in other words, the right by gunpowder.' Alright, ok, so this is all what it boils down to. Boot forth. And then I want you to ask yourself what is at stake in the larger, in terms of the larger project of writing a history, to end this chapter with what basically boils down to a fraud experiment. He says: 'ok, let's think about the people in the moon, the Man in the Moon people, and imagine that they are as superior to us in their civilization and their abilities.' He says this on page 49 in the first full paragraph. 'Superior to us in knowledge and consequently in power, as the Europeans were to the Indians, when they first discovered them.' And then he says, you know, he goes, these Moonlanders, they land on the planet, they do basically things that are all quite analogous to what the Europeans have done, and then towards the bottom of 51: 'But finding that we not only persist in absolute contempt of their reasoning and disbelief in their philosophy,' right? We won't be converted. 'But even go so far as daringly to defend our property, their patience shall soon, shall be exhausted, and they shall resort to their superior powers of argument; hunt us with hippogriffs, transfix us with concentrated sun-beans, demolish our cities with moon-stones; until having, by main force, converted us to the true faith, they shall graciously permit us to exist in the torrid deserts of Arabia, or the frozen regions of Lapland, there to enjoy the blessings of civilization and the charms of lunar philosophy, in much the same manner as the reformed and enlightened savages of this country are kindly suffered to inhabit the inhospitable forests of the north, or the impenetrable wilderness of South America.' Ok? So what I want you to see is the overall strategy here. We're writing a history, right? We destabilize history-writing by making a, using a trope that links it to romance. We then use actual philosophical arguments presented in a way that looks like actual philosophy, except there are subtle deflations through diction and style of the conclusions, and then finally we end up with an out-and-out fiction that nevertheless looks like it draws on a philosophical thought experiment. The Man in the Moon, right? What you can see then is, you know, this is the culmination of a process in this first book whereby you might say that Irving is weaning us from the authority of the historian by undermining slowly but surely the authority of the historian until finally we find much more reason in the kind of thought experiment that we have here, which verges on science fiction than most history writing. This was a big success, by the way. Part of the reason it was a big success was the style in which it's written, which is kind of engaging and you know, it sort of pokes fun, it's a kind of, it seems like vicious satire but it's also kind of leavened a little bit by the style in which it's written. But Irving also went on and was smart enough as a young man to engage in a kind of public relations campaign. He places an ad in the evening post on October 26, which supposedly comes from a landlord, who says some guy named Knickerbocker is missing, anybody seen him? He might not be in his right mind, P.S. printers of newspapers will be aiding the cause of humanity in giving an [inaudible] to the above. I mean, that's kind of the same grandiloquence that you have in the history. A little bit later on, some traveler reports having seen this Knickerbocker, and don't worry, you know, he's ok, a little bit, he had a hat and a small bundle tied in a red bandana handkerchief. Already a caricature of what a traveler looks like on the road, and he appeared to be traveling northward, was very much fatigued and exhausted. Ok. November 6, ten days later, placed by one Seth Handaside, landlord of the Columbian Hotel, 'A very curious kind of a written book has been found in his room, in his own handwriting. Now I wish you to notice him, if he is still alive, that if he does not return and pay off his bill for boarding and lodging, I shall have to dispose of his book to satisfy me for the same.' I'm going to sell this thing, right? And everybody's kind of in on the joke and not kind of in the joke. Washington Irving says this. I mean, you can see that the, a little bit later on, when he's writing the Sketch Book, he says, you know, the publicity campaign works, people get really interested and the thing is public. And many people know it's Irving, many people don't, but the interest has been peaked by this kind of sort of reality show public relations campaign. Irving, you know, says this, later on when he sends the manuscript of the Sketch Book back from England to his brother to be published in the United States: 'My talents are merely literary, and if I ever get any solid credit with the public, it must be in the quiet and assiduous operations of my pen under the mere guidance of fancy and feeling.' Now again, we should probably think of this as a kind of ironic statement. But the idea of talents are merely literary suggests that there are a lot of other talents that are much more appropriate. To be a literary person, then, in the United States in this period is almost to be un-American, right? What are you doing wasting your time on the merely literary? 'Do something with your life, you know. Go into business.' But Irving does go into business. He needs to make money writing the Sketch Book. And so you might say, it's once again time to do a kind of gut check and to think about the horizon of expectations and he does. And he produces a volume that is a huge success on both sides of the Atlantic, in part because it draws on established English form. It's the kind of magazine writing that was popular and that sold well in English periodicals and therefore, because Americans took their cue from English taste at this point, it would sell well in the United States, and added to those sorts of kinds of local knowledge that were prevalent in 'The History of New York' to create something that was new. So there are two major forms in this Sketch Book. I gave you one example of the sketch, which is the piece that was on Blackboard, called 'The Voyage, two examples of the tales. The most famous ones: 'Rip Van Winkle, and 'The Legend of Sleepy Hollow.' Ok. The sketch is again, like English magazine writing, you can imagine it, the sketch is basically a piece of writing that's fairly short in which nothing exactly happens, right? You might imagine it as a kind of piece of description that seems taken out of some longer tale, but it's sort of there. It's kind of like local color. It's just something that's of interest to the narrator and recalls a lot of British periodical writing. So it makes sense to people that this kind of thing should exist. The tale, though, in fact, you might say that the two tales that we have seem to be made all the more extraordinary precisely because of the context in the volume around them of the sketch where not much happens. Something does happen in 'Rip Van Winkle' and 'The Legend of Sleepy Hollow' and it kind of defies the rational. Unlike most of the sketches, which are first person, the tale is presented as a third-person narrative, or else you might say, the pseudonymous major narrator of the Sketch Book, this person who's called Geoffrey Crayon, has found the manuscript, and therefore the tale exists in somebody else's voice. So these two tales, 'Rip Van Winkle' and 'The Legend of Sleepy Hollow' are theoretically found amongst the papers in Seth Handaside's inn of Diedrich Knickerbocker. I just want to briefly sketch out a couple of things about these sketches and tales that will let you see the affinities between what Irving is doing, and the stuff that's come before, not only the gothic of Brown, but also the kind of Graveyard School poetry that we looked at in Freneau and Bryant. The Sketch Book, in fact, has a kind of obsessive fascination with death. Death hovers over all of it, but it almost becomes a kind of metaphor for a more generalized sort of alienation, right? An alienation with the modern world. Death becomes a way of thinking about what's wrong with the modern world in the way that it prompts the occasional for the imagination to come forth, right? You remember that moment in 'The Indian Burying Ground' where Freneau writes that fancy will no longer have to bow to reason here in the Indian Burying Ground, as if that's what happens all throughout the rest of the world. So, for example, 'Rip Van Winkle' is about somebody who wakes up from a kind of deathless sleep. A sleep that's almost like death, you might say. And well, I mean, this pun is intended, [inaudible], Right? So, and it's presented among this kind of posthumous things. Likewise, the story of 'The Legend of Sleepy Hollow' is presented to us as a story about a dead Hessian coming to life. So, death hovers over all these tales, especially, and you can see it in 'The Voyage' too, in that sketch 'The Voyage.' I mean, the basic, the thing that happens inside 'The Voyage' is that the narrator sees a wreck, and when he sees a wreck, you know, he all of a sudden starts expostulating. This is on page 748 of 'The Voyage': 'Where, thought I, is the crew! Their struggle has long been over. They have gone down amidst the roar of the tempest; their bones lie whitening among the caverns of the deep. Silence, oblivion, like the waves, have closed over them, and no one can tell the story of their end.' It's overblown, again, right? You find out later on that the sight of the wreck, he says, '...gave rise to many dismal anecdotes. This was particularly the case in the evening, when the weather, which had hitherto been fair, began to look wild and threatening...' right? So he gets a lot of stories, and he tells one of them. So what you realize is that the wreck becomes a prompting for storytelling, and that finally, once he's, you know, safely able to recollect this in tranquility, he says in the middle of 750, 'I might fill a volume with the reveries of a sea voyage, for with me it is almost a continual reverie, and we realize that, in some sense, that would mean that even that episode with the wreck is part of his larger reverie. He is able to domesticate it, he's able to make it literary. And so death becomes a way of making these sketches link up with this tradition of the Graveyard School of Poetry and this idea that the romantic poet, the romantic writer, is going to find in death a time to have a kind of meditation about the imagination. Reason regime, you might say, is weakened under the thrall of death. So that's one of the things that hovers over, I think, all of these three pieces. Another though, and perhaps even more pressing is a kind of struggle throughout, between you might say, on the one hand, the literary imagination, and on the other hand, this kind of bustling modern materialistic world of business, which doesn't really have time for the imagination. And frequently in these stories, is given to us as if it's a kind of contest between the old Dutch past, which should be hospitable to story-telling, and the new modern present. Now, if I were to ask you, in the story of 'Rip Van Winkle, which of those two things is it that the story prefers? What would you say? Does the story prefer the old Dutch past? Or does it prefer the modern Yankee present? What do you think? [ Silence ] You better read it before the midterm...Yes? >> The modern Yankee present. >> Why would you say the modern Yankee present? >> [Inaudible comment from audience] The modern day machine as opposed to the old outdated one. >> Ok, so you would say that there's a sense in which the Yankee present is what, is for those reasons. How different is the Yankee present from the Dutch past? >> In the story it is apparently pretty different. >> Ok. Why would we say it's different? Because of the hustle and bustle, that stuff? >> There's always this voice of people that are talking of camaraderie. >> Ok. And by the way, what is it that he slept through? >> The war. >> Yeah, he slept through the Revolution. >> I would say, I think I would follow that by saying that it's, you know, the Yankee present with a place for Rip Van Winkle. >> Ok. >> Because Rip Van Winkle wasn't happy, or the character wasn't happy, in the past because he had his wife and he had never had that place where he could go and just be him. [ Shouting ] [ Laughter ] And in the Yankee present, there's like, there's a place for him, and he's sort of like regarded as sort of a figure of [inaudible]... >> That's good. >> ...sort of affectionate. >> One of the things you might say is that in the Dutch past, I mean, many people when they read this story for the first time, think: 'Oh, this is why he prefers the Dutch past, it's all about local color, you know, this modern world, yuck, but I think you're clueing into some of the things like ambivalence that's there, which is that in the old past, Rip Van Winkle is an idler, right? There's no place for him. He drives his family into poverty. Now, he's an esteemed elder and storyteller. Everybody wants to come and listen to him. So he has a place, as you point out. Did you want to say something on the, did you want to add something to that? No? >> I was actually going to sort of disagree with that. >> Ok. Disagreement is good. Do it. >> Just because, I don't know, it seems like in the Yankee present he's allowed to sort of be idle, and because like, for example, a lot of the things that seem problematic about the pre-Yankee era seem to be allowed sort of at the end of the Yankee era, like the schoolmaster. He's very, just kind of pedantic and... >> In 'The Legend of Sleepy Hollow.' >> No, no. In, like, one of Rip Van Winkle's friends is the teacher [inaudible]. >> Ok. >> And now he's a member of Congress, and before he just sat lazily around talking about stuff. >> You don't want teachers in Congress. >> Yeah. [ Laughter ] Well, at that time, that's how it was kind of [inaudible]. >> Yeah, I know. [ Laughter ] >> I'm just taking it aside. [ Laughter ] Alright, let me ask you one other thing. You know, when Rip goes, he goes and he sees his son. He's like: 'Wow.' I mean, his son is called the very ditto of himself, he's exactly the same as Rip used to be. It's like they're doubled. But better than that, here's my favorite emblem about the difference between the Dutch past and the Yankee present. Do you remember the inn? The Union Inn now it's called, I think. The sign? What's on the sign of the inn? What was on the sign of the inn before? Yeah? >> It used to be King George, and then they just repainted it and wrote George Washington. >> One George, another George. 'Plus ca change,' right? There's a certain suggestion in which these two, there may not be as quite as much change as we think, or that the change might, in some certain ways, be superficial. And that's what I mean for you to see, that there's a kind of weird ambivalence. The stories seem to set up what looks like an opposition, and then they start to collapse them in interesting ways. Is the Yankee present better? Well no, right? It's hostile to the imagination, the old past is, you know, full of local lore and all that stuff, except they didn't like me in the old past, and now, they, you know are listening to my stories and I have this esteemed kind of place. Just think about 'The Legend of Sleepy Hollow' for, I mean...Ichabod Crane seems to be a kind of unappealing character, right? He's tall and crane-like, and he's described as consuming and devouring. There's a wonderful passage here. I was looking for a good picture to illustrate this with. If anyone can find me one I would be really, really happy. But in the middle of, you know when he goes and he imagines the Van Tassel farm, this is on page 971 if you have the anthology. Rip, you know, so he's a kind of voracious person. He comes from Connecticut, so he's a real Yankee, as opposed to Brom Bones, who's kind of like a burly Dutchman. 'The pedagogue's mouth watered as he looked upon this sumptuous promise of luxurious winter fare.' He's one of these skinny guys, so he has like an endless appetite. 'In his devouring mind's eye, he pictured to himself every roasting-pig running around with a pudding in his belly, and an apple in his mouth; the pigeons were snugly put to bed in a comfortable pie, and tucked in with a coverlet of crust; the geese were swimming in their own gravy; and the ducks paired, paring cozily in dishes like snug married couples, with a decent competency of onion sauce. In the porkers, he saw carved out the future sleek side of bacon, and juicy relishing ham; not a turkey, but he beheld daintily trussed up, with its gizzard under its wing, and, peradventure, a necklace of savory sausages; and even bright chanticleer himself lay sprawling on his back, in a side dish, with uplifted claws, as if craving that quarter which his chivalrous spirit designed to ask while living.' Did you ever watch Looney Tunes or things like that? I'm mad, I couldn't find a picture, I'm going to find it next time. Just so the, I don't know, the wolf is running around and in a thought bubble he sees the little chicky-chickies there and they are kind of presented as food, right? That's what he's doing. He's imagining. So there's something very materialistic about him, right? He feels the same way about Katrina. He just looks at that buxom lass and all of her buxom property, and thinks: 'Wow, all of this should be mine.' So the story would seem to have a kind of bias against Ichabod Crane, right? Except, think about this. Brom Bones, who always struck me as a kind of like a fraternity type, sorry to any fraternity types who might be in here. [ Laughter ] He's pretending to be what? What is he? What's the figure who rides the night? A Hessian who's also known as more famously the... >> The Headless Horseman. >> The Headless Horseman! Ok. What does it mean if you have no head? You're like most Americans. [ Laughter ] Alright, there's a kind of mindlessness about the Dutch, right? And look at Ichabod. Ichabod is a consumer of stories. So, who's the writer figure in this story? Is it Brom Bones crafting this, dramatizing this little spectacle for us? Or is it Ichabod who consumes these tales and teaches, and kind of involved in literary culture? Is it a good thing or a bad thing to be devouring? I mean, Ichabod actually ends up all right. I think he becomes a judge, right, at the end? That's probably a better place for teachers. Maybe. So I want you to see again that this is marked by a certain kind of ambivalence. Irving appears to set up a binary between the Dutch past and the Yankee present, appears to mark the Dutch past as associated with the marvelous and the literary and Ichabod is associated with something else. And then he makes them complicated in interesting ways. I think that's part of what we say is one of the hallmarks of romantic writing. Romantic writing, as we will see, especially with Melville and Hawthorne, is able to think about contraries and think about combining them in integrated ways. Romantic writing is, therefore, a kind of integrative mode, as opposed to something like allegory, which tends to have a logic of either or. So we'll say more about that as it progresses. One last thing. I sent you this poem, 'To a New England Poet.' That's of course because it is of this line here, right? Freneau's kind of bitter about the low state of literary culture. 'Why stay in such a tasteless land, where all must on a level stand, excepting people, at their ease, Who choose the level where they please,' right? Contra that Jefferson quote I've been talking about the last few days. 'See Irving gone to British court, To people of another sort, He will return, with wealth and fame, while Yankees hardly know your name. Young poet. Lo! He has kissed a Monarch's...' Yes, that's the joke. [ Laughter ] I think he's a little bit hard on Irving, because Irving manages to appropriate British forms, but he does go down in literary history as not only the first writer to make money from writing, but also the father of regionalist writing and the short story. There's a certain way in which people like Faulkner and Flannery O'Connor, and even Toni Morrison, are not quite imaginable without Irving in place in literary history. Alright, we'll leave it there. Thanks a lot. |
Open_Ed_Cyrus_Patell_American_Literature | Nathaniel_Hawthorne_I.txt | >> Unknown: All right, I've got a few more things to say about Uncle Tom's Cabin, so let's get started. I want to give you some sense today of what happens to the you know, the meanings of this novel as it is, as it works it's way further and further into popular culture. Close the door. [ door closing ] [ background noise ] So, if you have your book you can take a look at page 583 and if you don't, you can just listen. This is the moment when Tom addresses Legree, near the climax of the novel. Actually if you go down, the bottom of 582. Tom looked up at his master and answered master, if you was sick or in trouble or dying and I could save ye, I'd give you my heart's blood. And if taking every drop of blood in this poor old body would save your precious soul, I'd give them freely as the lord gave his for me. Oh master, don't bring this great sin on your soul. It will hurt you more than twill me. Do the worst you can. My troubles will be over soon, but if ye don't repent, yours won't never end. And this is about three chapters before the end, three pages before the end of a chapter that's called, The Martyr. And this is a moment you know, that's sometimes problematic for a modern reader, particularly who might not share Tom's and Stowe's belief in Christian salvation. You might have trouble accepting Tom's and Stowe's certainty about this. That Tom's troubles are about to be over but Legree's will never end right, because he is due to have everlasting perdition and damnation. A modern reader is probably more interested in another aspect of this, which we might call unending psychological torments. So we're interested in the kind of psychology of a character like Tom, the psychology of a character like Legree. In a way, readers have more readily identified some of the canonized male authors from this period of life, Poe and Hawthorn and Melboe [assumed spelling], as writers who were interested in psychology in the kind of more modern sense. Henry James would claim this. He said, the fine thing in Hawthorn is that he cared for the deeper psychology and that in his way, he tried to become familiar with it. And I think that Poe and Melboe also care about what James calls the deeper psychology and the way that they go about dramatizing it is to use the conventions of Gothic They use these conventions to probe it. But I think we think that Stowe is only about Christian salvation and Christian belief and not at all interested in this kind of psychology, then I think we are mistaking what's she doing at the end of a novel. I think she too, as we've seen, uses Gothic inventions to probe precisely. She is interested in what we might think of as psychological torment. Right? So that Cassie's successful hoax, directed in Legree, could only work because Legree is inwardly tormented and tormented in a way that we would think of as coming out of his feelings of guilt. The episode suggests more than that. It suggests that there are people like Legree, who's psychological torments are so great, who are so depraved you might say in psychology, have fallen so far into evil that they can no longer be saved by Christian feeling. It's too late for people like Legree. There are limits in other words, Stowe seems to suggest, to what Christianity can do. Although she quickly pulls away from that. Right? The career of Cassie demonstrates that. Stowe turns away from Gothic at the end of a novel, as suggested lax time and back towards here particular brand of Christian sentimental fiction and so finally, as we suggested at the very end but I want to reiterate, the form that the novel finally takes is the form of a sermon. Or perhaps we might say that what we realize is that what we've been reading is a sermon by other means. Right? A sermon that uses fiction to dramatize it and in that sense, we might think that it has profound affinities with other things that we've seen earlier in the course. Perhaps Wigglesworth's, Day of Doom, right, which has of those kind of inter textual references and clearly suggests to you that it is in some sense preaching a sermon to you. Right? So above all, Uncle Tom's Cabin is a Christian novel. It is a Christian novel that's also, as a result of it's being a Christian novel, profoundly against slavery. OK? The stance of being against slavery comes out of Stowe's belief in Christianity and it also links her to other female domestic writers of the, the period. But you might say there's a difference between what she shows us and what a lot of these other female domestic novelist tend to show. They tend to show that if you are Christian, if you lead a good life, you will in fact receive some kind of worldly success. That's not what Stowe was interested in. Stowe was profoundly not interested in the worldly and in fact, her two most exemplary Christian characters, Ava and then Tom, proved to die. Right? In and following that template of Christ's life. And you might say, the thing that she finally does, Stowe, is to go after slavery in profoundly Christian terms. In other words, what's wrong with slavery is that in some deep way, it is a sin. And so if you are a Christian and you perpetrate slavery or perpetuate it or even participate in it at all, you are committing a sin from which you need to be redeemed. And I think there's something about that then that's really what finally distinguishes her from Hawthorn, Melboe, Poe, writers like that. In other words, Stowe I think, is interested in psychology and she's interested in Christianity, but she isn't at the very end, interested in thinking about this in any way ironically. Right? She uses irony, we've seen in her narrative voice, to push forward her Christian agenda. But at the end there is no irony whatsoever, no second thinking, no second guessing, about Tom's final victory, as that chapter is called. Right? And that kind of a moment I think doesn't exist in the works of Poe or Hawthorn or Melboe, so that part of what's distinctive about Stowe is she can regard Tom's triumph absolutely without irony and that's part of the moral fabric of the book. Now one of the things that happens and you can see that here in this illustration from a later edition right. I mean this is Tom's ultimate moment here and we have you know, Christ appearing here basically. In that final moment. That element starts to get lost very quickly from adaptations of Uncle Tom and I want to just give you a sense of this. Because this has something to do with something that's been a theme for us, I think at least since Winthrop, which is that writers create certain kinds of meanings, certain kinds of symbols, they create text, they release these texts, they have a relationship these texts do, to something that we've called the horizon of expectations. A writer makes a decision about how to pitch his or her texts and symbols and literary creations, but ultimately the meaning of those things is going to be determined in large part by readers. Right? And meanings will circulate throughout the culture. So that Winthrop creates the idea of the city on the hill, which he means to be a figuration for the ideal relation between a community and individuals in which the communal quickly comes first. Immediately, it comes first. Individual is supposed to be subsumed by the community. The whole point of the sermon is that the city on the hill will exist if we really believe in the bonds of Christian love. Body politic that is linked together by the ligaments of Christ's love. By the time you get to Ronald Reagan, who considers himself a Christian, we he's nevertheless a different kind of Christian and he could appropriate Winthrop's symbol and turn it's meanings almost completely around. So that it becomes a way of suggesting that if the individual pursues his or her own version of the good, these communal benefits will follow afterwards. It really uses the logic of less a fair. Winthrop would have been appalled When we read the Scarlet Letter, we're going to see exactly that. I want you to think of it in those terms. Right? Here is a woman who is caught committing adultery and to be and the way she is punished is that the male you know, the puritan fathers in Boston, decide to make a show of her. They put her up on a scaffold, which is like a stage. They pin an A onto her chest, to stand for adulterer. Every time you look at her you're supposed to looked at the A. It's meant to aface her individuality, to typecast her, to make her you might say, into an actor and something akin to, a social medieval mystery play. But at the very beginning you might say, the meaning of that A starts to slip and slide and change. Right? Hester is allowed or I suppose it's a version of Hester is you know, as Christ was forced to carry his own cross, Hester is forced to sew her own A. But she's clever and she's a good seamstress and she's good a embroidery and so she puts this extremely lavish version of the A on herself and people are drawn to this and the readers eye is drawn to it by Hawthorn. And as you'll remember, as the novel progresses, the meaning of the A starts to become multiple, it starts to change. The official meaning therefore starts to give way to something else. And so that Hawthorn's novel can be read in large part, as a sort of study in what happens to meanings. How they evolve as they circulate in culture. Right? And you could say by the end, the very thing that the puritan fathers want Hester to do, to repent, is actually the opposite of what she does. But the fact of the A actually prevents them from seeing what's really going on with her. We'll talk about this more on Monday. But I hope, and I hope, my hope is that having you know, been through about three quarters of the course now, you will look at the Scarlet Letter in a way that's different than you might have looked at it not only at the beginning of the term, but whenever you read it last. Similar things happen to the meanings of Uncle Tom. I already suggested this to you last time. So the novel is serialized in 1851, it's scheduled for book form in 1852. It's already a wild success. And from 1852 on, into the twentieth century, there are adaptations of Uncle Tom's Cabin, almost continuously on the American stage and they're among the most popular theatrical productions that any theater company could stage. If you want to have a hit, stage Uncle Tom's Cabin. Still by the way, never earned any money from these adaptations, because and we talked a little bit about the copyright law and even the domestic copyright law, those are that didn't really apply to the stage production. Right? So she didn't earn anything from this. So even before the novel is published in 1852, it's adapted for the stage. Uncle Tom's Cabin or as it is and the subtitle is the southern Uncle Tom, is produced on January 5, 1852, at the Baltimore Museum and then there is this one, which is in August of 1852, by CW Taylor, at Purdy's [assumed spelling] National Theater, here in New York. Purdy's Theater was down on Tavern [assumed spelling] Street, just a few blocks south of Bowery [assumed spelling] and it was already known as a kind of popular place where you could often see black faced minstrel shows being performed and TD Rice was one of the most famous of these performers. According to the scholar Sara Mere, who's studied this stuff, she says that Taylor's was a typical sensation melodrama and after peace meant to fill a space in a program rather than to cause controversy. It played on different nights alongside a nautical drama, a tightrope walker and a black face burlesque of Othello And it was described by a newspaper in New York, the New York Herald as quote, an exaggerated mockery of southern institutions calculated to poison the minds of our youth with the principles of abolitionism. And it closed after only eleven performances. Now, listen to that. It's a newspaper in New York saying that the youth were being poisoned by the principles of abolitionism. There's a [inaudible] and this shouldn't surprise you I suppose, I mean New York was not clearly in favor of abolition and there was, there were factions in New York, particularly those who were identified as kind of nativists sentiments, who were sympathetic to the south and were profoundly racist. I'll show you a clip from Martin Scorsese [assumed spelling] gangs of New York, that not only shows you you know, how people took liberties with Uncle Tom's Cabin but also that gets that point across. The first version that did succeed was commissioned by DC Howard who was the manager of the Troy New York Museum and he wanted to feature his four year old daughter Cordelia [assumed spelling], as little Ava. So Howard played St. Clair, his wife played Topsy and their version of Uncle Tom's Cabin was written by his cousin, George Akin, who played the part of George Harris and got forty bucks and a gold watch for writing the adaptation. Akin's version is reasonably faithful to the novel. It adds a few Yankee characters for comic relief, but a lot of the dialog simply comes out of the book. The Troy production apparently was seen by 25,000 people in Troy, New York. The total population of Troy at the time was 30,000 people. So that's that. It moved onto New York City and the Howard family continued performing this play for the next thirty years, until 1887 when Howard himself died and when little Cordelia is, who's been playing the lead since her fourth birthday, celebrated her thirty fifth birthday. Not so little anymore. One of the set pieces in Akin's adaptation was Eliza crossing the Ohio, right. So this is one of the big moments that people always wanted to see. How are they going to do this scene. And subsequent dramatizations of this by Akin, by Howard and other people, became more and more elaborate. So the novel really doesn't have Eliza being pursued dogs, but dogs became dayrager [assumed spelling] later on and in fact, later productions would argue, would advertise that they had you know, real blood hounds and then really big blood hounds and just a lot of really big blood hounds, you know, double mammoth Uncle Tom, I guess that had really big dogs. [ laughter ] And eventually you have these adaptations closing with Tom, sometimes with actual machinery, in a kind of golden carriage that was ascending upwards and you would see Ava there and a father waiting for him, sometimes possibly at a certain point accompanied by an image of Abraham Lincoln you know, that kind of thing. But gradually what happens to this is that more and more of the elements of minstrel shows enter into performances of the play, particularly in the characterizations of Tom and one other character. Who do you suppose? Who seems right for characterization by black faced performers or as that kind of you know, is a butt of comedy. Topsy. Yes. Topsy. So you would go to see the, so by the end of the century these things became less and less adaptations and what they were referred to derogatively as Tom shows. And it's on that basis that the character of Uncle Tom, gets formed into this extreme, gets transformed into this extremely negative stereotype of African Americans. It becomes a symbol of black obsequiousness rather than idealized Christian humility. And you might say one of the things that happens to Stowe's story is that it's drained of both it's Christian imagery and therefore it's moral power and just becomes kind of melodrama. I wanted to give you a sense of this, so I'm going to show you some clips. The first two clips come from a 1903 silent adaptation of this. The first one is Eliza's escape. The second one is the death of Tom. And then there's another clip, which is from the 1927 version which gets at some of these minstrel, minstrel type motifs. Yes? [ music ] OK, you get the point. This is the death of Tom. [ music ] OK, you get the idea. Now this one is a later, it has higher production values, let's look at the stagy ones. But you can see, it just, it shows you, it'll give you a sense of how the kind of minstrel show motif's worked their way into [inaudible]. [ music ] OK, so you get the idea. And you can see how that what would happen is that in these productions, it would be little moments like that that would start to become what the shows were about rather than the larger plot. All right, this is from Gangs of New York. It'll give you a sense in the way in which productions were dramatized in scene. >> Unknown: The divisions between us. This war must cease. North and south must stand united. [ cheering ] Mister Legree, lay down your hood. Miss Eliza, join hands with Mister Shelby. And Topsy, dear little Topsy, cradle Uncle Tom's head. >> Unknown: There are certain things that are inaccurate historically about Martin Scorsese's [assumed spelling] movie, but it does a pretty good job of dramatizing certain aspects of life in the [inaudible]. If you're interested in reading a little bit more about going to plays is actually like, there are wonderful pieces by Irving and by Whitman, about the experience of theater in that time. All right, let's turn to Hawthorn now and in some senses by way of contrast. The writings of Hawthorn and Melville bring to a climax a tradition of writing that we've been looking at for a while now and that we tend to refer to as American romance. Right? So we would include in this most likely, Charles Brocton [assumed spelling] Brown, Washington Irving, Edgar Allen Poe, Emerson and Whitman and Thoreau writing in their slightly different way. But in fiction we're thinking about for us, it's Brown, Irving, Poe, Hawthorn and Melville. And one of the things, as the quote makes clear, one of the things that Hawthorn is doing is deliberately setting himself over and against the tradition of domestic fiction, for which he had mostly contempt. America is not wholly given over to a damned mob of scribbling women. I should have no chance of success, while the public taste is occupied with their trash and should be ashamed of myself if I did succeed. All right? Both Hawthorn and Poe, saw to create a new kind of reading public. I mean Poe, in addition to being short story writer, was also a journalist and critic and he was really doing everything that he could to mold public taste, according, to have a kind of greater appreciation of the aesthetic values that are within text. Hawthorn sought to create a form of writing that would be thought of as more elevated than typical prose. And that didn't have the association with the world of domesticity and this mob of scribbling women, that the novel did. So he called his form romance. And he called and so he referred to the four completely book lined fictions, the Scarlet Letter, The House of the Seven Gables, [inaudible] Romance and the Marble Fawn, as romances. And he's using it in contradistinction to the term novel, deliberately. And in the preface to the House of the Seven Gables, he suggests the reason why. If you have your anthology it's on page 1493. He says this. When a writer calls his work a romance, it need hardly be observed that he wishes to claim a certain latitude, both as to it's freedom and material, which he would not have felt entitled to assume had he professed to be writing a novel. The latter form of composition is presumed to aim at a very minute fidelity, not merely to the possible but to the probable and ordinary course of man's experience. The former, while as a work of art, it must rigidly subject itself to laws and while it sins unpardonably so far it may swerve aside from the truth of the human heart, has fairly a right to present that truth under circumstances to a great extent of the writer's own choosing or creation. If he think fit, he may also, he may so man also, he may so manage his atmospherical medium as to bring out or mellow the light and deepen and enrich the shadows of the picture. He will be wise no doubt to make a very moderate use of the privileges here stated and especially to mingle the marvelous rather as a slight delicate and evanescent flavor rather than as any portion of the actual substance of the dish offered to the public. He can hardly be said however, to commit a literary crime, even if he disregard this caution. Now I want you to look at this, since you've just sort of done this for as your second paper. I want you to look at this as a piece of prose and tell me how it works. [ no speaking ] It's very typical of Hawthorn's prose. So if we figure out something, if we figure out how this works, you'll have a leg up when you're trying to figure out how not only the two stories that we read for today were, but The Scarlet Letter. So, anything that anybody notices? Yes? [ inaudible ] As a dish. OK, good. So show me, let's just nail it down. Where is the theatrical stuff? [ inaudible ] Picture. [ inaudible ] Yes, I think it's both. I think you know, it's both of those things. You could say, manages atmospherical medium, you could certainly say it's like a stage manager, setting up his own [inaudible] and choosing to raise or lower the lights. You could also think of pictures like I don't know, a good example would be Carvagio [assumed spelling], you make use of cariscuru [assumed spelling] right, the shifting from light into darkness. So he's clearly evoking both of those kinds, that kind of pictorial imagination, whether on stage or in picture. OK, what was the second metaphor? >> Unknown: Food. >> Unknown: OK, so food. Actual substance of the dish offered to the public. OK, that's good. So there are two governing metaphor's here. Great. Anything else? Let's go back to the beginning. When a writer calls his work a romance, it need hardly be observed that he wishes to acclaim a certain latitude, both as to it's fashion and material which he would not have felt himself entitled to assume had he professed to be writing a novel. So how does that sentence work? What's that? [ no speaking ] It's very close to, I don't need to tell you that. Paralypsis [assumed spelling]. Good. What does it do for him? Yes? >> Unknown: He still needs to define what he means by romance. [Inaudible] define what romance is not [inaudible]. >> Unknown: OK, so he's defining things negatively. That's a good thing to notice about Hawthorn. He's going to start off with a term. When a writer calls his work a romance. But look what he actually goes and says about it. It need hardly be observed. So the impersonal construction creates the veneer of authority. It need hardly be observed. The paralypsis probably is there to heighten the sense of authority. That he wishes to claim what? A certain latitude. That's a paradoxical phrase. Because it's not certain at all. Right? A certain latitude. It seems like it's certain, but then when you think about it, how much latitude? A certain latitude both as to it's fashion and material he would not have felt himself to assume had he professed to be writing a novel. Right? So amtiphosis [assumed spelling]. It's one you know, one thing compared to the other. The latter form of composition, the novel, is presumed to aim at a very minute fidelity. Now again, look at this. It's a passive construction, so in this sense there's a way in which we could say it's meant to again, create this veneer of a kind of authenticity or authority, but by whom is it presumed? I mean, where's the agency there? It's presumed to aim at a very minute fidelity, not merely to the possible but to the probable and ordinary. So it's not just the possible, but the probable and ordinary. This is what the novel is supposed to do. The former and look at the way in which the prose breaks right. It's constantly qualified, it's hedged The former, while as a work of art, it must rigidly subject itself to laws and while it sins unpardonably so as far as it may swerve away from the truth of the human heart. All right so we assume that it's a work of art and therefore it has to subject itself to laws. And there's the implication I guess the novel presumes this, so it still has to, it still has to concern itself with the truth of the human heart. One of the, I mean, and why use this word? Sins unpardonably. That's the kind of word that Stowe might use, right. Why would you use the language of sinning? So far as it may swerve aside from the truth of the human heart, has fairly a right. What does that mean? Sort of a right or in all fairness? Has fairly a right to present that truth under circumstances. How many? How much? Too a great extent. Other writers don't choose an [inaudible]. What have we gotten to? How much? If he think fit also, he may so manage his atmospherical medium as to bring out [inaudible]. OK we've got that. He will be wise, no doubt, to make a very moderate use of the privileges here stated. And especially to mingle the marvelous rather as a slight delicate and evanescent flavor rather than as any portion of the actual. Now what's at stake in the [inaudible] of these two things? Sinning unpardonably and the dish metaphor. He's openly contesting the novel, saying that the romance does something different. So he's just distinguishing the romance. But why use that? And why use that? I've already given you a hint. Who you think is in these terms? Sinning unpardonably and who cooks? I mean isn't cooking is a big part of domestic life right. I mean, who cooks in Uncle Tom's Cabin? There's Mamie and Dinah. There's a certain way in which we might say the domestic novelist have a fire hydrant and Hawthorn is peeing on it. [ laughter ] Right? I mean, the sum text of this is you know, he will appropriate their language of sinning but we are going to turn it to the artistic or the aesthetic, which they claim not to be interested in doing. And we can do domestic imagery better than they can. Right? Here we go. Mingle it rather than slight delicate and evanescent flavor than as any portion of the actual dish offered to the public. So you might say he's taking their ground and appropriating it for himself. He oops, he can hardly be said however, to commit a literary crime, even if he discard this caution. So the question I leave, I ask you now is, how much of the marvelous does the writer get to use? According to Hawthorn here. [ no speaking ] How much marvelous is good? Yes? [ inaudible ] Exactly. He can use as much as he wants. So who is the arbitrar of what the right amount? The author, right. One of the things I want you to see here that hawthorn is doing, is creating a space for romance that's going to have it inhabit something that we might think of as the aesthetic and that is closer to idea now of what the literary is. That means propping up the author. Right? It's part of the project that we saw going on in Irving, too, when he makes use of the guise of the historian. Right? He tries to take some of the authority of the historian and then by mixing it with local facts that most historians would know and by certain things that he invents, he ultimately creates himself to be his own authority. Right? He's pushing in other words, the authority of the imagination over the authority of the regime of facts. So facts and history, that's about the possible, the probable, the ordinary. Fine as a ghost, but you miss something. It's not enough. It's not the whole story. To get the whole story you need more than that. You need some of the marvelous. You might need a lot of the marvelous. It's sort of up to you to judge. This is the same stance that you will see hawthorn adopting in the Custom House preface to The Scarlet Letter, which you'll read over the weekend. Right? He's talking about himself, in the Custom House, in the nineteenth century, talking extensively about how he comes to edit a manuscript that he has discovered, called The Scarlet Letter. Right? And he'll go and he tells you about it. Here's this manuscript and I opened it up and this piece of whatever it was, this cloth fell out and he almost says you can come and see it if you want. Right? Hes trying to say that he has the authority of authenticity. Of truth. This really happened. Of course, in the same way that he creates this, he can hardly be said to commit a literary crime, even if he disregard this caution. He will say of course, in The Scarlet Letter, I don't vouch for a word for word transcription, I vouch for the larger truth of the thing. The outlines of the tale. Which means that in the end, he's claiming just to be a mere editor of this manuscript, but we really have no idea how much of it is a really true manuscript, if we believe in that fiction and how much of it is his own imagination. Right? So one of the things I want you to see is he's going even further than Irving in attempting to take, appropriate some of the authority that even in this period, accrues to the historian and shift it someplace else. That's one thing. Towards the literary. Towards the province of the imagination. And then even within the province of the imagination and the literary, he wants to shift things further away from where they might be said to have kind of settled, at the beginning of the nineteenth century. Away from the novel to something more rarefied and he thinks of more imaginative, in some sense, more fictional even. Because it isn't so bound to the problem of ordinary course of man's experience and that is what he calls romance. So that's one of the things to bear in mind. Hawthorn is taking these terms and trying to shift them. He does not want to say that he has no relation to what we might think of as morality or proof. In fact, the argument would seem to be that the romance gets you closer to a sort of higher moral truth. Because it isn't bound simply by what we can see and experience in the every day. Right? It is linked to the marvelous and what are miracles for example, if not some aspect of the marvelous. Right? What I want you to see is that hawthorn is taking this idea of romance and appropriating it. Already that's a kind of appropriation itself of the term romance. I mean, later on he'll say in the Custom House, that this is a kind of figure for what happens in a romance. He says that we have the creation of what he calls a neutral territory. Somewhere between the real world and fairyland, where the actual and the imaginary may meet and each of them be themselves with the nature of the other. All right, so the sense in which romance is bringing things together. Its bringing together the possible, the ordinary, sure, but also something else beyond it and it's in that bringing together, in that fundamental reconciliation of things that might seem to be separate. That romance works. Right? So you think about it, this moment is the moment when he's talking about the child's playroom looks a certain way in the day, at night it looks and when it's really interesting is precisely that moment that he seems to refer to in the preface of The House with Seven Gables, when the shadows start to emerge and we get what he calls this neutral territory. Some kind, the gray. So that you might say, the thing that's interesting to hawthorn is the gray space. Some would call it the liminal space. In between one thing and another. So that overall I would say to you, a productive way of thinking about hawthorn is he's somebody who's trying to get away from a logic of either or to a logic of both and. And we'll try to see how that works over the next two times. Now he's deploying romance to help him in this project. Romance already meant something else and he's trying and something that's ennoble It's in sort of the same way that Gothic was a term that Charles Brocton Brown tried to ennoble and make a part of a larger public discourse. Hawthorn is trying to ameliorate the means of romance. Well later in the century, Henry James kind of captures what the standard sense of romance was in hawthorn's day. He said the only general attribute of projected romance that I can see is the fact of a kind of experience of which it deals. Experience liberated so to speak. Experience disengaged, disenbroiled, disencumbered, exempt from the condition that we usually know to attach from it. Right? There's something fantastic about it. It's not grounded in real life. Hawthorn I think wants it, wants contra to James, wants to say that in fact, there is a kind of tether. There is a link between these things. Now you know, James, by the way, James was on of the, James' major inspirations was hawthorn. In fact, it's possible to think of some of his later fictions as almost kind of rewrites of some of hawthorn's fictions. Walter Scott, roughly contemporary with certainly Irving and with hawthorn as well said, we now use the term romance as synonymous with fictitious composition. It's a romance just means, it's just another way of talking about fiction. Another representative comment comes from a retired general from the, from the army. The facts and scenes of the revolution he said, were so strange and heroic that they resembled ingenious fables or the dreams of romance, rather than the realities of authentic history. Right? So I want you to see how these dichotomies are being set up. Dreams of romance on the one hand, reality on the other, authentic history on the other. Hawthorn is trying to bridge this gap, both and, rather than either or. And even Charles Brocton Brown distinguished romance not from novels, but from history as well. He would, he said similar things. Romance for him was not one kind of fiction as opposed to fact, but all of fiction as opposed to fact. Hawthorn was going to do something different. He's going to divide fiction up, he's going to promote a certain view of a certain kind of fiction and he's going to call that kind romance. So I want you to understand that hawthorn is turning to romance in a climate, a kind of cultural climate that is hostile to it. That either it's suspicious of it because it's either a low form or because it's still there's a worry about the status of fiction. Isn't fiction telling tales? Isn't fiction lying? But hawthorn wants to do something different with it. He wants to say that it's radically different from a novel, because it doesn't limit itself to the probable and the possible, because it gets at this and this is important, this idea of the truth of the human heart. And I think you know, one way to think about it is, think about the kind of things that Poe is interested in. Right? Poe was interested in uncovering stuff that's within and that kind of makes itself come out. Just imagine, as a thought experiment, imagine if young Goodman Brown were told in the first person. If it were Brown himself who were telling the story. Suggest to you that that would probably be the way that Poe would do it. It would sound, it would seems to be a lot like a kind of Poe story. You can imagine it right? Guy tells a story of he's going to the woods and then all of a sudden he realizes that everybody around him is either mad or depraved or a witch or something crazy like that. And Poe would leave it there. I suggest to you that what hawthorn does is more interesting even than that. But to understand what it is that hawthorn is doing there, we need to put another category on the table and that is allegory If you have your book, you can take a look at page 1332 to get the full passage here that I'm going to read. This is from a famous story that unfortunately we don't have time to read, although it's terrific. It's called, Rapachini's [assumed spelling] Daughter. And again, you can see affinities between hawthorn and Irving here. Again, hawthorn creates a kind of fictitious alter ego, the writing, let's see, Rapachini's Daughter, the writings of one, Ovapine [assumed spelling], which turns out to be French for hawthorn and he says this to preface the story. Irvingesque. We do not remember to have seen any translated specimens of the productions of [inaudible]. Fact the less to be wondered at as his very name was unknown to many of his own countrymen as well as a student to foreign literature. As a writer, he seems to occupy an unfortunate position between the transcendentalists who under one name or other, have their share in all the current literature of the world and the great body of pen and ink men, who address the intellect and sympathy's of the multitude. Right? So this is another image of in between ness here, these literati types. These transcendentalists and then there's the normal people that most people you know, journalists and others that people are reading. If not too refined, at all events too remote, too shadowy and unsubstantial in his most development, to suit the class of a latter taste and yet too popular to satisfy the spiritual or metaphysical requisitions of the former, he must necessarily find himself without an audience, except here or there and individual or possibly an isolated clich right. So hawthorn is kind of writing about, I guess, what he perceives to be his own situation. And he perceives to be somebody who's caught in betwixt and between. He's sort of popular, but not as popular as he would like. He's not quite respected enough among the intellectuals perhaps. His writings and again, this is a typically Hawthornian sort of hedged sentence. We give and then we take away a little, this sort of sidal left to our description. His writings to do them justice, are not altogether destitute. So how much is there? Are not altogether destitute of fancy and originality. They might have won him greater reputation, but for an inveterate love of allegory, which was apt to invest his plots and characters with the aspect of scenery and people in the clouds and to steal away some of the human worth out of his conceptions. He is ventriliquizing, obviously, criticisms that were made of his own writing. All right, but it's interesting to see then that what people took a look at hawthorn and thought of him as doing something that we might link to allegory Now that's not a bad thing necessarily, allegory was in fact a very popular form. But allegory is exactly the kind of form that would bother hawthorn because it wants to map meanings exactly from one place to another. We'll see how this works in just a minute. So hawthorn is really interested in allegory right. He says that two of his favorite writers are Spencer and Bunyon. Spencer who was know as one of the premiere you know, both of them and Don Bunyon who is probably you know, one of the most widely read books in New England from the colonial period up to hawthorn's day. You'll remember that Miss Ofilia has a copy of Bunyon on her shelf next to her Milton. Right? So one of the things that we might say here looking at this description from Rapachini's Daughter, this idea of being what does it say, the aspect of scenery and people in the clouds and to steal away some of the human warmth. There's something cold and intellectual you might say, about allegory In other words, rather than trying to represent people and their fullness and complexity, allegory people have often thought, doesn't represent fully in that way, it's kind of illustrative. It's more interested in getting across certain concepts and therefore it's plots and it's people are simply there to serve as illustrations of these concepts. So Coalridge for example said that allegory was a translation of abstract notions into picture language. And the term allegory itself comes from Greek roots, which mean to speak other than openly. All right so one of those things where you're saying something in a different way than you might. But we were meant to understand, those are kind of one to one correlation between those two things. According to a guy named Angus Fletcher who's a famous scholar of allegory and who wrote the piece interestingly on the Whitman that I asked you to look at, he says, in simplest terms allegory says one thing and means another. Now you might say, what allegory actually says isn't exactly unimportant, to use a kind of Hawthornian construction. In fact, it may be very realistic. Hawthorn himself said that he read Pilgrim's Progress for the story. Has anybody read Pilgrim's Progress? Yes, I'll give you a little taste of it. Imagine reading Pilgrim's Progress for the story or for the characters. You'll see why that seems silly. Fletcher says, the whole point of allegory is that it doesn't need to be read in this biblical way, eclectically, often has a literal level that makes good sense by itself. But I would suggest to you that that is almost never the primary interest of the allegory That literal level. What we're interested in is the other meaningness of it, that other thing that all of those plot elements and character elements are pointing to. The sermon you might say, beneath the story. So the crucial part about allegory might be that it's illustrative and therefore it's relation to reality seems to be at a further removed than most fictions. Less interested in the real world, as it were, than ideas about the real world. Is interested in other words, in kind of abstraction and sort of abstract ideas. To illustrate what this, to illustrate this, let me give you a few snippets from Pilgrim's Progress. Which was published in 1678 and it's full title is, The Pilgrim's Progress from this World to that which is to come, Delivered Under the Similitude of a Dream, by John Bunyon. And again, next to the bible, it was the most widely read in New England during the eighteenth and the nineteenth centuries. This is the beginning. As I walk through the wilderness of this world, I lighted on a certain place where there was a den and I laid me down in that place to sleep and as I slept I dreamt a dream. OK, so important to remember this idea of the dreamer. I dreamed and behold I saw a man clothed with rags, standing in a certain place, with his face from his own house, a book in his hand and a great burden upon his back. Now this should remind you of your Wigglesworth, right. This is, he says, he's basically referring you back to the bible. If you went and looked in the bible you would realize that what this is is an allegory of the individual you know, sinner. And in fact, the maker of the back pack that he's carrying, is in fact, sin. All right, so he's carrying this weight of sin on his back. I looked and I saw him open the book and read therein. And as he read he wept and trembled and the not being able longer to contain, he'd break out with a lamentable crying, saying what shall I do. And again, this is meant to say, we're dramatizing something that's come from the bible. Now the narrator goes on. Now I saw in my dream, that just as they had ended this talk. This is a little bit later on. He's met somebody else. All right you know, this figure who's name turns out to be Christian Says, so as the hit the end of this talk, they drew near to a very miry slow that was in the midst of the plain and they, being heedless, did both fell suddenly into the bog. They name of the slow was Despot. Slow is an interesting word by the way. If it has to do with snakes, it's the kind of word my younger son hates, because it breaks all the rules and breaks it's own rules. Slough if it's for snakes, slough, usually with the slough of Despond, slough if you're British and possible if you come from New England, slew if you're talking about average ordinary bogs, but still slough if you're talking about this one. So I think for simplicity sake, let's just say slough. The slough was despond. Here therefore they wallowed for a time, being grievously bedobbed with the dirt and Christian, because of the burden that was on his back, began to sink in the mire. The burden of sin. All right, you start to understand how this is working? A little bit later on. Christian was left to tumble in the slough of despond alone, but he still, he endeavored to struggle to that side of the slough that was so further from his own house and next to the wicked gate. That which he did but could not get out because of the burden that was on his back. But I beheld in my dream that a man came to him who's name was, help, and asked him what he did there. Sir, said Christian, I was bid go this way by a man called, evangelist, who directed me also to yonder gate that I might escape the wrath to come. And I was going vither, I fell here. Help says, but why did you not look for the steps? And Christian says, fear followed me so hard that I fled the next way and fell in. And help says, then said he, give me thy hand. So he gave him his hand and then he drew him out, set him upon sound ground and bid him go his way. And again, it invokes the Psalms. Right? So I want you to see how this works. Right? I mean, how does that work? We can clearly see that what this is is an allegory of, it's really about the progress of the Christian soul. Away from things like sin and despair, with the you know, the temptations that you, the help that you get from others, to a place that Christian has to go. It's called the Celestial City. Right? So it's how a soul gets to heaven. And that's really what it is. It's kind of a sermon that's lightly dramatized. So I think you get the allegoryness of it right. I mean, there's a character. His name is, help. We don't know too much about help. He's not really described for us. Because what he looks like isn't important. What's important about him is that he is the embodiment of the idea of help. Right? So later on Christian meets people like Help. They have other names. Simple, slough, presumption, hypocrisy Yes. He goes on a little sightseeing, places like the valley of humiliation. Always fun. Even more fun, the valley of the shadow of death. He is joined, he has a few other people who help him along, serve as tour guides. These are people named hopeful, faithful. He's the one who actually helps convert Christian in the end. You get the idea. The narrative in which these characters are appearing is a sermon. It's a theological discussion about Christian salvation and that's the sense in which the allegory says one thing. It pretends to be telling a story about these characters but it means another thing. This is really a sermon about the progress of the Christian soul. OK. Hawthorn is interested in this form. He's interested at times in making use of it and we can say in part because of the form that people think they know how to read in his moment, but he's also interested I think in demonstrating it's limitations and as I'll suggest further on Monday, I think that's because he understands that allegorical thinking has an inordinate amount of power in the middle of the nineteenth century, as the result of the kind of continuing residue of Calvinism. So that's why he's going to go after it, you might say, in his writing. So now we turn to this, this story, which if you printed it out, please pull it out, called, The Celestial Railroad, which was woefully omitted from this edition of the Norton. But I think it'll get you, give you a sense of what's going on with hawthorn and allegory It's quite clearly openly, in fact it refers to Bunyon, it's like literally a send up of Bunyon's, Pilgrim's Progress. In fact, on page 1305 of this, he refers to Bunyon. He says, the respectable apolion was now putting on the steam at a prodigious rate, anxious perhaps to get rid of the unpleasant reminiscences connected with the spot where he had so disastrously encountered Christian Consulting Mister Bunyon's road book, I perceive that we must now be within a few miles of the Valley of the Shadow of Death. Right? So Bunyon is now like the guidebook. He's lead [inaudible] or let's go to Celestial City, right, that's what Bunyon is and he's making fun of it in that way. The story we imagine here therefore is a kind of updated, nineteenth century, transcendentalist version of the pilgrimage to the Celestial City. We don't have to walk anymore. We can take the train. That very emblem of nineteenth century American progress. We have all the modern conveniences. Take a look at page 1302 for example. This is the first full paragraph. It really seemed to me however, that the bridge vibrated and heaved up and down in a very formidable manner. In spite of mister smooth it away's testimony to the solidity of it's foundation, I should be loathed to cross it in a crowded omnibus, especially if each passenger were encumbered with as heavy luggage as that gentleman and myself. Now if we know Bunyon, we're starting to get the joke. Right? Heavy luggage? I mean all the luggage that, what's the luggage that Christian is carrying around? It's a bunch of sins. So if you've got really heavy luggage, you got problems. But luckily you've got a train to carry it for you. Nevertheless, we got over without accidents, sooner found ourselves at the station house. This very neat and spacious edifice is erected on the site of the little wicked gate which formally as all old pilgrims with recollect, stood directly across the highway and by it's inconvenient narrowness was a great obstruction to the traveler of liberal mind and expansive stomach. The reader of John Bunyon will be glad to know, that Christian's old friend, evangelist, who's accustomed to supply each pilgrim with a mystic role, now presides at the ticket office. Right? So you can see whats going on here. There's almost a kind of frank lineon, bringing down to earth, of some of this. As if we're making fun of Bunyon. All right, we're making fun of that kind of pious Christianity Or are we? Is that the only thing that we're making fun of? Take a look at the top of 1304. Right? There seems to be a again, this whole idea of making fun of pilgrims that do it the old fashioned way. Da, da, da, da, let's see. Just at the top of the page, second line. It was laughable while we glanced along as it were, at the tale of a thunderbolt, to observe two dusty foot travelers in the old pilgrim guys with cockleshell staff, their mystic rolls of parchment in their hands and their tolerable burdens on their backs. The preposterous obstinacy of these honorus people in persisting to groan and stumble along the difficult pathway, rather than take advantage of modern improvements, railway right, excited great mirth among our wiser brotherhood. We greeted the two pilgrims with many pleasant jibes and roar of laughter where upon they gazed at us with such woeful and observedly compassionate visages that our merriment grew tenfold more [inaudible]. Right? You can see what's going on here. What is the suggestion that the story is making? Is the story really making fun of these pilgrims? Who's the butt of the humor here? In a name like mister smooth it away. What's going on there? Mister live for the world. Mister hides it in the heart. How is this working? [ no speaking ] With whom or what are we supposed to agree? You read Bunyon, you know what you're supposed to think. You're supposed to avoid the [inaudible] despond, you're supposed to make your way with the aid of help and faith to through the Valley of the Shadow of Death, blah, blah, blah. You're supposed to get to the Celestial City. We're right there with the allegorists Where are we here? What's being made fun of? [ no speaking ] What's that? Yes, certainly in large part the narrator himself is part of the, is falling under the butt of the joke here you might say. This is an unreliable allegorist as narrator. Right? He doesn't quite see the problems that are going on. He's thinking like oh we're so modern, you know, I have these great traveling companions, mister smooth is away, mister hides it in the heart, and we're going to get really fast to the Celestial City. >> Unknown: I don't know. In some ways I feel it's more complicated than that though. Because the narrator [inaudible] isn't an allegorist He's sort of thinks [inaudible] at the same time [inaudible]. You know, he could be [inaudible] therefore use it as an allegory that is in some ways distracting. Doesn't represent [inaudible] you have to go through. But at the same time he's. >> Unknown: Wait so, we mean Bunyon as [inaudible] but means he's thinking of it literally. Like for the story and as a guide to the landscape. >> Unknown: Yes. >> Unknown: Not as an allegory >> Unknown: Yes, I don't know. It's hard, I haven't figure it out totally [inaudible]. >> Unknown: It's clever right. I mean. Yes? >> Unknown: I think he's making fun of everyone all at once. He kind of [inaudible] but he's also making fun of the narrator and you know, the you know, more bother that they have it all figured out [inaudible] modern you know, advantages. I think that he's trying to say that neither of them have it. >> Unknown: Right. You might say there is a certain amount and certainly the narrator seems to be promoting a certain kind of poking fun of these pious Christian pilgrims who are kind of like country bumpkins. They don't know how to take care of all the modern conveniences and why are they struggling with their things but we can have our really heavy luggage and have it taken, whisked away to the Celestial City. Except that you might say there is a problem of the naming. Right? To call somebody mister smooth it away, is probably a reference to a transcendentalist thinker like Emerson, for example. Remember we said with Emerson, part of the problem with Emerson is that he might be insufficiently attuned to the problem of evil. We just smooth it away. So there's a sense in which the allegory, let's keep it aside from the, keep it away from the narrator as allegorist figure. The allegory certainly wants us to agree with that right. I mean, we are smoothing it away. We most likely are hiding sin in our heart. And we really ought to be concerned with the fact that our train is being driven by a demon. Do we get where we want to go at the end of the Celestial railroad, we most certainly do not. This is the last paragraph of the thing. And then did my excellent friend, mister smooth is away, wrath outright, in the midst of which concranation, a smoke wreath issued from his mouth and nostrils with a twinkle of lured flame darted out of either eye, proving indubitably that is heart was all of a red blaze. The imputant feigned to deny the existence of tophit [assumed spelling] when he felt his fiery torches raging within his breast. I rushed to the side of the boat intending to fling myself on shore, but the wheels, they began the revolutions through a dash of spray on me, so cold, so deathly cold with that chill that will never leave those waters until death be drowned in it's own river. That with a shiver and a heart quake, I awoke. Thank heaven it was a dream. Right? It turns, it's a dream, a dream vision that turns out to be a nightmare. So one of the things that I want you to see is that hawthorn is at a very complicated way, manipulating the allegorical mode. I think you're absolutely right. As a story, it actually holds out interest in a way that Pilgrim's Progress doesn't. I mean, it's interested in details. It's referring back to the, it's referring back to Pilgrim's Progress, but it's representationally much more rich. It's almost like these people do have certain kind of characterizations. On the other hand, I would think it's a kind of manipulation of the allegorical mode that's still allegorical The meaning is still you know, even though we might be tempted to make fun of people who are too pious, we ought be very afraid of people who try to take shortcuts to moral behavior or to good behavior or think that they can be saved by doing the equivalent of taking the railroad. Because the railroad may turn out to be you know, run by demons in the end. We might have sold our souls in trying to do it the easy way in taking these shortcuts. So you might say this is almost because of the allegory, as suggesting that we should be critical of thinkers, like Emerson, who don't sufficiently understand the pull of evil. In that sense, we're meant to be there with the allegorists, the larger allegorist The one who's written this whole thing. Not so much the narrative figure that as to wake up from the dream and maybe is enlightened. But the story itself wants us to see that there's a problem with nineteenth century notions of progress. We're going too quickly. We're getting, we're disposing of original sin too quickly. And that would be a reason to remember back you know, Melville in hawthorn and [inaudible]. Right? Melville has the same thing that he notices in hawthorn. That hawthorn is still worried by and he dramatizes the pull of what we call you know, the Calvinist sense of depravy. Right? Remember that from Hawthorn and His Mosses? That we need something somewhat like original sin. Not thinking mind can do without that, to balance, weigh the uneven balance he says. We'll take a look at that again when we turn back to Moby Dick, next week. But you can see that that's what's interesting about, and I think that's illustrated by the story as it were. Hawthorn has a certain kind of critique in mind for those who would quickly dispose of these kinds, of the problem you might say of evil. Now that's relatively simple, I think, compared to what's going on in Young Goodman Brown. Because Young Goodman Brown takes us at one further removed. Right? Young Goodman Brown doesn't look exactly like this. Why would we think that Young Goodman Brown you might say, is why would we think that Young Goodman Brown has anything to do with allegory? What other, because there's no, there doesn't seem to be this kind of set up, right. This kind of set up that we have in Pilgrim's Progress, with a dreamer saying I'm going to dream a dream and then and that he uses here in the Celestial City. So what's allegorical about Young Goodman Brown? Yes? [ inaudible ] Well his wife's name is Faith. That's an allegorical element. Anything else? Yes? >> Unknown: I think the fact that it isn't dream vision or particularly a dream, it kind of sets up the allegorical situation. Because the dream is probably just like the realm of symbols where [inaudible] meanings that [inaudible] to other things. >> Unknown: OK. We want to list, we want to think I think a little bit more about how that story makes use of dream. Right? I mean, because in a dream vision, classical, medieval dream vision and that, the way in which that's appropriate by Bunyon, it's basically a dream is something that's sent by God as a kind of teaching moment. Right? We trust what's in dreams. The dreams reveal the progress of the Christian's soul. The dream that Goodman Brown may or may not have, is a little dodgier than that. Yes? [ inaudible ] OK, it's possible. I mean sort of the, I mean his name itself, right. It isn't Christian, but it's Goodman Brown. There's something generic about Brown and Goodman. He's about what happens to a good man. What I want to propose to you is this. I think it makes a difference the way the dreaming is treated, not only because the dreaming is a little bit uncertain, whether it is a dream or whether it isn't a dream, but again, think of the standpoint of the dreamer. Who's doing the dreamer, who's doing the dreaming in Bunyon and the Celestial Railroad? Who's doing the dreaming in Bunyon and the Celestial Railroad? The author or the narrator figure. Who's doing the dreaming in Young Goodman Brown? It's Goodman Brown. So we are what? What's the triangulation? We are, we have a narrator who is not the dreamer but is watching a figure who is doing the dreaming. Maybe, if that's what he's doing. So where's the allegorist? And the allegory, that we're going to look briefly at, the dreamer is the allegorist So where is the allegorist in Young Goodman Brown? It's Goodman Brown, right. Goodman Brown plays not necessarily the role of Christian but he is someone we watch, literally doing what allegorists do. Possibly having this dream vision. We're not necessarily having the dream vision. Let's turn to it and take a look. One of the things I want to suggest to you is going on here, is that this is a form of, if there's a way in which the Celestial Railroad is a kind of a manipulation of allegorical mode, then nevertheless partakes in allegory right. So it's a send up of allegory, but it nevertheless is using allegorical techniques to make fun of something else, other than allegory as well. In Young Goodman Brown, I suggest we really have a kind of anti allegorical manipulation of the allegorical mode. But the way to think about it is this. On page 1297. Right. Goodman Brown meets this guy and then he sees him again in the woods. He thinks. He's there with his wife, Faith. All right, 1297. He's watching what he thinks of as this kind of meeting of the devil's disciples. They did so and by the faith of the hell kindled torches, the wretched me beheld, man beheld his faith. And maybe that is allegorical right. I mean, maybe it's not just his wife, but it's his faith. Nevertheless, the wife of her husband, trembling before that unhallowed altar. Lo, there ye stand my children, said the figure in a deep and solemn tone, almost sad with this despairing awfulness as if his once angelic nature could yet mourn for our miserable race. Depending upon one another's hearts he had still hoped that virtue were not all a dream. Now are you undeceived. Evil is the nature of mankind. Evil must be your only happiness. Welcome again my children, to the communion of your race. Now, that's a statement. That's like a statement of the moral. That's the lesson. If it were Bunyon, that's what you would be supposed to believe and you wouldn't have a doubt about it. Evil is the nature of mankind you know. Christian should go to the Celestial City, yes, we agree. Is that what the story, Young Goodman Brown, wants you to believe in the end? Does the story promote the view that evil is the nature of mankind? What do you think? Is that what you came away thinking? Evil is the nature of mankind. We saw the devil, devil said, evil is the nature of mankind. Everybody in the hallowed whole town was a devil worshiper. Pretty much looks like evil is the nature of mankind. Yes? [ inaudible ] I think that you know, hawthorn is always interested again, I think that's right, in the both end and in ambiguity. Right? He's interested in probing at these in between spaces. So we ask the question now, so we've said like OK, in allegory there's a dream. We're not even sure this is a dream. Had Goodman, this is the bottom of 1297, had Goodman Brown fallen asleep in the forest and only dreamed a wild dream of a witch meeting? Now one of the things to say is that if allegory goes to the extent that what we are seeing is a kind of allegory of him losing his faith. So there's a literalized way in which what Goodman Brown sees is the literal loss of his faith because his wife is meant, is named Faith. So when he loses her to the devil, he's lost, not only his wife, but his Faith, with a capital F both ways. Right? Understand? But what I want to suggest to you is that's still internal to Goodman Brown. We are not saying that we have lost faith as leaders, we are watching someone losing faith. And what I suggest to you is that the story is dramatizing what it is like to think like an allegorist and how easy it is if you think in this black and white way, either everyone is evil or everyone is good, there's no in between, that you can lose your faith. Be it so if you will, alas it was a dream of evil omen for Young Goodman Brown. A stern, a sad, a darkly meditative, a distressful, if not a desperate man did he become from the night of that fearful dream. On the Sabbath day, when the congregation were singing a holy song, he could not listen because an anthem of sin rushed loudly upon his ear and drowned all the blessed strain. When the minister spoke from the pulpit with power and fervid eloquence and with his hand on the open bible of a sacred truths of our religion and of saint like lives and triumphant deaths and a future bliss or misery unutterable, then did Goodman Brown turn pale. Why? Because he's reading like an allegorist Right? They're saying one thing, but they mean another. They all look pious and good, but he is convinced that they are all evil. Only evil can he see around him. Then did Goodman Brown turn pale, dreading lest the roof should thunder down upon the grave last [inaudible] often awaking somebody at midnight, he shrank from the bosom of faith. And at morning or even tired when the family knelt down at prayer, he scowled and muttered to himself and gazed sternly at his wife and turned away. And when he had lived a long, when he had lived long and was born to his grave a whory corps, and look at the guy, he's got a wonderful big family followed by faith, an aged woman and children and grandchildren, a goodly procession, besides neighbors, not a few they carved no hopeful verse upon his tombstone for his dying hour was gloom. So think about it. We'll stop, we'll take this up again. But think about the way that that has worked. What is the difference between that rendering of the way allegory works and the rendering we see either in Pilgrim's Progress or Celestial Railroad. Again, I want to suggest to you, that you might say that what this is dramatizing is the cultural problem of allegory What happens to people, individuals and what happens to a culture that thinks allegorically? And I suggest to you that that in some sense is one of the larger projects of that longer work that we'll look at called, The Scarlet Letter. All right, that's it for now. Thanks. |
Open_Ed_Cyrus_Patell_American_Literature | American_Gothic_II.txt | [ Silence ] >> Today we're gonna continue the train of thought that we began last time, which has to do with the critique of The Enlightenment. And part of what I suggested to you is that you as poets move from Neoclassicism to The Enlightenment, part of what they're engaged in is you might say a critique of a kind of impoverished view of mind or consciousness that over-relies on reason. And they therefore try to develop a higher faculty than human reasoning which they refer to alternately as fancy and imagination. All right so that's one problem with Enlightenment thought, that it is impoverished. It doesn't, doesn't get at the fullness of human creativity or human thinking. There's another side of it and that's what we're gonna explore today. We started to look at it a little bit with Barlow's [assumed spelling] Raven poem with Poe. The idea that in fact there is something wrong with reason as a faculty, and this can take a couple of forms. One is that all of those nice ideals that come along with the enlightenment may in fact be parasitic precisely on the kinds of negative types of thinking that they are designed to get rid of right? So that in fact, it may not be accidental that The Enlightenment is patriarchal and racist. It may be that there are real reasons that all of the vaunted ideas of The Enlightenment in fact co-exist with those things, tolerate them, maybe even require them. The other thing is that reason itself may not be as powerful as we think, that there might be other things going in, on within human consciousness that are either hostile to reason or are its opposite. Things that go on when you're asleep and the unconscious mind takes over, things that go on when reason loses its purchase on the mind and the mind becomes maddened for example or goes insane. All of these things are things that Charles Brockden Brown starts to explore, right? So again I want to review some of the places that we've been. I mean we're moving towards the mid-term at the moment so we want to get our story straight here, we try to understand the larger story that we're talking about. Again the idea that enlightenment, from Kant, is an emergence from a self-incurred immaturity. Okay so we want to think about that. The cause is not lack of understanding, but lack of resolution and courage to use understanding without the guidance of another. I want you to think about this now, how does this quote look to you having read Edgar Huntly? Does it look at all different now? What is the story of Edgar? Is the story of Edgar Huntly a story of coming out of a self-incurred immaturity into something else, or is it a different kind of story altogether? Remember also that Edwards and Franklin right, are two men who are, roughly speaking contemporaries. They are poised you might say in the cultural exchange between Calvinism and The Enlightenment. They choose different strategies, all right. Edwards tries to appropriate enlightenment modes of thinking in order to bolster up US Calvinism. Franklin understands the continuing power of Calvinism as a mode of religious thinking but tries to minimize its cultural power, to use it where he must, but to promote a set of ideals that really do rely or promote the idea of reason as the prime human faculty right? So you remember again the idea with Edwards, this is how he uses enlightenment thinking, right? He, we called him also a kind of pre-romantic because he makes use of images that are drawn from nature. This is a very good passage for thinking about that. The soul of a true Christian appears like such a little white flower that we see. It's a literal process of enlightenment right? It opens itself up to the light of the sun, and we've talked I think over the past couple of days about the ways in which the poems and writing that have to do with The Enlightenment often use light itself as a trope that they are, that dramatizes the power of this new kind of thinking. Franklin thinks about moral perfection, all right he's gonna use enlightenment ideals, but he has a little bit of you might say that Calvinist self-denial about him. He's gonna set down a set of principles. Ultimately he's not a Calvinist right because a Calvinist would never say something like, the appearance of virtue was almost more important than the reality of it. So that, you know he prizes appearance in a way that no good Calvinist would. But remember Franklin's idea of the erota and these are just a couple, some examples right? He believes that you can identify error. And you might say that part of your goal as someone living life is to try to see error for what it is and correct it. And one of the things we suggested was that in the process of writing his life, which and I suggested to you that that shares something in common with you know the kind of confessional mode started in the west perhaps by St. Augustine, that idea of confession and conversion. Franklin in writing an autobiography changes himself from just a plain old self into a self as author which requires him to create a self as character. And in so doing he's able as author to pick out the defective font [phonetic] of type those errors, and either talk about the ways in which he was actually able to correct them in real life in his real life, or, saying I wish now that I would correct that, I can point that out as an error. He still is getting a kind of do-over. It's a sort of textural do-over as he rewrites his life. All right so there's a kind of belief in the idea of moral perfection that goes along with enlightenment thinking. And again these are some of the leading doctrines of the enlightenment. Now I want us to think about the ways in which what Charles Brockden Brown has written in Edgar Huntly might be a book that would seem at first to take many of these things for granted. Certainly in the persona of its character, Edgar Huntly would seem to be a kind of sturdy young man of The Enlightenment whose life is devoted under the tutelidge of his teacher Sarsefield to precisely pursuing all of these kinds of principles and these kinds of ideas. The question is, how well does it go for him? Is this something that happens to him that in the end should lead him to question all of those ideas? All right so what I want to suggest to you is that Edgar Huntly is in fact exploring the dark side of The Enlightenment, the underside of it. It's turning over the rock to see what's there. It's looking at what's in the shadows that are cast by this light of enlightenment. And if you look at the back of your, I think it's still on the back of the edition that you have, it describes this as a story of a young man who sleepwalks each night a threat to himself and each other, himself and others, unable to control his baser passion. All right so it's the whole question of passion versus reason. What's the relationship between that? Is it possible that The Enlightenment underestimates the power of passion? And we need to remember I think the etymology of the word passion, all right? Passion comes from a Latin verb that means to suffer. The passions are something that you suffer. That's why it's called The Passion of the Christ; it's what he suffers on the cross, all right? So, the passions are something you suffer. You're not entirely in control of them. But even more I wanted to point out to you the fact that the book, the back of the book tells you it's set in Philadelphia in 1787, all right? The same time as the Constitution is being framed a hop, skip, and a jump away. There's a way in which we might say this is also if not a critique, then a cautionary tale you might say about the principles of enlightenment that are enshrined in The Constitution. A kind of meditation on what the dangers to the new nation might be at the moment that the new nation is being formed. Now, Brown is an interesting character because he is one of the first US writers to try to take advantage of the first American copyright law which takes which is passed in 1790. Before that there is no official copyright law. The copyright law does something interesting; it makes a profession of authorship possible, because it suggests that writing is property, and if you can write and copyright what you write then you can sell what you write and be paid for what you write and therefore you can live off your writing. Now there's a slight problem with this, it isn't an international copyright law, so it doesn't protect US writers from being pirated abroad, and it does nothing to prevent US publishers from publishing pirated editions of well-known books already circulating in the continent. So it creates a kind of paradox. On the one hand we would like to be an author and though the copyright law makes the profession of authorship a possibility, at the same time there are sort of economic factors that militate against that. Why would a publisher pay for a young author like Charles Brockden Brown when he could print something that's already known to be a best seller that has good buzz, good word of mouth from the continent? You can just reprint it here, and it's guaranteed to sell. So that seems like a bad thing for the aspiring US author. On the other hand remember what I said before, there is no patronage system in place in the early republic; therefore, what is emerging is a kind of marketplace for writing. And one of the processes you might say that's in place is the growth of this marketplace precisely through the pirated editions. It's not all bad for there to be pirated editions of writers that are well-known like Walter Scott or other writers from England because they develop a market for a reading public. Without that market, a young American author wouldn't be able to sell his writings and sustain himself as a writer. So it's a kind of double edged sword and Brown is participating in it right at the beginning of it as even a possibility you might say. Okay, one of the things to think about Brown therefore, is that in writing he is trying to do what in another age you might have done as a philosopher, or a professor or even a lawyer. He gives up the law because he feels that the United States doesn't need another lawyer, or it certainly doesn't need him to be a lawyer. But he doesn't give up the idea of doing something that's morally good, all right? He thinks of himself as a teacher, and he says that the novelist should be thought of as a storytelling moralist. That's in the advertisement or the preface to a now lost early work that's called Sky-Walk. So I want you to see that there's a bridge to be made between the kinds of didactic neoclassical poetry that we were looking at. Someone like Phillis Wheatley for example, or the you know the poems of Barlow and others. People who are devoted to public poetry on public themes. We didn't look at a ton of the kind of hagiographic poems that are in the vein of say the praised poem towards the Reverend Whitfield, the poem by George Washington and others. All poems with a kind of didactic purpose. Brown wants to fulfill that didactic purpose, but he wants to reclaim a genre that already you might say is in bad repute, and that genre is the novel. So he publishes a first book that's called Wieland in 1798. Wieland: or, The Transformation, and he says that his aim isn't merely to please the idle and the thoughtless, which had previously which is previously thought to be in the province of the novel, but actually he says to engage those who study and reflect. So Wieland appears in 1798 and it's the first novel that he actually publishes, and he talked he echoes what he had said before there, and says that the novelist should be regarded as a moral painter. That that's part of his aim, to be a moral painter. And he proposes, he says, to illustrate some important branches of the moral constitution of man it's a very strange story actually, it plays on religious enthusiasm, it uses ventriloquism, it has an episode of spontaneous combustion because Brown, as a sort of man of The Enlightenment was very interested in science. And therefore he was interested in scientific oddities and brought them into some of his novels. So ventriloquism and spontaneous combustion, religious enthusiasm and fanaticism all in Wieland. In Edgar Huntly there's another kind of scientific fact that is played with right? Sleepwalking. And this is Wieland: or, The Transformation, the title page. An American Tale, right? He's stressing that he's doing something American. If you could read the little epigraph here it says from virtues blissful paths away, the double-tongued are sure to stray. Good is a forthright journey to still, and many paths but lead to ill. All right again a kind of moral note. And yes, if you can actually see it, that is not an F, that is an old fashioned way of setting an S. So you just, you've probably encountered that if you looked at early revolutionary documents. That's the way the S was originally printed at the beginning of a word. A colleague of mine who teaches renaissance told me he once observed a TA give a class in which she hung her whole reading of a renaissance poem on reading this as if it was an F rather than S and asking what does it mean to substitute F there. And that's one of those things where if you, he says he was aghast but he didn't correct it right away and then there was nothing to do but sit there the entire time. So don't make that mistake yourself. Okay, other thing. Copyright secured. See he's taking advantage of the copyright law which has been passed just 8 years before in his first novel Wieland: or, The Transformation: An American Tale. So, after Wieland he publishes a series of novel in quick succession. All right Brown is not a careful writer in the sense that he tries to bang them out. So 1, 2, 3, culminating in Edgar Huntly, all of them in 1799. Yes it puts them all to shame when we worry about how, you know how fast we are writing. And you can see that, if you notice, we'll talk about it a little bit but there is a certain kind of haste that is evident in the plotting of Edgar Huntly. There are red herrings, there are loose ends that are not exactly tied up, and that might be the result of the fact that it was the third book that he wrote in that particular year. So that's one of the things to bear in mind. Brown is writing for an emerging market. Brown is writing in order to transform the novel into a higher form than it's thought to be, and he's writing something that is not within the main line of novelistic writing. The main line of novelistic writing might be embodied famously in English by Samuel Richardson. His novels Pamela and Clarissa which are novels about you know heroines, you can see the pattern right? A female heroine, protagonist, name of the book. Happy, not happy, many, many pages. Has anybody read Clarissa or an abridged Clarissa? Clarissa's a seduction narrative right, in which a middle class heroine is menaced and finally seduced and raped by an aristocrat and then goes through pages and pages and pages of decline all done through the pages of letters. And you might say right away in the early English epistolary novel there's the worry about what it is we're writing and reading. Why would there be so many pages describing something and one solution early on was well, it would be realistic if these were letters that you were getting to read. Of course, the idea that people would spend that much time writing and then reading, would leave hardly any time for living right, if you write thousands of pages of letters. Laurence Sterne Tristram Shandy actually makes fun of this little thing [inaudible]. And one of the things to know about the novel is the novel starts to question its own devices early on. In Tristram Shandy, he has a writer who realizes that the more he lives the more he has to write and the more he writes, the more he lives and he'll never finish as a kind of you know, that you know paradox. He'll never get to the end. The more, the more he lives the more he has to write. It's an endless kind of thing. In the United States context, Susanna Rowsan's Charlotte Temple is probably the earliest example of this. Brown is not writing in this tradition. He is writing, trying to write over against this tradition and you could see that again, this is a front matter from an early novel. The Power of Sympathy which is thought to be the first American novel published. And you can look at it. To the young ladies of United Columbia, these volumes intended to represent the specious causes and to expose the fatal consequences of seduction to inspire the female mind with a principle of self complacency and to promote the economy of human life are inscribed with esteem and sincerity by the blah blah blah, okay? So that's what The Power of Sympathy is, but it addressed to young women. So there's something feminized about the form of the novel in this period which is part of why it is, you know regarded as a kind of lower form of writing, not really literary. And here is another example of a title page. The Coquette, or The History of Eliza Wharton, a Novel. But look at this note, founded on fact. Again, there's a worry that's probably a worry of Puritanism that there's something wrong with novels because they're fiction. And what is fiction, if not the opposite of truth? Fiction means lies, right? Why would you read this? If you do it's got to be only a guilty pleasure. There can be nothing improving by it. So fiction, as opposed to fact, fiction somehow has falsehood. Therefore early novels try to insist on their basis in fact. Don't worry about this, it's based on a true story. As if there were something that would then could be morally improving for that. Ask yourself now, I mean many TV movies, even actual movies say based on real events, or why does that make a difference? Why should you care if something is, does it have, does it hold your interest more? There's a certain way in which part of the problem for writers like Brown, and you might say for Romanticism, is how to take some of the prestige that is you know linked to the to some of the prestige factuality and history and transfer it over to fiction and literature. How to create the literary as a category that is separate from the bible and sermons and biographies and history and philosophy. A category that's going to be linked to this other faculty of the mind called imagination. This is part of the larger project of romanticism of gothic fiction and is part of Brown's project as well. All right so that's the kind of regime of facts, the tyranny of fact. And here's to give you some sense of the way novels were regarded in this period, this is a quote from the New England Quarterly in 1802. Without the poison instilled by novels into the blood, females in ordinary life would never have been so much the slaves of vice. It's no uncommon thing for a young lady who has attended her dearest friend to the altar, a few months after marriage which perhaps, but for her had been a happy one, to fix her affections on a friends husband and by artful blandishments allure him to herself. Be not staggered such moral reader at the recital. Such serpents really are in existence. Why? Because they read novels. I have seen two poor disconsolate parents drop into premature graves miserable victims to their daughter's dishonor and the peace of several relative families wounded never to be healed again in this world. Why? Because they read novels. Right, so there's okay there's another thing to mention here. I mean, really, I guess there are people that burn books you know you'll throw Harry Potter onto the fire if you live certain places in the United States because you feel that Harry Potter is dangerous. But really, come on. You know we're all late model English majors here. Do we really think books are dangerous? Most of us probably don't. I mean can you imagine that a book's gonna cause like what, social unrest? Should we you know persecute novelist? Maybe it's better to live in a culture where they actually do persecute the novelists 'cause it would mean that literature matters. Well literature mattered to these people. Here it's negative, but they thought that novels were actually dangerous. You could read a novel and become depraved. Brown is thinking you should be able to read a novel and become virtuous and that's part of what he is trying to promote Virtue comes from the Latin roots of man, so you see the emphasis on masculinity and also Virtus which means courage. All right when Machiavelli talks about virtue, he's not really talking about being a good guy. He's more like he's talking about these things, manliness and courage and the ability to act decisively, right? So Brown is trying to find a form of the novel that can be used to instill virtue and all of these other qualities. He's trying to wrest the novel away from its association with some kind of damaging femininity. In part because he wants to say that you know to accept that kind of separations of fear does neither men nor women credit. So if we could get away from this idea that somehow there's something feminized about the novel, it's good for both sexes. Oh we don't need that one anymore. One last quote, this comes from the Reverend Samuel Miller. He says this, the author has no hesitation in saying that if it were possible he would wholly prohibit the reading of novels, for it may with confidence be pronounced that no one was ever an extensive and especially a habitual reader of novels even supposing them to be well selected without suffering both intellectual and moral injury and of course incurring a diminution of happiness. Okay, this is the context in which Brown writes this book. Now, let's think about virtue again. The form that Brown decides to use is the Gothic novel. Now the Gothic novel isn't, is a forum that in the English context is probably pioneered by this guy, Sir Horace Walpole who wrote a novel that was called The Castle of Otranto that was published in 1764 on Christmas Eve and subtitled, A Gothic Story. Now Gothic, you know is a form of architecture I suppose, first and foremost. It's a kind of you know the pointy churches after the Romanesque arches that are more rounded. Gothic is more pointy. Chartes for example, it's a Gothic cathedral. They're gorgeous. But it becomes a pejorative term by this time that is, that takes on the medieval association and makes you think of you know it's so Gothic, it's medieval, which means if it's not modern, it's not enlightened, it's medieval and Gothic and dark, right? Romantic writers are gonna mobilize the medieval and Gothic and dark over against The Enlightenment to show you what's wrong with The Enlightenment. Story of the Castle of Otranto, a villain named Manfred who lives in the Castle of Otranto and rules his realm unlawfully. His grandfather has poisoned the rightful ruler whose name was Alonso, and it has been cryptically prophesied that the usurpers will prevail and continue to occupy the castle so long as the castle remains big enough to hold the rightful heir. Do you see the loophole forming? There are many strange incidents as it goes on. The villain who is now ruling named Manfred wants to marry the son, marry his son off to a woman named Isabella who's the daughter of a Marquis, but in one of the novel's many supernatural events, a giant helmet falls out of the sky and crushes Conrad. Do you see the loophole forming? So Manfred then decides to marry Isabella himself, whom he, you know he's hoping that it'll kind of firm up his succession when and he's, there's another figure, a young peasant named Theodore that Isabella is really interested in. Anyway, push comes to shove at the end of the thing, guess what happens? Alfonso's ghost the rightful king, rears up and he's huge. I mean he's a ghost that's a really huge knight. The castle is not big enough to hold him, therefore everything is exposed, and Theodore the peasant turns out to be the rightful heir of Otranto and we have a happy ending in the end, okay? The ghosts are real. And one of the things that Walpole said about The Castle of Otranto which he published anonymously, was that later on he said, it's not everyone that may play the fool with impunity. Right so again it goes back to that model of artistic production. He's a nobleman, he has spare time, he can write a book, he can publish it. It's no big deal. Later on however, with the success of the novel, he takes it more seriously and he says in fact that the novel, The Castle of Otranto had he said, freed up great resources of fancy that had been damned up by common life. All right? So think again of Freneau's Graveyard and fancy. The novel, The Castle of Otranto, this Gothic novel which seems like kind of a trifle nevertheless has a role to play because it frees up these resources of fancy. Okay. Sir Walter Scott is you know one of the great historical novelists in this period and he would write later on that even the name of romance now so venerable in the ears, in the ear of the antiquaries of book collectors was almost forgotten in the time of The Castle of Otranto when The Castle of Otranto made its first appearance. And he added that Walpole had a decided predilection for what may be called the Gothic style, a term which he contributed not a little to rescue from the bad fame into which it had fallen being currently used before his time to express whatever what was in pointed and diametrical opposition to the rules of bad taste. Right, so the Gothic is, [inaudible] good true taste. So the Gothic is bad taste. Walpole starts to reclaim it. Brown wants to do something similar to reclaim the Gothic in the American context, okay. And there you can see what he says about it. Diametrical opposition to the rules of true taste. But it's interesting that the novel, the Gothic novel itself as a form doesn't take off in 1764. It has to wait about 25 years in and around the French Revolution and then it really takes off when a woman named Ann Radcliffe writes her Gothic novels. And Radcliffe had a slightly different formula than Walpole did in the writing of her novels. She used this formula by the way over and over. It goes something like this. There's a kind of dream landscape in which a young girl is fleeing in terror from some unknown or unnamed persecutors. Usually the place is given some Italian name, right, something like that. There appear to be manifestations of the supernatural. She often finds herself in the various kinds of settings crumbling castles, dungeons, graveyards, darkened churches. Usually she almost escapes her persecutors, then they catch her. They are trying to get her out of greed or lust or both. And usually there's a Theodore-like protector who's kind of chasing after trying to save the day. Usually, they catch up, they don't catch up, they're a menace. In the end, all of the ghosts and supernatural manifestations that have tyrannized her are shown to be fakes. They're people in costumes or [inaudible] effigy's or there's some machinery. It's a very popular formula and it continues to this present day. Does it remind anybody of anything? >> Scooby-Doo. >> [Music] Scooby dooby doo, where are you, we've got some work to do now. >> And I want you to understand something about it, if you go back to classic Scooby-Doo which would be the early the first season, [inaudible] on DVD 1969, the ghosts are never real. It's always Mr. [inaudible] in the blah blah blah. You remember in Wayne's World, [inaudible] see Wayne's World? Okay fine. [laughter] So, later on there was one cartoon called Scooby-Doo and Zombie Island or something where it's much later on and Daphne's like oh my god [inaudible] she's now a reporter she says but you know what, the ghosts are always fake so I'd just once like to find a real ghost so they go looking around New Orleans for a real ghost and eventually they actually find one. So you might say in that movie it breaks the formula, and in so and by breaking the formula it reaffirms the formula. Later on, the Scooby-Doo canon has become a little slack and there's been just too much of the actual supernatural. Classic Scooby-Doo is Ann Radcliffe. The ghosts are fake. Okay, but there's another tradition of Gothic that happens at the same time and this is the tradition of Gothic that is pioneered by this man, Matthew Gregory "Monk" Lewis who got this nickname because he wrote a very famous book called, The Monk. And The Monk you might say is really horrific Gothic. In it the ghosts are real. It is blasphemous. And, this is a French an illustration from a French translation of The Monk. The story goes something like this, again it's Italian right so you can see there's almost always in English Gothic a a kind of political anti-Catholic, anti-Italian sort of strain and you know anti-French I guess as well. So Juan Ambrosio is the abbot of the capechins [assumed spelling] and he's presented as a kind of admired preacher. Those of you who know Shakespeare's Measure for Measure might think of him as a lot like Angelo in that play. A man who's so repressed and severe that Shakespeare calls, what does he say? He scarce confesses that his blood flows. This guy Ambrosio's that kind of guy, except his blood does flow and he's soon readily corrupted by a satanic woman named Matilda who gains access to his cell by disguising herself as a young nun, although it, we have to remember that he's kind of already been enflamed in secret by fantasizing about a portrait of the virgin Mary which is hanging in his church for which this Matilda has posed. They become lovers, naughty, naughty. But he soon gets tired of her and of course she's promoting this, and he dreams of possessing a 15 year old girl named Antonia, who is the daughter of Elvira who is a noble lady who is one of his, you know in his parish. He's her confessor. With the aid of the satanic Matilda who conjures up the devil also for added backup, Ambrosia gets into Antonia's room and is about to rape her when Elvira enters. So he kills Elvira by smothering her with a pillow, gives Antonia a sleeping potion, and throws her in the dungeon. And later on, he does manage to rape her among the rotting dead. She cries out so he kills her. Okay. At the same time there's another woman who is there named Agnes. She's been imprisoned for other reasons down there and she actually gives birth to a baby down in the [inaudible]. I thought I would read you a little bit about this because it might remind, it might remind us a little bit of, yeah might remind us a little bit of Mary Rowlandson. Anyway, let's just listen to this, I won't bother to put it up. My, this is Agnes speaking toward the end of the novel, my grief unavailing, my infant was no more nor could my sighs impart to its tender little frame the breath of movement. I [inaudible] my winding sheet and wrapped in it my lovely child. I placed it on my bosom, it's soft arm folded around my neck, it's pale, cold cheek resting upon mine. Thus did its lifeless limbs repose while I covered it with kisses, talked to it, wept, and moaned over it without remission day or night. And then she says this, I vowed not to part with it while I had life. Its presence was my only comfort and no persuasion could induce me to give it up. It soon became a mass of putridity, and to every eye was a loathsome and disgusting object. To every eye but a mothers. In vain did human feelings bid me recoil from this emblem of mortality. With repugnance I was stood and vanquished that repugnance. I persisted in holding my infant to my bosom and lamenting it, loving it, adoring it. Hour after hour have I passed upon my sorrey couch contemplating what had once been my child. And later on she goes to describe some of the other nice things about her captivity. My slumbers were constantly interrupted by some obnoxious insect crawling over me. Sometimes I felt the bloated toad hideous and pampered with the poisonous vapors of the dungeon dragging his loathsome length across my bosom. Sometimes the quick, cold lizard roused me leaving his slimy track upon my face and entangling itself to the trusses of my wild and matted hair. Often I have at waking around my fingers ringed with long worms which spread in the corrupted flesh of my infant. So this conflation of this kind of carnal house, you know disgusting flesh, morbidity, is part of this stream of the Gothic in which as I suggested the supernatural as real. We should go back to the story of Ambrosio. Ambrosio of course is being you know, finally the Napoleonic troops start to try to find him. He manages to escape their clutches by selling his soul to the devil. Except he doesn't quite specify the terms of the bargain well enough so he's immediately transported by a demon to the top of a mountain peak where he is told hey guess what Elvira, remember you murdered her? She was your mother. And that makes Antonia whom you raped and murdered, uh yes that would be your sister. And then he's thrown to his death. [laughter] All right. So that is the other kind of Gothic. The ghost's real. And you could see how there's a kind of weird conflation of supernatural demonic activity, sexuality, violent and disgusting death. I mean this is come all the way down to current slasher movies and other, and you know the kind of torture porn that people have been watching the last couple of years. It's all part of this larger idea of this strain of Gothic, the kind of anti-Radcliffe Gothic. And one last thing to say about this is the, what I just read to you from The Monk really might be considered a form that we could call the anti-sublime, right? Oh I've actually put them up. I guess I thought I wouldn't, but here we go. Shriek with terror and disgust while I shook off the reptile. Very good. So, one of the famous treatises in this moment was Edmond Burke's on the Sublime and the Beautiful what is well-formed and aesthetically pleasing, whereas the sublime is what has the power to compel and overwhelm us. All right so formal gardens are beautiful, but this, is the sublime. All right, and you could think again of those moments in Edwards. Edwards is pioneering the sublime when he thinks about the thunder and the kind of awful majesty. It's beautiful, but it's frightening at the same time. The sublime is kind of like the romantic emotion par excellence. It's what they are try, they are striving to recreate. In a sense, Matthew Lewis's you know disgusto Gothic is actually making fun of that. It's doing what might be called the anti-sublime. But you can see that this discourse of the sublime, is part of what Brown is drawing on in Edgar Huntly as well as he sends Edgar out into the wilderness. But the sublime, if the wilderness is about the sublime for many romantic writers, for Edgar Huntly the wilderness becomes about something else altogether. All right, one last thing. Terror and disgust is what Agnes feels in The Monk. Ann Radcliffe makes a distinction between what she calls, let me see if I have it here, the distinction between terror and horror. And she says that horror closes down the mind, whereas terror opens you up. So, and terror would therefore be linked to the sublime and the faculty of imagination. So Monk Lewis' Gothic is horror. Her Gothic she would've offered was a form of terror, okay? Finally, this is a rather famous if somewhat overstated account of what's going on in the Gothic novel. It comes from a moment when Freudian criticism was very much in the [inaudible]. This is still a very interesting book although if you read the subtext of the book, it suggests it's an account of American literature says that a lot of American literature is about cross-racial friendships and more between men. Huck and Jim for example [inaudible] American relationship. [Inaudible] he has a wonderful chapter on the Gothic novel and [inaudible] writes this, the guilt which underlies the Gothic and motivates its plots is the guilt of the revolutionary haunted by the paternal past which he has been striving to destroy. And the fear that possesses the Gothic and motivates its tone is the fear that in destroying the old ego ideas of church and state, the west has opened a way for the eruption of darkness, for insanity, and the disintegration of the self. Through the pages of the Gothic romance, the soul of Europe flees its own darker impulses. And I think there's a cultural reason why Gothic takes off, not when Walpole writes, but when Radcliffe and Lewis do, in the aftermath of the French Revolution, right? All those democratic ideals, liberty, equality, fraternity, turn into the horror of the terror, and that's a terror that is a horror. You know when all the heads being chopped off. And then finally the Napoleonic era which is the re-institution of anti-democratic principles. So, the experience, the cultural experience of the French Revolution would suggest that this regime of reason is not all that it is cracked up to be. And you could see that in the United States there's this idea that in overthrowing what [inaudible] calls the old ego ideals of church and state we're opening up a new, a new moment. Right what, remember Jefferson's quote, that not everyone is born to be booted and ridden by other people. There's grounds of hope for everybody, he says. But it also means destroying old systems of obligation. You know when things went wrong the Puritans could if not blame, they could understand that there was a reason for things because it was part of God's will. What happens when you take God out of that equation, and you say this is all you know we're gonna rest it all on human beings. And then human beings turn out to be not all they're cracked up to be. What if the total depravity of human beings is true, not because of something called the fall of human kind, but just because that's human nature? Then, we've got a big problem. All of this you might say is the context for Charles Brockden Brown's Edgar Huntly. Okay? Now, let's take a look at the first pages of this. This is the preface to Edgar Huntly on page 1 of the text. Edgar Huntly, Or, Memoirs of a Sleepwalker. It's in the part that's called, to the public, right? And this lays out what we might think of as the project of American Gothic. Look at the third paragraph, well no let's just look at the whole thing. So, he says America has opened new views to the naturalist and politician but it has seldom furnished scenes to the moral painter. Again that idea of the novelist as moral painter. That new springs of action and new motives to curiosity should operate that the field of investigation opened to us by our own country should differ essentially from those which exist in Europe may be readily conceived, the sources of amusement to the fancy, imagination, and instruction to the heart that are peculiar to ourselves as Americans are equally numerous and inexhaustible. It is the purpose of this work to profit by some of these sources to exhibit a series of adventures growing out of the condition of our country and connected with one of the most common and wonderful diseases or afflictions of the affections of the human frame, right, sleepwalking. One merit the writer may at least claim that of calling forth the passions and engaging the sympathy of the reader by means hitherto unemployed by preceding authors, right? So over against things called the power of sympathy, he's presenting this. Puerile superstition and exploded manners, Gothic castles and chimaeras are the materials usually employed for this end right? If you're not writing seduction obviously you're writing Gothic. And if you're doing English Gothic you're writing about these stupid things. But here in the United States we have an opportunity. The incidents of Indian hostility and the perils of the western wilderness are far more suitable and for native of America to overlook these would admit of no apology. These therefore are in part the ingredients of this tale, and these he has been ambitious of depicting in vivid and faithful colors. The success of his efforts must be estimated by the liberal and candid reader. So that's the project of American Gothic, and that whole question of what are we supposed to do. I mean you know again think of Barlow; I'm gonna use Neoclassical poetic machinery, I'm gonna give it a new world subject the hasty pudding and we're gonna come out with this great poem. Barlow's gonna say I'm gonna use these [inaudible] and frankly they were always kind of childish resources that the English Gothic novel has used. But I'm gonna give them teeth by setting them in real life. Come on there's no such thing as giant knights and you know demons and all that stuff, but there are monsters in those woods here in the United States, all right? I'm gonna write about those. Take a look at the beginning of the novel, all right? It is adopting this epistolary form. So it's a series of letters that Edgar Huntly is writing down. Page 5, I sit down my friend to comply with thy request. At length does the impetuosity of my fear as the transports of my wonder permit me to recollect my promise to perform it. At length am I somewhat delivered from suspense and from tremors. At length the drama is brought to an imperfect close in series of events that absorbed my faculties that hurried away my attention has terminated in repose. So, it's a quiet moment. It's all over. Look at that, the language that he uses already is the language of enlightenment right? My faculties. Terminated in repose. This will, proleptically remind us of what Wordsworth would later write about the way poetry springs, from emotion recollected in tranquility. That's theoretically what we're getting here, emotion recollected in tranquility. Turn the page. The second full paragraph he says this, how short is the period that has elapsed since thou and I parted, yet how full of tumult and dismay has been my soul during that period, exclamation point. What light has burst upon my ignorance of myself and of mankind, exclamation point. How [inaudible] and enormous the transition from uncertainty to knowledge, exclamation point. Look at the tropes. Light burst on my ignorance. Transition from uncertainty to knowledge. It sounds like you know he's talking about I don't know what, the defense of Fort McHenry all right the way we described that. So this is theoretically going to be a story about enlightenment. Is it? Is this a story about enlightenment? Let's skip a little bit further on. Let's take a look on page 15. You know the situation right? He has a good friend Waldegrave who's been killed. So this starts off as if it's almost kind of a proto-detective novel. He's gonna figure out who killed Waldegrave right? That would seem to be the issue of the text, and then he finds this guy kind of hanging around, and he's starting to put two and two together. So he starts being interested on this guy whose name happens to be Clithero Edney. So Edgar Huntly becomes interested in Clithero Edney right? Remember what I said about doppelgangers last time. Take a look on page 15. This is in the second chapter. Found it? He worries about the possibility of behaving rashly here he says. Take a look at the second, second to last paragraph on the page. But it suddenly occurred to me for what purpose shall I prosecute this search? What benefit am I to reap from this discovery? How shall I demean myself when the criminal, all right the one who murdered Waldegrave, is detected? I was not insensible at that moment of the impulses of vengeance. But they were transient. I detested the sanguinary resolutions that I had once formed. Right and that's a form of [inaudible] right, for talking about being bloody minded or being revengeful. Yet I was fearful of the effect of my hasty rage and dreaded an encounter in consequensive wish I must, I might rush into evils which no time could repair, nor penitence expiate. Okay good thing, he's worried about behaving rationally. But look how quickly he rationalizes and changes his mind. But why said I, should it be impossible to arm myself with firmness? If forbearance be the dictative wisdom can it be so deeply engraven on the mind as to defy all temptation, and be proof against the most abrupt surprise? My late experience has been of use to me. It has shown me my weakness and my strength. Having found my ancient fortifications insufficient to withstand the enemy, what should I learn from thence but that it becomes me to strengthen and enlarge them. No caution indeed, he says, can hinder the experiment from being hazardous. Is it wise to undertake experiments by which nothing can be gained and much may be lost? Curiosity is vicious if undisciplined by reason and inconducive to benefit. Now again, key terms from The Enlightenment here: Experimenting, progress, science. Right? Except that he's gonna be experimenting with a person who might well be a murderer and might well be insane. And he says oh curiosity if vicious if undisciplined by reason. Okay, so we can keep curiosity in check and disciplined if we use our reason. But how does that square with what he says in the next paragraph? I was not however to be diverted from my purpose. Curiosity, like virtue, is its own reward. Knowledge is a value for its own sake and pleasure is a next to the acquisition without regard to anything beyond. It is precious even when disconnected with moral inducements and heartfelt sympathies. But the knowledge which I sought by its union with these was calculated to excite the most complex and fiery sentiment in my bosom. Ask yourself is there something wrong with that pattern of reasoning. Seems reasonable at first but, is curiosity, like virtue its own reward? Virtue never killed the cat, right? Curiosity may not be as valuable or as you might say free from danger. Is knowledge a value for its own sake? And is it true that it's valuable, but it's even more valuable when you have a personal stake in it? There's something odd about Edgar's reasoning here, and the text is, you might say that this is again one of these texts where the way which Brown has put it down seemingly through the words of Edgar should be allowing us to open up space between what Edgar is ostensibly realizing about himself and what we are realizing about Edgar. Take a look a few pages on on page 31 now, and we'll see that as a man of reason, Edgar has now decided not to seek vengeance. He decides instead to be something like Clithero shrink or his comforter or perhaps blasphemously, his priest. Middle of the page on 31, I am a stranger to your knowing cares, to the deep and incurable despair that haunts you to which your waking thoughts are [inaudible] from which sleep cannot secure you. I know the enormity of your crime, but I know not your inducements. Whatever you were I see the consequences with regard to yourself. I see proofs of that remorse which must ever be attendant on guilt. That is enough. Why should the efforts of our misdeeds be inexhaustible? Why should we be debarred from comforter? An opportunity of repairing our errors may at least be demanded from the rulers of our destiny. Look at that Franklinian language there, right? If we admit that there's destiny come on the rulers have at least to give us the opportunity of repairing errors, our own and he seems to think here, other people's. So we're right in the Franklinian enlightenment mode here. I once imagined that he who killed Waldegrave inflicted the greatest possible injury on me. That was an error which reflection has cured. [Inaudible] laid open to my view and events with consequences unfolded, I might see reason to embrace the assassin as my best friend. Be comforted, he says. And he says Clithero was still incapable of speaking here. All right, this is the confidence of enlightenment thinking. This is the kind of thing that somebody like Franklin would believe. He can diagnose what's wrong with this person. He can help him. Right? Take a look a little bit further down on page 32. This is couple of sentences into the long paragraph there. My condition was not destitute of enjoyment. My stormy passions had subsided into a calm, portentous and awful, and that's the language of the sublime. My soul was big with expectation. I seemed as if I were on the eve of being ushered into a world whose scenes were tremendous and, now he uses the term, sublime. The suggestions of sorrow and malice had for a time taken their flight and yielded place to a generous sympathy which filled my eyes with tears but had more in it of pleasure than of pain. That Clithero was instrumental to the death of Waldegrave that he confers [inaudible] explanatory to every bloody and mysterious event that [inaudible] occurred that was no longer a possibility of doubting. He is indeed said I, the murderer of [inaudible] yet it shall be my promise to emulate a father's clemency and restore this unhappy man to purity and peace. That you might say is the ultimate statement of enlightenment principles and also of enlightenment hubris. The enlightenment will take the place of Calvinism, Christianity and everything else. Edgar will fulfill the role of a father confessor. He will dispense the healing balm of rationality and reason, right? How does that work out? Chapter 4, page 34. The bottom of the page, Clithero abrades him. You were unacquainted with the man before you. The inference with to have drawn with regard to my designs and my conduct are a tissue of destructive errors. You like others are blind to the most momentous consequences of your own actions. You talk of imparting consolation, you boast of beneficence of your intentions, you set yourself to do me a benefit, and what are the effects of your misguided zeal and random efforts? They have brought my life to a miserable close. They have shrouded the last scene of it in blood. They have put the seal to my perdition. It's anti-enlightenment right? Instead of having a design, it's a tissue of destructive errors. It's random efforts and misguided zeal. Clithero portrays Edgar here not as a redeeming confessor, but as an agent of perdition, of damnation. And if we look at what happens in these 4 chapters right, Chapters 4 through 8, which his Clithero's story, we see that it's clear that he actually has had nothing to do with the death of Waldegrave. And the story reinforces the novel's picture of identity as confusing and inconstant right? Think about the motif's in there. There's that strange co-partnership of being that Mrs. Loramer has with her brother Arthur Wyatt as if they weren't really somehow separate people that they might share the same kind of soul. Wyatt who was taken for dead, turns out to be alive, though he doesn't turn out to be alive for long. Clithero takes Clarice, who is Mrs. Loramer's niece, and his fiancee to be Mrs. Loramer and he almost kills her, and then he descends into madness which is a state of sleepwalking in which Edgar finds him. So that you might say that Clithero's story in these 4 chapters act as a kind of narrative counterweight to the primacy of reason that Edgar is trying to say this larger story is about, is a dramatization of. Take a look on page 88. Clithero is proof you might say that a rationality even madness is alive and well in the world and very powerful. And yet, you might say, Edgar refuses to believe this. On page 88, he describes himself as a dispassionate observer still. And later on, take a look at this on page 90, he still is unwilling to accept the evidence of what is in front of him. He says this, at the very bottom about 3 lines up from the bottom of 90, could I not restore a mind thus vigorous to tranquil and wholesome existence? Could I not subdue his perverse disdain and immeasurable abhorrence of himself. His [inaudible] were unmerited and misplaced. Perhaps they argued frenzy rather than prejudice but frenzy like prejudice was curable. Reason was no less an antidote to the illusions of insanity of his and to the illusions of error. So we're 90 pages in, we've heard this story about madness and unstable identity and Edgar still believes in reason. He believes in the ability to know another person, to be able to see what's going on within another person through the application of reason. Take a look at page 111. This is in the middle or about 3 lines into the [inaudible] first full paragraph, right? He's talking about trying to understand Clithero. If he were thoroughly known his character might assume a new appearance, and what is now so difficult to reconcile to common maxims might prove consistent with them. It's like it doesn't look like it makes sense but he believes there's got to be some design, something he can discover that will make it all make sense. I desire to restore him to peace but a thorough knowledge of his actions is necessary both to show that he is worthy of compassion and to suggest the best means of knowledge. So what is Edgar gonna do? A little breaking and entering. Take a look on the next page, Chapter 12, The Box. I surveyed it with the utmost intention. All its parts appeared equally solid and smooth. It could not be doubted that one of its sides served the purpose of a lid and was possible to be raised. Mere strength could not be applied to raise it because there was no projecture which might be firmly held by the hand and by which force could be exerted. Some spring therefore secretly existed which might forever elude the senses, but on which the hand by being moved over in all the directions might accidentally light. So look at that. He says physical force isn't gonna work, but he can use his reason to come up with a mechanism. But interestingly that mechanism has to make use of accident. Accidentally light. The process was effectual. A touch, casually applied at an angle drove back a bolt and a spring at the same time was sent in action by which the lid was raised above half an inch. No event could have been supposed more fortuitous, by chance than this. And a hundred hands might have sought in vain for the spring, the spot at which a certain degree of pressure was sufficient to produce this effect was of all the last likely to attract notice or awaken suspicion. I opened the trunk with eagerness. The space within was divided into numerous compartments, none of which contained anything of moment. Remind you of anything? Tools of different and curious constructions and remnants of minute machinery were all that offered themselves to my notice. My expectations being thus frustrated, I proceeded to restore things to their former state. I attempted to close the lid, but the spring which had raised it refused to bend. No measure that I could adopt enabled me to place the lid in the same situation in which I had found it. In my efforts to press down the lid [inaudible] in proportion to the resistance that I met with, he's trying to force it, the spring was broken. This obstacle being removed the lid resumed its proper place, but no means within the reach of my ingenuity enabled me to discover, to discover enabled me to push forward the bolt and thus to restore the fastening. I now perceive that Clithero had provided not only against the opening of his cabinet, but likewise against a possibility of concealing that it has been opened. So this is one of these da da da da scenes that you should be looking at as kind of an exemplary moment. What's going on here? What's the immediate ideas that this scene conjures up for us? It's a box. Anything? Any, yeah? >> [Inaudible] >> Okay so it's reason, used to open a box that can't be closed. Let's take that as a starting point and go further with it. Remind you of anything else? >> [Inaudible] >> Yeah, it's called Pandora's Box, okay? Pandora's Box. What happens in Pandora's Box? Don't open it, don't open it, don't open it. Then what happens? What comes out? >> All the bad things. >> All bad stuff. One thing doesn't come out. Stays in there for use later. The thing with feathers. >> Hope. >> Hope, yeah. Think about what that, so that's one cultural reference right? Clearly Pandora's Box, it's a way of understanding what's happened. But you might say it's also another way of figuring what's happened with Clithero's mind right? He says I want to know something about Clithero. He in fact has learned something. He through his, you know insinuation of himself into the circumstance, Clithero says you've sealed my the damnation right? You've opened Clithero's mind up. Now what's in there is out and it can't go back in. You've unleashed this madness, right? The box cannot be restored to its former state. And if you look inside it does look like it's a little bit of a kind of parody of the enlightenment mind. It has lots of compartments, it has kind of machinery. But Edgar can't understand it. Think back to your Columbus [inaudible]. No kings, no cities, people without [inaudible] nothing of importance. Edgar says well whatever's in here it's not important. But maybe he's missing something about what's important. Or maybe the important thing is you weren't supposed to break into the box and now that you have, there's no way to set things right again. But what we want to ask is if this is clearly a metaphor for the cultural situation, for the situation with Clithero, is it also a metaphor for what's going on with Edgar's mind as well? Is something happening to Edgar that he doesn't quite understand? It makes us doubt for one thing surely his neutrality, his rationality right? I mean again think of those [inaudible] that I told you about where they seem reasonable, they seem reasonable, they seem reasonable. Then they describe how they murdered somebody. Wow they're not reasonable anymore. They're kind of nuts. Is Edgar switching over into something else? And this this account of breaking into the box seems a little [inaudible] but, in a kind of neutral sentence like, in my efforts to press down the lid which were augmented in proportion to the resistance that I met with it, the spring was broken. I mean, you know the language is keeping you at a distance but you can see him starting to get a little pissed off, right? And reason is having a more tenuous hold here. Chapter 13, the chapter that follows cements our understanding of the perils between Clithero and Edgar. It give us an account of Edgar's relationship with Waldegrave. It gives us our first glimpse into Edgar's personal history. It comes fairly soon after Clithero's account of himself and so it invites us to compare the two. I mean, Clithero's actions suggest that Clithero is wracked by guilt. But the opening of Chapter 13 suggests that Edgar may be feeling guilty too because you might say he's torn by conflicting allegiances to his dead friend Waldegrave and to Mary. Take a look on page 124 where Edgar tells us that he isn't sleeping very well. But it isn't Clithero that appears in his dream. Third sentence, the top of the page. What however was nearly banished from my waking thoughts occurred in an incongruous and half seen form to my dreams. During my sleep the image of Waldegrave flitted before me. Me thought the sentiment that impelled him to visit me was not affection or complacency, but inquietude and anger. Some service or duty remained to be performed by me which I had culpably neglected, to inspire my zeal, inspirit my zeal to awaken my remembrance and insight to me to the performance of this duty, did this glimmering messenger, this half indignant apparition come. And now he recalls his promise that he's made to Waldegrave's sister to transcribe for some of Waldegrave's letters preserving for posterity what he calls at the top of the next page, the intellectual existence and moral pre-eminence of my friend. So he decides to postpone his searching for Clithero for a day in order to fulfill his promise. But then it occurs to him that maybe he's misinterpreted the vision of Waldegrave. Maybe Waldegrave is appearing to him in order to keep him from transcribing those letters. And now some dodgy things come to light. Bottom of 125 we find out that Waldegrave might have been thinking some things that he maybe shouldn't have been thinking about. Bottom of the page, and again this is maybe a critique of The Enlightenment. Waldegrave like other men early devoted to mediation and books had adopted a different [inaudible] different systems of opinions on topics collected with religion and morals. His earliest creeds tended to efface the impressions of his education to deify necessity and universalize matter, to destroy the popular distinctions between soul and body and to dissolve the supposed connection between the moral condition of man anterior, and subsequent to death. This creed he adopted with all the fullness of conviction and propagated with the upmost zeal. Soon after our friendship commenced, fortune placed us at a distance from each other and no intercourse was allowed but by pen. Our letters however were punctual and copious and those of Waldegrave were too frequently devoted to the defiance of his favorite tenets. But when Edgar looks for these letters, on page 128, he finds that they're missing. This is the second full paragraph. I've perceived, he says, thou canst not imagine my confusion and astonishment when on opening the drawer I perceived that the packet was gone. I looked with more attention and put my hand on it, within it, but the space was empty. Wither had it gone, and by whom was it purloined? I was not conscious of having taken it away, yet no hands but mine could have done it. On the last evening I had doubtless removed it to some other corner but forgotten it. And when he can't find the letter he finds himself lost in horror and amazement. I think it's this chapter if by now we haven't already that we start to realize that there is something wrong with Edgar's thinking process. Even more so perhaps on page 130 when his uncle starts quizzing him about what he was doing last night. But why did you go upstairs the uncle says. You might easily imagine that the sound of your steps would alarm those below who will be puzzled to guess who it was that had thought proper to amuse himself in this manner. Upstairs? I have not left my room this night. It is not 10 minutes since I awoke and my door has not since been opened. Edgar has no idea that he's sleepwalking, right? So one of the things that we have to realize here, already we're starting to see that Edgar has a somewhat mysterious personal history and it's a personal history that is not dissimilar to the personal history of Clithero. The two of them are being developed by the novel as doppelgangers, as doubles. Now, Chapters 14 and 15 are chapters that probably don't get fully worked out in the course of the novel. They are, they involve the appearance of a stranger named Weymouth who claims that Mary's inheritance from Waldegrave belongs to be their own. I mean, it's actually his own. And Waldegrave hasn't left a record of it, but Edgar believes Weymouth's claim, and something else comes out. This is on page 149. [ Pause ] Middle of the long paragraph. Oh wait let's start at the top of the long paragraph. Think upon the merits and misfortunes of your brother's friend, think upon his aged father whom we shall enable him to rescue from poverty, think upon his desolate wife, he's talking about Weymouth, whose merits are probably at least equal to your own and whose helplessness is likely to be better, greater. I mean he's a good guy, he wants to do the right thing, right? I am not insensible to the evils which have returned upon us with augmented force after having for a moment taken their flight. I know the precariousness of my condition and that of my sisters, that our subsistence hangs upon the life of an old man. My uncle's death, will [inaudible] will you know he's living, he and his sisters are living with his uncle after the death of his parents, by I think who were killed in an Indian raid. My uncle [inaudible] will transfer this property to his son who is a stranger and an enemy to us. And the first act of whose authority will unquestionably be to turn us forth from these doors. Marriage with thee was anticipated with joyous emotions not merely on my encounter on thine, but likewise for the sake of these beloved girls to whom that event would enable me to furnish an asylum. But wedlock is now more distant than ever. We start to see that there's a whole property motif that is sort of hidden and starting to come up to the surface here. You know, life, liberty and the pursuit of happiness means life, liberty and the pursuit of property. He's been banking his whole future on the fact that Mary is supposed to inherit from Waldegrave. What doesn't, what happens if that doesn't happen? All right? So there's a whole way in which you might say Edgar is self interested, that he only reveals to us you might say in the margins of the narrative. He doesn't actually address it. All of his future plans have in fact been prompted by Waldegrave's death. Because of Waldegrave's death he could imagine marrying, he said it's a disastrous event and yet it's paving the way for his future happiness. All the sudden just as it happened for Clithero the past is suddenly beginning to impinge on Edgar. Take a look at page 90, because now something decisive happens. We'll backtrack a little bit. Bottom of page 90, he's talking about the woods as a place where he learns and has aesthetic experiences, bottom of page 90. Thou knowest my devotion to the spirit that breathes its inspiration in the gloom of forest and on the verge of streams. I love to immerse myself in shades and dells and hold congress with the solemnities and delicacies, secrecies of nature in the rude retreats of Norwalk. The disappearance of Clithero had furnished new incitements to ascend its cliffs and pervade its thickets. And again you might say, it's this whole you know business of the sublime right? I mean that's what he's talking about there. As I cherish the hope of meeting in my rambles with some traces of this man, but might he still not live? His words had imparted the belief that he intended to destroy himself. This catastrophe however was far from certain. Was it not in my power to avert it? Could I not restore a mind thus vigorous to tranquil and wholesome existence? Right, we get back to that. So Edgar has thought of himself as a man of The Enlightenment, a man of science. He's gone for walks in the woods. But what we suddenly realize after all this has happened is that he hasn't fully mapped those woods. For one thing, he's only been there in the daylight. For another thing, he hasn't fully mapped his mind in the same way either, right? So one of the things that Brown does as you might say maps the woods onto Edgar's mind. In exploring the woods as you might say in exploring the box, Edgar starts exploring facets of his own mind that have remained hidden from view. Take a look a couple of pages on on page 151 and all of the sudden we see that there's a kind of a break in the narrative. And he says this: possibly the period will arrive when I shall look back without agony on the perils I have undergone. That period is still distant. Solitude and sleep are now no more than the signals to summon up a tribe of ugly phantoms. Famine and blindness and death and savage enemies never fail to be conjured up by the silence and darkness of the night. I cannot dissipate them by any efforts of reason. Reason now completely fails him. My cowardice requires the perpetual consolation of light. My heart droops when I mark the decline of the sun and I never sleep but with a candle burning at my pillow. Right, so from the confidence of enlightenment, now it's the pathetic I need to have a nightlight on, right? That's what Edgar has sunk to. What has caused all of this? His experience in the woods. And we'll take it up again on Wednesday, the experience of the woods. One thing I'd like you to do in addition to reading the short stories of Irving's that are assigned for next time which elaborate on this theme of Gothic and reason, is to take a little look at Edgar, the pit, and the panther. I want you to look for the motif of light in the panther scene, and also track one particular word, and that word is savage. All right we'll leave it there. Thanks a lot. |
Open_Ed_Cyrus_Patell_American_Literature | American_Puritanism_II.txt | >> Alright let's take care of a few business items first before we get started with today's fun and games. You've got a paper coming up. We've discussed it as a teaching staff and we decided to push it off a week. Of course you could always turn it in sooner. But we wanted, it's about poetry. And we're going to take the most challenging of the poets that we're going to have read up until that point and ask you to write about one of the poems that we're not doing in class. So we thought it might be a nice idea if all of you had at least one session in section in which you could talk about the analysis of poetry and particularly puritan poetry. And to sort of do the kind of analysis orally and together that you'll then be called upon to do in written form. So we're going to push that off but I am going to make the assignment available online almost immediately after the class or later this afternoon, later this evening. So that's one thing. At the same time I'm also going to make available the scavenger hunt assignment which isn't due then, it's due basically the Friday before the mid-term. So there's more time for that. But it's a good thing to have in mind as a task as you begin the process of reading the poetry that we're going to be doing over the next couple of weeks in part because the poetry provides the most fertile ground I think for discovering the kinds of things that you're going to be looking for. Typically speaking again we're asking you to do something that's related to using the literature major's tool box. Especially in formal terms. So we'll be asking you to look for stuff. A metrical foot, not an IM but something else like an anapest trochee dactyl spondee. And we'll be asking to look off of two other kinds of figurative language, figures of speech, and figures of rhetoric. We'll give you a few of these to choose from. And the goal will not only be to find it, but to figure out what it's doing there. Or you might say to figure out what the effect is that the poets, or really you could use it from prose too, the writer in general, what effect is the writer getting out of the use of that particular metrical foot or rhetorical device in that moment. Alright? So we'll be doing a little bit of, it's not only just finding, but it's talking about how it works. And of course to talk about how it works you'll need to be thinking about things like language, rhythm, syntax, diction, and also meaning. How is the way in which this meaning is being expressed affect the creation of that meaning itself. Okay? So that's, we'll have both of those things available and you should take a look at them if possible before section this week, so even tonight, so you could ask your sections row about questions that you might have. And there'll be opportunity to do that next week as well. But I think again the point of these two assignments is to get you to be thinking about what it means to do close reading and to think about what's at stake in it. One thing I should say about the paper assignment is it has a word limit indicated. We want you to adhere to that word limit. And part of the reason for doing that is we basically want you to go through these poems when you read them and mine for evidence of different kinds, evidence that has to do with meaning, and evidence that has to do with formal attributes. We would love you to find more evidence that you could actually use and to have to take out some of the things that you might have used in order to fit it in to the length. And we want you to make your best arguments using your best evidence. Okay? But to start with that, you'll need to kind of make a catalog of the possible evidence that you could use. Okay? So we'll have, we'll be able to talk a little bit more about that as the weeks go by. The second assignment in the course, we'll ask you to do basically the same thing for a piece of prose rather than poetry. And then later on you'll do a final paper of a topic of your own choosing in which we're hoping you'll put together the kinds of analysis that you've been doing in these shorter papers and may be able to mobilize it in the service of the slightly longer argument of your own devising. Okay. Are there any immediate questions about that? Alright. In that case we'll press on with the Puritans. I fought the law, the law won, right? It almost always does. A antinomianism is one of our subjects for today and it comes from the Greek words anti nomas [assumed spelling] which means, against the law. And one of the things are going to see is the way in which Anne Hutchinson sets herself against at least one version of what some puritans think is the law. And hence antinomianism is a kind of derisive term is applied to her and the people who were her followers and later on it becomes something of a caution for people in the romantic era. Both Emerson and Hawthorne are very aware of the idea of antinomianism and want in some sense, for Emerson he wants to be avoid being seen to be someone who follows Anne in that tradition. Hawthorne has a more complicated relationship to antinomianism as we will discover. But before we do that, I wanted to finish up some conceptual business from last time. So I'm going to show you a brief clip that I didn't have a chance to show less time, which comes from President Reagan. And it is his account of Winthrop when he finally names Winthrop and talks about him, but I also want you to just listen to the way this moment of the speech can be seen to work as a piece of rhetoric and to think about what it is that he is promoting in addition to, you know, thinking about the individual and the community. So let's take a look at this together. [ video/audio of President Regan ] >> I'm warning of an eradication of that, of the American memory that could result ultimately in an erosion of the American spirit. Let's start with some basics. More attention to American history, and a greater emphasis on civic ritual. And let me offer lesson number one about America. All great change in America begins at the dinner table. So tomorrow night in the kitchen I hope the talking begins and children, if your parents haven't been teaching you what it means to be American let them know and nail them on it. That would be a very American thing to do. And that's about all I have to say tonight except for one thing, the past few days when I've been at that window upstairs, I thought a bit of the shining city upon a hill. The phrase comes from John Winthrop, who wrote it to describe the America he imagined. What he imagined was important, because he was an early Pilgrim, an early freedom man, he journeyed here on what today we'd call a little wooden boat. And like the other Pilgrims, he was looking for a home that would be free. I've spoken of the shining city all my political life. But I don't know if I ever quite communicated what I saw when I said it. But my mind, it was a tall proud city built on rocks stronger than oceans, windswept, God blessed and teeming with people of all kinds living in harmony and peace. A city with free ports that hummed with commerce and creativity and if there had to be city walls the walls had doors and the doors were open to anyone with the will and the heart to get here. That's how I saw it and see it still. And how stands the city on this winter night? More prosperous more secure and happier than it was eight years ago, but more than that, after 200 years, two centuries, she still stands strong and true on the granite ridge, and her glow has held steady no matter what storm. And she's still a beacon, still a magnet for all who must have freedom. For all the pilgrims from all the lost places who are hurtling through the darkness toward home, we've done our part. And as I walk off into the city streets a final word to the men and women of the Reagan revolution, the men and women across America who for eight years did the work that brought America back. My friends, we did it. We weren't just marking time we made a difference. We made the city stronger. We made the city freer, and we left her in good hands. All in all, not bad. Not bad at all. And so goodbye, God bless you, and God bless the United States of America. [ end video/audio of President Regan ] >> The great communicator. And he had that kind of folksy homespun storytellers way. George HW Bush tried to emulate him, but it didn't work so well. And you might say that George W. Bush, his real political father isn't his own father but that guy, Ronald Reagan. And I think that's what George W. Bush aspired to. That vision of America, that Reagan had. It became a little bit, let's just say in the years after that maybe some of the assumptions that Reagan makes became a little more problematic. So what is the vision of America that Reagan talks about? I'm particularly interested in what you think some of the continuities and the discontinuities might be with say Winthrop's vision of America. I already suggested to you one thing last time. Winthrop is promoting the idea of community over and above the idea of the individual. We're going to harness individual energies, but we're going to harness them, they're going to serve the community, they're going to serve God's purpose above all. Reagan changes things a little bit around. I mean, he sort of thinks that the starting point has to be the individual. And then it's almost like with the logic of laissez-faire. You start with the individual, let the individual pursue his or her senses of the good, her economic interests and all good things will follow. But what else, what have some of you, did you notice some of the things that he said about America or how to be American? Yeah. >> What's interesting is that he talks about diversity in everyone. >> Okay diversity. >> Different and then coming together but his first point is, it starts at the family table. Which is interesting because that excludes, you know, I don't know, a percentage of people would not consider themselves to be part of a family table kind of atmosphere. But I mean, nowadays it's not uncommon to not have that family table kind of thing. So it's interesting to say this is where it begins and kind of inherently. >> Alright so there's a presumption of a typical or traditional American family perhaps? One that has the luxury of everybody gathering at the table. So clearly dad is not working the night shift and unable to be at the dinner or mom is able to be there and you know, there's a certain, so there's, you can see that there's a certain idea of the family that I think you're right about that behind that. But think about the logic of that then. If it begins with the family table and then he gets to the idea of diversity. You know, he hasn't talked right in the moment about the individual but you could see in his mind there's almost a kind of progression. Promote individualism, we promote family life. Why? Because you have kids and you want to care about them. And then ultimately we have the sense of the nation as one large family you might say. There's an interesting analysis, which we'll probably talk about later in the term of the fact that the family is an overriding metaphor for American people and yet one of the things we realize is when we start talking about families, and I think your point is getting at this, we may not all have the same idea of what constitutes a family or an ideal family in mind. And so we'll talk a little bit later on about really, you know, there's a kind of powerful metal metaphor metaphorical language of the family. But the fact that the metaphor obscures the fact that people have radically different notions about whether a family should be run by say a strict father figure who is an authoritarian and is kind of like, you know, like, God's representative in the family unit. Or by nurturing parents, both of whom are kind of equal who are setting a model for behavior for their children rather than laying down, as it were, the law. So I think that's some things to bear in mind. Yeah what else. Did you have something you want to add? >> Regan was talking about the doors being open and that he wants the heart and the will to make it [inaudible]. But I mean, I don't think Winthrop was at all interested in [inaudible] he saw differently than they did [inaudible]. >> Alright so the doors were opened for them. >> Right. >> And you might say yes, that idea of diversity is not something that comes along with Puritanism. So that would be another way I would suggest in which Regan is breaking with the Puritans at least in rhetoric. Although again we might want to think about you know, how deep that commitment to diversity actually goes. Or what it is that Regan thinks he means when, you know, all these people are coming and what kinds of people are they going to be really. There's a certain, there's a joke about the melting pot which is, I don't even know who told this joke originally, that you know, people come in from all different kinds of race, religions, and ethnicities and basically everybody comes out Presbyterian, right? [ laughter ] The melting pot is a homogenizing pot. You all come out the same thing. Well, we have a different conception I think, today of what diversity could and should mean. So that's one of the ways in which you might say Regan. Regan, that belongs to the moment before the so called culture wars in this country which take place kind of towards the end of Reganism and beyond, before multi-culturalism becomes kind of an assumption that most people have within institutions of higher education. So it's important to think about Regan in that moment. Anything else? I think he is right about the sense of ritual and I want to talk a little bit more about that today. And I think that's one of the ways in which there is a continuity between Regan and the Puritans. Both of them understand the power of rituals. For him. It's kind of like daily rituals like having the dinner table together. For the Puritans it was a larger sense of communal rituals mostly oriented around the church and around sermons. And of course around the Communion table as well. So these are some of the things that I think we'll want to talk about. But before we go onto that I wanted to just give you an example of the other kind of association in which the Puritans were engaged when they came to the New World. This is just a description of the joint stock agreement that the Plymouth Puritans had when they came, all right? So you can look at all the capitals invested by both merchants and the colonists and it's put into a joint fund. Divided into shares every person over the age of 16 is rated at 10 pounds, 10 pounds is a single share, any colonist outfitting himself with 10 pounds worth of provisions was considered worth 20 pounds or a double share, for example William Moens [assumed spelling], a well-to-do colonist left in his will his stock of 40 pounds worth of boots and shoes expecting it to increase to nine shares at the end of seven years. Investors who contributed only money and stayed at home, and the colonists both work to continue the joint stock for even years during which all profits were made from trade traffic, etcetera. Then they would eventually divide up, excuse me, that should be seven years. I think it was seven years during which all profits from trade would be in the common stock and then they would eventually divide it all up including the lands, houses and the goods. And a common stock will furnish the food, clothing and provisions during those seven years. And I think you could see that that's the, that's a more extreme version of a kind of communal orientation that the Plymouth Puritans had. There were different provisions for the Massachusetts Bay colony. But again they're very specific, they indicate, you know, actual pounds worth of value, and they're thinking in economic terms. So for both Bradford and Winthrop. We want the economic arrangements to reinforce the spiritual arrangements. But again, they belong to joint stock companies, it's an economic venture come to the New World as well as a spiritual venture. And I told you last time that one of the things that Winthrop is trying to do is to harness the energies of the individual. The economic energies of the individual in order to make this kind of arrangement work. And also, not get, you know, not so leave the individuals to pursue economic interests that the other kind of communal aspects of the venture would start to fail. So you needed to make use of individualism but find a way to rein it in. And so the antinomian controversy becomes an example of precisely the thing that is, you know, the subtext of Winthrop's sermon, what it is he's afraid of happening, right? And ironically, it happens not because of economics but because of doctrine, a theological doctrine, and spirituality, right? But it is a case in which individualism is threatening to get out of hand and what happens is the Puritans fathers as it were clamped down on it and it's worth talking about that notion of Puritan fathers because the antinomian controversy is very much to a large case of kind of feminist response to a patriarchal hierarchy, and it's quite clear that the people who were in charge of Puritan society at that point, recognized it as such. It made a big difference that Anne Hutchison was a woman mounting this particular challenge. Right? So that's what we call antinomianism, and this is the picture of Anne Hutchison. Now in order to understand the context for antinomianism we need to go back to some of the things that Bruce Tickler talks about in his article particularly the idea of preparationism [assumed spelling]. And preparationism is a way that the Puritans responded to the problem between, the problem of, you might say, the lack of fit between good works on the one hand, which you would think, you know, Christians would be interested in promoting and this idea of grace. I remember that for them arminianism from the Dutch philosopher Jacobus Arminius, the idea that, you know, good works would be the way that you could get yourself, earn a place, merit salvation. For them that's a heresy. Salvation occurs only because God is merciful only because he gives grace to his chosen few, right? So there isn't a necessary connection between good works and the reception of grace, although I started to say last time why it was that the Puritans would probably not want to completely misbehave because they would then be interpreting their own impulses to misbehave as a sign that you weren't among the elect and nobody wanted that. So you might say that this idea of preparationism is another form of compromise, right? The doctrine goes like this, since nobody can tell whether or not he or she is predestined to be a member of the elect, only God knows this. It made sense to engage in good moral behavior. So you should live your life acknowledging God's supreme power, you should be looking for certain signs that the life of the sincere penitent, right? Somebody who's accepting God's grace, would be exhibiting. And among these would be, not surprising, a kind of yearning for grace a natural inclination to good moral behavior and virtuous actions, right? Wanting to be good, you could be interpreted as one of the signs. Now none of these things would have any kind of causal efficacy. You've got to be clear about that. You can't merit grace. But they have this idea that you could sort of could prepare for grace. As if, I don't know, grace were seeds that were going to be planted. And then if you were preparing for grace, you were just going to make sure the ground was especially receptive or fertile or well watered. Or just some of those seeds are going to take root right away. Right? If you think about the parable of the talents when, or the parable of the seeds, the sower when Christ talks about certain seeds are going to fall on rocky ground and certain seeds, and they're not going to prosper, certain seeds are going to prosper. Well preparationism as the idea that you can prepare that ground and make sure it's, you know, grace is going to take root. And it doesn't actually from my point of view make a lot of sense. I mean, when push comes to shove there really isn't a way to prepare for grace. It shouldn't really shouldn't make a difference whether you're prepared or not, right? Whether you're getting it or not, you're getting it, right? Yes you wanted to say something. >> [inaudible] that they thought that God's grace was completely arbitrary? >> No, it's God's will. It's anything but arbitrary, it's the most determined and reasonable thing there is. Because it's God's will and who are you to ask about it at all? [ laughter ] You think I'm joking that's really what they thought. I mean, who are you? Do you remember the book of Job? Did anybody ever read the book of Job? The book of Job, okay? The book of Job is a wonderful book because it gets at the problem of why is there evil in the world. Does anybody know why? And so we know about Job. And by the way Job is a big intertext [assumed spelling] for Melville's Moby Dick, so, you know, if I, I should probably assign you to read the book of Job but I won't. But it would be good if you were familiar with it. Anybody remember why Job gets tormented the way he does by God? Yeah. >> Isn't it because Satan was sort of goading God by saying well this guy loves you and worships you but only because you've been so good to him. He wouldn't be so nice to you if he had a hard life. >> Yeah that's basically right. I mean, remember that the Satan that we see there is not Satan. Anybody ever watch reruns of Saturday Night Live? The word Church lady mean anything to anybody? [ laughter ] So, Dana Carvey is wonderful. So, but Satan's not that Satan yet. Satan is still the kind of advocate, the adversary, it's almost like the devil's advocate, that comes from that conception of Satan. He's going to pose the contrary just to test things out. So it's yeah, Job, you know, is your faithful servant. Because God's saying have you, Satan's kind of walking around the earth looking at everything, and God's really proud of Job, saying have you seen my faithful servant Job? Satan says yeah, you know your faithful servant Job, he only loves you because you've been good to him and maybe he fears you a bit. You take away all those good things and we'll see. So God says okay, test him. Don't kill him, but anything else, you can do. So he does. Alright? And this is a series of like terrible disasters. Job is kind of sitting there one day, and then all these messengers come to say, you know, everybody in your family was killed, all your livestock was killed, and I only escaped alone to tell thee. Okay so it goes on, right? But there's a reason for it. It's a way of, you know, testing God's principles, there's this, you know, it's almost like a thought experiment that God is allowing Satan to engage in. Alright? Do you remember, we'll cut to the chase, do you remember what happens at the end? Does Job get to find out why this all happened to him? He's covered with boils, and, yeah, why did, what happens to Job? >> God speaks to him and explains that, he tells him who are you to pretend to understand the divine providence. >> Exactly. So you might say the nicest thing that God could do to Job, Job is a, Job never wants to ask to die or anything like Jonah does. Jonah's kind of a wuss. But Job, Job takes it although he does complain, a little bit of whiny moments in Job's monologues. But for the most part, he comes, but he does, and he does sort of register the unfairness, I mean I can't really talk to you, you come, you speak in the whirlwind, you know, is that really fair? But okay. So anyway he comes in. Now the nice thing for God to do would be to explain it all. Look, this had a purpose, there was a reason, you were my representative, I've proven to Satan that my followers really believe, and they have faith, and it's not because they either want rewards or because they fear me. Does He tell him all that? Does He give him that satisfaction of knowing that it wasn't all arbitrary? He does not. Who are you to ask, who are you to presume, were you around when I created the world? Were you around when I put Leviathan in the sea? No. Quiet. He smacks him down. And that is the way the Puritans understand the world. They trust that there is a purpose, they also understand that they are not going to know it. So you don't get to ask that question if you're a Puritan. And you wouldn't. Wanting to ask that question, very bad sign. Okay? So, I mean that's kind of, but that's where the precedent for it comes in books like the book of Job. That's the way that they understand the relationship. Now that could drive some people to despair although I think when we get to Edward Taylor you will see that what he decides to think about is that, there's something fundamentally comic or comforting about the incommensurability between the divine mind and our own, right? It's kind of taken care of for us, we shouldn't worry about it, you shouldn't worry too much about grace not coming, it will come. You know, and in the meanwhile you sort of see human beings predicament not as a predicament but as, I don't know, an opportunity or the idea, you have kind of assurance that there's providence in place, right? So there's no connection between grace and works and preparationism, you say well, it's kind of a little, of course it doesn't have any affect, but it's not a bad idea, right? I mean, even if you're not predestined for grace, if you've been preparing the way for grace and you don't get it, still you've been leading a good life and it's benefitting to other peoples. So it's better than the opposite, right? But push it too far and it starts to look like arminianism. And that's what Hutchinson says. I mean, basically when preachers would get angry with one another, they would accuse one another of being Arminian, you know, they were falling into the trap of the Arminian heresy of preaching a doctrine of works rather than grace. So Anne Hutchinson started to get disaffected with some of the preachers in Boston because she believed that they were in fact producing a doctrine that was very close to arminianism. Too much preparationism, too little account of grace. And so she starts to create a kind of, well it starts out as a kind of book group or reading group of her own, and then she gets a lot of followers. Hutchinson and her family emigrated to Boston in 1634. She comes from a prominent family. Her husband William is elected to the deputy, is elected as a deputy of the Massachusetts court and she is somebody who is very active in community service. She serves as a nurse and a midwife and a spiritual advisor to women. And in effect that's where the problem sometimes starts. Sometimes in her first years in Boston she began to hold these weekly meetings in her home to discuss the sermon of the previous Sunday. And they soon became very big, I mean people heard about them, and she would get, you know, about 60 people in her house including the governor and other prominent figures. Now the trouble starts when she begins to criticize some of the leading clergy for basically preaching what she thought was a doctrine of works or she accused them of being legalists who suggested that people could earn salvation somehow. And that the conversion process could in fact be charted and understood. She wanted to go back to the hard-line, mainline Calvinism which regarded grace as inscrutable. That's a big word for the Puritans. Can't understand that. Inscrutable and individual. It's a mystical experience that happens only between God and the individual sinner. And they're really, when you think about it, the clergy has no role to play in that fundamental act of a Christian life. You don't need the clergy. So all of this stuff, the clergy, the churches, the prayers, everything, she thought of as what is called sanctification. Everything has to do with good works, and churchly trappings and all this kind of stuff, part of sanctification. Which is all well and fine. I mean, insofar as it promotes good behavior that's great with her. But what she's really interested in and what she thinks of as the center of the Christian's life is justification. The moment when the Holy Spirit becomes indwelling, when you get grace. And she says there is no connection between justification and sanctification. Let's take a look, and to say that she says is a form of arminianism. Let's take a look on page 160 of the Norton, there's a moment, we looked at the moment of the snake and the mouse last time, but let's take a look at another moment from Winthrop's journal in which he talks about Anne Hutchinson. This is on page 160 at the bottom. The entry that's October 21, 1636. And he writes this; One Mrs. Hutchinson, a member of the church of Boston, a woman of ready wit and bold spirit brought over with her two dangerous errors. One that the person of the Holy Ghost dwells in a justified person, that's a kind of obscure point of doctrine, and this is the bigger problem right? Two, that no sanctification can help to evidence to us our justification. From these two grew many branches as one, our union with the Holy Ghost so as a Christian remains dead in every spiritual action, have no gifts nor graces, other than such as are in hypocrites, nor any other sanctification but the Holy Ghost himself. They're joined with her in these opinions, a brother of hers, one Mr. Wheelwright a silence minister sometime in England. Right? So Winthrop is noting this. And you can see that the problem that they have is that if you push this doctrine, what you might say is a kind of, within puritan terms a kind of right wing conservative doctrine, it's the most conservative interpretation of Calvinism. If you push it too far you don't need the minister. You don't really even need the sermon. You don't need any of the church hierarchy. All you need is your own sense of you're leading a Christian life and your expectation that ultimately you will receive grace. So if she's mounting a challenge you might say to the church hierarchy by preaching this. And people are starting to listen to her. So finally they find a way to try her. She's tried twice. She's tried once in the civil court, the general court, in 1637, she's tried in the next spring by the church, she refuses to confess the errors of her ways and finally if you look at some of the transcripts, you'll see that she gets caught up in a kind of Achaean point of doctrine. Ultimately she and her family are banished in 1638 to Rhode Island. Right? So they clamp down. Now, the earliest sermon that still survives from Puritan Plymouth is one that's called the sin and dangers of self-love, and it was preached by a guy named Robert Cushman. And it was preached in 1620. Interestingly, again, there's kind of, you know Cushman had to sort of split interests. He was a Puritan, and therefore got to preach this lay sermon because he was the business agent for the colonies. So he was going back to England and before he goes he wants to make sure that everything is shipshape with that agreement that they have made with investors back home. Right? So the problem, the biggest threat to the Puritan enterprise is going to be this idea of self-love or egotism. And he wants to preach against that. Yes? >> So what exactly did they claim to be trying her for? What did they say? >> They tried her for these errors, what they consider to be errors of doctrine and preaching against the ways in which the ministers were preaching. So if you look at the two things that Winthrop identifies here are the reasons that they try her in court. The idea that the person of the Holy Ghost dwells in a justified person and so that it's a question of, is the Holy Ghost outside. Or is it actually inside? And I believe she says it's inside and they didn't want to say that. I mean, that's the obscure point of doctrine. But the other thing is important even perhaps more important. That no sanctification can help, evidence us to our justification. Right? Because they are developing this doctrine that goes by the name of preparationism. And that doctrine is the official doctrine. You're not supposed to challenge that. Even to say that it doesn't exactly make sense or, so when she starts to challenge that that becomes a reason for them to bring her up and to try her in both of these courts. I don't remember what the, I'll check it out and see if I can put it in the notes, I don't remember with the actual charges in a civil court was. It was something akin to disorderly conduct, but it was really, it was basically for promoting dangerous heresies among the people. That was both a civil offense and a theological offense. And there's a very complicated thing that goes on, John Cotton is a good friend of yours, she kind of saves some of the ministers who are interested by claiming that they aren't culpable at all, that it's all, you know, it's just her own idea. And ultimately she is the one that suffers most of the punishment, she and her family. But the point is therefore that self-love, egotism, is the thing that they're afraid of, so they kind of suggest that that's what she's preaching. Even though, if you look at it on the face of it you would say she's really just preaching the doctrine. The problem is that in trying to make the doctrine something that can serve as a template for society in some senses they have to compromise the doctrine. It needs to be a place for that kind of disciplinary powers of the church and the elders to be. And Hutchison wants to say, you know, that's kind of irrelevant. So they saw it as, you know, a form of individualism or egotism getting out of hand. They thought she was doing it impure motives. Because she declared that the church, which thought of itself as having this mediating role between the individual sinner and God, was actually unnecessary. So you see this kind of a double offense, it's theological, but it's also social and ideological. I mean she's going up against the church hierarchy on these grounds of doctrine. And more than that as I suggested earlier, she's a woman, who is openly challenging patriarchal structures. And if you look at the things that they write about, we'll look at a snippet right now, you can see that her gender is clearly an issue. Take a look at page 163. There is a sort of entry about, after, later on there's an entry about her child and the monstrous birth is attributed to her. So September 1638, Mrs. Hutchison being removed to the Isle of Aquitaine, in the Narragansett Bay after her time was filled that she expected deliverance of the child was delivered of a monstrous birth. Here upon the governor wrote to Mr. Clark a position and a preacher to those of the island to know the certainty there of who returned to this answer. I know this is kind of weird for you and interested in what's going on. Mrs. Hutchinson six weeks before her delivery, perceived her body to be greatly distempered and her spirits falling and in that regard doubtful of life, she said to me etcetera. And not long after in inmoderatofluoriauterino [assumed spelling] it was brought to light, and I was called to see it. Or I beheld innumerable distinct bodies in the form of a clove not unlike the swims of some fish so confusedly knit together by so many several strings, which I could see were the beginnings of veins and nerves. So that it was impossible either to number the small round pieces in every lump much less to discern from whence every string to fetch its original. They were so snarled within one another. The small globe to likewise open and proceeded to matter them, setting aside the membrane in which it was involved to be partly wind and partly water. The governor not satisfied with this relationship spake afterward with the said Mr. Clark, who thus cleared all the doubts. They want details of the monstrous birth. The lumps were 26 or 27 distinct and not joined together became the second on after them, six of them were as great as his fist in the smallest about the good bigness of the top of his thumb, globes were round things, included in the lumps about the bigness of the small Indian being, unlike the pearl in a man's eye. The two lumps which differ from the rest were like liver or congealed blood and had no small globes in them as the rest had. Okay. You can see that the kind of interest in this and the fixation on this. Here is this woman and she's delivered this monstrous birth. I mean, only, the only thing better would've been if she delivered an actual devil child that was walking around, right? But they can, you could see that anger is linked to the fact that they understand that she has committed that kind of gender offense. An offense against their hierarchy of gender. And so that comes across I think in the language that they use, the way in which they're particularly interested in the facts of her failed maternity in this instance. So the Hutchison's spent about five years in Rhode Island, and then they moved actually up to Pelham in the Bronx and on page 164 you can find out what happens to them. This is the middle of the page September 1643. The Indians knew the Dutch having killed 15 men began to set upon the English who dwelt under the Dutch. They came to Mrs. Hutchison's in the way of friendly neighborhood as they had been accustomed to taking their opportunity killed her and Mr. Collins, her son-in-law, who had been kept prisoner in Boston as it was before related and all her family and such other families that were as were at home in all 16 and put their cattle into their houses and there burnt them. These people have cast off ordinances and churches, and now at last their own people and for larger accommodation had subjected themselves to the Dutch and dwelt scatteringly [assumed spelling] near a mile asunder. She deserved what she got. Right? Is the message here. In other words, they see, you know, as to what happened to her and they saw it as a sign of God's divine judgment. That she was wrong and therefore she had this fate. So you would say her old enemies would've been satisfied by this outcome. And it would be a further justification for them of the way they think about history. And history is not secular, but history is part of a divine plan is unfolding. Yeah. >> How do you reconcile God punishing those who've done evil deeds with Job being punished or. >> Again, you're asking about God's purpose. It's a big black hole. You do not get to ask about that. God has his purposes who are you to presume? He's seen the past the present the future, he knows. It's all part of a plan. We call it Providence. >> Then wouldn't it be a sin to presume that she died because of what she had done? >> Yeah, probably, except that it suits their purposes. You know, yeah. Right? I mean one of the things that you would say about this is, I'm a mean, you know, I'm not even really religious myself let alone subscribing to a former fundamentalism like this, it made sense to them. And part of it was because there were certain lines that were drawn beyond which he wouldn't cross with reason. You only got to the other side, by faith. So you just had faith. And so you had an intuition about something, right? I mean, that's the point of it. That God has an invisible Church. What we have is a visible church. The Puritans are trying to make those two matchup as much as possible. So they have some ideals that some people are going to be, Winthrop, yet he's in the church. Bradford sure, church. You know, part of a problem arises later with the second generation. They're not so sure about them. Are they going to be a part of it. But they didn't do with these things so that you have these intuitions then you look for signs to try to interpret things so that that might be a sign of divine approval. So this would be a sign of divine disapproval. Again, you're trying judge this preparationism self, and you could say if you were absolutely hard-line, you shouldn't even be thinking about this, right? Because you're treading on God's ground. God knows and you should, but insofar as you could say that's a sign. It seems like were not presuming to ask why or to question the purposes, but it looks like God is approving these things, that's the way they thought. They live in a kind of haunted world where they are sure of the larger outlines of the story. They even know the end of the story. It's called the book of Revelation, the apocalypse, they even know the role that they play as a people in that. What they don't know, what no individual knows, is the role that he or she is going to play. Alright? So, you run into various kinds of theological problems. They tried to try to get around these. Yeah? >> But, I mean, you believe in this sort of thing, where you would know if you were my new [inaudible]. >> You still wouldn't know exactly until you'd actually had the experience of grace. See, here's the rub. And they actually feel like they have the experience of grace. In order, after the antinomian controversy in order to try to settle things down a little bit and so that someone like another Hutchison couldn't come along and say look grace is inscrutable. You know, who nobody can say whether you've had it or haven't, they start to develop, and again, this would seem to us to be counterintuitive, and certainly to Hutchinson, they started develop a series of steps by which individual sinner and those around him or her could recognize that you've received grace. And historians following somebody named Edmund Morgan have instead, they called this kind of a morphology of conversion. And these are kind of squishy steps, but Morgan said that the steps towards the reception of grace for something like this. Knowledge, conviction, faith, combat, and true and perfect assurance. Now, he would derive these by looking at lots of different conversion narratives. Because one of the things that came after this is the idea that in order to have full church membership you had to give an account of your conversion. And how could anybody know if you were telling the truth or not, well it's because people had an idea of what a real conversion would look like and so if your conversion matched their idea, your account convincingly matched their idea of what it was, it was going to be okay. And I just want you to look at this stuff. When we get to Edwards you'll, this will become a little clearer I think. But there's a sense in which we start off with knowledge, right? So that may be something like knowing the bible, listening to the ministers, understanding the principles. And we believe as a result of that. We move from a strong belief to actual faith that's beyond questioning or reason, and then something happens to us and we are forced to question everything or we're forced to put those principles into place. We're severely tempted. Or members of our family die, or something like that happens. We have this kind of struggle. And as a result of that struggle we emerge stronger, we emerge with an assurance that's true but we're always aware of its imperfection. It's the same logic I talked about before in moving from the covenant of works down to total depravity up to the covenant of grace. You start off in a place that's okay, you're tested, things get bad, and you rise to a place that's much higher. It's that same kind of Puritan logic. And so, I think it looks almost like a square root sign, or something like that. Anyway, that's one of the things they try to do. They try to develop a series of steps whereby you could actually tell. And so then they come up with this idea, it's called a Cambridge platform 1648, which they say all of these conversions must be personal and public. Personal meaning you have to account, you have to recount your own story of conversion, but public because you have to tell everybody else about it. Sometimes women who were afraid, you know, as women are of speaking in public, they were allowed to have somebody else recount is for them. And many of these things were written down and so we have some of them. John Cotton who was actually one of the people that was in Hutchinson's circle for awhile and was a conservative minister wrote this tract called the true constitution of a particular visual church. Again you'll see that terminology here, in which he gave a kind of question and answer, sort of an early FAQ for how you know all the mechanics of being saved and not saved and what you can know. So question, what manner of men hath God appointed to be received as brethren and members of his church. Answer, such as are called out of God, of this world to the fellowship of Christ and do willingly offer and join themselves towards the Lord and then to the church by confession of their sins, by profession of their faith, and by laying or taking hold of His covenant. And this doesn't actually map onto this, this are the things that you do after you've received this true and perfect assurance. Right? So this is sort of steps. In an earlier tract, he's made it even a little clearer what they did. Candidates are called for before the church and each one maketh confession of his sins and profession of his faith, in confession of his sins that it may appear to be a penitent confession, he declareth also the grace of God to his soul drawing him out of his sinful estate into fellowship with Christ. In the profession of his faith he declareth not only his good knowledge of the principles of religion, not only knowledge, but also his professed subjection to the gospel of Christ with his desire of walking here, therein with the fellowship of the church. So again you get the sense that knowledge isn't enough, there's got to be something more and that something more is what you get when you get to the experience of grace. Edwards is a very late Puritan by the way. I mean, this is, he's writing 100 years after these people. And he's the last great Puritan thinker I suppose. But in some of the things that you'll read, you'll get a sense of what it, you know, he's trying to get across, but he uses language that's much more familiar to us because it's a, just, it's a kind of proto-romantic language that, at that time, feels licensed to use examples from cultural life or from nature to get across what it is. But let's just say, anybody seen the movie The Wizard of Oz? Yes? >> Yes. >> People still watch The Wizard of Oz? Well before grace, the world is black and white. After grace, Technicolor. And you don't have to go back to Kansas because Oz is better. That's grace. Okay? So we'll talk about that some more. But so you see, I want you to see how it is, they are trying to figure out a way to make this rather impractical doctrine work in practical terms as the basis of, for a society. And so they come up with these various kind of compromised positions. And part of what happens is that these things, this whole idea of the morphology of conversion and other things become more and more standardized as they encounter more and more problems in Puritan New England. These include problems with the weather, there are earthquakes and bad weather and failed crops. Yes there actually are earthquakes in New England, not the way there are some other places, but they did occur. I experienced one myself back in the day. Had been out for awhile the night before so I thought it was something else when I woke up. But when you see that the room is not at right angles to itself you kind of figure out that it's just an earthquake. Anyway, one problem that I've already hinted at is that there's a problem with the second generation, the children of the supposed saints of the first generation who are not getting converted at the rate they should've been. So they came up with this idea called the halfway covenant by its opponents. In other words, they said, look we'll meet you half way. No they didn't say that. What they said was that the children of full church members could have their children baptized and they could have all, many of the rights and benefits, they couldn't go to the communion table yet until they fully receive church membership. But you know, you've got to be baptized. You've got to chose God to be baptized because you're not baptized, it's kind of a non starter. Not that baptism has any efficacy or anything, right? I mean, because you're baptized, you're not causing anything or creating anything. But let's just say if it turns out that you weren't baptized that would be the surest sign that you weren't among the elect. So you really want to make sure your kid is baptized. Okay. So that's another example and people talks about this. That's another example of the way in which Puritans are trying to make the, create these compromised positions that could make this society work. A form that arises as a result of these problems that Puritan New England is having is a form that's called the Jeremiad and it's a particular kind of sermon. Once a year in front of the general court, something called an election sermon was, and that's election was preached, and that's election in the sense of being among the elect rather than voting for anything. And this form called the Jeremiad, arose in part in response to the troubles that New England was having. And as you might imagine it was a kind of sermon that took as its text Jeremiah or sometimes Isaiah, you know, the Old Testament prophets who were constantly decrying the failure of the Israelites to keep their covenant, right? The prophets were howling in the wilderness you know, all that kind of stuff, that's them. So it's a kind of gloomy sermon. And the paradicmaraquan [assumed spelling] is one that was preached in 1670 in front of the general court by a man named Samuel Danforth [assumed spelling] and it was called a brief recognition of New England's errand into the wilderness And you might say that the content of these sermons was expected to integrate a kind of theory of puritan society with current and religious social practices. That's what the election sermons tended to do. So you've got a kind of familiar ritual in which the preacher would pick a text, summarize the larger historical picture, take stock, and then find some way to apply it, and typically follow the pattern of, text, explication, doctrine, reasons and propositions, and then application that I set out last time. The application became more and more important as Puritan New England started to have problems. And so we would see in Danforth's sermon this same kind of pattern. He gave it to the Massachusetts general court in 1670 and the larger question he was asking was this, what is it that distinguisheth New England from other colonies and plantations in America. And of course the answer is, what makes Puritan New England distinctive is exactly the thing that Winthrop talked about. It's the fact of its pursuit of religious annuls that will make it this kind of city on a hill. So I'm going to show you a passage, a very brief passage from Danforth's sermon, and you'll see how he's taking cues from texts like Bradford's with their depiction of a howling wilderness, into which the Puritans have come on this errand, and also Winthrop, this idea of serving as a model or a beacon and having made a kind of covenant. So this is part of Danforth's sermon. You have solemnly professed before God, angels and men that the cause of leaving your country, kindred and fathers houses and transporting yourselves with your wives little ones and substance over the vast ocean, into this waste of howling wilderness was your liberty to walk in the faith of the gospel with all good conscience according to the order the Gospel and your enjoyment of the pure worship of God according to his institution without humane mixtures and petitions, right? This is why you've wanted to do this. Good conscience and he talks further on about this kind of compact that you've made. And for a while, he says, it worked. When the people were saintly in the first generation was there we created out of this howling wilderness, a kind of garden, but we have not been tending our garden properly. And he takes as an additional text from Proverbs, the Vineyard is all overgrown with thorns and nettles cover the face thereof and the stone wall is broken down. Things are not good. Yes? >> I still don't understand what it would be a problem with the second generation. How do they know, when the first generation was more chosen than the second? >> Well, the first-generation were A, the leaders so you didn't really question them very much, and B, they are all have these professions of faith, and they were part of church members in the second generation became interested in other things. They actually became interested in exactly the things that winter was afraid of. They were more interested in their economic lives, perhaps in the spirituality. There were fewer confessions or professions of faith. You know, it's like kids these days. They'd say, it was an, something, it's an abiding problem, but they set it in this religious context. So they're saying like okay, now we understand why there are the earthquakes and Indian troubles and bad crops and all that stuff. Why hath the Lord smittened us with blasting and mildew, now 7 years together adding sometimes severe draught, sometimes great tempest floods, and sweeping rains. Blazing stars, earthquakes, dreadful thunders, lightenings, fearful burnings, right? The very, it's like one of these moments from a Shakespearean play, the very earth is erupting because of the bad stuff that the Puritans are doing. Every, this became a kind of ritual after this. It's like every week these sermons would be, whenever you go to church you'd be hearing these kind of Jeremiads preached over and over and over again. You find it very depressing, right? Well they didn't I don't think. And what we think is that they started to understand that this was a ritual. And it's been described by American scholars Americanist scholars is a ritual of consensus. Because remember the logic. God afflictest just most those whom he loves best. The worst it is the more he loves you. Think Job. And these sermons were for constantly, you know, excoriating those present for their failure to live up to the ideals of the fathers. Every week they would also end with the idea that it's not too late. You still are the chosen people. Get back with it. And everything will be fine. God's grace is waiting for us there, don't ask questions about efficacy please. This is the rhetoric of it, right? We're still the chosen people. Time to get back to where we're supposed to be, right? So is was a constant reinforcement of the idea that God, that the Puritans were God's chosen that they were that they had a role to play in the end of days, and the end of days were coming pretty soon. So pretty in general, best not to be caught out when the end of days comes. Okay. Are there questions about that? Yeah. >> [inaudible] half way covenant you said that the children of whole church members, is it their children? >> Well no, the children of full church members were allowed to have most of the privileges that full church members could have They couldn't go to the communion table but they could do some of these other things like participate and also, most important, baptize their children. >> So they could baptize their children. >> They could baptize their children even though they're not full church members because there was the expectation that if, you know, you're Winthrop's kids, you're going to get converted, just might be taking a little bit longer. >> Was that, [inaudible] , study the duration or do they see as just a [inaudible] >> Well again, you know, to say that baptism caused election or anything like that would be to preach a doctrine of works somehow. So it's not that. It's just, it's more like you have to think of a retrospect of logic. If it turns out that you weren't baptized, that's a pretty good sign that you're not among the elect. Again don't think too much about where the human agency falls within this. They all hate this right? Bitch to your section leaders about it. [ laughter ] But I mean, one of the things I'm saying is there are, the Puritanism is full of contradictions and they struggle with it. I mean, one of the earliest ways that people thought about Puritanism was that is was kind of fundamentalism, it was kind of monolith, everybody believed but for example, a history of New England Puritanism would look a lot different if you started not with Winthrop as we're doing, but say with a count of the Salem Witch Trials. You would get some of the same elements in place but they would take on a much more sinister kind of cast in which there are certain kinds of enthusiastic behaviors and it kind of works almost virally. People start to believe that they've seen things. And later on, if you read the transcripts of Salem, what you'll realize is that the people who were saved are the people that say I'm guilty. And I saw the black woman with the, I mean the black man with the cat on his shoulder and whatever it is they figure out that there's certain signs, not unlike the kind of flipside of the morphology of conversion. I say these things and then say I'm sorry about it, it's better than saying what are you talking about. I'm innocent It's the people that continue to profess their innocence until the very end. In Arthur Miller's play, the Crucible, it's a wonderful twentieth century capturing of this kind of hysteria. And of the refusal to kind of kowtow to this kind of ritualized behavior. The people that profess their innocence, they're the ones that died, right? So New England becomes a very, kind of ritualized society and people start to understand the way these rituals work. Alright. One other thing to say about the Jeremiad is it becomes a form that you might say, explodes beyond the boundaries of simply the sermon. And that many things beyond sermon start to take on this powerful kind of Jeremiadic form. We will read one of them next week which is Michael Wigglesworth's poem the Day of Doom which takes basically the form of a kind of instruction manual to, instead of mostly for young readers. It was written in a verse form that was very easy to memorize and it of course ends with the idea of God's grace, but that's like 10 verses out of 300. The rest of it, all hellfire and damnation, right? A lot of Jeremiadic kinds of elements. And some people have read the longer thing that we looked at for today also as a Jeremiad, the narrative of the captivity and restoration of Mrs. Mary Rowlandson. So let's turn to that on page 236 of the Norton. And this is a picture of Mary Rowlandson from a later edition. Actually they make her look more colonial probably, I mean like kind of later colonial than she probably did. But Rowlandson is thought of as the kind of paradigmatic captivity narrative and many of these things often follow the kind of Jeremiadic design in which somebody has a captivity happen, and they say, they berate themselves, take responsibility for it, say some kind of failing, I'm being punished or I'm being tested and then ultimately since you only get to write a captivity narrative if you're redeemed from your captivity, you find that in fact, you know, things have worked out well and that God has saved you. Rowlandson's captivity occurs during something that's known as King Phillips War which erupts in 1675 and proves to be devastating both, for both sides. Under the leadership of Chief Sechametacomet [assumed spelling] of the Wompanoads [assumed spelling] several Native American tribes banned together finally to keep basically, to keep the Puritans in check. I mean, they see, you imagine the situation. They've been living there, they see these puritans coming, they're taking control of the land, they have larger and larger settlements, they're increasing in number, they're pushing these tribes out of their homelands. So there's 18 months of citing in which both sides engage apparently in atrocities and suffer high casualties, and the economy of the English colony is completely disrupted. You can imagine a major refugee situation around Boston as a result of this. Metacomet [assumed spelling] is finally killed which marks the end, effective end, of Native resistance to the English. You might say the English win but it's a kind of purit [assumed spelling] victory. And people social and economic history suggest that the end of puritan New England comes in part, or in large part, because of the effects of King Phillip's war. Alright, February 10, 1676, a Wompanoad raiding party attacks Lancaster, kills 12 citizens, burns their homes, takes Mary and 23 others captive. Mary's brother in law, her eldest sister, her sister's son are all killed and her youngest daughter, 6 year old Sarah, who she is holding in her arms is fatally wounded by a bullet that also passes through Mary's side. Rowlandson carries her daughter, as you know from the account, for 8 days until she, the daughter dies on February eighteenth. She has two other children, 10 year old Mary, 13 year old Joseph, they are kept apart from her during the captivity, although she reports that she did see them. And they're eventually all ransomed about 3 months later in May. So, when she lived during her captivity she lived with and was the servant of Quantapin [assumed spelling] who was the chief of the Narragansett's. And in fact was the leader of the raiding party, on Lancaster. And with his wife. Okay. After that the Rowlandson's live in Boston for a year and then her husband becomes minister to the church in Wethersfield, Connecticut. And it's some years after, sometime after this, probably at least a year may be too that she starts to begin writing this narrative. We know it has to be, no more than two because her husband dies in 1678, and in fact, the last public record of Mary, we don't know what happens to her, of course in 1679 when she's given some money for his funeral. And until recently historians assume that you probably died sometime before the narrative was actually published in 1682 but there's actually new evidence that suggests she might've been remarried and that she lived in, Wethersfield, Connecticut until 1711 when she died at the age of 73. So, unclear about the completely about the fate of Mary Rowlandson. Now it's interesting to think about what's going on in this narrative. She was encouraged to write it by Increase Mather, the father of Cotton Mather, who was prominent minister and who was also a historian. He'd written a history of King Phillip's war and both the point of his history and the point of Rowlandson's narrative is to find some kind of providential understanding of the war. To convince people both in England and in the Americas that New England was still okay, the Puritan New England was still okay after the war. And that their ordeal was justified. But take a look at the title page of this. What do you notice about the title page of this compared with the first page of your, of the narrative that we had you read? [ silence ] >> What's the title of this narrative? >> [inaudible] >> Yes that's right, it is the sovereignty and goodness of God together with the faithfulness of his promises displayed. So it's often anthologies referred to in the short hand as a narrative of the captivity and restoration, it's spelled in a different way, of Mrs. Mary Rowlandson. But that's not the real title. The title we'll use is the sovereignty and goodness of God. Okay, what else might we notice about this title page? The footnote gives you the full title. The sovereignty and goodness of God, together with the faithfulness of his promises displayed being a narrative of the captivity and restoration of Mrs. Mary Rowlandson commended by her to all the desire to know the Lord's doings to and dealings with her especially to her dear children relations. The second edition, corrected and amended written by her own hand for her private use. And now made public at the earnest desire of some friends and for the benefit of the afflicted. Deuteronomy 32:30 See now that I even, I am He and there is no God with me. I kill and I make alive, I wound and I heal. Neither is there any can deliver out of my hand. Alright. Look at the structure of that. What do you notice about it? >> [inaudible] >> What's that? >> It's like a sermon. >> It is a sermonic set up complete with a reference to the bible. What else? Anything? Where is Rowlandson in it? She comes kind of late in the title doesn't she? So it's the sovereignty and goodness of God here, and then God here and she gets Mary Rowlandson here at her family. But what I want you to see is that her narrative is quite literally even by the title framed by a theological context. It's about God at the beginning and the end and she has one little role to play inside. So that's one of the things to bear in mind. The other thing to bear in mind is that the narrative itself is also framed by the doctrinal and by the patriarchal. It's introduced by Increase Mather and then there's a sermonic afterward by her son, her husband Joseph as well. Alright so that her own text is also bookended and framed by narratives that have to do with God and that are written by men as if she needs to be authorized to speak. And this is the first, you know, big prose thing by a woman that is published in the colonies. So it is a kind of unprecedented narrative to appear. And one of the things that Mather and Mr. Reverend Rowlandson are trying to do is give you a way of reading it. Right? So it's purposes are set for you as a reader even before you begin to read her narrative of the tenth of February 1675, right? We are taught how to read the narrative, we are taught how to read the war that is a part of. She has no sense throughout the narrative that there are larger social and political contexts for the war, right? Doesn't have any sense that this is really, this is an episode within a larger conflict between the settlers of Puritan New England and a larger Indian tribe. In fact, her understandings of the natives are almost holy at the beginning in line with the kind of representation of natives that we see in Bradford. Let's take a look, so on page say, I don't know, 237. And she's talking about her account. This is about 10 lines down or so. No sooner were we out of the house that my brother in law being before wounded in defending of the house in or near the throat, fell down dead whereat the Indians scornfully shouted and helloed and were presently upon him stripping off his clothes, the bullets flying thick. One went through my side and the same as it would seem through the bowels and hand of my dear child in my arms. One of the my elder sisters children named William had his leg broken which the Indians perceived and they knocked him on his head. Thus we were butchered, were we butchered by those merciless heathen standing amazed with the blood running down to our heels. My eldest sister being yet in the house and seeing these woeful sights the infidels hauling mothers one way and children another. Some wallowing in their blood and her elder son telling her that her son William was dead and myself was wounded. She said, and Lord let me die with them. So what you get here is a depiction of the Indians as heathens, as savages. Look at the bottom of the page. It is a solemn site to see so many Christians lying in their blood. Some here and some there like a company of sheep torn by wolves. All of them stripped naked by a company of hell hounds, roaring, singing, ranting, insulting, as if they would've torn our very hearts out. Yet the Lord by His almighty power preserved a number of us from death for there were 24 of us taken alive and carried captive. So it's a horrible thing happens to her. She tries to figure out a way of understanding what has happened to her. What does she come up with, do you remember? What does she do wrong? Why did she deserve this kind of punishment? Yeah. >> She ignored a few of the Sabbath days. >> yeah she didn't quite keep the Sabbath as holy as she might have. Anything else? >> It's most explicit and earlier [inaudible]. >> Well that's on 239 let's take a look at that. This is about 10 lines from the bottom. The next day was the Sabbath, I then remembered how careless I had been of God's holy time. How many Sabbaths I have spent lost and misspent and how evilly I have walked in God's sight which lays so close into my spirit, that it was easy for me to see how righteous it was with God to cut off the threat of my life and cast me out of His presence forever. Okay. Anything else? Anything, any other naughty bits? Well let's see. There's a bit about smoking, she does a little, she liked smoking every now and then. But I think when you look at it, you would find that the reasons that she has given somehow seem insufficient for the punishment that she has received. It doesn't seem to be quite enough to justify it. Right? And yet that's what it is. She says, the thing that most worried her was that she had been cast out of God's sight. Right? It isn't the punishment it's the idea that maybe God has forgotten about her, that she's no longer part of the chosen people for whatever reason. And then what happens? She receives a bible. And she reads in it and she starts to, you know, find comfort. Now I want you to think as you're thinking about this, about the portrayal of the Indians. She starts in a certain place with the Indians as kind of savages, right? And hell hounds and just the instruments of divine wrath. But as the narrative continues, they change a little bit. Take a look on page 253 in the fourteenth removed. The end of the fourteenth removed she says, thus the Lord dealt mercifully with me many times and I fared better than many of them. In the morning they took the blood of the deer and put it into a paunch and so boiled it. I could eat nothing of that, though they ate it sweetly. And yet they were so nice in other things, right? That's barbaric it seems. That when I had fished water and had put the dish I dipped the water with into the kettle of water which I brought, they would say they would knock me down for they said it was a slutters trick. In other words, they have manners, they have customs, and she starts to realize what they are. There are certain moments in this when she is the one that seems uncivilized in comparison to them. There are little reversals that the text records. More than that, when we finally meet in the nineteenth removed, King Phillip, who was completely demonized by the Puritans. Does he seem like a demon? Not exactly. This is about 10 lines down. Going along, having indeed my life, but little spirit, Phillip who was in the company came up and took me by the hand and said 2 weeks more and you shall be mistress again. I asked him if he spake true, and he said, he answered yes. And quickly you shall come to your master again who had been gone from us three weeks. After many weary steps we came to our chooses where he, her Indian master was, and I was glad to see him. He asked me when I washed me I told him not to smudge. Then he fetched me some water himself and bid me wash and gave me glass to see how I looked, and bid his squaw give me something to eat, so she gave me a mess of beans and meat and me a little bit of ground nut cake. I was wonderfully withvibed [assumed spelling] with this favor showed me. And again she has a biblical parallel for this. He made them also to be pity of all those that carried them captives from the Psalms. One of the crucial things to see as you look over this narrative again, is the moment at which the natives become more than just hell hounds for her. Is the moment in which she figures out that she can trade with them. She can engage in barter for things, she begins in other words, to see that they, or to intuit, she can't actually use language to say this but she begins to intuit that they have a kind of an economy, that they have a culture and she can partake in them. So they get names as precisely the result of these kind of economic transactions. I'll point some of these out to you in the notes and you can look at them. That's one thing to understand therefore. There's a kind of setup subtext that runs through this text that are in some sense counter to the doctrinal meanings that Mather and her husband are trying to establish as context. This idea of economic agency is one of them. And the other thing that you should look for as you read the text is moments when real grief seems to be coming through, right? She's supposed to process this grief in an almost impersonal way. It's not supposed to be about her and her own terrible experiences, it's supposed to have a doctrinal meaning. You should look for those moments where somehow the personal overflows, it isn't restricted, it isn't contained by the ideological context. There's some moments, I'm thinking particularly of the moments where she describes the death of her child, and how she used to be afraid to be in the same room with a dead body. Those are moments of detail that seem to be in excess of anything that the doctrinal purpose of the text would require. Real grief is seeping through in moments, and that's what interests historians about this. It shows you the kind of ruptures texturally within the ideological formations that Puritan New England is trying to set. She clamps down at the end to a doctrinal meeting, but in the middle they're really interesting bits. Alright let's leave it there for today. Take a look tonight at the assignments that are posted and ask your TA's if you have any questions about it. And we'll listen to one more version of a song. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | Tips_for_Physics_Educators.txt | I think for the physics educators I would suggest and to introduce the kind of big question we are trying to solve in the very beginning of the lecture then people will come in and to your lecture and annoying that we are trying to solve this specific question then we work on the theoretical calculation using our physics intuition and physical laws we learn from other class to solve this question and then we check if we have answered the big question which we actually introduced in the beginning and finally I would like to say that I would like to stress that comparison between cellular calculation and the demo is very very important okay because that gives you a chance to verify your theoretical assumption to see if our calculation actually making sense and finally I usually summarize the kind of take-home message or the conclusion from this course so that people can work out over classroom and knowing that this is actually what they learn from this lecture so actually I think that essentially a pre capo to all kinds of different physics course if we actually try to do that way then that would make the physics course much more enjoyable in general teaching a course the lecturers to show that he is so interested in this course it is true when the chorus when the lecturer I she knows about the course very well and knows the excitement about this course very well so why don't you just show it right because that will excite a lot of interest from this when the students in the classroom and also that will make your lecture much more enjoyable not only for the students but also for yourself because you feel really happy when you teach in the classroom |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | Making_Time_for_Individual_Questions_in_a_Large_Lecture.txt | so during class I like to take a few minutes of break so so that that will allow the students to take some rest because when you ready the country is so intense such that people it takes some time for the students to actually digest and to understand the concepts covered in the first part of the lecture and also it gives them an opportunity to interact with me and that usually during the break they bring a lot of questions which we didn't anticipate before there are many many questions about mathematics and also physics concepts here you have del square e right and the term square you have one two three turn three operators and you are good you if you write everything explicitly so basically you this operator is going to be operating on e x ey + ZZ and we can actually solve them during the class and I can even cover part of the the question asked during the break so that everybody actually can benefit from those interesting questions people before I should bring up during the break |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 21_Phased_Radar_Single_Electron_Interference.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: OK. So welcome back, everybody, to 8.03. So before we start the lecture today, we will give you, as usual, a short review on what we have learned, and also, an introduction about what we are going to learn today. So last lecture, we were discussing an interesting phenomenon, which is seeing film interference pattern. As you can see from this slide, we were wondering why the soap bubbles are colorful. And in the end of the class, we actually recognized that the reason why the soap bubbles are colorful is because of the interference phenomenon between the refracted light on the bubble. One puzzle path is that the light goes into the-- goes refracted directly from the surface of the soap film. The other possible optical path is to get refracted by the inner surface of the film. Therefore, the interference between these two paths actually created a colorful pattern on the bubble. So we also learned about how thick is the soap film. And I think just a quick reminder, actually, we concluded that in order to see a colorful pattern, the thickness of the wall or, say, the film, should be something like in the order of 100 nanometer. So that's actually pretty remarkable, because that's already in the order of the size of a virus. OK. OK that's actually pretty cool. So what are we going to do today? What we are going to do today is to continue the discussion that all kinds of different phenomenons, which can be explained by interference. We will learn interference phenomenon with a double slit experiment and using, for example, laser or water, and which I have a water tank here, which I will show you the interference pattern. And also, the second thing we are going to learn today is how does a phased radar actually works. OK? So by the end of the lecture today, you should be able to learn why we should construct the radar in the way and how to actually focus on the electromagnetic wave to work one specific direction. So that's essentially what we are going to learn today. The third goal is that we are going to make a connection to quantum mechanics from the lecture today. All right. So let's immediately get started. So before we start the discussion of a double slit experiment, I would like to remind everybody about Huygens' Principle, which you may already learned it from 8.02 or in the high school days. So what essentially is this principle? So this principle is saying that if I take a look at all the points in the wavefront, basically, you can treat all those points on the wavefront a point source. And this point source, essentially, a point source of a spherical wave. And it's immediate from all the points on the wavefront. So you can see from this slide, basically, if we choose to focus on the yellow point on the wavefront, you can see that from each yellow point, you can actually treat that as a spherical wave point source. And then what you actually need to do in order to calculate what would be the total electric field, for example, is to add up all those contribution from each point. And then you will be able to actually explain the interference pattern, which we see in the experiment. You may wonder where is this Huygens' Principle coming from? And although we are not going to derive that directly in the lecture today, but I can actually safely tell you that essentially, it can be derived from Maxwell's equation. OK? I will link some document, which actually shows the proof of the principle on the website and for your reference. The other thing which you may or you may not know is that we are really lucky so that we can use this Huygens' Principle in our universe. Why is that? Because if you look at the mathematical proof of this principle, it is because the number of dimension, number of spatial dimension is odd, which is three in our universe-- Or in my universe also is yours, OK, [LAUGHS] happened to be yours, as well-- such that the Huygens' principle actually works. On the other hand, if the number of dimension is even, there's no Huygens' principle, actually. So that's pretty interesting in that we are really lucky that it actually works in our universe. But I will not go into detail in 8.03. So let's get started with a concrete example, which we would like to further investigate to understand the interference phenomena. And those will prepare ourselves to the understanding of the design of the radar, for example. All right. So suppose I have experimental set up here which contain a wall where on the wall, there are two slit, A and a B. The upper one is A. The lower one is B, as designed here. And from the left inside there's an insert plane wave with a wavelength lambda, which is showing here. And this plane wave, plane electromagnetic wave, or can be water wave, et cetera, essentially approaching the wall with these two slits there. And we were wondering what would be the resulting pattern on the screen. This screen is actually pretty far away from the experimental setup, the wall on the left-hand side. How far is that? The distance between the screen, which shows the resulting interference pattern, and that the wall is actually defined. It's actually given here. It's actually called L, capital L. And in this experimental setup L essentially pretty, pretty large and is much, much larger than the d, where d, small d, is the distance between the two slits. OK? So our job now is to understand what will be-- and to predict what is going to be the interference pattern coming from the electromagnetic wave which pass through point A and point B, and what is going to happen over, say, what would be the result which we will observe on the screen. OK? So the first thing which we can do is that we can now assign observer, which is called P, one of the point of interest on the screen, which is located here. And then we can link or, say, the connect the point A, which is the location of the first slit and the location of the second slit, which is called B. We can link those points together by a line. And that is actually denoted by AP and the BP, these two lines. Since we are talking about L, which is essentially very, very large, assuming that the distance, the length scale of the distance between the wall and the screen is much, much larger than the length scale of the distance between the two slit, which is d. Therefore, I can safely assume that AP and the BP are almost parallel to each other. Right? And I can also try to express the location of the P point by using the angle between BP and the horizontal direction. OK? And the horizontal direction is actually showing there's a dash line here. And the angle between BP and the horizontal direction it's called theta here. OK. So since AP and the BP are almost parallel to each other, I can now calculate what would be the optical path length difference between AP and the BP. Right? So in order to actually calculate the phase difference between the electromagnetic wave coming from slit A compared to slit B, I need to calculate-- again, like what we did last time-- optical path length difference. OK? In this case, I can call the distance between A and P, rA. And then I can also call the distance between B and the P, rB. Then the optical path length difference is called rB minus rA. And then we can actually calculate that because we have already given you the angle between BP and the horizontal direction. And basically, we can safely conclude that the path length difference is actually this line here. Therefore, I can actually calculate and get the optical path length difference, the difference between rB and the rA to be d sine theta. OK? Once we have that, it's actually pretty straightforward to calculate what would be the phase difference. The phase difference between the field coming from slit A, which I will call it EA here, and the field coming from the slit B, which I will call it EB here. The phase difference, as you define a lot of time to be delta, delta can be calculated by the optical path length difference, d sin theta, divided by lambda, which essentially telling you how many period have passed when the light have to actually overcome this-- or say have to pass through this optical path length difference. And, of course, these things need to be modified by 2 pi in order to translate from a number of period to a phase difference. Therefore, you get the phase difference between AP and BP to be delta equal to d sine theta divided by lambda times 2 pi. OK. So you can see that all those calculations are pretty straightforward. Maybe you have already seen that before in an earlier class. But what I want to say is that it is actually because of Huygens' Principle, such that you can't expect something which will show up at point P, right? If you don't have Huygens' Principle what is going to happen? What is going to happen is that the light passing through this slit will just go straight. And they will never overlap each other. OK? So that's actually why, because of the Huygens' principle, all the points on the wavefront are treated as a point source of a spherical wave. OK? So that is essentially why you can expect that something will hit the P point, which is because, in this case, we have two points, two point source. And they are emitting spherical waves coming from these two points. OK? So it is really because of Huygens' Principle, which applies here, such that we can actually observe the phenomenon at the P. And now, we have managed to calculate the phase difference, which is delta, presented here. So what the next question is, what would be the intensity? Since we have already calculated the phase difference delta, what would be the intensity observed at P? So for that, we have already prepared ourselves from the last few lectures. So now, we can actually calculate what would be the total E. The total E will be equal to EA plus EB. And here, I'm going to use complex notation just for simplicity. And basically, you can rewrite EA and the EB as E0 exponential i omega t minus k times rA plus E0 exponential i omega t minus k rB. The first term is actually telling you the contribution from the first slit, slit A. And the second term is actually telling you the contribution coming from slit B. In this set up, I'm telling you that I have the plane wave coming from the left hand side of the experiment and actually hitting the wall. And you can see that from the drawing. Actually, the wavefront, essentially, actually telling you that the direction of the electric field is actually in the Z direction in my coordinate system shown on the board. So basically, the Z direction is actually pointing to you guys. And that means the electric field is actually oscillating in this direction. OK? So therefore, I have to be careful of those vectors. So therefore, I need to give it other direction. And in this case, it's actually the Z direction. And also, you can see that the amplitude is actually denoted by E0 because I always assuming that both slit have the same finite width. For the moment, ignore the width of the slit. And also, they are coming from the same plane wave. Therefore, the amplitude is all denoted by E0. OK? So now, I have the expression here. And I can now go ahead and simplify this expression and rewrite that in this form. So I can now extract the E0. And also, I extract the common factors here, which essentially the exponential i omega t and also, minus k rA. I can actually factorize some part of the exponential function out. So the choice I made is that I actually could factorize out exponential i omega t minus k times r. Basically, I take these out. And I get this term showing here, omega t minus k rA. I take this out. Then basically, what you are doing to get inside will be 1 plus exponential minus i delta, actually. times z. OK? Why is that delta? Because once you factorize out or take out exponential i omega t minus k rA, basically, you are left with something proportional to exponential i minus k rB minus rA, right? And that is actually the optical path length difference here. And also, of course, you can always rewrite lambda over 2 pi, right? Basically, you write this to be k times d times theta. Right? So therefore, you can actually immediately identify the second term is to essentially exponential minus i delta. OK? Any questions here? OK. Because d sine theta essentially is just rB minus rA, therefore, I safely replace that by delta here. OK? All right. So since everybody's on the same page, I can now, again, factorize out not only the omega t minus kA term, but I can actually do a trick to factorize out, also, exponential minus i delta divided by 2 out. And basically, what I'm going to get is exponential i delta over 2 plus exponential minus i delta over 2. This reason why I'm doing this is because, huh, now, I have this term identified. And this is actually just 2 times cosine delta divided by 2. All right? OK? So now, I'm really pretty close to the intensity. So what would be the intensity coming out of this electric field? That is actually going to be average intensity, as we discussed last time in the lecture. The average intensity is proportional to square of E vector. Right? In the complex notation, how do we evaluate the absolute value of E vector square? In the complex notation, basically, you get basically, E times E star, where E is actually the amplitude, which is the size of the E vector, the magnitude of the E vector. Then, basically, you will see that this will be proportional to cosine square delta divided by 2. Right? Because you can see that if I calculate EE star, then all the terms with related to exponential i something actually got cancelled. Right? So therefore, you can see the "aha" very, very quickly. We can show that the intensity will be proportional to cosine square delta divided by 2, where delta is the phase difference between the first path and the second path. OK? Any questions so far? OK. So we can see that the intensity essentially changing really rapidly as a function of delta. Right? So when I have a situation where delta is equal to 0-- let's actually stop here a bit and enjoy what we have as you learn from here. All right? So if you have delta equal to 0, what does that mean? That means there's no phase difference between the first and second electric field. Therefore, when you add them together-- just a reminder about the notation we were using before. So if you draw the vector in a complex frame, what you are doing is that you are actually adding EA and the EB together in the most efficient way, right? Because the delta is equal to 0, the phase differences is equal to 0. Therefore, you are actually adding them in a straight line. OK? So that actually will give you the maxima intensity. Because when delta is equal to 0, cosine 0 is 1. Right? Therefore, you are reaching the maxima in the intensity. So now, I can always increase my delta until a number which is actually pi. What is going to happen is that if I still use the notation which I was using for the complex frame, what it does this is that, huh. Now, I am actually completely cancel the electric field, because the phase difference now is pi, right? So therefore, in the complex frame, you are adding the two vectors in way such that they completely cancel each other. The magnitude of the two vectors are the same, as shown here, which is actually E0, right? Therefore, what you are going to get, as you expect, is going to be 0, because they completely cancel. OK? You can also see that from this formula we did right here. When delta is equal to pi, then essentially, cosine pi over 2. Then you get intensity equal to 0. OK? Everybody accept this? All right. Now, I can still continue and increase the delta, for example, until delta is equal to 2 pi. Then you are getting this again. Basically, you have EA and the EB, again, line up each other. And the difference is that this EB actually rotated maybe 360 degree. And basically, you will see that, again, the intensity become the maxima again. OK? So that is actually how we can actually understand this result. And, of course, you can also go ahead and plot or simulate this result in the computer and really draw the amplitude, really draw the intensity as a function of angle here, or, say, the delta here. As you can see from here, that the intensity is actually reaching the maximum in the center. Why is that? In the center, if I have observer here in the center, what is going to happen is that the path length, optical path length between AP prong and the BP prong is going to be the same by symmetry, because it's actually in the optical center. Therefore, you will expect that delta is actually equal to 0. OK? So that's essentially why you see the maxima there. And if you start to move away from there, you will see that the delta start to increase. And at some point, you'll reach a minima, which you can see that on the plot. And that is actually because now, due to the increasing optical path length difference and the phase difference, the two electric field is starting to cancel each other, which actually produce the black pattern there. And finally, after it pass delta equal to pi, then these two electric fields start to work together again. All right? They're collaborating again. And you can see that again. You would get another maxima afterward. OK? And here, you can see that is actually my calculation. And, of course, I can do a demonstration to you to really show that this is actually what we are going to see based on the demonstration we are going to show here. So now, I am going to turn the light off. And here, I have a device which actually contain a water tank. And I need to actually turn this thing up. On the water tank I have two vibrator, which is actually acting as a point source. So basically, those vibrator vibrating up and down to create waves in this tank. OK? So basically, you can see that, huh, really, you have two point-like source. And you can see spherical waves is actually really generated and is really propagating away from the point source. OK? And what I can do now, you can see that this picture is really dynamic, because we can see that wavefront essentially moving as a function of time. So what I'm going to do is to really change the frequency of the light, which is actually shining on this water, so that you can actually see the fixed pattern here. And now, I am going to change the light frequency. You can see now I only shine the water tank at the specific time which match the speed of the propagation of the water wave. And you can see, aha, I've actually managed to freeze the wavefront. We see? OK. So you can see, now, really, you can see coming from the source, they are circular wavefront, which actually mimicking the result from Huygens' Principle. And you can see that they are complicated interference pattern forming. You can see that at some point they have constructive interference. If you focus on the central part, you can see that the maxima is actually reach there. On the other hand, if you move away, a little bit away from the center, you can see that really, the intensity drop. And at some point, you will also see that, OK, again, I am changing the procedure in such that the phase difference between the contribution of our source A and the B essentially equal to 2 pi. In that case, you will be able to see that another maxima is actually created again. So now, we can actually also show you that a lot, in fact, based on this glorious pattern, let's actually take a look at the projector here. So if I look at on the individual slide, which I have here, you can see that those are actually a point-light source and is creating a circular pattern. And now, I can actually overlap with two patterns together. And you can see that when I have the center of the two circles pretty close to each other, you can see that really, you have very small d. In this case, you have very small distance between source number one and number two. Then basically, based on our expression, so you can see that delta is equal to d sine theta divided by lambda times two pi, right? And you can actually calculate sine theta will be equal to delta divided by k times t. OK? When delta is equal to pi, that is going to give you a minima where, essentially, also showing here, the minima is shown as the black pattern here. OK? You can see from on here. So what this says, your formula is showing you that when I have d, which is very small, what is going to happen is that I'm going to get sine theta to be very large when d is actually very small. And that can be shown here. When I have d, which is the distance between the center of these two point source, very small, you can see that the place you get the minima is really far away from the center, which is actually here. OK? Now, what I'm going to do is to increase the distance between these two source. According to our position, what is going to happen is that the central maxima will decrease. The position where you get a minima will be moving closer to the center, according to that formula, because it's proportional to 1 over d. And we can do this really carefully to see if I can succeed. And you can see that really, when I am moving these two slides away from each other, you can see that the pattern is changing, right? And the center maxima, or, say, this Gaussian-like curve there becoming narrower and narrower. OK? So that essentially what we can actually observe form here. And our calculation really works very well here. Very good. So do we have any questions regarding the demonstration we have here? OK. So all those things seems to be pretty straightforward to you. And what we are actually now is seeing a position where we can actually discuss how we actually can understand the radar, which is how actually radar works. So here is actually how radar works. Suppose you have some unknown object, which is like an airplane, OK? And you would like to know where is this object. What you do, actually, is to shoot whatever radio waves toward some direction and see if there are something coming back. Right? Then you know there's something on the sky because you can detect the refracted wave. Right? So we shoot this airplane. And then something is going to come back. And now, we can say OK. In that direction I have something coming back. That means there's something there. And I can also measure the time it takes for the wave to come back. Then I know where it's actually that object. Right? So that's actually a pretty straightforward thing to do. However, there's one difficulty. So this is actually the radiation pattern of oscillating dipole which we actually learned before. So the problem is that, OK, what we really need is electromagnetic wave, which is actually very, very narrow in angle and pointing to some specific direction. And then I would like to see if I can get some refractive wave coming from that direction. OK? The problem is that, look! if I oscillate some charge up and down, the radiation I'm getting is really, really broad. Right? So it's going toward all kinds of different direction. So if you use this to detect things, you are always going to get something coming back, because it's actually shooting the electromagnetic wave into random direction. And you are not sure any more where is actually this object you are trying to detect. OK? So that's actually apparently a problem. And what we can actually do is to make use of the interference phenomenon, which we can actually learn from here to actually try to make sure that the electromagnetic wave is actually pointing to some specific direction we want. So let's actually go ahead consider a three slit experiment. I have this setup changed. Originally, I have two slits. And now, I drew it in three holes on the wall. And, again, I have the distance between the slits to be d. And I call this slit number 1, 2, and 3. And we were wondering what would be the interference pattern on the screen, which is actually far away from the wall, as a distance of L. And I'm interested in their intensity at the point P on this screen. OK? So what I am going to do is to basically repeat what we have done in the previous example. I'm trying to connect 1 to the P, 2 P, and the 3 P, basically, connect the slit to the point of interest on the screen. And I can actually also-- you know this angle, this 1 P to the horizontal direction, this angle is called theta in my notation. Then clearly, I can go ahead and calculate what will be the optical path length difference between of the light coming from slit number 1, slit number 2 and the slit number 3. OK? And in this case, what I'm interested is delta 1, 2 and delta 1, 3. Right? Since the screen is really far away from the wall, therefore, I can actually savor the assurance that these two angle is actually theta because the three lines, due to the large distance, this L is actually really, really large. Therefore, they are actually almost parallel to each other. OK? So what is going to happen is that delta 1, 2, which is the phase difference between light from the first slit and second slit, is actually going to be equal to delta 2, 3. It's going to be equal to the phase difference between the second slit, the light from second slit and third slit. And what is actually that number? This number is going to be equal to d sine theta divided by lambda times 2 pi. It's exactly the same as what we actually get from the first example. OK? Therefore, what is going to happen is that no matter what theta I choose, the phase difference between nearby slit is actually a constant, which is actually this one. And I will call this phase difference to be delta. I would like to ask you a question now. The question is, how do we choose the delta here such that I have completely destructive interference? Now, I have three vectors, vector E1, vector E2, and the vector E3. The phase difference between E1, E2, and E3, the nearby phase difference is actually delta. So the question is, how do I actually completely cancel the electric field so that I have completely destructive interference? Can somebody help me here? The hint is that you can actually use this vector sum idea in the complex frame. STUDENT: [INAUDIBLE] PROFESSOR: Yes, very good. To form a triangle in the complex frame, right? So what we can do is now choose the phase difference delta to be such that E1, E2, and E3 actually form a triangle. You see what I mean? Therefore, you can actually already get what would be the required delta value. The required delta value is going to be 2 pi divided by 3. Right? OK? So very good. So now, we are not afraid anymore. So how about four slit experiment? I just add another slit, d essentially the distance between the fourth slit and the third slit. What will be the delta required to have destructive interference? Anybody can help me? STUDENT: [INAUDIBLE] YEN-JIE LEE: Very good. So if you have four slit, based on this intuition, which we developed from the complex notation vector sum, what is going to happen is that if you have four slit, the delta will be equal to 2 pi divided by 4. OK? So what does this tell us? So remember, the sine theta, sine theta is telling you the location where you get the minima. OK? So this is actually the power profile, or, say, the intensity profile. OK? And this is actually equal to 0. And this is actually delta. OK? The place which you get zero intensity is actually becoming closer and closer to zero. Right? Because sine theta, which is the angle between horizontal direction and this observer P, is proportional to delta. When you have destructive interference at angle which is smaller, smaller, and smaller, that means what? That means the central Gaussian-like structure is going to be becoming narrower and narrower. Does that make sense? Very good. So at least we found something interesting now. That means, ha, one idea to get very narrow electromagnetic wave pointing to some direction is to have a huge number of point light source and slit experiment such that I can actually construct something which is actually very narrow in angle. And I can use that to shoot the object which I would like to detect. You see what I mean? Does that make sense? OK? All right. So that's very good. So now, let's actually consider an N slit interference pattern OK? So suppose, now, I have not only 1, 2, 3, and then many more until N slit. All right? I can now go ahead and calculate the E total, which is the total electric field coming from all of the slit we have. Basically, this will be equal to E0 exponential i omega t minus kR where I define r1 is roughly capital R. OK? That's essentially the contribution from slit number 1 OK? And this contribution from slit number 1 is going to be looking like exponential i omega t minus kR minus delta, right, because there is a phase difference between the light coming from first slit and the second slit, which is actually delta. All right? So what would be the third term? So these actually coming from slit number 2. What would be the third term? Exponential i omega t minus kR minus what? STUDENT: 2 delta. YEN-JIE LEE: 2 delta, yeah, because you can see that coming from here, seems the distance between theta as constant, which is d. Therefore, the phase difference between nearby slits is actually a constant. Therefore, I accumulating the phase difference now. I get 2 delta here. And this is actually a contribution from the first slit. And the et cetera, et cetera, until the Nth slit, which is actually going to be exponential i omega t minus kR minus N minus 1 delta. And summing all those things together, and all of them are in the Z direction. OK? So I'm now going to calculate this dimension. So basically, you are getting E0 exponential i omega t minus kR. I can actually factorize these factor out. And what am I going to get is 1 plus exponential minus i delta plus exponential minus exponential minus i 2 delta plus blah, blah, blah. And basically, you will get exponential minus i minus 1 delta in the first term. And all those things are pointing to the Z direction. And this, I know how to actually calculate. Right? Just a reminder, basically, if you calculate summation N equal to 0 to N minus 1 r to the Nth. And these will give you 1 minus r to the N divided by phi minus r. OK? So basically, I can now go ahead and calculate this. And this will basically give you 1 minus-- OK, so the small r here has been replaced by exponential minus i delta, right? So therefore, what I'm going to get is 1 minus exponential minus i delta N for the upper part. And then I have 1 minus exponential minus i delta in the lower part. OK? So that actually make use of this formula, which are here. And, again, it should be simplify these series. All right? As usual, what I'm going to do is to use the trick similar to what I have done there to actually get cosine function out of the exponential functions. All right? So what I'm going to do is to factorize out exponential minus i delta N over 2 for the upper part. So basically, I get exponential minus i delta N divided by 2, exponential i delta N divided by 2 minus exponential minus i delta N divided by 2. OK? This is actually divided by exponential minus i delta over 2 exponential i delta over 2 minus exponential minus i delta over 2. All right? The reason I'm doing this is because I would like to actually make this a cosine function. OK? Any questions so far? OK. So if no question, then basically, this expression can be, again, rewritten as exponential minus i delta N minus 1 divided by 2, because I have this denominator nominator exponential i delta N over 2 and that exponential minus i delta divided by 2. OK? Therefore, I can combine them all together and then get this expression here. And this is actually exponential minus exponential. Therefore, I am going to get sine out of it. And basically, I get sine and delta divided by 2 divided by sine delta over 2. OK. So now, I can actually go ahead and calculate what will be the resulting intensity. Right? The resulting intensity is going to be proportional to the square of the electric field. Right? So basically, the intensity will be proportional to E square. And that is actually equal to E times E star. E and the E is a complex conjugate. And basically, you will see that this will be proportional to sine and delta divided by 2 divided by sine delta over 2 square. Therefore, the intensity will be equal to i 0 times sine and delta divided by 2 divided by sine delta over 2. And then square that. Any questions? So after all this work, we have arrived at expression which is very hard to understand. Right? [LAUGHS] So what I'm going to do to help you is to really plot the result as a function of delta on the screen. You can see there are four plots here. The first one is N equal to 3. The upper left one is N equal to 3. So you can see that the pattern looks like this. So at delta equal to 0, surprise nobody, you are going to get maxima. Right? Because delta is equal to 0, you are adding N vectors the most efficient way. Therefore, you are going to get the maxima, which is i equal to i 0. OK? And if you move away from the center, delta equal to 0, and you see that is a small bump in between. Then you can continue and continue. And you see that there's another big peak again. You see? So that's essentially the structure if you plot this result, i equal to something proportional to sine square this expression there. And that's essentially what you will get when N is equal to 3. OK? And this is essentially how I remember this pattern. OK? So when N is equal to 3, you have a family of two adult and one child. [LAUGHTER] Right? So basically, you have two big peak. And between them, there's a small peak. OK? That's actually how I remember this pattern. And I think it's pretty nice, right? So you can have N equal to 4. It's a bigger family. You have two adults. The adults are slimmer, OK? All right? [LAUGHTER] Because they have a lot of work to do. Then they have two child. All right? N equal to 5, how many children do we have? STUDENT: We have three. YEN-JIE LEE: Three. Therefore, the adults are really frustrated. So they are even slimmer in a happy way, making it positive. And N equal to 6, woo. Oh my god, I have four children in the family. All right? So there are two things which we learned from here. The first one is that the number of big peak, which I would call it principal maxima, the number of principal maxima is actually pretty similar as a function of delta. But the number of secondary maxima increase as a function of N value. N value is actually telling you how many slits you have in the experiment. And also, you can see that the delta is actually becoming-- the first minima, the delta value is actually decreasing as a function of N value. Right? So the parents are getting slimmer. All right? So therefore, you can see that if I would like to have a radar which is actually pointing to a very specific direction, what essentially the choice of N value which we will need? Infinity or a very large number. OK? For sure in your life, we cannot do infinity. But now, we have found a way to actually design our radar since sine theta is actually proportional to delta. Therefore, what we actually really need to do is to really maximize the number of slits we have so that actually we can create a radar which would really point toward the direction of the enemy, which is shown there, invading the earth. OK. [LAUGHTER] And we can actually detect it. OK. So we will take a five minute break before we actually go to the last part of the course, which is the connection to quantum mechanics. So we come back at 35. [SIDE CONVERSATIONS] [SIDE CONVERSATIONS] YEN-JIE LEE: OK so welcome come back from the break. So before we move to the connection to quantum mechanics, I would like to talk some more about what we have learned from the design of the radar. OK? So this essentially what we actually get. The position of the minima that required the phase difference delta is actually equal to 2 pi divided by N value, because it was this delta value. The N vectors is going to cancel each other. And you are going to form something like a circle if you choose delta equal to 2 pi divided by capital N. OK? And don't forget why this is actually delta. The delta is actually d sine theta divided by lambda. Right? OK? And times 2 pi. OK? Right? So therefore, you can see that the sine theta is actually proportional to lambda divided by N times d. OK? And in this case, you can see that if you increase N value, the resolution or the width of the central principal maxima is going to be decreasing as a function, though, N value you're putting. So in short, how do I actually design a high-resolution radar? What I really need is to have lambda to be small. OK? So that means I need to use high-frequency electromagnetic wave. I can maximize the N value. I can actually make d very large. That means I'm going to have a very large radar design. Right? Then I can have a very good resolution. OK. So we are almost done with radar. But there's a problem. The problem is that if you look at this, if this is actually the position of the principal minima, you can see that is always pointing to the center of the radar where the delta is equal to 0. OK? And then that means I can only scan in one direction. There is a reason why those radar are called phased radar. That is because now I can actually change the relative phase of all those point source emitted from the radar so that I can shift the direction of the central principal maxima. OK? So what is actually done here is like this. So basically, I can have introduced before emitting the electromagnetic wave, I can introduce a zero additional phase difference. And for the second one, I introduce additional phase difference of phi. OK? And for the third one, I introduce additional phase difference between the third slit-- or say the third emitter and the first emitter by 2 delta. And for N's emitter, I introduce a phase difference of N minus 1 phi. OK? If I add this phase difference into the setup, what I'm going to get is like this. So basically, delta will become 2 pi divided by lambda d sine theta minus phi angle. All right? And this phi is actually the artificial eddy phase difference between those source. OK? And that means I will require-- and this will be equal to 2 pi divided by N value, such as you have completely destructive interference. OK? I can now make this phi to be time-dependent. For example, it's increasing as a function of time, phi times t, right? Then what is going to happen is that as a function of time, I'm going to change the sine theta value so that I can get a complete cancellation, 2 pi over N. Right? So effectively, I'm changing the angle of the central principal maxima by introducing additional artificial phase difference between all those point source. OK? And this is actually the way we can actually rotate the place we are scanning up and down and get a very nice result to detect the enemy. OK? Any questions? No? OK. So now, I'm going to move on and discuss a very interesting experiment. So this is very exciting experiment content, billiard balls and the two slits. OK? And we will wonder, then, what is going to happen when those balls especially pass through the slit. Can anybody actually tell me what she is going to happen? And what will be the statistics, or say, the count, which I am going to go on to get in the receiver later? Anybody can actually tell me? If I actually shoot a lot of balls through this slit-- don't be shy, right? It's easy. No? Nobody wants-- STUDENT: They make [INAUDIBLE] YEN-JIE LEE: Yeah, that's right. Right? Doesn't surprise nobody, right? [LAUGHS] Yeah, too afraid of answering questions. OK, you can see that they make two path, right? No? Right? OK. Very good. So now, this is the exciting part. Now, instead of shooting billiard balls, what I'm going to do is to shoot electrons. So I can actually prepare an electron source and heat it up, such that it start to emit electrons. And I have two slits and have them pass through this slits. And I have a screen, which actually have an electron detector to count the number of electron which I am going to get on the screen. The reason why I call it single electron source is because each time I control my experiment such that it only emit one electron every time. OK? The question I'm trying to ask is, will I see some pattern, which is actually light like billiard balls, and they form two piles in a pack? That's actually option number one. Or I'm going to see really something crazy? It's the electron is going to be interfere-- it's going through the interference with itself. And that essentially option number two. OK? The lure of 8.03 is that everybody had to choose one. OK? So how many of you think what is going to happen is number one? Come on. I have only one electron each time. Nobody think so? Wow. Maybe all of you are wrong. [LAUGHS] How about the second option? STUDENT: [LAUGHS] YEN-JIE LEE: Hey, some of you actually didn't raise your hand. Come on. Come on. [LAUGHTER] OK, everybody. Wow. What is actually happening to you brain? [LAUGHTER] My brain is not functional like this. OK. So I really hope that I can bring the experiment to here. But unfortunately, that's actually going to be difficult. OK? So what I'm going to do is that I'm going to show you the experimental result, this video. And we are going to see what is going to happen. You see that there are dots popping out. What are those? Those are the detected electron one-by-one on screen. OK? So basically, you can see that the number of dots are increasing as a function of time. And I actually-- I mean, speeding up things a bit so that actually you can see the pattern quicker. OK. So you can see that there are more and more dots. And each time, you can see that I only get one electron per image here. Right? So you can see now there are more and more and more and more, and accumulating more data, like what we actually done in The Large Hadron Collider. We wait there, collect more data. And we are speeding things up. And you can see that, wow, something's actually developing. What is that? Can you see it? Now, you are speeding up like 1,000 times faster. You can see what pattern? STUDENT: Interference pattern. YEN-JIE LEE: Interference pattern. What is going on? You are not surprised? STUDENT: No. YEN-JIE LEE: Oh my god. What is going on? [LAUGHTER] I'm so surprised. Look at this. So I have emission of one electron each time. And that is actually the four snapshot which I took-- which actually this experiment, Hitachi Group actually did this experiment. You can actually click on this link to the more detail. And they took four snapshots of the experiment. And you can see that in the beginning, you can see clearly each time you only get one electron out of the source. OK? But as a function of time, you're accumulating more and more. And you see that clearly, there's a pattern forming, which, is actually consistent with what we see in this calculation. OK? So I think that's actually truly amazing. And what does that mean? That means the electron is playing with itself. It's interfering with itself. Right? That's really strange. What is going to happen? What is going on? So one single electron pass through both slit, which is actually the option you choose. Surprise me. And then they interfere like waves. And they produce the pattern which we see on the screen. That is actually really crazy to me. What is actually even more crazy is this situation. So now, if I make measurement in front of the slit, OK, so now, I puts on a little device. When the electron pass through one of the slit, I say, send me a signal. OK? So now, I can clearly know that which slit the electron is actually going through in the experiment. OK? And the crazy thing is that if I do that, then it becomes two piles. OK? Of course, maybe there are some diffraction pattern. But it really changes the pattern of the experimental result. And that is actually really very strange. And we are going to talk about that briefly in the next lecture. So before the end, I'm going to show you an additional demonstration which motivate the discussion what we are going to have in the next lecture. So now, I can actually turn off the light again and also hide the image. OK. I hope I can find the pattern. [LAUGHS] All right. So here, I have two laser. So I'm going to turn up the first laser. And this laser is going to pass through a two slit-- a two really nearby slit and form an interference pattern. As you can see on the wall-- I hope you can see, I don't know if you can see clearly-- that you can see there are many, many dots, nearby dots, which actually shows you the position of the principal maximas, right, because are actually two slit experiment. Therefore, how many children do we have in the family? Zero, right? Because they are-- OK, they just got married, maybe. [LAUGHS] All right. So therefore, you will see only adults. And that is actually the principal maximas. You can see many, many nearby dots. They are almost equally bright. OK? But there's something happening to this pattern as well. And you can see that-- wait, wait, wait a second. In the calculation we get the principle maxima to have the same height, right? That means you are going to get exactly those same intensity for all the maximas. But you don't see that here. You can see that if you move away from the center too much, the intensity is decreasing. You see at the edge? It actually even goes to zero. Right? What is actually happening? Something clearly is actually missing in our calculation. And that missing part is actually diffraction, which we will talk about that in the next lecture. So if you compare this pattern to the second demo, you can see in the right hand side setup, which I have here, which I should give you a projection on the wall, which is actually lower part of the demo, you can see that this laser actually pass through a single slit. But this slit is actually pretty wide. OK? And you can see that indeed, you see the laser coming out, but essentially, not a single spot. And it has some kind of pattern, which is actually popping out there. And this is also related to interference between infinite number of source. OK? And you can see that the pattern seems to really pretty similar to the pattern we see in the upper demo, except that upper demo have individual similar structure, which is the principal maxima from the two slit interference. And we are going to solve the mystery in the lecture next time. OK. So thank you very much. And if you have any questions related to the lecture today, I will be here to answer your questions. So this is a demo which we would like to show you, Single Slit and the Double Slit Interference Pattern. OK? So the first scene is the setup. So we have a laser beam, which is actually passing through this either single slit or double slit experiment. And then the laser beam will be going through this and interfere and show interesting pattern on the screen. And there are two setup. The left-hand side one is two slit interference experiment. And right-hand side is a single slit diffraction experiment. So you can see left-hand side one, I already turned it on. Laser beam passed through two slits. And they form complicated pattern on the screen. And you can see there are two kinds of structure here. The first one is the very fine structure, which you can see that it's like some row of dots in the center of the pattern. And there are larger scale pattern as well, which you can see that the overall intensity of all those little dots are also variating as a function of distance with respect to the center. So during the lecture, we were wondering what actually cause this kind of pattern. And the answer is that this is actually coming from the effect of single slit interference. The reason why we have this pattern is because the two slit is actually not infinitely narrow in my setup. Therefore, within a single slit, there is already a interference pattern coming out of it. Therefore, the compound effect, results in a very complicated structure we see on the screen. So to demonstrate this effect, now, I'm going to turn on the right-hand side setup. In the right-hand side setup, I am going to have the laser beam, which you see emitting from here, pass through a single slit. I actually set it up so that they have the same width between the single slit experiment and double slit experiment. And then you can see after I turn it on, you can see that now, we have two sets of pattern. The lower set is actually coming from a single slit interference experiment. And you can see very nicely that first of all, it has a similar pattern, like what we see in the double slit experiment. Secondly, you can see that basically, we carefully tune these two experiments so that the distance between the slit and the screen is roughly the same. Finally, we also set it up, as I've mentioned before, such that the width of the individual slit in the double and the single slit experiment are the same. And you can see that with single slit experiment, we also see a very similar pattern that you have a central maxima. You have a high-intensity light going toward the center of the pattern. And the intensity actually decrease dramatically really quickly as a function of distance. And also, you can see that the pattern actually matches with what you see in the double slit experiment very well. And that is actually pretty remarkable. And from these two experiment, we understand why we have also a complicated structure in the double slit experiment, not just like many, many little maximas, many, many little dots. But also, you have this overall modulation in the light intensity. And that is actually mainly coming from the single slit diffraction pattern. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 17_Polarization_Polarizer.txt | SPEAKER: The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: All right, so let's get started. So today, very happy to have you here. We are going to talk about continuing our discussion on the two-dimensional and three-dimensional, waves. So as I mentioned before, there are two interesting situation which we can actually increase the dimensional. So for example, I can have all the objects oscillating in just one direction, but I changed the way that I placed all those objects in the space. For example, I can have particles which are arranged in two or three-dimensional arrays. And we were talking about how to understand this kind of system. And all those objects are oscillating in just one direction-- for example, up and down in one direction. That's actually one measure we can increase the dimension. There's another interesting example which we will talk about today is to change the direction of the oscillation, even rotate the natural electromagnetic waves, for example. And how can we achieve that and how do we understand this phenomena, that's actually going to be covered by the lecture today. So before we move forward, we will have a short review on what we have learned from the last lecture. And this is actually what we discussed. If I have two materials, the left-hand side and the right-hand side are two different kinds of materials, or very thin membranes. And if I have an incident wave coming into the boundary of these two materials, which is just x equal to 0, as we discussed last time, basically the boundary condition require that in order to make sure that the membrane doesn't break, that means the k vector, the projection in the y direction of the k vectors has to be the same. That means the projection of the wave in the y direction, which is along this line, the wavelength of all the incidents refracted and transmitted wave, the wavelengths should be all the same. Otherwise, I can change y and make the membrane break, or break the boundary condition. So that's actually the first thing which we learned from the math we were doing last time. And also, the k value are not arbitrary, right? So we were already assuming that all three waves, all the three plane waves are oscillating at the same frequency. If they are oscillating at different frequencies, it doesn't work because I can change time, then make the membranes break. So therefore, all the three plane waves will be oscillating at the same frequency-- omega. And according to this formula, so we have defined and which is actually the refraction index, which is equal to some constant c divided by the speed of the propagation, the phase velocity of the left-hand side material. And we also can define n prime, which is actually equal to c, the same constant, divided by v prime, which is the speed of propagation of the right-hand side material. And according to the dispersion relation, we can calculate what will be the length of the k if omega is given. The omega for the left-hand side and right-hand, refracted, transmitted, and incident waves should be the same. Therefore, I can immediately write down what would be the length of the k vector. And that means the length of the k vector would be equal to n times omega over c. So c over n is actually just v. So basically it's just the non-dispersive median dispersion relation. And also you can go ahead and write down what would be the length of the k prime. And that is actually determined by n prime omega over c. So based on these two interesting formations, what we can conclude is that that means k prime and kr cannot be arbitrary. They have to be aligned to form a specific pattern. The pattern is that the projection in the right direction should be the same. And also at the same time, the length of the k vector is determined by the refraction index. So once we fix all that and put them all together, we can conclude that based on the projection in the y direction, we will conclude that theta will be equal to theta r, where theta is actually that incident angle and theta r is the refraction angle, which is describing the direction of the refractive wave. And also the second very interesting information we learned is that based on the boundary condition, we can conclude n sine theta will be equal to n prime sine theta prime. So that's actually Snell's law, which some of you actually learned from the high school days or from the earlier lectures in physics. And these two interesting results form the basis of geometrical optics or laws. That's two of the most important laws we learn from geometrical optics. So that actually gives you some examples and gives you some more feeling about what we are talking about. So what we are talking about is that if I have an incident wave coming into this boundary, and that incident angle is theta 1, what I would expect based on what we have just derived is that theta r, the refracted wave direction, the refractive wave angle, the refraction angle would be equal to the incident angle, according to what we have just derived. I was just rotating this by 90 degrees. And also we can calculate what will be theta 2 according to Snell's law-- n1 sine theta 1 equal to n2 sine theta 2. And if I continue and propagate the incident wave, here I assume that n2 is larger. If you have a larger refraction index, that means the speed of propagation is smaller. Larger n value give you a smaller speed of propagation. Therefore, you can see that the wavefront, which is actually the position of the peak, actually got delayed compared to the original projection. And you can see that the red line is actually really what you would see in the second median. And then we can also continue to propagate and you will see that, interesting, that means the plane wave would change direction because of the matching boundary condition, the membranes doesn't break. You can see that the peak position match from the median number 1 and median number 2. The peak position, which is the position of the line, match. And also, due to the slower speed of propagation, the plane wave actually change direction. So that's actually how we can understand the mathematical result which we derived last time by this interesting example. So that's considered a situation which is maybe a little bit interesting to you. So what will happen if I now shoot light from inside some material which delay the light slightly-- for example, n1 is equal to 1.5. I shoot something through the material, and then the second material I have has higher speed of light, which is actually having the speed of light equal to light in a vacuum case. So in this example, I have n1 equal to n2. Since n1 sine theta 1 is equal to n2 sine theta 2, so now I can calculate what will be the resulting theta 2 according to this equation. So the resulting theta 2 will be sine theta 2 will be equal to n1 over n2 sine theta 1. In this case, n1 is greater than n2, therefore, this term is greater than 1. In this case, actually, this ratio is equal to 1.5. So this is actually pretty interesting. That means this factor is actually greater than 1. I have sine theta 1, which is multiplied in this vector. So that means if I increase theta 1, if I increase theta 1, at some point I will not be able to get theta 2 because theta 2 will be arcsine 1.5 sine 1. And at some point, 1.5 sine theta 1 will be greater than 1, then I don't have a theta 2, which can satisfy this equation. So what will happen? Maybe the whole system explodes, I don't know. So we are going to do a simple experiment to see what is going to happen. So before we do this kind of dangerous experiment, we are going to turn this light off and be prepared. Hope everybody will survive. So here I have a laser, which is actually shooting a laser beam through this tank of water. So this is water, with n value roughly 1.33. And outside of water is air, so the speed of the light is roughly equal to c. So n value is actually roughly 1. So that's actually exactly the situation we are looking for. And let's turn on this experiment, careful. Wow, look at this. You can see that here there was no light coming out. Why is that? Because of the mathematics-- the mathematics say that, OK, sorry, guys, theta 2 doesn't work. Therefore, there will be no light really coming out. You can see my hand, you can see the light here. When I put my hand here, it's not burning my hand. But that's OK. All right, and you can see that nothing really comes out. And all the energy are bounced back into the water. The same thing also happened here. You can see that the light is actually bouncing back and forth and moving into the left-hand side direction until it passed through here, maybe into there, because it's actually still bouncing around inside this tank. So the good news is that no explosion, like what we have here. The interesting thing we find is that all the energy will be bounced back if you have large enough incident angle in this situation. As you can see from here that all the light's energy are bounced back into water. So that's actually very, very interesting. And that means we can probably make use of this property to send light through some large n material. So that's actually how optical fiber works. So basically you can actually shoot a light into the optical fiber. And the light is going to be bouncing back and forth between the boundaries inside the fiber. And then you can actually send those information through light by this kind of mechanism. So that's how optical fiber actually works. And we have a setup, which I have a light here, shooting light into the optical fiber. And I have paper here which tried to block part of the light. So from here, you can see the text which I put on the paper, because some of the light is blocked by this paper, the text on the paper. And this light goes through this optical fiber and continues and propagates and got captured by the camera. So you can see, can you read out loud what is actually written there? Can you see it? The-- AUDIENCE: Last question on the YEN-JIE LEE: The exam is-- oh, no, no, no, no, transmission interrupted. Oh my god. All right, so I'm sorry it didn't work, but it worked in the beginning, right? So you can see that this is a wonderful way to send optical signal. And we actually do that. We send signal from US to Asia through all those crazy lines under the sea. So that's really cool. And finally before we change the topic, I'm sure that you will enjoy doing the practice in your PSET number 8. We are going to learn that this is actually highly related to a beautiful phenomena we see in daily life-- the rainbow is actually really related to Snell's law, and that you are going to solve this problem in the PSET. All right, so any questions so far related to Snell's law and refraction index, et cetera? All right, so if not, we'll go ahead and talk about the second example. The second example is that instead introducing more objects in this array, we could change the direction of the oscillation as a function of time and see what is going to happen. For example, the direction of the electric field, I can make it rotate or change as a function of time. And that's actually called circularly polarized wave. And that means we are going to talk about polarization today. Before we start the real lecture, what we are going to do is that I will quote words from Feynman. "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are, but if it doesn't agree with experiment, is wrong." So that's actually a very important lesson. And I have been telling you that electromagnetic wave is predicted to be oscillating in the transverse direction, as you can see from that little figure. So if the directional of propagation is to the right-hand side, so that means electric field and the magnetic field can only be oscillating in a plane which is perpendicular to the direction of propagation. That's actually what we have learned from Maxwell's equation. But all those things are theory, right? Do you believe those theory? I'm not sure. Maybe light is actually oscillating in the longitudinal direction, right? If you are a physicist, you should ask this question. Maybe you'll find something which is inconsistent with the theory, then you'll feel really happy. So the question we are trying to answer is how do we know the electromagnetic waves are transverse waves. And we are going to work through a few examples to convince ourselves, maybe that's the case, maybe we have some hint. Of course, we cannot prove 100% but very likely this is probably the case. So let's go ahead and start the discussion today. So instead of adding one more dimension by arranging materials, we can actually discuss how the pointing direction of the electric field depends as a function of time. So in order to do that, I need to remind you how to write down electric field for the electromagnetic wave. So in a previous lecture, if I organize myself so that the electromagnetic field is going in the z direction-- the electromagnetic field is going in the z direction. All right, if I choose that, then basically electric field as a function of z and time will be equal to the real part of some vector psi 0 times exponential i kz minus omega t. If I assume that this electric field, the electromagnetic field is propagating to where-- the z direction, right? So by now, you should get used to this already. This is going to the positive z direction. Where I intentionally write psi 0 there is actually a vector which contains two components-- psi 1 in the x direction and psi 2 in the y direction. And you can see from here that you can immediately recognize that this can be returned as a superposition of two waves. So one is actually electromagnetic wave with electric field in the x direction. And the other wave, the other electromagnetic wave, is actually oscillating with electric field in the y direction and with amplitude psi 2. So that is one you can get immediately because of the superposition principle. So it's a superposition of two electromagnetic waves. And of course, in this case, I take the real part of this vector. So in general, psi 1 can be a1 exponential i phi 1. And in general psi 2 can be a2 exponential i phi 2. So in this notation basically, we write everything in terms of vector. And sometimes we write those things in terms of matrix, and that sometimes serve a better purpose for calculation. So we can also rewrite this thing in matrix form. So I have a matrix E which have two components, E x and E y. And this is actually equal to a real part of some Z matrix, which also contain two components, times a scalar, which is exponent i kz minus omega t. So as can see, I am now just setting up the language we want to speak so that we communicate. So in this case, the z matrix is written as psi 1 and psi 2, which are the two components. One is in the x direction, the other one is in the y direction. And we are going to use this language and see what we learn from it. So you can see that we have been discussing electromagnetic wave, which is propagating toward the positive z direction. And I have two component which I can have-- x direction electric field and y direction electric field. So let me try to go through some example and see what we can actually learn from this. So the first example I would like to talk about is that if I have two waves, E1. The first wave is actually E0 cosine kz minus omega t in the x direction. And then the second wave is E2 equal to E0 cosine kz minus omega t, in the y direction. Be careful-- the direction of the electric field is different for the first and the second plane wave. And if you actually notice from this expression, these two waves are in phase. So in-phase means that they reach maxima at the same time. So in this case, if I add two waves with no phase difference, what is going to happen? So I am going to have a E vector, which is E1 plus E2. And if I plug the locus of this kind of electric field in the two-dimensional space, x and y, so now I am plotting, so I am fixing my z position for example at 0. And I would like to see how the locus of the E vary as a function of time. In this case, since E1 and E2 have the same amplitude, which is E0, and also they have no phase difference, that means they reach maxima simultaneously. So that means originally, for example, in the beginning the electric field is 0. And this electric field projection to the xy plane will increase until some maximum. At the maxima, this will be E0, the x and y position will be E0. Then it goes back to minus E0, minus E0, in the x and y direction position. And it goes back and forth. So in this case, this is actually still not very different from what we had discussed before because the electric field is still oscillating up and down. But the difference is that it's not oscillating at the x-axis or y-axis, but in the axis which is actually 45 degree with respect to the x or y-axis. And now we can do a exercise to write it down in the matrix notation. Now I have this E matrix will be equal to the real part of E0, E0. And both E0's are real, exponential i kz minus omega t. And basically I can conclude that z will be equal to E0, E0, and this will be E0, 1, 1. In this kind of situation, the electric field is varying as a function of time. The position to xy plane is a line. When I happens, we call it linearly polarized. So this is actually just a name. But indeed the locus of the electric field on the xy plane is a linear line, so that we call it linearly polarized. And of course you can say, OK, this is just one example. I can have many, many examples which you also create a line when you plot the locus. So for example, I can have z equal to E0, 1, 0. Can somebody tell me what does that notation mean? AUDIENCE: That just means one wave electromagnetic wave in one direction. YEN-JIE LEE: That's right. So that means you only have electric field in the x direction. So this is the x direction, this is y direction. And this is also linearly polarized. Of course you can have very similarly E0, 0, 1. And in this case, you only have electric field in the y direction. Just want to tell you my language I'm introducing here so that we communicate. And of course, you can have z equal to E0 cosine theta sine theta. What does that mean? This means that when I plot the locus on the xy plane, I'm going to have a straight line still, but now the angle between this line and the x-axis is going to be theta. So all those examples, you can see that in the first case the oscillation is in the x direction. And in the second case the oscillation is in the y direction. And then in the third case it can be in an arbitrary line-- theta angle away from the x-axis. So all those things are linearly polarized. So so far, there is nothing to surprise you. So that's what we have been talking about. And you can say that, Professor Lee, you were just not doing a very good job. You didn't rotate the axis right so that all the electric field is in the x direction. So in principle for the discussion of the linearly polarized wave, you can do a good job by rotating your axis so that you only have one component in the x direction. So I say, OK, yes, I agree, but this is useful discussion. All right, so now maybe you're bored. They have no phase difference, right? So how about we introduce some phase difference and see what will happen. So now if I consider the second situation-- I have E1 is equal to E0 cosine kz minus omega t in the x direction. Now I consider E2, this would be E0 sine kz minus omega t in the y direction. I hope you can see it. And then you can see that now they reach the x component and y component electric field. They reach maxima at different times because of the phase difference. How big is the phase difference? Can somebody actually remind me? AUDIENCE: Pi over 2. YEN-JIE LEE: Pi over 2, very good. All right, so this I can write it down as E0 cosine kz minus omega t minus pi over 2, as you already figured out. And now I can also again write it in the language I like, the matrix format. Before I achieve that, I can write it as a real part of E0 in the x direction plus E0 exponential minus i pi over 2, because this minus pi over 2 sign, the factor here for the y direction. And all those things are multiplied by exponential i kz minus omega t. Both of them are actually oscillating at the same omega angular frequency. And you can see that now I can collect this phase difference back into a complex factor here, exponential minus i pi over 2. And exponential minus i pi over 2 is actually just minus i. So basically you can figure out that it's just minus i. So then I can write down my expression for the E matrix. This one look like real part E0, 1, minus i, exponential i kz minus omega t. And in this case, z vector will be 1 minus i in the language which I introduced today. Everybody is following? Am I going too fast? Very good. Thank you for the feedback. So now I'm going to do the same thing to plot the locus of the electric field as a function of time on the xy plane. So now you can see that it's pretty interesting. Since I have a cosine and sine, I assume that t is equal to 0, z is equal to 0, then I will only have electric field in the x direction. So this is actually when t is equal to 0. All right, and if I increase time, I fix the z to be equal to 0. If I increase the time, this locus is going to do an interesting thing. It's going to be rotating until it finish one period. Why is that happening? Because what I'm plotting is the locus of the electric field. And you can see that if I set z equal to 0, when z is equal to 0, this will give you E0 cosine omega t in the x direction and E0 sine omega t in the y direction. So E0 cosine omega t, E0 sine omega t-- wow, this reminds you about the previous discussion. If you have a cosine and a sine, they work together in different directions, that's going to get you a circle. So that's why in this locus you see a circle. And it's rotating in a counter-clockwise direction. And the speed of the rotation is related to omega t. And now if I increase the time, then this point is going to be going in a counter-clockwise direction. And you may be super surprised because what I have been doing is to add two linearly polarized waves together. The only thing which I always say, the magic I have been doing, is to introduce a phase difference. And you can see that instead of going up and down, up and down as a function of time, now it's actually doing rotation. So what is going to happen is that as a function of the time the direction of the electric field is going to rotate as a function of time. So we call this situation circularly polarized. By the way, because of the initial two components I put in, both of them have amplitude E0. Therefore, it's circularly polarized. I can also try to do something different. For example, I can change the x direction. So the third situation is that I can change the first x direction amplitude from E0 to E0 over 2. Then what I'm going to get is something like this. The only thing which I change with respect to 2 is that I changed the amplitude of the electric field in the x direction by a factor of 2. Can somebody actually tell me what is going to happen in this situation? What will happen to the locus? AUDIENCE: Gets squished. YEN-JIE LEE: Yeah, it gets squished in, so in the x direction. Yeah, that's right, very good. So what you are going to get is that instead of a circle you get something like this. So this is the x direction and this is the y direction. And this will give you a maxima x equal to E0 over 2. And of course the original amplitude in the y direction didn't change, and that gives you a maximum value of E0. And this becomes an elliptically polarized wave. So this kind of situation is called elliptically polarized. How do we actually visualize this situation? So that means, as in the beginning, when the electric field is aligned with the x-axis, it's pointing in the x-axis. It has a shorter length. And when it rotate, rotate as a function of time to the y-axis, the amplitude becomes bigger. And it gets smaller again, and increase again, it becomes bigger. So you can see the amplitude is actually changing as a function of time. When you have this kind of situation, they have different amplitudes, although they have a fixed phase difference, so pi over 2. Any questions so far? OK, so if you noticed that there's actually another way to produce elliptically polarized wave. What we could do is that instead of changing the phase by a factor of pi over 2, we can change the phase difference. The phase difference can be delta phi, which is the phase difference, can be a different value, arbitrary value, not equal to pi over 2 or 3 pi over 2. If the delta phi, which is the phase difference between x and the y direction, EM waves-- electric field. If the phase difference is not pi over 2 or not 2 pi over 2, then you can also create an elliptically polarized wave. So that starts from the original figure, which we actually discussed-- situation number 1. Situation number 1, I have delta phi, the phase difference equal to 0. When that happened, you have a linearly polarized wave. Basically what you are going to get is a line in this two-dimensional space. If I increase, so now I slightly delayed. If I slightly delay the electric field in the y direction. So if I slightly delay electric field it in the y direction so that delta phi now is greater than 1, what is going to happen is that it's going to look like this. This means that they will not reach maxima really simultaneously. There will be because of the phase difference. And you'll see that originally when there were no phase difference, you would be oscillating back and forth in this blue line. When you increase the delta phi slightly, then you are going to get also a elliptical shape, but now is tilted with some degree, which is 45 degree in this case. So therefore you can see that now I can also create this is also elliptically polarized wave, I can also create elliptically polarized wave by adding two components, which they have some slight phase difference. So that is actually how I can create a something which is called circularly polarized or elliptically polarized. Originally before you come into this class, it may look really completely bizarre that, oh, I can have electric field going up and down as a function of time. But how could I rotate this thing, right? Looks really strange. How can I see this from the Maxwell's equation? But now you get the idea. Basically, that's because I can now overlap two components. Both components individually are linearly polarized. But if I introduce a phase difference, then the superposition of these two components become something which is actually rotating as a function of time. And that's pretty interesting. So let's visualize what we have learned so far. The first one is linearly polarized. Actually, it doesn't surprise you-- that's the example which we have been using in the previous lectures. And this is the situation of circularly polarized wave. So let's focus on the figure at z equal to 0. So you can see that in this case the direction of the electric field is actually rotating as a function of time. And of course as we discussed, I can actually add two electric fields with different amplitudes or introduce slightly different phase, then you will see that not only that the direction is changing, but also the amplitude is changing. And in this case we call it elliptically polarized wave. Any questions so far? Yes? AUDIENCE: So the magnitude always is constant with time now? YEN-JIE LEE: Yes, so the magnitude, or say the intensity, is proportional to E squared, right? So it's actually a constant. So now let me add more excitement here. So now suppose I have a perfect conductor, all right. So what I am going to do is that I'm going to introduce some more excitement by shooting this linearly polarized wave through some material. If I have a perfect conductor where all those strips, I have only strips of perfect conductor instead of a plate-- we were talking about plate before. And the lesson we learned is that the plate is going to refract the electromagnetic wave because that electrons on the plate is so busy, it's trying to make sure that the electric field in the surface of the plate is equal to 0 because that all those electrons are really moving around. So that's making sure the electric field is canceled. And therefore, it's going to refract the electromagnetic wave. So how about I restrict the direction of the movement of the electron so that it can only move in the horizontal direction? What is going to happen is that in this case, the electric field is actually oscillating up and down. And the electrons see this field and they will say, no, no, no, this is not why we work. This is not we are going to vote for. And I'm going to rearrange ourselves to compensate that, all right. And they were asking, can I move. Oh yes, I can move in the horizontal direction. So they jump up and down, then they can actually cancel this electric field. Therefore, what is going to happen when we have this perfect conductor is that the electromagnetic field is going to be bounced back like what we had before when we talked about a metal plate, all right. So that's actually pretty nice. Now suppose I have another perfect conductor. If I have another perfect conductor, this time the perfect conductor is arranged such that all those charges can only move inside or outside of the board instead of going up and down. Now I have the incident wave, which is actually polarized in the horizontal direction. So you can see that this time the electrons are really nervous about this. And oh no, I have to do something, but they cannot move up and down. Therefore, what is going to happen is that there will be no cancellation of electric field at this boundary. And this polarized wave can pass through this so-called polarizer or perfect conductor without getting stopped or get refracted. And as you can see that in these two examples, I have so called the easy axis. So you can see that the easy axis, as the name should tell you, so easy axis is the axis which is easy. All right, so what does that mean? That means if I have electric field aligned with the easy axis, it will pass through. And the easy axis is perpendicular to the direction of all those streets I have in the perfect conductor. Let's look at the first example. It tells you that the electric field is not aligned with the easy axis. That means it's not easy, so it got refracted-- oh, life is hard. And the second electric field is smarter. It got aligned with the easy axis. So life is easy, it passed through. That's how I remember this so-called easy axis. Any questions? So we have been talking about all those crazy names of polarized light. And I hope that you also have learned about unpolarized light before. Most of the lights are unpolarized. For example, light emitted from those light bulbs are not polarized because every emission of a photon can be aligned in different direction. Therefore, as I was talking about, there are an infinite number of photons hitting my face and bouncing back to your eye. All those things are not aligned to the same direction as what we have been discussing before. In the case of linearly polarized wave, all the electric fields are pointing to the same direction. And apparently those lights hitting my face is not aligned and it's actually pointing to random directions. So that brings me to the fifth situation, which I would like to talk about. The fifth situation is that I could have unpolarized light. So what do I mean by unpolarized light? That means electromagnetic waves which were produced independently by a large number of uncorrelated source. You may ask, OK, wait, wait, wait-- unpolarized means that we have a lot of different light source pointing to different angles. Shouldn't it just look like this? So you have pointing this direction, all the directions, all the possible directions, pointing to all different possible directions, like this. Shouldn't that diagram actually tell you something about unpolarized light? Life is hard. If everything is aligned and also arriving at the same time like this, what is going to happen? They cancel, right? Because all those things are vectors. If they reach maxima at the same time, this means that they are emitting always at the same time, but in random direction. And emitting at the same wavelength, then they are going to cancel each other. So apparently that's not what I mean by unpolarized light. What I mean is that they can be pointing to different directions, but that emission time and the wavelength of all those emitted electromagnetic waves can be slightly different, otherwise they will just cancel each other completely. Any questions about what I just said? So very good. So now what I am going to do is to show you some examples related to polarizer. Before that, I will take a five minute break before we come back to the demonstration. So we will come back at 36. OK, so welcome back. So we would continue the discussion of the polarization and the polarized wave and the polarizers. So before that, I already introduced the polarizer by the perfect conductor arranged in the x direction or y direction, many of them are strips, aligned in the x direction and the y direction. And usually we use a simple diagram like this, a circle and an arrow, to indicate the easy axis to tell you about the property of the polarizer. So in this case, if I have a circle and I have an arrow, which is pointing toward the x-axis, in this case my coordinate system is here, horizontal is x, vertical is y, that means my easy axis is in the x direction. And I can actually write down what would be the matrix presentation of p0, which would present the effect of this polarizer. The p0 will be a matrix in this form, 1, 0, 0, 0. If I have this P0 acting on the z, for example, I can have the p0 acting on the z, then basically what would happen after the light passed through this polarizer will become z multiplied by p0. So basically all this p0 matrix does is to extract the position of the field in the x-axis. But I'm just writing it down in the matrix format. And on the other hand, for example, I can have this easy axis, which is 90 degrees, which affects the x-axis, which is in the y direction, then I write this down in the form of p pi over 2. This pi over 2 is the angle between the easy axis and the x direction. And in this case, you are going to get 0, 0, 0, 1 because all this matrix set notation does is to extract the component which is actually in the y direction. And you can of course multiply-- when you have an incident electromagnetic wave which you can extract the polarization z matrix, you just multiply p pi over 2 and z. Basically you can actually get the resulting polarization of the electromagnetic field after passing through this polarizer. What is going to happen is that only the y component will survive. In the case of easy axis aligned in the x direction, only the x component will survive. So now let me go through a short example here. So suppose initially I have an electromagnetic field polarized, it's linearly polarized in the y direction. And I have that electromagnetic field passing through a polarizer, which is actually theta degree away from the y-axis. So what is going to happen is that all the components which is parallel to the axis survive. All the projected components in the axis perpendicular to the easy axis didn't make it because the electrons are going to be oscillating up and down like crazy to compensate and then refract that component. So what is going to happen is that after passing through the easy axis, the direction of the polarization will be altered such that it's actually in line with the easy axis of the polarizer. So you can see that, after passing through this polarizer, the direction of the polarization, this is still linearly polarized, the direction is changed by theta degree. And also the amplitude also changed because only the component parallel to the easy axis survived. Therefore, the magnitude of the E vector becomes E0 cosine of cosine theta. And therefore, the amplitude of the light got reduced. It becomes I0 cosine theta squared because the intensity of the light is proportional to E squared. So after all this, this is time to take a look at some demonstration here. So here I have a setup. I have emission of linearly polarized microwave from the left-hand side, which is the source. And I have a receiver which is connected to this scope. You can see the result on the scope. You can see that indeed they are energy passing from this source. And it got accepted and then recorded by the scope. Now I have all of those-- OK, all are not so perfect, but those are metals which have many, many strips or many, many little rods here. And my initial linearly polarized wave is actually pointing in the vertical direction. So if I have my polarizer arranged in this direction, can you predict what will happen to the readout on the scope? Will I see signal or not? How many of you think we will see signal if I arrange that the electromagnetic wave is polarized in the up and down direction? OK, one, two, three-- only four people think so. How many of you think nothing will be observed by the scope? Most of you actually think so. So let's really do this experiment. Look at what is happening. Can you see it? Do I see a signal? No. All the signals are canceled, right? Why? Because all the hard work of all those electrons in the metal, they are like crazy, oh my god, this is a disaster. I am going to oscillate up and down-- cancel, cancel, cancel. Then it got cancelled. On the other hand, I can save all those electrons. So now I'm going to rotate this thing by 90 degrees and see what is going to happen. Can you see it? Nothing happened, right? Because those electrons-- oh my god, crisis coming, but now there's nothing I can do because I cannot move up and down. Therefore, there will be no refraction. So they have just to accept the fact that this electromagnetic field went through. All right, and that actually does something really interesting. Look at this-- so now I can actually make electromagnetic field completely destroyed, because originally the electromagnetic field is linearly polarized, up and down in this direction. So if I have a plate which is 45 degrees and I put in another one here-- it doesn't really work very well. The signal probably is too small. How about we do this demo in a different way. So right now here I have my computer here. Can you see my computer? You can see the screen, right? The screen essentially is made of LED. Those LED screens emit polarized light. And those are the polarizer, which is the equivalent version of those metals but arranged in a really fine grain-- so you cannot really see all those strips. And they look pretty transparent. But the idea is pretty similar. And the polarizing axis is in the horizontal direction. The easy axis is in horizontal direction. So let me put this here. Can you still see the screen? You cannot, right. But if I rotate this by 90 degrees, you can see it. That is because all those light emitted from the screen it linearly polarized up and down direction. So now if I have another identical polarizer which I insert between these two, so now you cannot see anything because all the light is pointing up and down, or the electric field is pointing up and down. And now if I insert another one, which is 45 degrees, can you see something? You can see it-- why? That is because if I insert this additional polarizer, like what I was discussing, it's going to take the position to the direction of the easy axis. And if I have another one, which is the easy axis pointing toward the x direction, then again since this vector is tilted already by some theta degree, then you can see some residual component which can pass through the second polarizer. On the other hand, if I remove this polarizer in between, then what is going to happen is that all the components is pointing to the y direction. Then you cannot see any component which pass through this polarizer. So that's actually pretty interesting. And I can rotate this, and you can see that the magnitude is changing. Only when I have 45 degrees, I see a maximum intensity. Any questions? Very good. So now what I'm going to do is to discuss with you an interesting question, which was posted by Einstein. Einstein said that, as I said, "God doesn't play dice with the world." So that's actually what he believed. So we can do an interesting experiment, which I have single photon source. So what do I mean by single photon source? I can emit one photon at a time-- just one, and then the second one, and the third one-- and have then pass through some imaginary polarizer. So let's suppose I have unpolarized light with intensity at 0. So basically, after it passed through this polarizer with a axis pointing to the x direction, in this case the x direction is pointing to this direction, what you are going to get is that you are going to filter from all those unpolarized direction, you are going to filter only the light which is actually parallel to the easy axis. So therefore, after the unpolarized light source passes through this polarizer, you are going to have all the electric field pointing to the x direction. Now everybody can accept. And of course if I have a second one, which is in the y direction, since there will be no component pointing to the y direction, you get zero electric field. That's very nice. So Einstein was really happy that, oh, that means unpolarized light maybe is just 50% of the polarized light in the x direction and 50% of the polarized light in the y direction. Because each time I emit one photon, the first half of them got stopped by the x direction easy axis polarizer. And then the second half got stopped by the second polarizer. So that probably makes sense. But how about-- as we did in the demonstration-- how about we rotate the second polarizer by 45 degrees? What will be the intensity? But now, hey, you cannot split a single photon because a photon is a photon. How can I split, right? Because if I describe my unpolarized light as 50% linearly polarized in x, the other half is linearly polarized in y, then I am in trouble because I don't know how to calculate what is this intensity. So basically maybe all of them pass through or all of them doesn't pass through. Then we can do this experiment. And this is the result-- what you are going to get is that the intensity is going to be I0 over 4. That is actually not 0 or I over 2. So that means really the nature of plate dies because a single photon is equivalent to something which can be described by a wave. So that gives us some possible connection to quantum mechanics, because that means a single photon is not like a single object, which is actually passing through all those polarizers. But they actually act also like waves. So that is something which we'll follow up with later lectures. When we talk about interference, et cetera, we are going to also discuss related issues about the connection to quantum mechanics. So today, we actually have learned about polarization, linearly polarized, circularly polarized, and elliptically polarized electromagnetic waves, and also unpolarized light source. And we have learned about how to produce polarized electromagnetic wave with polarizer. Basically have the unpolarized light source pass through a polarizer, you'll have a polarized light. We didn't cover quarter wave plate yet. We are going to cover that next time. And also, next time we will talk about how we actually can generate electromagnetic field. We have been talking about electromagnetic field for a long time, but how are they actually generated is an issue which we have actually touched. And that is actually going to happen after the midterm next week. Thank you very much. And if you have any questions, please let me know. AUDIENCE: [INAUDIBLE] |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 2_Damped_Free_Oscillators.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: OK, so welcome back, everybody. Welcome back to 8.03. Today, we are going to continue the discussion of the harmonic oscillators. And also, we will add damping force into the game and see what will happen, OK? So this is actually what we have learned last time from this slide. We have analyzed the physics of a harmonic oscillator, which we actually demonstrated last time. And you can see the device still there. And Hooke's law, actually the Hooke's law is actually far more general than what we saw before. It works for all small oscillations around about a point of equilibrium position, OK? And that can be demonstrated by multiple different kinds of physical systems. For example here, I have a mass, which actually can only move along this track here. And if I put this mass set free, then this thing is actually exercising harmonic oscillation, OK? We can do this with large amplitude. We can also do it with small amplitude. And you see that, huh, really, it works. Hooke's law actually works. And it predicts exactly the same motion as to what you see on the slide, OK? And we also have a little bit more complicated system. For example, this is some kind of rod. And you can actually fix one point and make it oscillate. And you see that, huh, it also does some kind of harmonic oscillation. But now, what is actually oscillating is the amplitude. The amplitude is actually the angle with respect to the downward direction. And finally this is actually the vertical version of this spring mass system, which you will be analyzing that in your P-set. And you see that, huh, it actually oscillates up and down harmonically. So that's all very nice. And we also have learned one thing which is very, very interesting. It's that a complex exponential is actually a pretty beautiful way to present the solution. And you will see it works also when describing the damped oscillators. And we will see how it works in the lecture today. I received several questions during my office hour and through email or Piazza. There were some confusions about doing the Taylor expansion, OK? So in lecture last time, the equilibrium position is at x equal to 0. Therefore, I do Taylor expansion around 0, OK? But in this case, if the equilibrium position or the minima of the potential is at x equal to L, then what you need to do is to do a Taylor expansion around x equal to L, just to make that really, really clear, OK? OK, I hope that will help you with the P-set question. OK, so let's get started immediately. So let's continue the discussion of the equation of motion we arrived at last time. So we have M x double-dot and this is equal to minus kx, OK? That is actually the formula from last time. And we can actually calculate the kinetic energy of this spring and mass system. And basically, this is going to be equal to 1/2 M times x dot squared. OK, and we can also calculate the potential energy of the spring. Potential energy, and that is equal to 1/2 kx squared. We also know what would be the total energy. The total energy would be a sum of the kinetic energy and of the potential. Basically, you get this formula, 1/2 M x dot squared plus 1/2 kx squared. One last time, we have solved this equation of motion, right? So the solution we got is x equal to A cosine omega 0 t plus phi. Well, omega 0 is equal to a square root of k over M. Therefore, we can actually calculate what would be the total energy as a function of time, right? So if we calculate that, we'll get E will be equal to 1/2 M A squared omega 0 squared sine squared omega 0 t plus phi-- so this is actually the first term here-- plus 1/2 kA squared cosine squared omega 0 t plus phi, OK? Then, we also know that this coefficient here is just kA squared, right? Because omega 0 is actually equal to the square root of k over M. And if you replace this omega 0 squared by k over M, then you actually arrive at kA squared, OK? So that is actually very good. So that means I can simplify the total energy. And what we are going to get is 1/2 kA squared. I can take this factor out. And that will give me, inside these brackets, I will get sine squared omega 0 t plus phi plus cosine squared omega 0 t plus phi. And this is actually equal to 1, right? Just a reminder, sine squared of theta plus cosine squared of theta is always equal to 1. So that gives me this result. This is actually 1/2 kA squared, OK? So that is actually the result. What does that mean? That means, if I actually pull this mass harder, so that initially it has larger amplitude, then the total energy is actually proportioned to amplitude squared, OK? So I am storing more and more energy. If I increase the amplitude even more, then I am storing the energy in this system. And it's proportional to A squared. And also, if the spring constant is larger, the same amplitude will give you more energy. So that means that you can store more energy if you have a larger string constant, OK? The most surprising thing is that actually this is actually a constant, right? What does that mean? The total energy is actually not variating as a function of time. You see? So total energy is constant, OK? So you can see from this slide the total energy is actually showing us the sum, which is the green curve. And the kinetic energy and the potential energy are shown as red and blue curves. You can see that the total energy is actually constant. But this system is very dynamical. You see? So that energy is actually going back and forth between the spring and the mass in the form of kinetic energy and in the form of potential energy. But they are doing it so well, such that the sum is actually a constant. So the energy is actually constant, OK? So that is actually pretty beautiful. And it can be described very well by these mathematics. Any questions from here? OK, so I would like to say simple harmonic motion, actually, what you are going to get is the energy is actually conserved and independent of the time. And later, you will see an example with damping. And you will see that energy conservation is now no longer the case, OK? So let's immediately jump to another example, which is actually involving simple harmonic motion. So let's take this rod and nail system as an example. If I actually slightly move this rod, and then I release that, then actually you will see simple harmonic motion, also for this system. So let's actually do the calculation as another example. So this is actually my system. I have this rod, OK? Now, I am assume that the mass is actually uniformly distributed on this rod and is nailed on the wall, OK? And the length of this rod is actually l. So that means the center of mass is actually at l/2 with respect to the nail, OK? And also, this whole system is set up on Earth, right? Therefore, there will be gravitational force pointing downward, OK? So that means you have gravitational force, Fg, pointing downward, OK? So this is actually the system, which I would like to understand. And just a reminder, what are we going to do afterwards in order to turn the whole system into a language we know describes the nature? What are we going to do? Anybody? We are going to define the coordinate system, so that I can translate everything into mathematics, right? So that's actually what we are always doing. And you will see that we are always doing this in this class, OK? So what is actually the coordinate system which I would like to use? Since this system is going to be rotating back and forth, therefore, I would like to define theta to be that angle with respect to the axis, which essentially pointing downward, OK? So the origin of this coordinate system uses theta equal to 0. This means that the rod is actually pointing downward, OK? And also, I need to define what is actually the positive value of the zeta, right? So I define anti-clockwise direction to be positive, OK? So it is actually important to actually first define that, then actually to translate everything into mathematics, OK? So the initial condition is the following. So I actually move this thing, rotate this thing slightly. Then, I actually release that really carefully without introducing any initial velocity, OK? Therefore, I have two initial conditions. OK, at t equal to 0, there are two initial conditions. The first one is theta 0 is equal to theta initial. The second condition is the same as what we have been doing last time. The initial velocity or angular velocity is actually equal to 0. So that gives you theta dot equal to 0, OK? Now, we have actually defined the coordinate system. Now, we can actually draw a force diagram, so that we can actually use our knowledge about the physics to obtain the equation of motion, right? So now, the force diagram looks like this. So this is actually the center of mass of this rod. And you have a force pointing downward, which is due to the gravitational force. Fg is equal to mg. It's pointing downward. The magnitude is actually equal to mg. And also, we know the R vector. This vector has a length, l/2. It's pointing from the center of mass of this rod to the nail, OK? And also, we know the angle between these vectors, pointing from the center of mass to the nail, and the vertical direction, which we have already defined, which is actually called theta. Therefore, now, we can actually calculate what would be the torque. Tau will be equal to this R vector cross the force, total force acting on the center mass. In this case, it's just Fg, OK? So now, we can actually write this down explicitly. Since the whole system is actually rotating on a single plane, so there's only one plane this is sitting on. And it's actually going back and forth only on this plane, OK? Therefore, actually, I can drop all the arrows and write down the magnitude of the tau directly. And this will be equal to minus mg l/2 sine theta t, OK? Any questions so far? OK, so now, we have the torque. And we can make use of the rotational version of Newton's Law to obtain the equation of motion, right? So that should be pretty straightforward. Tau will be equal to I, which is the moment of inertia of the system, times alpha t, OK? And just for your information, I already calculated the I for you. I is equal to 1/3 ml squared, OK? So you can actually go back home and actually do a check to see if I'm telling the truth. And if you trust me, then that's the answer, which is actually 1/3 ml squared, if the mass is actually uniformly distributed on this rod, OK? So that would give me minus mgl divided by 2 sine theta t, OK? So that is actually coming from this side, OK? So now, I can actually simplify this expression. I can now plug in the I value into this equation. And I will get 1/3 ml squared theta double-dot t, which is actually alpha, OK? Now, I write it as theta double-dot. And that will be equal to minus mgl over 2 sine theta, OK? I can move all the constants to the right-hand side. Therefore, I get theta double-dot t. This is equal to minus mgl. OK, actually, I can already simplify this, right? These actually cancel. And the 1/l actually cancels. So therefore, I get minus 3g over 2 sine theta t. OK, as you know, we actually defined omega to replace this constant to make our life easier. So I can now define omega 0 equal to square root of 3g over 2l, OK? And that will give you theta double-dot of t equal to minus omega 0 squared sin theta t. Any questions so far? A lot of calculations. But they should all be pretty straightforward. And actually, we are done now. We are done. Because we have the equation of motion. And the rest of the job is to solve just it. So it is actually now the problem of the math department. So can anybody actually tell me the solution of the theta of t? Anybody? AUDIENCE: Unfortunately, we'd have to approximate it. YEN-JIE LEE: That's very unfortunate. So now, we are facing a very difficult situation. We don't know how to solve this equation in front of you. I don't know, OK? Of course, you can actually solve it with a computer, or, if you want to go fancy, solve it with your cellphone, if it doesn't explode. But it's not really nice to do this in front of you. We don't learn too much. OK, so what are we going to do? So what we can do is actually to consider a special case. So we know that this equation of motion is exact, OK? So if you solve it, it would describe the motion of this rod. Even with a large angle, it works, OK? And now, in order to actually show you the math in the class, therefore actually I will do a small approximation. So actually, I would only work on the case that when the amplitude is very small and see what is going to happen. So now, I'm considering a special case. Up to now, everything is exact. And now, I am now going to a special case. Theta t goes to 0, OK? Then, we can actually get this. Sine theta t is roughly theta t, OK? Based on the Taylor expansion, you can actually verify this, OK? So in this case, if we take theta equal to 1 degree, then the ratio of the sine theta and the theta is actually equal to 99.99%, which is very good. If I take it as 5 degrees, then it's actually 99%. Even at 10 degrees, it's actually 99.5%. Now, that shows you that sine theta is so close to theta, OK? We are pretty safe. Because the difference is smaller than 1%. OK, so that's very nice. After this approximation, I get my final equation of motion. Theta double-dot t equal to minus omega 0 squared theta t. Just a reminder, omega 0 is equal to square root of 3g over 2l, OK? We have solved this equation last time, last lecture, right? It's exactly the same. OK, it happened to be exactly the same. Therefore, I know the solution will be theta of t equal to A cosine omega 0 t plus phi. From the initial conditions, which I have one and two, I am not going to go over these calculation again. But again, we can actually plug in 1 and 2 to solve the unknown A and the phi. If you do this exercise, you will conclude that A is equal to theta initial. And phi is equal to 0, OK? So the solution would be theta of t equal to theta initial cosine omega 0 t. You can see that this actually works for this system. Simple harmonic oscillation actually described the motion of this system as a function of time. You can also see a few more examples shown here. Two of them you are going to really work on in your P-set and also another one involving circuits. If you have a capacitor and you have an inductor, actually the size of the current is also doing a simple harmonic motion, OK? And as we actually discussed before, the energy is always conserved. And that is actually stored in different components of the system, OK? So we have done this. What is actually new today? What we are going to do today is let's actually observe this phenomenon here. So this thing is actually going to go back and forth. But it's actually not going to do that forever, right? Something is happening, which actually slows the motion down. I can also make use of this system, OK? I start from here. And I'm not worried that this actually goes out of this track. Because I know for sure it will stop there. Why? Because the initial amplitude is not going to-- the amplitude is not going to be larger than the initial amplitude, right? So I'm not worried at all, OK? But you can see that the amplitude is changing as a function of time. Apparently, something is missing. And that is actually a direct force, or friction, which is actually not included in our calculation. So let's actually try to make the calculation more realistic and see what is going to happen. So now, I will introduce a drag force, which actually introduces a torque tau drag, t, which is equal to minus b-- b is actually some kind of constant, which is given to you-- theta dot t, which is actually proportional to angular velocity of that rod, OK? And also of course, I keep the original approximation. The theta is very small, such that I don't have to deal with the integration of sine theta, OK? So solving this, theta double-dot equal to minus omega 0 squared sine theta is a complicated function. You may ask, why do I actually introduce a drag force proportional to the velocity? And why do I put a minus sign there? That is actually because, if you have a minus sign, that means, when this mass or that rod is actually going downward, then the drag force is really dragging it. Because it's actually in the opposite direction of the velocity of the mass or the angular velocity of the rod, OK? So I need a minus sign there, OK? Otherwise, it's not a drag force anymore. It's actually accelerating the whole thing. Secondly, why do I choose that to be proportional to theta dot or velocity? There's really no much deeper reason. I choose this form because I can actually solve it in front of you, OK? The reality is actually between proportional to theta dot and theta dot squared, for example, OK? This is actually a model which I introduced here, which I can actually solve it in front of you. On the other hand, you'll see that it's actually not bad at all. It actually works and describes the system, which will actually work to perform the demo here, OK? And once we have introduced this, the equation of motion will be modified. So let's come back to the equation of motion. So you have to theta double-dot t originally would be equal to tau total t divided by I, OK? And now, this will become tau t plus tau drag t divided by I. So there's an additional time here. OK, if I simplify this whole equation, then I get minus mgl over 2 sine theta. And this is actually roughly theta minus b theta dot divided by 1/3 of ml squared, OK? So you can see that I still make this approximation sine theta roughly equal to theta. Then, I can actually write this equation in the small angle case. OK, I get minus 3g over 2l theta t minus 3b over ml squared theta dot t. OK, and now, as usual, I define omega 0 squared equal to 3g over 2l. And I can also define gamma is equal to 3b over ml squared, just to make my life easier, right? Finally, we will arrive at this expression, theta double-dot plus gamma theta dot plus omega 0 squared theta. And that is equal to 0. So what you can see from here is that we have actually derived the equation of motion, OK? We have derived the equation of motion. And actually, part of the work is actually really just solving this equation of motion. And you don't really have to solve it. Because you already get the result from 18.03 actually, if you remember. And we are going to discuss the result. But before that, before I really try to solve this equation, I would like to take a vote, OK? So here, I have two different systems. They have equal amounts of mass. They are attached to a spring. If you do the same equation of motion derivation, you will actually get exactly the same equation of motion in that format, OK? So the form of the equation of motion will be the same between this system and that system, OK? I would like to ask you a question about the oscillation frequency. So you can see that one of them is actually a better mass. It's like a point-like particle. And the other one is wearing a hat, OK? What is going to happen is that this Mexican hat is going to be trying to push the air away, right? Then, you may think, OK, this Mexican thing is not really very important. Therefore, the oscillation frequency may be the same, right? How many of you think the oscillation frequency, if I actually tried to perturb these two systems, would be the same? Raise your hands. 1, 2, 3, 4, 5, 6, 7, 8-- OK, we have 11. So the omega, the predicted omega, will be equal to omega 0-- 11 of you. How many of you will think that, because of this hat, this pushing this air away, it's a lot of work to be done. Therefore, this is going to slow down the oscillation. How many of you think that is going to happen? 1, 2, 3-- OK, 17. It may happen to you that you think this idea of wearing a hat is really fashionable. Therefore, it got really exciting and it oscillates faster. Can that happen? How many of you actually think that is going to happen? OK, one-- you think so? Two. Very good, we have 2. What do you think? Where are the rest? Only 30 of you actually think that is going to happen. OK, all the rest think of the class think that this one is going to-- pew! Disappear to the moon, OK? So that is actually the opinion. And we have completed the poll. And what we are going to do is that we are going to solve this system and see what is going to happen. And we will do that experiment in front of you, OK? All right, so that's very nice. So now, we have this question of motion. And now, I will pretend that I'm from the math department for a bit and help guide you through the solution. So now, I can use this trick. I can actually say theta is actually the real part of the z, which is a complex function. And as we learned before, z of t, and I assume that to be exponential I alpha t. So alpha is actually some kind of constant, which I don't really know what is the constant yet. OK, I can now actually write the equation of motion in the form of z. Then basically, what I get is z double-dot t plus gamma z dot t plus omega 0 squared z of t. And this is equal to 0, OK? So remember, exponential function cannot be killed by differentiation, right? Therefore, it's really convenient. You can see from here. Now, I can plug in this expression-- which I did this and guessed to this equation of motion. Then what I am going to get is minus alpha squared. Because you take I alpha I alpha out of this exponential function, right? Because you do double differentiation. So you get minus alpha squared plus i gamma alpha-- because this is only differentiated one time-- plus omega 0 squared. And all those things are actually multiplying this exponential function, exponential i alpha t equal to 0, OK? So we will write this expression. That is very nice. And we also know that, this expression is going to be valid all the time. No matter what t you put in, it should be valid, right? Because this is the equation of motion. And we hope that this solution will survive this test. So I can easily conclude that this one is actually not equal to 0. It can be some value, not 0. So what is actually equal to 0? This first term is actually equal to 0, OK? Therefore, I can now solve this equation; minus alpha squared plus i gamma alpha plus omega 0 squared equal to 0. I can solve it, OK? If I do that, then I would get alpha is equal to i gamma plus/minus square root of 4 omega 0 squared minus gamma squared divided by 2. This is actually the second order polynomial. And that is actually equal to 0. Therefore, you can actually solve it easily. And this is actually the solution. And I can write it down in a slightly different form. i gamma over 2 plus/minus square root of omega 0 squared minus gamma squared over 4, OK? Any questions so far? Am I going too fast? Everything's OK? OK, So you can see that alpha is equal to this expression. And I would like to consider a situation where omega 0 is much, much larger than gamma, OK? Just a reminder of what is gamma, OK? Maybe you've got already a bit confused. What is gamma? Gamma is related to the strength of the direct force, right? It is actually 3b over ml squared, OK? b is actually determining the size of the direct force, OK? So I would like to consider a situation. The first situation is if omega 0 squared is larger than gamma squared over 4. So in that case, the drag force is small. It is not huge. It's small, OK? If that is the case, this is actually real, right? Because omega 0 squared is larger than gamma squared over 4. Therefore, this is real, OK? So now, I can actually define omega squared, define that as omega 0 squared minus gamma squared over 4, OK? And this will become i gamma over 2 plus/minus omega, OK? So that means I would have two solutions coming from this exercise. Z plus of t is equal to exponential minus gamma over 2 t exponential i omega t, OK? And the second solution, if I take one of the plus sign and one of the minus sign solutions, then the second solution would be exponential minus i gamma over 2 t exponential minus i omega t, OK? Any questions so far? OK, so we would like to go back to theta, right? So what would be the theta? So that means I would have a theta 1 of t, which is actually taking the real part. So it's theta plus maybe, taking the real part of z plus. And that will give you exponential minus gamma over 2 t cosine omega t, OK? I'm just plugging in the solution to this equation, OK? Theta minus t would be equal to exponential, and this gamma over 2 t sine omega t, OK? Finally, the full solution of theta of t would be a linear combination of these two solution, right? Therefore, you will get theta of t equal to exponential minus gamma over 2 t a (is some kind of constant) times cosine omega t plus b sine omega t. And of course, from the last time, as you will know, this can also be written as A cosine omega t plus phi, OK? Any questions so far? OK, very good. So we have actually already solved this equation. And of course, we can actually plug this back into this equation of motion. And you will see that it really works. And I'm not going to do that now. But you can actually go back home and check. And if you believe me, it works. And also at the same time, it got two undetermined constants, since this is a second order differential equation. Therefore, huh, this thing actually works. It has two arbitrary constants. Therefore, that is actually the one and only one solution in the universe which satisfies the equation of motion or satisfies that differential question, OK? So this thing actually has dramatic consequences. The first thing which we learn is that, as a function of time, what is going to happen? The amplitude is now becoming exponential minus gamma over 2 t times A. This is actually the amplitude. The amplitude is decreasing exponentially. So that is actually the first prediction coming from this exercise, OK? The second prediction is that this thing is still oscillating. Because you've got the cosine omega t plus phi there, you see? So the damping motion is going to be like going up and down, up and down, and get tired. Therefore, the amplitude becomes smaller, and smaller, and smaller. But it's never 0, right? It's never 0, OK? It's actually going to be oscillating down, down, down, so small I couldn't see it. But it's still oscillating, OK? Finally, we actually have also the answer to the original question we posed, OK? So now, you can see that the oscillation frequency is omega, OK? Originally, before we introduced the drag force, omega 0, which is the oscillation frequency, is actually an angular frequency. It's actually the square root of 3g over 2l. And you can see that the new omega, the oscillation frequency with drag force, is the square root of this, omega 0 squared minus gamma squared over 4. So what this actually tells us is that this is going to be smaller, because of the drag force, OK? So that's a prediction. Let's do the experiment and see what is going to happen. So let's take a look at these two systems. They have the identical mass, which our technical instructor actually carefully prepared. They have the same mass, even though one actually looks a bit funny. The other one looks normal, OK? Now, what I'm going to do is to really try and see which one is actually oscillating faster, OK? So let's see. I release them at the same time. And you can see that originally they seem to be oscillating at the same frequency. But you can see very clearly that the one with the hat is actually oscillating slower, OK? So you can see that, OK, 17 of you actually got the correct answer. And the most important thing is that you can see that this simple mass actually describes and predicts what is going to happen in my little experiment. So that is actually really cool. And I think it's time to take a little break. And then, we will come back and look at other solutions. And of course, you are welcome to come to the front to play with those demonstrations. So there are two small issues which were raised during the break. So the first one is that, if you actually calculate the torque from this equation-- so I made a mistake. The R vector should be actually pointing from the nail to the center of mass, OK? So I think that's a trivial mistake. So if you do this, then you can actually calculate the tau equal to R cross F. Then, you actually get this minus sign, OK? So if I make a mistake in pointing towards the nail, then you will get no minus sign, then that didn't really work, OK? So very good, I'm very happy that you are actually paying very much attention to capture those. The second issue is that-- so now, I'm saying that, OK, now I have the solution in the complex format. So I have a Z plus and I have a Z minus, OK? And then I would like to go to the real world, right? Because the imaginary thing is actually hidden in some kind of motion in the actual dimension, et cetera, I would like to go back to reality, OK? And what I said in the class is that I take the real part of one of the solutions. And I can also take a real part of i times one of the solutions. But of course, you can also do this by doing a linear combination of the solutions, right? As we actually discussed last time, the linear combination of the solutions is also a solution to the same equation of motion, since this one is actually linear. Therefore, what I actually do is actually to sum the two solutions, Z plus and Z minus and divide it by 2. Or actually, I can actually do a minus i/2 times Z plus minus Z minus, OK? And then I can also extract this sign term here, OK? So that should be the correct explanation of the two solutions in the real axis, OK? Any questions so far? Thank you very much for capturing those. Ok, so now, you can see that we have been discussing the equation of motion of this functional form. And the one thing which is really, really interesting is that the solution, when we take a small drag force limit, actually we arrive at a beautiful solution that looks like this, A exponential minus gamma over 2 t cosine omega t plus phi. That actually predicts the oscillation, OK? At the same time, it also says that the amplitude is actually going to drop exponentially, but never 0, OK? Finally, we also know that this solution actually tells us that, if we have a spring mass system oscillating up and down, if we have a rod like what we actually solve in a class, this object is going to pass through 0, the equilibrium position, an infinite number of times, right? Because the cosine is always there. Therefore, although the amplitude will become very small, but it's still oscillating forever until the end of the universe, OK? All right, so that's actually what we have learned. And also, one thing which we learned last time is that simple harmonic motion, like this one, which we were just showing here, or this one, which is actually a mass oscillating back and forth on the track, is actually just a projection of a circular motion in a complex plane, OK? And what we are really seeing here in front of you is actually a projection to the real axis, OK? So that's actually a really remarkable result and a beautiful picture. And of course, we can actually also plug in the solution with damping. So what is actually the picture in this language, in this exact same language? If we actually follow the locus, then basically what you are going to see is that this thing actually spirals. And the amplitude is actually getting smaller and smaller and is sucked into this black hole in the 0, 0, OK? So you can see that now the picture looks as if there is something really rotating in the complex plane. And it's actually approaching 0. Because the amplitude is actually getting smaller and smaller. But this whole thing is still rotating, OK? OK, that's really nice. All right, so now, this is actually a special case. When we actually assume that gamma is actually pretty small. So you have very small drag force, OK? So let's actually check what would happen. If I now start to increase the drag force, make this hat larger, larger, and larger, introducing more and more drag, what is going to happen? OK, so now, I consider the second situation, omega 0 squared equal to gamma squared over 4. OK, so when the gamma is very small, what we see is that this is actually underdamped, right? So the damping is really small. But if I increase the gamma to a critical value, now omega 0 squared happens to be equal to gamma squared over 4, OK? I call this a critically damped oscillator, OK? So what does that mean? That means omega is equal to 0, you see? This is our definition of omega, right? If omega 0 squared is equal to gamma squared of over 4, then omega is equal to 0. That is actually the critical moment the system stops oscillating, OK? So it is not oscillating anymore. So now, I can actually start from the solution I obtained from 1, OK? Then, I can actually now make use of these two solutions, the theta plus and the theta minus. Theta plus t would be equal to exponential minus gamma over 2 t cosine omega t. When omega goes to 0, what is going to happen is that this is actually becoming, which value? Anybody know? If omega is 0, what is going to happen? 1, yeah. OK, 1, right? So that will give me exponential minus gamma over 2 t. Theta minus t-- OK, I can do the same trick and see what will happen. So I take theta minus t, which is actually obtained from the exercise number one when we discussed the underdamped system. Then, you actually get exponential minus gamma over 2 t sine omega t. When omega goes to 0, actually then I get 0 this time, OK? So that doesn't really work, right? Because if I have a solution which is 0, then it's not describing anything, right? I can always add 0 to the solution. But that doesn't help you. OK, so instead of taking the limit of this function, actually we choose to actually do theta minus t divided by omega. And then, we actually make this omega approaching 0. Then basically, I get exponential minus gamma over 2 t sine omega t divided by omega, OK? If I have this omega approaching to 0, then this is actually roughly just exponential minus gamma over 2 t omega t over omega. And this is actually giving you t times exponential minus gamma over 2 t. Any questions so far? Yes. AUDIENCE: Completely unrelated, but is that a negative sign in front of the theta minus negative 1/2? YEN-JIE LEE: This one? AUDIENCE: Yeah. YEN-JIE LEE: Yeah. So actually, OK, yeah. AUDIENCE: In front of the 1/2 is that a negative sign? YEN-JIE LEE: Yes, this is a negative sign. OK, any other questions? OK, so you can see that now I arrive at two solutions. One is actually proportional to exponential minus gamma over 2 t. The other one is actually proportional to t times exponential minus gamma over 2 t, OK? So you can see that the cosine or sine term disappeared, right? So that means you are never oscillating, OK? So this is actually what we see in this slide, this so-called critically damped, OK? When actually, omega 0 squared is equal to gamma squared over 4. And you can see that what is going to happen is that this mass or this rod is going to pass 0 only one time at most, OK? And it could actually never passed 0, if you actually set up the initial condition correctly, OK? So one thing which I can do is I really shoot this mass really, really, very forcefully, so that I have a very large initial velocity. And what it actually is going to do, like the right-hand side diagram, is that, oh, you overshoot the 0 a bit. Then, it goes back almost exponentially, OK? So at most, you can only pass through 0 one time, if you do this kind of initial condition, OK? So that is actually pretty interesting. And there are practical applications of this solution, actually. So for example, we have the door closed. So it's also here, right? The door closed, you would like to have the door go back to the original closed mold, the position of equilibrium position actually really fast, OK? So what you can do is really design this door close so that it actually matches with the critical dampness situation, of your condition, so that actually you would go back to 0 really quick, OK? Any questions? OK, so now, what we could do is that, instead of having a very small drag force, or we'll a slightly larger drag force, so that actually reach the critically damped situation, what we could do is that we put the whole system into water, right? Then, the drag force will be very big, OK? And we would like to see what is going to happen, OK? So in this case is the third situation. The third situation is that omega 0 squared is actually smaller than gamma squared over 4. So you have huge drag force, OK? So that would give you a situation which is called overdamped oscillator. Now, I have, again, alpha is equal to i gamma over 2 plus/minus square root of omega 0 squared minus gamma squared over 4, right? I'm just copying from here, OK? And that will be equal to i-- I can take out the i, OK?-- gamma over 2 plus/minus square root of gamma squared over 4 minus omega 0 squared. Now, I can actually define gamma plus/minus equal to gamma over 2 plus/minus square root of gamma squared over 4 minus omega 0 squared, OK? Then basically, the solution-- actually now, I already have the solution. So basically, the two solutions would be looking like this. Theta of t would be equal to A plus some kind of constant exponential minus gamma plus t plus A minus exponential minus gamma minus t, OK? Because this is actually becoming already-- OK, so alpha is actually i times gamma plus/minus. Therefore, if you put it back into this, then basically what you are getting is exponential minus gamma plus t or exponential minus gamma minus t, OK? So that's already a real function. And the linear combination of these two solutions is our final, full solution to the equation of motion. OK, again, what we are going to see is that actually the drag force is huge. I just throw the whole system into water. And the water is really trying to stop the oscillation, really very much. Therefore, you can see that, huh, again, I don't have any oscillation, OK? If I am very, very strong, I really start the initial velocity or initial angular velocity really high, I actually give a huge amount of energy into the system, then, at most again, I can actually have the system to pass through the equilibrium position only one time. Then, this whole system will slowly recover, because exponential function we see here. The amplitude is going to be decaying exponentially, OK? Any questions? So let's actually do a quick demonstration here, OK? So here, this is actually the original little ball here, a metal one, which actually you can see that this is really going to go back and forth really nicely. And you can see that, because of the friction, actually the amplitude is becoming smaller and smaller, OK? So that actually matches with this situation, right? So it's actually an underdamped situation. This ball, in an idealized situation, is going to go through 0 infinite number of times, OK? So now, what I am going to do is now I change this ball to something which is different, OK? This is actually made of magnets, OK? And let's see what is going to happen. So now, you can see that, because this is actually made of magnets, therefore, the drag force will be colossal, will be very, very big. And let's see what will happen. You see that the drag force is huge. Therefore, you see I put it here so that it has big initial velocity. It only passes through 0 once, right? Of course, it now is actually approaching the zero really, really slowly, exponentially. But it is not 0, OK? So it only passes through the 0 if you believe the math, only once, OK? Just to show that this is a real deal-- OK, now, whoa, right? Oh, I'm not trying to destroy the classroom, OK? So you can actually play with this after we finish your lecture, OK? I would like to ask you a question. After we learned this from this lecture, there are three situations, underdamped, critically damped, and overdamped, OK? I would like to ask you two questions. The first one is through this demonstration, OK? So, now I have a system which is nicely constructed. I hope you can see it, OK? You can see it. And this system is made of a torsional spring. And also, there's a pad here, which is connected to the spring, OK? If I actually perturb this thing, it's going to be oscillating back and forth before I turn on the power, so that the lower part is actually you have a magnet, OK? It's not turned on yet, OK? And this magnet is going to provide a drag force to actually change the behavior of the system, OK? So you can see that, before I turn on the magnetic field, the whole system is actually oscillating back and forth really nicely. As we predicted, small amplitude vibration is harmonic oscillation, OK? So that's very nice. So now, what am I going to do is to turn on the power and see what is going to happen. After I turn on the power, there's an electric field, OK? And this is actually going to be-- OK, so the magnetic field is actually turned down. Therefore, it is actually acting like a drag force to this system, OK? So let's actually see what is going to happen. Now, I release this. The behavior of the system looks like this. It first oscillates, and then it stops. So the question is, is this a critically damped, underdamped, or overdamped system? Anybody knows? Yeah? AUDIENCE: Underdamped. YEN-JIE LEE: Yes, this is underdamped. How do I see that? That is because, when I do this experiment, you would pass through 0s multiple times. Therefore, there are oscillations coming into play. Therefore, I can conclude that the drag force is not large enough. So that is actually an underdamped situation, OK? And the next time, we are going to drag this system. I have a second question for you. So now, your friends know that you took 8.03. Therefore, they will wonder if you can actually design a car suspension system, to see if you can actually make this design for them. When you design this car, which condition will you consider to set up the car? Will you set it up as underdamped, critically damped, or overdamped? How many of you actually think it should be underdamped? No, nobody? How many of you actually think it should be overdamped? 1, 2, 3, 4, OK. How many of you actually think it should be critically damped? OK, the majority of you think that should be the correct design. So if you have the car designed as an underdamped situation, then, when you drive the car, you are going to have very funny style. You are going to have this. This is the style. So the car is going to be oscillating all the time, OK? Because it's going to be there. And it's really damping really slowly, OK? If you design it to be overdamped, it would become very bumpy, right? So let's take a limit of infinitely large drag force constant, OK? Then, it's like, when you hit some bump, you go woo! Wow! It doesn't really help you to reduce the amplitude, OK? So the correct answer is you would give the advice that you would do it critically damped, OK? So before we end the section today, I would like to pose a question to you. The thing which we have learned from simple harmonic motion is that the energy is conserved in a simple harmonic motion, OK? I have the Fs, the spring force, proportional to minus k times x. And the energy is conserved, OK? But if I add a drag force in the form or minus b times v, energy is not conserved, right? So you can see that it was actually oscillating. Now, it's not oscillating, right? This thing has stopped oscillating, OK? Why is that the case mathematically? OK, we know what is happening physically in this physical system. Because OK, this Mexican hat is trying to push the air away. So what is going to happen is that it's transferring the energy from this system to the molecules of the air, OK? So it's accelerating the air. So the energy goes away. But why the mathematical form looks so similar and it does different things? And think about it. And I'm not going to talk about the answer today. And thank you very much. And we will continue next time to see what we can learn if I start to drive the oscillator. Bye-bye. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 3_Driven_Oscillators_Transient_Phenomena_Resonance.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: OK, so welcome back everybody. Happy to see you again. So today, we are going to continue our exploration and understand single harmonic oscillator. And this is actually a list of our goals. And we would like to learn how to translate physical situations into mathematics so that we can actually solve the physical problem, so we actually have and predict what is going to happen afterward. And we also sort of started this course by solving really simple examples, single harmonic oscillators. And as a function of time, you will see that, for our next class, the next lecture, we are going to bring in more and more objects. And of course, more objects means more excitement also, in terms of phenomena, but also more complication on the mathematics. So we will see how things go. And then after that, we are going to go through infinite number of oscillators to see what will happen. Of course, we will produce waves. That's very exciting. Then we'll do all kinds of different tricks to do those waves. So what we have we learned last time? So last time we went over example, a simple harmonic oscillator. It says you have a rod fixed on the wall, and you can actually go back and forth. And we also introduced a model of the drag force, or drag torque, and that's actually proportionate to the velocity of the motion of that single particle. And the interesting thing we learned last time is that we have three completely different behaviors if we actually turn on the drag force. The first one is on that damped. Damping is actually very small. Then we have the solution in this form. It's oscillating. The amplitude is decaying exponentially. As we make the drag force larger and larger, you will pass a critical point, which actually give you a solution, which you don't have oscillation anymore. The cosine disappeared. Finally, if you actually put the whole system into water or introduce something really dramatic-- a very, very big drag force-- then you have overdamp situation. And there you see that the solution is actually a sum of two exponential functions. So this is actually the one equation which actually works for all the damped situation we discussed up to now. And this is actually the map. Basically, if gamma goes to zero-- gamma actually controls the size of the drag force. Then we got no damping. Then you have a pure, simple harmonic motion. And as we increase the gamma, then you get see that the behavior is changing as we increase the gamma. So you can see that we can use a quantity, which is called Q. Q is actually defined as a ratio of omega at zero, which is basically the natural angular frequency of the system. And gamma is a measure of how big the drag force is. If we make a ratio of this to quantity, then you'll see that, at Q equal to 0.5, it reaches a critical point, which actually the behavior of the whole system changed. And you can see that the oscillation completely disappeared. So that is actually what we have learned last time. So what are we going to do today? We have been really doing experiments really with our hands, hands-on, right? So basically we will prepare the system. Then we release it. Then we don't touch it again and see how this system actually evolves as a function of time. So that's what we have been doing. So today, what we are going to do is to start to drive this system. We can introduce some kind of driving force and see how the system will respond to this external force. So that is actually what we are going to do. And that will bring us to the situation of damped driven harmonic oscillator. So let's immediately get started. So we will use the example which we went through last time as a starting point. So set example from the last lecture is a rod, which is fixed on the wall. And the lens of this rod is over two. And I define a counter-clockwise direction to be positive. And I measure the position of the rod by this theta, which is the angle between the vertical direction and the pointing direction of the rod. And we have went through with the math, and we got the equation of motion without external force, which is already shown on the blackboard. So now, as I mentioned at the beginning, I would like to add a driving force, or driving torque, tau drive. This is equal to d0 cosine omega d t. So I am adding a driving torque. The amplitude of the torque is actually d0. And there's actually also a harmonic oscillating force, or torque, and the angle frequency of this torque is omega d. And that means our total torque, tau of t, will be equal to tau g t-- this is actually coming from the gravitational force-- plus tau drag, which is to account for the drag force. So this time we are adding in a tau drag. So I'm not going to go over all the calculations on how did the right from the beginning to the end. But I will just continue from what we actually started the last time. So if I have additional driving torque there, that means my equation of motion will be slightly modified. This time, my equation of motion will become theta double dot plus gamma theta dot plus omega 0 squared theta, and that is equal to d0 divided by I. This is actually divided by I because, in order to get the acceleration, I'll need to divide my torque by a movement of inertia of this system and cosine omega d t. This is actually the oscillating frequency of the driving torque. And just a reminder, gamma is defined to be equal to 3b m l squared. And the omega 0 is actually defined to be square root of 3g over 2l. So as I mentioned in the beginning, this is actually giving you a sense of the size of the drag force. And the right hand side, the omega 0 is actually the natural angular frequency. So, of course, we can actually simplify this by replacing this term, or this constant, by symbol. So the symbol I'm choosing is f0. And this is defined to be d0 divided by I. Therefore, I arrive at my final equation of motion-- theta double dot plus gamma theta dot plus omega 0 squared theta, and that is equal to f0 cosine omega d t. So I hope this looks pretty straightforward to you. So this is our equation of motion you can see from this slide. So we have three terms in addition to the theta double dot. The first one is actually related drag force, or drag torque. The second one is actually related to so-called spring force. So that is actually be related to the spring constant or, because of the restoring force of the gravitational force. The third one is actually what we just add in as a driving force. So one question which I would like to ask you is-- so now I bring one more complication to this system. So now I am driving this system with a different frequency, which is omega d. The question is, what would be the resulting oscillation frequency of this driven harmonic oscillator? What is going to happen? Well, this system actually follows the original damped oscillator frequency, omega, which is actually close to omega 0. Or what this system actually follows the driving force frequency. Finally, maybe this system chooses to do something in between. We don't know what is going to happen. So our job today is to solve these equation of motion and to see what we can learn from the mathematics. Then we can actually check those results to see if that agrees with the experimental result, which is through those demos, OK? So as usual, I have this equation of motion here. So one trick, which I have been using, is to go to complex notation, right? Therefore, I can now re-write this thing to be Z double dot plus gamma Z dot plus omega 0 squared Z, and that is equal to f0 exponential i omega d t. So basically, I just go to the complex notation. And we would like to solve this equation. So in order to solve this equation, I make a guess, a test function. I guess Z of t has this functional form. This is equal to A-- some kind of amplitude-- exponential i omega d t minus delta. Delta is actually some kind of angle, which is actually to account for the possible delay of the system. So if I start to try-- for example, this is a system, which I am interested-- I start to drive this system, it may take some time for the system to react to your driving force. So that's actually accounted for by this delta constant. And the amplitude is actually what we were wondering, what would be the amplitude. Therefore, you have some kind of a constant in front of the exponential function. And you can see that this exponential is actually having angular frequency, omega d. And that is actually designed to cancel this exponential i omega d t here in the drag force. So now we can as you calculate what z dot of t would be equal to i omega d Z. Z double dot t will be equal to minus omega d squared Z. With those, we can now plug that back into this equation of motion and see what we can actually learn from there. So basically, what I'm going to do is to insert all those things back into the equation of motion. And that is actually going to be like this. Basically, the first term, the double dot, you get a minus omega d squared out of it. The second term, gamma Z dot-- I have Z dots here. Basically, I would get plus i omega d gamma out of the second term. That's third term, I get omega 0 squared out of it. And that is actually multiplied by Z. And this is equal to f0 exponential i omega d t. All right, and we also know from this expression Z is equal to A exponential i omega d t minus delta. That's the test function. So this is actually equal to A exponential i omega d t minus delta. So now what I can do is-- I have some constant in the front. Multiply it by exponential i omega d t. And now I can actually cancel this exponential i omega d t with the right hand side term. Very good. The whole equation is actually exponential free. Now I don't have any exponential function left. And exponential i delta is actually just a constant. So now this equation is actually independent of time. So what I getting is like this-- basically if I multiply the both sides by exponential i delta, then I get minus omega d squared plus i omega d t plus omega 0 squared A. And this is going to be equal to f exponential i delta because I multiply both sides by exponential i delta. And this is equal to f cosine delta plus i f sine delta. Just your last equation. Any questions so far? So look at what I have been doing. So I have this equation of motion. As usual, I go to complex notation. Then I guess Z equal to A exponential i omega d t minus delta because my friends from the math department already solved this, and I'm just following it. Then I can calculate all those terms, plug in e, and basically, you will arrive at this equation. This equation is a complex equation. So what does that mean? That means one equation is equal to two equations because you have the real part, you have the imaginary part. Therefore, that's very nice because I have two unknowns. The first one is A, a constant. And the second one is delta. Now I have two equations I can solve what would be the functional form for A and the delta. And let me go immediately solve this equation. So if I take the real part from this equation, basically what I'm going to get is omega 0 squared-- this is real-- minus omega d squared-- this is also real-- times A. A is actually some real number. This is actually equal to f cosine-- f0. Sorry, I missed a zero here. So that zero I missed. This should be f0. f0 cosine delta. And I can also collect all the terms, which is imaginary terms. Then I get only the second term from the left hand side is with i in front of it. Therefore, I get omega d gamma A from the left hand side. And from the right hand side, there's only one imaginary term. Therefore, I get-- this is equal to f0 sine delta. So now I have two equations. I have two unknowns. Therefore, I can easily solve A and delta. So I call this equation number one. I call this equation number two. So now I can-- sounding in quadrature the two equations-- in quadrature. And the left-hand side will give you A squared omega 0 squared minus omega d squared squared plus omega d squared gamma squared. That is actually coming from the second equation. That gives you the left hand side. It's a square of the sum the first and second equation. And the right hand side will become f0 square cosine delta cosine squared delta plus sine squared delta. And this is equal to 1. So that's actually the trick to get rid of delta. Then I can get what will be the resulting A. A is actually a function of omega d. Omega d is given to you. It's actually determined by you-- how fast do you want to oscillate this system. And this is equal to f0 divided by square root of this whole thing. So this will give you omega 0 squared minus omega d squared squared plus omega d squared gamma squared. Then we can also calculate what would be the delta. The trick is to take a ratio between equation number two and the equation number one-- 2 divided by 1. Basically, you will get tangent delta. This is sine divided by cosine. f0 actually cancel. This is equal to what? Equal to the ratio of these two terms. After you take the ratio, A drops out. Basically, what you get is gamma omega d divided by omega 0 squared minus omega d squared. So we have solved A and the delta through this exercise. So what does that mean? Originally, I assume my solution to be A exponential i omega d t minus delta. Therefore, I would like to go back to the real world, which is actually theta. So basically, if I take the real part, I would get theta of t, which is actually the real part of Z. And that will give you A omega d cosine omega d t minus delta is also a function of omega d. So we have done this exercise. And you can see that the first thing which we see here is that there's no free parameter from this solution. A is decided by omega d. And delta is also decided by omega d. There's a lot of math, but actually we have overcome those and that we have a solution. But it is actually clear to you that this cannot be the full story. Because you have a second-order differential equation, you need to have two free parameters in the solution. What is actually missing? Anybody can tell me what is missing. AUDIENCE: The homogeneous solution. YEN-JIE LEE: Very good. The homogeneous solution is missing. So that's actually why we actually have no free parameter here. Once is the omega d is determined, once the f0 is given, then you have the functional form which decides what is actually theta. So what in actually the full solution? A full solution should be, as you said, a combination of homogeneous solution and the particular solution which we actually got here. So if I prepare the system to be in a situation of, for example, underdamped situation. Then what I'm going to do is actually pretty simple. What I am going to do is to just copy the underdamped solution from last lecture and combine that with my particular solution, which I obtained here. So that actually to see what actually the full solution looks like. I have A omega d cosine omega d t minus delta is a function of omega d. This is actually so-called steady-state solution. And, of course, as you mentioned, I need to also add the homogeneous solution and basically the no -- this actually -- according to what I wrote there, I have a functional form of exponential A exponential minus gamma over 2t equals sine omega t plus alpha. So I changed A to B because I already have the A there just to avoid confusion. Then basically, you get B exponential minus gamma over 2t cosine omega t plus alpha. Basically, they are two free parameters, B and alpha. Those two free parameters can be determined by initial conditions. So, for example, initially I actually release the rod at some fixed angle of theta initial. And also the initial velocity is 0. Then I can actually practice solution A using those initial conditions to solve B and alpha. Any questions so far? Yes. AUDIENCE: Are we assuming it's underdamped? YEN-JIE LEE: Yeah, I'm assuming it's underdamped, the situation. So that's the assumption. So it depends on the size of gamma and the omega 0. Then you have actually four different kinds of solution. If gamma is equal to 0, then what you are going to plug in is the solution from no damping as a your homogeneous solution. And if you prepare this system underwater, damping is colossal, it's huge, then you actually plug in the overdamped solution to be your homogeneous part of the solution. Any other questions? Very good question. So now maybe you got confused a bit. I have now omega d. I have also omega. And there's another one we just called omega 0. What are those? So omega 0 is the natural angular frequency without given the drag force. If you remove everything just like without considering any drag force, et cetera, and that is actually the natural frequency of the system. And what is omega? Omega, according to the function, omega is defined to be omega 0 squared minus gamma squared over 4 square root of that. That is actually the oscillation frequency, which we actually discussed last lecture, after you add drag force into it again. Finally, omega d is how fast you actually drive this system. So that is actually the definition of these three omegas. So you can see that, if I prepare my solution to be underdamped situation, then basically you will see that this is actually so-called a steady-state solution because A omega d is a constant. So it's going to be there forever. And the second term is actually B exponential minus gamma over 2t. It's decaying as a function of time. So if you are patient enough, you wait, then this will be gone. So that is actually how we actually understand this mathematical result. And now, of course, you can actually take a look at this. This is actually just assuming some kind of initial condition and plug in the solution and plot it as a function of time. And you can see that this function looks really weird, looks a bit surprising. What does that mean? It looks really strange. But at some point, this superposition of these two functions-- because one of the functions actually dies out, disappears-- then you will see that, if you wait long enough, then you actually only see a very simple structure, which is oscillation frequency of omega d. And that means a large t. In the beginning, the system will not like it. You drive it, and the system don't like it. Like if I go and shake you, in the beginning, you would not like it-- maybe. And if I shake you long enough, and you say, come on, OK, fine. I accept that. So that is actually what is going to happen to the system. So now I would like to go through a short demonstration, which is actually the air cart, which you seen before. There's a mass and there are two springs in the front and the back of this cart. And, of course, as usual, I would turn on the air so that I make the friction smaller, but there's still some residual friction. And you will see that this mass is actually oscillating back and forth. And the amplitude can become smaller and smaller as a function of time. Now in the right hand side, I have a motor, which actually can drive this-- I can actually shorten or increase the length of the right hand side string. Then I actually introduce a driving force by the right hand side motor. If I turn it down, this is what is going to happen. So we can see now this motor is actually going back and forth. And it has a slightly higher frequency compared to the natural frequency. So the frequency of the motor is higher. And you can see that this cart is actually oscillating. But you can see that sometimes it pulls and sometimes it moves faster. So you can see that it's actually moving. And it stops a little bit because they are all superposition of two different kinds of oscillating functions come into play. You can see that now. It got slowed down, and it can become faster and slower and faster. But eventually, if you wait long enough, what is going to happen? What is going to happen? If we wait long enough-- AUDIENCE: [INAUDIBLE]. YEN-JIE LEE: Exactly. So basically, if you wait long enough, as you said, you will actually just oscillate at the frequency of the driving force. You can see that this motion looks really bizarre, right? Sometimes it stops, and sometimes it actually continues to move. And are you surprised? Probably you are not surprised anymore because we know math is the language to describe nature. And indeed it predicts this kind of behavior. That's really pretty cool. In order to help you to learn a bit how to actually translate a physical situation into mathematics, what I am going to do is to introduce you another example so that actually we can actually solve it together. So now I would like to drive a pendulum. So I prepare a pendulum at time equal to 0. This is a string attached to a ball with mass equal to m. And the length of the string is equal to l. And the angle between the vertical direction and the direction of the string is theta. And, of course, I can actually give you initial condition X initial, which is actually measured with respect to the vertical direction, and time equal to t. This is actually the original vertical direction, the same as this dashed line. And I can actually move the top of the string back and forth to some position. And, of course, this string is connected to the ball. And this system is actually driven from the top by the engine's hand, so the engine is actually shaking this system from the top. And I do it really nicely. So basically, I define that the displacement, d, as a function of time, is equal to delta sine omega d t. So that is actually what I'm going to do. OK, and I would like to see what is going to happen to this pendulum. So, as usual, the first step towards solving this problem is to define a coordinate system. So what is actually the coordinate system I'm going to use? So now I define pointing upward to be y. I define the horizontal direction pointing to the right hand side of the board to be x. So that's not good enough. I still need the origin, right? So now I also define my origin to be the original position of the ball which is actually completely addressed before I do the experiment. So that this is actually the equilibrium position of this system actually. Then I define here to be 0, 0. So once I have that defined, I can now express the position of this mass of this ball to be xt and yt. And see what we are going to get. Of course, as usual, we are going to analyze the force actually acting on this ball. So therefore, as usual, we will draw a force diagram. So basically, you have the little mass here, and you have actually two forces acting on this little mass, or little ball. This is Fg pointing downward. It's a gravitational force. And now this is actually equal to minus mg y. And there's also a string tension, T. Since we have this definition of theta here, basically I have a T which is actually pointing to the upper left direction of the board. Oh, don't forget-- actually there's a third force, which is actually the F drag. F drag is actually equal to minus bx dot in the x direction. Now I would like to write down the expression for also the string tension, T. The T is actually equal to minus T sine theta in the x direction because the T is pointing to upper left direction. So therefore, the position to x direction will be minus sine theta and plus T cosine theta in the y direction because the tension is actually pointing upper left. As usual, this is actually pretty complicated to solve. I have this cosine. I have this sine there, right? So what I'm going to do is to assume that this angle theta is very small, as usual. So I will take small angle approximation. Then basically, you have sine theta is roughly to be equal to theta, and that is actually equal to what? Equal to-- here. Basically, you can actually calculate what will be the theta. The sine theta, or theta, would be equal to x minus d divided by l. And of course, taking a small angle approximation will bring cosine theta to be 1. Then after this approximation, my T will become minus T x minus d divided by l in the x direction plus T in the y direction because sine theta is replaced by this approximated value because sine theta is actually replaced by 1. Any questions? Yes. AUDIENCE: Is that a constant or is that the change in sine? YEN-JIE LEE: It's a constant. Yeah, I was going too fast. So this is actually a constant of my amplitude. AUDIENCE: And the drag force is only in the x direction? YEN-JIE LEE: Yes, it's only in the x direction. So I'm only trying to actually move this point back and forth horizontally. So now I have all the components T, Fg, f drag. And, of course, you can see that I already ignored the drag force in the y direction from that formula because I am only considering the system to be moving in the x direction. Therefore, I can now collect all the terms in the x direction. Basically, you will have m x double dot. This is equal to minus b x dot, which is actually coming from the drag force, minus T x minus d divided by l. This is actually coming from this term in the x direction. Let's look at those in the y direction. And y double dot would be equal to minus mg plus T. The minus mg is from the gravitational force. And this T is coming from the y component of the string tension. And of course, since we are taking a very small angle approximation, there will be no vertical motion. Yes. AUDIENCE: Why did we use the small approximation for sine theta when we're going to use x minus d over l, which represents psi instead of just theta? YEN-JIE LEE: Yeah, so also in this case, they happen to be exactly the same. And why I care is actually the cosine theta. Otherwise, I would have to deal with cosine theta. And also, this y double dot would not be equal to 0, which is what I'm going to assume here. Good question. So the question was, why do I need to take an approximation? Because I want to get rid of cosine theta. So now from this y direction, I can solve T will be equal to mg because I assume that there's no y direction motion. And I can conclude that-- originally, I don't know what is actually the string tension. It's denoted by T. Now, from this second equation, I can conclude that T will be equal to mg, which is the gravitational force. Then, once I have that, I can go back to x direction. Basically, I get m x double dot. This is equal to minus b x dot minus mg over l x minus d. Everything is working very well. And I just have to really write down the d function explicitly. What is d? d is just a reminder, delta sine omega d t. So I will plug that into that equation. And also I will bring all the terms related to x to the left hand side just to match my convention. All right, so now I will be able to get the result, m x double dot plus b x dot plus mg over l x. And that is actually equal to mg over l d. And this is equal to mg over l delta sine omega dt. So basically, I collect all the terms, put it to the left hand side. And I write down T explicitly, which is this. Then I can divide everything by m. Then I get m x double dot plus b over m x dot plus g over l x. And that would be equal to g over l delta sine omega dt. Now, of course, as usual, I will define this to be gamma, define this to be omega 0 squared. And I would define this to be f0, which is equal to omega 0 squared delta. It happened to be equal like that. And then this actually becomes x double dot plus gamma x dot plus omega 0 squared x equal to f0 sine omega dt. Am I going too fast? OK, everybody is following. So we see that ha! This equation-- I know that. I know this equation, right? Because we have just solved that a few minutes ago. Therefore, I know immediately what will be the solution. The solution is here already. I have A omega d and the tangent delta, the function of force there. Therefore, I can now write down what will be the A. So A is actually just equal to f0 divided by square root of omega 0 squared minus omega d squared squared plus omega d squared gamma squared. So now the question is-- what does the result actually mean. I have this function. I have that function, tangent delta. It's solved. It's actually the amplitude of the steady-state solution and also the phase difference between the drag force phase and the steady-state oscillation phase. So that's actually the amount of lag and the size of the amplitude. But through this equation it is very difficult to understand. So what I'm going to do is to take some limit so that actually we can help you to understand what is going on. So suppose I assume that omega d goes to 0. So what does that mean? This is the engine's hand and is moving really slowly and see what is going to happen. If I do this, then you will find that A omega d-- since omega goes to 0, this is gone, this is gone. Therefore, you will see that omega A will be equal to omega 0 divided by-- I'm sorry-- of f0 divided by omega 0 squared. And that is actually equal to g delta over l divded by g over l. And that will give you delta. So what does that mean? This means that, if I drive this thing really slowly, then the amplitude of the mass will be equal to how much I actually move, which is delta. OK. Do you get it? In addition to that, tangent delta-- since I am taking the limit omega d goes to 0. Therefore, tangent delta will be equal to 0, and that means delta will be equal 0. Any questions? So that means there will be no phase difference. The system has enough time to keep up with my speed. The second limit, obviously, omega d goes to infinity. What does that mean? That means I'm going to hold this as a string and shake it like crazy really fast and see what will happen, OK? So in that case, you will get A omega d, and that one goes to 0, because omega d goes to infinity. This one goes to 0. And also, tangent delta will go to infinity. Therefore, delta will go to pi. So that means they will be out of phase. Any questions so far in these two limits? OK, so what I'm going to do now is to take a small toy, which I made for my son, who is one-year-old now. Because I would like him to learn wavelength vibration before he goes to quantum, right? Hey? So I made this toy. And he looked at it. So you can see now, I can demonstrate what is going to happen when omega is approaching to 0. OK? I am already doing it. Can you see it? No? It's a very exciting experiment. Can you see that? You see that this is the origin vertical direction. If I do it really, really, really slowly, you can see that the amplitude of the ball is actually exactly the same as the displacement I introduced. So that's kind of obvious. So now, let's see what is going to happen if I drive this system like crazy. OK, not going up and down. Eeeee-- that's the maximum speed I can do. Maybe you can do it faster. But you can see that nothing happened. So amplitude is close to 0, because what you have been doing is-- disappear, you sort cancelling each other. And it's actually not going to contribute to the motion of this ball. So now, you can see that I can also test, what is actually the natural frequency? And what I am going to do is to oscillate at around the natural frequency to see what is going to happen. Let's see what is going to happen. You can see that the delta is really small, right? Can you see the delta. It's really small-- very small-- very small. But you can see that the amplitude, the A, is huge. What does that tell us? What does that tell us? Yeah? AUDIENCE: Well, we're experiencing resonance. YEN-JIE LEE: Yes, we are experiencing resonance. And also, that also tells you that the system is under-damped very much. The Q value is very big. So if I calculate the amplitude, A-- now, I can calculate the amplitude, A, at natural frequency. What I'm going to get is-- now, I can actually plug in omega d equal to omega 0. So if I plug in omega d-- omega d equal to omega 0-- then what is going to happen? So this term is working. So you have A is equal to f-0 divided by omega 0 gamma. Omega-d is now equal to omega 0. And that is going to give you-- so f-0 is actually omega 0 square delta divided by omega 0 gamma. And the one omega 0 actually cancels. Then, basically, you will get Q times delta. What is Q? Just a reminder, it's actually the ratio of omega 0 and the gamma. When the Q is very large, what does that mean? That means it's so close to an idealized situation that direct force is very small. You can see that in the example which I have been doing. So you can see that, ah, it is really the case. So you can see that if my delta is something like 1 centimeter, but the amplitude is actually at the order of 1 meter, maybe. What does that mean? That means that Q is actually, roughly, 100. So you can actually even get a Q out of this experiment. Any questions so far? OK, that's very good. So now, we can go ahead and take a look at the structure of the A and the delta. As we demonstrated before, we make sense of those three different kinds of situations-- omega d goes to 0, omega d goes to infinity. And of course, I would like to know the force structure of A and delta. Therefore, what I'm going to do is to plug A omega d as a function of omega d. So what I'm going to get is this will be equal to delta when omega d goes to 0. We just demonstrated that. And this will increase to a large value and drop down to 0, when omega d goes to infinity. And you can see that this is around omega 0. And you are going to get a huge amplitude at around omega 0. But not quite. The maxima is actually slightly smaller than omega 0. You can actually calculate that as part of the homework. So that makes sense. Now, I can also plug the delta, which is the phase difference-- and you can see that this phase difference will be, originally, 0, when the omega d is very small. And this is actually the omega 0. I hope you can see it. And this will be increasing rapidly here and approaching to pi. So that means, when you are shaking this system like crazy-- very high frequency-- then the system cannot keep up with the speed. The amplitude will be very small. And also, the amplitude will be out of phase completely. So let's actually do us another demonstration, using this little device here. This is actually what you see before, the ball with a Mexican hat. And you can see that there is a spring attached to this system. And on the top, what I am going to do is to use this motor to drive this system up and down, as a direct force. So now, what am I going to do is to come from a very low-frequency oscillation. So you can see that the natural frequency is sort of like this. And you can see that, now, I am driving this system really slowly. You can see, this is actually going up and down really slowly. And you see that-- huh-- the amplitude is actually pretty small. There's no excitement for the moment. All right, so what I'm going to do is, now, I increase the speed of the motor and see what will happen. So you can see, now, it's actually driving it with higher and higher frequency. You see that-- huh-- something is happening. You can see the amplitude is getting larger and larger. I'm still increasing the frequency-- increasing, increasing-- until something-- something happened! Right? Did you see that? It starts to oscillate up and down. Because right now, you can see that-- look at the top. The frequency of the motor is now really close to the natural frequency of this system. So a resonance behavior will happen. And what you are going to get is that, OK, omega d around omega 0. Then you are going to get large time amplitude. So now, what I am going to do is to continue to increase the driving frequency to a very large value. OK, now it's actually doing the "mmmmm"-- doing it really fast. You can see on the top-- very fast. OK, I even get it even faster. You see that-- huh-- indeed, this system is now oscillating at a larger frequency. It's trying to keep up with the driving force. But you can see that the amplitude is actually much smaller than what had happened before. So before the class, you may actually think that, OK, drive it really fast. Maybe we'll increase the amplitude. But in reality, actually, it will give you a very small amplitude. Another thing, which is interesting to know, is that you can see that, when the driving force is actually at the maximum. And actually the position of this mass is actually at the minimum. So they are actually out of phase. I hope you can see it. It's like this. OK, so what you can see is that, when I understand the system and I try to drive it with the natural frequency, what is going to happen is that I'm exciting this system to a state of resonance. So basically, you'll get some resonance behavior. So I have shown you that this works for driven mechanical oscillator. It also works for the spring-mass system. And there are many other things which also work, which is around you. For example, if you happen to be my office hour, you would notice that the air-condition in my office is actually creating a resonance behavior. You'll see low frequency sound-- "mm mm mm"-- something like that. And that is because the pipe actually happens to have the frequency match with the resonance frequen-- OK, the airflow actually happened to excite the pipe, so that it's actually oscillating up and down at that frequency. So what I did was I tried to turn it down to low and see what happened. But unfortunately, it actually excited another resonance. I see, now, not a low-frequency sound, but a very high-frequency sound. I will post a video, actually online. So my life is hard, right? But I'm a physicist. Is So I choose to use the median. Then I actually stay between the two resonances. Then I don't hear the additional sound, which bothers me. Another example is that, when I was in Taiwan as a undergrad, I was living outside in a apartment. And with my flat-mate, we owned a very old washing machine. So in the middle of the night, the washing machine would started to walk around, like my flat-mate. And we are not scared. That is because the oscillation frequency-- actually, the rotation-- happened to match with the frequency of the washing machine. Therefore, when we started to wash our clothes, it start to walk around in the room. So as a physicist, what we have decided is to make the spin slightly slower, or even faster. Then, actually, you can see that, when you do that, then you get rid of the resonance behavior. So it's not walking around any more. We can control it. Another thing which is interesting is that the resonance behavior is not only in the physical objects, which we actually deal with these days also. But either you learn quantum mechanics and upon the field theory, you will find that there are resonance also in a mass wave function. So basically, you can see that these are examples of the Z boson resonance peak. So if you scatter a electron and positron then, basically, you'll see that the cross-section have a resonance peak at around 90 GeV. And that is actually another very interesting example of a resonance in particle physics. Finally, the last example, which I am going to go through is an example involving a glass. We have prepared a very high-quality glass here. Maybe you have seen this glass before. They are pretty nice. And I usually use it to enjoy my red wines, which you cannot, enjoy, probably now. So you can see that this is the glass. And if I put a little bit of water on my hand and I rub it-- [VIBRATING TONE] --carefully, I can actually excite one of the resonance frequencies. So you can see that we have all everything working on a single particle. And that will give you one resonance frequency. If I work on two particles, which you will see that in the next lecture, I would get two resonance frequencies. And this glass is made of infinite number of particles. Therefore, I will have infinite number of resonance frequencies. When I'm rubbing it, I'm actually giving input of all kinds of different frequencies. But the glass will be smart enough so that it will pick up the one it likes the most, which is the resonance frequency. So you can see that the sound is actually, roughly, 683 Hertz. And you can actually measure it with your phone. So on the TV commercial, you may have seen that there's a lady singing. And she's singing so loudly such that the glass-- "bragh!"-- breaks. Can we get a volunteer today to sing in front of us? Oh-- singing. Can you sing it-- high frequencies? "Ahhhh." [LAUGHTER & APPLAUSE] Very good try. But it didn't work. OK, I guess it's really difficult to perform that in front of so many people unprepared. But fortunately, we are MIT. So we have designed a device, which actually can help us to achieve this. So this device actually contain a amplifier here. And I can now control the frequency of the sound through this scope. And this amplifier will actually amplify the signal and produce a sound wave and try to actually isolate this glass. So we are going to do this experiment. So we will need to change the loud setting a bit. Because the sound is going to be, probably, too loud. Just for safety-- some of you may not survive. [LAUGHTER] So I'm handing out these. OK, who is closer? OK, maybe you. AUDIENCE: [INAUDIBLE] YEN-JIE LEE: Oh. Oh, sorry. [LAUGHTER] I'm so sorry. What? I don't need that. OK. So just for safety, I will put this on. And what I am going to do is also put these glass on. OK, maybe I'll do this first. AUDIENCE: [INAUDIBLE] YEN-JIE LEE: OK, so what I am going to do now is to start producing sound wave. [LOUD TONE] So through the camera, you should be able to see what is actually shown on the screen. So you can see that, if this glass is actually moving, the wood inside would also vibrate. So you can see that, clearly, we don't have resonance yet. So what I am going to do is to increase the frequency and see what happens. So now, it's actually 643. It's actually still below the resonance frequency. Now, I have measured the frequency. It should be 684. So now, it's actually 653-- 663 Hertz-- 673 Hertz. Can you see the movement? You cannot see the movement yet. 683-- you see? You see, now-- AUDIENCE: Yes. YEN-JIE LEE: --the frequency of the sound is actually matching with one of the natural frequencies of the glass. Apparently, the glass likes it. And now, you can see that it is still vibrating. And the next step, which we are going to do, is to try to increase the amplitude, increase the volume of the sound, and see what happens. Maybe you want to cover your ears, just for safety. [LOUD TONE] OK, then the glass may break, if we are lucky. Let us see what is going to happen. [INCREASINGLY LOUDER TONE] Oh! [APPLAUSE] TECH SUPPORT: Good job. YEN-JIE LEE: Very good. TECH SUPPORT: Perfect. That's the quickest one we've had. YEN-JIE LEE: Yeah, thank you very much. Thank you, glass. [LAUGHTER] So you can see the power of resonance. So if I tune down the frequency slightly more, then you will be where? You'll be here. Then you will not have enough amplitude to break the glass. And also, as we discussed before, the quality of the glass should be really, really high, such that the resulting amplitude will be very large. Then you can actually break it with a external sound wave. And if we go above the resonance frequency, then you would not also move a bit. Because if you go to very large omega d, then amplitude will be pretty small. OK, let me try to switch back to my presentation. I think we did. Sure. So this is actually what we have learned today. We have learned the behavior of a damped driven oscillator. We have learned the transient behavior. So what is actually transient behavior is a mixture of steady state solution, which was coming from the driving force, and the homogeneous solution. If you wait long enough, this will decay and disappear. Is And we have learned resonance. So an IOC circuit, which you actually solved that in your P-set, in pendulum, which I just show you, which helped my son to learn wavelength vibrations-- and air condition, washing machine, glass-- particle physics. We can see damped os-- driven oscillator or resonance almost everywhere. So I hope that you enjoyed the lecture today. And what we are going to do next time is to put multiple objects together so that you see the interaction between one particle to the other particle and see how we can actually make sense of this kind of system. Thank you very much. And I will be here if you have additional questions related to the lecture. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | Exam_Review.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: So welcome back, everybody. This is the final exam checklist. For the single oscillator, we need to make sure that you know how to write down the Equation of Motion. We have discussed about damped, under-damped, critically damped, and over-damped. We did that. Oscillators, and we have tried to drive oscillators. We observed transient behavior in steady state solution. Resonance, right, so which we actually demonstrated that by breaking the glass. And then we moved on and tried to couple multiple objects together. And that brings us to the coupled system. What are the normal modes? And how to actually solve M minus 1 K matrix, the eigenvalue problem. What is actually the full solution for the description of coupled systems. And can we actually drive the coupled system, and we found out we can. So the system would respond as well similar to what we have seen in the single oscillator case. We see resonance as well. We can excite one of the normal modes by driving the coupled system. Then we put more and more objects until at some point, we have infinite number of coupled objects. What is actually the solution of refraction and the transmission-- refraction and the translation symmetric system. That is actually the discussion of symmetry. We go to the continuum then, and we actually found wave and wave equations. So we found that finally, we made the phase transition from single object vibration to waves, and that is actually an achievement we have done in 8.03. We have discussed about different systems, massive string, massive spring, sound wave, electromagnetic waves, and we have discussed a progressive wave and standing waves. For the bound system, we have also normal modes. We discussed about how to actually do Fourier decomposition, and what is actually the physical meaning of Fourier decomposition in 8.03. For the infinite system, we also learned about Fourier transform and uncertainty principles. And we learned to apply boundary conditions so that we constrain the possible wavelengths of the normal modes. Therefore, we also learned about how to put a system all together. Finally, how to determine the dispersion relation, which is omega as a function of K, the wave number. Until now, we discussed idealized systems, and we also moved on to discuss dispersive medium. We have learned some more, even more about dispersion relation for the dispersive medium and signal transmission, how to send signal through a highly dispersive medium. The solution we were proposing is to use an amplitude modulation radio and also the pattern of dispersion. The group velocity and phase velocity, we covered that. As I mentioned before, the uncertainty principle. A 2D/3D system. We have bound system, which we have normal modes for two-dimensional and three-dimensional systems, as well. Because we're all over the place, so just make sure that you know how to actually dewrap all those standing waves for different dimensions of systems. We showed and approved geometrical optics, which essentially is the direct consequence of waves. Wave function, a continuation of the wave function and boundary condition. We learned about the refraction rule and also Snell's law. We talked about polarized waves, linear, circularly polarized, elliptically polarized, and the polarizer and quarter-wave plate. At the end of the discussion of 2D/3D systems, we discussed about how to generate electromagnetic waves by accelerated charge. Finally, we went on and talked about how those EM waves propagate in dielectrics and again, boundary conditions, which leads to interesting phenomena, which belongs only to electromagnetic waves. For example, Brewster's angle. So the refraction amplitude-- refraction-- the wave amplitude is governed by the property of the electromagnetic waves, which is coming from the laws which governs electromagnetic waves, which is Maxwell's equations in matter. We were trying to also manipulate those waves by adding them together, and we see constructive and destructive interference and diffraction phenomena. Then we connect that to quantum mechanics by showing you a single electron interference experiment. That connects us to the beginning of the quantum mechanics, which is the probability waves, which behave very different from other waves we have been discussing. But you are going to learn a lot more in 8.04. OK, so don't worry. All right. So that is the checklist. You can see that I can write it in two pages, so it's not that bad, probably. I hope that there was nothing really sounds like new to you by now. If you find anything is new, you have to review that part. That means you missed a class. All right. So what I'm going to do now is to go through all the material faster than the speed of light. All right. So that you will get nauseated. No, you are going to get a list of the topics. You just have to feel it. If you feel good, like when you are having a cupcake, right, then you are good for the final. If you don't feel good, what is Professor Lee talking about? He's talking about nonsense now. Then you are in trouble, and you have to review that part. All right? OK. So that's what we'll do. So let's start. All right. Why 8.03? We started a discussion-- welcome, We started a discussion of 8.03 and it's vibrations and wave systems, is name of this, 8.03. And the motivation is really simple, because we cannot even recognize the universe without using waves and vibration. You cannot see me, and you cannot hear anything, and you cannot feel the vibrations-- sorry, the rotation of a black hole by your body anymore, then it's not very cool. Therefore, we study 8.03 to understand the basic ideas about waves and vibrations. And we found that waves and vibrations are interesting phenomena. Waves are connected to vibrations. Because if you look at only, for example, a single object on these waves, you see that it is actually a single object which is oscillating up and down, oscillating up and down, and this is your vibration. So there's a close connection between single particle vibration and the waves. And that is the first thing that you learned. Therefore, we need to first understand the evolution of a single particle system. And we make use of this opportunity to start the discussion of scientific matter. So using this opportunity, basically, what we have been doing for the whole class is the following. So the first step is always to translate the physical situation which we are interested into mathematics, right? Because mathematics is the only language which we know which describes the nature. If you come out with a new language, and that is going to be a super duper breakthrough, it cannot be estimated by Nobel Prize. But the problem we are facing now is that this is the only language we know which works. Therefore, we really follow this recipe, which is similar to many, many other physics classes. And we have a physical situation, we use laws of nature or models, and we have a mathematical description, which is the Equation of Motion. And this is actually the hardest part, because you need to first define a coordinate system so that we can express everything in a system in that system, then you can make use of the physical laws you have learned from the previous 8.01 and 8.02 to write down the Equation of Motion. And most of the mistakes, and also most of the problems or difficulties you are facing is always in this step. Then we can solve the Equation of Motion, which is, strictly speaking, not my problem. It's the math department's problem. Yeah, that's their problem. Then we solve the Equation of Motion, and you will be given the formula. Then we use initial conditions and then make predictions. And then we would like to compare that to experimental results. And that is the general thing which we have been doing for physics. So let's take a look at those examples. Those are examples of simple harmonics motions. And you can see that these, all these systems have one object, which is oscillating. And you can see that their Equations of Motion are really similar to each other. It's theta double dot plus omega, zero squared, theta equal to zero for those idealized simple harmonic motions. And we learned that the solution of those equations are the same, which is a cosine function. Then we went ahead and added more craziness to the system. So basically, what we tried to do is to add a drag force into the game. And we were wondering if this more realistic description can match with experimental data. So this is the Equation of Motion, and the additional turn is the one in the middle, the gamma theta dot turn. And after entering these turns, not only is this an interesting model to describe the physical system we are talking about, but the mathematical solution is far more richer than what we talked about in the single harmonic oscillator case. Basically, you see that a general solution depends on the size of the gamma compared to omega dot zero, which is the oscillation-- the natural frequency of the system. OK. And then you can see there are three distinct different kinds of solutions. They have different mathematical forms. And we call them under damped solution, critically damped solution, and over damped solution. So those equations will be given to you. And the excitement is the following. So you can see that those solutions, if you plot the solution as a function of time, they look completely different as a function of time. So in the case of no damping, the amplitude is actually the constant, it's not actually reducing as a function of time. But when the damped system, the damping is turned on, then in the under damped situation, you can see that they end up reducing as a function of time. And if you have too much damping, you put the whole oscillator into some liquid, for example, and you see that oscillator disappear. The cool thing is the following. The excitement from-- as a physicist is that all of those crazy mathematical solutions actually match with experimental results. Wow. That is really cool. Because there is nobody saying that these should match and how, naturally, I should learn that OK, when should I change the behavior of the system. So this is really a miracle that this complicated mathematical description is useful and that it is super useful to describe the nature. Once we have learned that, we can now add a driving force into ligand. From the equation here, we can see that there is a natural frequency, omega dot zero, of this system, and there is a drag force turn, which is actually to quantify how much drag we have, we have a gamma there. We are driving it at a driving frequency omega t. So what we have learned from here is that if you are driving this system, you are-- for example, I am shaking that student, shaking you. OK, in the beginning, this student is going to resist. No, don't shake me. Come on. But at some point, he knows that Professor Lee is really determined. Therefore, he is going to be shaked at the frequency I like. OK. So that is actually what is happening here. This is so-called transient behavior. So in the beginning, the system doesn't like it. So this is making use of the superposition principle. So you can solve that homogeneous solution, which is on the right-hand side. It depends on the physical situation you are talking about. You choose the corresponding homogeneous solution. And lamba and psi is the driving force from E and G, right, and that is going to win at the end of the experiment, because I'm going to shake it forever, until the end of the universe. So you can see that at the end, you-- what is left over is really the steady state solution. And it has this structure, A omega d, depends on omega. And you get resonance behavior. Don't forget to review that. So you have a delay in phase because when I shake the student, the student needs some time to respond. Therefore, the delta is non-zero if the student is damped. All right. So now we have learned all the secrets about a single object system. Then we can now go ahead and study coupled oscillators. There are a few examples here, which is coupled pendulums or coupled spring-mass systems. And we found that a very useful description of this kind of system is to make use of the matrix language. So originally, if you have n objects in a system, you have n Equations of Motion, and that looks horrible. But what is done in 8.03 is that we introduce a notation with a matrix. Basically, if you write everything in terms of matrix, then it looks really friendly, and it looks really like a single oscillator. OK? Although solving this equation is still a little bit more work. And basically, you can see that from this example, we can actually derive M minus 1 K matrix, and the whole equation won't be-- the Equation of Motion problem solving problem becomes an M minus 1 K matrix eigenvalue problem. What is an M minus 1 K matrix? This is describing how each component in the system interacts with each other. Once we have this, we can solve the eigenvalue problem, and we are going to be able to figure out the normal modes of those systems. So what is a normal mode? Normal modes is a situation where all the components in the system are oscillating at the same frequency and they are also at the same phase. So that is the definition of normal mode. And those are what is used in a deviation, also, which leads us to the eigenvalue problem. We define Z equal to X 1 H or I omega t plus 5. Everybody is oscillating at omega and also at phase 5, right? So that is what we actually learned. And what is actually the physical meaning of those normal modes? So if we plot the locus of the two coupled pendulum problem, what we see is the following. So basically, you will see that the locus looks like really complicated as a function of time if you plot X1 X2 versus time. But if we rotate this system a bit, then we find that there's a really interesting projection, which is the principal coordinate. You see that all those crazy strange phenomena we see with coupled systems are just illusions. Actually, you can understand then by really using the right projection. To one-- to the right coordinate system. Then you will see that actually the system is doing still simple harmonic motion. So that is actually the core thing which we learned from coupled systems. So we learned about how to solve the coupled system, and we also learned about going to an infinite number of coupled systems. So then this is an example here. So for example, I can have pendulum and springs, and we connect them all together, and I need to hire many, many students so that they plays it, plays until it fills up the whole universe. So this is the idea of an infinite system. You can see that that means my M minus 1 K matrix is going to be an infinite times infinite long matrix. It's two dimensional. And the A is infinitely long. And that sounds really scary. And in general, we don't know how to deal with this, really. And it can be as arbitrarily crazy as you can imagine. What we discuss 8.03 is a special case. Basically, we are discussing about systems which are having a spatial kind of symmetry, which is translation symmetry, as you can see from all those figures. And you can see that all those figures will have to all have the same normal modes because of this base translation symmetry. What we discussed about is that we introduce an S matrix, which is used to describe the kind of symmetry that this system satisfies. And if we calculate the commutator S and M minus 1 K matrix, if this commutator shows that the evaluate-- if you evaluate this commutator and you get zero, now it means they commute. And the consequence is that the S matrix and the S M minus 1 K matrix will share the same eigenvectors. So you don't really need to know how to derive this-- to arrive at this conclusion, but it is a very useful conclusion. So that means instead of solving M minus 1 K matrix eigenvalue problem, I can now go ahead to solve the S matrix eigenvalue problem. And usually, that's much easier. So for the exam, you need to know how to write down S matrix. You need to know how to solve eigenvalue problems, including M minus 1 K matrix and the S matrix. And then we can get to normal mode frequency, omega squared, and we can also solve the corresponding normal modes. And here is telling you what would be the solution for space translation of the matrix system. And basically what we will see is that making use of the S matrix should be-- brings you to the conclusion that A, j must be proportional to exponential i, j, k, a, where this A is the length scale of this system, the distance between all those little mass. And the j is a label which tells you which little mass I am talking about. And k is the-- some arbitrary constant. But by now, you should have the idea basically that's-- that's what? That, essentially, is the wave number, right? So that is really cool. So that's all planned in advance. And basically, you can see that we can also write down the A, k because we know that A, j will be proportional to exponential i, j, k, A, after solving the eigenvalue problem for S matrix. Then we actually went one step forward to make it continuous. So basically, we made the space between particles very, very small. And also, at the same time, we make sure that the string doesn't become supermassive. And we concluded that we get some kind of equation popping out from this exercise. M minus 1 K matrix becomes minus T over rho L partial square, partial x squared. You don't have to really derive this for the exam, but you would need to know the conclusion and that psi j becomes psi as a function of x and t. And the magical function appeared, which is the wave equation. Oh my god, this is the whole craziness we have been dealing with the whole 8.03. This is actually really remarkable that we can come from single object oscillation, putting it all together, making it continuous, then this equation really popped out. And this equation really describes multiple systems. Then we went ahead to actually discuss the property of the wave equation. It looks like this. Basically, I replaced the t over rho L by v, p squared. By now, you know the meaning of v, p is actually the phase velocity. And we discussed two kinds of solutions, special kinds of solutions. The first kind is normal modes. The second one is progressive wave solution, or traveling wave solution, whatever name you want to call it. Let's take a look at the normal modes, what have we learned. So if you have a bound system, a bound continuous system, the normal mode is your distending waves for the wave equation we discussed. And basically, the functional form is A, m, sine, k, m, x plus alpha, m and sine, omega, m, t plus beta, m. So what we actually learned from the previous lecture is the following. So basically, you can decide the k, m and alpha, m by just boundary conditions. So before you introduce boundary conditions, which are the conditions allow you to describe multiple nearby systems consistently. So that is the meaning of boundary condition. Before you introduce that, k, m and alpha, m are arbitrary numbers. Whatever number you choose is the-- can satisfy the wave equation. But after you introduce the boundary condition, you figure that out from the problem you are given, then k, m and alpha, m cannot be arbitrary anymore. And they usually become discrete numbers. OK. So that is what we learned from the previous lectures. And finally, we also see that omega, m is determined by the property of the system, by a so-called dispersion relation. In this case, it's linear, it's proportional to k, m, because we are talking about non-dispersive medium for the moment. And we have this beta, m, which is related to the initial condition. And the a, m, which can be determined by a Fourier decomposition. So if you are not familiar with this, you have to really review how to do Fourier decomposition. I know most of did very well on the midterm, but maybe some of you forgot how to determine a, m and it will be very, very important to review that for the preparation for the final. Now the second set of solutions is the following. So you have progress-- progressing waves. And the functional form is really interesting. So you can see this can be written as F, F is some arbitrary function, x plus-minus v, p, t. Basically that is that you're describing a wave which is traveling to the positive-- to a negative or positive direction in the x direction. Or you can actually write it down as G function k, x plus-minus omega, t. Actually, they all work for wave equations. Now we went ahead and applied approach which we learned from the general solution of wave equation to massive strings, and we discussed about sound waves. For the sound waves, it will be important to review what are the boundary conditions for the displacement of the molecules in the sound wave, compare that to the pressure deviation from the room pressure. So I think it's important to make sure that you understand the difference between these two, what are the boundary conditions and basically it should be very similar to the solution-- the boundary condition for the massive strings. And we also talked about electromagnetic waves. And that is another topic which you will really have to review. Several things which are especially interesting is that an electric field cannot be without a magnetic field. They are always together, no matter what. So if you have trouble with the electric field, then there must be trouble in the magnetic field. And that is governed by the Maxwell's equation. Before we go into the detail of those, we also discussed about dispersive medium. So in the case of dispersive medium, we used a special kind of example, which is strings with stiffness. So basically, what we found is that if you have a certain kind of wave equation, like this one, I am writing this one here. Basically, if I add the additional term to describe the stiffness, then what is going to happen is that the dispersion relation, when I ask you to plot the dispersion relation, you will be-- I am requesting you to find the relation between omega and K. And I'm going over this in more detail because I see so many similar mistakes on the midterm. So basically what I'm asking is omega versus K. And in the-- if we don't have this turn, then basically, you have a straight line. Straight line means you have a non-dispersive medium. And if you add this turn, you need to know how to evaluate the dispersion relation. The quickest way to evaluate the dispersion relation is to just simply plug in the progresssing wave solution for the G function or harmonic progressing wave solution, find omega-- K, x plus-minus omega t, into this equation, then you will be able to figure out the dispersion relation. And what we figure out is the following. If we include stiffness, then you can see that the dispersion relation is not a line anymore and is actually some kind of curve, and the slope is actually changing. And there are dramatic consequence from this thing. That means if I have a traveling wave with different wavelengths, that means the phase velocity v, p equal to omega over K is going to be different for waves with different frequencies, or different wavelengths. So that is how you clear the problem. Because if I have initially produced a signal which is a triangle and I let it propagate, what is going to happen is that the slow component will be lagging behind. Those are the slow components. And the fast components will go ahead of the nominal speed. So there will be a spread of the signal. Originally, maybe you have some kind of a square wave, and this thing will become something which is actually smeared out in space, and then you lose the information. And we are going to talk about that later. And we also learned about group velocity. So what is your group velocity? Group velocity v, p-- oh, sorry, v, g is actually partial omega, partial K, which is the slope of a tangential line here. And where the phase velocity is connecting this point to that point, and the slope of this line is the phase velocity, and the slope of the line cutting through this point, which is giving you the group velocity. And we actually learned the definition of-- the consequence of group velocity and phase velocity by introducing you a bit phenomena. Basically, we add two waves with similar wavelengths, or wave numbers. Basically, what we see is the following. So basically, you see some behavior like this. We see this-- the superposition of these two waves which produce a bit phenomena can be understood by something which is oscillating really fast modulated by a much slower more variating envelope. Basically, you can actually understand the bit phenomena by actually identifying these two interesting structures. And the speed of all those little peaks is traveling at phase velocity. And the speed of the envelope is found to be traveling at group velocity. So that is what we have learned. And we can have group velocity and the phase velocity traveling in the same direction. And we can also have a negative group velocity. So that is a technique which is really, really very difficult. And I'm still trying to practice and make sure they I can demo that in 8.03. Basically, it's like the whole system, the whole detailed structure moving in a positive direction. But the body, or say the envelope, is actually moving in the negative x direction. So that is also possible. And you can actually construct a system which has a negative group velocity. So once we have done that, we also tried to understand further the description of the solution for the dispersive medium. So basically, what we actually went over during the class is that OK, now, if the f function f of t is describing Yen-Jie's hand, and I'm holding an infinitely long string and I shake it as a function of time, and that essentially, this motion, is actually described by this f function. What we know is that this oscillation, OK, I can do one, but I won't, but all kinds of f functions can be described as superpositions of many, many, many waves with different angular frequencies. So that's a miracle which we borrowed from the math department again. And you can see that f function can be written as the sum of all kinds of different waves with different angular frequencies with population c omega. This is the weight which makes that become the f function. And we can figure out the c omega by doing a Fourier transform. And finally, what will be the resulting wave function, psi, x, t, which is the wave function generated by the oscillation of my hand. And those are governed by the wave equation, which gives you the relation between omega and the k can be returned in that functional form. So the good news is that with the help of Fourier transform, we can also describe and predict what is going to happen no matter if this system is dispersive or not dispersive using this approach. OK. So that is really cool. And you can of course can do a cross-check just to-- assuring that this is a non-dispersive medium. And you are also going to get back to what you should expect the solution to non-dispersive medium for the psi, x, t. So that is one thing which is really remarkable. And I think what is needed to know is not a deviation of all those formulas, but how the plotting and the derived c omega by using the formula you are given and how to then put together all the solutions and it becomes the resulting solution for the psi, x, t, which is really the solution we really care. So for that, you need to know how to do the integration. You need to know how to derive the dispersion relation. Then one thing left over is to put the problem into that equation, which is also given to you in a formula. And we will not ask you to do a very, very complicated integration for sure on the final. So what is the consequence? Basically, one thing which is interesting to know is that if you have a wave in a coordinate space, which is really widely spread out, and you can do a Fourier transform to get the wave population in the frequency space, what we find is that when this wave is really, really wide in the space, then what we find is that the wave population in the frequency space is very narrow by using a Fourier transform. And that just gives you the result. And on the other hand, if you have a really-- a very narrow pulse in the coordinate space, for example, I do this-- shwhew --very, very-- really quickly. I create a very narrow pulse. And then what is actually happening is that I will have to use a very wide range of frequency space to describe this very narrow pulse. So that leads to-- direct consequences of that is uncertainty principle. And this is closely connected to the uncertainty principle we talk about in quantum mechanics. Delta, p times delta, x greater or equal to h bar over 2. All right. So we have done with the one-dimensional case. And we also talked about a two-dimensional and a three-dimensional case. And this is the example of two-dimensional membranes, and they actually are constrained so that their boundary condition at-- the boundary is equal-- no, the wave function is equal to zero. And you can identify all those normal modes. And we went ahead also to talk about geometrical optics laws. Basically, how we derive that is to have a plane wave. First, you have a plane wave propagating toward the boundary of two different mediums, and we were wondering well, what is the refracted wave and the transmitting wave. By using the-- by making sure just one point, which is that the membranes don't break, the wave function is continuous at this boundary. That's the only assumption which you use. We went through the mathematics, which you don't really need to remember all of them. But you really need to remember the consequence. The consequence is the following. Basically, what we see is that if you have incident plane wave with incident angle theta 1, the refractive wave will be having an angle of theta 1 as well. So that's the first law of refraction, refraction law. And then the second one which we learned is that the transmitting wave will satisfy Snell's law, n, 1, sine, theta, 1 equal to n, 2, sine, theta, 2. And that is very interesting because this, Snell's law has also nothing to do with Maxwell's equation. You see? Right? That's actually what you can learn from here. We usually use electromagnetic waves to demonstrate Snell's law. But from 8.03, we learned that it has nothing to do with Maxwell's equation. It applies to all kinds of different systems, which you can-- which can be described by wave functions. So that is actually the very important consequence. But on the other hand, as we all discussed later, the relative amplitude of the incident wave, refracted wave, and transmitting wave, the relative amplitude is governed by Maxwell's equation. So I would like to make that really crystal clear. So the relative amplitude is governed by really the physical laws, which actually governs the propagation of those plane waves. OK. So I think we can take a five minute break to have some air. And of course, you can-- you are welcome to continue to use all this juice and coffee. And coming back at 38. OK. So welcome back, everybody, from the break. AUDIENCE: [INAUDIBLE] YEN-JIE LEE: So we are going to continue the discussion. We have learned about the two important laws for the geometrical optics. And we also went ahead to discuss the polarization that's solved in greater detail. So for example, we can have linear depolarized wave. So basically, the wave is essentially moving up and down, up and down. But the direction of the background field doesn't change. It's always, for example, initially, if it's in x direction, then it is x direction forever. And in that case, I call it linearly polarized. Of course, I can also have the case that I can have a superposition of two waves. One is having the electric field in the x direction. And the other one is in the y direction. And they are off by a phase of pi over 2. If that happens, then basically, you will see that it produces something really interesting. That direction of the electric field is going to be rotating as a function of time-- as a function of the space these waves travel. And we call it circularly polarized waves. And we can also have elliptically polarized wave. Then we learned about how to do a filtering, which is the polarizer. So suppose I have a perfect conductor here, where I have the easy axis, which is described by the green arrow there. And you can see that easy axis means that if you have electric field parallel to the easy axis, and then since that's the easy axis, so it is supposed to be easy, therefore, this electric field is going to be passing through the polarizer. On the other hand, if the electric field is perpendicular to the direction of the easy axis, that means it's taking the perfect conductor in the hard way. Therefore, when it pass through-- when it is trying to pass through with the perfect conductor, the electrons in those conductors are going to be working like crazy to deflect this wave when the direction of the electric field is perpendicular to the direction of the easy axis. So that is how this works. For example, in the first example, you can see that in this case, you have an easy axis which is perpendicular to the direction of the electric field, which is the red field, then this wave actually got refracted. There will be no transmission-- sorry, no electromagnetic field passing the perfect conductor. And on the other hand, if you have another perfect conductor, in which you have easy axis which is parallel to the electric field, then you can-- you will see that it will pass through the perfect conductor. So that is the polarizer. And also, we discussed about quarter-weight plate, which I would suggest you to have a review about the concept which we have learned about polarizer and quarter-wave plate so that you make sure that you understand how to calculate the electric field after passing through a polarizer and quarter-wave plate and how the secondary, or the elliptically depolarized waves are created using all those wave plates, et cetera. All right. So the next thing which we discussed during the class is how do we produce electromagnetic waves. I think by now, you should know that a stationary charge doesn't produce electromagnetic waves. Even a moving charge at constant speed doesn't create electromagnetic waves. So how do we create an electromagnetic wave which propagates to the edge of the universe? That is-- the trick is to create a kink in the fuel line. So you have to accelerate and stop it. Accelerate and then try to actually stop the acceleration. So then you can create a kink. And this kink is going to be propagating out of the-- as a function of time. And this kink is creating the so-called radiation from this accelerated charge. So you don't really need to remember all the deviations, but you really need to know the conclusion. So what is the conclusion is the following. The radiated electric field is equal to minus-- very important that there's a minus sign in front of it, which is a common mistake to drop it, and the q is the charge of the oscillating-- the accelerated charge, proportional to the charge. If the particle is more charged, then you have more radiation. Aperp is the acceleration projected to, which is-- the perpendicular projection of the acceleration of the particle with respect to the direction of propagation is so-called the Aperp. And only the perpendicular direction acceleration counts. The one which is parallel to the direction of propagation doesn't really count, as you can see from this equation. And the t prime what is t prime? t prime is t minus r divided by c. So t prime is the retarded time, so that is telling you that it takes some time for the information to propagate from the origin, which is the position of the moving charge to the observer, which is r, this distance, away from the moving charge. So the information takes some time to propagate, and you cannot know what is really happening, for example, 100 light years away from Earth. You have no idea about what is happening. Maybe a black hole is created there and is going to suck everybody up in a few years. But nobody knows, and we don't care because we cannot control it. All right so that is very important. And also very important to know the magnetic field must be there. You can see the relation between magnetic field and the electric field. And the Poynting vector is also its joint field. And when we went ahead, given all the knowledge we have learned, we discussed about how to take very beautiful photos using a polarizer filter. And we discussed about how to filter out the scattered light from the sun. And it would be nice to figure out why this is the case, how these polarizer lines, scatter lines are created. It's purely geometrical. And also, we discussed about Brewster's angle and also how it leads to the explanation of the filtering of the light, the refracted light from the, for example, window of a car or from the water. And this is the demonstration of-- the summary of Brewster's angle. So somebody reminded me that the amplitude should be given. So I think, this is the amplitude formula for Brewster's angle will be given to you. If not, it's asked in the final exam. So don't be worried about it, and you don't have to remember this formula. And I'm not going to ask you to derive that just in such a short time, the three hours in the final exam. But what is very important is to know how this Brewster's angle, why there's no refracted light polarizing in a way that the polarization should be-- why the refracted light is polarized, for example. And also why the transmitting wave is slightly polarized. And I think the conclusions you need to remember, and you need to know how to calculate the angle, at least. Because for this purely polarized light to be produced in a refracted light, you need to have normal angle between the direction of the refracted light and the direction of the transmitted light. And that, you should be able to remember. And you should be able to derive that also from your mind as well, because that means the direction of the oscillation of the molecule at the boundary will be in the direction of propagation of the refracted wave. Therefore, that cannot be the solution to the progressing electromagnetic wave. Therefore, the refracted waves are polarized. So if you follow this logic, then you don't really need to memorize all those formulas. All right. So finally, in the last part of the course, we focused on the superposition of many, many electromagnetic waves so you can produce constructive interference. Or that means all those waves are in phase. And you can have destructive interference when they are out of phase. And that is a very important topic, so you should review that for the preparation of the final. And you can see that there are three concrete examples which we used during the class. A laser beam. We talked about a water ripple in a demo. And we also studied how it make use of this phenomena to design a phased radar. So to detect this unknown object in the sky, what we really need to have is electromagnetic waves pointing to a specific direction. And that can be achieved by using multi-slit interference. And this is the property of the two-slit interference pattern. And you are going to have many, many peaks. They have equal height for two-slit interference If you ignore any effect coming from diffraction. So we've assume that the slit is infinitely small. The slit is super narrow. And then we can ignore the diffraction-- single-slit diffraction. In fact, then all the peaks due to this two-slit interference will have the same height. On the other hand, when we start to increase the number of slits, for example, unequal to 3, unequal to 4, unequal to 5, unequal to 6, as you can see that, the structure of the intensity as a function of delta, which is the phase difference, is actually changing. And you can see that the general structure is the following. So if you have unequal to 3, then basically, you have 2 of adult, and between them, you have 1 child. And if you have unequal to 6, then basically, you have 2 adults and somehow there are 4 children in this collection. So basically, that is what we learned from the solution of the multi-slit interference. And in this way, we can actually make the width of the principal maxima as narrow as you want. So that is why phased radar works. And then we discussed about diffraction. So that is related, again, to the explanation of laser beams. And we discussed about the design of a Star Trek ship, the gun for the ship. And we also talked about resolution. And what is actually happening here is the following. A single-slit diffraction essentially can be viewed as an infinite number of source interference. And you just need to integrate over all the point-like sources between the two walls. And all of them are acting like a spherical wave source. So basically, for every point-- continuously, every point between these two walls are a point source of spherical waves. And that is Huygens' principle. And we can see that the structures is-- of the intensity as a function of position is the following. So basically, you have a principal maxima, which is a peak in the middle. And at some angle, basically, you have destructive interference such that if you integrate over all the contributions from an infinite number of sources in this window, basically, you would see that they completely cancel each other. So that is the origin of all those deep structure minima. And then, after the minima, actually, you will see another peak, but the height of the peak is suppressed by 1 over beta squared. And it would be good to review that. And what is the consequence? So if you shoot a laser beam to the moon, the size of the laser beam will be very large. After you learn 8.03, you know that the size of the laser beam is going to be very, very large due to interference between all the point-like sources from the laser beam. And finally, we can put them all together. So the single-slit diffraction and the multi-slit interference, you can put them all together, and basically, what you get is the following. So basically, you have a multi-slit interference pattern, which is showing there. But now the intensity of the multi-slit pattern is modulated by the single-slit diffraction pattern. And of course, the full formula will be given to you. But on the other hand, you are also requested to know how to calculate, just to add the contribution from multi-slit together in case if we change the amplitude of the incident light or we change the phase, like what we did in the homework. And I think that is one important point, and you should review that. And if you are not sure about how to proceed with that, it would be good to review Lecture 22, Lecture 23. So finally, we talk about the connection to quantum mechanics. Einstein already told us that "I have said so many times, God doesn't play dice with the world." But what we actually find is that there are two very interesting things which we found. The first thing is that if we have a single photon source, and basically, if we don't play dice, we cannot explain the intensity of the-- after this single photon source passes through two polarizers. And what happens is the following. Basically, the result of a single photon source tells you that you really need to play dice so that you can get the resulting polarized light intensity. And also, the second pseudo-experiment we discussed is that if you have billiard balls, basically, you have them pass through the two-slit experiment, what you are going to get is two piles, Gaussian-like distribution. And if you have a single electron source, what it does is that it interferes with itself. An electron, a single electron, can interfere with itself and produce a pattern which is very similar to what we see in the double-slit interference pattern. So that is really remarkable. And also, we talked about a single-slit-- single electron experiment. That gives you also a diffraction pattern. We have to use the wave function to describe the position-- the probability density of the position of the electron on the screen. And know this issue closely connected to the uncertainty principle, which we discussed earlier, delta, p, delta, x is greater than or equal to h bar over 2. So if you have a very narrow window, that means you have very similar delta x, so you have very, very good confidence about the location of the electron. And then the momentum is in the x-- in the momentum in the x direction, you have large uncertainty, according to this equation. And that can be seen from this single-slit diffraction pattern and it is closely connected to what we have learned before. So where is this-- how to actually describe what this is really the dispersion relation of the probability density wave is actually coming from Schrodinger's Equation. And this is given here. We briefly talked about that. And the consequence is the following. You can describe the evolution of the wave function as a function of time by using this wave equation. And this wave equation is slightly different from what we have learned before. And we also can use what we have learned from 8.03 to solve a particle in a box problem, which is covered in lecture number 23. And I just wanted to say that you need to know the general principle, but I'm not teaching 8.04, so I'm not expecting you to solve a quantum mechanics problem. But I would like to say that OK, from this point, it's motivating you to take 8.04, right? Because there can be a lot of fun there as well. And it is closely related to what we have learned from 8.03. So I just want to say, the last point is that this is really not the end of the vibrations and waves. It's just the beginning. And that there is a path toward the peak. And it may take a long time to reach the peak. All right. And I would like to let you know that I'm really, really very happy to be your lecturer this semester. And I really enjoyed teaching this class and getting your responses when I asked questions. Thank you for the support. And I would like to say good luck with the final exam. And we have 800 contributions on Piazza, many thanks to Yinan, who is actually doing all the hard work, day and night. And thank you very much, and see you around MIT in the future. Thank you. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 9_Wave_Equation_Standing_Waves_Fourier_Series.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: So welcome back, everybody, to 8.03. Happy to see you again. So here is the current status of the 8.03. So right now, we have finished the discussion of coupled oscillator. And then we go to infinite number of coupled oscillators. And we found that there's a wave equation coming out of it. And that means, in short, waves are really a group effort. So many, many objects are working really together, so that they create a wave phenomena. And you can also see, there's a close connection between vibration of a single object and the formation of the wave structure. So what we are going to do today is to give you a short review of what we have done last time. Then we actually will continue to our understanding of wave equation today. So what we have learned last time, we have learned how to solve infinite system with space translation symmetry. And also, we learned how to use it to solve finite systems by imposing-- or adding boundary conditions. That would limit the infinite number of normal modes to finite number of normal modes based on-- I mean, it's actually closely related to how many objects you have in the system. And also, we went ahead and go to a continuum limit. And we found out, there is a surprising result coming out of this. And this is actually the wave equation. So what do we mean by going to continuous limit? So the limit we are talking about is that, before when we discussed this closed system of infinite number of objects holding together by strings, there is a length scale, which is the separation between objects, which is called a in my notation. And to make it continuous, we are taking a limit such that the a, which is the separation between objects, is so much smaller than the wavelength. Basically, the wavelength is actually the sinusoidal shape you see when I perturb a system. And what I assuming is that the distance between objects are so much smaller than the wavelengths. So that's actually what I called continuous limit. And that is actually true for most of the example, which we see in the previous lectures. For example, I was holding a giant spring. And I oscillate that. And all the little components, or, say, all the little mass on that spring, the space between all those little mass on the spring are so much smaller than the length scale we are talking about, which is at the order of 1 meter. So that actually is a sensible limit, which describes the physics we are interested. When we go to a continuous limit, we find that something really interesting happens. So M minus 1 K matrix originally is infinite times infinite dimension matrix. It becomes the operator, which is actually minus T over rho L partial square partial x squared. And also-- OK, I changed the notation here. It was aj, and I changed it to psi, because what we are going to use later on, when we describe wave functions, et cetera, especially in 8.04, we usually use psi. And the psi j, which were discrete and evaluated in the individual discrete position in the x direction, it's becoming a continuous function, which is psi x and is also a function t. Therefore, from this exercise, we found out we see wave equation, actually after we go to a continuous limit. And for more information, you can also take a look at the textbook in the relevant page. So what are we going to do today? So today, what we are going to do is to understand the wave equation, the structure, and what does that mean, and also what are the normal modes coming out of this wave equation. And the next time, in later lectures, we will also discuss another special kind of motion, which is progressing wave solutions. So let's immediately gets started by looking at a concrete example and also to derive the normal modes from this wave equation. Before we do that, let's take a look at this wave equation. This wave equation is actually equivalent to infinite number of equations of motion, if you think about it. Why is that? That is because each x-- each partition x you put in will produce a equation of motion. So basically, originally, when we were doing a discrete case, those are labeled by c. c is actually telling you which mass I'm talking about. Now, it's actually replaced by x. And what we are actually doing is to solve infinite number equation of motion in one go. And that is actually the wave equation. So the first question we ask is, what is actually normal modes based on this infinitely long continuous system described by wave equations? So let's get started immediately. So basically, we can first assume what is actually the functional form for normal modes. So what we can actually do is we can assume that psi x, t is actually equal to A, is actually a function of x, times B, is actually a function of time. So what I am doing is actually have a meaning actually. So A of x actually give you a description of the functional form-- the shape of the normal mode as a function of x. So that's actually giving you the shape as a function of x-axis. And B, which is a function of t, is actually giving you information how individual component goes up and down or move as a function of time. So that actually control the time evolution. And we were using this wave equation to describe a continuous system, like, for example, a string with tension t. So what we could do is the following. So we are interested in the solution of the wave equation, which is shown there. So what we could do is that, OK, let's first assume this functional form, assuming that every component is actually following the same time-depend evolution. And then we can actually plug in this functional form to the equation of motion and see what we will get. So if we plug this in into the wave equation, so what we are going to get is, if you look at the left hand side, it's actually a partial derivation with respect to time. Therefore, what we are going to get is A of x times partial square of B, which is a function of t, partial t squared. The right hand side of the equation, which is actually equal to vp squared, is a partial derivative with respect to x. Therefore, you have B is a function of t only times partial square A of x partial t squared. So actually, we can just for convenience-- oh, sorry, that's supposed to be partial x. Thank you very much-- partial x squared. So just for convenience, we can actually divide the whole equation by A times B times the vp squared. We can issue divide the whole equation by A times B, for example, and the vp squared. If we do this, then basically I'm moving this part to the left hand side. So I get 1 over vp square B of t partial square Bt partial t square. And the right hand side, because I also divide AB vp square, therefore, I get 1 over A of x partial square A of x partial x square. So far so good. And basically, what I'm doing is just plug in the functional form, which I assume here and then divide everything by AB times vp square. And what I immediately find is that left hand side is a function which only depends on t. Left hand side only depends on t. And right hand side is a function which on the depends on x. So in short, I have in this situation f of t, which is left hand side, is equal to g of x. You will see this over and over again in later lectures related to physics. This is actually the so-called separation of variables. So basically, you are facing a situation f of t equal to g of x. If you think about this situation, that's actually really, really helpful, because, OK, now what I can do is I can stay at a specific x. For example, I choose this point. Then I let the time go forward. Of course, I cannot stop time, but if it goes forward, then left hand side equivalent, if it's changing, you will change, because I change t. If the left hand side equation is changing, then that's actually not going to-- this equation is not going to work, because I am not changing x. I am fixing myself at a specific location, and a lot of time go on. Then if left hand side is changing, then this equation cannot work. You see? Therefore, what is the consequence of this equation? That means, left hand side, f of t, must be a constant. Therefore, no matter what I do, if I change time, it's not going to change anything. I can put in whatever time, like 1 billion years after this lecture or now, it doesn't matter. It's a constant. So this must be a constant. I can do the same trick. I froze the time. I fix the time, and then I compare this point to that point, or, say, something billion billions of light years away from this class room. I am changing the x, but I'm not changing the t. The same argument also holds-- if this function is changing as a function of x, then I am screwed, because-- [LAUGHTER] --it doesn't work, right? I mean, this-- Therefore, it has to be a constant also as well. Constant also equal to a constant, that's really lovely, right? [LAUGHS] That means, I can say this is equal to that is equal to a constant. As usual, I call this constant really, really strange fancy name-- minus Km square, which you will not like it. But later, you would like it. [LAUGHTER] Very good. So we make tremendous amount of progress. Originally, we saw that we are in trouble. It's A times Bt-- Ax times Bt, sounds really horrible. Now, actually, you see that this equation is really simple to solve. So let's actually take a look at the solution to the f function and the g function. So the first thing, if I take the left hand side, which is a time-dependence part, I can copy there-- this is actually 1-- copy the equivalent here-- is 1 over vp square B of t partial square Bt partial t square. And this is equal to a fancy name of this constant-- minus Km square. And of course, I can multiply everything by vp squared B. And I get partial square B partial t square. And this is equal too minus vp square Km square B. Wait a second. We have solved this equation infinite number of times in this lecture. You remember the solution? What is the solution? Anybody can help me? AUDIENCE: [INAUDIBLE]. YEN-JIE LEE: Anybody? It's sine or cosine function, right? This is harmonic oscillation. It's almost like equation of motion of a spring-mass system, right? I hope that you are already bored. And that means I very successful. [LAUGHTER] B of t will be equal to-- [LAUGHS]---- B of m sine omega m t plus beta m, where omega m is actually equal to vp times Km. I define omega m equal to vp time Km. So surprisingly, the solution of B is really simple. It's actually Bm sine omega m t plus beta m. So what does that mean? That means the overall motion or overall time-dependent evolution of the system is like harmonic motion. If you do get individual component in this system. So that's really nice. So let's take a look at the right hand side. The right hand side what we have is 1 over A A of x partial square A x partial x squared. And now, this equal to minus Km squared. I don't want to go over this again. This is actually the same thing as number one. The only thing which is different is that now the partial derivative is actually the x. It's partial square A partial x square. Therefore, I can immediately write down the solution. A of t-- oh, sorry-- A of x will be equal to Cm sine Km x plus alpha m. Any questions so far? So until now, you accept the fact that f of t and the g of x has to be the same constant. And I call it minus Km square. And I didn't actually tell you what Km I'm choosing. In reality, according to this result, Km can the anything, can be any number, as long as it's a constant. Therefore, I would like to write the corresponding psi, which is the wave function, is actually labeled by m. m is it just label which K I was using, nothing fancy. It's just a label. Psi of m is a function of x and t. And that will be equal to Bm times Cm sine omega mt plus beta m sine Km x plus alpha m. Bm and Cm are just arbitrary constant. Therefore, I can merge them. And I will call it just Am. And, of course, don't forget we have this condition. Omega m is actually equal to vp times Km. So this is actually defined here. So here, since this is actually a second order differential equation, you have unknown factor, which is beta m. You have also Bm is a unknown. And the right hand side, you also have a Cm, which is unknown, and alpha m, which is unknown. When we combine them, I replace Bm times Cm by Am. Therefore, what we have is that Am is actually some kind of amplitude, which can be determined by initial conditions, which I will talk about that later. Beta m is the unknown coming from the left hand side derivation. Alpha m is also unknown, which is actually coming from the right side derivation related to the shape of the normal mode of the system. And finally, there's one additional unknown coefficient, which is Km-- it's kind of arbitrary now-- control actually the wave number, or say the wavelength of the shape of the normal mode. So when you see this, doesn't this surprise you? May not surprise you any more, because we have solved infinite number of coupled oscillator. And you have learned that, OK, the normal modes have a shape of sine function. It's like a sine function-- before it was like a sine as a Ka. And the Ka is performing x. So what we are actually getting here is that doesn't surprise you since this system also satisfy space translational symmetry. Therefore, the functional form of the shape of the normal mode is also a sine function. So that's actually pretty satisfactory and also come out as what we would expect based on what we actually have learned. So let's actually take a look at the structure of this function. So basically, as I mentioned before, everything is oscillating at the frequency omega m with a phase beta m. So that satisfy the condition of normal mode, what is the condition. All the components in the system are oscillating at the same frequency and the same phase. Indeed, yes, that's correct. Also as a function of time, it's actually going up and down harmonically as we already discussed. And the relative amplitude, as I said, is a sine function. And of course, I already demonstrated this before, that you can see that in this is system, you can see a sine function when I start to drive it. So what I am doing is actually to convert the kinetic energy from my hand to energy stored as potential or kinetic energy in this string-rod system and in this bell wave machine. So you can see that beautifully those are sine function. And, of course, if I do a higher frequency one, you can see the hand oscillation frequency changed. And that is actually controlled by this equation, this dispersion relation. And this dispersion relation is actually relating two physical quantity. One is actually the wave number. Of course, if you are more familiar with wavelength, it's actually 2 pi over Km. Lambda m is actually the wavelength of the shape of the normal mode. And the oscillation frequency is actually controlled by this dispersion relation, this function. And you can say that, Professor Lee, I have been so tired of this demo. I've seen this 1,000 times, right? And basically, you are showing me that, OK, you can actually oscillate this system and excite this system so that it's oscillating at some natural frequency the system like, right? It's actually some kind of resonance behavior. So I can actually excite-- I can-- no. I can randomly shake this system. And then it's going to be a linear combination of all the excited normal modes, right? We have seen this many, many times. What I am going to show you is that there's another machine here, which is actually demonstrating the resonance of some wave. So here is actually so-called the Rijke tube. So the structure is like this. So basically, you have a metal tube, which is red thing there. And inside the tube-- you cannot see it now-- but inside the tube, there's a wire mesh, which the air can flow freely up and down in this mesh. And what I'm going to do now is to heat up the mesh and see what is going to happen. I will just heat it up by like six second and see what is going to happen. So now, I'm going to do this very carefully. [RESONATING SOUND] Can you hear that? [LAUGHS] OK, very good. So listen, what is happening? So you hear a mono frequency sound generated from what? Generated from the heat I gave to the wire mesh. So what is actually happening? So when I heat up the mesh, what is going to happen is that the air around this screen is going to be heated up. Therefore, because the air is heated up, it goes in the upward direction. And also, the volume of the air is expanding, because of the increased temperature. And that actually goes through this system. And why it does is really like what I'm doing to the bell lab wave machine, is actually tyring to oscillate-- or excite any possible normal modes, which this system actually like. So you can see that, after a while, once the pressure and also the air inside the tube get then self-organized, then you hear a very loud sound. So that means there are energy flowing from the tube to your ear. And that is actually coming from what? Coming from the heat I put into the system. So it's actually a heat sound wave conversion. So I hope you enjoyed this demo. And we will take a five-minute break to take questions before we move on. And of course, you are welcome to come here and to play with the demo if you want. [LAUGHS] So welcome back from the break. So what we are going to do next is to understand how to determine all those unknown coefficients. So you get to see here, there are Am, which is the amplitude. There are beta m, which is basically the phase. There are Km, which is actually the wave number, and alpha m, which is the phase for the shape. So what I'm going to show you is that Am and the beta m, these two quantity will be determined by initial conditions. Well, Km and alpha m, as you may guess, those can be determined by boundary condition for the Km and alpha m. So why don't we just immediately get started with a concrete example. So let's take a look at this situation. So this equation and those all the possible Km are allowed when we talk about infinitely long system. So far, we have not imposed any boundary conditions. And what I'm going to do now is to show you a example boundary condition and see how we can actually fix Km and alpha m. So suppose we are interested in this system. So I have a wall in the left hand side. And I have a string with length L. And it's actually connected to massless ring. And this ring can actually move up and down a long rod in the right hand side. And I also assume that this string have a constant tension T. And also the density is rho L. So basically, it's a mass per unit length. So that's the system which I am interested. And, of course, I need to define my coordinate system as usual. I define horizontal direction to be x direction. And I define the vertical direction to be y direction. And I define y equal to 0 is the equilibrium portion of the string. When psi is equal to 0, that means this string is actually at rest. And not moving-- is actually in the equilibrium position, it's not displaced at all with respect to y equal to 0. And I can also define that x equal to 0 is the position of the left hand side wall. So this is actually the physical situation. And I would like to actually find out what are the boundary conditions. So what are the boundary condition? So from what we actually discussed last time, left hand side, since this string is actually fixed on the wall, I nailed it there, it cannot move. Therefore, what is actually the first boundary condition? Why is actually the first boundary condition? Anybody can tell me? Which describes the situation, the physical situation on your left hand side? AUDIENCE: y0 is 0. YEN-JIE LEE: y0 is 0. Very good. So when x is equal to 0, y0 is 0. So on my note, I was using a different notation. So I would just use psi. So psi 0 is equal to 0. Apparently, there's another boundary of this system. The other boundary condition is actually happening at x equal to L. What is actually the boundary condition? Can somebody help me? Yes. AUDIENCE: Is it the derivative of psi is 0? YEN-JIE LEE: The derivative of the psi is equal to 0. So we will explain to everybody why is that the case. The answer proposed is that partial psi partial x L t is equal to 0. And this is 0, t, because that has to be true no matter when I actually invented this boundary condition. So what is actually giving us this strange boundary condition? So suppose I focus on the force diagram on this ring. So this ring is actually connected to a string with string tension T. Also, there's another force which is actually trying to balance the string tension, which is a normal force-- normal force coming from the rod, which is actually trying to stop the ring from moving in the horizontal direction. So there's normal force then. And we also know that this ring is actually massless. So m is equal to 0. Suppose that this partial psi partial x, the slope is not 0. If slope is not 0, that means the string may be pulling this ring to some direction. What is going to happen? So if this happens, it is actually clear that the normal force cannot balance the string for us. Everybody get it? What will happen? If this happened, then this massless ring will suffer from infinitely large acceleration. Because F is equal to ma. And m is 0, so a goes to infinity. So that means this ring will- peeew- disappear, go to the edge of the universe. Did that happen? No, it didn't happen. Therefore, this condition must be satisfied. You see? So the slope of the string cannot be nonzero. Otherwise, some crisis will happen. Very good. So we have the two conditions. And the second thing, which we are going to demonstrate you, is that, OK, I promise you that boundary condition can fix these two constants. So therefore, we are going to demonstrate that. So let's use the first condition we have in the right hand side board. And basically, from 1, you can actually get psi m 0, t. I am plugging in this condition-- plugging in this solution to boundary condition number 1. And basically, what I am going to get is this is equal to Am sine alpha m sine omega m t plus beta m. And this is actually equal to 0. So you only have a alpha m here because I am setting x to be equal to 0. I'm setting x to be equal to 0. Therefore, you already have that functional form. So now, we are facing a choice. So you can set Am to be equal to 0 is arbitrary number. But if you set m equal to 0, everything is 0. And it's not fun, it's not moving. Therefore, I don't want to set Am to be equal to 0. And you can say, huh, maybe this is equal to 0-- sine omega m t plus beta m is equal to 0. But this is really a sine function. And this condition has to be satisfied no matter at which time you are revisiting this boundary condition. At all times, this boundary condition has to be satisfied. Therefore, this cannot be equal to 0. Therefore, I conclude that this is the 0. So what does that mean? That means I can choose alpha m is equal to 0. So that's actually given by the first boundary condition. So let's actually take a look at the second boundary condition-- partial psi partial x evaluated at x equal to L and any time t is equal to 0. So now, I can plug in, again, the solution in the middle board partial psi m L, t, partial x. And that will be equal to Am Km sine omega m t plus beta m cosine Km x. And this is equal to 0. So I am taking a partial derivative partial psi partial x. Therefore, the sine become cosine. The sine Km x plus alpha m becoming cosine. And also, I know already from the first boundary condition, alpha m is equal to 0. Therefore, I get cosine Km x here. And this is evaluated at x equal to L. So that means this thing must be equal to 0 based on the second boundary condition. Of course, we can have a losing argument-- Am should not be equal to 0. Otherwise, you will be equal to 0 all the time, the whole wave function is 0. And this is actually changing as a function of time, the same argument, because this boundary condition has to be satisfied at all times. From the beginning of the Universe to the end of the Universe, this condition has to be satisfied. Therefore, these cannot be equal to 0. And what is actually left over is cosine Km x evaluated at L equal to 0. So cosine Km L is equal to 0. So that means you cannot arbitrarily choose Km anymore. Before we introduced boundary conditions, we were saying, ah, Km is actually some arbitrary constant. And now, it's not arbitrary any more. It has to satisfy this condition. What does that mean? This means that Km has to be equal to 2m minus 1 divided by 2L times pi. You can actually check this. And this small m is equal to 1, 2, 3, et cetera, et cetera. And then you can see that there are many, many different solutions. So you can see that, as I mentioned before, the boundary conditions determine Km and alpha m. So you can see that the first condition at x equal to 0 determine alpha m. The second boundary condition also help us to determine what are the possible Km value. And that is actually listed here. Any questions? No? So in order to help you to visualize what we have learned from here, I can now choose m is equal to 1. So you can see that I carefully choose my notation from the beginning. So therefore, m is now the index of the normal mode I am referring to. So now, if I choose m equal to 1, then I can actually evaluate what would be the resulting K. So K1, according to last formula 2 minus 1 is giving you 1. Therefore, you'll get pi over 2L. And, of course, you can also calculate based on the wave number what will be the wavelength. So the wavelength lambda 1 will be equal to 2 pi over K1. Wine And that will give you 4L. Don't forget, once you actually already decide K, the omega is also determined, because omega, which is the angular frequency of this normal mode, is determined by that dispersion relation omega m equal to vp times Km. So therefore, I can now calculate omega 1. That will be equal to vp times K1. And that will you square root of T over rho L pi over 2L. So this is actually coming from the last lecture, the formula of vp. So that means, if you fix the shape of you are normal mode, then the angular frequency is also fixed, according to this dispersion relation. So of course, I can now visualize this situation. And basically, I can plot this system as a function of time-- as a function of x, not as a function of time. So when this system reach the maxima amplitude, it would look like this. And this is actually amplitude A1. Because I am talking about the first normal mode labeled by m equal to 1, and there is an unknown amplitude A1. And that is actually showing here. Of course, I can go ahead and calculate if m is equal to 2, what is going to happen? If I increase the m, what is going to happen is that K is also increased. So K is increased. Then that means the wavelength is decreased. I have calculated the K for you. And that is equal to 3 pi over 2L. And those are the lambda 2 will be equal to 4L over 3. You can actually double check this at home. And of course, I can now demonstrate what would be the resulting shape of the massless mode. It would look like this. And this is essentially telling you the amplitude A2. You can also do m equal to 3. If you doing that, basically what you get is something like this, et cetera, et cetera. Any questions? And the motion of this system that is a function of time is that this whole shape, this shape, is multiplied by sine omega m t plus beta m. So the whole shape is going to scale up and down harmonically. And so if you focus on one of the point here, it's going to be going up and down harmonically. Very important, there's no back and forth movement. Everything is only moving up and down. If you focus on only one of the particle in this string, everything is moving up and down. Like here, right? So when I create a curve-- when I create some kind of wave, all the components are always moving only up and down, instead of back and forth, because they can't. They can't move back and forth. But you maybe cheated by the shape-- the evolution as a boundary of time, it seems to me that, ah, something is actually moving back and forth. But never-- all the particles are moving up and down-- very important. Finally, we have shown you the first three normal modes. And what is actually the most general solution? What is a general solution? Of course, as we had before, general solution would be a linear combination of all the possible normal modes. So now, I would like to write psi x, t, as the general solution is going to be the sum of all the allowed normal mode. In this specific case, it's going to be a summation from 1-- m equal to 1 to infinity Am sine omega m t plus beta m sine Km x plus alpha m. And in this specific case, it become cosine-- the Km is there-- cosine 2m minus 1-- sorry, it should be sine. It should be sine 2m minus 1 over 2L pi. And the alpha m in this case is equal to 0. So the upper formula is the most general case. You're summing over the possible m's. And the Km and alpha m can be determined by boundary conditions. And in this specific case, the right hand side expression is reading like sine 2m minus 1 over 2L times pi. So that's very nice. And then you can see another sets of example here in the slide. So this is another set of normal modes from m equal to 1 to m equal to 6. And you can see that in this example both ends are fixed, instead of one end is actually attached to a massless ring. If both ends are fixed, then you get these normal modes. And of course, in the later-- in your p set, you will be exercising this kind of normal modes and solve the corresponding Km and alpha m. And you can see that, if you focus on the upper left corner, you will see that the oscillation frequency is low. Why is that? That is because the wave number Km is small, therefore, wavelength is long. According to that formula, omega m is proportional to wave number. Therefore, you can see that the oscillation frequency is actually two times slower compared to m equal to 2 case, which is the upper right corner result And you can see that, if you increase m more and more, you get larger and larger K. And therefore, you see that the oscillation frequency is getting larger and larger. So now, we are actually facing an issue here. Wait a second, so now we have solved the functional form of the normal mode. We have learned how to determine Km and alpha m. But we are facing a difficulty here, because Am is very difficult to solve, because you have infinite number of terms here. And beta m, how do we solve this? So it's getting really, really difficult. So what I am going to tell you is that we can actually, again, use the help from the math department. They have actually proposed the solution. They actually say that, huh, this is actually identical problem that we solved in the math department, is just for the decomposition and for the series. So what is actually for the series? So you can see, from here, there's a triangular shape between 0 and 1. It's a function-- probably is a function of x. And between 0 and 1, it looks like a triangle. And if you do for the decomposition, it can be decomposed as small k sine function plus the second normal mode and plus a second massless mode. And you can see that, if you increase the number of terms included in this Fourier series, then you will see that the shape is actually getting closer and closer to the triangular shape. In order to help you with the visualization, here is actually what I prepared. So this actually extracted from essentially a real example, which I really used a computer to calculate. And I tracked the contribution from m equal to 1. This means that the first term in this summation-- infinite number of term summation-- the first term looks like this. And if you include the first and second and third term, it becomes something like a plateau. And then if you increase 1 to 5, it's evolving as a function of m, becoming more and more-- hm, strange shape. And that is actually including the summation from first term to 11 terms and, finally, 11 to 19. Huh, what this is-- what is actually the function I put in? It's actually a MIT function! [LAUGHTER] I put in a MIT function into this again. And you can see that-- wow, 1 to 59 term. I need to use 59 terms to describe this really wonderful shape. [LAUGHS] So in order to help you with the visualization, listen you can see I prepared a little program, which actually can show you the evolutions as I increase more and more m terms. Let's take a look. You can see that, originally it looks-- doesn't look-- oh, you cannot see anything. Wait a second. What is going on? Let me see if I can-- I hope I don't screw this up. Sorry. I need to restart. So let's get started. So you can see that from the first few terms, it doesn't look anything. But very soon, when you have 20 terms added to each other, it looks really pretty much like a MIT dome. And you can see that this program is really trying really hard to describe the sharp edge in the left-hand side and the right-hand side. You can see that those kind of really infinitely sharp edge will need infinite number of terms, so that if your m is really huge, then the K, the wave number, is going to infinity. Then you can actually produce infinitely sharp edge in this function. And that is actually, you can see from this demonstration the program is really struggling with this really super sharp edge. So look at the left hand side and right hand side corner, originally the slope is clearly not high enough. And thus, we include higher, higher m value terms. And you can see the description becoming much, much better at the edge but, of course, still are not perfect, because you need infinite number of terms to describe the shape of MIT dome. Of course, we can also take a look at other example, just testing my eyesight I'm not sure if I-- OK, so I can increase the speed to save on time. So this is actually a square pulse, which you can see from the scope pretty often when you do experiment. And you can see that a square pulse is really difficult to reproduce, as I said before, due to these sharply rising h. And of course, I can also demonstrate you another example, which is a triangular shape. And you can see that-- ah, still, you can see it works pretty nicely. And the function doesn't like at all the right hand side edge, because of exactly the same reason. OK, very good. So let's come back to the presentation. Can you see-- OK, very good. So the question is, how do we actually extract Am and beta m? OK, I have done that with a computer program. And what I'm going to do now is to show you a concrete example. And we are going to go through it together to see how we actually can extract Am and beta m. So suppose I give you an initial condition. It's exactly the same system I am talking about. But now, I prepare this system at t equal to 0 some specific kind of shape. This L/2 is actually the first half of the system, is actually untouched. The first part of the string is actually at the equilibrium position. And this is actually x equal to L/2. Suddenly, I actually move the string sharply up. And the rest half of the string is actually at the height of h in this case. And of course, the right hand side edge is x equal to L. And this is actually a snapshot, which I actually took with my camera at t equal to 0. And also, I assume that at t equal to 0, the string-- all the components of the string is at rest. So based on this information, which I give you, I can now translate this information into mathematics. So that corresponds to two initial conditions. The first one is that, since the string is at rest, that means psi dot x evaluated at t equal to 0 is 0, because the string is at rest. The second initial condition is that psi x 0 is known and is actually shown in this graph. So from this, we would like to see if we can actually extract information about capital Am and the beta m. So let's immediately get started to see how we can use those initial conditions. So from the first initial condition, a, related to the initial velocity of the string, basically, we can get psi dot x, t. And this will be equal to, let's see, the sum over m equal to 1 to infinity. So basically, I'm taking this equation when I plug in that equation into the first initial condition. So basically, what I have is Am omega m sine omega m t plus beta m. Oh, this will become cosine-- sorry-- because I'm doing a derivative, psi dot. So this will become cosine. And sine Km x plus alpha m. And this is actually equal to 0 when psi dot x, t, is actually evaluated at t equal to 0. And this is equal to 0. So if I plug in t equal to 0 to this equation, this becomes 0. And then we know that the shape of the normal mode is some kind of sine function from the previous discussion. And I am now requiring this thing to be equal to 0. Of course, I cannot make Am omega m equal to 0. That's what we discussed before. And this sine function can be evaluated at any place, any x value. Therefore, this cannot be equal to 0. Therefore, what is actually the result? The resulting condition is that cosine beta m will be equal to 0. Therefore-- huh, from this initial condition, actually I can conclude that beta m is actually equal to pi/2, for example. So therefore, you can see that very clearly from the first initial condition, the string is not moving at the beginning, I can conclude that beta m is equal to pi over 2. And just as reminder, alpha m is actually equal to 0 from the previous discussion. And Km is actually equal to 2m minus 1 pi divided by 2L, because I just want to copy here, because somehow the board is covered by another board. So now, I have done with the first initial condition. And the other initial condition I have is that, OK, I provided you the picture I took at the beginning of the experiment. Therefore, psi x, 0-- at t equal to 0-- is known. So very good. So I have this condition. But now, I am facing a difficulty, because all those terms-- all the terms, m equal to 1 to infinity-- contribute, as we demonstrated before, to this shape. It's very difficult to actually evaluate Am. So the trick is to make friends from the math department. So what we could do is that we can use the orthogonality of the sine function to overcome this difficulty. So let me immediately write down what do I mean by orthogonality of the sine function. So if I do a integration from 0 to L on dx sine Km x sine Kn x, if I do this integral, integrating from 0 to L, so what I am going to get is that basically you either get L equal to 2 if m is equal to n, or you get 0, if m is not equal to n. So basically, I have two sine functions multiplied to each other. And I do integration from 0 to L multiplied by delta x. And this is Km. This is Kn. If Km and Kn are different, you can actually go ahead and do this exercise. And you will find that, indeed, if they are the same, then you will get L/2. On the other hand, if they are not the same-- the K value are not the same for the first and second sine function-- you are going to get 0. So that's very good news, because if I do this-- if I do this calculation, I do 2/L integration from 0 to L psi x, 0, sine Km x dx, what is going to happen if I do this integration? Remember, psi m is a linear combination of infinite number of massless modes with different sine Km x. If I multiplied that by sine Km x, this is a very crazy thing to do, because all the other terms will become 0. If the K value of one of the terms is not equal to the dictator's value Km, it's 0. Otherwise, it's L/2, and it is designed here to cancel that factor. So you can see that this is like a mode picker. I'm picking up a mode with this tool. This is like, this tool, yeah, I'm picking this mode, which is actually matching my Km. It's a miracle that this become Am. I hope you get this idea, even if probably you haven't heard about with your decomposition before. But essentially, what we are doing is that I'm going to evaluate infinite number of integrals. And you are going to do that in the exam, hopefully easy. [LAUGHS] What is going to happen is that, if you do this integral, you are going to pick only one mode out of it. And you are going to be able to know the amplitude of that mode. So let's do this immediately in this example. So Am is actually equal to 2/L. Since the amplitude is actually 0 between 0 and L/2. So I can safely just integrate from L/2 to L. So I do a integration from L/2 to L, because between 0 and L/2, the initial position is 0. So what I'm going to get is h sine Km x dx. And of course, everybody know how to do this integral. It doesn't look that horrible. And this would become 2/L minus h over Km. And basically, this will become cosine Km evaluated at L minus cosine Km evaluated at L/2, and where this Km, as just a reminder, is basically equal to 2m minus 1 pi divided by 2/L. So I hope this actually help you to understand the procedure to determining all those unknown coefficients, starting from this equation. Am and the beta m can be determined by initial conditions. As we actually show here, you can use the initial condition of velocity and the initial condition of the shape and the help of a mode picker to pick up the amplitude from that tool function. And also, you can see that Km and alpha m related to the shape of the normal mode can be determined by boundary conditions-- boundary conditions, how this system is actually connected to the nearby systems. The nearby systems are the rod and the wall. So that is actually the two boundary conditions, which determine the shape of the normal mode. And finally, very important, as usual, the most general solution is, of course, a linear combination of all of those possible massless modes from m equal to 1 to infinity. And omega m, don't forget, is determined by the dispersion relation, vp times Kl. Before the end, I would like to mention to you something which you might actually not notice when we were discussing this. So you can see that omega is now proportional to Km. So if you plot omega as a function of k, actually you can see that it's becoming a straight line in this graph, which is very straightforward. And on the other hand, if you remember what we got last time with discrete system, with length scale between little mass is actually a, you get omega square is equal to 4T over m sine squared ka over 2. So if you plot this omega as a function of k, you will get the black curve. What does this actually tell you? That is actually telling you that, if you prepare a system at a specific normal mode based on the oscillation frequency, you can actually know the internal length scale of individual mass, just in case you didn't notice this interesting fact. So thank you very much. I hope you enjoyed the lecture. And I will see you next Thursday-- not here in the Walker room-- Walker Memorial. So good luck, everybody. Maybe see some of you in the office hour tomorrow. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 19_Waves_in_Medium.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: OK, so happy to see you again. Welcome back to 8.03. So in the beginning of the class, I will give you a reminder about what we discussed last time. Then the main topic we are going to discuss today is about how to take good photos. So let's get started. So last time we have been working together trying to understand how to produce electromagnetic waves which can travel to a distance which is actually very, very far away, a place which is very, very far away from the source. And what we actually figured out is that in order to do that, you have to create a kink in the electric field line such that you will propagate and produce radiation. And this is actually what we have done last time. And what we concluded is that if you want to produce electromagnetic waves, you have to introduce acceleration of that charge, such that you will be able to produce electromagnetic waves. And also, we have derived, based on geometrical arguments, what would be the magnitude and the direction of the radiated electric field and magnetic field. And it's actually showing here. The radiated electric field is going to be in the opposite direction of the projection of the acceleration, a perp. The magnitude is proportional to a perp, but only evaluated at retarded time, t prime equal to t minus r/c, where r is actually the distance between the observer and the radiating charge. And the reason why we have this t prime, the retarded time, is because of the speed of propagation of information. So that's actually what we discussed last time. And you cannot actually instantaneously send the information about the acceleration of this charge to somewhere which is very, very far away. Therefore, the acceleration, a perp, is evaluated at t prime, which is t minus r/c, the amount of time for the speed of the information traveling at the speed of light. And also, the corresponding magnetic field can be also evaluated, whether it's through Maxwell's equation or using this formula, this t here. And finally, we will be able to evaluate what would be the pointing vector, the energy flux direction or energy flux through exactly the same equation which we used before. That's actually what we have learned last time. And today, what we are going to do is to learn how to take photos. So we have prepared ourself. We know how to produce electromagnetic waves. We also know about polarization of electromagnetic waves. And we also know how the polarizer actually works. So that means we will be able to make very good photos, theoretically. So yeah, that's what we all care about. Theoretically, we can actually make very good photos. So the first thing which we would like to discuss is how to make very good contrast when you actually take a photo of the sky. So as you can see, the left-hand side is a photo taken without a polarizer. And the right-hand side is the photo taken with a polarizer. You can see-- aha! -- the contrast, or say the sky is actually darker, therefore you can see the cloud much more clearly. And also on the same graph, you can see there is a photo at the beach. And you can see exactly the same phenomenon. And now we are in the position to understand what is going on. So this is actually why we can use polarizer to make such a good photo. So now we know what is actually happening at the sun, right? So at the sun, there are something which is oscillating-- OK, some kind of emission from the sun. And those emissions are not correlated to each other. And that produces unpolarized sunlight. So if you're looking to the sun, you are looking at unpolarized light. On the other hand, if you are looking at the sky, roughly like 45 or 90 degree-- OK, 45 degree from on the sun, what is going to happen is that what you are actually seeing, all this light from the sky, actually, the sunlight after scattering between sunlight and the dust in the air. So basically, on this guide, in our air, there are many, many little dust, right? And when light-- as you shine on this dust, they change direction, this so-called scattering. And those light are collected by your camera. The interesting thing is that if you have a molecule which is actually here, and you have some unpolarized sunlight shining on this molecule, and it changed direction by 90 degrees, what is going to happen is that all the things-- originally you have an unpolarized sunlight. Therefore, you have all kinds of different polarizations, if you look at the electromagnetic wave. However, if you only choose the light which are scattered and are going toward this direction, apparently, the electromagnetic wave, or the polarization, or let's say the direction of the electric field, has to be perpendicular to the direction of propagation. Therefore, what is going to happen is that only this direction, only the polarization in this direction, which is perpendicular to the direction of propagation will survive. All the other components, like the one which is pointing upward or pointing downwards, or coming from the original sunlight will not survive. Therefore, what is going to happen is that when you do get 45 degrees-- the sky 45 degrees from the sun, the sunlight is actually what kind of sunlight? Is polarized sunlight. Therefore, if you tune your filter to be aligned with the polarization, you will be able to filter a large amount of the scattered sunlight. And that is actually how this works. And then you can see that, indeed, the sky becomes darker after you apply this polarizer in front of your camera. So that's essentially the first thing which we learn. The second thing is that, OK, we also found that the polarizer is particularly usefull for the filtering of the reflected light on the window. And of course, we can also use exactly the same technique to filter out the reflected light from the water for dipole. And how does this work? And it turns out that this actually much more complicated than what we thought. And we have to actually derive this. And that is actually related to the electromagnetic wave propagation inside the material, and also related to Brewster's angle. And that is actually the main topic which we are going to talk about today. So let's immediately get started. So now what we are interested is, how does this actually work? And why is this happening? And why is the reflected light become polarized? So that's the question we are trying to answer. So we have talked about electromagnetic waves in vacuum. And we also know how to generate electromagnetic, and now we are interested in electromagnetic wave in dielectrics. So we have talked about two kinds of materials already. The first one is a perfect conductor. And the second one which we are going to talk about is a dielectrics material. In case of perfect conductor, it costs nothing to move all the charges inside this conductor around. And basically, that will give you a zero electric field inside the conductor. And also, we have a limited supply of charges. And therefore, inside this kind of perfect conductor, there will be no electric field. On the other hand, if you have a dielectrics material, what is going to happen is that there are a lot of charges inside the material, but all those charges are attached to a specific atom or molecule. They cannot be moving freely all over the place. And that is actually so-called bound to the atom or the location of the molecule. And that introduces a little bit of complication. So this kind of material, they also respond to the external magnetic field or electric field. For example, in this case, I have electron cloud which is around the nuclei in this-- around the positive charge nucleus in this figure. And you can see that before we apply an external electric field, it's symmetric around zero. After we introduce this electric field, external electric field, there can be some kind of polarization produced, because the electrons around this nucleus can be moved slightly, such that this material is actually trying to compensate a little bit the effect of the external force. So that is actually leading to a modification of the electric field. But as I mentioned, you are not going to cancel all the effect of the external field. So how do we understand this? The idea is the following. So since this system is complicated, you have a free charge. It could have free charge as we really kick out or add some electrons into this system. It can have bounce charge. And if becomes a rather complicated description. So the idea is the followiong. So in order to actually-- for our convenience, to be similar to what we have been doing in vacuum case, our goal is to define a field which is actually with the material itself subtracted. In this case, what we can do is to define a D field, which is related-- we hope that this is actually only related to the free charge inside the material. And then we can actually do all the tricks which is actually similar to what we have already learned from the vacuum-- Maxwell's equation to solve the problems inside material. So that's essentially our goal. In order to do that, we have to classify the total charge density, rho, into two components. The first component is the free charge, which essentially is the charges which can travel freely inside the media. And the bound charge, which is actually, as I mentioned, for example, those electrons-- the electron cloud. And essentially, they are bound around central location in the media. So the idea is the following. So I can now define a D field. This D field is a so-called electric displacement field. It's defined as epsilon0 times E field plus a P vector, which is the polarization vector. Where this P vector is defined in the following way-- minus divergence of the P factor is actually equal to the bound charge density, which is rho. If we have this definition and we actually continue and write down the Gauss' law-- and we can see that this is the Gauss' law, epsilon0-- divergence of E will be equal to rho. And we also-- under our classification, essentially, there are two components, rho f and rho p. The bound charge and the free charge. And according to our definition, this can be written as rho f minus delta P vector. And now what we can do is that we can use the definition of the electric displacement field and collect all the terms except the rho f to the left-hand side. Then you will conclude that the divergence of D will be equal to rho f. So after this calculation, you can see that what we have achieved is that we have defined a field, a displacement field D, which is totally related to the effect of the free charge. In this case, what we derived is actually delta D equal to rho f. And this actually looks pretty similar to the situation in vacuum, right? Because what we actually have is epsilon0 delta E equal to rho. And after we actually remove the contribution of the bound charge, this becomes this expression. Any questions so far? All right, so this is actually a purely definition. And we can also do a very similar thing to the current. So the total current, J, will have the following three components. The first component is the free current, which is the current related to free charge moving around inside this dielectrics method. There can be contribution from the bound current. The bound current is actually the current which is only moving around some specific location. And finally, the polarization contribution. So changing polarization also introduced a current, because polarization is actually defined as q dot times D, which is the distance between charges. And that if I have a changing polarization, that means also there are some charges floating around. And that actually gives you the third contribution, which is, let's say, P. Once we have classified the current into three pieces, and basically, we can define H field, which is actually defined as B over mu0, and the minus M, where M is a magnetic dipole moment. And the M field is actually defined as the curl of M defined as the magnitude and direction of the bound current. And once we have finished this definition, we can actually plug that into Ampere's law. Ampere's law, just a reminder, is curl B will be equal to mu0 times J. J is actually the total current. Plus a component which is actually added by Maxwell. So that actually results in the electromagnetic waves, which is epsilon0 partial E partial T. By using those definitions and classification, we can immediately write down-- so if we divide both sides by mu0, basically, you conclude that left-hand side is 1 over mu0 curl B. And right-hand side, you have the contribution of free charge current. And you have the contribution of bound current. And you have the third contribution which is related to a change in polarization. And finally, you have the term which is added by Maxwell epsilon 0 partial E partial T. By using the definition which we defined here for the D displacement field, and H, which is actually defined here, you can see that now we conclude that the curl of H will be equal to Jf plus partial D partial P. So remember why we are doing this. The reason is the following. We would like to classify the effect coming from free charge or free current inside the material by subtracting the effect from the bound current and the bound charge. So that's actually what we have been doing. Then once we define new fields, which is actually showing here, D, which is the displacement field, is only related to-- which is the field related to the free charge. After all, those are actually just definition. And the edge field, the magnetic field which is actually only related to the displacement field and the free current, we actually arrive something really, really similar to the vacuum case, Maxwell equation. So that's, essentially, the excitement. And you will see that in 8.03, we will use immediately those conclusions. And also, we would limit ourselves in the discussion of linear homogeneous and isotopic materials. And only work on this kind of material. And that is, you would need to highly simplify the solution for the electromagnetic field or waves inside material. Any questions so far? I hope those are just different issues. Yes. STUDENT: [INAUDIBLE] PROFESSOR: The bound current is actually inside the whole dielectric material. But of course, you can have many, many small loops and they will cancel. Because if you are looping-- for example, you can have many, many bound current, which is actually surrounding the atom. But you can see that all those things-- all the nearby little bound current will cancel each other. So therefore, you could do an integration, and it becomes a total bound current, which is happening around the surface of the dielectrics material. So it depends on what you mean by how this bound current actually moves. So you do have little ones. And then if you do integral, then it becomes a surface bound current. So if we step these two conclusions we arrive here, basically, we can immediately write down what would be the Maxwell's equation in matter. So now, instead of electric field and E and the-- E field and the magnetic field, B field, we also have-- oh, I think there's a typo there probably. Ah, there's a typo in the lower left. So the lower left equation, which is, unfortunately, propagated to many places, should be like this. So the lower left equation should be del cross H. That would be equal to Jf plus partial D partial t. So somehow, this is actually propagated to many places. So basically, we have Maxwell's equation in matter, which is actually really similar to what we have in the vacuum case. So very similar to a discussion we had in the vacuum case, what we actually do is to set the Jf and rho f equal to 0. If I set the Jf equal to 0, the last equation will become curl of H. And that would be equal to partial D partial t. So you can see that this is very similar to what we had before, but the problem is that we have the H field and the D field. The question is, how do we actually relate H field and the D field with the electric field? So as we mentioned before, the D field is as we defined as epsilon0 D field plus P, which is actually the induced polarization of the material. And in the case of very small electric field, and there is more magnetic field, and also a linear and homogeneous isotropic material, this induced polarizaiton can be proportional to the size of the electric field. So if this polarization is proportional to the electric field, I can immediately write down that the D field is actually some kind of constant epsilon times E. On the other hand, I can also discuss the H field. H feel is defined as 1 over mu0 B minus M, which is the magnetic dipole moment. In the case of very small magnetic field and the linear material, basically, this and M vector can be proportional to the B vector. Therefore, I can quickly rewrite this saying since the M field is also proportional to the B field in this linear material, therefore, I can rewrite that H will be equal to B divided by mu. What is epsilon and the mu? Epsilon is the permittivity inside the material. Permittivity is actually-- they tell you the resistance, the resistance of forming electric field in some place. So if you have a large epsilon, that means there'll be large resistance coming from the material. So this makes sense, right? Because that means you can easily introduce, or say induce, larger amount of polarization in your material. Then that means this material is not happy. It's going to try to cancel your electrical field. Therefore, if you have a large P, that will give you a large epsilon. And therefore, that means you have a lot of resistance of forming electric field, which is still the E field here. in matter. On the other hand, this mu is actually permeability of the, material, which is the resistance of forming-- it's related to the resistance of forming a magnetic field. And basically, these two quantities are actually telling you the D field and the H field are related to the electric field and the magnetic field. So if we assume a linear relation between D and E, and elsewhere at H and B, then we can actually immediately rewrite our Maxwell's equation in matter in the following way. So you can see that the resulting Maxwell's equation in matter considering a linear material is really remarkably similar to what we have in the vacuum case. Where is that difference? Can you see that? The only difference is in the last three equations, which essentially, in the lower right part of the equation, instead of mu0 epsilon0, you now get mu times epsilon. So what does that mean? This means that the speed of the propagation of the electromagnetic field is changed. It's now changed to-- instead of 1 over-- in the vacuum case, you have c equal to 1 over the square root of mu0 epsilon0. Instead of c, we are going to get c over n, which n is the refractive index. And that is actually equal to 1 over the square root of mu and epsilon. It's as simple as that. So based on what we have prepared in the last few lectures, we can now immediately make sense of this equation. And now that we know that almost everything is the same, what is different is that now we have a difference speed of propagation, which is actually related to the refractive index we discussed last time. And now we understand what is actually this refractive index. n is actually equal to square root of mu epsilon divided by square root of mu0 epsilon0. Any questions? Yeah. AUDIENCE: What are the D fields and H field? Are they just coefficients? PROFESSOR: Yes. So the D field and the H field are the fields which is actually related to only the free charge. So you can see that now the gradients-- sorry, now the divergence of D field is actually only equal to the density of the free charge. So basically, in short, the D field absorbs the effect of the bound charge into this field. And when you try to actually understand what would be the field associated or induced by the free charge, it is actually the D field. But the D field is not the full story of the electric field. How is that related to the electric field in the exact form? This is actually defined here. And from the D field, you will be able to evaluate what would be the corresponding E field. And in the linear material, there's a spatial relation between D field and the E field, because the induced polarization is proportional to electric field in the linear material, which is a special case. And in that sense, D field is proportional to E field. And this factor is actually so-called epsilon, which is permittivity of the material. Describing how large is the resistance of forming an electric field inside a material. OK? Is that clear? OK, good. And the H field is similar argument. All right, so now we have made sense of the electric field and magnetic field and the Maxwell's equations in matter. And in 8.03, we will only discuss linear material. You can imagine that the relation between the polarization and the external electric field can be very complicated. So for example, it depends on how large is the wavelengths of the external force. So if you have very slowly varying electric field, you can imagine that you will not be able to create a polarization, which is the inner electron ground level. Because the variation of the electric field is too slow. But instead, you will be able to excite the polarization related to ions inside this material, or inside the plasma. So on the other hand, if you have a very, very fast oscillating electric field, then you will be able to measure the shift or create a polarization which is actually related to the displacement of the electron cloud inside that. So it really depends on many, many factors. But what we have been discussing here and elsewhere is highly idealized linear materials. And a lot of interesting things to explore in the future beyond 8.03. So once we have this relation, we will be able to get Maxwell's equation in matter. And we would like to understand, just to remind you, why are we doing this? So we have a physical question. We have a question about a phenomenon which we see in this slide. So when we use the polarizer, very strange, you will be able to filter out the reflected light from the sun and through-- when the sunlight hit the window and got reflected, this kind of contribution can be filtered out almost completely by polarizer. So that means the reflected light is somehow also polarized. And then why is that the case is the question we were trying to answer here. So therefore, what I am going to do is to, again, take a look at the boundary between two materials. The one side is actually in the air, which we call it number 1. And the other side is actually the glass, which I call it material number 2. And now I have, again, some incident prime wave, which is coming from the sun. And actually, this incident prime wave actually goes into this surface which is the boundary between air and glass in the discussion which I am trying to get into. I assume that this glass is actually very wide. It's actually fielding the whole universe. Therefore, this is actually just a simple plane, a boundary which actually divides our world into air and glass. We know from the discussion of previous lecture, so there must be a reflected light and there must be transmission into the glass. Because this is actually the general property of waves. So OK, it has nothing to do with electromagnetic wave yet, but if you have wave, and you have an incident wave, you are going to have a reflected wave and the transmitted wave. We learned from the two laws of geometrical optics, we know that the incident angle, theta i, will be equal to the reflective angle, theta r, with respect to the normal direction of this surface. And we also know that the KI, which is the wave number of vector of the incident wave, KR, which is the wave number vector, the K vector, of the reflected wave, and the K vector for the transmitting wave, KT. And this is actually theta T. These three K vectors must have a fixed relation so that the electromagnetic field, or say all those three wave equations-- the sum of these three wave equations in the left-hand side world and right-hand side world, they are connected to each other. They don't break. There's no discontinuity between the sum of the left-hand side plane waves and the sum of the right-hand side plane wave. So that means it has to obey Snell's law. And there will be a fixed-- the size of the projection of the K vector onto the direction of this surface will be the same. Otherwise, you will have different wavelengths in the vertical direction. Then the electromagnetic wave will break, right? Because you can-- as you always change your position when evaluating the total contribution of the incident, reflected, and transmitted waves. So once we have all this information in hand, we can actually write down the expression for the incident wave, EI, which is actually a function of r and t. And of course, I would like to define my coordinate system first. So this is the x direction. And this is y direction. OK, sorry. This is usually the z direction actually. The x direction is going up. y direction is actually pointing to you. And the z direction is pointing to the right-hand side of the board. And this is actually at z equal to 0, this interface between glass and air. And now I can actually write down what will be the incident wave electric field. And that is actually equal to E0I, which is a vector, tell you about the polarization of the incident wave. Cosine-- by now this should look pretty familiar to you now. This is actually just a KI dot r, which describes the direction of the propagation. Minus omega t. So this is actually describing the incident wave, which I call it EI. And I will assume that since I know what would be incident wave, that E0I is a known quantity. So I say that this is actually a known quantity. So now I can also do the same thing and write down what would be the reflected wave. ER as a function of r and t. And this will be, very similarly, E0R, which is actually telling you the magnitude and the polarization of the reflected wave, cosine KR dot r minus omega t. All right, and finally, you have the ET, which is a function of r and t again. And this will be E0T cosine KT times r minus omega t. Of course, they will have three electric fields, therefore, you must have three what field? AUDIENCE: Magnetic. PROFESSOR: Magnetic field, yes. So you must have the corresponding magnetic field. So you, for example, BI. It's a function of r and t. Will be equal to 1 over V1, which is the velocity in the air. V1 is actually equal to c. KI hat, the direction of the propagation cross-- OK, so I'm not going to write down BR and BT, because this is actually a very similar expression as the corresponding associated magnetic field for the incident wave. All right, so basically, we have actually translated the physical situation into mathematics using the coordinate system, which we defined here. So one thing which is actually very interesting is that we have solved half of the question in the previous lecture. So in the previous lecture when we discussed two-dimensional or three-dimensional waves, we have concluded that if you have a wave, and it's continuous at the surface, z equal to 0, you can immediately conclude that basically KI dot r will be equal to KR dot r. This will be equal to KT dot r. This is the first thing which we actually conclude. That actually leads to what? What law? Snell's law. Yes, very good. Snell's law. If this expression doesn't hold, then your left-hand side and right-hand side total electric field doesn't match at the surface of z equal to 0. The second thing which we learned is that theta I will be equal to theta R. OK, so basically, that's actually what we have learned from the previous lecture. Therefore, this match in between left-hand side electric field and right-hand side electric field becomes much simpler. Since that they are actually just some E0 times cosine, a functional formula showing here. Since these three products are identical, therefore, what is going to happen is that the location dependence and the time dependence of this relation completely cancels. Because you just have the individual vector, E0I, E0R, E0T, multiplied by a cosine function which is identical for those three incident transmitted and the reflected waves. Therefore, in the discussion of this kind of thing, you can actually ignore the location dependence and the time dependence, since they always cancel. So that's actually a pretty useful thing to have. And don't forget what is our goal, right? So our goal is to know, OK, so if I have a given incident prime wave, what would be the resulting reflected wave, what would be the resulting transmitted wave? And I would like to tell you the conclusion first. The relation between the reflected wave, transmitted wave, and incident wave depends on the Maxwell simulation. You can see that this relation have nothing to do with Maxwell's equation so far. It's actually really related to the wave description we are using. And also, the the match in between the left-hand side and right-hand side wave equation. So you know, now we have learned this is actually only related to a generic property wave equation. So now we need to get the help from the Maxwell's equation in matter so that I can make sense about the relation between E0R, E0T with respect to what is given, E0I. So how do we do that? So the first thing which I would like to do is that, as you see from here, I divided the whole universe into two parts. The left-hand side wall, I call it 1, is air. The right-hand side wall is glass, which is I call it 2. Therefore, I can now calculate what will be the sum of the electric field in the world number 1, which is actually defined as E0I plus E0R. So here you can see that I already dropped the cosine, because they always cancel. Therefore, I just write down E0I and E0R without the cosine. And of course, I can also calculate what will be the total electric field in the right-hand side world, inside the glass. And that is actually equal to E0T. The question is how to relate E1 and E2. And for that, as I mentioned, I need the help of Maxwell's equation in matter. How do we actually do that? So what we could do is that since we have Maxwell's equation, the first thing which we can do is that we can look at the perpendicular direction. The perpendicular direction means the projection of the electric field in the perpendicular direction to the surface. That's what I mean by perpendicular direction. So for that, I can make use of the first Maxwell's equation in matter, which is actually del dot D equal to 0. We are considering the case without any free charge. So that means I have Gauss' law, which is actually D times da. I do a surface integral. And that will be equal to 0. So this means that I can have a pillbox again, like this. I arrange this pillbox like this. And this is actually the surface. The size of one side perpendicular to the direction of the surface is actually called D here. And I have this box here. And the left-hand side, D1, will be equal to epsilon1 E perp-- D1 perp, actually, will be equal to epsilon1 E perp 1. Epsilon1 is the permittivity of the material number 1, which is actually equal to epsilon0 in this case, because it is actually air. And the right-hand side, you have D perp 2. This is actually equal to epsilon2 E perp 2. So now I have figured out what would be the field going into this pillbox and the field going out of this pillbox. What I can do now is the following. I can now shrink the size of the pillbox, having d goes to 0. And it becomes smaller, smaller, and smaller. So what is going to happen is that when this d goes to 0, this surface integral will go to what? Go to also 0. Therefore, I can immediately conclude that epsilon1 E perp 1-- OK, so when I have this d goes to 0, the contribution from the side goes to 0. I know already the sum of all the contribution of the surface integral will be equal to 0, but I don't know what is the contribution from the side. But if I have that d goes to 0, then the area of the four-- 1, 2, 3, 4-- sides, it's actually going to go to 0. Therefore, you have zero contribution to this surface integral. Therefore, I can conclude that epsilon1 E perp 1 will be equal to epsilon2 E perp 2, based on this discussion. All right, any questions so far? I hope everybody is following. Now, I can also use the third equation, which is actually del cross E-- the fourth equation-- which is actually the-- oh, sorry for that. I can actually use the second equation, which is the curl of E would be equal to minus partial B partial t. So that means I can have an integral E dot dl. And that is going to be equal to minus d dt, B dot dx. All right, so if I used the third equation in Maxwell's equation, basically, I have an integral over a loop, over some closed surface, and that would be equal to minus d dt, B dot-- this the actually the integral looking at the flux going through this little area. So what I can do is now I, again, zoom in to the surface which connects the two worlds. And I can now define a loop which is like this. With width equal to d. And there can be a contribution from the magnetic field in the right-hand side integral contributing to this equation. I can immediately write down the left-hand side will be E parallel 1. Why? Because right now we are actually looking at the component of the electric field parallel to the surface. And I can also immediately write down the right-hand side of this loop integral. You are going to have E parallel 2. And now I can do exactly the same trick, having this d goes to 0. The effect of this is the following. So if I have this rectangular loop, and now if I have this side d goes to 0, that means you will have no area to integrate the flux for the B field. So therefore, if I have d goes to 0, this will be equal-- this also goes to 0. Therefore, I can immediately conclude that this means that E parallel 1 will have to be equal to E parallel 2, based on this discussion. So this means that, well, we can immediately conclude that first of all, in order to figure out the relation between the incident wave, reflected wave, and transmitted wave, we need the help not only from the general property of the wave equation, and also some matching boundary conditions, we also need the help to provide additional boundary conditions to relay the electric field in the left-hand side and right-hand side. That is actually coming from our understanding of Maxwell's equation in matter. So you can see that the second two boundary conditions, epsilon1 E perp 1, perpendicular, will be equal to epsilon2 E 2 perpendicular. And that's essentially related to this surface integral D. And the second condition which tells us, will relate the field in the parallel direction is actually also coming from Maxwell's' equation. And we conclude that E parallel in the left-hand side will be equal to E parallel in the right-hand side. So we are almost there to solve the puzzle. So now what I have to do is the following. So now I would like to assume that we have some kind of polarization for the incident and the transmitted waves. So I assume that the polarization, it should be the following. The polarization is actually in parallel. I assume that the polarization is in parallel to the xz plane. So that's actually my assumption. So now I introduce a new assumption, which is that the incident wave is actually having a polarization. The electric field is actually oscillating up and down in this direction, which is actually parallel to the xz plane. So I can write down the corresponding E0R vector. And finally-- and this will be perpendicular to the direction of propagation. And finally, I will be able to also write down what will be the corresponding polarization for the transmitted wave, which is also, again, perpendicular to the direction of propagation So therefore I can now make use of the boundary condition one and boundary condition two to actually figure out what would be the relation between E0I, E0R, and E0T. The first thing which we consider is to consider the perpendicular direction. For equation number one, I will be able to conclude that epsilon1 minus E0I sine theta I. So basically, that is actually the contribution from the first vector, E0I. You can see that now I am trying to project everything to the direction perpendicular to the surface. And you can see that I have a minus sign. And that this angle is actually theta. So therefore, I have-- So this angle is actually what? This angle is actually I minus theta. So therefore, I have the cosine theta I. And I have this minus sign, because it's pointing to the left-hand side of the board. So that's actually the contribution of the incident wave. And I have a second term, which is the contribution of the reflected wave, E0R sine theta I. So E0I, E0R with all vector is actually just the length of the vector in my definition. And based on the first boundary condition, I have the left-hand side looks like this. On the right-hand side, I will have minus epsilon2 E0T sine theta T. Again, I am looking at the projection of this E0T vector in the direction which is actually perpendicular to the surface. So that's the first expression I can get. And then from the expression number two, I can now-- taking the projection, which is parallel to the surface, so now this is actually the parallel direction. And basically, what I'm going to get is E0I cosine theta I plus E0R cosine theta I-- oh sorry, theta R. Theta R is actually equal to theta I, so therefore, I actually replaced that by the I already. And that will be equal to E0T cosine theta T. Any questions so Far so I was pretty fast. So here, I already immediately write down this is actually theta R. Theta R is equal to theta I, so therefore, I already replaced that by theta I. Do you have any questions? So the painful period is going to end in like 3 minutes, OK? So we are almost there. And look what we have been doing. We basically figured out the boundary condition from Maxwell's equation. Then we are plugging in that. So we assume that the polarization is actually parallel on the plane of xz plane. And now we are actually just evaluating the parallel component and the perpendicular component. So that's actually what we've got. The goal, as a reminder, is to write E0R and E0T in terms of the known part, which is the E0I. I would like to relate these three-- the magnitude of these three vectors. So from equation number one, I can actually rewrite that. Basically, I can actually conclude that I can divide everything by epsilon1 sine theta I. So what I'm going to get is E0I minus E0R. And this will be equal to epsilon2 sine theta T divided by epsilon1 sine theta R. And this is actually E0T. So basically, I'm dividing everything by minus epsilon1 sine theta I. Then basically, what you are going to get is this expression. And this actually can be related to another expression, which is epsilon2 n1 divided by epsilon1 n2. Because I can use Snell's law. n1 sine theta I will be equal to n2 sine theta T. Therefore, I can replace this ratio of sine angle by refractive index. Everybody's following? OK, very good. And this will be multiplied by E0T. I can now define this. This is actually defined as theta E0T to make our life easier. The same thing can be done for the second expression. What I'm going to get is E0I plus E0R. Basically, what I'm doing is to divide everything by cosine theta I. So what is going to happen is that you are going to get cosine theta T divided by cosine theta I E0T. And that is actually defined as alpha E0T. So alpha is defined as cosine theta T divided by cosine theta I. Therefore, I can already immediately, based on these two expressions, to solve what would be the E0R. I can write down the solution. So basically, you can actually quickly derive what would be the E0R. And that is actually going to be my alpha minus beta divided by alpha plus beta, E0I. And you can also solve based on these two equations what would be the E0T. And now we will conclude that this will be equal to 2 divided by alpha plus beta, E0I. So this means that the refractive index will be equal to alpha minus beta. Sorry, refraction coefficient will be equal to alpha minus beta divided by alpha plus beta. And the transmission coefficient is actually 2 over alpha plus beta. So we will take maybe a three minute break for you to be able to ask some questions. But you can see that we have solved the relation between E0I, E0R, and E0T. And what we have to do in the rest of the time is to enjoy what we actually already derived, and what actually that means, after the break. So we come back at 45. OK, so very good. So we have survived this. And now it's time to enjoy what we have learned from this equation. All right, so welcome back everybody. So we have actually saw what would be the refraction coefficient and the transmission coefficient tau. And those are the functions of alpha and beta. So that's considered three different interesting cases. So if I have normal incidence. And that means alpha will be equal to cosine theta T divided by cosine theta I. This is the definition. If I have no more incidence, that means both theta T, theta I, and theta R will be equal to 90 degrees. And in this case, basically, you will have the same cosine theta-- I mean cosine I. Theta T and cosine theta I. And that means your alpha will be equal to 1 in this case. So in normal material, mu1 is roughly equal to mu2 and roughly equal to mu0. So therefore, this means that if mu1, mu2, and mu0 are very close to each other, then actually, the refractive index based on that equation which is showing there, will be basically, roughly equal to square root of epsilon divided by epsilon0. So therefore, beta would be equal to epsilon2 divided by epsilon1, n1 divided by n2. This is actually the definition. And this will be basically equal to-- since this is actually proportional to epsilon2 divided by epsilon1. And n is actually proportional to epsilon, square root of epsilon. Therefore, you can conclude that this actually will be equal to n2 squared divided by n1 squared, n1 divided by n2. And that will give you n2 divided by n1. You can actually cancel one of the n2 and one of the n1. So beta will be equal to n2 divided by n1. And therefore, you can conclude that R will be a function just related to the refractive index, which means that you are going to get n1 minus n2 divided by n1 plus n2. Which means that the amount of reflected light is related to the difference in the refractive index. Then the amount of the transmitted light will be equal two n1 divided by n1 plus n2. So what does that mean? This means that if you have some material which is essentially like diamond, diamond have an n2 equal to something like 2.6, that means a lot of light will get reflected, even if you have no more incidence. So that's actually why the diamonds are so beautiful, because a lot of light, pretty bright, and a lot of things are actually reflected. The transmitted fraction is actually pretty small. I can also assume that there can be a grazing incidence. That happens-- this means that I am going to have theta I. This theta I should be here. This theta I is going to be roughly 90 degrees. In the case of no more incidence, theta I should be equal to zero. Maybe I misspoke in the beginning. So what does that mean? This means that alpha will go to infinity, because theta I is going to 90 degrees. Therefore, you have R roughly equal to 1, because R is actually alpha minus beta divided by alpha plus beta. If alpha goes to infinity, then R will go to 1. And the tau will be-- actually, roughly goes to 0. So that means if you have a grazing incidence, then basically, most of the light are reflected. So that's actually why when we see, for example, reflected light from the sun, which is actually on the road, we see that a lot of light are reflected. When we see a lake which is actually very far away from me and the sun in front of it, you see a huge amount of lite got reflected and going to your eyes. Looks really bright. So finally, there is a very interesting angle, which is actually considering a situation when alpha is equal to beta. This is a very interesting angle, theta B. If we choose this theta B such that alpha is equal to beta, what is going to happen? Somebody can tell me. If I make-- STUDENT: [INAUDIBLE] PROFESSOR: Exactly, right? So if you choose an angle such that alpha is equal to beta, then R will be equal to 0. There will be no reflection. And everything goes through the material. So that is actually so-called Brewster's angle. And this happens when theta B-- which theta B is actually the incident angle-- plus theta T is equal to pi over 2. There's a proof of this Brewster's angle in the lecture notes. But we are kind of running out of time. But the conclusion is that you will need to have theta B, which is actually equal to theta I, the incident angle, plus the transmission light angle, theta D. If that is equal to 90 degrees, then you can make alpha equal to 0. And what is going to happen is that there will be no reflected light. So when this happens, when the reflected light and the transmitted light have an angle of 90 degrees, then the amplitude goes to 0. This is actually a very interesting property and it only works for electromagnetic waves, because this is actually coming from, really, the effect of Maxwell's equation. So now what I'm going to say is that basically, we look at this demonstration. So if we have an incident light, and the transmitted light. Originally, the incident light is unpolarized. So you can have all kinds of different polarization. So we can become post polarization into a component which is actually pointing to you, which is the dot. And the component, which is actually the parallel to my slide, which is actually what we have been working on, that situation. So what is going to happen is that the component which is pointing you is actually never gets suppressed, because there will be no perpendicular component. So therefore, even if you add Brewster's angle, it should get reflected. On the other hand, all the components which essentially heavy polarization parallel to this slide is eliminated because of this relation. So that means the reflected light will be highly polarized. Do you believe me? Maybe not. We can do an experiment and really show you that's the case. So we are almost there. So now I need to turn off the light and hide the image. And you can see that there is a setup here which I produce unpolarized light. And there's a glass here, which actually I reflect the unpolarized light. So now you can see that if I have some random angle, and I have a polarizer here-- I hope you can see it-- you can see that the polarizer cannot eliminate all the light. So basically, no matter what kind of direction, it will not be able to eliminate all the reflected light. This means there's some mixture of all kinds of different polarization. But now, if I change the direction to Brewster's angle, it's roughly here, so you can see that now, indeed, I can actually eliminate all the contribution of the reflected light. Because the reflected light is highly polarized. As you can see from the slide, all the component which is actually parallel to the slides is actually eliminated due to Brewster's angle. And that produces a polarized light. And that can be filtered out by the polarizer. So coming back to the question which we had before, so why can we take such a good photo? That is because of Brewster's angle. So once the sunlight gets reflected by the window, it becomes linearly polarized, and therefore, you can actually filter out the majority of the contribution by using polarization filter. OK, thank you very much. And I hope you enjoyed the lecture today. And hope this will improve your technique, your skill, for taking good photos. If you have any questions, please let me know. Hello, everybody. So today I'm going to show you a demonstration of Brewster's angle. So during the class, we were discussing about how to make very good photos, how to use polarizer to filter out the reflected light from the sun. Usually, when you actually take a photo of water or a car, there are refracted light from the sun on the window or on the water. And then you can actually use polarizer to filter them out. And that has to do with the property of the electromagnetic wave and the Brewster's angle. So here I have an experimental setup here, which consists of three components. The first component is a polarized light source. And it meets unpolarized light. And those light are getting refracted by glass here. And the unrefracted light will actually be shown on the screen as a spot there. So at first, if I have my glass, which essentially-- the position of the glass is in a way such that it's actually not on Brewster's angle. And now I can actually check if this light is actually polarized by using a polarizer here. And if I put this polarizer between the screen and the glass, you can see that, huh, as a function of the angle which I am rotating this polarizer, you can see that no angle can actually completely eliminate the reflected light. So that means that the reflected light is actually not perfectly polarized. But on the other hand, you can also see that in some angles, you can actually significantly lower the intensity. And that, essentially, is also pretty good for photo taking, because that means all the reflected light, although now the angle is actually not at Brewster's angle, you still have the reflected light slightly polarized. So that actually your polarizer in front of the camera will still do some work. Now what I'm going to do is to change the angle so that it matches with Brewster's angle. So now you can see that if I insert a polarizer between the glass and the screen, you can see that at some angle, for example, now we can actually filter out or completely eliminate the spot on the screen. So that means at Brewster's angle, basically, the reflected light is actually completely polarized, as we actually predicted from the lecture. And the reason is the following. There's only one direction of the polarized light from the unpolarized source can get reflected due to the boundary condition of the electromagnetic wave. And therefore, we see this very unique phenomena which we can only see in electromagnetic waves. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 14_Fourier_Transform_AM_Radio.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: OK, so welcome back to 803. Happy to see you again. So today, we are going to continue our discussion of dispersive medium. And there are two questions we are going to ask in this lecture, and we will answer also these two questions in this lecture. So just to warn you in advance, this lecture will have a lot of mathematics, so fasten the seatbelt and follow me. And stop me any time you don't feel like you know you understand something. So let's get started. OK, so today, we are going to talk about phenomena related to dispersion. And last time, we started a discussion about how to send information from one place to the other place right. So what we should be before was to send square pulse. So if I do have a machine which can produce a square pulse, then I can define something like this. So over some ratio, which I set, I can actually separate 0 and 1. So if I have a pulse which is actually having an amplitude greater than some threshold and I say, OK, I've got 1, and if it's actually below some straight line, say, OK, I've got a 0. And with that way, we actually can send information from one place to the other place. So that sounds really nice. However, if we work on a dispersive medium, which is really very common-- for example, light and gas is actually-- not all the lights with different wavelengths are traveling at the same speed, and also, as you've seen before in the p-set, deep water, and also the strings, considering a realistic string with stiffness, et cetera, et cetera-- to the wavelength of the input wave is going to affect the speed of this travelling wave. So in short, the speed of the wave propagation in a dispersive medium will depend on the wavelengths of this wave. So that brings us a lot of trouble because, for example, here we are trying to send a Gaussian pulse through the medium, but after a while this pulse actually becomes wider and wider because of the dispersion. Because all the components with different wavelengths which actually construct this narrow pulse, actually are traveling at different speeds. Therefore, if you wait long enough, all the different frequencies, or all the different frequency harmonic waves are travel at different speeds, therefore you get the, dispersion, which results in a much wider pulse in the end. And at some point, this pulse is going to be really wide, such that it's actually going to be very difficult to separate 0 from 1. So that's the problem. And we also did some simulations with computer. We do see this behavior also in our computer simulation. If I put in triangular pulse and allow it to evolve, and like what we did before, we assume that there's a stiffness in this string system. And you will see that, OK, as a function of time, this part is now longer a triangular shape, but you have a very complicated structure. So that is actually a problem we are going to try to solve today. And during that discussion last time, in the lecture, we also introduced dispersion relation omega k and also tried to overlap two travelling waves with similar wavelengths. And that would give you beat phenomenon. That probably doesn't surprise you any more. As you can see from this example, you have the beat phenomenon, and you can see the amplitude is actually variating slowly, the function of position. And if you follow the red point, which is actually associated with one of the peak, in the structure called carrier, OK, it's actually moving at the phase velocity, the P, which we introduced last time. The formula for BP, which is actually the speed of harmonic, oscillating travelling wave is actually defined as vp equal to omega over k, and the green point, which actually always at the minima of the distribution, which is actually associated with the speed of the envelope. You can see that, indeed, it actually can move at different speeds. It depends on the dispersion relation omega as a function of k you have in this system. And we call the speed of these envelope, which we construct from these two overlapping travelling waves to be-- we call it group velocity. And the definition of group velocity is vg equal to d omega dk. So that's what we have learned last time. OK, you may ask, OK, what do I mean by group velocity? And can I use it beyond what we have done for the beat phenomena. But what do I mean by group velocity? Is that really useful, and it's actually which part of the structure I was talking about. So in that case of two overlapping progressing waves with similar length or similar frequency, when we see that the group velocity actually present the speed of the envelope, right? Can we actually learn something more general about group velocity? The second question which we are asking is, OK, now we have this problem of dispersion. This square pulse is going to be something which is really wide after some period of time. So that's clearly a problem, and how do we actually solve this problem, and how do we actually send information like, for example, music over a large distance from one place to another place. So that's essentially what we're going to try to understand today. So let's start with an infinitely long string. And this string is actually very long, and this began from here, and it goes to some place which is really, really far away. And, of course, as usually, I can actually hold one end of this string and shake it a bit, then I can actually create some kind of pulse which is going to travel along this string towards a positive x direction. In this case, I defined the x coordinate will be pointing to a right hand side, and thus the positive direction. So of course I can hold this string, and I just shake it, and I would prepare a pulse on this medium, which is a string with constant tension. So I can describe the motion-- you can describe the motion of Yen-Jie's hand by a function. So you can say, OK, Yen-Jie is somehow doing a really nice job and oscillating at constant frequency. Like I can say, OK, Yen-Jie is shaking this thing to produce a harmonic wave, for example. And that, I can actually describe the motion of the hand by f of t. That's very good. And from what we have learned in the last lecture, we've found that, basically, waves, harmonic waves with different frequency, or with different wavelengths, are traveling at different speeds. Therefore, we would like to actually decompose the motion of Yen-Jie's hand into many, many harmonic waves-- then attack them one by one, to follow them one by one, then I can solve this problem. So that's actually what we are going to do. And that will involve some math, which we would follow from the math department. And before that, I would like to introduce the imitation first. As I said f of t is actually the displacement as a function of time as x is equal to 0. So basically, I'm holding this string, and I move things up and down, so that, actually, I move this string away from the equilibrium positive, which is actually y equal to 0. Then what is going to happen? What is going to happen is that I'm going to produce some kind of pulse, and this pulse, I can actually describe it by a function, which is psi x and p, this psi is actually describing the displacement as a function of x, and as a function of t. Apparently, if you put x equals to zero, then you go back to f of t, right? Basically that's the idea. OK. So what we have learned before we introduce dispersive medium is that, if I have a non-dispersive medium, OK, if I have a non-dispersive medium, then things are pretty simple because omega over K is actually a constant, which is the phase velocity, vp. And omega is actually just equal to vp times k. That means, no matter what kind of wavelength we are talking about, no matter what kind of angular frequency we are talking about, harmonic progressing wave is going to travel at the speed of Vp. No matter what's the frequency, or what's the wavelength. So that makes our life much simpler when we work on non-dispersive medium. In this case, if I have a non-dispersive medium, then psi would be equal to-- maybe I write it here-- if I have non-dispersive medium where, no matter what kind of frequency, the speed of the harmonic traveling wave is a constant, which is actually Vp, I can write down psi x t to could be equal to f of t minus x over v. Just remember f is actually describing how I shake one end of the string, and, basically you can see that ha! What is happening is that my hand is actually generating the shape of the pulse as a function of x, as a function of time, and it can be described by a really simple formula here. So this is actually really nice for non-dispersive. As I introduced before, when we talk about dispersive medium, then, if I go to dispersive, omega is actually a function of k, and can be a non-linear function. So what does that mean? That means, if I evaluate vp, which is actually the phase velocity, which is the formula there, this is going to be omega of k divided by k. That means BP is going to be a function of k, the wavelength-- wave number. It's not going to be a constant in general-- unless omega is actually equal to vp times k, in general, vp can actually be some quantity which is variating as a function of k. OK? Then we have trouble because that means, when I produce progressing wave from the left hand side end, it's actually made of many, many harmonic waves, right, with different angular frequency. So I can shake this like [MAKES NOISE],, different speed. And I can always decompose the motion of Yen-Jie's hand into many, many harmonic waves. The problem is, all those harmonic waves are going to be travelling at different speed. How do we actually describe this? So that's the trouble. And I was really frustrated when I think about this problem, and my friend from the math department said, hey, we have solved this problem a long time ago. [LAUGHTER] So this is not the problem anymore. And I say, oh, what is the idea you're talking about? And they actually told me that you should use Fourier transform to attack this problem. OK? This is the idea. The idea is that I can now write down f of t, which is motion of Yen-Jie's hand, and this can even returned as a superposition of infinite number of waves. I can integrate from minus infinity to infinity, t omega, which is the angular frequency. And each contributing wave has an amplitutde associated with it, which is, as you see, is a function omega. And the actual wave is actually written in terms of exponential minus i omega t. So now, let's actually you look at this thing really carefully. What am I doing? I am saying that I, now, can shake one end of the string up and down according to my will. And, if I do this for a long time, I can actually describe the motion of my hand by infinite number of harmonic waves, which is actually kind of like exponential i omega t describing the frequency of these waves, and each of them got associated amplitude. And you may ask, OK, wait a second, you call this Fourier transform, and I have learned that before, but I learned a different version. I learned a version of cosine and sine? And what is going on? Actually, they are all the same. No matter what you do, you can actually also do that with cosine and sine, but what I actually found is that it's actually easier to deal with exponential functional form You can always write exponential i omega t in terms of sine and cosine and absorb the i into a c omega. Basically, these things are identical between these two forms of this answer. So therefore, in this lecture, I'm going to stick with this functional form. OK, any questions? STUDENT: We don't include dx in the [INAUDIBLE]?? YEN-JIE LEE: Not yet. We are going to include that. Because, for that, in order to actually-- OK, so now I actually decompose the motion of my hand into many, many waves-- which should be or is say it many, many oscillation with different frequencies. So I actually describe the motion of my hand infinite number of oscillation with different frequency. And the trouble we are facing is that all those oscillations are going to be charged travelling at different speeds because of the dispersion relation. Therefore, what I am going to do afterwards is to show you that, OK, I can write down the functional form for psi in this general case. So for that, that's actually what I'm going to do now. So now, I would like to know what would be the psi xt, which actually the position of the string as a function of x, and at some specific time equal to t. And that can be written as, I do the an integration from minus infinity to infinity over frequency omega, and I have the usual amplitude associated with the angular frequency omega, and the exponential i omega t-- minus i omega t because that's the convention I'm using here-- and I say, OK, plus ik, which is a function omega-- x. So now you can to see that what I'm doing here is that I am now progressing, I am making infinite number of progressing waves. Each of these exponential functions is a progressing wave with angular frequency omega. And why do I write k as a function of omega x here? It's because they are going to be travelling at the speed of omega over k. Therefore, I need to actually put k here, and this k is actually-- this k is actually not the independent parameter. It's actually a function of omega. So we can see that, here, we do an integration over omega from minus infinity to infinity-- for each omega you can actually find the corresponding k, right? Because of the dispersion relation. Because omega is a function of k, therefore you can always solve the corresponding k, right? Then you put it there? Because you are now trying to propagate how many waves with different angular frequency at different speed-- then we are done. That looks like a wonderful solution, and we can actually see how it works for our purpose. Any questions? All right. So that's really nice. And I can now do a really simple test to see if this really works. Let me try a very simple case. OK, a spatial case. If I now go back to use this description to describe non-dispersive medium and see what will happen. Now my k as a function omega is actually rather simple. It's actually omega over vp-- according to the dispersion relation here. I can solve k, as I was mentioning, with these dispersion relation formula. And then I can conclude k as a function omega is omega over vp. Then I can now put that into this equation, and I'm going to get psi x of t-- this would be equal to minus infinity to infinity d omega, c omega, exponential minus i omega t minus omega over vx. And we can actually take omega out of this, minus infinity to infinity d omega c omega exponential minus i omega t minus x divided by v. And you can see that, huh, indeed, this is actually ft minus x over v. OK. I'm dropping the vp here. This should be vp all over the place. So you can see that, now, if I have solved the k as a function omega, and I plug it in in this special case, which is non-dispersive medium, omega over k equal to vp, then I really calculate this integral, then I can quickly identify that-- huh, I can write the functional form in this way. And this is actually really familiar to me because that's actually using this definition, f is actually equal to integration minus infinity to infinity, d omega, c omega, exponential minus i omega t. If I replace t, by t minus x over vp, then I'm done. So I have evaluated this integration, which is actually just f t minus x over vp. So that's exactly what guessed from the beginning. So if I have a non-dispersive medium, then psi xt will be equal to this function. So that gives us some kind of confidence that, OK, at the easy case, it works. All right, so that's very nice, all sounds very good. But wait a second. How do I actually extract this c, which is a function of omega? I'm troubled because this is an infinite integral from minus infinity to infinity. And that means I have infinite number of constants, which I have to determine the c omega. How do I actually do this? So that is another point which I would like to discuss before we actually go ahead and really use this function for the dispersive medium case. So how to we actually extract c as a function of omega? So for that, we really need to employ a few uses for formula, which are actually documented here. How many of you actually have not heard about delta function before? OK, a few of you actually have not heard about delta function. So what is actually your delta function? This is a delta function. So a delta function is actually a notation which actually shows you a function, which is should only be non-zero, at x equal to zero. And the x equal to zero, the size of this function as you're going to infinity, and on the other hand, all the other points at x not equal to zero, the delta function is equal to zero. So that's actually the kind of function I was talking about. And the area of this function, if you're doing the equation over minus infinity infinity over x, the integration of these delta m the area is actually 1. So that is actually the kind of function. So essentially, it's a really, really narrow function, OK, very narrow, very narrow, very narrow. But the area is finite, which is why. So you can have a square. You can actually start with a square pulse, or square function, and you can actually make the width of the square narrower, smaller and smaller and smaller, go to 0. Then what you are going to get is essentially the delta function. That's actually how we understand this delta function. All right, really quickly. And also, we would like to use a few formula which are documented here. So if I do an integration from minus infinity to infinity, exponential i omega minus omega prime, t over the t which is integrating over time, t, here. And then divide the whole formula by 1 and over 2pi. What I'm going to get is a delta function, which is a delta function which is omega minus omega prime. So that means when this delta function formula tells us that omega is equal to omega prime, then this function is actually going to infinity. And only when omega equal to omega prime, this function is not zero. Any other place, this function is always zero. And this strange integration should give you this delta function. So that's the first thing which we will use, was one useful formula. The second thing which what just I talked about, if I do an integration over minus infinity to infinity, delta x dx, then basically you get 1. The third one is actually kind of interesting. Let's take a look. So if I do an integration over from minus infinity to infinity, delta function x minus alpha. Let's look at this delta function first. This function is only non-zero when x is equal to what? AUDIENCE: Alpha. YEN-JIE LEE: Yeah. When x is equal to alpha, only when that happen, this is actually non-zero. If you multiply this delta function to some function which is f of alpha, and integrate over alpha from minus infinity to infinity. And that means that when alpha is equal to x, or x equal to alpha, this integration give you non-zero result. All the other ways, you will get zero. The interesting thing is that if you do this integration, what you are going to get is that OK, when I integrate over alpha, only when alpha is equal to x this thing is non-zero. Therefore what you are going to get is, you get only one point of the width, which is actually f of x. So that's the intuition about this formula. That's just fine. Any questions related to those formulas? AUDIENCE: [INAUDIBLE]? YEN-JIE LEE: Hm? AUDIENCE: [INAUDIBLE]? YEN-JIE LEE: Yeah, this is actually pretty complicated, so it would take a few 10, 20 minutes to explain that. But let's just take the words from the math department-- we trust them. All right, so once I have those formula, I can now demonstrate you how I can actually track C as a function omega. So this is actually the goal, right? So don't forget why we are doing what we are doing, is to try to extract what is actually the C omega, so that we can actually finish this formula. So how do we do that? So suppose, if I evaluate this. This function, 1 over 2pi, minus infinity to infinity dt, ft, exponential i omega t. If I evaluate this function. This is coming out of nowhere, right? So coming out of Yen-Jie's hand, maybe, I don't know. Suppose if I evaluate this function, and now I have ft here, right? I can replace ft by these interesting formula. If I do that, then basically I get 1 over 2pi minus infinity to infinity dt, minus infinity infinity C omega prime, exponential minus i omega prime t. And the last is actually integrating over d omega prime. So this is actually the f of t. This is actually f of t. I'm just replacing that formula into this integral. And then I have the rest, which is exponential i omega t. And of course, I can continue and collect all the relevant terms together. This is actually equal to 1 over 2i, minus infinity to infinity. I collect all the terms related to omega prime to the left hand side. Basically what I get is C omega prime d omega prime. This is actually coming from here, except-- yeah, OK, it is actually coming from here. And I have another integral which is from minus infinity to infinity, this time integrating over delta dt. And I have dt here, exponential i omega minus omega prime t. So basically I'm collecting these two terms together. They now become exponential i omega minus omega prime t. So basically, no magic happened, but I'm just re-writing things and we are arranging things from this formula to that formula. Then if we look at this formula, this formula here, and the formula sheet we have. 1 over 2pi minus infinity to infinity to this integration over t, exponential i omega minus omega prime t. That will give you delta function, which is delta omega minus omega prime. Therefore, I can continue this calculation here. Thus it's going to give you minus infinity to infinity. I identify this part, this part, and this part, to be the delta function. Therefore, what I get is minus infinity to infinity, C omega prime, delta omega minus omega prime, d omega prime. Am I going too fast? Everybody's following? So you can see that what we have been doing, I use this formula coming out of nowhere. I replace f by the formula I was writing there. And then I collect the terms I like together. That's all I did. And then I found, aha! One part of the formula is actually the delta function. Then I put the delta a function here. And then finally, I use the third formula here, which I have related to delta function, and I found, aha! If I do this integration, I know how to do this integration even without knowing the structure of C. This is actually just changing the omega prime to omega. So that's actually what this integration actually does. Therefore, I get C omega. Look at what we have done. What we have done is that, we have proof that this formula coming out of nowhere, to be a continuous version of mode picker. You remember the fourth year decomposition before? You were using the orthogonality of the sine function, and I can do some kind of fancy integration to actually extract a m from one of the-- which is associated with one of the normal mode, right? What we are doing here is actually a continuous version. Now omega is actually continuous. And I'm now using the orthogonality of the exponential function. If I do this integration, that will only give you non-zero value when omega is equal to omega prime. It's exactly the same thing, right? Then I can construct an integration like this. And now will give you the redoubting C as a function omega, which is like the amplitude of one of the associated harmonics exponential i omega t. So in short, from this exercise, we have shown you that C of omega can be extracted using this formula 1 over 2pi, minus infinity to infinity dt, f of t, exponential i omega t. That's actually how we actually can determine all the amplitude associated to a specific exponential function. Any questions so far? OK, so if no question, then we can actually continue. So let's actually go back to the original question, which we were posting. So we have a problem related to the transmission of information. So this is actually where we got started. If I send a square pulse on a dispersive median, then I have some trouble, which is that this pulse is going to disperse and become wider and wider. It's changing as a function of time, as a function of distance it travel. That's not cool. All right, so therefore what I am going to do is this. There was a very smart idea which were discovered long time ago, during maybe World War I, and widely used in World War II, which is the AM radio. What is AM? Is actually amplitude modulation radio. This smart idea is the following. I will describe it before we take a break. So this smart idea, AM radio is the following. If I have some kind of information which is fs t. s here means signal. If I have some kind of information I would like to send, I can send it by oscillating one end of the string. And this is what I want to send. And there are two ways you can send this fs function. The first one is actually what did before, I send it directly. I just said OK, if I want to send this function, then I just oscillate the string according to the functional form. Yen-Jie just have to be really careful, right? So that you can send this function. And that fails miserably. Why? Because all the components which actually produce the fs, in this case the square pulse, all those components are travelling at different speed. Therefore, the information will never get there, because of the dispersion. So now what should we do instead? Instead of doing sending fs as a function of t directly, what you could do is that I can now send f of t, which is equal to f of s t cosine omega0t. Where omega0 is a very, very large number. And basically, look at what we have been doing. So that means I, instead of sending fs directly, I send fs, but modulated by a really high frequency function, cosine omega0t. And this will work. And you will only know that after we come back from the break, which is twenty first. Let's take five minute break. And if you have any questions, you can actually ask me here. So we will continue the discussion about AM radio. So before the break, actually we introduced this one possible solution to solve this dispersive median problem, is that I can now actually send instead of fs as a function t, which is actually the signal I want to send, I could send fs, but multiplied by cosine omega0t. If I assume that fs is some really slow function, slowly varying as a function of time, compared to cosine omega0t. Cosine omega0t is a really fast function, oscillating up and down like crazy, really fast. If I multiply fs by this function, what is going to happen? We are going to show you that actually that means I am going to only have non-zero C function, or a large contribution of C, in a very thin middle range of omega. So we'll show that. So in a typical case, fs is really slow, which is like, for example, my sound, et cetera, in the label of one kilohertz. And you can actually design a system which will actually multiply this fs by cosine omega0t. Omega0 can be as fast as 1.1 to 30 megahertz. If you do this calculation, then you will find that OK, the range of omega, with sizable C omega is small. It's roughly equal to omega0 minus omega s, to omega0 plus omega s, where omega s is the typical frequency in your signal. And the omega0 is the typical frequency of-- the frequency of your cosine omega t term, which is actually, later, you will recognize this as carrier. So what I want to say is that if I do this trick, what is going to happen is that the range of omega, which you have sizable contribution from C omega-- C omega is the associated amplitude, associated amplitude. It's going to be confined to a really small region from omega0 minus omega s, to omega0 plus omega s. So that's the trick which actually makes this problem solvable. How do we know this? That is because, if I now, for example, I send fs equal to cosine omega st. If this is actually the signal which I would like to send, just a harmonic wave, then what is going to happen is that I'm going to get ft is equal to cosine omega st cosine-- so this is actually multiplied by cosine omega0t. So I have cosine omega0t here. I have cosine multiplied by cosine. Therefore I have the question which I prepare here, the formula, of cosine alpha times cosine beta will be equal to the functional form. There's a remainder, therefore I can now write it as 1 over 2 cosine omega s minus omega0 t plus cosine omega s plus omega0. You can see that when I actually multiply two cosine functions together, then what I get is actually the omega0 minus omega s. You can actually put the minus sign there, it didn't matter. And cosine omega0 plus omega s times t. So therefore, you can see that the frequency, there are only two frequencies which contribute to this C of omega, which is actually these two frequencies. So that is actually why, if you do this trick, you actually try to modulate your slow signal function by a fast carrier frequency. Then you are going to confine the effective range of omega into a very small range. Why is that useful? That's actually what I want to answer to you. Suppose I have this crazy dispersion relation, which is omega as a function of K. You can graph it, and suppose it looks really crazy like this. And if I set my carrier oscillation frequency to be omega0, and that will give you a corresponding wave number which is K0. I hope you can see it. That's the corresponding K0. Before we actually multiply this function, it's a slow function. It's not exactly one cosine function. So if you just have a cosine function harmonic wave, then you don't really need this trick, because it's actually going to be traveling at a speed of some constant speed. It's a harmonic traveling wave. But if this is actually a slow function, but not really a single harmonic wave, then what is going to happen is that you are going to need a wide range of K value or omega value to describe fs. Then you are in trouble because now, all the waves with different wavelengths are going to be travelling at different speed. Then you have this dispersion problem. On the other hand, if I multiply this function, this slow function, by a fast oscillating function, I am confining the effective range of omega into this small box, which is actually between omega0 minus or plus omega s. This is actually omega0 plus minus omega s. This is actually the range of the possible omega, which contribute to this resulting f of t. Therefore, the behavior of this function is actually much easier to understand. So with that given there, suppose now I have a large difference between-- suppose I have a large difference between omega s and omega0. Then I can actually focus on a very small range in this dispersion relation diagram. Then I can write omega as a function of K, the dispersion relation equal to omega0 plus K minus K0, partial omega, partial K. Evaluate it at a equal to K0, plus higher order term. Basically I can do this Taylor expansion. And maybe it surprised you, you can immediately identify, ha! This is delta d omega dk, is the group velocity. Suddenly it show up in the Taylor expansion of the dispersion relation. so if I focus on the region which is around omega0, then I can actually re-write omega in this functional form. Omega is actually equal to omega0 plus K minus K0 times Vg, which is the group velocity. Suppose this is happening, then now I can actually go ahead and really calculate the functional form for f of t. So suppose I have this definition of t. The definition of t is equal to fs t times cosine omega0t. Or say I can actually write it in a complex form, instead of writing it in a cosine omega0t functional form, I can write it in exponential functional form. Exponential minus i omega0t, which is actually more convenient for the discussion. So what is going to happen if I actually do this calculation? Then basically that's one example signal which I would like to send on the slides. So if I am trying to send a progressing harmonic wave, then after multiplying by this exponential i omega0t function, or a cosine function, basically you get something which is actually oscillating really fast, which is actually the AM signal we are trying to send through this media. So we can actually identify, this is actually the structure of this, actually the carrier. And this signal become the analogue, in analogy to what we actually have discussed for that beat phenomenon case. So now, if the omega range is really small, then I can actually write this down. Write a functional form of omega in this functional form. Or I can actually take out the kVg term, and the rest is actually going to be something like some constant a, where a is actually equal to omega0 minus Vg times K0. So basically I'm just taking out this K term here, and this become this term. With this formula, I can solve what would be the functional form for K, as a preparation for what I'm going to do later. So K can be also expressed as omega over Vg. So basically I just solve the K plus b. b is actually just some constant. Just do it for convenience, I can write b equal to K0 minus omega0 divided by Vg. What we learned here is that if the range of effective omega is really small around omega zero, then the relation between omega and the K becomes a linear function. Of course, it's still not like the case for the non dispersive median, where omega over K is a constant. But at least it becomes a linear function, which is actually much nicer. So finally, with all those preparation we have done, we would like to show one important consequence. So what we are trying to do is to show that psi xt. Now I send, I oscillate the median, the string, by this f of t, which I designed there. ft is actually fs times exponential i omega0t. That's actually designed there. I would like to show that the resulting amplitude will be equal to fs t minus x divided by Vg, exponential minus i omega0t minus K0x. Of course I need to take the real part of this in, to go back to the real axis. Basically I dropped the i sine omega t contribution. So this is actually what I want to show. Before I go through all those math, let's do get the conclusion which we would like to draw, before we actually really go through the math. The conclusion which I would like to draw is that, OK, this is actually my analogue. My analogue is going to be travelling at the speed of Vg, which is the group velocity. That's the conclusion which I would like to draw from this exercise. And this thing is actually cosine omega0t minus K0x. Therefore, this is actually a harmonic wave. The carrier is a harmonic wave travelling at Vp equal to omega0 divided by K0. That's the kind of conclusion which I would like to draw from this exercise. Any questions about what we have discussed so far? OK, then really you have to hold tight and follow me really, 100% focus, because this is actually a complicated calculation. So now what I can do is, now I need to express my fs in terms of C. So I do integration from minus infinity to infinity, d omega, C omega, exponential minus i omega t. So basically I can write my f of s in a functional form, which we introduced before. Then my f function is actually equal to fs times exponential i omega minus i omega0t. So that's actually what we defined there. And this would be equal to minus infinity to infinity. I do this integration number, omega C omega exponential minus i omega plus omega0 times t. So there's nothing special, I just take my expression for fs, multiply that by exponential minus i omega0t. Then that's actually what I get. So since this is actually integration over omega from minus infinity to infinity, therefore I can always have the freedom to shift the origin. So that means f of t can be returned as minus infinity to infinity d omega C omega minus omega0 exponential minus i omega t. Then we can see that is fix a relation between C of the f function, and the C of the fs function. So so far, everything is exact. I haven't made any approximation so far. So now, I can take this function and propagate that to all x. In other words, I can now take this ft, and write down the psi as a function of x and t. So that means all the different components are traveling at different speeds. So basically, I can write it down like d omega C omega minus omega0, exponential minus i omega t, exponential ikx. Kx k is actually a function of omega. Any questions? So that's actually just identical to what we actually have done before. So now I can go from f of t to sine, if you are following me. So until here, everything exact. You have all the problems you have, like you know this dispersion essentially, because all the little components, as you can see here, can be travelling at different speeds. So now, what I could do is that if I assume that C omega is only sizable at the small range around, it's only sizable around omega0. If now I take this assumption and propagate into this formula, then I can write this psi function roughly like minus infinity to infinity d omega C omega minus omega0 exponential minus i omega t exponential i. Now I can take the formula which I actually did an approximation, around omega0. Around omega0, K can be returned us omega over Vg plus b. This is actually where I take the approximation. Only consider the first order in the Taylor expansion. So you can see now here, it's not exact anymore. But now I write approximate function of form for K omega. So what I'm going to get is omega over Vg plus b, multiplied by x. Any questions? Now I have the approximation. And of course now I can gather all the terms related to omega together. I'm getting minus infinity to infinity d omega C omega minus omega0 exponential minus i omega t minus x over Vg, exponential ibx. So basically, I am merging this term and that term. This term and that term will give you this term. And what is essentially the rest is the exponential ibx. We are almost there. So now I would like to use this board, so I need to erase that. So now I continue from here, and I can now again, I can again change the origin of this infinite integral so that this can be written as minus infinity to infinity, d omega C function of omega, exponential minus i omega plus omega0, t minus x divided by Vg, and exponential ibx. So what I come from this board to that formula, if you are following me we are almost there, because I am changing the origin again, so that omega minus omega0 becomes omega, become a new omega. Is everybody accepting this fact? And that means the original omega will become omega plus omega0. I'm trying to go really slow, so that everybody can follow. I hope you are following. All right, then now I can actually redistribute, arrange all those terms and the magic will happen. So that means rearrange all those terms, minus infinity to infinity d omega C omega exponential minus i omega t minus x divided by Vg, exponential minus i omega0t, exponential i omega0 over Vg plus b x. So basically, there's really no magic. What I'm doing is really to rearrange all those terms, so that this term is actually rearranged so that it's now omega times t minus x over Vg. It's an independent exponential term. And I actually extract this term times t to be returned here. I'm just rearranging things, OK? I'm not changing anything. And finally, I can merge this term and that term, and become this function field. I can immediately recognize that after this rearrangement, this is just re-writing the formula, putting all those terms in different place. Of course, you can actually review this part of the lecture in the lecture notes later. But basically, we're not doing anything fancy but rearranging things over in different place. Then I can actually quickly identify what I am trying to integrate. So this integration is over omega. Therefore all those terms are now related to omega. Therefore, they are just some terms which are sitting there, they don't participate. And if you focus on this part, what is this? If you compare that to the original equation of which I have here. If you compare that to the original fs equation here, you can't immediately identify that actually that's a function of fs. Originally this function fs is a function of t. And I'm going to that board now. This is actually fs with t minus x over Vg. Surprisingly simple. Now let's look at the right hand side, this mass here. This is actually K0, which actually you cannot see anymore. It's in the back of this board. And then if you combine these two terms, basically what you get is exponential minus i omega0t minus K0x. So look at what we have done. I got started with this Fourier transform functional form of fs. I multiplied fs by cosine omega0t and go to the complex notation. It becomes exponential minus i omega0t. If I multiplied that, I get my f function, which is like this. You get additional term there. I rearrange things and change the origin, and I can rewrite ft in this functional form. And I can have a relation between the C related to fs to the C related to f of t. I propagate ft over the full space, and attain my sine, which is the amplitude as a function of place and the time. Until here, everything is exact. Then I have introduced assumption, which is C of omega is only sizable, only contributing, around omega zero, therefore I can do approximation form for the K function, which is this functional form. Then I just do the integration. Then I found that, interesting! This side is-- you should be taking the real part of this thing. This side have two components. The first component is fs, which is the original signal you put in, the signal you want to send. It's actually progressing at the speed of group velocity. So now you understand what this group velocity means. That's the speed of the signal you want to send in the AM radio. And this thing is actually modulated by exponential function, which is actually the propagating at the speed of Vp, equal to omega0 over K0. So the carrier still, after you actually include many, many terms contracting the f function, the sine which is the amplitude, the trick is that only the omega value around omega0 contributes. If that happen, then you can see that there are two structures actually propagating at different speeds, and that you can actually understand the structure independently. That means your signal will not be distorted if you're sending it this way. But the difference is that the speed of the signal you are sending is actually at the speed of group velocity. That is actually the amazing fact which actually enables us to send signal over thousands and thousands of miles away from the source. So what is actually done is actually that, suppose you have some kind of radio station. You can send the radio, and the radio will go over the place, and got refracted by atmosphere-- the atmosphere on Earth. Got refracted, and the receiver from some place which is really distant from the source can still see it without any dispersion, as we show here. And it's actually going to be propagating at the speed of group velocity. So you may not actually believe that. How about we do a simulation like what we did before with MIT wave? So this is actually the example which we did last time. We have an nit wave. We can compose that into many, many pieces. And then see how it evolved as a function of time. This is actually without dispersion, therefore everything is perfect. So now I would like to introduce some excitement there. If I have dispersion, like 0.1, alpha is equal to 0.1, and see will happen. Then just a reminder that things will not go super well. Wait a second, what am I doing? This is actually still without dispersion. Sorry for that. It should be-- OK, so let's take a look at the triangular case. This is now with dispersion. And you can see that as a reminder as a function of time, the shape of the signal which you would like to send is actually changing as a function of time. And after a few thousands of miles, you will not even recognize the original structure we put in. So that's the trouble we are actually facing. You can see that it's getting wider and wider et cetera. So now what will happen if I send this kind of signal. This is a signal which you have some kind of shape. You can imagine that there's sounds kind of analogue. And I am now doing the calculation to actually map all the individual components. And now I'm going to propagate through the median. And the blue is the original non-dispersive median situation. And the red is actually the propagation in a dispersive median. You can see the propagation in a dispersive median is faster, because alpha is actually larger than one-- larger than zero. So it's actually, in this case it's 0.1. And you can see that the red cosine omega0t modulated signal is progressing, and the shape of the analogue is not changing. You can see that, right? So it's very different from what we actually see before with a single triangular pulse. Now you can see that, ha! Only when n gets very large, I start to be able to feed all those little structures. That means the end value, or say the omega value, which I need is you really narrow, a very narrow range, which will actually match with what we have been doing. And now I start to propagate all those things. And you can see that the red is actually traveling faster than the blue, which is what we expect. And you can see now, in the instance they actually overlap each other, you can see that envelope, the shape of the envelope, is still the same. It's exactly what we actually printed. And that actually brings me to the end of my lecture. We have on understood how the AM radio actually works. And next time, we are going to talk about uncertainty principles. What the hell? What happened? And believe me, they are actually connected to each other. Uncertainty principle is actually highly related to wave and the vibrations. Thank you very much, and let me know if you have any questions. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 4_Coupled_Oscillators_Normal_Modes.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: And welcome back, everybody, to this fun class, 8.03. Let's get started. So the first thing which we will do is to review a bit what we have learned last time. And then we'll go to the next level to study coupled oscillators. OK. Last time, we had learned a lot on damped driven oscillators. So as far as the course we've been going, actually, we only study a single object, and then we introduce more and more force acting on this object. We introduce damping force, we introduce a driving force last time. And we see that the system becomes more and more difficult to understand because of the added component. But after the class last time, I hope I convinced you that we can understand driven oscillators. And there are two very important things we learned last time. The first one is the transient behavior, which is actually a superposition of the homogeneous solution and the steady state solution. OK. One very good news is that if you are patient enough, you shake the system continuously, and if you wait long enough, then the homogeneous solution contribution goes away. And what is actually left over is the steady state solution, which is actually much simpler than what we saw beforehand. It's actually just harmonic oscillation at driving frequency. Also, I hope that we also have learned a very interesting phenomenon, which is resonance. When the driving frequency is close to the natural frequency of the system, then the system apparently likes it. Then it would respond with larger amplitude and oscillating up and down at driving frequency. So that, we call it resonance. This is the equation of motion, which we have learned last time. You can see is theta double dot plus Gamma theta dot, is a contribution from the drag force, and omega 0 squared theta is the contribution from the so-called spring force. And finally, that is equal to f0 cosine omega d t, the driving force. And as we mentioned in the beginning, if we prepare this system and under-damp the situation, then the full solution is a superposition of the steady state solution, which is the left-hand side, the red thing I'm pointing to, this steady state solution. There's no free parameter in the steady state solution. So A, the amplitude, is determined by omega d. Delta, which is the phase is also determined by omega d. There's no free parameter. OK. And in order to make the solution a full solution, we actually have to add in this homogeneous solution back into this again. And basically, you have B and alpha, those are the free parameters, which can be determined by the given initial conditions. OK. So if we go ahead and plot some of the examples as a function of time, so the y-axis is actually the amplitude. And the x-axis is time. And what is actually plotted here is a combination or the superposition of the steady state solution and the homogeneous solution. And you can see that the individual components are also shown in this slide. You can see the red thing oscillating up and down harmonically, is steady state solution contribution. And also, you have the blue curve, which is decaying away as a function of time. And you can see that if you add these two curves together, you get something rather complicated. You will get some kind of motion like, do, do, do, do. Then the homogeneous solution actually dies out. Then what is actually left over is just the steady state solution, harmonic oscillation. And in this case, omega d is actually 10 times larger than the natural frequency. And there's another example which is also very interesting. It's that if I make the omega d closer to omega 0-- OK, in this case it's actually omega d equal to 2 times omega 0, then you can produce some kind of a motion, which is like this. So you have the oscillation. And they stayed there for a while, then goes back, and oscillates down, and stay there then goes back. OK, as you can see on there. The homogeneous solution part and steady state solution part work together and produce this kind of strange behavior. OK. And that's just another example. And if you wait long enough, again what is actually left over is the steady state solution. OK. So what are we going to do today? So today, we are going to investigate what will happen if we try to put together multiple objects and also allow them to talk to each other. OK. So if we have two objects, and they don't talk to each other, then they are still like a single object. They are still like simple harmonic motion on their own. But if you allow them to talk to each other, this is the so-called coupled oscillator, then interesting thing happen. So in general, coupled systems are super, super complicated. OK. So let me give you one example here. This is actually two pendulums that are a coupled to each other, they are actually connected to each other, one pendulum, the second one is here, OK. And for example, I can actually give it an initial velocity and see what is going to happen. You can see that the resulting motion-- OK. Remember, we are just talking about two pendulums that are connected to each other. The resulting motion is super complicated. This is one of my favorite demonstrations. You can actually stare at this machine the whole time. And you can see that, huh, sometimes it does this rotation. Sometimes it doesn't do that. And it's almost like a living creature. So we are going to solve this system. No, probably not, he knows. [LAUGHTER] But as I mentioned before, you can always write down the equation of motion. And you can solve it by computer. Maybe some of the course 6 people can actually try and write the program to solve this thing and to simulate what is going to happen. So let's take a look at this complicated motion again. So you can see that the good news is that there are only two objects. And you can see-- look at the green, sorry, the orange dot. The orange dot is always moving along a semi circle. But if you focus on the yellow dot, the yellow is doing all kinds of different things. It's very hard to predict what is going to happen. So what I want to say is, those are interesting examples of coupled systems. But they are actually far more complicated than what we thought, because they are not smooth oscillation around equilibrium position. So you can see that now if I stop this machine and just perturb it slightly, giving it a small angle displacement, then you can see that the motion is much more easier to understand. You see. You even get one of these questions in your p-set. OK, that's good news. So our job today is to understand what is going to happen to those coupled oscillators. Let me give you a few examples before we start to work on a specific question. The second example I would like to show you is a saw and you actually connect it to two - actually a ruler, a metal ruler, which is connected to two massive objects. Now I can actually give it the initial velocity and see what happens. And you can see that they do talk to each other through this ruler, this metal ruler. Can you see? I hope you can see. It's a bit small. But it's really interesting that you can see-- originally, I just introduced some displacement in the left-hand side mass. And the left-had side thing start to move or so after a while. There are two more examples which I would like to give you, introduce to you. There are two kinds of pendulums, which I prepared here. The first one is there are two pendulums that are connected to each other by a spring. And if I try to introduce displacement, I move both masses slightly and see what is going to happen. And we see that the motion is still complicated. Although, if you stare at one objects, it looks more like harmonic oscillation, but not quite. For example, this guy is slowing down, and this is actually moving faster. And now the right hand side guy is actually moving faster. Motion seems to be complicated. Also, you can look at this one. Those are the two pendulums. They are connected to each other by this rod here. And of course, you can displace the mass from the equilibrium position. I'm not going to hit-- not hitting each other. So you can displace the masses from each other. And you can see that they do complicated things as a function the time. How are we going to understand this? And I hope that by the end of this lecture you are convinced that you can as you solve this really easy, following a fixed procedure. In those examples, we have two objects that are connected to each other. And therefore, they talk to each other and produce coupled motion. Those are a couple oscillator examples. There's another very interesting example, which is called Wilberforce pendulum. So this is actually a pendulum. You can rotate like this. And it can also move up and down. It's connected to a spring. The interesting thing is that if I just start with some rotation, you can see that it starts to also oscillate up and down. You see? So initially I just introduced a rotation. Now it's actually fully rotating. And now it starts to move up and down. And you can see that the energy stored in the pendulum is going back and forth between the gravitational potential, between the potential of the spring, and also between the kinetic energy of up and down motion and the rotation. They're actually doing all those transitions all the time. So you can see-- so initially it's just rotating. And then it starts to move up and down. And this one is also very similar. But now the mass is much more displaced. And if I try to rotate this system without introducing a horizontal direction displacement, it still does is up and down motion, like a simple spring mass system. So what causes this kind of motion? That is because when we move this pendulum up and down, we also slightly unwind the spring. That can generate some kind of torque to this mass and produce rotational behavior. And you can see that this is just involving one single object. But there's a coupling between the rotation and the horizontal direction motion. So that's also special kind of coupled oscillator. So after all this, before we get started, I would like to say that what we are going to do is to assume all those things are ideal, without them being forced, without a driving force. We may introduce that later in the class. But for simplicity, we'll just stay with this idea case, before the mass becomes super complicated to solve it in front of you. And also, we can see that all those complicated motion are just illusion. Actually, the reality is that all of those are just superposition of harmonic motions. You will see that by the end of this class. So that is really amazing. OK. Let's immediately get started. So let's take a look at this system together and see if we can actually figure out the motion of this system together. So I have a system with three little masses. So there are three little masses in this system. They are connected to each other by spring. Those springs are highly idealized, the springs. And they have spring constant k. And the natural length's l0. And they are placed on Earth. And I carefully design the lab so that there's no friction between the desk and all those little masses. So once you get started and look at this system, you can imagine that there can be all kinds of different complicated motions. You can actually, for example, just move this mass and put the other two on hold. And they can oscillate like crazy. They can do very similar kind of motion. There are many, many possibilities. But if you stare at this system long enough, you will be able to identify special kinds of motion which are easier to understand. So what I would like to introduce to you is a special kind of motion which you can identify from the symmetry of this system. That is your so-called normal mode. So what is a normal mode, a special kind of motion we are trying to identify? That is actually the kind of motion which every part of the system is oscillating at the same frequency and the same phase. So that is your so-called normal mode, and is a special kind of motion, which I would like you to identify with me. And we would later realize that those special kinds of motions, which are easier to understand, actually helps us to understand the general motion of the system. You will realize that the most general motion of the system is just a superposition of all the identified normal modes. And then we are done, because we have a general solution already. So that's very good news. That tells us that we can understand the system systematically, and step by step. And then we can write the general motion of the system as a superposition of all the normal modes. So let's get started. So can you guess what are the possible normal modes of this system? So that means each part of the system is oscillating at the same frequency and the same phase. Can anybody and any one of you guess what can happen, each part of this is an oscillating at the same frequency? Yeah? AUDIENCE: If the two masses on that side are displaced the same amount and then they're -- YEN-JIE LEE: Very good. So he was saying that now I displace the right hand side two masses all together by a fixed amount, and also the left hand side, right, by a fixed amount and then let go. So that's what you're saying, right? OK. So the first mode we have identified is like this. So you have left hand side mass displace by delta x. And the right hand side two masses are also displaced by delta x. So basically you hold this three little masses and stretch it by the same-- introduce the same amplitude to all those three little masses, and let go. So that is actually one possible mode. And if we do this, then basically what you are going to see is that this is actually roughly equal to this system. They're connected to each other by two springs. And the right hand side part of the system, both masses are oscillating at the same amplitude and the same phase. They look like as if they are just single mass with mass equal to 2m. And if you introduce a displacement of delta x, then what is going to happen is that if I take a look at the mass, left hand side mass, and the force acting on this mass, the force will be equal to minus 2k times 2 delta x, because that's the amount of stretch you introduce to the spring. And that will give you minus 4k delta x. And we have already solved this kind of problem in the first lecture. So therefore you can immediately identify omega, in this case, omega a squared will be equal to 4k divided by 2m. This is actually the effective spring constant, and this is actually the mass. So that is actually the frequency of mode A. Can you identify a second kind of motion which does that? So in this case, what is going to happen is that the three masses will-- OK, one, two, and three. The three masses will oscillate as a function of time like this with angular frequency of square root of 4k over 2m. What is actually a second possible motion? Yes? AUDIENCE: All masses being stretched [INAUDIBLE] YEN-JIE LEE: Compressed. AUDIENCE: Compressed the same-- YEN-JIE LEE: Very good. I'm very lucky that I'm in front of such a smart crowd today. And we have successfully identified the second mode, mode B. So what is going to happen is that the left hand side mass is not moving. And you compress the upper one slightly and you stretch the lower one, the lower little mass to the opposite direction. The displacement is delta x, and the displacement of the second mass is delta x. So what is going to happen? What is going to happen is that the left hand side mass will not move at all because the force, the spring force, acting on this mass is going to cancel. And apparently, these two little masses are going to be doing harmonic motion. Since this left hand side mass is not moving, it's as if this is a wall and this were a single spring, k, that's connected to a little mass. And it got displaced by delta x. So what will happen is that this mass will experience a spring force, which is F equal to minus k delta x. Therefore, we can immediately identify omega b squared will be equal to k over m. So you can see that we have identified two kinds of modes, which every part of the system is oscillating at the same frequency and the same phase. Everybody agree? No not everybody agree. Look at this guy this guy is not moving. How could this be? This is not the normal mode. Isn't it? OK. I hope that will wake you up a bit. I can be very tricky here. I can say that this mass is also oscillating, but with what amplitude? AUDIENCE: Zero. YEN-JIE LEE: Zero amplitude. Right So the conclusion is that, aha, everybody is actually oscillating at the same frequency, but these guy with zero amplitude. AUDIENCE: Are they oscillating at the same phase as well? YEN-JIE LEE: Yeah. Oh very good question. Another objection I receive. So life is hard for me today. Hey. This guy is oscillating out of phase. These two guys are out of phase. But I can argue that the amplitude of the first mass is actually has a minus sign compared to the second mass. Then they are again in phase. So very good. I like those questions. And I hope I have convinced you that everybody is oscillating, although you cannot see it, because the amplitude is small, is zero. And they are all oscillating at the same phase. Yes. AUDIENCE: How come there's only one mass? YEN-JIE LEE: Oh, the right hand side? AUDIENCE: Yeah. YEN-JIE LEE: Oh, yeah. That is because the left hand side mass, the 2m one, is actually not moving. Because they are two spring forces, one is actually pushing the mass, the other one's pulling the mass. And they cancel perfectly. Therefore, it's as if those two guys are not-- they don't find each other. And then it's like, they are just tools mass connected to a wall along. And then you can now identify what is the frequency. OK. Very good. So we make the made a lot of the progress from the discussion. And now I would like to ask you for help. What is the third oscillation? Yes? AUDIENCE: There's no third normal mode. YEN-JIE LEE: There's no third normal mode. AUDIENCE: There's no third normal mode because there are restricted to one dimension. I can not imagine another mode that would not displace the central mass. YEN-JIE LEE: Very good. That's very good. On the other hand, you can also say, I also take the center mass motion as one of the normal mode. I think that's also fair to do that. Very good observation. You can see that the whole can move simultaneously. I can also argue that they are oscillating at the same frequency and the same phase, because they are all moving together. So these are the 2m connected to mass one. All of them are moving in the same direction. So now I can calculate the force. What is the force? F is 0. Therefore, omega c is 0. So you can the small limit of omega. So of course, I can pretend that those mass are connected to a really, really small spring to the wall with is a spring constant k'. And I have k' goes to zero. And they are actually going to oscillate with omega c goes to zero. So in this case, the amplitude is going to increase forever, because you have A sin omega c t. And this roughly A omega c t. And this is just vt. So what I want to argue is that this is actually also oscillation, but with angular frequency zero. And the general motion can be in written as vt times c, for example, some constant. Any questions? So what I'm going to do next may amaze you. Very good. So we have identified three different kinds of modes. We have mode A, which is with omega a squared equal to omega a squared. Where is omega a squared. There. It's 4k over 2m. And also, the motion is like this. x1 equal t A cosine omega a t plus phi a. x2 is equal to minus A, because they have different sine. So if the motion is in the left hand side direction, then the two masses are oscillating in the opposite direction. So therefore, I get a minus sign in front of A. Cosine omega a t plus phi a. x3 will be also equal to minus A cosine omega a t plus phi a. Of course, I need to define what this x1, x2, x3. That's why most of you got super confused. So the x1, what I mean is that is that the displacement of the mass 2m, I call it x1. The displacement of the upper mass, the upper little mass, I call it x2. And finally, the displacement of the third mass, I call it x3. Therefore, you can see that mode A, you have this kind of motion. The amplitude of the first mass is A. Therefore, if I define that to be A, then the second and third one, or the amplitude will be defined as minus A. And you can see that all of them are oscillating at fixed angular frequency, omega a, omega a, omega a; and also fixed phase, phi a, phi a, phi a. Of course, we can also write down what we get for mode B. For mode B, the left hand side mass is not moving, stay put. And the other two masses are oscillating at the frequency of omega b. And amplitude, they differ by a minus sign. OK. Omega b squared is equal to k over m from that logical argument. And then we get x1 equal to 0 times cosine omega b t plus phi b. x2, I get B cosine omega b t plus phi b. x3, I get minus B cosine omega b t plus phi b. Any questions here? Finally, mode C. All the mass, x1 is equal to x2 is equal to x3, is equal to C plus vt. So you can see that we have identified three modes, mode A, mode B, and the mode C. And there are three angular frequencies which we identified for all of those normal modes, omega a, omega b, and omega c. And you can see that we also identified how many free parameters. One free parameter, two, three, four, five, and six. If you careful, you write down the equation of motion of this system, you will have three coupled differential equations. And those are second order differential equations. If you have three variables, three second order differential equations. If you manage it magically, with the help from a computer or from math department people, how many free parameter would you expect in you a general solution? Can anybody tell me well how many? I have three second order differential equations. Yes? AUDIENCE: 6? YEN-JIE LEE: 6. So look at what we have done we identified already 1, 2, 3, three normal modes. By there are 1, 2, 3, 4, 5 6, six free parameters. That tells me I am done. I'm done. Because what is the general solution? The general solution is just a superposition of mode A mode B and mode C. You have six free meters to be determined by six initial conditions, which I would like-- I have to tell you what are those initial conditions. So isn't this amazing to you? I didn't even solve the differential equation, and I already get the solution. And you can see another lesson we learned from here is that, oh no, you can imagine that the motion of the system can be super complicated. This whole thing can do this, all the crazy things are all displaced, and the center of mass can move, as you said. But the result is actually very easy to understand. It's just three kinds of motion, the displacement, and two kinds of simple harmonic motion. We add them together. And then you get the general description of that system. So everything is so nice. We understand the motion of that system. But in general, life is very hard. For example, now I do something crazy here. I change this to 3. What are the normal modes? Can anybody tell me? It becomes very, very difficult, because there's no general symmetry of that kind of system. So we are in trouble. One of the modes maybe still there, which is actually mode B. But the other modes are harder to actually guess. So you can see that that already brings you a lot of trouble. And you can see that I can now couple not just two objects, I can couple three objects, four objects, five objects, 10 objects. Maybe I will put that in your p set and see what happens. And you can see that this becomes very difficult to manage. So what I'm going to do in the rest of this lecture is to introduce you a method which you can follow in general to solve the question and get the normal mode frequencies and normal modes. So we will take a four minute break. And we come back at 12:20. So if you have any questions, let me know. What we are going to do in the following exercise is to try to understand a general strategy to solve the normal mode frequencies and the normal mode amplitudes, so that you can apply this technique to all kinds of different systems. So what I am going to do today is to take these three mass system, and of course as usual, I try to define what is this coordinate system? The coordinate system I'm going to use is x1 and x2 an x3 describing the displacement of the mass from the equilibrium position. And the equilibrium means that there's no stretch on the spring. The string is unstretched. It's at their own natural length, l0. So once I define that, I can do a force diagram analysis. So that starts from the left hand side mass with mass equal to 2m. I can write down the equation of motion, 2m x1 double dot. And this is going to be equal to k x2 minus x1 plus k x3 minus x1. So there are two spring forces acting on this mass, the left hand side mass. The first one is the upper spring. The second one is coming from the lower one. And you can see that both of them are proportional to spring constant k, and also proportional to the relative displacement. And you can see that the two relative displacement, which is the amount of stretch to the spring, is actually x2 minus x1, and the x3 minus x1. Am I going too fast? OK. Everybody's following. And you can actually check the sign. So you may not be sure. Maybe this is your x1 minus x2. But you can check that, because if you increase x1, what is going to happen? This term will become more negative. More negative in this coordinate system is pointing to the left hand side. So that makes sense. Because if I move this mass to the right side, then I am compressing the springs. Therefore, they are pushing it back. Therefore, this is actually the correct sign, x2 minus x1. The same thing also applies to the second spring force. So that's a way I double check if I make a mistake. Now, this is actually the first equations of motion. And I can now also work on a second mass. Now I focus on a mass number two. The displacement is x2. Therefore the left hand side of Newton's Law is m x2 double dot. And that is equal to the spring force. The spring force, there's only one spring force acting on the mass. Therefore, what I am going to get is k x1 minus x2. Everybody's following? You can actually check the sign carefully, also. And finally, I have the third mass, very similar to mass number two. I can write down the equation of motion, which should k x1 minus x3. So that is my coupled second order differential equations. There are three equations. And all of them are second order equations. So this looks a bit messy. So what I'm going to do Is no magic. I'm just collecting all the terms belonging to x1, and put them together, all the terms belonging to x2, putting all together, and just rearranging things. So no magic. So I copied this thing, left hand side. 2m x1 double dot. And the dot will be equal to minus 2k x1 plus, I collect all the times related to x2, plus k x2, there's only one term here, then plus k x3. I'm just trying to organize my question. So you can see that I collect all the terms related to x1 to here. Minus k, minus k, I get minus 2k. And the plus k for x2, plus k for the x3. And I can also do that for m x2 double dot. That will be equal to k x1 minus k x2 plus zero x3, just for completeness. I can also do the same thing for the third mass, m x3 double dot. This is equal to k x1 plus 0 x2. There's no dependence on x2, because x1 and x2-- x3 and x2 are not talking to each either directly. Finally, I have the third, which is minus k x3. Now our job is to solve those coupled equations. Of course, you have the freedom, if you know how to solve it yourself, you can already go ahead and solve it. But what I am going to do here is to introduce technique, which can be useful for you and make it easier to follow. It's a fixed procedure. So what I can do is the following. I can write everything in them form of a matrix. How many of you heard the matrix for the first time? 1, 2, 3, 4. OK. Only four. But if you are not being familiar with matrix, let me know, and I can help you. Let the TA know. And also, there's a section in the textbooks, which I posted on announcement, which is actually very helpful to understand matrices. But sorry to these four students, we are going to use that. And maybe, you already learn how it works from here. So one trick which we will use in this class is to convert everything into matrix format. What I am going to do is to write everything in terms of M, capital X, capital M, capital X double dot equal to minus capital K capital X. Capital M, capital X, and capital K, those are all matrices. Because I write this thing I really carefully, therefore we can already immediately identify what would be M, capital M and capital X and a K. So I can write down immediately will be equal to 2m, 0, 0, 0, m, 0, 0, 0, m. Because there's only one in each line, you only have one term. X1 double dot, x2 double dot, x3 double dot. And also, you can write down what will be the X. This is actually a vector. X will be equal to x1, x2, x3. Finally, you have the K? How do I read off K? Careful, there's a minus sign here, because I would like to make this matrix equation as if it's describing a simple harmonic motion of a one dimensional system. So it looks the same, but they are different because those are matrices. But therefore, I have in my convention I have this minus sign there. Therefore, when you read off the K, you have to be careful. So what is K? K is equal to 2k. You have the minus 2k here in front of x1. But because I have a minus sign there, therefore this one is actually taken out. So we have 2k there. Then you have minus k, minus k, minus k, k, 0. Minus k, plus k, 0. And finally, you can also finish the last row. You get minus k, 0, k. K becomes minus k. Minus k becomes k. So we have read off all those matrices successfully. So you may ask, what do they mean? Do they get the meaning? M, K, X, what those? M, capital M matrix, tells you the mass distribution inside the system. So that's the meaning of this matrix. X is actually vector, which tells the position of individual components in the system. Finally, what is K? K is telling you how each component in the system talks to the other components. So K is telling you the communication inside the system. So now we understand a bit what is going on. And as usual, I will go to the complex notation. So I have xj, the small xj are the position of the mass, x1, x2, and x3. xj will be real part of small zj. Small xj equal to real part of zj. Therefore, I can now write everything in terms of matrices again. So now I can write the solution to be Z, the capitol z is a matrix, exponential i omega t plus phi. This is the guess the solution I have. A1, A2, and A3. Those are the amplitudes, amplitude A of the first mass, amplitude of the second mass, amplitude of the third mass, in their normal mode. And all of those are oscillating at the same frequency, omega, and the same phase, phi. Does that tell you something which we learned before? Oh, that's the definition of the normal mode. I'm using the definition of the normal mode. Every part of the system is oscillating at the same frequency in the same phase. And we use that to construct my solution. The complex version is exponential i omega t plus phi, oscillating at the same frequency, oscillating at the same phase. And those are the amplitude, which I will solve later. OK, any questions? I hope I'm not going too fast. If everybody can follow, now I can go ahead and solve the equation in the matrix format. So now I go to the complex notation. So the equation M X double dot equal to minus KX becomes M Z double dot equal to minus KZ. And also, I can immediately get the Z double dot will be equal to minus omega squared Z, because each time I do a differentiation, I get i omega out of the exponential function. And I cannot kill that exponential function, so it's still there. Therefore, I get minus omega squared in front of Z. I hope that doesn't surprise you. So that's very nice and very good news. That means I can replace this Z double prime with minus omega squared Z. Then I get minus M omega squared Z. And this is equal to minus KZ. And I can cancel the minus sign. That becomes something like this. So, I can now cancel the exponential i omega t plus phi, because I have Z in the left hand side. And exponential i omega t plus phi is just a number. So therefore, I can cancel it. So what is going to happen if I do that? Basically, what I'm going get is I get M omega squared A equal to K A. I'm trying to go extremely slowly, because this is the first time we go through matrices. So now you have this expression. Left hand is a matrix, M, times some constant, omega squared. I can actually get omega squared in front of it, because this is actually just a number. A is just a vector, which is A1, A2, A3, also a matrix. K is actually how the individual components talks to the others. So that's there, times A. Now I would like to move everything to the right hand side, all the matrices in front A to the right hand side. Then I multiply both sides by M minus 1. So I multiply M minus 1 to the whole equation. M minus 1, what is M minus 1? The definition is that the inverse of M is called M minus 1. M minus 1 times M is equal to I, which is actually 1, 1, 1. Therefore, if I do this thing, then I would get omega squared. M minus 1 times M becomes I, unit matrix. And this is equal to M minus 1 K A. And be careful, I multiply M minus 1, the inverse of M, from the left hand side. That matters. So now I can move everything to the same side. I moved the left hand side term to the right hand side. Therefore, I get M minus 1 K minus omega squared I. Those are all matrices. Times A, this is equal to 0. Any questions? So a lot of manipulation. But if you think about it, and you are following me, you'll see that all those steps are exactly identical to what we have been doing for a single harmonic oscillator. Looks pretty familiar to you. But the difference is that now we are dealing with matrices. AUDIENCE: What is A? YEN-JIE LEE: Oh, A. A is actually this guy. I define this to be A. And that means Z will be exponential i omega t plus phi times A. I didn't actually write it explicitly. But that's what I mean. Any more questions? Yes? AUDIENCE: [INAUDIBLE] is for [INAUDIBLE]?? YEN-JIE LEE: Can you repeat that? AUDIENCE: So this whole process, this is mode A, right? YEN-JIE LEE: Yeah. So this whole process is for, not really the for mode A. So that A may be confusing. But in general, if I have a solution, and I assume that the amplitude can be described by a matrix. So it's in general. And you'll see that we can actually derive the angular frequency of mode A, mode B, and mode C afterward. I hope that answers your question. So you see that for in general, what I have been doing is that now, all those things are equivalent to the original equation of motion. What I am doing is purely cosmetic. You see, make it beautiful. So all those things, this thing is exactly the equivalent to that thing, up there. Up to M X double dot equal to minus K x. Cosmetics. Beautiful. Looks-- I like it. All right. Then what I have been doing is that now I introduce using a definition of normal mode. I guess the solution will have this functional form. Z equals to exponential i omega t plus phi, everybody oscillating at the same frequency, the same phase. Frequency omega, phase phi. And everybody can have different amplitude. You can see from this example, normal modes, they can have different amplitude. The amplitude is what? I don't know yet. But we will figure it out. Then that's my assumption. The definition of normal mode. And I plug in to the equation of motion. Then this is what we are doing to simplify the equation of motion. There's no magic here. If I plug in the definition on normal mode to that equation, this is actually going to bring you to this equation, matrix equation. So if you have learned matrices before, you have something, some matrix, times Z. This is equal to zero. A is not zero. I hope. If it's zero, then the whole system is not moving. Then it's not fun. So if A is not zero, then this thing should be-- this thing times A should make this equation equal to 0. So what is actually the required condition? I get stuck, and of course again, my friend from math department comes to save me. That means if this thing has a solution, this equation has a solution, that means that determinant of M minus 1 K minus omega squared I has to be equal to 0. So that is the condition for this equation to satisfy this to be equal to 0. And just to make sure that I don't know what is the angular frequency omega yet. I don't know what is the phi yet. We can actually solve the angular frequency, omega. So now, turn everything around. And basically now, using this normal mode definition, and some mathematical manipulation, the condition we need for this equation to satisfy equal to 0, is determinant M minus 1 K minus omega squared I. I can write down M minus 1 K minus omega squared I explicitly, just to help you with mathematics. M minus 1 K is equal to 1 over 2m, 0, 0, 0, 1/m, 0, 0, 0, 1/m. It's just the inverse matrix of the M matrix. Therefore, now I can write down the explicit expression of M minus 1 K minus omega squared I. This will be equal to k over m minus omega squared, minus k over 2m, minus k over 2, minus k over m, k over m minus omega squared, 0. I will write down all the elements first. Then I will explain to you how I arrived at the expression. OK. So this is M minus 1 k. The definition of M minus 1 is that. And the definition of K is in the upper right corner of the black board. Therefore, if you multiply M minus 1 K, basically, the first column will get-- wait a second. Did I make a mistake? No. OK. So basically, what you arrive at is k/m, k/m, k/m. And also, the minus k over 2m for the rest part of the matrix. And the minus omega squared I will give you the diagonal component. Yes? AUDIENCE: Why do you have to take the determinant and set it equal to 0 instead of just setting that equal to zero? AUDIENCE: This is a matrix. So these are the matrix. So a matrix times A will be equal to zero. The general condition for that to be satisfied is more general. It's actually the determinant of this matrix equal to zero. Because this is actually multiplied by some back to A. So I think there are mathematical manipulation. Basically, you would just collect the terms. And then calculate M minus 1 K first. And the minus omega squared I will give you all the diagonal and terms have a minus omega square there. And that is actually the matrix. And of course, I can calculate the determinant. So if I calculate the determinant, then basically I get this times that times that. So what you get is k over m minus omega squared times k over m minus omega squared times k over m minus omega squared. So these are all diagonal terms. And the minus 1 over 2 k squared over m squared, k squared over m squared. sorry. Minus omega squared. So that's this off diagonal term, this times this times that. OK. It will give you the second term. And the third one, which survived because of those zeros, many, many terms are equal to 0. And then the third term, which is nonzero, is again minus 1 over 2k squared over m squared, k over m minus omega squared. And this is actually equal to 0, because the determinant of this matrix is equal to zero. Everybody following? A little bit of a mess. Because I have been doing something very challenging. I'm solving a 3 by 3 matrix problem in front of you right. So the math can get a bit complicated. But next time, I think we are going to go to a second order one, 2 by 2 matrix. And I think that will be slightly easier. But the general approach is the same. So basically, you calculate M minus 1 K minus omega squared. Then you get what is inside, all the content inside this matrix. Then you would calculate the determinant. And basically, you can solve this equation. Now I can define omega0 squared to be k/m. And I can actually make this expression much simpler. Then basically, what you are getting is omega0 squared minus omega squared to the third minus 1/2 omega0 to the fourth, omega0 squared minus omega squared. Minus 1/2 omega0 to the fourth, omega0 to the square, minus omega squared. And this is equal to 0. And you can factor out the common components. Then basically, what you are going to get is, you can write this thing to be omega0 squared minus omega squared, omega squared. Because all of them have omega squared. And omega squared minus 2 omega0 squared. And that's equal to 0. So I am skipping a lot of steps from this one to that one. But in general, you can solve this third order equation. And I can first combine all those terms together. And then I factor out the common components. Then basically, what you are going to arrive at is something like this. A lot of math here. But we are close to the end. So you can see now what are the possible solutions for omega. That is the omega, unknown angular frequency we are trying to figure out. You can see that there are three possible omegas that can make this equation equal to 0. The first one is omega equal to omega0. The second one is square root of omega 0, coming from this expression, that omega squared minus 2 omega zero squared. If omega equal to square root 2 omega0, this will be equal to zero. And that will give you the whole expression equal to 0. Then finally, I take this term. And then you will get zero. Omega squared, if omega is equal to 0, then the whole expression is 0. I have defined omega0 squared to be equal to k over m. Therefore, I can conclude that omega squared is equal to k over m, 2k over m, and 0. Look at what we have done, a lot of mathematics. But in the end, after you solve the eigenvalue problem, or the determinant equal to zero problem, you arrive at that there are only three possible values of omega which can make the determinant of M minus 1 K minus omega squared I equal to 0. What are the three? k/m, 2k/m, and 0. If you look at this value, then we'll say, this is essentially what we actually argued before, right? Omega A squared is equal to 4k over 2m is 2k over m. Wow. We got it. The second one is, we think about really keep a straight question in my head and understand this system. The second identified normal more is having omega squared be equal to k/m. I got this also here magically, after all those magics. And finally, the third one, the math also knows physics. It also predicted that this is one mode which have oscillation frequency of 0. Isn't that amazing to you? But that also gives us a sense of safety. Because I can now add 10 pendulums, or 10 coupled system to your homework, and you will be able to solve it. So very good. This example seems to be complicated. But the what I want to say, I have one minute left, is that what we have been doing is to write the equation of motion based on force diagram. Then I convert that to matrix format, and X double dot equal to minus KX. Then I follow the whole procedure, solve the eigenvalue problem. Then I will be able to figure out what are the possible omega values which can satisfy this eigenvalue problem or this determinant. M minus 1 K minus omega squared I equal to 0 problem. And after solving all those, you will be able to solve the corresponding so-called normal mode frequencies. You can solve it. And of course, you can plug those normal mode frequencies back in, then you will be able to derive the relative amplitude, A1, A2, and A3. So what we have we learned today? We have learned how to predict the motion of coupled oscillators. That's really cool. And then next time, we are going to learn a special kind of motion in coupled oscillators, which is the big phenomena. And also, what will happen if I start to drive the coupled oscillators? So I will be here if you have any questions about the lecture. Thank you very much. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 12_Maxwells_Equation_Electromagnetic_Waves.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: Welcome back, everybody to 8.03. So today we are going to continue discussions on the examples which we started the last time, sound waves, and, this time EM waves, which can be described by wave equations. So far, what we have learned is that there are three different kinds of systems we've discussed in a lecture or in a textbook. And the first one is actually a string, a very long string, system with constant tension and mass on the string. And the behavior of the string obey wave equation, and can be described by a wave equation. We also can produce a density wave with a spring. And basically the density wave or spring can also be described by wave equations. So that's as you described in the textbook. Finally, last time we actually discussed sound waves. We have an open pipe, and then we can have air inside the pipe. And the behavior of the air, or the molecules inside the open pipe, can be described by wave equations. Crashes So what we are going to do today is to discuss with you a special kind of wave, which is electromagnetic waves. And that's actually slightly different from what we have learned in the last few lectures. And we see what this is different today in the lecture. All right. So this essentially is a reminder of Maxwell's equations. So basically what is written here is the differential form of Maxwell's equations. So the first law is Gauss law. It says should the divergence of e, the electric field, is equal to rho, which is the charge density as a specific point, divided by epsilon zero, which is actually a constant. We'll call it permittivity of this constant. OK? Which should relay the divergence of e and the density of the charge at this specific point. And the second law is actually Gauss law for magnetism. This is actually the divergence of b equal to 0. So divergence b is always equal to zero because we haven't yet discovered the magnetic monopole yet. Right? So maybe you have discovered it one time, at some time, in your experiment. Please tell me now. I want to be the first with who knows how to do that. [LAUGHS] All right? So promise me. The third one is Faraday's law. It's curve of e equal to minus partial e partial t and the b, as a reminder, is a magnetic field vector. And in the last law is actually Ampere's law. It's actually the curve of b equal to mu 0. Mu 0 is actually a constant, permeability. Which would lay the current and displacement current. Epsilon 0, partial e, partial t, to the curve of b. OK? And I would like to draw your attention to these term. This very important term is actually Maxwell's addition. OK? Without Maxwell's addition, there would be no electromagnetic wave. Then you could not see me. OK? [LAUGHS] All right. So, what we are going to discuss today is a simpler case at the beginning. So what will happen if we go to a vacuum? Going to vacuum means there will be no material charges floating around, and that means rho will be equal to 0. Therefore, the divergence of e will be equal to 0. And also in the last question Ampere's law, say which is that the current density will be equal to 0. Therefore, the function of curl of b equal to mu 0, epsilon 0, partial e, partial t. OK? So before we go into the discussion of Maxwell's equation's implication, I would like to remind you about some mathematics which will be used in this lecture. I hope you have seen this in other courses or 8.02. So as you can see, we use del here, which is a vector. This vector is defined as partial x, partial y, and partial z, in the x, y, and z direction. OK? So this is actually some kind of operator. You see that again. A lot more operators in 8.04. And we make this definition because I'm lazy. Because I don't want to write so many partial, partial x, partial, partial y, partial, partial z again and again. Therefore we define del, which is like this. Looks really crazy, but it really makes our lives much easier. OK? So that's the whole reason. As a physicist. And as we discussed before, we have divergence, which is defined here: del times a, both of them are vectors. Y is the operator vector, the other y is actually really a vector. You basically get partial ax, partial x, plus partial ay, partial y, plus partial az, partial z. So basically you just multiply them like a normal operation. And you can actually get this question. OK. Then finally there's curl. Curl is actually del cross a. So basically, maybe in the past you see this complicated formula. You know, it had maybe no meaning to you. And one easy way to remember this curl is to not care about this. Don't look at the right hand side part. But just remember that you can actually construct this curl by determining a matrix. In the matrix, I can fill the first row by x, y, and z unit vector. And the second row, I filled it with the counting of del. Finally I feel the content of the matrix with a vector. Then you will be able to calculate the determine of this back matrix, then you naturally would get this very long formula. So you don't really need to remember the formula, but you will be able to know how to calculate it really easily. OK? OK. So we talk about divergence. We talk about curl. What does that mean? Divergence, curl, what does that mean? So divergence is actually some kind of measure which measures how much the vector v spreads out, or diverges, from a point of interest. So in this example, this vector field-- vector field means at any point in the space which I am discussing, there is a vector associated with that. I call it vector field. We know scalar field very much. For example, the temperature as a function of position is a scalar field, right? So, every point you have scalar corresponding to that point. And in the case vector field, every point you have a vector connected to that point. And if I arrange the vector field like that, each arrow is actually a straight dimensional the vector. Then if I evaluate the divergence and you see the heart, it looks like something is really spreading out from the center of that graph. And that will give you positive divergence. OK? So that's the physical meaning of this formula. And the second formula which we discussed is the curl. So curl is actually del cross a. It's a measurement of how things are curling around a point of interest. OK? So you can see that if I arrange my vectors in a space like that, then you will see that something is really rotating around that specific point. Therefore, if we evaluate the curl, you would get the nonzero value. So that's actually the physics intuition which we can or the mathematics intuition which we can actually get before the discussion of Maxwell's equations. So if you accept those ideas, let's take a look at what we have here, especially in the vacuum case. OK, so in a vacuum case, you have a curl of e equal to minus partial p, partial t. What does that mean? That means, if you change the magnitude of the magnetic field, now we introduce a curling around thing in the e field. So if you change the size of the b field, then the e field will start to curl around, doing this. And on the other hand, if you change the electric field, that will do something, which is curling around in the b field. All right, so do you have any questions? I hope everybody's familiar with this notation. So from here actually Maxwell, see the light. [LAUGHS] Can you see it? Maybe not yet. Maybe we are slightly slower than Maxwell, but we will see that together in this lecture. For that I would need as usual help from the math department. So we are going to use this identity. This identity is curl of curl of a would be equal to del, divergence of a, minus del dot del, a. So this is an identity which we learned from the math department. And of course, if you are patient enough, you can actually expand all those terms and compare the left hand side of the formula and right hand side of the formula. And you will see that really this works. So I'm not going to do that here in front of you. So if you accept this is an identity, and then usually when we have del times del, we call it Laplace. And usually we write it as del squared. With this formula, I can now put my electric field into this formula. assuming that I am working in a situation of a vacuum and I plug in my electric field into that formula. Then this is actually what I am going to get. Curl of e. And this will be equal to del, divergence of e minus del squared e. OK? And based on the four Maxwell's equations, we can immediately recognize that divergence of e is equal to 0, because I don't have charges around. Therefore you, cannot not introduce a gradient or divergence. You can introduce positive divergence in the electric field. Therefore, when you evaluate the divergence of the electric field, that is equal to 0. According to that formula, Gauss law. And you can also take a look here. We have curl of e, according to this formula. Basically you can conclude that this will be equal to minus partial b, partial t according to Faraday's law. So if I look at the left hand side, that would be equal to the curl of minus partial b, partial t. And this will be equal to basically, I can take the minus sign out and take the partial partial t out. And basically you have curl of b. And according to Ampere's law, this would be equal to minus mu 0, epsilon 0, partial square e, partial t. OK, everybody is following? So basically what I have been doing is copy the left-hand side and make use of the Ampere's law. And basically you get minus mu, epsilon zero, partial square e, partial t squared And this thing, the left hand side, is equal to the right hand side. On the right hand side, what is left? This is equal to 0. So this is gone. This is equal to minus del squared, e. I can cancel the minus sign. Then basically what I am going to get is del squared e. And this will be equal to mu zero epsilon 0, partial square e, partial t squared. Wow, this is what? This looks like, what? Wave equation again. Oh my god. [LAUGHTER] But there is some difference. This is different from what we've seen before, right? Before, the wave equation only has partial squared partial x squared. This time, you have this del square. Very strange, right? So what is this? Del square is actually partial square, partial x squared cross partial square partial y square, plus partial square, partial z square is the operator, which will have three components. And basically, if you do this calculation, you are going to have how many times? If you do this del square e, how many times you have? You have how many? Any anybody help me? Yeah, you have three times in x direction, you have three times in y direction, you have three times in z direction. Therefore how many times? You have nine times, because each operator is acting out the vector. OK. So it's very important because this is a common mistake. So you have nine times. and it looks really like the wave equations it tastes like wave equation, it looks like equation, it feels like equation - that wave equation - and therefore is really the wave equation, right? [LAUGHTER] OK so this is a three-dimensional wave equation. Very cool. So we are increasing the dimension. So I can write it down more explicitly. So basically what I'm getting is partial square e partial x squared, partial square e, partial y square, plus partial square e, partial z square. And this is equal to mu zero, epsilon zero, partial square e, partial t squared. OK? So Maxwell sees this when he adds this additional term here. As you can see, if I don't have this additional term, the displacement of current from Maxwell, what is going to happen? This curve of b will be equal to zero. So what is going to happen to this identity? This left hand side part will be equal to zero. There will be no electromagnetic waves. OK? So that's really thanks to Maxwell's work. And this is actually really an equation which changed the world, because that actually gave us a lot of insights about how we can send energy, how we can actually understand the phenomenon related to light. So what is the velocity of this wave equation? The velocity, Vp, would be equal to what we usually call c. Because you have been using this constant for a long time. And that will be equal to 1 over square root of mu zero epsilon zero. And to measure the speed of light, it takes a long time to achieve that. Let's take a look at the history. So the first attempt was done by Galileo so 1638. He was doing an experiment, and that he was trying to track the speed of light. But he was not super successful. So his conclusion was that if the speed of light is not instantaneous, then it is super fast. He says it's at least 10 times faster than the speed of sound. He said OK, this is super awesome, very fast. OK. So that's what he found. And later Romer actually made use of the orbit of Jupiter. Basically he use Jupiter and Jupiter's satellite to measure the speed of light. So when the earth is closer to Jupiter, then somehow the satellite of Jupiter appears faster than when the earth is actually away from Jupiter. Because that light have to travel through additional time. Two times the radius of the orbit the Earth. Basically that's the math that he was using. He is actually making the first computative measurement of the speed of light. And what number he found is 2 times 10 to the 9 meters per second. Then finally, again using the star the observation as a tool to actually calculate the speed of light. James actually nailed it. He found a value which is really close to the current understanding of the speed of light, which is 3 times 10 to 9 meters per second. Therefore, if you calculate that using all those constants here, you will be able to see that, indeed, from Maxwell's equation, you get-- oh, it should be 3 times 10 to the 8, not to the 9. I was saying 10 to 9. It should be 3 times 10 to the 8 meters per second. So indeed, this equation is actually predicting the speed of light to be 3 times 10 to the 8 is matching the experimental result. So that is pretty nice. And you may ask a question-- so wait a second. You said this is actually an electromagnetic wave, right? So that's actually what I was talking about. But this equation only talks about electric fields. What is happening to the magnetic field? What happened? Can we actually choose arbitrary magnetic fields? Is a magnetic field also described by the three dimensional wave equation, right? The answer is that indeed you can actually do the same exercise. You can now instead of plugging in electric field, you can plug in a magnetic field. And you will extract exactly the same conclusion. You will conclude the del square B, will B equal to Mu 0, epsilon 0, partial square, B partial to square. OK, so it is actually very important to see that the magnetic field also obey this wave equation. OK? And also from Maxwell's equation, you can see that the changing electric field will produce a curling around a magnetic field. The same thing also happens here. A changing magnetic field also produce a curling around electric field. So what does that mean? That means E, electric field create magnetic field. Magnetic field create electric field. And this happens all the time. Therefore, one cannot live without the other. They are living together. They are all together, forever. All right, so what is actually oscillating is actually both electric field and the magnetic field, right? So you may ask, OK, we are talking about vacuum. Vacuum means there is no material, no charge, no whatsoever in vacuum. So what is actually oscillating? Who is oscillating? Is the electric field and the magnetic field. This so-called field, all those vectors-- which are actually oscillating-- it's not the material, but all those vectors associated with the space, which is actually oscillating up and down. All right, so originally I would like to show you a pulse of light in front of you. And show that it's moving, but it's too fast. So I couldn't do that. [LAUGHTER] Fortunately, we have photos. Photos are actually collected the recorded photons. Emitted from the object of the interest. So this is actually how we make applesauce at MIT. We shoot-- bullet through the apple then we have the sauce. [LAUGHTER] But not sure if that's tasty enough or not. But that's how we do it in MIT-- MIT style. And the good thing is that this kind of technique is improved dramatically in these days. I would like to show you a short video, which is actually recording a video of-- it's recording experiment, which you shoot some beam of light through some plastic container. And the speed of this recording corresponds to one trillion frame per second. So this is super fast recording. And they can actually reconstruct the propagation of light through this bottle. The credit is actually to the Media Lab Camera Culture group. And let's take a look at the video. Just one second. OK, so this is actually recording at one trillion frame per second. So you can see that there's a light pulse-- a very short pulse created. And is really pass through the bottle. And it can be recorded with the technique created by Media Lab. So you can see that the pulse is really propagating through it. And the reason why we can see the pulse is because there are air, there are material which will actually change the direction of the light. And therefore, those are recorded by the camera. And they take trillions of frames of this thing, and put them together. Then basically-- and they take many, many frames, and they put them together to reconstruct this movie. So as you can see that indeed you can see the propagation of the light through this kind of video. So I hope that we enjoyed this video. And let's actually take a look at some concrete example which make use of the wave equation, which we did right here. So let's consider a plane wave solution. Things we are entering a three dimensional world. So that's actually consider so-called a plane wave. So in this example, I am considering the electric field that's actually equal to the real part of E0 exponential i, kz minus omega t. And this electric field I actually consider here is in the x direction. And if I write all the terms from this expression expressively, that's actually what I'm getting is-- x component will be E0, cosine kz minus omega t, 0 and 0. So what does this mean? What is actually a plane wave? The plane wave basically is actually fielding the whole space. What I mean by plane wave is I feel the whole space with electric field. This electric field only have one-- only one direction have non-zero value, which is x direction in this example. And then the other direction, there's no-- the magnitude is actually equal to 0. So that's actually what I mean by plane wave. And also the electric field is filling a whole space in the discussion-- in the example which I discussed here. And if I define my coordinate system like this, x is in the horizontal direction. Then that means everything is actually-- all the electric field is actually pointing toward the x direction in this coordinate system. So we have discussed progressing wave in the past few lectures. Can somebody actually tell me the direction of propagation of this plane wave? So the hint is that this is actually equal to E0, that the magnitude of the x component is equal to E0, cosine kz minus omega t. What is actually the direction of propagation of this electric field? AUDIENCE: z. YEN-JIE LEE: It's in the z direction. Yeah, very good. Because we know that this is actually going in the positive z direction. Because this is actually kz minus-- there's a minus sign-- omega t. So therefore it's going toward the positive z direction. Not x direction. x direction is where the electric field is pointing to. And the direction of propagation is toward the z direction. So there's a difference. So first thing which I would like to do is to check if this so-called plane wave solution actually satisfy the equation-- the wave equation which we derive here. Del square E equal to Mu 0 epsilon 0, partial square E, partial t square. So I can now plug that in to that equation. I can now plug in to this equation. If I plug in the wave-- the plane wave solution, which I have here to that equation-- basically, I can get the left-hand side. The left-hand side of the equation, you will get minus E0. Only one term which contribute is the partial square E partial z square term which contribute. Right? Because the magnitude of the electric field only depends on z and t. Therefore, you get minus E0, k square, cosine, kz minus omega t in the left-hand side of the wave equation. How about the right-hand side? Right-hand side actually you are taking partial derivative, which is fed to t. Basically, you get minus Mu 0-- Mu 0, epsilon 0-- I copied from that formula there. And you basically get omega square out of it because of the partial square, partial t square operator. And then you basically get cosine kz minus omega t. And of course I missed the E0 term. E0 should be copied from-- on there. So now I can show that-- OK, this cancel. Basically, this is the same cosine kz minus omega t. And E0 also cancel. And I can cancel the minus sign. What I'm going to get is k square is equal to Mu 0, epsilon 0, omega square. So that means there should be a fixed relation between k and omega, which is actually omega over k will be equal to 1 over square to the Mu 0, epsilon 0. And this is equal to c. If this is satisfied, then the plane wave is a solution to the wave equation-- only when this is actually satisfied. Otherwise we can write arbitrary plane wave equation, but they are not the solution of that equation from Maxwell's equation. So now, I have derived the electric field and also know the relation between omega, the angle frequency, and the k, the wave number. And now, what about magnetic field? So I just mentioned before, magnetic field cannot live without electric field. And electric field cannot live without magnetic field. So what is actually responding magnetic field? We can actually evaluate that. So now, the question is what is actually the magnetic field? And how is that vary as a function of time and as a function of position in the space? So we are facing a choice. So there are two equations, which relate electric field and the magnetic field. It is actually very important you make the right choice when you start your calculation. So we can use Faraday's law. We can also use Ampere's law. But there's only one, which is actually much easier to derive a solution, which is the choice of Faraday's law. If you choose to use Ampere's law to evaluate B, then you are going to get a really super complicated problem to solve. But on the other hand, if you choose to use Faraday's law to solve this problem, then you can see that the unknown is the magnetic field-- the field which I would like to evaluate. And the expression for the B is actually rather simple. It's actually just a partial derivative, partial B, partial t. So it's pretty simple and you can actually evaluate the known part. This curl looks pretty complicated. So you can actually evaluate that because you know what is the electric field. On the other hand, if you will use Ampere's Law then you will be in trouble because you don't know what is a B, xBy and Bz. And you have to evaluate curl. And you get a lot of terms, and that is actually equal to something from-- the information from the electric field. And that would be very difficult to evaluate. So therefore, what we are going to do is to use Faraday's law, curl of E will be equal to minus partial B, partial t. So basically, as I mentioned in the beginning, we can make use of the equations the determinant of matrix to evaluate the curl. So therefore, I am going to use that. And then what I'm going to get is x, y, z unit vector for fill the first row. And the partial partial x, partial partial y, partial partial z, which fill the second row of the matrix. Then I get Ex, 0, 0 because the electric field is only in the x direction. And this will be equal to-- only two terms survive because of these two 0's. So all other terms are killed, and only two terms are now 0. The first term is actually partial Ex, partial z in the y direction. And the second term is actually minus partial Ex, partial y in the z direction. Any questions? Am I going too fast? All right, so you can see that the electric field only depends on the position z. It's independent of y. Therefore, partial Ex, partial y, is actually equal to 0. Wow, this become much, much easier because there's only one term which is surviving. This is a operator. Then basically what we're going to get is I can now calculate partial Ex, partial z based on that equation, E0 cosine kz minus omega t. Then basically, what I can get is minus-- I get a K out of it, E0 sine kz, and it's omega t. So this is actually the result of the left-hand side. The right-hand side of that equation of the Faraday's law is minus partial B, partial t. So this will give you equal to minus partial B, partial t. So very important-- I don't want to drop the y direction. So this is just y direction. And this is actually a vector and this is also a vector. So what I could do is to do a integration over t. And those will cancel the minus sign. So if I integrate over t, then basically what I'm going to get is K over omega is 0, cosine kz minus omega t in the y direction only. So I'm doing a integration of t, cancel the minus sign, then this is what you want to get. And of course, k/omega is actually 1/c. So therefore, you have E0-- you can actually simplify this fraction-- and this is actually equal to E0 over c, cosine, kz minus omega t in the y direction. OK, look at what we have learned from here. What we have learned from here is that-- I got started with a plane wave solution of the electric field. And I can show that only when omega over k is equal to the speed of light this is actually a solution to my wave equation. And also because the electric field and the magnetic field have to satisfy the Maxwell's equation all the time-- because that's the fundamental law-- therefore, I can use those equations to evaluate and to find what is actually the corresponding magnetic field. And using Faraday's law and plugging in and the solving the question, I will be able to figure out that B is also what kind of wave? B is also what kind of wave I was talking about-- also? AUDIENCE: Plane wave. YEN-JIE LEE: Plane wave, right? It's also plane wave. You see? So if I got started with a plane wave in the electric field side, and I also get the plane wave in the magnetic field side. They are proportional to each other. Originally, the magnitude of the electric field is E0. The corresponding magnetic field-- the magnitude is proportional to E0. But there's a factor of 1/c difference between the magnetic field amplitude and the electric field amplitude. The third thing which we learned from here is that electric field is actually in the x direction. B field is actually not in the x direction, it's in the y direction. What we learn from here is that the direction of the B field can be determined by a simple calculation. So basically, the B is proportional-- the magnitude of B is proportional to the electric field. But you have to multiply the magnitude by 1/c. And also this is actually not correct because the B is actually in the y direction. So the original direction of the electric field is in the x direction. Also we know the direction of a propagation is in the z direction. Therefore, if I take unit vector K-- K is actually the wave number, but now I make it a vector and I take the unit vector is equal to z-- so direction of propagation. If I make this definition then I can now rewrite this relation. Basically, I can express the magnitude of B by K hat, which is the direction of propagation cross the E field. And we can check this. And then basically what you are going to get is z cross E-- then actually really z cross x, you are going to get y direction. And that is actually telling you that B and the E have a rather simple relation. And also you don't really need to go through all those calculation again because now you can see that if you know the direction of propagation and you know the direction of the electric field, then you can already evaluate what will be in the B field. So we will take a five minute break. We'll come back in 29, and we will continue the discussion of this solution. Let me know if you have any questions about the content we discussed. Welcome back, everybody. So we will continue the discussion of what we have learned from the wave equation. So basically we start with plane wave in the electric field. And this electric field is in the x direction. And we evaluated the corresponding B field which is in the y direction. And what we found is that actually we can find a pretty simple relation between electric field and the magnetic field, which is actually magnetic field vector is equal to 1/c, K hat cross E. And the K hat now which is-- you find here-- is actually the direction of propagation. So basically, in this case in the discussion we had before, the direction of propagation is in the positive z direction. So if I go ahead and visualize the whole-- solution-- plot the magnetic field and the electric field is a function of z, x and the y-- it's a function of z actually here. And I only evaluate the value at x equal to 0, and the y equal to 0. And basically, this is actually what you have. So basically, you have two sine wave. One is actually pointing to the x direction. And the other one is actually pointing to the y direction, which is the B field. And those lines doesn't mean a lot because those lines are just connecting the end point of all those vectors. So you can see that they are cosine wave structure when you connect all those vectors. And keep in mind that those are evaluated at x and y equal to 0. Therefore, what we actually get is actually a lot of vectors. So those individual arrows are vectors. And this whole thing-- this whole electromagnetic wave is propagating to the positive z direction. And those electric field and the magnetic field are propagating at the speed of light, which you see. And also you can see that the magnitude-- also I plotted here-- the magnitude, there's no phase difference between electric field and the magnetic field. This is actually not always the case. In which we will show a example probably later in the lecture. So in general, what we can actually do is to write down a general expression for the plane wave. So for example, I can have a plane wave, which is actually propagating in some direction. Which is actually given by this K vector. K vector is actually giving you information about the wave number. And also the direction of propagation. And in this case, what I am trying to construct is a solution, which is actually propagating along in the direction of the K vector. And the electric field is actually going to be pointing to a direction perpendicular to the direction of the K vector. So basically, what I can do is I can write this plane wave in this functional form. E0 is actually a vector, which is actually telling you the direction of the electric field-- E0 vector-- is actually have this function of form. And the K vector is actually placed in the exponential function-- inside the exponential function. Exponential i, k dot r minus omega t. And what is actually r? r is actually x x hat, plus y y hat, plus z z hat. And omega is actually the angular frequency which we are familiar with and that's actually equal to c times the magnitude of K, which is actually the wave number. And you can actually show that-- OK, indeed this expression can satisfy the wave equation, which we did right for the electric field. And of course there are some requirements, which is actually that the direction of the electric field have to be perpendicular to the direction of propagation. Which you can actually derive that. And finally, this expression B field equal to 1/c. K, which is the direction of propagation cross E field is still valid because basically we have shown that it works for the plane wave pointing to the x direction propagating to the z direction. We can always redefine the coordinate system because we can actually rotate this coordinate system and the physics should not change. Therefore, you must see that this expression must be still valid. And also that the direction of the electric field, which is actually proportional to E0, must be perpendicular to the direction of propagation. So that is actually what we can actually learn a general description of electric field pointing to some random direction. So we have talked about the progressing wave solution and also the plane wave and also the corresponding magnetic field. I hope that you can actually apply this-- the technique which we learned here-- if you are given a magnetic field, you must know that there must be a corresponding electric field because they cannot be separated from each other. And you can actually obtain the corresponding electric field if you are given magnetic field by using Maxwell's equations. So what is going to happen is that now if I emit this photon-- or say this electromagnetic wave from the light source, for example, that one-- the one of which is pointing at my face. Basically, my face is going to bounce some of the electromagnetic field around. And some that actually go out of the window. And then when they go out the window, maybe they are lucky they are not hitting any building in the MIT. Then what is going to happen is that they're going to propagate forever toward the end of the universe. Really, they are going straight forever as you can see from this solution. It's like some kind of wave propagating forever at the speed of light. If they don't encounter anything before the end of life of the electromagnetic wave, it's going to be propagating forever toward that direction-- escaping from that window. So that is actually fascinating and-- but we would like to introduce some more excitement to see what is going to happen. So what I'm going to do is now instead of only discussing about the plane wave-- what I'm going to do is that I would like to add a perfect conductor into the game and see what is going to happen. So what do I mean by a perfect conductor? A perfect conductor can be seen in a musical, like in a concert. [LAUGHTER] But the one which I am talking about is not that one, which is also fascinating, but this is a different system. The interesting thing is that both the conductors in the concert and this one is very busy. It's a very busy system. What do I mean by perfect conductor? That means all the little charges inside the conductor can move freely. So if they move they don't actually cause any energy. They can move around-- all the electrons inside the conductor can be moved freely without costing anything, without any of this energy dissipation. So that's actually what I mean by perfect conductor. What do I mean by a very busy system? That means whenever there are any distortion on the electric field-- any electric field approaching to this conductor-- what is going to happen is that this conductor will, oh, this is electric field, so I have to move from some of my electrons. Then it's going to cancel all the electric field inside the conductor because it cost nothing. So you have fast-- really fast the react to this change in the electric field and they really carefully arrange all the electrons. And so that the electric field is canceled. Otherwise, all those electrons will continue to move around until this happens-- this cancellation happens. So that's actually what I mean by a busy world and what I mean by a perfect conductor. If I put this conductor into game, what is going to happen? What is going to happen is that if I consider a situation-- if I have my x's defined here pointing up to be the x-axis, pointing to the right to the z-axis, pointing to the-- pointing toward you is actually the y-axis. So I can now again take the plane wave which I started with. There will be a plane wave like this. And it's going toward a piece of perfect conductor. What is going to happen is that as I actually mentioned before there are many charges all over the place. They are going to quickly rearrange-- all those charges to cancel the electric field. So if you have a plane wave going toward the perfect conductor at the surface of the perfect conductor-- the electric field will become 0. But if you have only one plane wave it cannot be-- the magnitude cannot be equal to 0 because I know the functional form. I know that the functional form of that electric field is E0 cosine kz minus omega t. If I place this perfect conductor at Z equal to 0, then I can evaluate the electric field is not equal to 0 because it is actually equal to E0 cosine minus omega t. So what can I do to cancel the electric field? This is actually very similar to the situation when you have a progressing wave on this string hitting a wall. Because the magnitude of the string which is fed to the equilibrium position is actually equal to 0. That's actually what we have learned in the last few lectures. And this is actually exactly the same situation, right? You have a progressing wave. And there is some kind of boundary, which is actually when this progressing plane wave encounter this perfect conductor. There-- the electric field-- the boundary condition-- has to be E is actually-- E, x, y, 0, which is actually the position of the z of the perfect conductor. As a function of time will be equal to 0. The whole plane will have 0 electric field. So that means there must be what kind of wave? There must be a reflective wave because of the presence of the perfect conductor. It's actually similar to the situation which we discussed there's a progressing wave hitting the wall. And this string wall system-- there will be a reflecting wave coming out of it. So therefore, what we are expecting is some kind of-- refracting wave which actually cancel the magnitude of the electric field at Z equal to 0. And then this progressing wave is going to the left-hand side direction. So now, I can actually write down the incident wave-- expression. The incident wave-- I call it Ei, this is Ei-- is expressed as E0 over 2, cosine kz minus omega t. This is actually what I putting to the system. The magnitude is E0 over 2, and it's actually propagating toward the z direction, as you can see from here. And that the direction of the electric field is in the x direction. And of course the E field will have a corresponding magnetic field, which is actually-- you can actually write it down directly using this formula-- B equal to 1 over c, K cross E. K here is z, therefore you can quickly evaluate and then conclude that the magnetic field must be in the y direction. And that the magnitude of the magnetic field would be E0 divided by 2 c. Cosine Kz and this omega t. So that is actually the incident wave. And of course I also need, as I discussed, there must be a reflective wave, Er, which you actually cancel the electric field at z equal to 0. If that cancels the incident wave, that means the magnitude must be in the opposite direction of the incident wave. Therefore, I can quickly write down what would be the resulting reflective wave that would be equal to minus E0 over 2, cosine minus Kz, minus omega t in the x direction. And then the corresponding B field, I can also write it down using exactly the same formula. And basically what I conclude is that this will be equal to E0 over 2 c, cosine minus kz, minus omega t in the y direction. So you can actually check this expression after the direction. So now, I would like to check what would be the magnitude of the electric field at z equal to 0. So basically, at z equal to 0, you have something which is proportional to cosine minus omega t for the incident wave. And then the magnitude is E0 over 2. And if you evaluate z equal to 0, basically you get minus E0 over 2 cosine minus omega t. Therefore, they really cancel and give you the desired boundary condition, which is actually E equal to 0 and the surface of the perfect conductor. So that's very nice. And this is actually the physics of which we already learned from this string wall system. So what I can do now is to calculate the total electric field if I add them together. Basically, I would get E-- total electric field, which is actually overlapping the incident and the reflective wave. What I am going to get is Ei plus Er. And basically, what I get is E0 over 2 because the incident wave and the reflective wave of the electric field is always in the x direction. Therefore, I only need to take care of the x direction. So basically, I have cosine kz minus omega t, minus-- right, because there's a minus sign here-- minus cosine minus kz, minus omega t in the x direction. And there should be-- And of course this is a cosine minus cosine. So we have all the formulas-- one from, for example, Wikipedia, or from your textbook. So you can actually calculate this-- rewrite this expression to be E0 sine omega t, sine kz. And then this is actually in the x direction. Everybody's following? I hope it's not too fast. All right, and of course, I can also calculate the corresponding B field. So it's actually again, exactly the same thing-- Bi plus Br. And basically, I will skip the step. Basically, you can add this term and that term. And you will be able to conclude that the B field will be equal to E0 over c cosine omega t, cosine kz in the y direction. This is actually pretty interesting. If you look at this result, I have a electric field, which is proportional to E0, the magnitude, sine omega t, and sine kz. What does that I mean? This is a special kind of wave which we learned before. What kind of wave is this? AUDIENCE: Standing. YEN-JIE LEE: It's a standing wave because the shape is actually fixed, the sine kz. And the magnitude is actually changing up and down at the angle frequency omega t. It's a standing wave. Another thing which is really interesting is that if we look at the expression of a electric field and the magnetic field-- if we compare that-- one is actually sine, sine. The other one is cosine, cosine. That's kind of interesting because this is actually different from what we actually usually learn from the progressing wave solution, or traveling wave solution. Where the electric field and the magnetic field are in phase. There's no phase difference. In the case of the superposition of the incident and the reflective wave-- the solution of a standing wave-- actually you can see that the phase of the B field and the E field are different. Finally, very important-- you will see that-- look at this expression-- B equal to 1/c, K cross E-- that means this only work for traveling wave. Clearly, this doesn't work for standing waves. So very important. So don't blindly apply this expression. This is only useful for the traveling wave solution. And you can see a very concrete example here. This doesn't work for standing waves. That's kind of interesting. And if you look at this result, you will see that if I don't have magnetic field-- if I only have the electric field-- there will be a instant of time, for example, t equal to 0. When t is equal to 0, sine is equal to 0. What is going to happen? You will have no electric field. That means electric field completely disappear because we are operating this system in vacuum. There's nowhere to hide. Where is the energy? The energy, fortunately-- electric field have a very good partner, which is actually B field. All the energy's actually stored in the form of magnetic field. You can see that now magnetic field is reaching the maximum. So of course I can now calculate the Poynting vector. Poynting vector is E cross B divided by mu zero. And these will be equal to one over Mu 0, Ex, By, and the z direction. There's only one term which survive. So Poynting vector is not pointing vector. It's not pointing around. There's a gentleman who is called Poynting and he has a vector. And this vector is a directional energy flux. It's a directional energy flux, or the rate of energy transfer per unit area. So that is actually the meaning of Poynting vector. And then each magnitude is proportional to E cross B divided by Mu 0. So I can calculate that. Basically, I have the E and the B-- Ex and By, then I can calculate. That would be equal to E0 square, over Mu 0, sine omega t, cosine omega t, cosine Kz, sine Kz in the z direction because I have x cross y. And I'm going to get the z direction. And I can simplify this. I have the sine, cosine. And also all have cosine, and sine. Basically, you can simplify this expression and get E0 squared divided by 4, Mu 0c sine 2 omega t, sine 2kz in the z direction. So you can see that the directional energy flux is in the z direction. It has a vector-- it has a wave number 2 times of the original wave number. And it's actually going up and down 2 times of the speed of the oscillation of the original electromagnetic wave. And this energy is actually vibrating up and down. And the shape of this energy transfer Poynting vector is actually a sine wave. So that this is actually how the microwave actually works. So basically, what we are doing is to have generate microwave inside your device. And in the oven this microwave is actually bouncing back and forth because you have metal walls, which actually bounce the electromagnetic field back and forth. And it really can cook the food by vibrating the molecules inside the food back and forth. So as you can see the magnitude of the Poynting vector is actually isolating up and down. That actually cause additional vibration and that heat up the food. So after this lecture, you will be able to say proudly that you understand the physics of microwave oven. [LAUGHTER] Thank you very much. I hope you enjoyed the lecture today. And you have any questions, I will be here. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 18_Wave_Plates_Radiation.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Today we are going to continue discussion about two very important issues. The first one is the understanding of so-called quarter wave plate. That may not mean anything to you in the beginning, but I hope after this lecture, you will know what does that mean and why that is actually interesting. The second thing is that-- the second topic we want to talk about in the lecture today is, OK, we have been talking about electromagnetic waves for a long time already, since the last few lectures. But we have never touched the topic, how do we actually create electromagnetic wave, right? And we are going to answer that in the lecture today. So that's my plan about these two topics. OK, so before we start, it's a reminder about why we have learned last time. So we have learned several situations related to polarization. So we have learned linearly polarized wave. What is linearly polarized wave? If you plot the wave amplitude as a function of time as a function of space, it's going up and down, up and down, up and down. And the direction of the field doesn't change as a function of time. So that is actually called linearly polarized light. And we also learned circularly polarized light, right? When you have two components, one is in the x direction, the other one is in the y direction, if the two components are out of phase, say, they differ by 90 degrees, for example, and they the same amplitude, then the superposition of these two waves will be a circularly polarized wave. So basically, the wave propagation looks like this. So basically, the pointy angle of the electric field is rotating as a function over time as a function of the distance it travels. And the other case, which is also interesting, is that when you have-- OK, for example, different phase difference. Like delta phi different from 90 degree, or say you have different amplitude, although the phase difference is 90 degree but you have different amplitude in the x and the y direction. If that's the case, then you have a situation which not only the direction is changing, but also the amplitude is changing as a function of time. And that we call it elliptically polarized. So that's actually the three situations we learned. And also we learned about how to make polarized light during the class. So usually, the light source we are talking about, or even present in this room, like the light from the light bulb, et cetera, those are unpolarized light, right? So that means you have a lot of electromagnetic wave emitted from the light with different initial time, emission time. And those are in slightly different angular frequency, slightly different pointing direction. So you can have all kinds of different emissions. And the sum of all those emissions is unpolarized light, which is actually the light source I have here. And you can use so-called polarizer. So the polarizer can actually kill one of the direction, and only keep all the projection to the easy axis. And in this presentation, the easy axis is in the x direction. And you can see that if you start with unpolarized light, and basically, you have that pass through a polarizer, then the resulting electric field will be pointing toward the so-called easy axis. So the easier axis to pass, right? So therefore, all the electric field perpendicular to the easy axis is illuminated. And what is left over is the electric field, which is actually parallel to the easy axis. And of course, you can rotate this polarizer and you would see that, OK, if you have a linearly polarized wave passing through polarizer, because easy axis is actually now in line with the polarization, what is going to happen is, as I said, still only the component which is actually parallel to the easy axis will passed through. And the resulting electric field will still be pointing to the direction of the easy axis. So that's actually what we have learned last time. OK, so that means we know how to generate linearly polarized wave, right? Because you just need a polarizer and put it in front of your light source, then you produce a linearly polarized save. But we didn't talk about how to produce a circularly polarized wave, right? OK, so that is actually the topic which I would like to talk about. So let's take a look at the diagram here. So assuming that I have a single layer of sheet, which I call wave plate. This is actually the zoom in and zoom in of that sheet. And the interesting property of this wave plate sheet is that the refraction index in the x direction and the refraction index for the linearly polarized wave in the y direction, they are different. That can happen, right? Because when we were discussing two-dimensional and three-dimensional waves, the dispersion relation can be dependent on the k vector, right? So that should not surprise you by now. And it depends on the structure of the material you use to make this wave plate. So therefore, you can have different velocity when you have an incident where pointing in the x direction, and compared to an incident where pointing in the y direction. So in short, we can actually summarize this kind of information, the dispersion relation, into two components. One is the velocity, the phase velocity in the x direction, which is denoted as nx. Just a reminder, the speed of the light will be equal to c divided by nx, right? So larger n means smaller speed of light in material. And if that happens, if nx is different from ny, what is going to happen is that if you have an incident wave, when it passes through this wave plate, what is going to happen is that the x component, the delay in phase in the x component, would be different from the delay in phase in the y component. And that is, essentially, how we can actually make use of that to create elliptically polarized wave or circularly polarized wave, OK? So let's take a look at this example together. So suppose I have incident light with angular frequency omega, OK? Since I give you already the omega, what I really need is the speed of light, then I can calculate the resulting wave number and wave lengths. So this is actually the incident wave angular frequency. And the lens of the-- or say the thickness of the wave plate is called little l. And we can actually check immediately what would be the corresponding wave number in the median for the linearly polarized wave in the x direction and linearly polarized wave in the y direction. So we can actually calculate Kx will be equal to nx over c omega, because this is actually just omega divided by v, which is the phase velocity in the median for waves in the x direction. And that would be equal to 2 pi over lambda x. Similarly, you can also conclude that Ky can be written as ny divided by c times omega, which is 2 pi over lambda u. Kx and Ky are the wave numbers inside for the progressing harmonic waves inside the median, OK? One is in the x direction. The other one's in the y direction. So if we keep those in mind, you will see that, huh, if I have different nx and ny, when the same frequency light goes through this median, its x component will travel through different amount of period, where is a different amount of phase difference. Compared to the light polarized-- compared to the component in the y direction, as you can see from this demonstration. Therefore, we can actually conclude that there must be a phase difference between the x component and y component. And we can calculate that-- this is actually delta phi, the phase difference between the x direction and y direction will be equal to 2 pi times l divided by lambda x. So basically, it's the number of waves times 2 pi. l over lambda x is number of periods past. And the times 2 pi translates that to phase. And we are taking the difference between the x and the y direction. And we can conclude that based on what we have written here. As you see that this is just nx minus ny divided by c times omega times l, OK? So this is actually how the wave plate works. Suppose I have a linearly polarizer wave coming into this plate. And the direction of the polarization is not in the x direction or y direction. So they are positioned-- they are components in the x direction and y direction. For example, I can have an incoming polarizer like this. And this is actually the x direction. This is actually the y direction. And I can now decompose this kind of linearly polarized wave into two components. And after this wave passes through the wave plate, x component will be-- the phase difference between x and y will be increased by delta phi. So if originally there were no phase difference because this is actually a linearly polarized wave, and after it passes through the wave plate, it will be increased. And then the phase difference between x and y will be delta phi. All right, so that's really nice tour. And the so-called quarter wave plate is a device which we intentionally set the delta phi to be pi over 2. Why is that interesting? That is because initially you have Ex equal to E0 cosine omega t minus Kz, and this is actually the y component. If initially you have this kind of incident wave, now it corresponds to a polarization which is actually 45 degree with respect to the x-axis. So this is actually the x-axis. And this is actually the y-axis. When I have this kind of linearly polarized wave pass through the quarter wave plate, what is going to happen? What is going to happen is that one of the components will be delayed by delta phi or pi over 2. That will make you a circularly polarized wave. Because that will become sine and cosine. Therefore, if you plot the locus of the electric field in two-dimensional xy plane, you will see a circle. So that is actually why we want are interested in a special setup which delta phi is equal to pi over 2, OK? So let me go through a few examples so that actually you get some feelings about what is actually a quarter wave plate. Usually, instead of drawing this complicated diagram, we actually simplify the presentation into a diagram like this. So basically, you have a fast axis, which is the axis with smaller phase shift. And you have slow axis, which is actually the axis with larger phase shift. So basically, we just reduce the whole complicated setup into a simple diagram like that. So suppose I have an incident wave which is actually linearly polarized in this direction. In this direction, which I can call it x direction. And this is actually y direction. And I have that pass through a quarter wave plate, where the fast axis is in the x direction, and there's a slow axis in the y direction. Can somebody tell me, what would be the resulting polarization after this electromagnetic wave passes through this quarter wave plate? Somebody want to try it? Yes. STUDENT: It would be polarized in the y direction. PROFESSOR: Polarized in what? STUDENT: In the y direction. PROFESSOR: No. Basically-- OK, maybe I didn't explain that clearly. So initially, in this example, all the electric field is in the x direction. Therefore, in the y direction, there's nothing there. So that's actually a linearly polarized wave. The direction in actually in the x direction. And this quarter wave plate is going to slow down the y component by a phase of pi over 2. So what would be the resulting polarization? Yes. STUDENT: Very similar to [INAUDIBLE].. PROFESSOR: Yes, that's right. So because we are dividing something which is zero. But zero is zero. So zero is zero is zero, right? So therefore, what you are going to get is this. It's still a linearly polarized wave, right? OK, doesn't surprise you after I explain to you more clearly. And then you can see that if you have this-- OK, now I change the situation. So this is the x direction. This is the y direction. And I have something which is 45 degrees. And I have that pass through the same setup. Slow axis is in the y direction and the fast axis is in the x direction. What will we get? What kind of polarized light will we get after it passed through this quarter wave plate? Somebody can help me? STUDENT: Circular. PROFESSOR: Circular, yes. Thank you very much. So that's actually exactly what I was talking about in the beginning. The y component will be delayed by pi over 2. Therefore, it would become a circularly polarized wave. How about I change this to 30 degrees? What is going to happen? STUDENT: [INAUDIBLE]. PROFESSOR: Yeah, it will be elliptically polarized, right? Because now the projection to a different component is different. So therefore, it would be elliptically polarized wave. Very good. It seems to me that most of you actually understand what we are doing. And now it's time to do some experiment to actually show you what we have done. Yes. STUDENT: It's a little more complicated than that because the slope the refraction is [INAUDIBLE] be much, much slower than the fast axis. PROFESSOR: Yeah. Yeah, that's right. You are absolutely right. So it depends on the delta phi, right? So if delta phi is not pi over 2, then it can be elliptically polarized. And in this setup, I say that this is actually a quarter wave plate, therefore, the delay is always delta phi equal to pi over 2. Yeah. So then-- thank you for that. This is what we have been discussing is always quarter wave plate. Therefore, the delta phi between the slow and fast axis is always pi over 2, OK? So that everybody is on the same page. Yes. STUDENT: How can you have a material that has a different refraction index for different directions? PROFESSOR: For example, we were talking about materials-- or say the two-dimensional discrete case, right? So we can have little mass arranged in the x and y direction. But the space between mass in the x direction and y direction are different, then you have a dispersion relation which is actually different for the harmonic wave in the x direction compared to y direction. And that's just some random example. And that can be achieved by engineering the material we will use for the wave plate, OK? Good question. All right, so we will go ahead and I'll show you some demonstration. We prepare. The first thing I have to do is to turn off the light to have some more excitement. I cannot even see where is my experiment now. Oh, right here, yeah. OK, woo. OK, so look at what we have here. This is a projector. So what is the polarization of that light? STUDENT: Unpolarized. PROFESSOR: Unpolarized. Yeah, very good. OK, I'm very happy to hear that. All right, so now I have the polarizer and I put it on it. What is the polarization of this light? STUDENT: [INAUDIBLE]. PROFESSOR: I couldn't hear you. STUDENT: It's linear. PROFESSOR: Linear, yeah. Linearly of-- don't be afraid. OK, you can say that. No, this is not linear. The edge is not linear, right? But it's OK. I'm talking about everything inside of this material. Very good. So now what I'm going to do is to put two polarizers on top of each other. And of course, I can rotate such that the polarizer, the easy axis is perpendicular to each other, OK? So you see that ha, I almost black most of that light. So the first thing which I have been doing is that I first turn this unpolarized light polarized. And it's actually oscillating in one direction. And I block it again with the second one. And then you see that it's black. It's consistent with what we expect. So we are happy. We are not happy? No? Yes, we are happy. All right, so remember the discussion we had before. So what I could do is to add a third one, a third polarizer. So I can have the first polarizer which actually makes the direction of the oscillation in this direction. Then I put a second polarizer, where the easy axis is in this direction. Then I actually-- I'm going to extract all the components which projected to this axis. Therefore, after passing the second polarizer, the oscillation of the wave will be in this direction. Therefore, aha, now I put the third polarizer on, you can see that in the middle, because it changed the direction of the polarization by 45 degrees already by this polarizer, therefore you can see that there's some residual light survived. And then you can actually calculate what will be the intensity of the light surviving these three polarizers. And you can see that the ones which didn't pass the second polarizer is actually completely blocked by the two polarizers, which their easy axes are perpendicular to each other. So now, the interesting thing is that now I have a quarter wave plate here. OK, it's here. Hope you can see it. And I'm going to insert this into this experiment and see what is going to happen. Look at what we have here. Oh, this is actually much brighter, right? So basically, this water-- this quarter wave plate-- sorry, it's not water-- quarter wave plate, OK? Quarter wave plate actually turned the polarized light into a circularly polarized light. And after this circularly polarized light continued and passed through the third polarizer, you can see that, huh, the light passed through this kind of combination is a lot more than this experiment which was three polarizers. And we can also calculate what would be the expected intensity. And the good news is that we are not going to calculate that now, but in your P set. So you will be able to show that, indeed, the intensity you expect with quarter wave plate will be higher than why you expect with three polarizers. So that's actually the first experiment I would like to show you. The second experiment is also very interesting. So I have here-- OK, first I need to see if I can turn on the light. I have to turn on this light. Very good. So look at this tube. This tube is made of water and sugar. So we all love sugar. And I love it too much, so I add too much into this tube. So it's actually oversaturated sugar water. And so there is sugar inside and there are some animal or whatever living inside. But we don't care. We are not studying biology. But what is actually interesting is that, OK, now I have a light source from the lamp inside emitting what kind of polarized light? Unpolarized light, right? And I have that pass through a polarizer, which is here. There's a polarizer here. And therefore, what I want to say is that the incident light into this tube is polarized. That's the first thing I want to say. The second thing I want to say is that, OK, a linearly polarized light, due to superposition principle, actually you can decompose that into two circularly polarized light. Both of them are actually rotating in different directions. You can actually work on the mass and you will see that, ha, indeed, it works. So our linearly polarized light you can always rewrite it as a superposition of two circularly polarized light, but rotating in different directions. The interesting thing is the material which we use in this demonstration is oversaturated sugar. And we know that the molecule for the sugar and those kind of material is asymmetric under mirror transformation. It's asymmetric. It's a chiral material. OK, chiral is actually just some name, but it doesn't mean anything to you. But what is actually interesting is that this material is asymmetric. If you have a mirror and this material is looking at the mirror, in the other side of the mirror, it looks different. It's like your hand, right? So in a mirror, it's asymmetric. So what is interesting is that due to this kind of structure in the material that the light passed through, the circularly polarized light, counterclockwise polarized light, will have different refractive index compared to clockwise. Clockwise and counterclockwise light will have different refractive index. Therefore, you see that now you can see some kind of rotation or some kind of change in the polarization as a function of distance the light travels through. So basically, this material would rotate the linearly polarized light, because the refractive index for the clockwise and counterclockwise are different. So if you accept that, I would like to add another complication. In addition to that, the refractive index also depends on the frequency of the incident light. Therefore, you will have different amount of rotation for different color. So therefore, you can see that once I have incident light which is linearly polarized, all the colors are lined up. You can see that here. What is the color here? It's kind of bluish or white, essentially, right? But if you move slightly more, then it becomes pretty blue. And then if you move more, because of the dependence of the refractive index as a function of wavelength, therefore, you can see that this whole thing is actually changing color. And in the end, I have another polarizer which filter one of the directions. And I can change the direction, and you will see that I can filter out different colors. Which color do you like? Now it's red. And of course, I can rotate this polarizer, and I am sampling different color. Because at the time different color of light passes through this material, they are rotated by different amount of degree. Therefore, I can filter out and create all kinds of different color on the wall. The other thing which is interesting which I can do is that I can now change that direction of the incident light, or the direction of the polarization of the incident light, by rotating this one. You can see that the whole tube is changing color, like why you see in the barber shop, right? OK, so maybe this is a fancy way to make that kind of tube. No? A physics barber shop. Maybe we should do that. OK, so I hope you enjoyed this demonstration. And we will take a five minute break to take questions. And the next topic we are going to talk about is how do we actually create electromagnetic wave at all. So let's come back in 15. OK, so I hope you can hear me. All right, so welcome back from the break. So we are going to talk about the second topic we would like to cover in the lecture today. The question we are asking is, how do we actually create electromagnetic waves and so-called radiation? So this is actually a picture from Hubble telescope. And you can see that light can travel through billions, or tens of billions, of light years and arrive at Earth. And you can actually measure them and see you what is actually going on in the past. And that means if you have a source and you have some kind of radiation, and this source is going to emit energy towards somewhere, which is actually really, really far away toward the edge of the universe. So that is actually what we call electromagnetic wave and radiation. But the what is actually requirement for that to happen? What is the requirement for us to be able to see the stars which are so far away? That's the question. So let me actually make a simple argument here. Suppose I have some kind of a light source. It's a source in the center. And we have learned about pointing vector, right? So what this actually pointing vector? It's not really the pointing vector, right? So it's rate of energy transfer per unit area. So it's kind of pointing, but it's pointing to the direction of the energy transfer. So this is a vector. And it's actually highly related to the direction of the electric field and the magnetic field. And now, if I-- since this is essentially the energy transfer per area, I can now capture the average pointing vector times area. And what is going to happen is that if I do this calculation at this surface-- this is actually a sphere which is covering this source. I can do this at sphere number 1. And I can actually also do that in the sphere number 2. Since there are absolutely no other source-- I'm assuming that there's only one source here. There's only one light source in the universe, which is kind of lonely. Apparently it's not my universe, but somebody else's problem. And then I will conclude that since there's nothing outside, I will conclude that S times A, if I evaluate that in the first surface, will be equal to S times A in the second surface. That's equal to power, OK? So that should not surprise anybody. So that means the pointing vector will be proportional to 1/A, which is the surface area. And that means, based on simple mathematics, that would be proportional to 1 over r squared for this constant power transfer to happen. So this means that there's a source. And if I integrate all the energy transfer from some kind of surface, it's going to be a constant, no matter what surface you are choosing. So that means if I look at the structure of the S vector, the pointing vector, we can conclude that at least the electric field and magnetic field has to be proportional to 1/r, which is the distance with respect to the source. Otherwise, it's going to be decaying faster, or reducing faster than 1/r, then the total power will approach zero when you increase r enough. Then that means if you have that happen, you will not see anything if you are far enough. So if that's actually the case, we can now come back and discuss two situations which we are very familiar with. For example, you can say, how about I have a stationary charge? So I can have a stationary charge and see what will happen. And apparently, if I have a charge here without actually moving it, it's going to emit-- basically, it is going to have an electric field around this. But electric field, based on what we learned from 8.02, is going to be 2 divided by 4 pi epsilon zero r squared r hat. It's going to be proportional to 1 over r squared. It's already not very good news, because it's proportional to 1 over r squared. And it's hitted by this. The magnetic field is zero. If I have something times zero it's zero. Then there will be no energy transfer if you have a stationary charge just sitting there. So apparently, this is not a good way to create electromagnetic wave, based on our argument. The pointing vector is actually equal to zero. So now you can say, OK, this is actually too boring, so let's introduce some excitement. How about we make this charge moving at a constant speed? What we can do is like this. Basically, if you have a positively charged particle, you can actually make it move at a constant speed, velocity equal to v. And what you are going to see is that, oh, indeed, there will be some changes in the electric field and the magnetic field. And I'm not going to go through the calculation of this kind of situation. And I will leave that as an exercise. But I would like to tell you what would be the conclusion. So if you have a single charge, which is essentially moving at a constant speed, and what is going to happen is that the electric field density, or the field line density will change. And you will be more concentrated in the direction, which is essentially perpendicular to the direction of the motion of this charge. And we can actually calculate what would be the electric field. The electric field will be equal to q divided by 4 pi epsilon0 r squared, 1 minus beta squared. I will define bet in a moment. 1 minus beta squared sine squared theta 3/2 in the r direction. And where the beta is actually defined as u/c, which is u is actually the velocity of this little charge. And of course, you can also calculate what would be the corresponding B, right? The magnetic field will be actually equal to u plus E divided by c squared. And that is actually proportional to 1 over r squared. As you can see from here, the bad news is that, OK, you indeed now have both electric field and the magnetic field. There is some improvement. But the problem is that the reduction of the electric field and the magnetic field is a function of distance. It's too large. Both of them are proportional to 1 over r squared, proportional to 1 over r squared. Therefore, the magnitude of S will be proportional 1 over r to the fourth. So if you are far enough, you can conclude that the total power will approach zero, even if you integrate over the whole surface surrounding this moving charge. So apparently, that's actually not the solution we are seeking. Therefore, we have to do something more aggressive to accelerate the charge. So you can now have a charge moving at a constant speed. We see that it didn't do anything. Therefore, we have to make the velocity increase and see what'll happen. So what I am going to do now requires concentration. So I will hope that you don't take notes. Just follow me so that you get what I am trying to argue. And of course, if you are really good in mathematics, you can actually also go through page 356 to 360 in George's book. There are some really mathematical deviations of the radiation from an accelerated charge. So let's try to see how can we actually understand an accelerated charge and what is actually the associated electromagnetic field. So my goal is to have some kind of acceleration. So I would like to set up the stage. So let's take a look at the slide here. At t equal to zero, time equal to zero, before I introduce any excitement, I have a charged particle initially at rest. And it's sitting there. What I'm going to do is that at some point, at t equal to zero, I try to accelerate this charge until t equal to delta t. The original position of that charged particle is at a. And I try to accelerate this charge by acceleration a. And that only happened in a very small amount of time, which is delta t. So what is going to happen is that this charge will get accelerated. And you can see that the velocity of the charge-- you can see velocity as a function of time here-- is increasing linearly in this period, and reaching maxima, which is a delta t. So after that, I stop the acceleration. So originally, the charge is at rest. Then I accelerate it for some period of time. And I stop the acceleration at A prime, or t equal to delta t. And what is going to happen afterwards to the charge? Everybody is following? You will be moving at constant velocity. Very good. So that's actually what you see here. And the wave can actually-- this information can propagate as a function of time. So that's actually the whole setup, which I would like to discuss. Before that, I would like to bring your attention to the graph I was trying to draw here. So you can see that originally there is a line which is pointing up, like 45 degree with respect to this charge. So that's one of the field lines I was drawing here. That's actually the electric field line. And as you can see that as I manipulate this charged particle, this is a sphere-- or a circle I should-- on this slide, which is actually telling you where this information already propagated in the space. So for example, if I am sitting here in the position of my little mouse here. Can you see that? No, you cannot see it. If I'm sitting in the upper right corner of the slide, and I try to-- then the experiment starts and I move the charge, the observer at the upper right corner would not feel anything. Because it takes time for the field, or for the changes, or for the information to be sent from the position A to the observer, which are far away from the charged particle. And the surface which-- the surface is actually where the information has propagated. So this information that my charge is accelerated, this information has already propagated to a sphere, which is actually far away by c times delta t away from the center, which is the location of the charged particle. And you can see that as time goes on, this black circle is actually becoming larger and larger, which contains the information that, OK, I accelerated the charge. This is actually where you can see that out of this circle is as if the charge is stationary. So you can see the field line is still linear. And passing through this line, or say, this surface, the information is already propagated. If you standing inside this line, like for example, next to the question mark, if you are there, you feel, aha, now I observe the acceleration to the charged particle. Finally, if I go toward the charged particle even more, and I will see, aha, if I am now inside the green circle, I know that this charged particle already stopped the acceleration. It's now moving at constant speed. So that's the meaning of these two little circles. And now I am looking at the situation at time equal to t where the charge is at position B. And I should see something really interesting. As I mentioned before, if you have a constantly propagating charge, the field line is actually still a straight line, actually, right there in the equation. If you have a stationary charge, it's also a linear straight line. And you can see that you have two straight lines, but in between, there's a kink which connects these two lines. So between these two lines, basically this is actually what we have here. So we have the original particle. And this is actually where the particle have the field line as a moving charge. And there's another surface, which actually out of the surface, it's like there is no acceleration at all. The charge is still stationary at A. You can see that these two field lines are linear, and also essentially in the radial direction. But the excitement is that since the field line has to be continuous, the excitement is that I have successfully created a kink, which is actually propagating in the radial direction. And this kink is going to be our electromagnetic wave because it has a component which is perpendicular to the direction of propagation. Just a reminder, what is actually an electromagnetic field looks like, it looks like this, right? So basically, you have the electric field oscillating up and down in one of the directions, the polarization-- linearly polarized electromagnetic wave. And the whole wave is actually propagating toward the right-hand side of the board. And the electric field is in the perpendicular direction of the direction of propagation. And this kink is actually what we are looking for, OK? And that really becomes the electromagnetic wave right there from the point source. Any questions so far? Everybody's following? OK, so now, that's good. We have managed to create this situation. And I would like to be more concrete about several settings. The first one is actually we have a constant acceleration a, and this delta t is really small. Very small delta t, very small acceleration. Therefore, I would assume that u defined as delta t, the resulting velocity is much, much smaller than the speed of light. So that's actually the setup which I would like to use. Then the question now is, how do we actually evaluate what will be the magnitude of this so-called kink electric field? So for this, it's actually also pretty easy. So now I would like to copy the geometry which I have there. I am trying to draw a copy of that to my board here. So basically, originally the charge is stationary at A. And it's emitting an electric field, which is actually only in the radial direction. And it got accelerated by a really small time. I'm exaggerating in that figure, OK? So it got accelerated a really small amount of time. And after that, it reached a prime, which is the exaggerated version is actually probably there. And A and A prime is, in fact, very, very close to each other, because this is actually just a very, very small delta t. I can have delta t goes to zero. Then A and A prime would be very, very similar. And now I let the time go on, and now this charged particle is now at point B. It's moved to point B. And I can connect B to A and A prime. And I can actually conclude that, OK, since the resulting velocity of the charged particle up to a prime is actually equal to u, defined as a times delta t, and we are now at time equal to t. Therefore, the distance these charged particles pass through, or travel through, is actually u times t. Doesn't surprise you, right? So that's velocity times t. And also, we can actually calculate this lens. This lens is actually-- I call it this point D here, which is the intersection between the second surface and the original field line. And I call this one E, which is the intersection of the field line from the moving charge and the second surface. And finally, I also have the intersection, which I call it F, which is actually where the field line and the surface actually join, which is actually the information about the charge has moved is actually the surface, which within that surface, people know the charge is actually already moved. So once I have all these, I can now evaluate what will be at D and F. D and F are actually pretty straightforward as well, because all those surfaces are traveling at the speed of what? Light, right. So what is actually the delta t between these two surfaces? It's delta t, right? Because I actually stopped the acceleration at delta t, therefore, the distance between D point and F is actually just c times delta t. And of course, now I have this. I can connect E and D. And roughly, because a and a prime are very, very close to each other, and also t is very large, therefore the BE, this line, is roughly parallel to these AF line. So these two lines are actually roughly parallel to each other. Therefore, I can now evaluate what will be this line, D and E-- what would be the size of the distance between D and E. And that can be evaluated. And it's actually just u perpendicular times t-- perpendicular to the direction of the field. And I can copy that here. The distance between D and E is just u perpendicular times t. And of course, I can approximate that is actually just a line. And I have a theta angle which is actually DEF. So now I can actually try to use this information, this geometrical argument information, to figure out what will be the electric field, this kink. So now I can have the electric field, the same triangle here, this is angle theta. And this is the electric field parallel to the AF line. And I can have also E perp, which is actually the perpendicular to AF, this line. And the kink, E kink, is actually what we would like to figure out as well. And basically, this E kink is what we want to figure out. And the E has the following two components. One is the E parallel. The other one is the E perp, which is the perpendicular and the parallel components to the AF line. And we can already make use of the similarity of these two triangles, right? Basically, this field line is actually pure geometrical, therefore, I know what is actually theta from this geometrical argument. So what is actually theta, basically, you can get that from the information of c delta t. And then u perp times t. So therefore, I can conclude that the magnitude of E perp divided by magnitude of E parallel will be equal to u perp t divided by c delta t. And this E kink is like this. It actually has a direction. However, you can see that, wait a second, you have this ratio, right? But the E kink is actually pointing to this direction. And this ut is pointing up to upward direction. Therefore, if you take this ratio, the E kink will be pointing to the upper left direction. Therefore, you really need a minus sign here, right? Therefore, the E perp would be pointing downward. Therefore, that's actually how you get this minus sign there. From this pure geometrical argument, you can actually conclude what would be the ratio between E perp and the E parallel, which is actually equal to that. And I can write it down explicitly. Basically, that's going to be equal to a delta t times t divided by c delta t. Remember, u is equal to a times delta t. Therefore, I can now cancel delta t. Then basically, what I get is minus a perp t divided by c. And now this is actually equal to minus a perp r divided by c squared, where r is actually just c times t. r is actually the distance between the position you are evaluating this field and the origin, which is A, OK? So you can now conclude that-- based on this geometrical argument, you can conclude that E perp is highly related to the E parallel. The E perp is equal to minus a perp r divided by c squared E parallel. Any questions so far? Yes. STUDENT: How'd you get r real quick? PROFESSOR: R is actually-- yeah, so r is actually just c times t. So it's the whole distance is the r. Cool. All right, so you can see that right now all of those things are purely geometrical, right? So this is really no magic. And no even integration. So now we are going to do some integration. So now we are almost there. I would like to figure out what would be the E kink. And I am especially interested in E perp, because E perp is the direction which is actually perpendicular to the direction of propagation. It's really cool. So that's actually related to the magnitude of the electromagnetic field radiating. So I would like to know E perp, but I don't know what is E parallel. So what we could do is to use Gauss' law in this example. So now what I could do is that I can draw a pillbox, which is actually through the surface number 1. This is actually surface number 1. What I could do is I can draw a pillbox which is actually passing through the surface number 1. Out of surface number 1, we know the physics very well, which is actually the electric field of a single stationary charge. So therefore, I know what is actually the electric field outside. Which is actually pointing outward in the radial direction. And the E parallel is actually what we are stuck with. So we don't know what is actually the magnitude of E parallel. That's the electric field inside the surface number 1. Makes sense? So now we also have the component which is actually perpendicular to the direction of propagation. So this is actually the contribution of the E perp and the contribution of E perp, which they go from the side to the site. Go in from the side, go out from the side of this pillbox. So I can now immediately conclude that the total contribution of this surface integral will be equal to 0, because of Gauss' law. There's no charge in my pillbox. Therefore, all those things should cancel. Apparently, these will cancel, because side in, side out, the same magnitude, which is E perp. Therefore, that cancel is trivial. And the interesting thing is that we can also figure out that e parallel will have to be equal to E out. So that the sum of all the integral will be equal to 0, because of Gauss' law. That's actually a very big amount of information, because I know how to write down E out. So E parallel will be equal to E out. We learned from 8.02 this is actually just q divided by 4 pi epsilon0 r squared. Does that surprise you? Should not, right, because out of the surface, people think nothing actually really happened to the charged particle. So it's actually still stationary sitting there. So therefore, I have the information of E parallel, therefore, I can now conclude what would be the E perp. Now, E perp will be equal to minus q a perp divided by 4 pi epsilon0 c squared r, because this is actually just a perp minus a perp r divided by c squared times E parallel. Look at what we have achieved. Look at this. This is actually proportional to what? 1/r, right? So that means the decaying speed of this E perp is really slow compared to the electric field from a stationary charge. So that's actually very encouraging. And of course, you can also write down what will be the resulting magnetic field. And it's going to be also proportional to 1/r. So what we can actually conclude is that the E rad is a function of direction of the-- evaluating this E radiated electric field is a function of t. And we can actually-- based on this exercise, this will be minus q. a is a vector, but now I only take the perpendicular direction. And this thing is actually evaluated at t minus r over c divided by 4 pi epsilon0 c squared r. Let's take a look at this formula closely together, since we have spent a lot of time trying to get this result. So look at this structure. So basically, the radiated energy has a minus sign in front of q and a perp, because the E kink is actually pointing in the opposite direction compared to the directional acceleration, as you can see from here. The E kink and the E perpendicular is pointing to the opposite direction of the acceleration. Therefore, we have this minus sign there. And only the perpendicular direction motion, acceleration, works. And there's this little component here, t minus r/c. This is actually-- now multiplying this factor is evaluated at the t equal to t minus r/c. It's evaluated at that time. So this is actually evaluated at retarded time. So that means I am really slow. I need to wait for the information to arrive my detector so that I know there are acceleration happening. Finally, I can now also conclude what will be the magnetic field. The magnetic field rad, as I mentioned, would be proportional to 1/r. And of course, I also give you the explicit formula in the lecture notes. And now we can actually conclude that s will be proportional to 1 over r squared. So that means I can now send energy to the edge of the universe, because of all this hard work we have been doing here. Any questions? All right, before the end of the lecture today, I'm going to show you an experiment here. So here I have an antenna, which you can have electron going back and forth, oscillating harmonically really, really fast like this. Therefore, there will be acceleration, because of this harmonic oscillation. And I'm going to turn off the light. Also probably hide the image. OK, this is good. But I have to be able to see the button. Can I see it? No. Oh, I'm in trouble. Ah, here. OK, here I have a receiver. It's also a metal rod. And I have a light bulb in between, which is actually trying to receive the information from-- or say that it receives the electromagnetic wave emitted from that source. Which you have electrons going back and forth in that direction. So now, first, I am trying to align my setup in this direction so that it's really-- what would be the polarization of an electromagnetic wave? The polarization is going to be in a horizontal direction. Yes, very good. Therefore, if I have this set up like this, it's actually perpendicular to the direction of the polarization, therefore, I see nothing here, It is also possible that the light bulb is actually broken, but let's see. So now what I'm going to do is to change the direction. You see that? I am moving also closer really carefully. Now you can see what happened. You can see that now I receive the signal from this machine. The emitted light is actually polarized in the horizontal direction. And now I have also the electron going back and forth, and that actually can light up the light bulb. Now, if I change the direction, you can see that this is actually gone. And I can do this again. And I can go farther away from the source. You can see that now the light is actually disappearing. Why? That is because you get the 1/r term. Therefore, it's actually disappearing. And if I move closer to the source, it's reappearing. So now I need an assistant to hold this thing for me. Who can volunteer? And I would like to rotate that. I can actually also rotate my setup. Can you help? Yes. OK, be careful. And I hope you can survive this. So now what am I going to do-- OK, so stay there. And what I'm going to do is I can rotate the whole setup, the same concept. If I rotate the setup, I have to be careful so that I am not touching this more. I want to survive. And you can see now what is actually the direction of the emission. It's actually in this direction, right? The direction of the polarization is in the back and forth direction. And you see that that the light bulb is actually turned off. And now I can turn it back on. And you see that it's still there. OK, thank you very much. You survived. Not everybody actually survives this. [LAUGHTER] So you can see it now I can move really close to this thing. And what is going to happen? The amount of energy will be too high, and probably this light bulb will explode or broken. Do you want to see that? STUDENT: [INAUDIBLE]. PROFESSOR: Oh, my god. Let's see. Ooh, [INAUDIBLE]. [LAUGHTER] OK, very good. So now this experiment is dead. And then we can-- it's a very good time to close the lecture today. And thank you very much for attending the lecture today. And I hope now you understand how we actually create light. And enjoy the homework, because you will be able to figure out why the quarter wave plate combination will give you a higher light intensity. OK, so if you have any questions, I will be here and just standing up here. OK, hello everybody. Today I'm going to show you a demonstration, which actually demonstrates the effect of polarizer and quarter wave plate. Here is the setup. I have a projector here, which emits our polarizer light. And if I put a sheet of polarizer on top of it with easy axis in the vertical direction, like what my finger-- in the direction oscillation along the direction of my finger, then basically, you will see that the intensity of the light is reduced. Because for the unpolarized light, light component which is actually oscillating along the easy axis can pass through the polarizer, but the component which is actually oscillating perpendicular to the easy axis, like this, is not going to pass the polarizer. Therefore, a large fraction of unpolarized light is actually filtered out, and you will see a reduction in the intensity on the screen. So what I'm going to do now is to place another polarizer on top of the first one. So now we have two sheets. And you can see that after adding the second sheet, you see some change in the intensity. But if I rotate this sheet so that now the easy axis of the first and the second sheet are perpendicular to each other, you can see on the screen that all the light which are emitted from the projector is actually filtered out. Why is that? That is because now the first sheet actually filters out all that light which is actually oscillating in the direction perpendicular to the easy axis. If I actually introduce another filter which has easy axis now perpendicular to the one from the first sheet, then I'm going to filter out both directions. Therefore, all the light are filtered out due to this putting perpendicular setup. Now, if I introduce a third sheet, insert that between the two existing sheets, but now I am trying to actually insert that such that the direction of the easy axis is actually 45 degrees with respect to the easy axis of the first sheet. According to our calculation in class, also in your homework, you should see some light which will pass through this setup. And let's take a look at the experimental result. You can see that, indeed, after you insert a third sheet, you see that now the easy axis is actually 45 degrees with respect to the first sheet. And you do see the intensity of the light becomes larger, or you see a brighter light output passing through these three polarizers. And if I rotate it so that actually the easy axis of the second sheet is actually changing, you can see that it reached maxima at roughly 45 degrees, which is actually consistent with what we predicted from your homework. And then the other thing which you predicted from the homework is that if we insert a quarter wave plate between these two sheets, you are going to see a brighter light passing through this setup. So let's actually take a look at what will happen by inserting the quarter wave plate between these two sheets. And this is actually the result. You can see that, indeed, the intensity is higher compared to the three polarizer experiment. And also, the intensity actually reached maxima when the fast axis of the polarizer is 45 degrees with respect to the easy axis, as we predicted from your homework. And we can actually put both experimental results side by side. Indeed, the results from the-- so now I am inserting the polarizer also between the two sheets. And you can see that, indeed, the light passing through three polarizers, the intensity is actually lower than two polarizers and the one quarter wave plate setup. Hello, everybody. So today, we are going to show you a demonstration of dipole radiation. Here is the setup. So we have a radiator here with two antenna. And when I turn it down, there will be current going back and forth through these two antenna. And therefore, this setup is going to emit polarized electromagnetic wave. And we are able to detect those electromagnetic waves by using a detector here, which consists of two antenna and one light bulb here. When there are current on this antenna, you will see the light emitting from the light bulb. And the intensity of the light bulb actually can help us to understand the structure of the radiation from the dipole radiator. So what I am going to do now is to turn this setup on. You can see now, the setup is on and the light is on. And there will be current going back and forth through these two antenna. So since the oscillation of the charge will generate electromagnetic wave-- since the direction of oscillation is in the horizontal direction, therefore, the electric field of the electromagnetic wave is going to be in the horizontal direction. So this can be actually verified by using the detector here. When my detector-- the direction of the antenna is actually perpendicular to the direction of the oscillation, you basically don't see any light emitting from the light bulb. Now I'm going to rotate my detector. You can see that as we actually rotate so that the antenna is parallel to the direction of the oscillation, then you will see that, huh, we will see a large intensity of light emitted from the light bulb. But on the other hand, if we actually rotate such that the direction of the antenna is perpendicular to the direction of oscillation of the charges, then you will not see any light emitted from the light bulb. This can also be demonstrated from on the other side of the experiment. So now, instead of standing in front of the setup, I'm going to go to the side of this dipole radiator. So here is actually roughly 90 degrees with respect to where I was standing. And you can see that no matter which angle-- no matter which angle of my detector is in, basically, you will never see light emitted from the light bulb. That is because the direction of the oscillation is in this direction. And according to our formula, our prediction is that there will be no electromagnetic wave traveling in this direction. And therefore, no matter which angle you are actually trying to detect the emitted light, the light bulb will never light up. So that's essentially consistent with our declaration. The second thing which I would like to actually show you is that we can also detect the nodal point of the emitted electromagnetic wave by moving this detector around in the classroom. For example, if now I move farther away from the dipole, now I am here and you can see that the intensity goes to zero at this point, because we are actually in one of the nodes of the electromagnetic radiation. And if I now move further away from the setup, you can see now the light is actually emitting again. And also, the intensity increases. And again, if I move farther and farther away from the setup, you can see that the light becomes dimmer and dimmer, and disappears again. Here is actually another node in the classroom. And also, you can see that as a function of distance, the maxima intensity emitted by the light bulb is also decreasing because of the larger and larger distance with respect to the source. So this demonstration actually shows that we can understand the dipole radiation. And the other experimental results are consistent with the calculation we have done in class. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 5_Beat_Phenomena.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. BOLESLAW WYSLOUCH: Good morning, everybody. I'm Bolek Wyslouch. I'm a teacher substitute for Professor Lee, who is now at some conference in China, and he asked me to talk to you about coupled oscillators. I understand that he introduced the concept last time. You worked through some examples. So what we are going to do today is to basically go through one or two examples of very straightforward coupled oscillators, where I will introduce various kinds of systematic calculational techniques, how to set things up, how to prepare things for calculations. And also, we may, depending on how much time we have, start driving, have driven coupled oscillators. And we will work on two, again, simple physical systems, one that consists of two pendula driven by forces of gravity, each of them. And then they are connected with the spring. So each of those pendula, each of those masses, will feel the effects of gravity and effects of springs at the same time, and they will talk to each other. There will be coupling between them. So that's one physical example which we'll consider. The other physical example consists of two masses in the horizontal frictionless track connected by a set of springs. So they are driven by forces of spring. And those two systems are very similar to each other, almost identical in terms of calculations, and they exhibit the same phenomena, and I will be able to demonstrate several of the neat new things. And this particular system is set up to introduce external driving force, which will create a new set of phenomena. And we'll talk about it today. And what I would like to stress today when we go through all those calculations is, A, how do you convert a given physical system with all the forces, et cetera, into some sort of fixed form, fixed type of notation, with which you can treat all possible coupled oscillators? And also we will discuss various interesting-- even though the system is very simple, just two masses, a spring, a little bit of gravity on top of that, the way they behave could be extremely complex, but it can be understood in terms of very simple systematic way of looking things through normal modes and normal frequencies, so the characteristic frequencies of the system. So let's set things up. So we'll start. This will be our workhorse. And by the way, once we understand two, we will then generalize to infinite number of oscillators, which is actually-- so this model, which consists of weights hanging under the influence of gravity plus the springs will be then used for many applications of the concepts later in this course. So let's try to convert this physical system into a set of equations. So we have a mass, m, hanging from some sort of fixed support, another mass here, same mass for simplicity. We connect them with a string, and we know everything about this system. We know the length of each of those pendula, which is the same. We know masses. We know spring constant of a spring connecting those two things. The spring is initially at its rest position such that when the two pendula are hanging vertically, the spring is relaxed. But if you move it away from verticality, the spring either compresses or stretches. And everything is in Earth's gravitational field, g. We assume that this is an ideal system, highly idealized. We only consider motion with small angle approximation, only small displacement. There's no drag force assumed. The spring is ideal, et cetera, et cetera. Of course, this thing here is very far from being ideal, but hopefully basic behaviors are similar. It's approximately ideal. To study the motion of this thing, to understand how it works, let's try to-- let's try to parameterize it, and displace it from equilibrium, and look at the forces, and try to calculate equations of motion. So we will characterize this system by two position coordinates. We will have x. We'll give this one number one. This will be number two. And we will have x subscript 1, which in general would depend on the time. This is the position of this mass with respect to its equilibrium position. We will have x2 as a function of t. Again, this tells us everything. And the full description of the system is to know exactly what happens to x1 and x2 for all possible times. And we will impose some initial conditions. We can come back to that later. So again, so the coordinate system is this. When we start talking about the system in principle in the case of somewhat larger angles, you have to worry about vertical positions as well. So we will introduce. So there is also a coordinate y, which we will need temporarily to set things up. So x is, as I say, x is measured from equilibrium. Y is positioned vertically. So to calculate the equations of motion, we have to look at the forces. So let's look at what are the forces acting, for example, on this mass, the mass, which is-- if it's displaced from a vertical position. Let's say this mass, mass 1, has moved by some distance away from thing Temporarily, let's introduce an angle here to characterize this displacement from vertical. And let's write down all the forces acting on this - force diagram acting on this mass. So there is a tension in the string or the rod. Let's call it T1. There is a force of spring acting in a horizontal direction. This is a vector. And there is a force of gravity acting on this in the vertical direction. We can write down those forces. We know a lot about them. This one is minus mg y-hat. This one is equal to k x2 minus x1 in the x-hat direction. So this is the force which, when the spring is displaced from equilibrium, there is a spring force, Hooke force, in the direction of -- in the usual direction. In this case, it's actually in the opposite direction. And then there is a tension the spring, which has to be calculated such that we understand the acceleration of this object. So let's write down the equations in the x-hat direction. This is m acceleration of object number 1 in x direction is equal to minus T1 sine theta 1 plus k x2 minus x1. And in the y-hat direction, we have m y1 direction is equal to T cosine theta 1 minus mg. At the small angle for theta 1 much, much smaller than one, we can assume, that cos theta 1 is approximately equal to 1 and sine theta 1 is equal to angle. We do the usual thing. So basically, in this approximation, and also by looking at the system, it's clear that the system does not move, and the vertical direction can be ignored. Yes? AUDIENCE: How do you know which way [INAUDIBLE]?? BOLESLAW WYSLOUCH: Excuse me? AUDIENCE: The [INAUDIBLE]. How do you know which way it [INAUDIBLE]?? BOLESLAW WYSLOUCH: How do I know? AUDIENCE: Yeah. [INAUDIBLE] BOLESLAW WYSLOUCH: The spring force is-- well, you have to look at the mass 1. You are just looking at mass 1. So the spring is connected to mass 1. And the force of the spring on mass 1 is k times however the spring is squashed or stretched, all right? So it knows about the existence of mass 2, but only in a sense that you have to know the position of mass 2. So we just assume that x2 is something, and we just look where the spring is. So that's why-- the force of spring depends on the difference of position x1 minus x2. So this is written here. And in fact, interestingly, the position of the mass 1 itself is a negative sign here. So if you move mass 1, the spring force is in the right direction, minus kx. All right? So there is no motion x1, so we can conclude from here the T cosine1 is approximately equal to 1. So T is simply equal to mg. So the tension in the spring can be assumed to be mg. We don't have to worry about it. And then we just plug in-- also the angle can be converted into position by realizing that the distance times the angle is equal to displacement, the usual geometry. The net result is that by simplifying things, I can write down equations for acceleration in the horizontal direction for mass 1 is equal to minus mg x1 over l plus k x2 minus x1. OK? So this is an equation of motion for mass 1 in our coupled system. And I could say most of the terms have to do with a motion of mass 1 itself. Mass 1 is its own pendulum. And mass 1 is feeling the effect of the spring force. But because the force of the spring depends on the difference between positions, there is this coupling-- so the motion of mass 1 knows of where mass 2 is. And motion of mass 2 influences the motion of mass 1. That's how the coupling shows up. So for most of those problems, what you do is you simply focus on the mass in question. You take all the forces, you calculate them, and then this coupling will somehow appear in the equations. So we can repeat exactly the same calculation focusing on mass 2. And then the equation which you will get will be very similar. Let me just slightly rewrite this equation here to kind of combine all the terms which depend on the position of mass 1 with terms that depend on mass 2. So where m x-acceleration is equal to minus k plus mg over l times x1 plus k times x2. So this is the coupling term. This is what makes those pendula coupled. All right? And then I can write almost exactly the same equation of mass 2 with the proper replacement of masses. So let me write this down in the following way-- kx1 minus k plus mg over l times x2. So the motion of mass x1 depends on x1 itself multiplied by something with a spring term and gravitational term and depends on the position of mass 2 only through the spring. Mass 2 also is mostly driven by its own gravitational force of itself plus the spring depends on the position of x2. But there is this coupling term that depends on position of mass 1. So both of them feel the neighbor on the other side, right? So if I keep this one steady of x2 equals 0, then basically the forces here is just the spring plus the gravity. If I move this one and keep this one at 0, the force on this spring spring and gravity. But if this one is displaced, and I move that guy, the forces on this one are affected by the fact that number 2 changed. OK? Again, I was able to determine those coupling terms by simply looking at mass 1 itself, mass 2 itself. All right, so this is the set of two coupled equations. I have accelerations here for x1, x2, and I have positions here. It's like an oscillator of position acceleration with a constant term except that things here are a little mixed. And the trick in this whole mathematics, and calculations, and the way we do things is how do you solve those coupled equations? OK? So what I would like to do is-- and there is multiple ways of doing that. So let me do everything. Let's write down everything in the matrix form, because it turns out that linear matrices are very useful for that. We will use them very, very-- in a very simple way. So let's introduce to them and show vector, which consists of x1 and x2. So basically, all the position x1 and x2 are here. So we will be monitoring the change of this x2 as a function of time. We will introduce a force matrix k, which is equal to k plus mg over l minus k here, minus k here, k plus mg over l there. This is a two by two matrix. And then we need a third matrix, mass matrix, which simply says that masses are mass of first object is m and the other one is also m, right? So these are three matrices that basically contains exactly the same information as out there. I probably need another matrix. I need an inverse matrix for mass, which basically is 1 over m, 1 over m, 0 and 0. This is a inverted matrix. OK, and it turns out that after I introduced these matrices, this set of equations can be written simply as X, the second derivative of the vector capital X, is equal to minus m to the minus 1, this matrix, multiplying matrix k and then multiplying vectors x again. All right? So this is exactly the same as this, just written a different way. So it's only the question of notation. So it turns out it's very convenient to use matrix calculation to do things faster. So instead of repeating writing, all the x1s, x2, et cetera, instead I just stick them into one or two element objects. I use matrices to multiply things, and if I want to know x1 and x2, I can always go, OK, the top component of vector x, lower component of vector x gives me the solution. Simple. Right? So let's try to use this terminology to find solutions. So the question is how do we find solutions to coupled oscillations. What is the most efficient way of finding the most general motion of a coupled system? Anybody knows? What's the first thing? Yes? AUDIENCE: [INAUDIBLE]. BOLESLAW WYSLOUCH: Introduce what? AUDIENCE: [INAUDIBLE] using complex notation. BOLESLAW WYSLOUCH: Coupled? AUDIENCE: Complex. BOLESLAW WYSLOUCH: Complex oscillation. Yes, that's right. So all right, let's do it. But hold on. But what form of oscillation? OK, all kinds of complex numbers can write, but any particular-- AUDIENCE: [INAUDIBLE] BOLESLAW WYSLOUCH: That's something. That's the physics answer, all right? Complex notation is a mathematical answer, how to solve a mathematical equation. But the physics answer is to find fixed frequency modes us such that the system, the complete system, oscillates at one frequency. Everybody moves together. This is so-called normal mode. It turns out that every of the system, depending on number of dimensions, will have a certain number of frequencies, normal modes, that would-- the whole system oscillates at the same frequency, both x1 and x2, undergoing motion of the same frequency. We don't know what the frequency is. We don't know it's amplitude, et cetera. But it is the same. OK? So this means that I can write that the whole vector x, both x1 and x2, are undergoing the same oscillatory motion. So I propose that-- so of course, we use the usual trick that anytime we have a solution in complex variables, we can always get back to real things by taking a real part. So I understand you've done this before. So let's introduce variable z, just kind of a two-element vector, which has a complex term, a fixed frequency, plus a phase, a rhythm complex, multiplying vector A, a fixed vector A. OK? And vector A is simply has two components, A1, A2, or maybe I should write it differently. So vector A contains information about some sort of initial conditions for position x 1 2. Anyway, these are two constant numbers. And also, we will, because we have this phase here, because we keep phase in this expression, we can assume and require that is a real number. So A is real. It's a slightly different way of doing things, but we can assume this for now, right? So the solution which is written here-- it's some two numbers, oscillatory term, with both x1 and x2 oscillating with the same frequency, and this is our postulated solution. So we plug it into the equation, and we adjust things until it fits. So let's plug this into our matrix calculation. And what you see here is that-- so what do we have? So this is the term, which is second time the derivative vector X. And because vector-- or vector Z really. So I have to do-- so I plug this here. So Z double dot is simply equal minus omega squared times Z. Right? Like this. So this is a simple thing. When I plug this in here, my equation becomes an equation for A. So I have minus omega squared z-hat, which maybe I just write it immediately in terms of a complex term by times the vector A. So I have e to i omega t plus y times A is equal to minus M to minus 1 K times e to the i omega t plus phi times vector A. OK? And this term is a proportionality constant at any given moment of time. So it goes through the matrix multiplication. So you can just delete this. You can divide both sides. You have signs here. And then I have an equation which is a linear matrix equation, which is M minus 1 K times vector A. And I can rewrite it a little bit again. So I can rewrite in this minus 1 K minus omega squared times unity matrix times vector A is equal to 0. So this is the equation which we need to solve to obtain the solutions to at least one normal mode, and we expect that there will be two normal modes, because we have two masses. So now, this is-- so this is some matrix, two by two matrix, which we can know very easily how to write. Multiplying a vector gives you 0. It turns out that for this to work, there are two-- there is a criterion, which has to be satisfied, namely the determinant of the two by two matrix has to be equal to 0, because if you take the determinant on both sides, you have to have 0 on this side to be able to obtain 0 on the other side. So mathematically, the way to find out the oscillating frequency is you take a determinant of m minus 1 K minus i omega squared must be equal to 0. So let's try to see how to calculate things. So let's write down this matrix explicitly using this and that. So let's write this down. So I take a big object like this. And so in this element here, I have to multiply this matrix times that. If I multiply this matrix, I simply divide all those effectively multiplication of m minus 1 times this matrix divides all the elements here by m. That's all there is to it. I just divide everything by m. So the first M minus 1 K is k over m plus g over l. This is minus k over m minus k over m k over m plus g over l. So this is multiplication. This is this term here. And then I have to do minus unity matrix times omega squared. All this will do is it will subtract omega squared here. I should write this. OK? So this is in this one. Maybe it would be more clear if I move it over here. All right, so this is the matrix that contains all the information about our system, the mass, the gravitational acceleration, the length, the spring strength, et cetera. And we assumed they oscillate with a fixed frequency. So I have to find the determinant of this matrix equal to 0. So how do I get that? And by the way, you have a matrix, and you want to make sure that its determinant is 0. It turns out the only variable which we have to change parameters of this matrix-- you know, the spring constant and the mass this affects is given. The system has been built. It's hanging over there. I cannot change anything. So the only parameter here, which I can change, or adjust, or find is omega square. So I will try all possible matrices of this type until I find one or two that have a determinant equal to 0. But if I find them, this would correspond to the normal frequencies. OK? So how do I calculate the determinant of a two by two matrix? I do this by this minus this by that, right? So that of this matrix is equal to k over m minus g plus g over l minus omega squared. The two identical terms so I can put the square and then minus this minus k squared over m squared must be equal to 0. Right? So this is the equation which we need to solve. We need to find which parameter omega sets this to 0. And then this is a pretty straightforward calculation, except if I don't have-- I'll just use this one. OK, so let's rewrite this a little bit. So this is basically equivalent to the following equation g over l plus k over m minus omega squared must be equal either to plus or minus k over m. Right? I took a square root of both sides. If you take a square root, you have to worry about plus and minus signs, right? So there are two solutions which corresponds to plus here. The other one corresponds to minus here. So solution number 1, which corresponds to plus sign right here, it basically says that omega squared is equal to g over l. Right? So there is one solution, one oscillation, that does not depend on the spring constant, because the spring constant cancels. And there's a second solution which corresponds to minus, where omega squared is equal to g over l plus 2k over m. Right? Because there are two possible solutions. And this is what we have. So we have a-- so what this says is that if I set my frequency to g over l, if I set the system to oscillate to this frequency, then it will be-- I will be able to set things up such that it oscillates forever at this frequency, one fixed frequency forever. And this is interesting. This is a frequency. It does not depend on the strength of the spring. How is it possible? Somehow spring is irrelevant for this motion. And it turns out that there is a very simple oscillation, easy to see, if basically that this is a frequency of a single pendulum. So basically, you got both pendula going together, each of them happily oscillating by themselves. And the spring is completely irrelevant for this motion. If I cut it off, the motion will not change. It just happens that two identical pendula are going at their own natural frequency. So the force of spring is irrelevant. Nothing happens. This is a normal mode. And it can go forever at this particular frequency. OK? The other option is usually symmetrically. I move them away from each other. And this is the motion where, again, it's not exactly ideal small angle oscillation, but let me try again, I guess with less. So this is the situation where the spring really comes in at full force. It's being stretched maximally, because they go away from each other. So very quickly, the spring is stretched. And they go together so it's stretch from both sides. And the whole system oscillates at the same frequency, and because of this additional force of spring, the frequency is actually higher, it's larger. It oscillates faster. All right, so that's the first step in understanding the system. We now know that there are two oscillations and two normal frequencies. And the next step to finish our understanding of the system in a mathematical way, to describe it fully, I have to know what is the shape of oscillations. I simply showed you here so you know what to expect. But I have to be able to dig it out from the equations. And the way to dig it out is to find vector A. See, our real equation of motion is up here. This is an equation of motion. This is, I have to now find the vector A, which when you plug it in, it works-- it satisfies this equation. So I already know what are the two possible omegas-- they can do it, but still I have to find vector A. So I have to solve two separate independent problems. One is finding vector A for this situation and then find the vector A for that situation and see if it works. So I had to plug in the whole. I had to plug it into the whole equation. And you can show that if you set-- if you set omega squared to g over l, and you plug it into-- if you plug it into this equation, what you get is a matrix equation which looks like this-- k over m minus k over m minus k over m k over m. And this is because-- [I try to-- so if you plug omega squared here equal to g over l, then this cancels out, and this cancels out. So you plug it in here, and you get this very simple, very simple matrix that has k over m terms. So the question is what sort of thing can you put here to get 0. What kind of vector you can plug into those two places such that the matrix times vector will end up with 0? One example is that basically amplitude is the same. Both of them move together. So you plug 1 here and 1 here. Right? So this is a good solution. And every other solution is a linear multiplication of this one for this frequency, right? There is k over m times 1 minus k over m gives you 0. So this is a good solution for-- so this is solution number 1. What about this thing here? If I plug this omega squared into this matrix, it's g over l plus 2k over m. If I plug it in here, then this matrix is way more complicated. It will actually look very similar, but with important differences. So this one will look minus k over m minus k over m minus k over m minus k over m. OK? And then again, for this second possible normal frequency, I have to find the vector A, which corresponds to that frequency motion. And it turns out that they are the same, but the sign changes. So one possible solution is 1 and minus 1. If I plug in 1 minus 1, then this matrix times the vector gives you automatically 0. So this is the second possible normal mode. All right? So this is a systematic way to solve equations. You plug in all the information you know about the system into a two by two matrix. And then you calculate the normal mode. And then you calculate a shape of a normal mode. Is that clear? Any questions at this time? Right? So in principle, we know, now, at the end of the day, I still want to know how much 1 moves, how much 2 moves. So we have to put it all together. We have identified the frequency and the kind of, in the matrix notation, shape of the node. But of course, the final solution is a linear superposition of all possible normal modes with described position of mass 1, position of mass 2, et cetera. So let's do a little bit of-- so maybe graphically I can write down that this is the-- this is the oscillation that corresponds to this type of mode, to those two masses move together. And this is oscillation that corresponds to the mode where masses move in opposite directions. At any moment of time, in this normal mode, at any moment of time, wherever mass 1 is, mass 2 is minus the distance away from its own equilibrium. So if this one is plus 1 centimeter here, the other one is minus 1 centimeter. This one is minus 5. This one is plus 5 and so on. Whereas in this mode, both of them move together. All right? So let's try to go back to the-- you can get rid of this one. Let's try to go back, and now with this knowledge, let's write down x1 and x2 for positions of the two masses. So x1-- so basically, the x will have to be-- I used z there. So x will be real of vector z. So I take my complex numbers and take a real of them. So from an exponent, I will end up with a cosine appropriately and so on. And then I will use the [INAUDIBLE].. So this is real part of e to the i omega plus phi where omega is one of the two possibilities. Omega t plus phi times vector A, which we've identified here, and times some additional-- these are those vectors A this is one possible amplitude of notation. But in general, it can be anything. You can multiply. You can have small oscillations, large oscillations. So there is some overall amplitude. But the shape always has to be simple. They either go together, or they go opposite. So to make it more general, I have to give some multiplicative factor there. So if I do everything, I end up with x, the mode 1 will in general have some sort of overall constant C, cosine omega 1 t plus phi 1 times the vector 1, 1. This will be for x1. This will be for x2. And the mode number 2 will be C2 cosine omega 2 times t plus phi 2 times 1 minus 1. All right? So let's see what things are adjustable and what things are fixed. So the omega 1 and omega 2 are fixed given by the construction of the two coupled oscillators. This shape, 1 and 1, and 1 minus 1 is fixed, because these are the shape of normal modes, which corresponds to those frequencies. So we have only four constants-- overall amplitude c1 for normal mode 1. Overall amplitude c2 for normal mode 2 and then the relative phase of those two normal modes. And the superposition of x1 plus x2 gives you the most general combination of possible motion. So if I write this down now in terms of position of number 1 and number 2, so I have a position of x1 as a function of time. In general, it will look like this. It will be some sort of constant alpha, cosine omega 1 t plus phi plus constant beta cosine omega 2 times t plus phi 2 plus phi 1. So mass number 1, this is position of mass 1, will in general be a superposition of the two possible oscillations. The position of mass 2 will be very similar, but there will be a very important difference between the alpha cosine omega 1 t plus phi 1 minus beta cosine omega 2t plus phi 2. This is very important to understand exactly how this equation came about. You see, this is the influence of the symmetric mode, where the two things are together. So they are multiplied by alpha, some sort of arbitrary constant, but with exactly the same sign. And this is the part which corresponds to a second mode, which is with different frequencies. And there is an opposite sign between this amplitude and that amplitude. So you have only four coefficients-- alpha, beta, phi 1, and phi 2, which are determined, which need initial conditions. So any arbitrary mode-- this is the most general motion of the two coupled oscillator systems. And to describe it in specifically-- defined for a specific configuration, you will have to determine the values of alphas and phis. OK? So what I want to do is I want to write down a specific motion for the following situation. So I keep position of x1 at 0. It's not moving, so the velocity is 0. I displaced this one by a small positive amount. So the position of number 2 at t equals 0 is different than 0-- some displacement x0 or something. And its velocity is 0. And then I let it go. Again, this is not the ideal decoupled oscillator, right? OK, and then you see the things start moving. Let me try to show it again, because it's not exactly here, so this one will be going on. So let's say this one is running, and then I let this one go. And what you see here is that this one is moving, and then that starts to move. This one stops. That starts moving. It starts being complicated, right? It's kind of complicated motion. But whatever this motion is, we know that it's simply those cosines which are kind of adding up to give you this impression of rather a complicated motion, right? So again, I let this one out. I let it go. This might be 0. So this one slows down. This starts going. And this one then slows down. The other one starts going. They kind of talk to each other. And it's this combination of cosines. All right, so let's try to write to simplify this for a specific case of specific initial conditions. So I said x1 equals 0, to equal 0 x1 velocity at 0 is equal to 0. So those ones are not moving. X2 at 0 is equal to some sort of x0 and x2 velocity at 0 is equal to 0. So this one is displaced. They are all stationary. This one is at position 0. If I plug this in, it turns out without lots of details that what you will get to is that alpha will be equal to x0 divided by 2. Beta will be equal to minus x0 divided by 2. And phi 1 will be equal to phi 2 equal to 0. You can check. If you plug it into those equations, if you plug t equals 0, phi is equal to 0, et cetera, you will see that it works. So you can write down the specific case of x1 of t to be x0 over 2 cosine omega1 t minus cosine omega2 t. It's because beta has a negative sign. And x2 of t will be equal to x0 over 2 cosine omega1 t plus cosine omega2 t. OK? So each of those objects effectively feels the effects of omega 1 and omega 2, but in a slightly different way. That's why their relative motions are different. So what I will do now is I will show you an animation. Hopefully, it works. And we will have time-- since on the computer, you can make things perfect. Let's do it. So I'll have-- running a MatLab simulation. Let's see how it goes. Large. So what is going on here is the following. I took some initial conditions. I'm not sure if it's exactly the same. This was for the course that I taught some time ago. What you see here is the following-- you have the green is the normal mode, number 1. The magenta is normal mode number 2. And blue and the red are the actual pendula. All right? And the motion of blue and red is simply a linear sum of the two. And what you see here is-- and then I plot the position of the blue and red in color, the function of time. So you see this-- the fact that let's say red is now stopped, and the blue is at maximum. And now, the red is picking up. And now the blue stopped, and the red is going full swing, et cetera. And this is exactly what-- this is the computer simulation that shows you that one of them is going up, the other one down, et cetera. And this is for the certain combination of initial conditions. I could go change initial conditions in my program and have a different behavior. But whatever happens, I would be able to-- it will always be a combination of the two motions. Now, is there a way to disable one of the normal modes? How would you disable one of the normal modes? Is there a quick way to set things up such that the second normal mode, whichever you choose, doesn't show up in their equations at all? AUDIENCE: You said [INAUDIBLE]. BOLESLAW WYSLOUCH: Hmm? AUDIENCE: [INAUDIBLE] BOLESLAW WYSLOUCH: Yeah, so what you do, is you just change the initial conditions. So you set it up at T equal to 0. I have initial conditions that basically favor or demand that only in this general equation either alpha or beta is equal to 0. So for example, one possibility is I move both of them at the same distance, and I just let them go like this such that the spring is irrelevant, right? How would I do it in my program? I don't know. I can, for example-- I can, for example, set one of the initial conditions to-- this is still running. The old one is still running. So this is the moment. So what I did is I just changed the initial condition. And you see, this is the type of motion where one of the modes has stopped, just you switched it off, and the other one is going on, and then, of course, the total motion is equal to that. And both of them happily go with a constant amplitude. There is no shifting of energy from one to another. So you can have all kinds of motions by simply adjusting initial conditions. And those motions can be done a very different way. So do you know-- so this is how we can have different shape of motion, depending on the initial condition. Is there another way for me to change the way this system behaves? Let's say I take-- I have exactly this system, and I want to change, for example, the frequency of oscillations. How will I do it? It could be a very expensive proposition, yes? AUDIENCE: Drive it? BOLESLAW WYSLOUCH: Yes, but I don't want to drive it yet. I just want to have it free oscillation. Yes? AUDIENCE: [INAUDIBLE] BOLESLAW WYSLOUCH: Yeah, I could come and scratch it away a little bit. And yes, the equations depends on the mass. But I don't want to touch. I want to just have this thing. I don't want to make any physical modification to the system. However, I can move it into different places, any place you can think of where I could really modify the solution. Yeah? AUDIENCE: To the moon. BOLESLAW WYSLOUCH: To the moon, exactly. I could put it with me some spaceship, and go to a place where the gravity is different, right? Why not? So what would happen? So if gravity changes, then basically what will happen is both this term and that term will change. The spring will remained the same. The mass will remain the same. So the relative magnitude of omega 1 and omega 2 will change. OK? So let's say, in fact, do I have it in this one here? Yes. So let's say I do again. So this is what I had before, right? So this is the one here which is operating here on earth, and I let it go. I displaced it by a certain distance. Let's say 1 millimeter, and that's how it's gone. So now, let's take it to, for example, Jupiter. So what do you think will happen when we go to Jupiter. Jupiter, g, is much larger. OK? So what would happen to those? So the frequency would be larger. Things will be faster, right? That's the higher frequency. But also the difference between two frequencies will be smaller. And what happens when the difference in frequency is smaller? You saw that there's the fact that the energy was moving from one to the other. The thing would take-- so one of them was oscillating, the other one is stationary, then the other one would pick up, et cetera. Do you think this transfer of energy will be faster or slower? Two omegas closer to each other. Any guesses? AUDIENCE: Smaller. BOLESLAW WYSLOUCH: Take kind of longer. Let's see what happens, right? So we go on the rocket, and nowadays, you don't have to go to the rocket. Just remove one comment. And I went from about 10 meters per square second to 25 meters per square second, and this is what is happening. Look at this. So first of all, this identical system-- everything at the same time. It's the same. And so you see that oscillations are much faster. So a number of amplitude changes per second is larger. But it takes much longer for the energy. So the red one is now stopping. It's now slowly coming up. So because the two frequencies are closer to each other, they stay-- it takes longer for them to shift from one to the other. OK? So we are done at Jupiter. Let's now go to the Moon, which has much lower gravitational acceleration. Let's see what happens. Again by logical argument-- if something-- so the smaller gravitation accelerations means that the frequency is now lower. So the pendula will move slower. However, the difference between frequency will be larger, because the spring is still the same strength. So it turns out that even though everything is slower, but the energy transfer will actually be faster. So let's try to see what happens on the Moon. It's OK. It's a little bit not completely clear what's going on, but you see, actually the motion is kind of a little strange. Look at the red one. The red one is stopping. Then it's going halfway out. It looks kind of messy, doesn't it? And so it doesn't show up here very well, because the parameters have changed so much that I have-- I have those fixed pictures which are-- just a second. I'll show you. So this is the picture on the-- some sort of stationary picture on the Earth. I saw one of them up, the other one-- you see them shift from one to the other. And you can see kind of the frequency of how the energy shifts from one to the other. And also you can see the frequency going up and down for the same exact conditions. This is now, just a moment, this is a Jupiter. So Jupiter, you see that the frequency itself it's much higher. And the energy transfer between the two things takes longer. And on the Moon however, the oscillations actually look really weird. This is an example of one of them. It's kind of, you know, the two frequencies are so far away, and it's really not even a nice oscillatory motion. It's some sort of-- it's much less obvious that this is a superposition of two cosines, because they kind of are exactly out of phase. So the motion is kind of complete. Anyway, so this is-- actually, so the lesson is that the exact shape, the exact motion, we know that can always be decomposed into simple motions. If you put them together, things may get really interesting and complicated, depending on what sort of frequencies we are running and what sort of-- what sort of initial conditions we have. All right? Yes? Any questions? Yes? AUDIENCE: It's talking about the center mass of the system or just one of the two --? BOLESLAW WYSLOUCH: This one, I think, this one is just one of them. Actually, the one-- on the difference-- it normally doesn't matter. What matters this is the frequency and how these move to the other. OK? Let's just forget about it. Just keep it. So let me now talk about this thing, which is called beat phenomenon, because when you look at the motion of one of those objects, or the difference between them or whatever, there's something kind of interesting which can be extracted for those equations. Let's look at these equations here. Let's look at mass 1. This is mass 1 and mass 2. So I can rewrite those solutions a little bit different. And so what I want to do is I want to-- you see, this is a difference of two cosines. This is a sum of two cosines. There are lots of neat trigonometrical identities which we can use. So we just-- we do zero physics here. We just rewrite the trigonometrical formulas. So I do exactly this, but I rewrite it. I use, for example, some of-- you have cosine alpha plus cosine beta is equal to-- two cosine-- is equal to two cosine alpha plus beta divided by 2 multiplied by cosine alpha minus beta divided by 2. Right? That's the trigonometric identity. Right? So let's just use this to write this down and what you get is x1-- x1 of t is equal to minus x0 sine of omega 1 plus omega 2 divided by 2 times sine omega 1 minus omega 2 divided by 2 times t. And x2 t is equal to x0, some amplitude cosine omega 1 plus omega 2 divided by 2 cosine omega 1 minus omega 2 divided by t. So again, we did zero physics here. We just rewrote the simple trigonometric equations. But what you see is something interesting here. So there is-- we have those two frequencies which are playing a role. And for example, at Jupiter, those two frequencies are actually very close to each other, because everything is dominated by the gravity, and we have a very weak spring. So the omega 1 and omega 2 actually are very close to each other. So this thing, this term here, kind of goes omega 1 plus omega 2 divided by 2 is like omega, right? 100 plus 105 divided by 2 is about 100. Whereas this one here carries information about the difference of frequencies-- 100, 102, the difference is 2, which is very small. So how would this look like? So if you make a plot under some conditions, you can, let's say, so the two frequencies are close to each other. So if omega 1 is close to omega 2-- for example, omega 1 is 0.9 times omega 2, right? This is roughly what we have on Earth in case of our system here. Then omega 1 plus omega 2 divided 2 would be about 0.95 omega 1, omega 2, I think, which is approximately equal to omega 2 or omega 1 and omega 1 minus omega 2 divided by 2 will be about minus 0.05 times omega 2-- much, much smaller than that. So we have-- so this term here-- it basically oscillates at the frequency of omega, of the frequency of the individual pendulum. And the other term is much, much smaller. How does this look? Well, it turns out that if you make a sketch of this, if you do signs, for example, it looks like this. OK? So there are in fact two-- when you look at this picture, you can see two frequencies. One which is clear the oscillation of the-- high-frequency oscillation of things moving up and down. But there's also this kind of overarching frequency of much smaller frequency, and this is what corresponds to a difference of two things. So in a sense, if you look at this formula here, you have oscillation, which is happening very quickly with a typical oscillation of the system. But this is like a modulation of the amplitude. So the amplitude of the signal is changing. And this is what you see here. This is exactly the picture out there. So the system oscillates. So one of those pendula, either of them, is moving fast. But it's going faster. It's amplitude is larger, and after some time, it slows down to 0. It goes higher and slows down to 0. And you've seen this. We can do it again here that both of them oscillate at roughly the same frequency, but their individual amplitudes are changing. And this transmission of-- you know, one of them moving full blast, the other one moving full blast. There's this kind of frequency of energy moving from one to the other, which is something called beat. This a beat system, beat phenomenon somehow that energy is moving from one place to another one. And we can have some demonstration of how this happens. So we see this here. We see it on the pendula. We saw it on the computer simulation. But now what we are going to do is we're going to try to hear it, right? So this is a demonstration which maybe it works, maybe not. So let me-- it will work, OK? So let me explain what we have. So we have two speakers. And they basically go on very, very similar frequencies, all right? So they both work at similar frequencies. And so when I switched on, you should hear-- hear the sound. [HUM SOUND] OK? So this is the frequency. I believe it's just one of them is working, and you know, this is just one pendulum that is going on that given frequency, right? Then I will switch a second loudspeaker. [HUM SOUND] Can you hear this kind of-- wiggle? We'll change the frequency a little. This is another frequency of the original sound. And it's kind of the loudness of the sound overall is changing. All right? This is faster. This is kind of extra, extra sound which you hear is the difference of mainly the frequency is not stable here, so I'll change it. Right? So this is, again, this is a single one, perfectly constant frequency, no change in amplitude, no change in loudness. Put them together, right? That's what they do. So if you have two, and I can adjust the frequency, and the frequency is close, then this frequency of changing is very slow. So you can actually hear it. Let me switch it off. So this is the effect of beats. I can maybe show you another simulation of this works. Let's See. This one is oops, just a second. Let's see what it is. OK, so this is just a single frequency. OK, again, I plot some pendulum. Then I can plot-- sorry, no this one is this. I can-- this one. OK, we'll just plot it here. Maybe we can see. So there's a red one, and there's a blue one. And I plot two plots independently on top of each other. So they have an amplitude of 1. And clearly, you see that they have a different frequency. So the red one is going with some frequency. The blue one is going with some other frequency. Sometimes they agree. Sometimes they do not agree, right? And the places where they meet-- they are on top of each other. This is where when you add them up together, this is where they will be large. In the places where they're out of phase, they will cancel each other. So if you take two of those together, same amplitude, just slightly different frequency, and you simply make a linear-- superposition of the two, you will get exactly the beating effect. So I just took two of those pictures before I added them together and got exactly that. You have a maximum, minima, et cetera. And you see this overall beat frequency, and the carrier, it's called carrier frequency. And this is something that, again, happens very often. There's another demonstration here. I have two tuning forks, and they are very similar frequency. So first, I will show you that they are coupled. They are coupled because I gave this guy some initial condition. It's going. Then I stop it. But there's still sound, because the second one picked up some energy, and it took off. Of course, you don't see them. So basically, what I'm saying is that I [TONE] give this energy. This one is completely stationary. Now energy is slowly moving to the other one. I stop this guy, and this guy is still going. So the energy is being transferred by this air oscillating here. The coupling goes through the air to the sound here, right? And they have very similar frequency. So they are nicely coupled. But what we can also do-- we can [TONE]. Right? So they're both going. Do you hear the beats? [TONE] Not really. In fact, if they would have exactly identical frequency, right? If they will be perfectly the same, then the difference would be 0, and there will be no beats at all. The period of beats will be infinitely long, so it will take forever for us to hear anything. So what we can do-- we can break one of them. We can add some sort of weight. Some are here. There's some magic place where it works best. So what I would do is I will break this one. I will modify its frequency. That's another way to modify. I don't have to go to Jupiter to modify it, because this one is just a little mass here, right? [TONE] Ah, cool. AUDIENCE: Is that [INAUDIBLE]? BOLESLAW WYSLOUCH: Really, this is actually a huge effect. [TONE] You can clearly see that they are going up and down, up and down, because the frequency is slightly different. So now, this thing is probably-- I know it's a period, a fraction of a second, right? Yes? AUDIENCE: Should both of those sine and cosines have Ts in their arguments? BOLESLAW WYSLOUCH: Of course always. They are both time dependent, yeah. This is the fast thing, and this is this time-dependent modulation, yeah. All right, so where are my notes? So this is the-- this is how the-- so we were able to set up the system, put in some of the matrix equation, kind of solved it, found two frequencies, et cetera. There is one more-- one additional trick, which you can do to describe the motion of a coupled pendula. And that is, in a sense, force mathematically, force the normal modes from sort of early on, to instead of, so far, when we talked about pendula, we describe their motion in terms of motion of number 1, motion of number 2. It turns out we can rewrite the equation into some sort of new variables, where, so-called normal coordinates, where you'll simultaneously describe both of them and then kind of mix them together to have a new formula, just rewrite the equation in terms of new variables. So you do change of variables. So instead of keeping track of x1 and x2 independently, you define something which I called u1, which is simply x1 plus x2, and I define u2, which is x1 minus x2. So instead of talking about x1 and x2 independently, I have a sum of them and difference. Why not? Right? Two variables. I can always go back and get x1 and x2 if I want to. So if one tells me that u1 is 1 centimeter and u2 2 centimeters, I can always go and get x1 and x2 if I want to, right? So I can do it. And it turns out that if I plot those variables in, in other words, I take the original equations, which I conveniently erased and make a sum or difference, it turns out that this coupling kind of separates. So I will end up having two separate equations for this one. So in general, the equation of motion would be-- would look like, so let's say I can write down m x1 plus x2 is equal to minus m g over l times x1 plus x2. OK, this is when I add two equations. And the other equation when I subtract them-- minus x2 is equal to minus mg over l plus 2k x1 minus x2. I think that's what is coming out. So if I add and subtract the two original equations of motion, which I don't know if I have them somewhere, and you can look back, then you end up having those crossed terms drop out. And you have one, which has only this coefficient, the other one which has that coefficient. And this immediately-- and it looks-- if I now write it in terms of normal coordinates, then I have that m u1 double dot is equal to simply minus mg over l, u1, and m u2 double dot is equal to minus mg over l plus 2k times u2. And if you look at those two equations, it turns out that they are not coupled. Each of them is a question of a one-dimensional harmonic oscillator. The first part one only depends on u1. The second one only depends on u2. And you can see the oscillating frequency with your own eyes. So no, the determinants needed no matrices, no nothing. We just added and subtracted the two equations, and things magically separated. All right? So sometimes, especially in case of very simple and symmetric systems, if you introduce new variables, you can simplify your life tremendously, and these are called normal variables, normal coordinates. And it turns out that you can always do that. So you can always have a linear combination of parameters for arbitrary size coupled oscillators system where you combine different coordinates, and you basically force the system to behave in a way in which it induces the single oscillation, single frequency. So this is, again, a very powerful trick, but usually for most cases, you can do that only after you have solved it, after you've found out normal modes, et cetera. So after you know your normal mode, then you can say, ha, ha, I can I can introduce normal variables and make things simpler. But at the end of the day for complicated systems that work is the same. But for simple systems like this one where there is a good symmetry, you can do it. Anyway, so I think we are done for today. And on Tuesday, we'll continue with forced oscillators. All right? Thank you. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | Using_Humor_to_Enhance_Learning.txt | yeah so I think a sense of humor is really a very very good tour of you in a teaching so so I use the insert interesting figures in my slides then people will be really focusing on your slides and your lecture and that because people don't want to miss the joke right and also lab makes the lecture much more enjoyable as well because everybody wants to learn things happily okay so and also those jokes I insert most of the time that they are relevant physics interpretation of those jokes so that's actually my idea to make the lecture much more enjoyable and also keeping the students very focused and the material recovered so my idea is to have a much more relaxed customer-owned so that you can actually then people feel that they can ask whatever questions they have because I not like super serious I mean asking for everybody to keep quiet we cannot react to any funny things right I have been doing from here I should be Maxwell see the light can you see it maybe not yet maybe we're slightly slower than Maxwell but but we will see that together in this lecture first of all I will feel very relaxed because I ever I want to help the students and also the students will feel that there's racial passing questions were greatly reduced if the instructor is actually very funny very very humorous so that's actually my idea and which drive me to the decision to insert a lot of interesting pictures and the jokes during the lecture |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 6_Driven_Oscillators_Resonance.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. BOLESLAW WYSLOUCH: Let's get started. So today hopefully will be a busy day, with lots of interesting insights into how things work. We talked about coupled oscillators last time. We developed a formalism in which we can find the most general motion of oscillators. So let's remind ourselves what are the coupled oscillators. Coupled oscillators, there are many examples of them, and they have more or less the following features. You have something that oscillates-- for example, a pendulum. You have to have more than one, because for coupled oscillators you have to have at least two. So let's say you have two oscillators. So each of them is an oscillator, which in, for example, in the limit of small angles, small displacement angles, undergoes a pure harmonic motion with some frequencies. And then you couple them through various means. So for example, two masses connected by a spring is an example of a coupled oscillator. We could have two masses on a track and another track, also connected by several springs. This is also an example of a coupled oscillator. Each of those masses undergoes harmonic motion, and they are connected together such that the motion of one affects motion of the other. You can have slightly more complicated pendula. For example, you can hang one pendula from the other. Each of them-- again, in the limit of small oscillations-- will undergo harmonic motion. And they are coupled together because they are supported one on top of each other. And you can have-- we have another example of two tuning forks sitting on some sort of boxes. Each of them was an oscillator, with audible oscillating frequency, and by putting them next to each other they coupled through the sound waves transmitted through the air. So one of them felt the oscillations in the other one. This was an example of coupled oscillation. Two masses and the thing. You can build oscillators out of electronics. Some capacitor and inductor together, with a little bit of-- maybe without resistors. You have two of those. They constitute a coupled oscillator if you put a wire between them. So there are many, many examples. And of course, these are all examples in which you have two oscillating bodies, but it's very easy to have three or more oscillating bodies. Then basically the features of the system are the same, except the math becomes more complicated, and we have more types of oscillations you can have. And there's a couple of characteristics which are the same for all oscillating systems. And it's very important to remember that we are learning on one example, but it applies to very many. Number one, any motion-- I can maybe summarize it here. So if you look at the motion of an oscillator, you can have-- let's say arbitrary oscillation. Arbitrary excitation. Excitation means I-- I kick it in some sort of arbitrary mode. I just come in and set up some initial condition such that things are moving. And motion in this arbitrary assertion is actually-- looks pretty chaotic. It looks pretty variable, changing. It's difficult to understand what's going on. So And it clearly doesn't look harmonic. Non-harmonic. There is no obvious single frequency that is driving the system. If you look at amplitude of the objects here-- for example, two pendula, pendulum one and two. At any given moment of time they are oscillating, there's a characteristic amplitude. But what we saw is that motion changes, looks like things are flowing from one to the other. One of them has a high amplitude. After some time, it cools down, the other one grows. So the amplitudes are changing in time. So they are variable. Are variable. And also, we didn't calculate things exactly, but you know from study of a single oscillator that if the things are moving, it has a certain amplitude, there's certain energy involved-- with some potential, some kinetic-- and it's proportional to the square of amplitude. So it's clear that energy is moving from one pendulum to the other. This one was oscillating like crazy. So all energy was sitting here. After some time, this one stopped. So its energy is zero. And the other one was oscillating like crazy. So the energy's flowing from one to another. It's not sitting in one place, but it's flowing. This one has lots of energy right now, but now that one is picking up. So the energy-- you see the energy flowing here. And this one will eventually stop-- well, this is a pretty crappy oscillator, but it will eventually stop, and this one will have all the energy. And this is, again, characteristic in every system. We can see energy flowing around from one to the other, growing, stopping. So it's-- in general, in the most general case, it's a complicated system. Energy is migrating between different masses. However, every single one of those coupled oscillating systems has a magic. There's a magic involved, namely the existence of normal modes. Every single coupled oscillator system has normal modes, and those modes are beautiful. Those modes are-- everything is moving in sync. So this is normal mode excitation. There's a very special way, a special setting of initial conditions, that leads to the-- that results in a pure harmonic motion. So this is a harmonic motion, with a certain frequency omega, characteristic frequency for this particular motion. The amplitudes remain fixed. Once you set initial conditions, you get it moving, everything is moving, simple harmonic motion means its amplitude is constant. So if I-- and remember, for example, this system. It was something like this. Symmetric or antisymmetric motion. And if not for the friction, the amplitudes would remain constant forever, if it will be a perfect oscillator. So amplitudes-- in fact, it's not amplitudes themselves, but amplitude ratio. The ratio of amplitude between the different elements in the system is constant. So in a sense, every harmonic motion has a characteristic shape. And then by-- since everything is constant, nothing changes, this energy stays in the place it is. So energy is-- once you put energy to mass number one, mass number two, mass number three, the energy sits there. The energies are constant, as the system undergoes harmonic motion. Energy does not migrate. So this is a very nice-- and there is another beautiful feature, that any arbitrary excitation can be made out of some linear sum-- sum of normal modes. Linear sum, of superposition of normal. Any arbitrary excitation with all its complicated motion can be made into some of normal modes. So since normal modes are easy and simple and beautiful, the description of motion of any coupled oscillator, the best way to approach it is to decompose it, to find all possible normal modes, and then decompose the initial condition to correspond to this linear sum of normal modes. Once you know the normal modes, you add them up, and then you can predict exactly the motion. And this is what we've done. So we have a-- we have introduced a mathematic mechanism in which we put all the information about forces and masses in the system in some sort of matrix form. In our example, it was a two by two matrix, but if we have three masses or four masses, the dimensionality of the matrix will have to grow. But the equation will remain the same. So this equation of motion, we rework it a little bit. Since we are looking for normal modes, we know that normal modes occur with this one single frequency. So we postulate an oscillation with a frequency. We plug it in. We obtain a simple algebraic equation. Doesn't have any time dependence, doesn't have any exponents. It's a simple algebraic equation, basically a set of linear equations, which we can solve and find the eigenvalue, or the characteristic frequency for normal modes. And you can show that the number of those frequencies in general is equal to the number of masses involved in the system. And you solve it, and then once you know the characteristic frequencies, then you can find shape, you can find the eigenvectors. What is the ratio of amplitudes which corresponds to the mode. And in case of our two pendula, there are two of such things. One is where both amplitudes are equal, and this corresponds to oscillation in which two pendola are moving parallel to each other, with a spring being-- not paying any roll. So this is one mode. And then amplitude is-- as I said, any given moment is the same, so the ratio is 1. And then you have a motion in which the two pendula are going against each other. So any given moment of time, they're in their negative position, so the ratio is minus 1. The motion of one of them can be obtained by looking at where the first one is and multiplying by minus 1. So these are the two modes, and any arbitrary-- any complicated, nasty excitation with things moving around is a linear sum of the oscillation. So we know that. We've worked it out. We used this example. And by the way, today, we'll be using two examples-- one which is the same thing with two pendula and the spring, and the other one with two masses, or maybe later three masses. And the exact values of coefficients in matrix k are different in two different cases. But in all types of other motion, the shape of motion, the behavior of the system is identical. So the solutions to the two cases are identical. The difference is basically numerical in how the spring constants and masses come in. So we can in fact treat those two systems completely the same. So I'll be jumping from one to another, but we don't have to worry. But let's now look on the system. So what we are trying to do today is, we are trying to apply external force so we'll have a driven coupled oscillator. And I assume that you know everything about driven oscillators. So the idea was that you come with an external . In 8.03, we assumed that this external force is harmonic force. So there's a characteristic frequency which is given by external-- let's say by me. It has nothing to do with normal frequencies of the system. It's an external frequency, omega d, which I apply. Driven frequency. And then I look at how the system responds. And I look for steady state oscillations-- the ones where everything oscillates with the same driven frequency-- trying to look for solutions. And as you know from a single oscillator, what we were calculating is what is the the response of the system? What is the amplitude? And the certain frequencies that-- you wiggle it and the system doesn't do anything, but if you apply a certain resonant frequency, then the response is very large. The system starts moving like crazy, et cetera. And the same type of thing will happen here, except that we have multiple frequencies. So there will be a possibility of a resonance for several frequencies. All right? So let me quickly set this up. Just-- yeah. Doesn't matter. So there were some-- let's just start working on the example. So just a reminder, this is our system. A pendula of some length L. There are two identical masses, M. There is a spring of constant k. They are all-- and for simplicity, we assume that we are all in Earth's gravitational field. So we don't have to worry about traveling to Jupiter or the moon. And-- except that the difference will be that we apply an external force to one of those masses. How, it doesn't matter, but there is an external force F-- F with subscript d, which is equal to some-- it has some amplitude F0 cosine omega d times t, along the x direction. And this is applied to mass one. OK. And there is a little bit of just a warning. We will be assuming that there is no damping in the system. For the single oscillator, there was always a little bit of damping. So between you and me, remember there's always a little damping. So in case we need damping-- it will come in and will help us, but if we try to use damping in calculations, calculations become horrendous. So for the purpose of calculations, we will ignore damping. It'll get some. But if things go bad with the results, like dividing by 0, then we will bring in damping and say no no, it's not so bad. Damping helps you. We are not dividing by 0. OK? So let's write those equations of motions. Equations of motion. So we have-- so the forces and accelerations on mass one is the same as before. There was a spring. There is mg over l. That's the pendulum by itself. Depending on position x1. There is the influence of a spring, which depends on where spring number two is. And, plus, there is this new driven term, F0 cosine omega d times t, where omega d is fixed, arbitrary, externally given. So both F0 and omega d are decided by somebody outside of the system. Now, the second mass M X2 dot dot, is-- actually has feels position of x1, through the spring. And there is this-- its own pendulum effect plus a string, depending on position x2. Interestingly, there is no force here, because the force is applied to mass one. So mass two a priori doesn't know anything about the force. But of course it will know through the coupling. Yes? Questions? Anybody have questions so far? So it's the same as before, with the addition of this external force. Again, this is writing all coordinates one by one. We immediately switch to matrix form. We write it MX double dot, where X is the same as we defined before, minus KX. I think I will stop writing these kind of thick lines. But for now, let me-- F cosine omega d times t. So this is now a matrix equation for the vector XD. And let's remind ourselves what those matrices are. Matrix M is M 0 0 M. This is just mass of the individual systems. We use M minus 1, which is 1 over M, 1 over M, and diagonal 0 and 0. So this carries information about masses, inertia of the system. Matrix K contains information about all the springs in the system, and some pendula effects. So we have a k plus mg over l, minus k, minus k, k plus mg over l. And now there is this new thing, which is this vector F. Vector F is equal to F0 0 cosine omega d times t. So this is in a vector form, this external force, which is applied only to mass number one. OK? So these are the elements which are plugged in. So now the question is, what do you want to do with this? So we have the equation of motion. And so what do we do with this? So there are two steps that we have to do. Number one, we have to remind ourselves what are the normal modes of the system, in case-- because we will need-- the information about normal modes will come in as-- into solutions for a driven motion. So let's remind ourselves what this was. Well, this was a solution. I'll just rewrite it very quickly such that we have it for the record. It should fit here. Now let's try. So there were two solutions. There was omega 1 squared, which was equal to g over l. And the corresponding normal mode was a symmetric one. It was 1, 1. OK. So this was one type of solution, where the two masses were moving together. There was a second frequency which was equal to g over l. The square of it was equal plus 2k over m. And this was the characteristic normal frequency for the second type of oscillation, which you can write it 1, minus 1. And the criterion for when we were looking for solutions, we would find them by calculating the determinant of this two by two matrix. It was the determinant of m minus 1 k minus omega squared times unit matrix was equal to 0. So this was the equation that had to be satisfied for frequencies corresponding to normal modes with zero external force. Interestingly, if you do the calculations, it turns out you can-- algebraically, you can write-- after you know the solution itself, you can write it in a very compact way. So this determinant can be written in the following way-- omega squared minus omega 1 squared, times omega squared minus omega 2 squared. And this is-- the condition was zero. And you see explicitly that this is a fourth order in frequency equation, fourth order frequency, which is 0 for omega 1 and for omega 2. In a very explicit way. So this is a nice, compact form of writing this particular eigenvalue equation. And again, as a reminder, the motion of the system-- the most general motion of the system with no external force was a superposition of those two oscillations, which we can write as some sort of amplitude-- 1, 1 cosine omega 1 t plus phi 1, plus beta 1, minus 1 cosine omega 2 t plus phi 2. So this is oscillations of two different frequencies. This is the shape of oscillations, the relative amplitude of one versus the other. And then there's the overall amplitude alpha and beta, which has to be determined. And then there are arbitrary phases. So there are in fact four numbers, which can be determined from four initial conditions. So typically two positions for the two masses, and two initial velocities for two masses. So everything matches. So this a so-called homogeneous equation. Homogeneous solution. What about driven solution? Driven solution, as we remember from a single oscillator, results in a motion in which all the elements in the system are oscillating at the same frequency, and that's the driven frequency. It's a fact. I come in, I apply 100 Hertz frequency, and everybody oscillates on the 100 frequency. That's the solution for a driven oscillating system. And we saw it for a one-dimensional oscillator, and we will see it here as well. There's one frequency, omega d. So we will be now looking for a solution which corresponds to the oscillation of the system with this external frequency, which a priori is not the same as one of the normal frequencies. So the complete motion of the system consists of two parts. One is this homogeneous self-oscillating motion with two characteristic frequencies. And there will be a second type of motion, which is a driven one. So how do we go about solving that? So equations of motions of course will be the same. The solution, the way that we solve it will be very similar. So lets try-- start working. Maybe we can work on those blackboards here. So what is going on? So we know that if we apply external frequency omega d, everybody in the system, all the elements will be oscillating with the same frequency. So we can then introduce a variable Z, which will be defined B e to the i omega d t. This will be the oscillating term. And this will be the amplitude of oscillation, which we'll try to make real for simplicity. And then we plug this into the equation of motion, which is listed up there on the screen. So the equation of motion is Z dot dot plus M minus 1 K times Z is equal to now M minus 1 force e to i omega d t. You see our external force is F cosine omega d t, with a vector 1, 0. But of course, in the complex notation, this is exponent. So this is the challenge, what we would like to have. And we assume that all the elements in the system-- position, acceleration-- oscillate at the same frequency omega d. If you do that, then the equations become somewhat simpler, because the oscillating term drops out. So when you plug this type of solution into here, what you get is minus omega d squared-- that's from second differentiation with respect to time-- plus M minus 1 K, multiplying vector B e to i omega d t. This must be equal to M minus one F e to i omega d t. This is vector B, this is vector F. And there is this oscillating term. But both sides oscillate at the same frequency. That's what we assume. So we can simply divide by this, and we are left with an equation that equates what's going on in the oscillating system with the external force. So now, let's see here what is known and what is unknown in this equation. M minus 1 K carries information about the construction built of the system of accelerators. Strength of springs, masses, gravitational field, et cetera. So this is fixed. This is given. Omega d is the external driving frequency, and it's also given. It's a number. I said this is externally given. I just set it at some computer. Say 100 Hertz, and it's driven at 100 Hertz. So we know that. We know exactly what this number is. External force, we know what it is. We defined it. It's F0. We know what its magnitude-- so everything is known except for vector B. And vector B are the amplitudes of oscillation-- remember, everything oscillates at omega d-- of mass one and mass two. So in general, if I apply external force, this guy will oscillate with some amplitude. That guy with some amplitude, a priori different. And this will be B1, this will be B2. And we don't know that at this stage. So this equation will allow us to find it. And it is possible because-- this is actually a very straightforward equation. It contains-- actually, to be very precise, I have to-- this is a number, this is a matrix. So I have to put a unit matrix right here. So it's omega d times unit matrix plus this matrix that carries information about the system. And so we can write this down again in some sort of more open way, for our specific case. So this will be k over m plus g over l, minus omega d squared, minus k over m, minus k over m, k over m, plus g over l, minus omega d squared. So this is this matrix here. This matrix is applied to vector B, which is our unknown. Let's call it B1 and B2. These are the amplitudes of oscillations of individual elements in our system. And this is equal to m-- the inverted mass matrix times vector F, which-- without its oscillating part, which is simply F0 over m and 0. All right. So this is the task in question, and we have to find out those two values depending on these parameters and the strength of force, et cetera. So this is actually not a big deal. It's a two by two equation, two equations with two unknowns. We solve it, and we are done. However, we want to learn a little bit about slightly more general ways of calculating things. So let's call this one matrix E, with some funny double vector sign. Let's call this one vector B, and let's call this one vector D, because we will use this-- use it later. And what we are trying to do is, we are trying to use the so-called Cramer's rule to find those coefficients B1 and B2. And for some historical reasons, 8.03 really likes Cramer's rule. I like MATLAB or Mathematica. I just plug things in, and it crunches out and calculates. But it turns out that for two by two, you can always do it quickly. Even for three by three, if you just sit down and do it, you can actually work it out. It's not scary. By five by five-- but even four by four, I'm sure you are mighty students who can just do it in the exam. I have never seen an 8.03 exam with four masses, unless they're general questions. But three-- well... All right. So do we go about finding this B1 and B2? Because, again, this is a simple two by two question. So maybe just to again bring it even closer to what we are used to, let me just quickly write this down as a set of two by two equations. So there is a coefficient here, k over m plus g over l minus omega d squared, which is-- this is a number, times B1 minus k over m times B2 is equal to F0 over m minus k over m B1 plus k over m plus g over l minus omega d squared is equal to 0-- times B2 is equal to 0. So you see two equations with two unknowns. Couple of coefficients, all fixed. You can eliminate variables. You can calculate B2 from here, plug it into-- you can work it out if you want to. However, there is, again, a better way. It's Cramer's rule or method. Should have known if it's method or rule. Rule. Right. And so the way you do it is the following. So you look at those questions-- you calculate all kinds of determinants, and by taking the set of two equations and plugging into-- replacing columns in the matrix. So B1, what you do is you take the original matrix, which is here, and you replace the first column of the matrix with vector B. So you-- no wait, with-- sorry, with vector D. Take this matrix, and you plug in this. So what you do is-- so it turns out-- so B1 can be explicitly calculated, but taking the determinant of the first column replaced, F0 over M0, and keeping the second column, which is minus k over m. m and then k over m plus g over l minus omega d squared. So this is-- you calculate the determinant of this thing, where-- original matrix with the first column replaced. And you divide it by the determinant of the original matrix. Let's call it E. So you calculate this determinant again for the frequency omega d. So this can be written very nicely, in a very compact way. This determinant is easy. It's just this times that. So have 0 over m multiplying k over n plus g over l minus on I got the squared remember this is a given number divided by n Here comes this nice compact form for the determinant, which is omega d squared minus omega 1 squared, times omega d squared minus omega 2 squared, where omega 1 and omega 2 were the normal mode frequencies. Yes? AUDIENCE: Where are you getting the minus k in the [INAUDIBLE]?? BOLESLAW WYSLOUCH: This one? AUDIENCE: Yeah. [INAUDIBLE] BOLESLAW WYSLOUCH: This one? This is the second column. See? I'm taking-- so this is the first column, second column. I take the first column, I replace it with driven equation-- with a solution. I plug it here. So I have F0 for M0. And I keep the second column. All right? That's for the first coefficient. For the second coefficient what you do is, you put a driving term here and you keep the first column. All right? So this is actually an explicit solution for B1. This is magnitude of oscillations of the first element. And you can do the same thing for B2. And I'm not trying to prove anything, I'm not trying to derive anything. I'm just using it. And I'll show you a nice slide with this to summarize. So B2 is the determinant of-- I keep the first column. It's k over m plus g over l, minus omega d squared, minus k over m. That's the first column. And I'm plugging in F0 over M here, and 0 here. So this is-- and divided by omega d squared minus omega 1 squared times omega d squared minus omega 2 squared. That's the determinant of the original matrix. And this one is also very simple It's this time this is 0. I have minus that. So I simply have F0 k over m squared divided by omega d squared minus omega 1 squared, omega d squared minus omega 2 squared. All right. So we have those things, and also what? Do you see anything happening here? Yeah, there are some numbers, but what do they mean? What does it mean? Yes, we can calculate it. You can trust me. These are the-- I'm not sure that you can trust it, but most likely these are good results. And so we know the oscillation of the first mass, oscillation of the second mass as they are driven by the external force. Now, one of the interesting things to do is to try to see what's going on. One of the-- when we talked about normal modes, the ratio of amplitudes carried information. Remember, we had those two different modes. Either amplitudes were the same, or they were opposite sign. So let's ask ourselves, what is the ratio of B1 and B2? So let's just divide one by the other. So let's do B1 over B2. Let's see if we learn anything from this. If you divide B1 over B2, this bottom cancels out, and I have k over m plus g over l minus omega d squared over k over m. And-- yeah. So now comes the interesting question. This omega d can be anything. So let's say omega d is-- so we can analyze it different ways. So for example, when omega d is-- you can look at small, large, and so I can compare it. But one of the interesting places to look is, what happens when omega is very close to one of the-- to the characteristic frequencies? Because, remember, when we analyzed a single driven oscillator, the real cool stuff was happening when you are near the resonant frequency. Things, you know, the bridges broke down, et cetera. So let's see if we can do something similar here. Now we have two choices. We have omega 1, omega 2. So let's see what happens if I plug in omega 1. Omega d being very, very close to omega 1. Let's say equal to omega 1. Omega 1 is-- omega 1 squared was g over l. So if I plug omega 1 here, I have k over m plus g over l. So I have k over m plus g over l, minus g over l, divide by k over m, which is equal to what? Those two terms cancels. k over m, it's plus 1. That's interesting. So if I drive at a frequency which corresponds to omega 1-- and omega 1 was the oscillation where both masses were going together. So the characteristic normal mode had the ratio of two masses equal to one. And here I'm getting the system to drive at this type of mode. Again, I have-- the driven amplitudes are the ratio is equal to one. So what happens if I drive at omega d close to omega 2? Omega 2 squared was equal to g over l plus 2k over m. If I plug it in here, I get that the ratio is minus 1. Again, the ratio is strikingly similar to the ratio of the normal mode corresponding to frequency omega 2. So it's like I'm inducing those oscillations. So what does this all mean? There's, by the way, a little catch here for all of your mathematicians. What happens to equations if I set omega d equal to minus 1-- to omega 1, for example? I just plugged it here, and nobody screamed. But there was something fishy about what I did. Yes? AUDIENCE: --coefficient [INAUDIBLE] BOLESLAW WYSLOUCH: If you took-- AUDIENCE: Oh, sorry. [INAUDIBLE] BOLESLAW WYSLOUCH: Exactly. So the ratio of the two was one, but both of them were infinite. So infinite divided by infinite equals what? I mean, this happens. So what's going on? Why can I do it? One-- we should not really scream. Damping. Exactly. This is where the damping comes in. So the amplitude is enormous, but it's not infinite, because there's always a little damping. The system will not go to infinity. So in real life, there's a little term here that makes sure things don't blow up completely. There's a little damping here. Yes? AUDIENCE: Does it at all matter-- also the fact that those equations are inexact in the first place, because we had made theta smaller-- BOLESLAW WYSLOUCH: No. That's not-- no. This doesn't actually matter. It's the absence of damping that makes things look nonphysical. AUDIENCE: But as the frequency-- as the amplitude increases, when we're in resonance, eventually those equations wouldn't hold any longer, and perhaps-- BOLESLAW WYSLOUCH: Yeah, that's right. But you could-- that's true. That's true. But you can come up with, for example, an electronic system which has a huge range of-- enormous range of possibilities. And then-- or of amplitudes. Many, many-- so the damping is much more important in that. So in reality, there is some damping here and so forth. All right. So why don't we do, now, the following. So let's try to see how this all works out. First of all, such that we can get started, I will make a sketch for you. I'll calculate these formulas-- just a second-- and display you as a function of frequency, such that we can analyze what's going on. So where is it-- OK. It's still slow. All right. So this is what those-- OK, so let's say-- I don't know which is which, but let's say B1 is the red one, B2 is the blue one, or vice versa. It doesn't matter. These are the numbers which I plug in for some values for some system. So we see that-- and this is as a function of frequency. So first of all, you see a characteristic frequency around one, characteristic frequency around three on my plot. And in the region in the vicinity of frequency number one, you see that both the blue and red, the individual amplitudes are basically close together. So the ratio is close to one. If you look at this plot, you should believe me that it's plausible that if you are very close to the frequency, basically the red and blue will move together. If you go around the second frequency, you see that red goes up, blue goes down, or vice versa on the other side. So the ratio is minus 1. So this plot actually carries in formation. And in fact, what you see also is that there is some sort of resonant behavior. So the amplitudes are enormous if you are close to any of those characteristic frequencies, but they're much smaller if you're further out. There is some motion, but not as pronounced as when you're at the right driving frequencies. All right. So let's try to see it. Why not? So let me go to another system-- a system which consists of two masses, has the same type of behavior, slightly different parameters. There is no g here, but everything looks the same. It's just much easier to show. And I can remove most of damping. And you'll see there are again two modes, one which is like this-- that's number one, that slow motion. They move together. And the other one, which is like this, where the amplitudes are minus 1. This is the frequency number two. So now let's try to drive it. How do I drive it? I have some sort of engine here which is applying frequency. So let's start with some sort of slow motion. So you see they are moving a little bit. Very small, minimally. Just a tiny motion. But they're kind of together, more or less, right? Slowly, but together. And this is what-- this is this area here. I don't know if you see that. This is this area. I'm driving at a very slow frequency. I'm somewhere here. The two masses kind of go together, but very slowly. So let me now crank up the frequency and try to be in the region of oscillation. So you see? All I did is I changed frequency. The effect is enormous. I'm somewhere here now. You see? Enormous resonance. And very soon, I will hit the limit. The system will break. OK, so we are somewhere here. I'm driving it. Interestingly, this really looks like a harmonic motion of first type. There is no other things. OK, so now let's swing by and get to this area. So all I'm doing is, I quickly change frequency to- this one. So now what you see is that there were some random initial conditions, so we have a homogeneous equation going, but the driven is coming in. All I did is I changed frequency. And suddenly the system knows that it has to go like that. Isn't that cool? So this is the region here. And all I'm doing is I'm bringing the amplitude up, because this is close to zero. And then I'm keeping the ratios close to the characteristic modes. So I think-- to be honest, this is one of the coolest-- all I'm doing, just changing frequency. And the system just responds and starts going with a resonance of one particular mode. So imagine a system that has 1,000 masses, and you come in with 1,000 frequencies. You tune one frequency, and suddenly everything starts oscillating in one go. And imagine you have multiple buildings, each with different frequency, and there's an earthquake. And the frequency is of a certain type, and one building collapses, and all the other ones are happily standing. Why? Because the earthquake just happened to hit the frequency that corresponded to one of the normal frequencies of that particular building. And it's an extremely powerful trick. It fishes out normal modes through this driving thing. And we are able to calculate it explicitly. So now what I will do is, I will modify the system and I will make it into a three mass thing, which will have a somewhat more complicated set of normal modes. And then I will show you that I can in fact go with three different frequencies, and pull out those even complicated modes. So this will be it. So this is a three mass system. Now before, since we didn't calculate it, what I will do is, I'll go to the web and I will pull out a nice example. Let me go to my bookmarks. Normal modes. So this is a nice applet from Colorado. And you can-- I suppose preso ENG will send you links, et cetera. You can simulate-- you can do everything with it. So it has two masses. It has different amplitudes, different normal modes. And you can see nothing happens. So I have to give it some initial condition. Sorry, I have to change polarization. Where is polarization? Here. I give it some initial condition. So this is basically what you just saw. I'm just demonstrating to you that this applet looks the same as our track. So this is you can see normal modes. It's a combination of normal modes. There's one which is first frequency, second frequency. This is first normal mode. This is second normal mode. You can very quickly see what happens. So this is what we just looked at. This is what we calculated, more or less, and so on. Now I want to show you three masses where things are somewhat more complicated. In general, three normal modes. For the three mass elements, the first normal mode is like that. All the three masses move together. And slightly different-- the ratio of amplitudes is slightly different. The second mode of operation is actually quite interesting. The central mass is stationary, and those two are going forth and back, like this. And then I have a third frequency where the middle one is going double the distance, and the two other ones are going up. So this is the third normal mode. All right. So this is the system which we now have standing here. Let's quickly see if it works in reality. So this is the first-- so this is the first mode. This is the second one. All right. And the third one will be-- Sometimes I do five of them, and then it's really difficult. OK. But-- so we have a computer model, we have a real model. Let's now do the calculation of the frequencies, the ratios, such that we can see what happens. So I'm coming here, I'm changing mass to three. I'm running my-- the terminal calculating thingy. OK. It's very slow. It's busy, busy, busy. Imagine-- OK. Spectacularly slow. Where is it? I hope it's not-- oh, here it is. OK, so this is what's coming out. So this is the same calculation as we did, except for three masses. So what do we have here? Where's my pointer? So we have, again, three characteristic frequencies, we have three masses, and the same type of behavior. See, if you are far away from resonance, if you have very low frequency, everybody goes together. I haven't shown you this one here, which is also interesting. I'll show you in a second. And then-- so presumably if you are close to the first frequency, you see all three of them go together. And this is the first mode. So I should see, if I set the proper frequency, the thing should respond in mode number one. This is the one where two of them go opposite to each other, and the red one is stationary. It doesn't move. And then you have those things where they're kind of more complicated. It's difficult to read them from here. And I can do it for more masses, et cetera. So generally it's calculable. It can be calculated and can be actually demonstrated. So let's try it. So-- 32. So there's this magic frequency number one. I'm setting frequency by turning a knob. That's omega d. I'm a supervisor of this operation. It stops because of other reasons, but it will continue. Then I go to 56. By the way, remember that every-- this is the particular solution. This is a steady state distillation with omega d. But we also have all those homogeneous solutions, which have to die down with damping. Remember, it's a combination of homogeneous plus particular. So the motion is actually a little bit distorted because we have this homogeneous stuff hanging around. But hopefully, if I can start it with little homogeneous stuff, it will be better. So you see? Pretty cool. Almost there. It's almost in assembly. Then it kind of stops. You see? I get two of those going forth and back, more or less, and this one going. I could probably tune the frequency a little bit higher or lower. I'm not exactly at the right place, but I'm close. And now let's go to the last one, which is 68 according to my helpers here. You see? This one goes opposite phase, and those two more or less together. Then they keep going. See now, those two move a little bit forth and back, but they are in phase. They move together. The ratio is 1. And this one-- the ratio is minus 2. Right? Make sense? That's the beauty. You drive it at some frequency, and those normal modes pop out. It's actually very, very cool. And as I said, you encounter those type of behaviors very often. Sometimes you drive a car and something starts vibrating, it's just because the car driving on the road creates a frequency, provides a driving frequency which corresponds to oscillation frequency or some piece of-- old car. Usually it happens in old cars. So I think that's the message we can-- and we have all the machinery to be able to do it. We can set up any matrix at K, which has information about all the forces acting on anything, and we can set matrix M with the masses. We can put it all together, we can find normal modes, and then we can use Cramer's equation to take care of the arbitrary external forces. And what comes out, just as a-- for summary, for future reference, the oscillation of the system is-- this is conveniently written. This is vector X. In general, this homogeneous solution this plus the particular solution, which is plus vector B, which is very important. Vector B depends on the driving frequency. Those amplitudes of a particular solution during emotions are dependent on driving frequency. Cosine omega d times t. So in the most general situation, we have some homogeneous solution here, and there is this driven solution which we observed in action, with proper amplitudes. So in fact, what you've seen is the sum of both, because this depends on the initial conditions. Now, in reality, as with a single oscillator, this homogeneous equation, there's always a little damping, which we ignore it. And the damping comes in, and it only affects the homogeneous solution. So this part will eventually die down, whereas a driven solution is always there. There's external force that is driving the system forever and ever. So this part, this steady state or particular solution will remain forever, because there's an external source of energy which will always provide it. So these guys will die down. And of course, because of damping the exact value of coefficients B will be slightly modified, because as you know from the from a one oscillator example, the presence of damping actually slightly modifies the frequency. Whereas here, we-- for simplicity-- if we introduce damping here, those calculations are really amazing. So we don't want to do it. All right. Any questions about it? Yes. AUDIENCE: If we were doing Cramer's rule with a three by three matrix, would we only replace the column that corresponds to the B that we're trying to find, and then keep the other two? BOLESLAW WYSLOUCH: Yes. So it's always-- you'll be doing always that. In fact, I should have some slides from Yen-Jie on Cramer's rule. Let's see. OK. So this is some reminder of last time. So this is Cramer's-- there's Mr. Cramer. So this is an example of what-- this is the two by two, three by three. OK? That's what you do. Question? AUDIENCE: So it makes sense that the Cramer's rule [INAUDIBLE],, but what does that mean for physical system? BOLESLAW WYSLOUCH: Well, basically-- so the Cramer's rule is Cramer's rule. The question is what do you plug in? And what you plug in depends on the omega d. So it is true that if you insist on plugging in omega d exactly equal to one of the normal frequencies, then things blow up mathematically. In reality, there is-- this is the situation of resonance. So as I discussed this before, in reality there is a little bit of damping. So those equations have to be modified. There will be some small additional terms here that will prevent this from being exactly equal to 0. So this will be a very large number. The amplitude will be enormous. If I would have a little bit more time, I'll fiddle with frequency, I could actually break the system, because those masses would be just swinging forth and back like crazy. So you basically go out of limit of the system. So physically, there's always a little bit of damping. You do not divide by zero. On the other hand, it's so close that, for simplicity and for most of the-- to get a feeling of what's going on, it's OK to ignore it. Just have to make sure you don't divide by 0. So you can do this Cramer's rule with arbitrary omega d. Make sure you don't divide by 0, you solve it, and then you can interpret what's going on. Again, Cramer's rule has nothing to do with physics. It's just a way to solve those matrix equations. As I say, you can do it anyway you want. Two by two, you can do it by elimination of variables. Five by five I do by running a MATLAB program. Anything you want. But for some historical reasons, 8.03 always does Cramer's rule. All right? And, yeah, it's useful, especially for three by three. All right? OK. So I have to start a new chapter. I'm much slower than the engine, by the way. I don't know if you noticed. And that is the-- there's a very interesting trick that you can do which is of an absolutely fundamental nature in physics, which has to do with symmetry. You see, many things are symmetric. There's a circular symmetry. There's a left and right symmetry. Example, two little smiley faces are mirror images of each other. There is some-- this thing is symmetric along this vertical axis. This one is symmetric around rotations by 30 degrees. That house seems to be symmetric along this way. This is part of our experiment in Switzerland, also kind of symmetric in the picture. The rotational symmetry, there's reflection symmetry, et cetera. It turns out, if you have a system that is symmetric, then the normal modes are also symmetric. And there's a way to dig out normal modes just by looking at symmetry of the system. So let me explain exactly what this means. So let's take our system here-- OK, so we have one mass, the other mass. There is a spring here. This one is x1, this one is x2. If I take a reflection of a system-- let's say this mass is displaced by some distance. Some x2. This one's some x1. If I do the following transform-- I replace x1 with minus x2, and x2 with minus x1, this is mirror symmetry. I basically flip this thing around. In other words, what I do here is I look at the system here-- hello-- and I go to the other system. Hello. Right? I did a mirror transform. I looked at it from this side, that side. Now, when I look at it I see the one on the left, one on the right. I call this one x1, this one x2. It's oscillating. You are looking at it, this is your x1, this is your x2. When I move this one, is it-- it's your negative x1. For me this is positive x2. This one is positive x2 for you. It's negative x1 for me. Do we see a different system? Does it have different oscillations? Does it have a different frequency? No. It's identical. They're completely identical. So the physics of those two pendula doesn't depend on if he's working on it or if I'm working on. That's the whole thing. And this is how you write it mathematically. And if you have a solution which-- x1 of t, which consists of some sort of x1 of t, x2 of t. Let's say we find it. Now it's over there. We know alphas, betas and everything. Because of the symmetry, I know that for sure the equation which looks like this-- x1-- no, it's not x1. It's x of t. That's the vector x of t. I have another one with a tilde, which is identical functions, everything is dependent, except that this one is minus x2 of t minus x1 of t. And I know for sure that if this is the correct solution, this is also a correct solution. Why? Because he did x, and I did x tilde. But the system is the same. Completely identical. And you don't have to know anything about masses, lengths, springs, anything like that. Just the symmetry. All right. How do you write it in matrix form? You introduce a symmetry matrix, S, which is 0, minus 1, minus 1, 0. And then x tilde of t is simply equal S, x of t. And we can check that. That's simple you just multiply the vector by 0, minus 1, minus 1, 0, and you get the same thing. Turns out-- and if this is symmetry, if this is a solution, this is also a solution. So we can make solutions by multiplying by matrix S. So what does it mean? So let's look at our motion equation. The original motion equation was-- equation of motion was minus 1 k matrix times x of t. This is what we use to find solutions. Usual thing, normal modes, et cetera. Let's multiply both sides by matrix S. I can take any matrix and multiply by both sides. So I get here S X double dot of t. And of course, S is a fixed matrix, so it survives differentiation. And this is equal to minus S M minus 1 k x of t. Just multiply both sides by S. However, if MS is equal to SM, and KS is equal to SK-- in general matrices, the multiplication of matrices matters. But it turns out that if the system is symmetric, if you multiply mass M by S, you just replace-- it will just change position of two masses. So nothing changes. Also, if the forces are the same, then multiplying mass S, you flip things. Nothing changes. And mathematically, it means that the order of multiplication does not matter. It means that they are commuting. And of course, M minus 1 S is equal to S M minus 1. If this is the case, then I can plug it into equations and see what happens. So I can take this equation, and I can take this S here and I can just move it around. I can flip it with M1 position, because the order doesn't matter. So I can bring it here. And I can flip it with K, because the order doesn't matter. I can bring it here. So after using those features, I get that S X dot dot is equal to minus M minus 1 K S X, which means that X dot dot-- remember, this was-- I'm using this expression. I'm just-- S times a variable x gives me X tilde. X tilde dot dot is equal to minus M minus 1 k X tilde. X tilde. Which basically proves-- this is a proof-- that x tilde is a solution. So if a system is symmetric, it means that it commutes-- that mass and K matrices commute, and you can-- and this means that this holds true. If I have one solution, the symmetric solution is also there. All right? Let's say x-- yes? AUDIENCE: So in the center equation, you introduced negative S. I didn't really get that. BOLESLAW WYSLOUCH: So this negative is simply the-- Hooke's law. This is this minus sign here. AUDIENCE: Yeah, but where did the S come from in the-- BOLESLAW WYSLOUCH: Oh, I multiplied both sides by S. AUDIENCE: Oh, OK. BOLESLAW WYSLOUCH: I just brought the S and I put it here. S, X dot dot, and S after-- minus commutes with S, so I kind of shifted my minus. But then I waited before I hit the matrices, because I wanted to discuss. OK? So now comes the interesting question. Let's say X is a normal mode. Right? We have normal modes. Let's say X is a normal mode. It oscillates with a certain frequency. So I have X of t. Let's say it's equal to-- let's say it's a normal mode number one. Cosine omega 1 t. And we know that X tilde is also a solution. So what happens to mode number one when I apply matrix S? So X tilde-- so matrix is a constant number. It's just a couple of numbers I just reshuffle things, et cetera. Try So if I have X, which is oscillating with frequency omega 1, if I multiply by some numbers and reshuffle things around, it will also be oscillating in number one. So it will be also the same normal mode. So if I take matrix S, I apply it to the normal mode, I will get the same normal mode, with maybe a different coefficient. Linear coefficient. Plus, minus, maybe some factor, something like that. So if this is the solution, it means automatically that X tilde is proportional to A1 cosine omega 1 t. And the same is true for omega 2. So the only way this is possible, since cosine is the same in both cases-- matrix S to normal solution gives me normal solution with some sign. So the only way this can work, matrix S actually works on vectors, on A1. This is just an oscillating factor. So we know for sure that S A1 must be proportional. to A1. Similarly, S times A2 is proportional to A2. So let's try to see with our own eyes if this works. So let's say S is 0, minus 1, minus 1, 0, times 1, 1 is equal to what? 0 minus 1, I get minus 1 here. This one, I get minus 1 here, which is equal to minus 1 times 1, 1, which is vector A. So vector 1, 1, which is our first mode of oscillation, is when you apply the matrix S, you get a minus 1 the same thing. And similarly, if you do the same thing with matrix S-- so you see, the simple symmetric matrix consisting of 0s and minus 1s has something to do with our solutions, which is kind of amazing. So if I have 0, minus 1, minus 1, 0, I multiply by 1, minus 1, I get 1 here, I get minus 1 here. Just a moment. Something is not right. Something's not right. No, it should be-- AUDIENCE: [INAUDIBLE] BOLESLAW WYSLOUCH: Hmm? AUDIENCE: [INAUDIBLE] AUDIENCE: It's 1, minus 1. BOLESLAW WYSLOUCH: 1, minus 1. Yes. I don't know how to multiply here. I should be fine. OK. That's right. This is-- sorry, this is 1, because it's minus 1 times minus 1, and this is-- yeah, that's right. Which is 1 times 1, minus 1. So this is something that-- I get the same vector multiplied by plus 1. So this is, of course-- these are eigenvectors and eigenvalues. So the matrix S has two eigenvectors, one with eigenvalue of plus one, the other one plus 2. So we have an equation SA is equal to beta times A, and beta is-- OK. So this is something-- so it turns out-- and I don't think I have time to prove it, but it turns out you can prove it-- if I would have another three minutes-- you can prove it that the eigenvalues of matrix S-- eigenvectors, sorry, eigenvectors of matrix S are the same as eigenvectors of the full motion matrix. So in other words, our motion matrix M minus 1 K-- this is the matrix. Then we have a matrix S. And normal modes are, you have a normal frequency and they have a shape. You have a normal vector, the ratio of amplitudes. And turns out that eigenvectors here, so the A's are the same. And again, I don't have time to show it, but you can show that this is the case. So if you have a symmetry in the system, then you can simply find eigenvectors of the thing to obtain the normal modes. So if I look at my two pendula here, the symmetry is this way, so I have to have one which is fully symmetric, like this, and I have another one which is antisymmetric. Plus 1, minus 1, plus 1, minus 1. Similarly, here I have-- let's say if I have two masses, there is one motion which is like this, and one motion which is like that, because of the mirror symmetry. And you can show that if you have some other symmetries, like on a circle et cetera, that you have a similar type of fact. So you can build up on this symmetry argument. And finding eigenvectors of a matrix 0, minus 1, minus 1, 0 is infinitely simpler than finding matrix with G's and K's and everything, right? All right. So thank you very much, and I hope this was educational. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | Course_Iteration_Incorporating_Theoretical_Content_and_Demonstrations.txt | I have been teaching three for more than three years already so I was given a charge to change the course to make it even better than what is actually done previously in previous years and we actually made a lot of adjustment during this few years with many other professors in the physics department so what we actually did is to change the the textbook the textbook is actually now much more theoretical oriented so that we benefit from that for the preparation for the other course like ao4 which is actually the quantum physics and and also the other course which are related to waves and vibration the benefit is the following so the students who are have equipped it with more mathematics background will also find it much more interesting compared to previous years because in the previous years we are mainly focusing on a very practical problem solving reducing more theoretical orientated content that can help us to systematically understand sync oscillator coupled oscillator infinite number of coupled oscillator and two were continuous and in phonetic cup of the system in very very well-defined theoretical framework and finally I think what we really did is to introduce a lot of demos made much more demos actually than previous years so that it goes with the lecture so that people can actually look at those demos and compared to our cellular calculations and I think that is actually evolving as a function of time and we were adding or subtracting the demos which we think is more useful or thus used for the semester and not essentially what you see now in the 2016 version |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 10_Traveling_Waves.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: OK, welcome back, everybody, to 8.03. Today we are going to continue the discussion of wave equation starting from last lecture. So what have we learned last time? As a reminder, we have started to study the behavior of a wave equation. We understood basic behavior of the wave equation, and also are trying to solve the general solution of the wave equation. The first thing which we learned, as usual, is the normal modes. What are the normal modes in the case of wave equation over continuous translations in metric system. What we found last time is that they are standing waves. And of course, as usual, the full solution, which is a general description of this system, is the superposition of infinite number of normal modes. And that means one can understand this kind of system systematically the using Fourier series. So this is just a reminder. So what we have done is that basically we start with infinite number of coupled oscillators. And we make the space between those massive objects in the system smaller and smaller until it become continuous, right? And a very interesting thing happened that automatically already give you wave equations, OK? Which is as you're shown here. Last time, as I mentioned, we discussed the normal modes, which are standing waves. Those are the first few normal modes, and those are the functional form of the normal modes, which are standing waves. So the structure just looks like this. So you have A m, which is the amplitude, sin k m x plus alpha m, which can be determined by boundary conditions. And the sin omega m t plus beta m, that means all the points in the system are oscillating at the same frequency, omega m, and as the same phase, which is beta m. And those are based on the wave equation. If you plug this solution back into the equation, you will find that omega m is actually not a free parameter. It's actually proportional to k m, which is the wave number of m's normal mode. And this constant of v p, we will find out today, this is actually the speed of the wave in the case of traveling wave. And if you look at the individual normal modes and make product of those normal mode as a function of time, you can see from here there are six different normal modes. And they are like a sinusoidal shape in terms of amplitude as a functional position on the string. And there you can see that if you distort the string more, then you get a higher oscillation frequency, as you see from m equal to 1 to m equals to 6 case. So as I mentioned today, we will talk about another interesting kind of solution, which is progressing wave solution, OK? Why is this solution exciting? Not just because this actually matches what we actually already learned about waves, right? And this solution should enable us to send, for example, energy from one point to another point. This is actually what I am doing now, right? I'm sending energy from my mouth to your ear so that you can hear what I have been talking about, right? About 8.03, right? So that's really cool. And we will try to understand how actually we can get this solution out of this strange wave equation, OK? So what is showing here is the normal mode. And we are going to talk about a second kind of solution, which is the progressing wave solution. And this solution have this form, psi (x, t) will be equal to some kind of function, f. And this is actually a function of x minus v p times t. This is actually a general form of the progressing wave. And f function is some kind of well-behaved function of your choice. OK, so the first thing which I would like to do is to show that this functional form is actually the solution of the wave equation, right? So fairly straightforward. We can actually go ahead and plug them into this equation. And before that, I will define tau to be x minus v p times t, OK? So in order to prepare for plugging in this functional form to a wave equation, I would calculate using chain law. Partial f partial x will be equal to partial f, partial tau. Partial tau, partial x. And this will give you partial f, partial tau times, in this case, partial tau, partial x will give you 1, OK? And that will give you f prime tau, OK? Therefore we can go ahead and calculate as well partial square f, partial x squared, OK? That will give you f double prime tau. So this is actually the first set of equation I need in order to describe the right side of the wave equation. The other equation which I need in the preparation for plugging in the whole thing into the wave equation is to calculate partial f, partial t. And according to chain law, partial f, partial t is equal to partial f, partial tau, partial tau, partial t. In this case, f is actually a function of x minus v p t, and tau is defined as x minus v p t. Therefore you can actually immediately conclude that these would be equal to minus v p, partial f, partial tau. And now it is actually equal to minus v p f prime. Similarly, you can calculate partial square of f, partial t squared, and that would give you a v p squared f prime. Oh, f double prime because we did the double differential. OK, all right. So from the first equation and second equation, which I have on the board, we can actually plug that into the wave equation. And what I'm going to get is partial square f, partial t square. That would be equal to v p square, partial square f, partial x square. So that is actually exactly the wave equation, which we showed from the beginning. So that means this functional form satisfy the wave equation. And I didn't even specify what is actually f function. f function is some kind of well-behaved function. And it can have all kinds of different shape, which we will discuss later. But that is actually pretty encouraging. And that means if you try to distort the string and if this shape is actually propagating at-- have the functional form of x minus-- If you have any function which you have a functional form of f of x minus Vpt-- no matter what kind of shape it is, this shape is going to be-- first of all, this function is a solution to the wave equation. Secondly, we will show you that this shape is going to be propagating at the speed of Vp. And the shape will not change. It will stay like that forever according to the wave equation. There's another function of form which can also be the functional form of the progressing wave. We usually write it as f KX plus or minus omega t. And in this case if omega is actually Vp times k, which is actually already required from the discussion of normal modes. Then this equation-- this kind of functional form is also the solution of wave equation. And of course you can actually go ahead and prove that probably after the lecture. The proof will be very similar to what we have done here. So now, actually try to understand what does this function mean? So I have a function which is f of x minus Vp times t. Where x is actually the position of the-- on the string. And the t is actually the time, which I go ahead and check this function. And for example, if I can give you an example-- a function, for example, I can make it like a triangular shape like this. And this is actually plotted as a function of Tau. So f of Tau is actually giving you the information of the shape of the progressing wave. So let's discuss if I write f of x minus Vt, what does that mean? OK, first of all, I can take t equal to 0. What will what happen is that a lot instants of time, t equal to 0, x is equal to Tau. That means at t equal to 0, the shape of the string-- well, it looks like this-- like this function. Now, I would like to know how this string is going to evolve as a function of time. So that's actually all we care, right? And that means I'm going to increase t to a larger value. So suppose originally, I have a t equal to 0, I'm sitting on this point. I sample the f at this position. If I increase t-- if I increase t from 0 to a larger value where I will start to sample, will I move to a left-hand side, or a right-hand side? Anybody can help me. Because this functional form is actually x minus Vt. What will happen if I increase t? Tau will increase or decrease? AUDIENCE: Decrease. PROFESSOR: Decrease. AUDIENCE: Yeah. Move to the left. PROFESSOR: Very good. So decrease, right? So that means at the fixed x, I am going to sample this point. What does that mean? That means originally, if I plot everything in terms of x-- originally, it have this shape. Now, if I increase t, what is going to happen is that originally I was sampling this shape here. And now I am sampling the shape here. That means if t equal to t prime, which is larger than t, this shape first of all is unchanged. Secondly, it's actually moving. The shape looks like as if it's moving in the horizontal direction. And the direction of this movement is in the positive x direction. If I'd write my progressing wave solution in a functional form of f of x minus Vt-- this should be Vt here, sorry for that. Any questions? So look at what we have done. First of all, we have proved that f of x minus Vpt, this function of form is a solution to the wave equation. It's a solution. Secondly, we also discussed the property of this functional form. So that's essentially describing a shape. And the whole shape is going to move as if it's moving as a function of time and to the positive x direction. So let me ask you another question. So what will happen if I write the solution in the form of f of x plus Vt? Anybody can help me with the direction of the propagation of the wave. AUDIENCE: Go to the left. PROFESSOR: Yeah. Go to the left-hand side of the board. That means if I have another expression. I'm using the same f function which is defined here. In this case, if I write f of x plus Vt, that means the shape will be moving in the negative x direction. It's symmetric. Of course you can also discuss what will happen if you take this functional form and you are going to get exactly the same conclusion. So right now I have been talking about moving shape. So what is actually really moving? Professor Lee, you just told us before that every point on the string can only move up and down. Now, you are talking about something moving in the positive x and negative x direction. What does that mean? So that mean-- take y example. So if I have a Gaussian pulse, and I write this thing in the form of x minus Vt. At t equal to 0, this shape looks like this. In the next moment, if I increase time to t equal to 1, what is going to happen is that this shape move toward the positive x direction. And of course 0's are the equilibrium position of this waves-- of the string. And what is happening is it's like this-- so basically, all the points on the string are really working together to produce this shifting-- this progress Gaussian wave. So what is happening is that if I focus on this point, this point will go down. And this point will go down, go down, go down, until I touch this point. So basically, what is happening is like this-- all the points are only moving up and down horizontally. But they all move in a manner such that if you look at just the shape of the amplitude-- the amplitude is a function of x-- it looks as if the amplitude-- the shape is actually moving toward positive x direction. Moving toward the right-hand side of the board. So what is actually moving? What is moving is actually all the point like mass on the string-- they are only moving up and done. But they are moving together so nicely such that it looks as if the whole shape is actually shifting toward the positive x direction. Any questions so far? So I hope that's straight forward enough. And I would like to discuss with you a interesting situation. So we have learned that, OK, I can have, for example, triangular pulse. And I can have this triangular pulse moving in the positive x direction. And that we will also find out that the speed of the propagation is actually Vp because that's actually if you increase t and that's actually the speed of movement when you sample the shape and the f of Tau. So therefore, we can conclude that the speed of this triangular pulse is going to be Vp. If I have another triangular pulse starting from the right-hand side end of the string, they have exactly the same shape, exactly the same amplitude. So of course, according to what we actually wrote there, they are going to move forever. And at some point they will actually meet each other. And what is going to happen is that you will have some pulse, which is actually two times of the shape at some point. Because of the linearity of the wave equation. So that's actually pretty straight forward. However, if I consider another case, which is like this. So I have two progressing waves. One is actually going in the right-hand side direction. The other one is going to the left-hand side direction. They have exactly the same shape, but they have-- the amplitude is actually taking the minus sign. So they actually are exactly-- they have exactly the same amplitude, but pointing to a different direction. One is actually pointing upward. The other one is actually pointing downward. So at some point these two waves is going to overlap each other. When they overlap each other, what is going to happen? It's like this-- they are going to overlap each other. That means the amplitude will be cancelling each other. Then from the experiment you will see something like this. So now, this is the question I would like to ask you. What will happen next? The first possibility is that they cancel. Completely, they disappear. The second possibility is that, OK, they pass each other. The third possibility is that, OK, it depends on the mood of the string. Maybe something interesting is popping out. Maybe it decide to produce two circular waves. Get creative, right? Creative. OK, everybody have to vote. OK? How many of you think that you will cancel and disappear. Anybody? Nobody? Really? So you can see that here, nothings there. Right? Why didn't you think that will be canceled? OK, nobody think that will cancel. Very good. Maybe we are all wrong, right? [LAUGHTER] Second, they'll pass each other. How many of you think so? Very good. Finally, how many of you think that will be, oh, no, it depends on the mood of the string. Get creative. One, two, three-- thank you for the support. [LAUGHTER] There are four people. OK. So let's discuss these three situations carefully. So the first situation, if they cancel exactly, which sounds logical because if you look at this string how could this string remember what happened before? How could it remember? Therefore, shouldn't answer number one be a logical choice? The catch is, OK, if they cancel then that means energy is not conserved. So somehow the energy I put in-- I work really hard to shake the string, use my energy. And it disappear. Oh my god, disappear. [LAUGHTER] Then the energy is sad. The second one is, OK, I believe in energy conservation. So they will pass each other. But that means the string have memory because right now there's nothing there. What is going on? OK, since most of you think that is actually what is happening, can some of you explain to me how this string actually remember what happened before? Anybody can help me. AUDIENCE: Maybe the two light forms reflect off of each other. Bounce off of each other or something. PROFESSOR: Yeah, they balance each other, but how is this different from a stationary string at rest? Of course, I mean at some point it looks identical, right? But there's something which is different between this one and that one. AUDIENCE: There's no [INAUDIBLE].. No [INAUDIBLE] in the string. [INAUDIBLE] PROFESSOR: Very good point. This one, which is actually unperturbed, has zero velocity. And this one, no. It actually have a got velocity. Actually, this string is already or starting to-- it's already ready to move down. And this part of the string is already ready to move up. So that is actually how the string can remember what happened before. It remembered it by the velocity. So what is actually not plotted here is a trick. It's actually the velocity. The velocity is already nonzero compared to this situation. And what is going to happen is that afterward you will produce two corresponding triangular pulse, continue and then pass each other. Finally, the third condition, creative. That may not happen because all the memory is still there in the form of kinetic energy. So we can actually go ahead and do a small demonstration here. So let's focus on the right-hand side part of this setup. So this is actually the Bell Lab machine we had before. So now, what I'm going to do is now I'm going to create a square pulse-- positive square pulse from the lab inside. And the negative pulse in the right-hand side and see what is going to happen. No, not like this. Stop. Stop. OK. All right. Let's do it. You see? They pass each other. And the shape actually continues. So let's do that again. They cancel at some point, but they do pass each other and continue. And there are some refractions, et cetera, which we are going to discuss afterward. Let's do that again. You see? At some point, they cancel. But the positive pulse continue traveling to your left-hand side. And then the negative pulse travel to your right-hand side. Continue, please. So based on the experiment most of you actually were correct. The answer is number two. And I would like to show you a few more examples based on my little simulation. So first of all, I would like to show you a triangular pulse. They pass each other. And you can see that they pass each other, and the shape is actually changing as a function of time. And actually, afterward, they continue, and they keep the same shape based on this computer simulation. Another interesting thing to notice is that if you focus on the point at x equal to 0, you will see that at this point actually never change amplitude. Because those two pulse are really symmetric. One is positive, the other one is negative. As usual, we can actually change the shape of the pulse. For example, I can changed it to circular shape and see what will happen. Oh. [LAUGHTER] And again, the position at x equal to 0 is unchanged. Let's take a look at that again. It really does something really funny. It looks like, voom. And then you can see that it is actually the velocity of the individual component of the string. Which it remember though in the original shape. So it can see the velocity by eye looks different from what you see it before in the first example. And finally, as usual, we have the MIT waves. [LAUGHTER] And it does really, really crazy things. And the amazing thing is that the string have such a good memory. It really remember what is going to happen before they touch each other. So what is going to happen to these two MIT waves? They are going to be propagating forever. Cannot stop until the edge of the universe. Maybe they dig out of the universe, but not my problem anymore. So we talk about the energy stored in the string and et cetera. So how about we go ahead and calculate the kinetic energy and the potential energy. So the first part is the kinetic energy. Only one is actually half mv square. So if I consider a small segment on the string, which have a width of delta x. And I can now calculate delta m. If I assume this string have a mass per unit length Rho L, and the string tension t. If that's actually given to you when we set up the experiment, then we can actually calculate the mass of this small portion of the string. Then delta m, the mass, will be equal to Rho L times dx. Because Rho L is the mass per unit length. Therefore, what is actually the kinetic energy is becoming pretty straight forward. It's the integration over the whole string. Integration over the whole string is 1/2-- based on this equation-- Rho L, dx, and times v. But what is actually v here? v is actually the velocity of individual point-like mass on the string. And we actually already talked about that. The velocity of individual mass is actually only in the y direction. And the position of individual mass is described by the function Psi. Therefore, what is actually velocity? Velocity is actually partial Psi, partial t. So that is actually giving you the velocity of individual mass on the string. And then if you square that, that is actually giving you the total kinetic energy-- is in this functional form. Let's also discuss what is actually the potential energy. The potential energy as you remember delta W, the work, is equal to F times delta S, the displacement. F is the force, and the delta S is the displacement. So originally, before we actually perturb and make some displacement with respect to equilibrium position-- this string have originally-- if I look at this small part of the string I join in this region. This looks like this. This is delta x, and it has a constant string tension t. Now, I can actually introduce some displacement. And what is going to happen is, look, it's going to look like this. This string is actually a little bit stretched. And this is actually the original delta x. The width of this little segment. And this direction is actually a small change in the y direction, which is actually showing us delta Psi. And of course, we can calculate the length. The length of this string and that will give you square root of delta x square plus delta Psi square. We can now go ahead and calculate the delta W. So delta W will be equal to F, which is the force, times delta S. We know in the force-- the magnitude of the force is what? Is the string tension. So therefore, I put T here. And delta S, what is delta S? Is how much I stretch this string. So this is actually the difference between the resulting length and the original length, delta x. So that is actually giving you the delta S. So that means I can write it in this functional form. dx square plus d Psi square minus dx. I can of course take delta x out of this square root thing, and basically I get delta x, square root of 1 plus d Psi dx square minus dx. Remember what we have been discussing until now, we were always discussing small amplitude-- or small vibration. Therefore, that means I can use a small angle approximation. That means delta Psi is going to be very, very small with respect to delta x. So that means the first turn will be roughly delta x 1 plus d Psi dx squared 1/2 because you have a square root of that, plus higher order turn. And of course we assume that delta Psi is actually much smaller than delta x. Therefore, we ignore all those higher order terms. So if we actually replace this expression back into the original equation, you will see that the first turn, 1 cancel with this minus dx turn. This actually cancel that. They actually cancel. Therefore, I can calculate dW will be equal to T times delta x, times 1/2 d Psi dx square. Therefore, what will be the total potential energy. The total potential energy will be in the equation of the work dW over the whole range from-- of the system. And basically, you can actually write it down as 1/2 T Psi. Partial Psi, partial x square dx. All right, so we can actually understand and calculate the kinetic energy and the potential energy. So before we take a break, let's take a short example to check if we understand what we have learned so far. So for example, if I have a function Psi xt, and that is actually equal to 1 over 1 plus x minus 3t to the fourth. It's a crazy function. If I assume that I can do a very precise thing, manipulate this string so that I produce a wave function of this functional form. 1 over 1 plus x minus 3t to the fourth. Can somebody tell me what is actually going to be the velocity of the wave? Can anybody tell me? The first thing which you can do is to express this crazy function in a functional form of fx minus Vpt, right? And the Vp is actually the speed of the wave, right? So anybody know what is actually-- yes? AUDIENCE: Three. PROFESSOR: Yeah, the three because the whole function can be written as f x minus 3t. Therefore, the velocity Vp will be 3. Of course if you are not sure, you can actually calculate Vp square by the ratio of partial square Psi, partial t square, and partial square Psi, partial x square. And that will give you of course the Vp square, according to that wave equation. All right, so we will take a five minute break from now. And during the break I will try to return the exam to you. So we will come back at 24-- 12:24. So welcome back, everybody. So we will continue the discussion of traveling wave. So we have the very interesting discussion of two waves that are canceling each other. And somehow the string have a way to remember what happened before, which is actually the velocity of each individual point on the string as a function of x-- that instance of time. So let's actually take a look at this example. So make use of what we have learned so far. As we see here there is a triangular shape, which I create in the lab. And this triangular shape is actually there and it's stationary. It's not moving. The strings are at rest, but have a triangular shape, which I setup there. So based on what we have learned so far-- we have learned normal modes, we have learned about traveling wave. I believe before we learned this class, the first reaction to you is to do what? What kind of decomposition. AUDIENCE: [INAUDIBLE]. PROFESSOR: Fourier decomposition. So what you are going to do is, OK, very good. I have this shape. So I do a Fourier decomposition and I have infinite number of terms. And I am going to evolve infinite number of term as a function of time and see what will happen to the system. So that's actually what you would do before we learned traveling wave. What I would like to say today is that if I really prepare this string at rest, stationary, at t equal to 0-- in contrast to what I just said before, brute force measure, which I used computer to decompose it and evolve all the infinite number of terms. What we could do is that I can show you that this situation is a superposition of two traveling waves. Then the question becomes super simple. So instead of doing a brute force calculation using computer-- decompose it to infinite number of normal modes-- what I can actually show you is that, OK, if I have a g function, which is equal to f x plus Vpt plus f x minus Vpt. So these three function is superposition of two traveling waves. The shape is described by f function. And one of them is traveling to the right-hand side. The other one is actually traveling to a left-hand side. If I assume that the superposition of these two traveling wave is g then I can now calculate the velocity, partial g, partial t. And that will give you Vp f prime minus-- right, because here it's actually x minus Vp-- so I got minus Vp out of it, f prime. The first term, if I do this partial differentiation, then basically I get the positive Vp out of it. And then the second term I get minus Vp out of it. And these two terms cancel exactly. What does that mean? That means all the points-- this g is actually a function of x and t-- on the point at t equal to 0 have initial d velocity equal to 0. So in other word, if I have any random kind of shape-- in this case is a triangular shape-- I can always decompose this stationary shape into two traveling wave. One is actually traveling in the positive direction. The other one is traveling in the negative direction. So that means what is happening? This is equal to a superposition of two traveling waves. If I assume the height of this mountain to be h then I need to have h over 2 as the height for the individual traveling waves. One is actually traveling to the right-hand side. The other one is actually traveling to he left-hand side of the board. So based on this trick, actually we can see that I don't need to do infinite number of terms anymore. I don't need to do a Fourier decomposition and get really crazy and take forever to write the code on your computer. And maybe there are some bug in your code, which is frustrating. And what we could do is to simply decompose it into two traveling wave. And I can now predict what will happened at time equal to, for example, 5 what is going to happen. So what is going to happen is that you have two triangular shape waves. Each of them actually traveled a distance of 5 times Vp. So that is actually a very interesting fact. And of course we can see from here if I quickly create a triangular shape, and you will see that it really did become two triangular shape wave. So I can do this. I can do this. You see? So originally, I'm creating some stationary shape. And I release that. It does become two traveling waves with amplitude half of the original height-- original displacement. I can also do it in the opposite direction, a positive wave. You see? It does work. And of course, after the class you can make even more complicated shape if I have many more than two hands. Maybe I can do that, but unfortunately I'm human. You can see that I can create different slope in the positive and negative h. And it does create two traveling wave. And that's amazing because this is actually looks like just some kind of mathematical trick. And it really match with what we can do experimentally. So finally, I would like to talk about the last topic of the lecture today, which is to connect two strings together. So suppose I have two strings-- the left-hand side string is actually thinner. It has mass per unit length Rho L, and string tension t. In the right-hand side you can have a thicker string with mass per unit length 4 times Rho L, and the string tension is as you keep constant t. Based on what we have learned before, the velocity Vp, is equal to square root of t over Rho L. So that's actually from the last few lectures. So left-hand side you will have V1, which is the velocity of the traveling wave, equal to square root of t over Rho L. And the right-hand side you will have square root of t over 4 Rho L. And that will give you one half of V1. So what does that mean? This means that if I have a traveling wave in the left-hand side, the speed of the traveling wave will be 2 times the speed of the traveling wave in the right-hand side based on this calculation. So what I would like to do is the following-- so I would like to ask a question about this system. What will happen if I introduce a displacement and a traveling wave from the left-hand side. And the question is, what is going to happen to this system as a function of time once I actually give this input traveling wave. And the answer is that this traveling wave is going to pass through the boundary of two systems. And there may be refraction. There may be transmission, et cetera. And that we are actually in the good position to understand this phenomena. So let's take a look at this situation carefully. So now I define here the position of the boundary is at x equal to 0. And I can now go ahead and write down the conditions, which is-- need to be satisfied in order to connect these two systems properly. Which you actually already see this several times, the boundary condition. So what are the boundary conditions which I need in order to connect the left-hand side and the right-hand side systems? So the first boundary condition is that the string is continuous. Therefore, if I have some kind of y is actually-- y of x t is describing the displacement of all the time mass on the string in a horizontal direction. Then that means y the left-hand side evaluated at 0 minus in the slightly left-hand side of the boundary will be equal to YR, which is actually evaluated at the slightly right-hand side of the boundary at x equal to 0. And the YL is actually the wave function for the left-hand side thinner string. And the YR is actually the wave function, which describe the right-hand side of the string. So this means that the boundary condition tells us that the string cannot break. It should match carefully so that these two systems are connected to each other properly. The second condition is that, OK, since this boundary actually have no massive particles left, I can't actually assume that this is massless ring there. Therefore, the slope of the left-hand side, partial YL, partial x, s equal to 0, will have to be equal to the slope at the right-hand side. If the slope doesn't match between the left-hand side and right-hand side, that means since they have constant tension that means the tension-- the string tension cannot cancel each other. Then the massless ring will be transferred to, for example Mars, in a second. Because it has few infinite amount of acceleration. And that didn't happen. When I actually tried to actually displace the string or the Bell Labs system, I didn't see crazy things happen. Therefore, the tension at this, which acting on this massless ring must cancel each other. So that's the second boundary condition we have. So now, I would like to make some assumption. So first of all I have an input pulse, which is actually coming into this system. Looks like this. And I call it fi, is traveling toward the positive x direction. So therefore, I can of course write it down as minus k1x plus omega t. So this is actually the incident pulse, I call it fi. And after it pass the boundary-- so I can actually expect that there may be some kind of refraction, which happened at the boundary, fr, I call it fr. And this time this fr is going to be traveling to the negative x direction. Therefore, I can express this function as fr is a function of plus k1x plus omega t. Finally, there can be also transmission wave. So you get the refraction and there can be some energy, which somehow pass through the boundary. And I call this transmission wave ft, which is actually in a form of minus k2x plus omega t. And in this case, I assume that the system is actually having a k1 in the left-hand side, and k2 in right-hand side. Which is actually the wave number and the k1 is actually equal to omega over V1. And the k2 is actually equal to omega over V2. So that is actually the set up. And then also the three traveling waves, which we actually demonstrate the situation. So we can now go ahead and plug those three traveling wave solution into the boundary conditions. And then we will be able to solve their relative amplitudes. So let's make use of the first boundary condition. So YL is now a superposition of fi and fr. YR will be just the transmission wave, ft. So now, I can plug this expression back into the equation number one. Then basically, what I get is fi omega t. Originally, it's actually minus k1x plus omega t, but this thing is actually evaluated at x equal to 0. The wave function has to be continuous between the negative side of 0 and the positive side of 0. Therefore, if I plug in x equal to 0, minus k1 turn disappear. And what is left over is omega t. And this is the second turn fr, I can write down expressively. You get fr omega t. And then right-hand side of the expression is YR, only have 1 turn, ft And now you are going to get ft omega t. So now we can also go ahead and plug in this equation to equation number two. What is going to happen is that I do a partial differentiation with respect to x. And the plug in x equal to 0 to the expression. And what I'm going to get is minus k1 f prime i, as a function of omega t, plus k1 fr prime omega t. And this will be equal to minus k2. In the right-hand side you only have one turn, which is ft. So you are going to have minus k2 ft, the function of omega t. Any questions so far? AUDIENCE: [INAUDIBLE]. PROFESSOR: Yes, thank you very much. OK, very good. So we are making progress here. And what I can do now is to do a integration over t for the equation number two. So if I do a integration basically, what I'm going to get is minus k1 over 2 fi omega t. I do a integration over t, plus-- over omega, sorry-- and the plus K1 over omega fr omega t. And this is actually equal to minus K2 over omega ft omega t. Based on the equation, which we have before-- K1 over omega is actually 1 over V1. So basically, what we have is actually-- this is actually 1 over V1. This is actually 1 over V1. And this is actually 1 over V2. So in short while we are going to get in the second equation will become minus V2 fi omega t plus fr omega t. If I multiply both sides by V1 and V2 then I get the minus V2 here. And this will be equal to-- there should be a minus here because I am taking out minus V2 there. And this will be equal to the right-hand side because I multiply both side by V1 and V2. Actually, I get minus V1 ft omega t. So what is actually left over is that now I have equation number one, and I have equation number two. Those are just functions of fi, fr, and ft. So that means we can actually easily solve the equation and write everything in terms of fi. So we can now solve one and two and write in terms of fi, which is actually the incident wave. That's actually what we could do. So if I do that-- if I solved the equation one and two, basically I get fr omega t, will be equal to V2 minus V1 divided by V2 plus V1 times fi omega t. If you trust me, if I try to solve one and two, and express fr, and ft in terms of fi-- then basically the second thing which I get from this solution is that ft will be equal to 2V2 divided by V1 plus V2, fi omega t. So look at what we have done. Basically, the first thing which we did is to identify what are the boundary conditions. Under the condition one is the string doesn't break at the boundary. The slope match between the two boundary because you have constant tension. Then I assume the solution have the functional form of three traveling wave. The incident traveling wave, fi, traveling to the positive direction. The refraction is expressed as fr going to the negative direction. And finally, ft is going to-- is the transmission wave going to the positive direction. Then I plug those equation in to the boundary condition. And I solve everything, fr and ft, in terms of fi and this is actually what I get. So that's actually in short what I have been doing. So basically, this expression is actually equal to R time fi, where R is actually V2 minus V1, divided by V1 plus V2. And in this case this is equal to transmission, which I am writing as Tau, times fi, the initial incident wave. And this Tau is equal to 2 times V2 divided by V1 plus V2. So in this example, V2 is equal to 1 over 2 V1. So I can now plug it in and see what I get. Basically, V2 will be equal to V1 over 2. Then I can evaluate, will be the R and Tau. So the R will be minus 1/3. It's a negative value. And the Tau will be equal to 2 over 3. So what have we learned from here? So if I create a pulse starting from the one which is actually have-- which is lighter or have smaller Rho L-- smaller mass per unit length-- when it passed through the boundary there will be a refracted wave, which the amplitude will change it's sign. So what is going to happen is that you will get a reflective wave and the amplitude changes sign. And then there will be a transmitted wave, which is actually going to the positive direction. So this is actually a demonstration we have here. So left-hand side is the system, which I was talking about-- the smaller Rho L system. And right-hand side is the larger Rho L system. And now I can do the experiment and see what happen. And I connect the two system with this ring, so that they are coupled to each other. I hope you will work. All right, so now I can create-- oh, I'm in trouble now. One second. Hopefully will-- this is not easy. OK, now I can create a pulse from the left-hand side. Oh, no. That is the pressure. So now I can create a pulse from the left-hand side. And you can see that there is a small pulse actually that pass through the median-- pass through the boundary, but unfortunately this demo is not setup already. Ah, gosh. OK, so we will see what we can get from here. Now, it works. Very good. So now I can actually create a pulse from the left-hand side, and you can see that it does pass through this boundary if I setup the ring. The ring was falling down somehow during the lecture. And this ring is actually presenting the boundary and connect these two system. Based on what we predict from the equation-- basically you will see that if I have a positive amplitude passing through the boundary there will be a negative pulse going backward and a positive pulse going through the boundary, which is the transmission wave. And let's see what is going to happen. You see? It does have a negative pulse going backward. And you do see that there is a pulse, which is actually going through this system. Let's see this again. You see that there's a positive amplitude pulse going through the boundary and that there's a refraction through this-- which is actually going backward in the left-hand side system. So on the other hand, if I start a traveling wave from your left-hand side, that means V2 is going to be larger than V1. V2 is actually going to be larger than the V1. So what are we going to get is a positive amplitude refraction and also a positive value transmission wave. And let's see what is going to happen. You see? The refraction is positive this time. And the transmission wave have also positive amplitudes. Let's take a look at this thing again. A very nice pulse and you can see the refraction because of this mathematics. Interesting thing is that it match with experimental result. And the prediction was that you are going to get the positive amplitude reflective wave, and it does agree with the experimental data. So this is actually what we have learned. So we have learned traveling wave solution. Energy of a oscillating string, and also the potential kinetic energy. And also we learn how to actually match two media and passings-- how this traveling wave pass through the median, et cetera. And next time we will talk about more systems described by wave equation. And also dispersion relation, what does that mean, et cetera. Thank you very much, and see you on Thursday. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | Taking_a_Vote_to_Engage_Learners.txt | so during the class I usually do a little boat and the physical situation we are interested the to proceed will be the outcome of the of the calculation I think that is actually very very interesting things to do first of all Dow will attract the attention of the students that we are going to do a prediction of a physical situation okay so that that's actually the first purpose to encourage participation of the students into class and the secondly I can know if the majority of the students already know the outcome or not by looking at the boat result so if I have if I have my polarizer arranged in this direction can you predict what will happen to the readout on the scope where I see signal or not how many help you as you think we will see signal if I arrange that the the the electromagnetic wave is she pointing polarized in the up and down okay one okay on these four people think so how many of you think nothing was nothing over change Nancy I'm sorry not nothing will be observed by them let's go okay most of you as you think so so that's actually really 2d his experiment I choose to use an analog master instead of clicker and over or the poor with utter take taking called course and that is because I would like this process to be a smooth side I I could achieve so it doing it by raising your hand first of all they they have to do a lot more by raising your hand instead of clicking a button so that's actually makes a difference for then to focus on my question okay so secondly I don't want to do automatically country because usually they provide a graph and I have to switch back and forth between graf and my lectures or other lecture slides and la usually takes some time and also that introduced in turn into any interruptions during my lecture |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 22_Diffraction_Resolution.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MITOpenCourseWare at ocw.mit.edu. PROFESSOR: Welcome back, everybody to 8.03. Very happy to see you again. So as you can see from the slides, we will continue the discussion from last time. We were talking about interference phenomena, which involve two or multiple point light source. And they actually interact with each other and produce interesting phenomenon, which we see with laser, with water ripples, and also we discussed how to design a phased radar together. And one thing which we learned is that if you, for example, have two slit interference, OK. And if you look at the intensity of the resulting interference pattern as a function of angle, you will see that there are peaks, periodic peaks as a function of angle. And we also know how to calculate where would be the principal maxima, what would be the minima, which will have destructive interference between the two point light source. OK? So as usual, we go from one electromagnetic wave to two electromagnetic waves and two unelectromagnetic waves. And today we are going to do infinite number of electromagnetic waves and they are going to interact with each other or superpose an infinite number of electromagnetic waves all together. And that brings us to that discussion of diffraction. OK? So what are we going to talk about today is, for example, a point light source, a laser pointer. And what would the image of a laser pointer look like? When these lasers pass through a single slit or just the laser itself. The laser beam itself, what will happen to this laser beam? And also we will make some comments on the Star Trek, for example. Right? They have this super weapon which they shoot enemy with this laser beam. And we'll see how practical that is by the end of this course. And the third thing is that it's related to resolution. So we are going to design a phone, screen of your mobile phone together to see what is actually practical, what is actually not practical. If Yen-Jie is opening a new company to develop jPhone, what should be the requirement for the screen, for example? Which, I'm not going to do it. So this is actually what we are going to discuss today. So we are interested in a situation where you have plane waves, and those plane waves are approaching from the left-hand side of the screen toward a single slit. So basically, the setup is like this. So you have those wavefront basically is traveling to the right-hand side, the plane waves. And on the wall, there's a slit or hole, which is actually a opening, and the waves can actually penetrate through this hole. The width of this hole is denoted by, or essentially given to you, which is actually D. And we were wondering what is going to happen to-- what are we going to observe on the screen, which is actually pretty far away from the wall. And this screen is actually used to observe the pattern of the interference pattern of the electromagnetic wave passing this hole. So, as we discussed last time, due to Huygens' principle, every point is actually like a point-like source of spherical waves. So, as you can see now, we actually consider the size of our slit. Therefore, there must be a lot of point-like source inside, in this slit. When this wavefront actually pass through this wall, there should be infinite number of point-like source. And all of them, due to Huygens' principle, is going to be like point-like source of spherical waves. And they are all emitting from all those possible location, and that they are overlapping each other and they have constructive or destructive interference with each other. So that is actually what is happening with this single-slit experiment. And we call that diffraction. So you may be wondering, why do I call it diffraction? Why not interference? Because it's basically the same phenomenon, right? I think it's just a matter of wording. Feynman actually commented on this, and he said that, nobody was able to define the difference between diffraction and interference in a satisfactory way. Which is actually true. So it's just a matter of wording. So we are looking at exactly the same phenomena when we actually discuss this experiment. So what I am going to do today is now to introduce to you the way we can deal with this. I'm sure you have seen this experiment before, maybe in 8.02 or in high school days. On the other hand, what we are going to do today is to really make use of the mathematics which we have learned from 18.03 or from the previous lectures to attack this problem. So what is actually the mathematics I am going to use today? So the mathematics which I would like to use to attack this problem is to use a two-dimensional Fourier transform. I think by now you should not be afraid of Fourier transform any more. It should be pretty natural. It's just integration, and you evaluate, and then you are going to get the corresponding number whatsoever. But the cool thing is that 18.03 give them physical meaning of those numbers, and I'm going to talk about that. So what is actually the Fourier transform I'm going to use? So I am going to evaluate C, which is a function of kx and ky. And what is actually this C function? This C function is equal to 1 over 4 pi squared, which I really don't care too much. It's just a constant. And I do the integration from minus infinity to infinity for dx, and I do a integration from minus infinity to infinity dy, a small letter scale, dy. And I have a f function, which I will introduce you what the f function mean, what does the f function actually represent. And exponential minus i, k is the vector which is actually telling you the direction of the propagation of the spherical wave, times r, which is actually a function of x and y. And this is actually the kind of integration which we will employ in order to attack the problem we are interested in this lecture. So, what does this integration mean? So we have basically some kind of this two-dimensional Fourier transform. The f function is actually telling you the shape of the source. So basically, this is actually telling you about the shape of the source. As we discussed before, the shape of the source, every point on this shape is a source of spherical wave, by Huygens' principle. So that is actually telling you where should I do the integration. This one, exponential i k dot r, what is that? This is actually telling you about the spherical wave. So remember, we were doing two-slit interference before, and we have actually two exponential function, if you remember from last lecture. So now, this is actually put there because each source you are going to get exponential function, which is actually presenting the propagation of the electromagnetic wave. You can say that, oh, wait, wait, wait. The omega t disappeared, right? There's no omega t here, right? But I don't really care because everybody is actually oscillating at the same frequency, the same phase. Therefore, I factorize out. After I have done all the calculation, I can multiply the whole thing by cosine omega t, and probably some phi. Then that is actually modulating and oscillating up and down as the plane wave, as you approach the wall. So, therefore, I actually already factorize it out. So this is actually telling you about the electric field. And what is actually here? This is actually the unit area you are performing this integration. And you can actually do integration over the full universe. So you have a plane which actually extend to the whole full universe. But what is actually really contributing is defined by this f function, which is actually the shape of the source. And some normalization factor, which I don't really care too much. So this looks really fancy, but is actually not that fancy. And what product you are getting here is our C function, is that C is actually a function of kx and ky. What is kx and ky? It's actually telling you the direction of propagation. The k vector is actually telling you the direction of the propagation. If you evaluate C with a specific given kx and ky, basically you are evaluating the total electric field going some direction, which is actually defined by kx and ky. So the big picture is the following. So basically you have some source. It can look like this in the xy plane. This is x and y plane. All those things, all those points, all those little areas inside this hole is spherical wave source. And the f function actually define the shape of this hole. And this integration is actually integrating over all those little areas. And then calculate the contribution from each small area, sum them together. Then, finally, you are getting something which is actually a function of kx and ky. What is kx and ky? It's actually giving you the direction of propagation from this point-like source to observer P. And this C function is actually proportional to the total electric field. So you can see that, hah, we have learned this Fourier transform from the math department, and we give life to this function. Now actually we understand what we are doing now. We are actually really summing all over the, summing over the available point-like source. And add all the contribution of the electromagnetic wave together. Then what we are getting, the C function is actually proportional to the total electric field. So that is actually the big picture. Any questions so far? I hope you can actually understand what we are doing. So now what I am going to do is to really use this formula and attack the problem which we are actually trying to understand, the single-slit problem. So suppose I have a single slit which looks like this. I'm zooming in this thing maybe 100 times, 1,000 times. And this is actually a wall. It's very, very long. I would like to define first my coordinate system. The x direction, as I actually drew from there, is actually pointing upward. The y direction is actually parallel to the wall. And the z direction is actually going to where the screen which I am trying to display the outcome of this experiment. And the distance between these two walls is actually D, which is actually given there. So I would like to actually understand what is going to happen when the plane waves pass through with this single slit. Therefore, before I calculate the C function proportional to the total electric field, what I really need is a functional form, f, which describe this single slit. And just to make sure that everybody is on the same page, this wall is actually infinitely long, from minus infinity in y to positive infinity y. So it's actually a super long wall. And these two edge is actually-- the distance between the edges is actually D. So what would be the f function which describes the shape of the light source? f function is a function of x and y. And I define a f function, and I give you this function to describe the experimental setup. So the f function can be either 1, which actually shows that there are point-like source there, or 0 when I am talking about things on the wall, because there's no point-like source there. Because the wall is actually blocking the light. So it can be either 1 or 0. When is that equal to 1? When minus D over 2. If I define-- this is actually x equal to 0. The middle of the slit is actually x equal to 0. Then it is actually equal to 1 when minus D over 2 smaller than or equal to x, smaller or equal to D over 2. So that will give you a slit with width of capital D. On the other hand, if the absolute value of x is greater than D over 2, then I get 0. So now you can see that is actually the meaning of f function. f function is actually giving you a map of the point-like source. And what I am going to do now is to really do the integration to sum over all the spherical electromagnetic waves coming from all those point-like source, and to calculate the total electric field. So now I can go ahead and calculate C function, which is actually a function of kx and ky, related to the direction of propagation, or, say, the relative position of the observer and the overall point-like source. And this is actually equal to 1 over 4 pi squared, according to my formula. And now I'm going to do an integration from minus infinity to infinity. But I found that there's a shortcut I can take. f x y is only nonzero between minus D over 2 and plus D over 2 in the x direction. Therefore, this integration becomes integration from minus D over 2 to positive D over 2 dx, exponential minus i kx times x. I'm taking part of the k vector dot r out of this formula. The relevant part related to x direction integration is exponential i kx times x. And now I can actually do the integration in the y direction. So you can see that, in the y direction, this slit is infinity long, covering the from the left-hand side edge of the universe to the right-hand side edge of the universe. Really long. Super long. Minus infinity to infinity in the y direction. The relevant part of the exponential minus k dot r is exponential minus i ky times y. So, before I do this integration, I would like to remind you one thing which is actually we have learned from the past, from the help of math department. So we know delta function x minus a is actually equal to 1 over 2 pi, integration from minus infinity to infinity, exponential i p x minus a dp. So we know about this formula. So that means I can easily evaluate this function. So this function, I'm actually doing the integration over y. Therefore, what I'm going to get is, I take 1 over 2 pi out of this. I take 2 pi out of this. Then, basically, I can actually arrive expression, which is actually delta function is a function of ky. After you do this integration using this formula here. So p here is actually y in my integration I'm doing. And what I'm going to get is actually ky equal to 0, minus 0, and I simplify that to be delta function of ky. So basically, you are going to get the ky contribution is going to give you a delta function. So how about the integration which is the other part of the integration? The other part of the integration is related to x direction, is here. So, basically, what is actually left over? I took already 1 over 2 pi from here. Therefore, I have 1 over 2 pi, and I do the integration. It's just a exponential function. I'm not super worried. Basically, I get 1 over minus i kx. Exponential minus i kx x. And evaluated at D over 2, x equal to D over 2, and x equal to minus D over 2. I hope this part is straightforward enough. Any questions so far? Everybody's following? All right. Very good. So I will continue the red part. So I will just look at the red part and then continue on this board. I'm using the red pen, right. So, basically, what I am going to get is, basically you have 1 over 2 pi, 1 over minus i kx, exponential minus i kx D over 2, minus exponential i kx D over 2. So the red part of the left function become this. And you can actually easily realize that this is actually proportional to a sine function, right? So basically I'm going to get 1 over 2 pi minus 2i sine kx D over 2, divided by i kx. This is actually coming from there. And this is actually coming from-- this minus 2i sine function is coming from the exponential function I can cancel this 2, and basically I get 1 over pi kx sine kx D divided by 2. So if I put everything together, so basically what you are getting is delta function of ky, 1 over pi kx sine kx D over 2. Am I going too fast? Everybody is following? So I hope this mathematics is straightforward enough. And don't forget what we are doing. So what we are doing is the following. So we have this two-dimensional Fourier transform. And the goal is to sum over all the waves coming from a shape defined by f function. And I'm going to evaluate the C function, and the C function is proportional to the total electric field. C is a function of kx and ky. kx and ky give you the information about the direction, relative position of the source and the observer P. And from this exercise, what we actually learn from here is that the C function is a function of y, but essentially only nonzero when ky is equal to what? AUDIENCE: 0. PROFESSOR: 0, right? Does that surprise you? No, probably not. Why is that? Why should we expect that? Because in the y direction this slit is infinitely long. So if you have contribution of many, many spherical wave, and this slit is infinity long, the sum of all those spherical wave is going to be still like a wavefront. You can do this in your head. So that means the direction, if I choose a direction which is actually pointing to somewhere which is actually with a ky not equal to 0-- so that means I have a specific direction-- what I'm going to get is that the electric field, the total electric field, will be equal to 0. And, of course, you can actually also talk about what will happen in the x direction. So that is actually the dependence of the C function to the kx. And we found interesting dependence. It's actually sine kx D over 2 divided by kx. So what I'm going to do is to make our life slightly easier by defining something which is actually easier to understand. But before that, I would like to say that the electric field, as I mentioned before, is going to be proportional to the C function. And now I would like to drop the y direction, because it's just a delta function. Therefore, I can actually drop it in the discussion. Then I will say that this electric field is going to be proportional to the sine kx D over 2, divided by kx. Since we have the electric field, the magnitude of the electric field, then I can actually calculate what will be the intensity. Intensity is actually what we care. It's going to be proportional to E square, and that is actually proportional to C square. And what is actually that value? That is going to be proportional to sine square kx D divided by 2, divided by kx squared. Any questions so far? So remember what is actually we are discussing. So we are discussing about a single slit, and we were wondering what will happen to observer point P when they actually do get, when these observer do get the interference pattern of all the point-like source between these two walls. We can actually make it much more understandable by using angle, which is actually theta, which is the measure of AP, which is the direction of the-- which is a vector connecting the slit to the observer-- to the horizontal direction. And I can define the displacement with respect to the center to be x. And I can actually also express AP by a vector which is r vector. Basically, after this definition, we can actually calculate or express sine theta. Since the distance between the screen and the wall is very, very large, therefore the theta angle is very small. Therefore, I can safely assume that sine theta is actually x divided by r. And also, at the same time, this is actually equal to kx divided by k. Because the k vector is actually telling you the direction of propagation. So, therefore, I can actually rewrite this. This will become kx. The magnitude of k vector is actually basically 2 pi over lambda. So, therefore, you can actually calculate that, and you will get kx times lambda divided by 2 pi. Therefore, the goal is to rewrite kx in a form which we understand, which is theta. So now we have achieved that. What is actually kx? kx is actually equal to 2 pi sine theta divided by lambda. And this means that my intensity, which I appended there, will be proportional to sine square pi D divided by lambda sine theta, divided by 2 pi sine theta divided by lambda, squared. So basically what I'm doing is to replace kx and then write it in terms of theta. If I define beta to be equal to pi D sine theta over lambda, if I define this, basically you are getting sine square beta, this will be proportional to sine squared beta divided by beta squared. And this beta is actually proportional to theta and D. Any questions so far? I'm just doing a replace, I'm just replacing the variables so that it's actually in terms of theta and in terms of some variable which actually simplify the expression dramatically. So, that's very good. So we have actually evaluated the intensity, the resulting intensity which will show up on the screen. And then we found that essentially proportional to sine square pi D divided by lambda sine theta, divided by something squared. And then I called this constant, sorry, I called this expression, I defined this expression to be beta. Then the functional form become much simpler. It's become sine square beta divided by beta square. So what I am going to do now is to visualize this result. So what I'm trying to do now is to plot the intensity I as a function of sine theta, for example, using this expression. So what I'm going to get is something which is actually going to be decreasing. Something is going to be decreasing as a function of beta. So that's the dashed line. This dashed line is actually proportional to 1 over beta squared. And sine theta very small, you actually reach a maximum value of I0. When you move away from theta equal to 0, you actually will hit a minimum when the sine theta is equal to lambda over D. Because if sine theta is equal to lambda over D, then this expression become what? Become what value when sine theta is actually lambda over D? Pi. Sine pi is 0, right? Therefore, you have a destructive interference. This point is really interesting. Why? Because that means all the point-like source, all of them between these two walls, are working together so nicely such that the total field is completely cancelled. Isn't that remarkable? That's really, really crazy when this happens. Takes a lot of work, infinite number of source, to do that. Then, if you actually increase further the sine theta, move away from the center of the screen, basically you see that this will increase again and reach a smaller maxima, and again reach 0 when this is actually equal to 2 lambda over D. And this pattern continues. And, of course, because of the symmetry we observe in this expression, everything is actually proportional to sine squared something. Therefore, this distribution is actually symmetric. So you have minus lambda over D, minus 2 lambda over D, et cetera, et cetera. Any questions so far? So what you can see here is something really interesting. Sine theta, if you multiply that by r, is telling you the position which you will see on the screen. So this is actually-- if you are interested in some place, point of interest P, and this actually just r times sine theta. And this is actually the slit. And I will move this thing closer here. And the size of this slit is called D. So one thing which is actually very interesting in this result is that, if we look at the width of the central principal maxima. The width is actually the measure between the center and the first minima, where you have complete destructive interference. What you actually see here is that this is actually something very interesting is happening. When you increase D, if you increase D, what is going to happen to the position of the first principal minima, of our first minima? It's going to what? Going to become smaller. Right? So suppose I have a gap here and I'm shooting a gun like crazy, boo-boo-boo-boo boo-boo-boo-boo. And I produce huge amount of bullet, which I don't recommend to do that, for sure. What I'm going to do, what I'm going to get is a distribution like this, which are the bullets passing through this wall. If I increase the size of the wall, the distribution I'm getting is becoming what? Wider. Right? But the result here is actually surprising. Why? When you increase the width, when you increase the width of the D, this function becomes smaller. That means the central maxima will become narrower, as you can see from this demonstration. So the left-hand side is an experimental setup which you have a very, very narrow slit. And basically you get a very wide distribution in the intensity as a function of position on the screen. Right-hand side is another situation where you have wider distribution. I'm sorry, wider slit, and you are going to get a narrower central maxima. Which is actually different from the other experiment which we were actually doing. So that's the first thing which we learn from here. And, also, the distance, the distance between the maxima and the minima is proportional to wavelength. So that means I can measure wavelength by using the position of the minima. And we are going to do that to measure the wavelength of the laser beam. And, finally, the last thing which we learn is that, in the central region, you have a maxima of I0, and this intensity is going to be going down, proportional to 1 over beta squared, where beta is actually defined here. It's proportional to D sine theta and inversely proportional to wavelength. So now what I'm going to do is experiment which I would like to measure what would be the wavelength of my laser. So I have a laser here. Oh. OK, I don't want to hurt anybody. So I have a laser here. And I have a slit, which you cannot see, unfortunately. And I can read off the width of the slit for you. The width of the slit is carefully designed to be really small, is 0.16 millimeter. This is my width. The D is actually equal to 0.16 millimeter. And on the screen, you can see that there's a pattern formed here, which you probably cannot see very, very clearly, so I will try to lower the intensity of the other source. So you can see, then, see that there is an interference pattern or diffraction pattern which is actually showing here. So what I really need in order to calculate the wavelength is the sine theta angle. Which I will really need the sine theta angle. Then I can actually calculate what will be the wavelength of this laser. So that means I will need help from a volunteer. Who volunteer to help me to measure the distance between this slit and the large screen? Can somebody volunteer? Yes, please. So we are going to measure the distance. Can you hold this? And can you actually put it? OK, try to pull this thing, and we will try our best to make it straight. Thank you very much. We don't want to destroy the experiment as well. This is not working? Let me do this in the other way. So how about-- trial and error, right? How about this. You hold that thing, and I'm going to actually measure the distance from here. And I need to really make it really carefully, measure this very carefully. And I don't want to destroy anything, which is very possible. So what I'm getting? I get 7.5 meter. So that's actually the distance between the screen, the screen and the source. Hold that for a second. I am going to measure the width of, the distance between two minima. The distance between two minima is 7 centimeter. Thank you very much. Thank you for your help. So we have now everything we need to calculate the wavelength. I'm going to clean this up first. We have what? We have the distance now. The distance between the source and the screen is 7.6 meter. So now I would like to calculate what will be the lambda. And also I know the distance-- the distance between these two minima is 7 centimeter. So that means this will be 3.5 centimeter. So lambda divided by D is actually equal to sine theta. Which is actually small d, which is the distance between the minima. The small d is here. The small d is the distance between the minima and the center. Divided by r, which is the distance between the source and the screen. Therefore, I can have lambda will be equal to capital D times small d divided by r. So what is actually the answer? So basically I have capital D, which is actually 0.16 millimeter. So that is actually shown there but you cannot see it. So I will use a different board for this calculation. So, basically, we will actually get lambda is equal to capital D times small d divided by r. Capital D is 0.16 times 10 to the minus 3 meter. And what is actually the small d? The small d is actually 3.5 centimeters. And, finally, I have 7.6 meter, which is actually the small r. Divided by 7.6 meter. Can somebody actually calculate this for me? Anybody have a smartphone? This means that I haven't done this experiment myself, and we will see what is going to happen. I hope it will work. What is actually the value? AUDIENCE: 7.368 times 10 to the negative 7. PROFESSOR: 7.368 times 10 to the minus 7. This is actually equal to 7.37 times 10-- oh, wait. This is actually 737 nanometer. Actually, the wavelength of the red is actually between 620 and 750. And actually we are actually getting the correct value. You see? So, actually, now you can actually tell your friends that, although the wavelength is so small, but I can't measure it with such a square feet experimental setup. So that's a successful experiment. So that is actually telling you that it's a proof that this formula, which we actually do all the crazy work of this Fourier transform in two-dimensional integration, it should really work. And the result is actually not really far from what you can get from Wikipedia. So, at this point, I would like to take a five-minute break to take some questions. And then we are going to come back in, at 31, and we are going to discuss another very interesting issue, resolution. So welcome back. So there are a few questions about-- there were a few questions about the pattern here, which is interesting. So you can see that what we actually concluded from here is that the width of the central principal maxima is actually two times of the width of the secondary maxima. So you can see that the width here between these two points is actually lambda over D. But the width between these two points, which actually give you the width of the central principal maxima, is actually 2 times of lambda over D. And now this actually can be seen from the experiment there. Maybe not easy for the moment. But this is actually the width, and the smaller structure is actually having a width half of the central peak. So that is actually something which is interesting, and I would like to share that with everybody. So now we actually come back to the original question we were actually discussing last time. So one interesting thing we observed in this two-slit interference experiment is that you not only see all those little structures, which is actually kind of periodic structure, and that they are coming from the two-slit interference. And you also see this larger structure which is showing up there, which is actually going up and down, and also it produce minima at some specific point. Now we understand what is actually happening. Suppose I have two-slit interference experiment, where I have the width of the slits to be capital D, to be very small. D is very, very small. And the distance between the slit is actually called small d. Which is kind of weird, but you have to accept that because it's on my note. And you can see that, interestingly, if this is the situation, then you have this periodic pattern and you will see no decrease in amplitude as a function of distance with respect to the central point of the screen. So that's actually very nice. However, if you consider a realistic situation, where the size, or say the width of the slit is not negligible, is sizable. And what is going to happen is that-- OK, let's forget about the second one for a moment. We already learned that the output intensity of a single slit is already varying as a function of angle. So I have this pattern. Therefore, if you have these two realistic slit interacting with each other, have interference pattern, what you are going to expect is that you are going to have the two-slit interference pattern modulated by diffraction pattern. Because, originally, coming from a single slit, you already have a varying intensity as a function of sine theta, as we already discussed there. So, if we put all those information together, we are going to get I. The intensity is going to be equal to I0, which is some maxima, sine beta divided by beta, square of that, sine N delta divided by 2, divided by sine delta divided by 2, squared. So basically what I'm talking about is that, if you have N-slit experiment, each slit have the same width. And what you are going to get is-- this is actually the N-slit interference pattern. And that is actually modulated by diffraction pattern. Where beta, just a reminder, in this summary is pi capital D divided by lambda sine theta. And the delta, which is the optical path length difference we defined before, is k times d sine theta, and that is actually equal to 2 pi times d sine theta divided by lambda. So that is actually why, when we perform the experiment of a double-slit experiment in the last lecture, we get complicated interference pattern like this, and it has a very complicated structure. And now we actually understand why the structure is like this. The small structure in this case is actually coming from interference, two-slit interference. And the additional structure, larger-scale structure, is actually coming from diffraction, is coming from the varying intensity of a single slit as a function of sine theta. Any questions so far? We are making a lot of progress. So what I would like to move on is to discuss with you something really interesting. So we discussed and learned how to explain why we have actually colorful soap bubble. So I have something totally unrelated. So we have a soap bubble also in the space, which is the Soap Bubble nebula. Which is really interesting, and you can actually Google it and see what is actually happening there. But, actually, that's actually not my point. Then my point is that you really need very good resolution telescope so that you can actually observe those really beautiful objects which are already there and cannot be made by human. Made by somebody else. So this is actually what I'm getting into. So the resolution is really something important. So when you take a look at this picture, the resolution is not very good. So as you can see, now the peak position of two nearby peak is actually connecting to each other. Then what do we see from this picture? You see maybe a lion? I don't know. Maybe, maybe not. But if you improve the resolution, what do you see? It's actually zebra. So this is actually the kind of thing which we would like to discuss with you. We are actually touching this important phenomenon, which is actually needed for observing an interesting phenomena which is actually happening really far away from the Earth. What is actually the resolution? And we are going to talk about that as well. And I would like to show you another interesting example. So this is a comparison between not so serious picture and the picture from Hubble telescope. So I was using some telescope with D equal to 40 centimeter. And that's actually the best thing which I can achieve, shooting the same planetary nebula M57. That object is actually 2,500 light year away. And you can see that I cannot get really a lot of detail from this image. And now, if you compare that to D equal to 240 centimeter Hubble telescope, and also, at the same time, this thing is actually above the atmosphere. So that's actually very, very important. And you can see that you do get a much, much better resolution, and you can actually see all the fine detail, very, very fine detail of this image. And we are in the position to understand the resolution and the limit which we can have due to diffraction, actually. So if I consider now a pinhole with diameter equal to D. So right now what we are actually doing is not a single slit any more, but a hole with radius D over 2. And we can do the same, exactly the same calculation using this formula. But I'm not going to do that for the sake of time. So we can do exactly that same C function calculation. And what we are going to get is I as a function of theta is equal to I0 J1 beta divided by beta, squared. Where J1 is the Bessel function of the first kind. Sounds really scary, but it's actually not. So what I really need is the zeros of the Bessel function, so that I can actually extract the interference pattern and the width of the central maximum. So now, since we are having a pinhole, basically all of those things are, all those patterns are actually two-dimensional. And I was wondering what will be the needed beta value so that I can actually reach the minima. Why is that important? That is actually telling you the limit of the optical resolution. If I have two peaks which are actually placed too close to each other, like what we actually see in the previous slide, then we can actually not separate very well these two light source. On the other hand, if the distance between these two peak is larger than the first minima, then I can actually be very safe. I can actually separate. I can say that, ha, this is really two peaks. Two stars, two light source. I can tell. So that is actually why this is actually important. And where is actually the minima? And I can already solve that for you. And that is actually when x is equal to roughly, the numerical value is roughly 3.83. So that's actually not important. Those numbers are not important. The important result is really the conclusion. So beta is equal to 3.83, and that is actually equal to pi D sine theta divided by lambda. So that is actually our original definition. And I can solve what will be the sine theta, which is actually telling you the position of the minima. So sine theta will be equal to actually 1.22 lambda divided by D. So what does that mean? That means the position where you have the first minima is actually happening when you have sine theta-- this is the theta-- when you have sine theta equal to 1.22 times lambda divided by D. So that is actually very nice. Doing exactly the same exercise, and we now understand where my minima is. Then that is actually telling you something about the resolution. So what I'm going to try to get into is that, now, let's design a phone together, a mobile phone together. So what is actually the width of the human pupil? The width is actually roughly 2 to 4 millimeter-- when narrow, when you see a lot of light all over the place-- or 3 to 8 millimeter. So that is actually the typical length when wide. So that is actually the width of the pinhole. So, typically, the visible light, as we calculated, is something like 500 nanometer. And the width of the human pupil, we can actually take a number of 5 millimeter. And now we can actually try to give input to the phone design. So what will be the resolution if we take these two parameter together? So, basically, the resolution of your eye, we can now calculate that. So what is that? That is actually 1.22 times 500 nanometer divided by-- OK, my function is D-- so divided by D is equal to 5 millimeter. 5 millimeter. Basically, what you are going to get is 1.22 times 10 to the minus 4. This is actually the resolution. Sine theta, roughly equal to theta, is actually equal to 1.22 times 10 to the minus 4. I have a iPhone 6 or 7, whatever you have. Basically is 401 ppi. 401 ppi is actually what is that? Pixel per inch. So what is actually the delta x? So if I have a phone, OK, it has a camera there. That is my phone. And this is my eye. Looks like an eye. The distance is 20 centimeter. I do this, which is unusual. We have 400 ppi. So what is actually the delta x, the delta x between the pixels? The delta x is equal to 2.54 centimeter divided by 401, and that will give you something like 6.3 times 10 to the minus 3 centimeter. If I am trying to be healthy and I do this, then what is actually the delta theta? The delta theta is delta x divided by 20 centimeter, and that is 3 times 10 to be minus 4. If you compare this value to the limit I calculated here, you can see that, what is the conclusion? Can I resolve the pixels on the phone? The answer is yes. So that means this phone is not good enough. They have to do more work. And now I'm going to design a jPhone. Maybe at some point I got really crazy and I decided to open a company, which is Yen-Jie's phone company. And, of course, I will say this is jPhone because it's Yen-Jie. And I'm going to put 40,000 ppi in this phone. Will you buy it? AUDIENCE: No. AUDIENCE: Sure. AUDIENCE: How much? PROFESSOR: $1. You'll buy it? We'll see. Maybe you will buy it because you are my student. But it's not worth it. Why is that? Because you cannot resolve this kind of fine or small distance between pixels. So it's actually useless. So what is actually the limit? You can also probably give that to your friends. 2,000 pixel per inch is roughly the limit. Beyond that, maybe the next generation of our students will be using this like this. Then it works, and it is worth it. You can actually read this distance. It doesn't work for old people like me, but for young people it works. So very good. So that's another thing which you have learned. So, finally, as I promised you, we are going to go back to this business of designing the Enterprise for Star Trek. So what does Enterprise do to their friends? They shoot laser beam. And they try to attack the other ships. And what I'm going to do now is to calculate for you what is going to happen. OK, now I have this laser beam here. And, in principle, before you take 8.03, you are going to say, aha, I can shoot the moon. And this light is going to be really narrow and it's going to hit the moon, a very small area on the moon. Do you believe that now? I hope the answer is not. How crazy is this idea? What is the size of the spot? Can you guess? Is that 1 millimeter? 10 meter? Or 200 kilometer? How many of you think by now is 1 millimeter? Nobody? Fortunately. How about 10 meter? One, two, three. OK. Three of you. How about 200 kilometer? You believe that? Really? The answer is really 200 kilometer. It's the size of Missouri state. So now you can see that this is not practical at all, and you have to really do what? Increase or decrease the radius? AUDIENCE: Increase. PROFESSOR: Increase. By the end of this lecture everybody get this idea. Thank you very much for the attention. And I hope you enjoyed this lecture. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 16_2D_and_3D_waves_Snells_Law.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: So let's get started. This is our goal for 8.03. So you can see, during the exam number one, we have covered the first half of the goal, and we are actually making progress to learn about boundary conditions in one dimensional system and also in two dimensional system today. And we will actually talk about phenomena related to electromagnetic waves and optics today, which we will be able to learn two very important fundamental laws related to geometrical optics. OK, so that's the excitement. And then we started a discussion of two dimensional or three dimensional wave last time. And just in case you haven't realized that, there are two ways to go to higher dimension. So the first way is to increase the number of objects and place that in two dimensional or three dimensional space. And that is the kind of things which you will discuss today. So for example, I can have particles arranged in two dimensions which form membranes. And then we can also, on the other hand, change the direction of the electromagnetic wave, for example, as a function of time, and that's another way to go to a higher dimension. And today, as I mentioned before, we are going to talk about the first case, and on Thursday we are going to talk about the second way to go to higher dimension, which is related to polarization, et cetera. In general, higher order dimensions are hopeless. They are super complicated. And, in general, we don't really know how to solve this kind of system. Fortunately, in 8.03, what we have been doing is focusing on a small subset of questions of which are actually highly symmetric. Therefore, we can actually solve it analytically. So that will be the focus of 8.03, so that we can actually learn some physics intuition out of this kind highly idealized system. And the system which we are going to focus on today is shown here. It's a two dimensional system, which you have array of masses placing the x and y, x, y plan. And that is the system we are going to solve today. And we will learn a lot of interesting phenomena coming from the solution of this kind of system. Before we start a discussion of two dimensional system, I would like to remind you of what we have already learned from lecture eight. So that was about a system which consists of infinite number of mass and the infinite number of strings, and each string have string tension T. And all the mass, when they are in equilibrium position, the distance between all those mass in the x direction is a, OK? So we have solved this system before with space translation symmetry. And this is just a reminder that the dispersion relation, which we got a lot time, omega, as a function of k, is t over ma sine Ka over 2. So that was just a reminder of what we have learned from lecture eight. So by now you should realize that, OK, dispersion relation is unusual. This is actually telling you that this is a dispersive media, right? Because if you calculate the ratio of omega and k, you'll see that this is actually not a constant. So after all the discussion from previous lecture, you should be able to immediately realize that. And any wave propagating on this kind of system, there will be a dispersion phenomena happening in this kind of system. OK? And also from the previous lecture, we'll have learned that the eigenvectors based on space translation symmetry, it's exponential of ikx, where x is defined as j times a, where it's a is a label to tell you what which mass I was talking about. Now today, we are going to extend this to a two dimensional system. So instead of a one dimensional system we have a two dimensional array. So all the little mass all have mass equal to n, and they are placing xy plan. The coordinate system, which I defined is here. x is horizontal, and the y is vertical, and the z is actually pointing to you. And all those little mass can only oscillate toward you or going away from you, so in the z direction. It can only oscillate up and down in the z direction. And in this system we have the length scale, which is the horizontal distance between mass, is called aH. And in the vertical direction, the scale of the distance between mass is av. Also, we have string tension-- two different kinds of string tension for the vertical and horizontal direction. The vertical direction, you have string tension Tv, and in the horizontal direction you have string tension Th. OK So how do we actually describe this kind of system, right? The first thing, as we did before, is to label those little mass by my label. And my label is called Jx and Jy, which tells you which mass I was talking about in this system. Once I have defined that, the labels, I will be able to write the position of all those mass, the x direction position and y direction position, in terms of J and the A. So for example, x position of 1 over the mass will be written as Jx times ah. And y position of a specific mass, you can write it down in terms of a Jy times av. So all those things should be pretty straight forward. The interesting part is that, as we identified in the last lecture, this system is highly symmetric. It has space translation symmetry, right? Therefore, we can actually immediately figure out what will be the eigenvectors for this system. So the eigenvector-- very similar to what has been discussed here, where you have a one dimensional space translation symmetric system. Exponential of ikx was the eigenvector. Now you have eigenvector which is in two dimension, because you would like to describe not only the x direction but also y direction. And the eigenvector have exactly the same functional form because of space translational symmetry, and it is like exponentional of ixk times x. Multiply that by another exponential function-- exponential iky times y. So I think, until now, nothing should surprise you because this is what we have learned from the one dimensional system analysis. Based on what we have learned before, we can also immediately write down what would be the dispersion relation. Since we are always considering very small vibration, and this formula is still applies, therefore you can actually write down the dispersion relation-- omega squared k will be equal to 4 Th over Mah sine square Kx Ah, divided by 2 plus 4 Tv divided by Mav sine square Ky Av divided by 2. So this is actually pretty straightforward. And you can see that omega is a function of both Kx and the Ky. From the eigenvector we can also write down what would be the possible Psi xy. Now the Psi is actually the displacement in the z direction, with respect to the equilibrium position. And that is actually proportional to the eigenvector. So basically it's going to be a exponential ikx times x exponential iky times y. And of course I can write these two terms together, right? So basically what I would get is a exponential i, k is a vector times r, which is a vector. So basically k contains two components, Kx and Ky, and r have also two components, which is x and y. Again, we see that this is actually a non dispersive medium. And what we are going to do is to make linear combination of all those eigenvectors and figure out what would be the behavior when this system is oscillating at a specific frequency omega, and that is actually the corresponding normal mode at the angular frequency omega. So that is actually pretty similar to what we have done for one dimensional system. So this is a two dimensional system. Just a reminder about one dimensional system for a while. So there are two eigenvectors which have identical omega, right? So the first one is exponential ikx, and the second one is exponential of minus ikx. What we have done before is to do a linear combination of the two exponential functions, right? So what we can do is that-- OK, now I can create cosine Kx. This is actually 1 over 2 exponential ikx plus exponential minus ikx. Or I can also create sine Kx. And this is actually 1 over 2i, exponential ikx minus exponential minus ikx, for this one dimensional system. So that's how we figure out when the system is doing one of the normal mode. The shape of the system is like a cosine or a sine. Or in general, you can add these two together, and in general it can be something like cosine Kx plus 5, but 5 is actually some phase angle, which you can figure out by boundary condition. But before we introduce any boundary condition, all the k values, all the five values are allowed. Just a reminder about what we have learned before. So the situation is pretty simple. You have just plus and minus k, and then you make linear combination of these two, then you know what will be the shape of the normal mode. On the other hand, we are now talking about two dimensional case. So let's take a look at this dispersion relation. The dispersion relation we will have here, omega is a function of Kx, is a function of Ky as well. OK, what does that mean? That means I can have multiple choice of Kx and Ky, which they all produce the same omega value. So it's not as simple as this one any more, as you can see, right? Because when I slightly increase Kx, what I could do is-- OK, I can slightly reduce Ky to compensate the difference. Therefore, I can still keep omega, which is the angular frequency of the oscillation the same. OK, so that can be seen from this demonstration on the slide. You can see that this is actually one example dispersion relation. This is actually the formula which we have on the board. And what about if I set all those parameters and get, example, omega squared equal to 5 sine squared Kx, and the plus 5 sine squared Ky? OK, so what will happen? If I set my aht and the m value, so that I have this example. What will happen if I have that dispersion relation? So if I go ahead, and then plot allowed Kx and Ky value, which gives 1, you see a very beautiful pattern, right, on this. So you can see that ha, all those things on the circle can produce angular frequency omega equal to 1. And 1 will be their-- 1 will be the-- normal mode will be all possible linear combination of all those possible Kx, Ky pairs. You have a question? AUDIENCE: [INAUDIBLE] YEN-JIE LEE: In general, I think this-- you mean a circular shape? AUDIENCE: [INAUDIBLE] YEN-JIE LEE: I think, in general, yes, you do have determinacy because you can-- but the shape will not be circular, for example. OK, so it can be a general function which is like the formula above, but this argument still applies. So if you have some intermediate omega value, you can always slightly increase Kx and slightly decrease Ky, and that will still satisfy the same omega value. Therefore, all the normal modes, we set specific omega will be a linear combination of all those possible normal mode. All those possible Kx and Ky pairs if you have an infinitely long system. And the law also applies to the other example, when I have omega equal to 5, then you have slightly different behavior. But the take home message is that there are many, many pairs of Kx and Ky, which can create the same amount of omega. So that makes things pretty complicated. Potentially, we can always still try to understand this by investigating all the possible k pairs of Kx and Ky. On the other hand-- this is what we have discussed before. Before you introduce boundary condition for the one dimensional system, there are infinite number of possible k value, right? All the possible k values are allowed. But after you add boundary condition-- for example, I add walls around this system, so that I basically have a fixed boundary condition. So basically, the boundary condition is that the amplitude at x equal to 0, y equal to 0, or x equal to 5ah or y equal to 4av. At the boundary, the amplitude has to be equal to 0, because it is attached to a wall. OK, when this happens this means that we will have have four wall which will have a corresponding boundary condition. So that means I have to satisfy this four boundary consideration of side 0,y evaluated at any time will be equal to Psi Lh, y, t, will be equal to Psi x,0,t, will be equal to Psi x,Lv,t. And this is all equal to 0. So those are not very difficult to understand. Those are just the four walls around the system. Once you have all those conditions-- and of course I define Lh will be equal to 5 times Ah, because there are 5 strings between the two walls in the horizontal direction. And of course I also have defined here, Lv will be 4 times equal to av. So once I have all those four boundary conditions in place that means I cannot arbitrarily choose k value and the fact, right? Otherwise, I will not be able to satisfy these four boundary conditions. So now we actually will be able to figure out that there will be only four modes in this two dimensional problem, which will give the same omega. What are the four possible nodes-- what are the four possible eigenvectors? Those are a exponential plus or minus ikx times x, exponential plus minus iky times y, where the Kx-- because of the boundary condition, which we have solved in the one dimensional system-- Kx will be equal to Nx pi divided by Lh-- in order to match the boundary condition, add x equal to 0 and x equal to Lh. And Ky will be equal to y times pi divided by Lv. That's actually designed to match the boundary condition at y equal to 0 and then y equal to Lv. So you can see that, like when we've seen before with one dimensional system, after you introduced the boundary condition it's not an infinity long system anymore that allowed k value, which is the length number in the x and y direction. For example, in this case, it's also become limited, and only a limited number of possible values are allowed. In this case, Nx is allowed to be equal to 1, 2 until 4, and Ny is equal 1,2,3 in this system we are talking about. Any questions so far? Yep? AUDIENCE: I think you mentioned that Kx and Ky are directly related rather than inversely related, but I'm sort of confused as to why that is. Because if you want to maintain the frequency, it increases the wave numer and [INAUDIBLE].. YEN-JIE LEE: Yeah, so I was talking about when I choose Kx and Ky in the infinitely long system. OK, all of the possible values of Kx and Ky are allowed because I have a infinitely long system with no boundary condition. And in that case, going back to this dispersion relation, I have the freedom to-- OK, so when I increase a little bit, Kx, I can always decrease a little bit, the Ky. OK, so the question is why that's not the case, right, for the discrete case. As you can see from here, after we introduced the boundary condition, the four boundary conditions especially describe the boundary of the four walls. And what is going to happen is that you will also see that the allowed Kx value is becoming limited, because you cannot arbitrarily choose with lengths, right, if you choose a side along the wavelengths like what we have been trying to do for the infinitely long system-- not that it matched the boundary condition. Therefore, you don't have this degree of freedom to choose slightly higher or slightly lower Ky when I change a Kx. So you can see that the allowed value are discrete. Therefore, the number of possible combinations of Kx and Ky is also limited. And in this case, it's actually very likely to be limited to be only four pairs, which is actually plus, minus Kx and the plus, minus Ky. All right. Thank you for the question. OK, then once I have those I can do a linear combination of these four possible eigenvectors. And also, at the same time, I will try to match the boundary condition. So if I jump forward, basically what you can conclude is that Psi Nx and y, so that's with an Nx value y value chosen for the determination of Kx and Ky. And is this actually a function of x and y and of course also time, when I also make it oscillate as a function of time. This will be equal to some arbitrary constant, A of amplitude Nx, Ny sine Nx pi x, divided by Lh sine Ny times y divided by Lv. And of course, you can see that this is actually sine, right? It's actually, the same as what we have done for the one dimensional system, right? So if you have two boundary conditions that said, look, the beginning and the end, therefor, the corresponding normal mode is always a sine function. So that's what we have learned from the one dimensional system. And this is also the case for the two dimensional system. And of course, don't forget this wave function is changing as a function of time oscillating up and down harmonically. Therefore, you have sine omega Nx, Ny times T plus Theta, which is a phase to be determined by initial conditions. And you can see that the whole equation, a sine sine is multiplied by a sine omega T plus 5 because of beta function, right? So that means the shape is actually going up and down harmonically. So the shape is fixed, which is sine times sine, and the whole thing is oscillating at the same frequency at the same phase, which is the definition of normal mode, right? Just a reminder. And how do we actually imagine what is actually happening? That brings me to the demonstration, so we can really visualize how this kind of system will look like by a little simulation. So, suppose I choose Nx and Ny equal to 1 and see what will happen. This is the kind of oscillation you will expect, right? So if you choose Nx equal to 1, Ny equal to 1, then this is a system. Basically you have sine function with no node in x and y direction. Therefore, if you do get this simulation, you can see that there will be no node in the x,y plane, and all those particles are either going toward you or going away from you. They only oscillate in the z direction in this simulation. And also, you can see that now I can increase, for example-- I can increase the Kx by setting Nx to be 2 and see what will happen. So what is going to happen is that if I have higher Kx in the x direction-- so the next possible normal mode is that you have a full sine wave in the x direction, then you are going to see two components in this demonstration. And one part of the system is actually moving toward you while the other half part of the system is actually moving away from you. And you can actually see the node, or nodal line in this case, because we are talking about a two dimensional system in the middle of the distribution. Of course, we can always go crazy, right? I can set this to a really high value. So in this case, the highest value I can set these is 3 and 4, and see what happens. And this is actually a beautiful shape which is actually complicated but understandable, as you see in this demonstration. And all those little particles in this system are oscillating up and down at the same angular frequency and also at the same phase. Any questions? OK, so now we have done the discrete case, right? And of course we can also go to the continuous case. So if we go to a continuous limit, now I can assume that there is a symmetry between a horizontal direction and the vertical direction. I assume that Th is equal to Tv is equal to T. And also I assume that the length scale in the x direction and the y directions is equal, and the length scale is A. In order to make the whole system continuous, I need to increase the number of objects in the system, and at the same time I also need to decrease the distance between all those objects. So therefore, I need to have-- this length scale goes to 0. And what is going to happen is that if I rewrite my omega, which is a dispersion relation, what I am going to get is 4T divided by Na Kx squared, A squared, divided by 4, plus 4T over Na, Ky squared a squared over 4. This is issue because I am taking-- Ah and V need to be equal to-- and also having to be a very, very small value. Therefore, sine theta is roughly theta, right? Therefore, I can immediately write down this expression. And this will be equal to Ta divided by N, Kx squared plus Ky squared. So we are facing exactly the same situation. When I decrease A, I am going to add more objects into the system, but I don't want to have an infinitely large mass. Therefore, I also need to ensure the fix the ratio of m and a, so that when I actually increase the number of objects, I don't actually make the total mass go to infinity. So what I could do is I can define Rho S is actually the surface mass density. So the surface mass density is defined as m divided by a squared. And I can also define a surface tension. Surface tension Ts will be equal to T over a. And in this case, basically, I will be able to control, so that when I increase the number of objects, mass doesn't go to infinity, and I have constant surface tension and constant surface mass density. If I have defined this to quantity then this will become Ts divided by Rho S Kx squared plus Ky squared, and this will be equal to Ts divided by Rho S, k vector squared. And this k vector is a two dimensional vector. So we are actually almost there to make it continuous. So now I can make a goes to a very small value. We fixed the Ts and the row S. Very similar to what we have learned from the one dimensional case. Basically what we actually found is that time in the one dimensional case is that M minus 1 K metrics become minus T over Rho L, partial squared, partial x squared in the one dimensional case. And in the two dimensional case, without working through all the detail of mass, basically what we are going to get is partial square partial T square Psi xy-- It's actually a function of x and y and the time, right, because this is actually a two dimensional system. And this will be equal to V squared, partial squared, partial x squared plus partial squared, partial y squared, Psi xy and T-- very similar to what we have done for the one dimensional system. And of course I can, as you define this, as del squared. And basically what you are going to get is V squared, del squared, Psi x,y,t. So basically we again see this wave equation, but this wave equation is now a two dimensional wave equation. And we can also figure out what will be the V value, right, so what will be the velocity? The velocity which is going to be square root of Ts over Rho S. This is very similar what we have done for the continuous case, and in this case, what replaced T over Rho L is Ts over Rho S. Therefore, what we actually see that if I increase the surface tension, then the velocity will increase. If I decrease the mass per unit area, Rho S, then I will be able to have a much faster traveling wave from this kind of media. And what we can actually immediately also write down is that the Psi will be proportional to A sine Kx times x, sine Ky times y, and Psi omega T plus 5, where omega is calculated from the input Kx and Ky for this standing wave solution. And very similarly, I can also argue that-- in the three dimensional case I can actually follow exactly the same argument. Basically, in the three dimensional case, as well, we already see in the electromagnetic wave discussion, the three dimensional wave equation can be written as partial squared, partial T squared Psi is a function of x, y, and z and T. And this will be equal to V squared, partial squared, partial x squared plus partial squared, partial y squared plus partial squared, partial V squared-- Psi is a function of x,y,z, and T. Any questions so far? Nope? OK, so everything is crystal clear, right? OK, so this is actually the animation, which I showed you before already. So this is actually the two dimensional vibration of membranous. So basically the first one is what I have shown you when I choose a very small K value, which only make half of the sign and which match the boundary condition. Basically you see that there are oscillation, which you have the middle part, which is either going toward you or going away from you in this continuous system. So basically the solution is actually remarkably the same as what we have seen in the discrete system. OK, that's actually what I wanted to say. And also, of course, you can increase the k value, so that you go to the higher frequency normal mode. And you can see that if you have more and more nodal lines, which is actually the lines describing the-- the lines which you actually have no oscillation at all on the surface. For example, in this case, the nodal lines, as you're passing through the middle of this figure-- because all those little mass, all the other high particles are vibrating like crazy. But all the particles on this line, the nodal line, they're not at all moving, because that's actually at this position-- which is having one of the sine function equal to 0. Therefore, no matter what you do as a function of time, how you evolve the system, all those particle at that line will not move at all. And this was demonstrated from this table here. It's actually Chladni figures. You can see that in a two dimensional case the figures can look very complicated. So basically what it's showing here is that you have a square plate and it's attached to a vibrator, and basically this vibrator can be controlled. I can change the frequency of that vibration. When I reach resonance, which excites one of the normal mode, then this plate will be oscillating in a specific pattern. And those lines are actually showing you that the plates, which you have no oscillation at all as a function of time. Because if I, for example, turn on this demo again, you can see that if I turn on this demo-- you can see that all the sand on the plates are vibrating because now I am oscillating this plate by the vibration generator and the button-- by the motor and the button. And if I change the oscillation frequency so you can see that this frequency doesn't match with one of the normal mode frequency. Therefore, they will not be a lot of activity. But if I now change the frequency, so that it matches with one of the oscillation frequency for one of the normal mode of this system, you can see the, oh, some really cryptic pattern is formed! You can see that, oh, it have a very complicated pattern. And if I put my finger in one of the lines here I don't feel the vibration, but on the other hand, if I put my finger here, I can actually feel that there's lot of vibration at that point. I can always change the frequency and see what will happen. And then you can see that now I increase the frequency, and now I am actually trying to excite another mode. Now I need some more sand. You can see that I randomly throw sand on this plate, and then you can see that those centered as you bounce it around until it sits on the nodal line, which no vibration actually happens. OK, so let's go back to one of the lower frequency mode, which we showed you before. Now the question is, OK, you can see this complicated pattern almost look ridiculous, can we actually reproduce this pattern by our calculation? So we have seen that, OK, I can conclude that the normal mode looks like this, right? So therefore, I must be able to explain all those patterns, which is actually shown in this experiment. So that's actually what I am going to do to give you a try. So this is a little demonstration which I actually wrote. This demonstration actually has the solution to this two dimensional problem. And also the boundary condition is that-- or say, the condition which, as you can see on my solution, is that I require the center of the plate to be driven, because that's where I start to vibrate this plate. And I drive this plate up and down to see what is going to happen. So from this analytical calculation you can see that you expect a circle in the middle and also four lines which actually cover this circle. And also there are some strange structure at the edge of the plate. And you can actually compare this calculation to this result. It doesn't really match perfectly. So you can see that there is some imperfection, but you get that ring in the middle, and you do see these 1-2-3-4-5-6-7-8, 8 lines produced in this experiment. So this experiment is not perfect because there's a, you know, stiffness of this thing and also some energy dissipation, et cetera. But you can see that, sort of, we can actually use our calculation to explain this pattern! That's really cool, right? And the advantage is that now I have this wonderful simulation. I can put in all the crazy numbers, and you see that, huh, if I increase the K value, I can really make all kinds of ridiculous patterns out of this. And all these things can be kind of realized by this experiment. So you can see that, for example, I can now also turn on this, and I can actually increase the frequency to a very high frequency, for example. Then I can see that, oh, the pattern really becomes much more complicated. Now I have a circle and there are many, many more structures which you're seeing in the surrounding area. And of course I can again increase, increase, and see what happens. I don't know what is going to happen because every time I do this experiment I get a different pattern. OK, now this seems to be a very nice frequency. It's getting harder and harder. You can see that this is really crazy. Holy mackerel, right? What the hell is this? So you can see that all those crazy patterns can be created. And of course, during the break, you are welcome to come forward and play with this. So you can see that we can actually understand, sort of, the pattern produced from this experiment. That's actually very exciting, because that's actually why we are physicists, right? We would like to know why those patterns are formed, and now you know why. Those patterns are formed because there are nodal lines in this two dimensional normal mode modes. And the little sands really love to sit there, because you want to sit in a place which you don't have a lot of vibration. It's not very comfortable, right? So you sit in the place, which, hm, vibrates? Your problem. Vibrate's your problem. I sit here where there is no vibration. So that's basically how we explain these strange figures which we can see. And just for fun you can see that I can also generate all kinds of craziness. You can input all kinds of different Nx and Ny values, and you get all those wonderful figures for free. Maybe we can actually make some T-shirts with all those figures on the T-shirt, right? OK, so we had a lot of fun with this two dimensional plate. How about what will happen if I have a circular plate? What does it do? Unfortunately, I would not be able to solve the two dimensional plate problem in front of you because that will give you a Bessel function, which is not the end of the world, but that's actually kind of complicated. If I put it in mid-term exam, that's actually not very encouraging, right? But I can actually tell you what will be the solution. The solution will be a Bessel function. Basically you will have a lot of ring-like structures if I have a circular plate. And I can actually do an experiment which actually shows you the behavior of the circular boundary condition and see what kind of pattern can we see. So here I have a kind of complicated experiment. So here I have this ring, which I would like to produce some film on this ring. So see if I am successful. Kind of. OK. Now I can put this a soft film in front of the speaker. I can actually oscillate this thing-- membranes by the speaker. Oops, don't want to destroy everything here. All right, so now I can turn on this, so that we have light. And of course I will turn on the signal generator, so that I can hear-- I can actually start to vibrate the membranes. Before I do that, I have to turn everything off, hide images. All right, I hope you can see something. Can you? Can you see something on the-- it's kind of difficult to see it, but that should be there. OK, now I can turn on this speaker, and you can see that there are some patterns which it's probably difficult to see. Kind of see, right? There are rings. You can see it on the speaker. So you can see that now I have one, two, three-- three rings, right? Because I couldn't turn off the light, which is actually emitted from the sun, right? So I cannot turn off sun. Therefore, you can barely see this figure. So we shall explain the result of this experiment. And you can see that if I increase the frequency, according to the solution from Bessel function, you will see more rings got excited. So you can see that now I have one, two, three, four-- four rings. And of course I can continue to increase, increase, and increase. And you will see that there are even more rings produced. Essentially what I'm doing is actually really trying to vibrate and excite one of the normal mode by this loud speaker. And you can actually kind of see-- I hope you can kind of see it. If you can still see it, that means you need to check your eye because the membranes is broken. OK, so I think you sort of get this idea, and I'm going to turn off this wonderful machine and go back to the lecture. So this experiment is kind of hard to reproduce in your study room, right? I think everybody will agree. And there's another one which is actually kind of easy to reproduce, which I will encourage you to try it-- so if you have time. So this is from Jake. He sent me this wonderful video when I was teaching the 8.03 class. They found that they could excite two dimensional waves in this way. Can you see it? It's wonderful. You can see there are very high frequency oscillation, which actually excite these two dimensional wave. And you can see that lots, and lots, and lots of rings are excited. And then you can see very clearly from this simple experiment, what you really need is a cup of water. And you rub it against the surface of a table, then you'll be able to excite all the crazy patterns, which you can actually see from this two dimensional system and with two dimensional boundary conditions. OK, so we will take a five minute break before we enter the next part of the discussion. And we come back at 35. OK, welcome back, everybody. So what I'm going to do now is to continue the discussion, the one we actually got started, of the two dimensional and three dimensional system. And we have actually studied the behavior of standing wave, or normal mode, for this two dimensional system. And what I am going to do is discuss with you, a two dimensional progressive wave. So I will stick to a really simple example, which are plane waves. OK, so in the case of plane waves, which we discussed when we actually discussed the EM waves, you have the following functional form. Psi is a function of r and the t. And this will be equal to A exponential i. The k is a vector now, and it's pointing to the direction of the propagation of this plan wave. And this k is dot with r vector minus omega T, which is the oscillation frequency-- angular frequency. And evaluated at a specific time. And this is expression actually describes a plane wave where the direction of propagation is described by this k vector. And of course you can actually have the wave front, which is actually the peak position of this plain wave. And the distance between the peak position-- so if you can imagine that this is like this. So if you look at the distance between peak position that will give you the wavelengths, right? The wavelengths, now that will be equal to 2 pi divided by k, right? In this case, it's the length of this k vector. Just a reminder about what we introduced in the previous lecture. And we were using this to describe electromagnetic wave and such a kind of expression can be also be used to describe sound waves and also vibration on the membranes, et cetera, progressive waves. So if there are no other medium like what we actually have in this slide-- so we have nothing else. I have a membrane with a surface tension Ts, and Rho S is the mass per unit area. Then basically, this progressing wave is going to be traveling at the speed of v, which is equal to square root of Ts over Rho S, and I can actually define that to be some constant c divided by n. So c is some constant, and m is another constant which actually, the ratio c and n is equal to v. And I will need that expression later, only later, not now. If I have nothing else and that this system actually filled the whole universe, then what is going to happen is that this progressing wave is going to be propagating, propagating, propagating, propagating. Nothing will change until the edge of the universe. It doesn't actually introduce any excitement. So that's what we have already learned from when we have discussed electromagnetic interaction, and now the same expression can also be used for the description of the membranes. And then now to make this problem more exciting, what I'm going to do is to introduce a boundary. So the boundary is in the middle of this slide. And I will assume that the horizontal direction to be x equal to 0-- the horizontal direction to be in x direction and the boundary is at x equal to 0. And when you pass this boundary, there's another kind of material with surface tension Ts prime and slightly different mass per unit area, your s prime. Based on the expression we got for the velocity we will be able to conclude that v prime will be equal to square root of T prime S divided by Rho S prime. And that will be equal to c over n prime. And c is the same constant which I used for the left hand side system. And n, later, you will realize that that's a refraction index in a discussion. So the question which I would like to ask is, OK, now I have a prime wave propagating in the first system. And it met a boundary, and the question is what will happen when I have the incident wave coming into the system? So before that, I also need to write down the dispersion relation, right. So dispersion relation can be attempted by plugging in a normal mode Psi function into the wave equation. So what I can immediately obtain is that the dispersion relation, omega squared is equal to V squared, Kx squared, plus Ky squared. You can actually check this expression by plugging in this function into the two dimensional wave equation, and you will get that expression, OK? And that means omega cannot be arbitrary number. It's as you decided by Kx and the Ky. Or say, if omega is the side and one of the k is the side, then the third number, for example in this case, Kx, is as you decided by the dispersion relation which we have here. So, coming back to the original problem we are posting, I have, now, the incident wave coming into this system. I would like to know what will happen at the boundary when I have two systems with a left hand side propagating at-- the speed of the propagation is v, and right hand side's speed of propagation is v prime. What is going to happen? Assume my guess that I am going to get a refractive wave and a transmitted wave. So that's based on what we have learned from the one dimensional system. If I call this the left hand side, and call the right hand side system right hand-- the right hand system, r. So I can write down the wave function Psi L describing the left hand side. This will be equal to A exponential of ik dot r minus omega T. This is actually the incident wave-- describing this incident wave. And as you might guess, there should be some kind of refraction, right? So once this wave actually passed through the boundary, or touch the boundary, there should be some kind of refraction, right? So the refraction, I can actually write it down in this form as sum over alpha, r alpha is actually the coefficient over amplitude as function of the normal modes-- as a function of the progressing wave number, which I have shown. And I can actually sum over all kinds of progressing wave numbers. Exponential ik alpha times r minus omega T. So this is a general form of refracting wave. k alpha is describing the direction of the individual refractive wave, and alpha is labeling the individual refractive wave. But I don't know what will be the functional form for the k alpha for the moment. So therefore, I try to sum over all the possible alpha. And I would like to figure out what will be the allowed alpha by matching the boundary condition. So in short, the right hand side turn essentially is actually describing the refractive wave. And finally, passing through this boundary condition, let's look at the right hand side. Right hand side, Psi r, is going to be sum over beta on the transmission coefficients tau beta, which is the original amplitude, exponential of i, k beta times r minus omega T. So again I don't know what will be the behavior of the transmitted wave. Therefore, I have summed over all the possible values. And this is actually the functional form for the transmitted wave. I also know that k alpha vector squared will be equal to omega squared Rho s over Ts, and this will be equal to omega squared v squared, because of the dispersion relation in the left hand side. So basically, if you look at the left hand side dispersion relation, the length squared of this k vector will be equal to omega squared times v squared, right? This is just a dispersion relation of a non-dispersive medium. And also, I can actually figure out what will be the-- allowed length for the k theta. So the k theta squared will be equal to omega squared v prime square, because this progressing wave is actually the transmitted wave, is actually traveling in a second medium. So look at what we have done here. So we have an incident wave. We will wonder, then, what is going to happen. Our physics intuition tells me that, you must get a refracting wave, oscillation frequency should be the same. Otherwise, as a function over time, you cannot match the left hand and right hand side. And you also get a transmitted wave. But I'm now in trouble because I have so many turns. I'm summing over alpha infinite number of turns, and I don't know what will be the coefficient for the r alpha and the tau beta, which are the transmission coefficient and then refraction coefficients. So what I need to do, as you might guess, is to use the boundary condition. So now I am writing down, already, the general expression. Now I'm going to use the boundary condition to actually limit the choice of the possible k alpha and the k beta. What is actually the boundary condition? The boundary conditions are that at x equal to 0-- that's actually at the position of this line-- the membranes doesn't break. Otherwise, suddenly the membranes break, and this is the end of the discussion, right? Like, what we have done before, right? So the membranes doesn't break, so that the propagation can continue. So what does that mean? This means that if I evaluate Psi L and Psi r at x equal to 0, Psi 0, y, t. The left hand side will be equal to A exponential i, Ky times y minus omega T, plus summing over all possible alpha, r alpha, A exponential i, K alpha y times y, minus omega T. This is the incident wave transmitted wave evaluated at the left hand side, which is the upper formula. And that will be equal to the right hand side, which is containing only the transmitted wave. So basically you have summing over beta, tau beta, A exponential i, k beta, y times r minus omega T. And this expression, this boundary condition, should hold true for all the possible y, right, because the boundary condition is valid at x equal to 0. I didn't specify the value of y. So therefore I can actually put in all the possible-- oh, this should be y. Sorry for that. I can actually vary the y, and I will figure out that, ah, if I have Ky not equal to k alpha y, that means the wavelengths of the refractive wave and the incident wave will be different. If I have Ky not equal to beta y that means the transmitted wavelengths is going to be different from the incident wave. That means, no matter what I do as a boundary of y, the membranes will break. Therefore, in order to make this equation valid, the only choice is that when k alpha y will be equal to k beta y and equal to Ky. So that means the wavelengths projected in the y direction should be equal for the incident wave, transmitted wave, and the refractive wave. Otherwise, as you always move a little bit in the y direction, the membranes will break. So that's actually the condition which you can actually get. And the interesting thing is that, based on this expression, k alpha, the length of the k alpha, and the length of the k beta is fixed. And I also know what will be the component for the y direction. Therefore, that means the x direction Psi's for that k alpha x and the k beta x are also fixed because of the dispersion relation. So that immediately brings me to this conclusion that basically k alpha x will be equal to minus omega squared over v squared minus Ky squared, and that will be equal to minus Kx. So this is the x component of the refractive wave. And the transmitting wave, k beta x, will be equal to square root of omega squared over v squared minus Ky squared. If I draw, visualize the relative direction of all the three components, basically, this is essentially the direction of the incident wave, k, and the incident angle is theta. And from this expression, you see that the Ky is equal to k alpha y. Therefore, you have a refractive wave. But actually only the x direction has changed sides. Therefore, you have a refractive wave with exactly the same angle as the incident angle theta. The refraction angle will be zeta as well. And that there will be a transmitted wave with theta prime. And this is essentially the direction of the k prime. And the interesting thing is that the projection toward the y direction, that k prime y, has to be equal to the progression of the original incident wave in the y direction. So that means I will be able to conclude that-- the y components are the same. Therefore, I can conclude that k sine theta will be equal to k prime sine theta prime. I'm kind of running out of time. And if I define, already as I defined here, velocity is equal to c over n, and the v prime is equal to c over n prime, what I can immediately conclude is that-- give me one more minute-- is that if I have n equal to c over v and the n prime is equal to c over v prime, I can conclude that sine theta will be equal to n prime sine theta prime. Does this look familiar to you? This is essentially Snell's law. How many of you haven't heard about Snell's law. There were a few before. Yeah, OK. No problem at all. Then you learned it. So that means if I have two kinds of systems in my hand, and I will be able to relate the transmitted wave according to what I have in the incident wave. And you can see that Snell's law-- which were famous for the discussion of optics-- and here, I have no knowledge about optics or electromagnetic waves. So in short, what I want to tell you is that, we have just proved two of the most important laws of the geometrical optics, the refraction angle is equal to incident angle and the Snell's law without using any information about the dynamics. That means all those laws are coming from purely boundary condition and the waves. Therefore, you will expect that this will work for water wave, sound wave, electromagnetic wave, et cetera. O So we will continue the discussion next time. Thanks for the attention. And if you have any questions, let me know. I will be here. Hello, everybody. We are going to show you a demonstration, a really nice one. It consists of the following setup. So basically I'm going to place some film here. And then behind that there's a loud speaker, which I use as a signal generator and to actually produce sound wave. And this sound wave is going to oscillate the soft film, and then you are going to see the oscillation, or the normal mode's pattern, on the screen. OK, so that is actually the setup which we can actually demonstrate to you two dimensional normal modes. So the first thing which I am going to do is to produce a soft film. Now I am going to put it back into this setup here. You should be able to see the pattern on the screen. Then I am going to turn on the sound wave generator. You can see, immediately, that the pattern on the screen changed because of the sound wave trying to oscillate the soft film. You can see it directly from here, but it actually looks much more prominent on the screen. And now what am I going to do is change the frequency of the sound wave. And you can see that I'm changing it to a higher frequency. And you can see that there is a more and more complicated pattern formed on the screen. That is because I'm now exciting higher and higher frequency normal modes. And you can see that now I can actually continue and increase the frequency. And you can see that-- now we can see that the pattern becomes really, really infinitely complicated. You can see this grid developing. And then you can see that eventually that's basically two sine functions multiply each other. One sine function is in the x direction. The other one is in the y direction-- horizontal and the vertical direction. And you can see a really beautiful pattern forming due to the solution we derived during the lecture. And the higher frequency I go, I can see more and more complicating patterns, many more lines developing on the screen due to oscillation of the soft film. You can see now we have even more lines. And it's actually getting more and more difficult to see the pattern because now the lines are really close to each other. The nodal line, we can see clearly on the screen. Now I am going back down to a lower frequency, and you can see that at low frequency oscillation, the number of lines is actually smaller, and that is because of the smaller oscillation frequency and the longer wavelengths of the normal modes. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 11_Sound_Waves.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: So welcome back again to 8.03. Today, my plan is to continue the discussion of the two string system, which we were working really hard last time but we sort of run out of time. So we didn't have time to enjoy what we have done, right? So today we are going to discuss all the outcome of that calculation. And so we will start to discuss more examples which can be described by the wave equation. Today we are going to talk about another example, which is sound waves. It's a very exciting topic. And afterwards, we will start the discussion about electromagnetic waves. So this is the wave equation which we have been using, and over the last few lectures, we have been discussing two specials kinds of solutions-- the normal modes, which is actually standing waves in the end, which we identified, and the progressing wave solution, which is very powerful in describing the phenomena which we are familiar with. Last time, in the end of the lecture, we were discussing about an interesting example, which involves two strings in the system. One essentially in the left-hand side have mass per unit length, rho l equals to rho 1, and right-hand side one is thicker, and therefore, the mass per unit length, rho, is larger, which is called rho 2. What we did last time is to assume that we have a progressing wave, which essentially going into this-- which essentially first initiated in the left-hand side string and it's going towards the boundary of the two systems-- the more massive one and the less massive one. And see what is going to happen. And what we actually tried to describe last time is that we actually define incident wave described by this fi function, transmitting wave, ft, and the refractive wave, fr. By using boundary conditions which we described last time we can conclude that there's a fixed relation between the three waves equation-- wave functions. What we actually concluded that last time is that fr is proportional to fi, which is the incident wave function, by some constant, which is called r. And what is r? As we solved last time, it's V2 minus V1 over V1 plus V2, which are the velocities of the first and second string. And the transmitted wave, ft, is actually also proportional to the incident wave. And the coefficient-- we call it tau-- to describe the amplitude of the transmitted wave. So what we can do is the variance. So we actually discussed two examples last time, plugging in V1 and V2. And there are two more examples we can actually make use of this equation we obtained last time to discuss what would be the physics outcome of this kind of situation. So the first example which we can actually discuss is that, OK, now I have this string. Assume, though, they're connected to a wall. So this time we can say, oh, wait, wait, wait, wait a second. There's only one string now, right? But last time we were solving two strings, right? But what I'm doing now is to treat the wall as if it's a string. But this wall is really massive. Therefore, the rho l, or the mass per unit length, is really large. OK. It goes to infinity. If that's the case, if you're set this idea-- this is still a two string system-- then I can now go ahead and calculate what will be the velocity. The velocity V2 goes to 0. Then I can go ahead and plug into my equations. So we spend a lot of time in the last lecture to obtain those equations. And we will find that if I have V2 goes to 0, I have r equal to minus 1. And the tau, which is actually related to the amplitude of the transmitted wave, is equal to 0, which you can see from this equation. What does that mean? That means once we solve that question, we also know what would be the outcome of this experiment, this physical situation. When we have a string attached to a wall and we have an incident wave, as a function of time, what is going to happen afterward is that this wave is going to propagate and hit the wall and get refracted completely. The amplitude ratio is minus 1. Therefore, all the energy is refracted by the wall in this highly idealized situation. So that's kind of interesting. The second example is also very interesting. So if you have a string attached to a massive ring, and this ring can go up and down freely without any friction, you can again say, no, no, no, this is again a single string system, right? But what I'm going to argue now is that, OK, there's another string which is so light mass per unit length is close to 0. So it is actually in the air. If I do that, what is going to happen? The rho l is going to go to the limit of 0, because the right-hand side you almost cannot see it. And the V2, which is the velocity of the transmitted wave, goes to infinity. If that's the case, you can then again, plugging into this equation we obtained, and then you conclude that r would be equal to 1 and tau will be equal to 2. So what does that mean? This means that if you have this end, which is the open end, attached to a ring which can move up and down, then you get that refraction. The amplitude of the refractive wave doesn't change, because i is equal to 1. So it's still in the positive direction we defined. But now, it goes backward. Again, all the energy is actually refracted, as you can see from this equation. But the curious case is that-- the strangest thing is that the tau is equal to 2. That's kind of strange, right? Tau is equal to 2. What does that mean? That means you are going to predict a transmitted wave with amplitude exactly the two times the incident wave, and it's going to be propagating in the right-hand side and the speed goes to infinity. What does that mean? Does that mean the energy is not conserved? Have we found the cure of the energy crisis? Because now-- I can actually take all those energy. I can design this thing, and then this thing will bounce around all over the place. And that is going to emit energy. Oh my god, we solve all the problem. You should be really excited about it, right? No? But unfortunately, rho l goes to 0. So there's actually nothing oscillating out of this system. So therefore, there is no additional energy radiated out of this system. Too bad. Go back to work. All right. So that's actually what we discussed last time, and I hope that complete the loop. And today, before we actually move to sound wave, I would like to talk about, very briefly, harmonic progressing waves. So now, we can see that harmonic progressing wave looks really beautiful, as you can see here. And it can be described by a cosine kx minus omega t plus 5. 5 is actually the face. And you can always write it in different forms. And since we have learned how to describe in general the progressing wave, this is just to remind you that, OK, there's no proper notion to describe a harmonic progressing wave. So since we have learned about waves, which involve oscillation in the transverse direction. So basically, we always say, OK, things are oscillating up and down in the case of string. Before I start, though, the sound wave, there's a different kind of wave which we can also see very often in the daily life. This is called longitudinal waves. For example, I can have a spring wave, and I can actually-- imagine I have a spring wave. And I can do this. I oscillate in the horizontal direction. Then that can produce displacement with respect to the equilibrium position. And this kind of behavior is like a density wave. We call it longitudinal waves. This is exactly what is happening with sound wave. So what is actually sound wave? Essentially, a collection or motion of air molecules. And they are actually oscillating back and forth. And we may use that to extend energy all over the place. And today we are going to discuss the sound wave. And by the way, just for simplicity, because drawing all those dots really take a lot of time. So what we sometimes do is that, OK, we can now draw the pressure, the amplitude of the pressure, or the amplitude of the displacement of individual molecules in the discussion as a function of time. So if we draw the amplitude as a function of time or as a function of location, then it looks exactly the same as what we discussed before for the transverse waves. So just some clarification. It's not like the molecules are going up and down. They are going back and forth, and it's just a matter presenting that these are. So this is actually an example of a travelling wave in the longitudinal direction. And you can see that it is actually the density which is actually changing as a function of time. And as you can see, it's actually traveling at a fixed speed and going in the right direction of the blackboard. So those being said, we can actually get started with a concrete example. So I would like to discuss with you now a system, which is like you have a tube, with cross section area, A. So A is actually the area of the cross section. And I can now wonder-- now the physics question I'm asking is, what would be the-- what would be the behavior of the air inside this tube? So before I go ahead and solve this problem, I need to define and give you some more information about this tube and also the condition or the environment this tube is living in. So the first information I would like to give you is that the pressure, the room pressure, is actually P0 in this example. So the P0 is actually the room pressure. And I can now define coordinates is the x direction is actually in the horizontal direction pointing to the right-hand side. And now, I can actually try to describe a small unit volume inside the tube by location x. And the width of this volume, I call it delta x. And if I go ahead and prepare this system and at time, t, something is happening to this system-- so now, you need length. You need volume, I was discussing. This get displaced with respect to the equilibrium position. So that means, assuming that something happened at the t equal to t, the left inside edge of the volume is shifted toward a positive direction, which is described by wave function psi x. And the position of the right-hand side edge of this volume is shifted to side x plus delta x. So something happened to this system. We can also say that-- we can also describe this system, the pressure of this system, by P function. P of x is actually equal to P0, which is actually room pressure-- P0 is the baseline room pressure-- plus some kind of displacement in pressure, psi P. So now we describe the pressure acting on the left inside edge of the small unit volume, and the right-hand side, you can also do the same thing. P of x plus delta x will be equal to P0 plus psi P, describing the displacement or how offset the pressure is as a function of x but now evaluated at x plus delta x. So once we have all of those elements defined-- these are essentially just a copy of what I have in the slide and those are a reminder here-- now, we can actually calculate the motion of all the molecules in this volume, because I have pressure, I have displacement. The displacement is described by psi, end position is described by psi, the change in pressure is described by psi P. And now I can go ahead and apply, for example, Newton's law. Then I can calculate what would be the acceleration for all the molecules inside this volume. But wait a second. That sounds all great, but I don't know yet how to relate pressure and the volume, because pressure is actually expressed by psi P and the volume is related to psi. I need to know is actually the relation between pressure and the displacement or pressure between psi so that I can make progress. So that this actually the main discussion which I would like to do in this lecture. So given those information, I can now calculate what is actually the change in this little volume. So I can calculate the change in volume, which is described by delta V. But delta V can be actually calculated by a, which is actually the area of the cross section, times psi x plus delta xt minus psi xt. So basically, just calculate how much the boundary is actually displaced. And if we always take very small amplitude approximation, then basically this expression is roughly equal to A partial psi partial x times delta x, where the delta x is really very small. So a very small volume I was talking about. And I can also calculate the pressure. What is the pressure difference? The pressure difference is between the pressure acting in the left-hand side edge and the pressure which is acting on the right-hand side edge. So I can now calculate pressure difference, delta P. Delta P would be minus psi P x plus delta x t plus psi P x t. So basically, one is essentially the pressure pushing the body in the right-hand side. The other one essentially pushing it in the left-hand side direction. Again, I can take very small delta x approximation. And basically, what you are going to get is minus partial psi P partial x delta x. So we have prepared all of those information about volume and the pressure. As I mentioned before, the big question which we would like to ask is, how do I relate pressure and the volume so that I can make progress? If I can relate pressure and volume, then I can know what is the relation between psi P and the psi. Then I can ask you to make use of Newton's Law. Then I can calculate the resulting equation of motion. So there's two possible interesting scenarios which we can relate temperature-- so sorry, relate pressure and the volume. The first one was proposed by Newton. Newton said that, OK, this is an interesting phenomena. In my opinion, although you actually displaced this volume-- make the displacement for those molecules in the tube-- but because the heat was conducted from one region to the other region, all those regions are connected to each other. And the speed of this heat transfer is so fast. It's really fast, like instant. This heat is actually transferred from one direction to the other-- one position to the other position. Therefore, over the course of this evolution, the temperature should be unchanged. No matter what you do to the air inside the tube, the temperature should be unchanged, because Newton thinks that heat should be-- the speed of the heat distribution is really, really fast. Much faster than all those vibration happening in the tube. If that is the case-- that is the case-- then that means we can use ideal gas law. P times V is equal to nRT. I hope that you have learned this before in 8.01 and 8.02. If that's the case, that means-- so all those things are constant, because we assume that temperature is unchanged. Therefore, the right-hand side is essentially a constant. Therefore, P times V would be some kind of constant. The V would be proportional to 1/P. So that essentially is the first idea, which is coming from Newton, in order to relate pressure and the volume. The second idea is coming from Laplace. Laplace says, OK, he has a different opinion on this matter. He think that this essentially is an adiabatic process. What does that mean? That means the heat flow from the compressed region to the other region is really negligible, because the oscillation is really fast and the speed of the transfer of the heat is really slow compared to the time scale of the oscillation. Therefore, in Laplace's opinion, he thinks that the whole process is adiabatic process. If that's the case, which I will show you later, that means you have this relation between pressure and the volume. P times V to the gamma. Gamma essentially related to the decrease of freedom of the molecule, which we will discuss later in the class. This would be equal to constant. So the very interesting thing of this lecture is that we are going to be able to test which one is correct. You will be able to see if Newton win or Laplace win. So as I mentioned before, one is assuming the heat transfer, the speed of the heat propagation, is really, really much larger than the speed of oscillation. The other viewpoint from Laplace is that the heat flow is actually really negligible compared to the oscillation we are talking about here. And now, as usual, I would like to have a vote now. How many of you support Newton's idea? 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11-- so 15 of you vote for Newton. How many of you saying Laplace is correct? How about the others? OK, very good. So we have a majority of you support the idea of Laplace, and some of you actually support Newton. And we are going to see what is going to happen in the lecture today. So let's go ahead and apply these two ideas. So PV gamma equal to constant. So in the case if ideal gas law, gamma is equal to 1. Therefore, I just have to work on these function of form. And then also later we will figure out what is gamma all together. So that's consider only small vibration. Small vibration means-- small vibration means that I have psi P, which essentially, from this definition, psi P is the change in pressure with respect to the room pressure, P0. So psi P, assuming that's much, much smaller than P0. And also, I assume that the changing volume, delta V, which I calculated there, is much, much smaller than P0, which is essentially the original volume of this little area-- original volume of this area I was working here. All right. So that's the two assumption. Before I change the position of the boundary, which essentially is the upper graph, if I change anything, I have P0 V0 gamma. This is equal to some constant, C. And gamma can be equal to 1 so that you have ideal gas law. After the vibration initially happened, after the wall's initially displaced from the equilibrium position, what I'm going to get is-- I will have P plus delta P times V0 plus delta V to the gamma. This is equal to C. So based on those, actually I have already calculated delta P and delta V. So in this case, this delta P should be-- OK, this is actually not the delta P I was talking about there, so I should change it to delta P. Because that's, essentially, the difference between the resulting pressure and the original pressure. It's not the difference between the left-hand side pressure and the right-hand side pressure, which essentially is showing there. So this delta P, which I have already defined, essentially called psi P. Therefore, I will derive this to be P plus psi P. And I can now also copy these. You are going to get V0 plus delta V to the gamma. And this is equal to C. So as I mentioned before, I'm considering small vibration. Delta V is much, much smaller than V0. Therefore, this expression can be written as P-- sorry, this should be P0. I'm making some mistake here. This expression should be written as P0 plus psi P. V0 to the gamma. 1 plus gamma delta V over V0, because delta V is much, much smarter than V0. Can everybody follow? So here I will already take small vibration approximation. And basically, I can now rewrite this thing. I just expend all those terms. Basically, I call this equation number two. Equation number two will become P0 V0 gamma plus gamma delta V V0 gamma to the minus 1 P0 plus psi P V0 to the gamma plus gamma delta V psi P V0 to the gamma minus 1. So there's no magic. Essentially, it's just expanding these terms. Then, basically, you are going to get four terms. And basically, if you do write down the equation number two especially, that is essentially what you are going to get. So we are making progress, and we would like to simplify things. And you can quickly identify the hardest term, P0 V0 to the gamma. I know what is the value of that, right? That essentially is the original situation, and that is essentially equal to C. Let's take a look at also this term. This term is proportional to what? Proportional to delta V, which is a very small quantity, and proportional to psi P, which is another very small quantity. Therefore, taking a small vibration approximation, I would just simply ignore this term. Is everybody following? All right. So this term, this original term, is equal to C based on this expression. So we start from the system before the vibration happened. After the vibration happened there's a change in pressure, there's a change in delta V. But if you multiply PV to the gamma, this expression is still equal to C, some kind of constant. And then, now I do small vibration approximation, and I drop the term which is actually proportional to delta V times psi P. And basically what I get is that C is equal to C plus gamma delta P V0 gamma minus 1 P0 plus psi P V0 to the gamma. This term, these two constants cancel. And now, I can actually move one of the terms to the left-hand side. Then basically, what I am going to get is psi P V0 to the gamma would be equal to minus gamma delta V gamma 0 gamma to the-- V0 to the gamma minus 1 times P0. We can't immediately cancel V0 to the gamma. Therefore, what are we going to get? I'm getting psi P would be equal to minus gamma P0 over V0 delta V. Everybody following? So this is essentially the expression. And we also know why essentially is delta V. Based on this expression, delta V is essentially A partial psi partial x delta x, if we look at the upper board, which we actually just derived a moment ago. Therefore, I can write, replace delta V by that expression. Then basically what I get is psi P would be equal to minus gamma P0 A delta x divided by V0 partial psi partial x. I'm just plugging in the expression for delta V to that equation. A lot of mathematics, but all of them should be pretty straightforward. You don't actually have to copy because all of them are in the lecture note. OK? All right. So here, you can see I can, again, simplify this expression. A is actually the cross section of the tube, and delta x is the width in the x direction. So A times delta x is just V0. Oh, very good! I get this very simple expression, minus gamma P0 partial psi partial x. So we have achieved our goal to simplify the expression and to find the relation between psi P and the psi. That's actually what originally we were hoping to do, and we have achieved that. And I call it equation number three here. Don't forget what is psi and psi P. Psi P is the amount of change in pressure, and the psi is the amount of displacement of the wall-- of the molecule in the volume. So now, I'm really close to my solution, because now I can now calculate the force acting on this little volume, because now I know what is the pressure. So what is the F total? The F total is essentially delta P, which is the difference in pressure from the left-hand side end compared to the right-hand side end. So that's what we calculated before. Now this, A partial psi P partial x delta x. We also know what would be the mass. We know that the little mass in this volume, delta m, will be equal to rho, which is the density of the air, times A, which is the cross section, times delta x. That will give you the little area, V0. So rho times A times delta x will be your delta m. We are almost there. I have the m, I have the force, what kind of law do I need to use to get my equation of motion? AUDIENCE: Newton's law. YEN-JIE LEE: Newton's law, right? Newton's law. So F is equal to m times a, right? So therefore, I can now calculate and essentially I can now plug in rho times A times delta x. What is A? A is essentially psi double-dot. That's essentially describing the displacement with respect to the equilibrium position. And now I know this is equal to force, which is A times delta x partial psi P partial x. And you can see that both ends you have a delta x. So I can cancel that. Both ends you have an A, so now I can cancel that. Then basically you get rho psi double-prime. This is equal to partial psi P partial x. From the beginning we're talking about the relation between psi P, the displacement in pressure, and psi, how much the molecules are displaced. And then we have the solution here. If you assume the relation which was given by Newton or by Laplace, basically, you can conclude that this would be equal to gamma P0 partial square psi P partial x square. All right. And I can now put all the constants to the right-hand side. Basically, what you get is psi double-prime. So here it should be partial square psi partial x square, because I replaced psi P by psi. And I must miss one-- I must miss one negative sign somewhere. AUDIENCE: Over there. YEN-JIE LEE: Where? AUDIENCE: [INAUDIBLE] YEN-JIE LEE: Oh, this essentially-- there's a minus sign there, right? AUDIENCE: [INAUDIBLE] On the left side. YEN-JIE LEE: On the left-hand side. Yeah. That's right. AUDIENCE: Oh, no. There should be A. That's wrong. YEN-JIE LEE: Yes, you are right. And the minus sign should belong there. So that actually-- sorry for that. So there should be a minus sign here. And there should be a minus sign here. And after I plug in equation number three, then I get psi double-prime equal to gamma P0 over rho partial square psi partial x square. Any other problems you find? Not yet? OK. So look at this equation. Oh my god! What is this equation? AUDIENCE: Wave. YEN-JIE LEE: Wave equation. Again. Again. Wave equation. You can say that, huh, I'm not surprised, because this system is used so many times. I have learned this so many times, but I am still surprised that this is so identical to the physics which we have been studying for the strings for over the few lectures. So that's very nice. And now, the question we have an answer is that, OK, what essentially is gamma? What is essentially gamma? So gamma, in the case of the adiabatic process, gamma is actually equals to alpha plus 1 minus alpha. And alpha is related to the number of degrees of freedom. So if you haven't done this before, I have a concrete proof of the adiabatic process. And this is actually coming from the first law of thermodynamics. And basically, you will be able to conclude that gamma will be equal to alpha plus 1 divided by alpha. The value of alpha-- the value you get for alpha is related to how many degrees of freedom you can actually have in this system. For example, if I have a system which is made of atomic gas-- so there's only one atom in a molecule-- and basically you have 3 degrees of freedom. So you can move this thing in the horizontal direction. You can move this atom upside down or back and forth. So there are three degrees of freedom. And if you calculate alpha, that will give you 3/2. And basically, if you calculate gamma according to the equation you are going to get 1.67. On the other hand, if you have atomic gas, that means you have more degrees of freedom. So basically, you have not only the translation of degrees of freedom-- the three ones which are identical to the atomic gas-- you can also have two rotational degrees of freedom. So you can have these two atoms rotating like this, you can have that rotating like that. The trickiest thing is this one vibration degree of freedom, as you learned from the couple equations before. But this one, very trickily, is not excited at all at low temperature. You have to go to really, really super high temperature so that this actually contribute to the overall degrees of freedom. So therefore, you have a total of available degrees of freedom of 5. And if you calculate the gamma, you basically will get 1.4. So let's now calculate what will be the resulting speed of light. Sorry, no. Not speed of light. The speed of sound So if the temperature remain unchanged, if you take this equation here, this is a wave equation. Therefore, I know how to calculate the speed of sound. The speed of sound will be equal to-- P will be equal to the square root of gamma P0 divided by rho. So I have figured out the rho and the room pressure for you. So the P0 will be 10 to 5 kilogram ms squared, and the rho will be equal to 1.2. Rho is actually the density of the air. It's essentially 1.2 kilogram per meter cubed. If I have a gamma equal to 1, which is the case for ideal gas law temperature unchanged, if I calculate the resulting speed of sound you are going to get something like 389 meters per second. So that's the prediction for Newton. And the second case, if we have-- if we are believing what Laplace actually said, the heat flow is really, really negligible compared with the speed of oscillation, then we have, as we discussed last slide, gamma would be equal to 1.4. Therefore, you would be able to calculate the resulting speed of sound, and that is actually 342. So those are the predictions. And what I'm going to do now is to really demonstrate that we can actually measure the speed of sound in front of you. So the first thing which I will need to do is to switch so that you can see the camera. And now, I have a set up here. Basically, this set up is like the following. So basically, very similar to the setup we have here. But at one end, we actually have a speaker which produced sound wave. So this is essentially what we have. This is the tube, and we have, one end, there's a speaker attached to here, produce a sound wave. And basically, the amplitude will look like this. So basically, this will create some kind of standing wave inside the tube. And I have another device, which is actually a microphone. A microphone is connected to this scope, which shows you the amplitude of the-- basically, the amplitude measured by this microphone. And you see that if I move this, as a function of position you see that the am is changing. It's getting smaller when it is actually hitting the note here, because here there's almost no oscillation in the air. Therefore, you will measure a very small signal at that position. And if you continue to move, then you can see that, aha, I move away from the note, therefore I see some kind of maxima. Then, I see that this amplitude is dropping again. If I continue-- if I continue, then say that, aha, again, this amplitude is increasing to a very large value. Then it decreases to a minima around the note. So what I going to do now is to measure the distance between notes. And since the sound waves, which I actually put into the system, have a frequency of-- let me see. The frequency I put in-- the frequency I put in is actually 1 kilohertz. With the location of the note, I can know what will be, what? What will be the wavelengths of the sound waves. So therefore, I can now measure the distance between those three notes. Then I would be able to measure the wavelengths. Then I would be able to know who is correct-- if Newton is correct or Laplace is correct. So let's do that. So let me find the first minima. So the first minima is around 64. 64 centimeter. And you can see that. Say stop when you see that it's reaching the minima again. Stop. OK, very good. So this is actually the first note, the location of the first note, and I was trying to find the next note so that I can actually readout the wavelengths. Now, this will increase again. And reach-- stop? Is that a stop sign? OK, very good. All right. So I get the value, which is actually 30 centimeter. So now I can calculate what would be the lambda. The lambda is actually 64 minus 30. Then, what I get is 34 centimeters. And if I calculate the velocity of the sound wave, then basically I have F times lambda, and that will give you-- this is actually equal to 0.34 centimeter. So that would give you 340 meters per second. Oh my god. This is so close to the prediction of Laplace. First of all, this is amazing. Why? Because with this looks really crappy thing, I can measure speed of sound. Secondly, ooh, the measurement is really great. It match within 1%. You guys did a good job of stopping me. Very nice. And finally, very unfortunately, people who voted for Newton is wrong. So what happened is the following. What happened is that Newton actually assumed that the speed of propagation of the heat is really fast, but actually that's not true. Because, for example, I'm standing here and heating up the air. In the last few lecture, I even heat up the air by some kind of fire in front of you. But you don't feel the heat, right? So the heat propagation is really not really, really fast compared to the speed of vibration. The vibration is really quick, because it's really vibrating up and down 1,000 times per second. So that means what is actually much more reasonable is to describe this process is adiabatic process. So we will take a five minute break here so that we can take questions, and then we'll come back at the 39. So welcome back, everybody. So we can see that from the last-- so from the discussion we had before the break, we see that the sound wave can be described by something which we are now very familiar with-- the wave equation. And also, we know what is the speed of the sound, which, based on this wave equation, the speed of sound is actually equal to square root of gamma P0 over rho. So gamma is actually obtained from this discussion of how many degrees of freedom we have. So the first case we discussed is, if you have a single atom of which you make your air, then basically the gamma is actually higher. On the other hand, if you have diatomic gas, then the gamma is actually slightly smaller. It's 1.4. So what would happen if I change the air in my lung to monatomic atom? So what is going to happen is that the speed of sound is going to be increased. The speed of sound will increase. And I have a fixed sized of lung. I didn't increase the size of my lung. Therefore, the frequency of my sound will what? Will increase. So how about we do that experiment and see if it works? So here, I have a balloon here, which is full of helium. Let me see if it works. I'm not sure if it will work, but let's see. Fingers crossed. We'll see what happens. Now I'm going to do a measure of operation to replace all the air in my lung by this. Does my sound change? [LAUGHTER] No? Didn't work. Let me do that again. I speak more aggressive. [LAUGHTER] Did you hear any difference? No. (HIGH PITCHED) Any difference? Works? Works now? Very good. Maybe we should use some-- maybe we should use that sound to go over all the lecture, right? It's a very dangerous experiment, because you are replacing all the air in your lung. So you may choke. Fortunately, I survived this experiment and hope you enjoy. [APPLAUSE] What happened is the following. So basically-- basically, the gamma becomes large. Therefore, the speed of sound in my lung becomes large. Therefore, the frequency of my sound increased and you hear some really strange sound. OK, very good. So before the end, I would like-- poor Newton. Before the end, I would like to discuss with you something which I hope I would not see again in the exam but I saw before. So if I create a progressing wave in a single-- in a closed end, open end tube, this progressing wave is going to be propagating at the speed of what? The speed of what? AUDIENCE: Sound. YEN-JIE LEE: Sound, yes. It's going to be propagating at the speed of sound, and you would reach the boundary. The question is, will we see this? Would this progressing wave just simply leak out of the tube. How many of you think that's going to happen? I hope I will never see that again in the exam. This would never happen. Why? That means you will have a super narrow collimated progressing wave going straight out of a tube, and that will not actually match the boundary conditions at the end of the tube. So that means, basically, first of all, there was no refraction. That means that all the energy is transferred outside of the world. And according to what we discussed before, what you would expect is that, OK, now you suddenly change to environment which you have really very large volume. Therefore, you it will be very difficult to change the pressure outside of the tube. Because what you are actually connected to is a reserve of infinite number of molecules outside. It's going to be really hard to change the pressure. Therefore, apparently this behavior doesn't match the boundary condition. And therefore, what you should expect is something like this, which I can show you here. So in this case, you have both side opened. What is going to happen is that at the boundary-- actually, it's like the case of hitting a wall, because outside of the tube you have really, really large volume, huge amount of air out of it. Therefore, it's like hitting a wall. The amplitude of the progressing wave changes sine and goes back through the tube. And of course, this system is actually not perfect. Therefore, there can be some leaking out-- some energy leak out of the tube, which essentially must be happening, because we can actually roll the tube and we can hear the sound. That is because some of the sound wave actually leaks out of the tube. And this process will go over and over again. And this progressing wave is going to be going back and forth, like that. So I hope that after this demonstration everybody will expect that, OK, this will be not-- the result will be like this progressing wave is going to be reflected because of the boundary condition and also change sine in terms of amplitude. So what we have learned today-- so it's already close to the end. We have learned example of a longitudinal wave And basically, longitudinal wave is actually in the form of density wave in the example which we covered today. And the mathematical description of the sound wave is going to be almost identical to what we have learned from the string case, which we actually discussed last time. There are two boundary conditions which I would like to briefly discuss before we end the lecture today. So in the case of open end, as we discussed before, we can have a system which contains a closed end and an open end. What will be the boundary condition for a closed end? So the closed end have a wall here. Therefore, when you have your molecule, the air molecule oscillating back and forth, when they are actually close to the wall, they cannot vibrate. Why? Because it's hitting the wall. It cannot vibrate so that actually, the boundary condition at the closed end, where you have a wall closing the tube, is psi equal to 0. And on the other hand, if you have an open end-- if you have an open end, that means outside of the tube the pressure is equal to what? It's equal to P0. The room pressure. And you have so many stuff there. Therefore, it's not possible to actually change the pressure dramatically at the edge of the open end. Therefore, what will be the condition? Psi P. Psi P is again the displacement with respect to the room. Pressure will be equal to 0. Based on what we actually have learned from this expression-- sorry for that, my finger slipped. From this expression, psi P is equal to minus gamma P0 d psi dx So psi P is proportional to partial psi partial x. Therefore, this boundary condition actually translates to partial psi partial x equal to 0. So this issue looks really familiar to you, because in terms of psi, if you forget about this system, what those boundary conditions mean to you is exactly the same as you have some kind of a wall in the left-hand side and it's connected to a string, and the right-hand side of the string is connected to a massless ring which can actually move up and down. These two systems, if you actually don't look at the detail-- only look at the wave functions and the boundary conditions-- they are identical. So that's actually the first lesson we learn from here. So when I talk about sound wave or when you think about sound wave problem, there's nothing to be afraid of anymore, because that's actually the same as what we have learned with wall and a string system. That's the first thing we learned. Secondly, that only works when I write my wave function in the form of psi. So now I can actually get the first normal mode would be like this if I plot psi as a function of x. The second normal mode-- doesn't surprise you-- will look like this, et cetera, et cetera. If I plot psi-- if I plot psi as a function of x. On the other hand, we also know that psi P is proportional to d psi partial psi partial x. Therefore, you can also plot psi P as a function of x. Then what you are going to get is something like this. In the closed end, the psi P is actually reaching the maxima, because it's got the wall. Therefore, it can actually produce pressure on top of the wall. But you cannot move the position of all of those molecules in front of the wall. Therefore, that makes sense. You will see exactly in the opposite direction, if you plot the amplitude as a function of x, you see a picture which is almost like flipped. Of course, you can also do the same thing for the second one. And basically, what you are going to get is something like. The second normal mode, et cetera, et cetera. So be careful about the matching between the boundary condition obtained from the tube and string-wall system. They are identical. Open corresponds responds to open, closed corresponds to closed when you express your equation of motion in terms of psi. On the other hand, if you change that to psi P, then the relation is actually flipped. Thank you very much, and I hope you enjoyed the lecture today. And I will see you next week. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | Combining_Chalk_Talks_and_Slides_in_a_Complementary_Way.txt | I think chalkboard is much more nature for the students in their form ears because if I write all the equations on the slides first of all all those equations appear at the same time and and so so it is actually harder for the students to follow the logic between formulas and in my feeling is that it is so much natural to see all those equations popping up in a logical sequence for them and by writing down then on the chalkboard people have time to sink as well what is actually happening and I have also the freedom to point to the red urban equation on the board slowly so that people everybody who is not very familiar with the mathematics can follow factorial x squared plus 3 triple prime 0 divided by 3 factorial X plus infinite number of times and we 0 is the position of where you have minimap so I think that is your decision to use chalkboard in combination with slides do to my slides content information which is actually already covered from the previous lecture so that's a purpose to fresh through the information which is actually already covered during the last few lectures to remind people that ok you have learned this before right and so so I don't have to waste a lot of time to copy then on the chalkboard because they already learned that and secondly I can use slides to include interesting figures interesting videos interesting pictures etc so that actually that is complementary to my chalkboard teaching style |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | The_Role_of_Recitations.txt | so during the semester we have a few recitation instructors they help with the students during the recitation section so during those sections your the the instructor will solve a similar problem like what is actually covered during the same during the lecture and that give the students another chance to look at more example and to get for media will get used to the calculation which we carry how for the first time during the the lecture so also the recitation section and during the recitation section the instructors help the students they can actually ask more questions during the recitation sections including the questions they have the pset or any additional questions they they thought about after the lecture ok so that they get some chance another chance to clear some of the concept which they don't really understand during the during the lecture so we did not record the recitation sections during the fall semester in 2016 on the other hand we included problem-solving videos from Professor with Busha which is similar to what we do during the recitation sections from previous years to to go with the lecture videos done during the semester |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 20_Interference_Soap_Bubble.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: So I hope you can hear me. Welcome back, everybody. I hope you have the full energy back from Thanksgiving vacation. Everybody, welcome back. So before we start, we'll talk about where we are now. So this is actually the goal, which we said, for 8.03, at the beginning. So what we have been discussing is to learn about how to translate physical situations into mathematics, simple harmonic oscillator, coupled oscillators, et cetera. And we tried to put together infinite number of oscillators. And we found waves from this interesting exercise. And of course, we learned about Fourier decompositions of waves and also learned about how to put together physical systems. In order to do that, you need to define boundary conditions. And those conditions need to be satisfied, so that you can describe multiple physical systems all together. And the third part of the course, we have been focusing on many, many applications, for instance, for the phenomenon related to electromagnetic waves and also many practical applications in optics. And we are pretty close to the discussion between wave and vibrations and the future course, which is 8.04, the connections to quantum mechanics. And if we have time, we will talk about gravitational waves if we manage to do that. It depends on how fast we progress. So let's start the lecture today. So first, we will give you a short review. Before Thanksgiving, we were talking about polarizer filters. And we have been researching how to make a very good photo so that you can post it on Facebook, right? So that's essentially what we learned. So if you want to take a picture of the sky, which is deep blue, then you need to use a polarizer. And the reason? We also understand that it's because, if you look at the sky, which is actually, roughly a 45 to 90 degree wave from the direction of the sun. Basically, what you get is that all those light fronts scattering, between the sunlight and the molecules or little dust in the sky, polarize the light. Therefore, you can actual filter them using the polarizer. Of course, you have to tune your polarizer carefully, so that you can actually minimize the light from the sky, so that you get a sharper image in your photo. And also, we discussed about, with a polarizer, polarization filter, we can actually filter out also the reflected light, for example, from the water or from the window of a car. And that is because something which is closely related to the boundary condition, which we learned about from Maxwell's equation in matter. And this is actually the four equations, which we discussed last time. And in that issue, we were using that to explain the incident light, from air to something which is denser, for example lighter gas. And then we found that, if we start with unpolarized light-- this incident wave unpolarized light-- what we found is that the transmitted wave, which is actually in the bottom of this diagram, is actually still pretty close to unpolarized light but slightly polarized because of the transmission and the boundary condition. And the reflected light, something very interesting happens. Only the component, which is actually polarizing the direction, such that the electric field is oscillating in a direction perpendicular to the surface of this light, will survive. And that actually gives you polarized light, which is actually reflected from the surface. And this interesting phenomenon reaches the maxima, where you get the fully polarized light, when you actually set the incident angle of the unpolarized light at so-called Brewster's angle. And this Brewster's angle is happening when the reflected light and this transmitted light direction actually are orthogonal to each other. And that actually gives you the maxima effect we are looking for. So that's actually what we have learned from electromagnetic wave in matter and, also, matching the boundary conditions between the electromagnetic waves inside the material and in the air, such that we actually learn about all those interesting phenomena. And basically, we have learned how to describe electromagnetic waves, how to add electromagnetic waves together, how they propagate from one position to the other position, and how the boundary condition works and your equation of motion, et cetera, and something related to dielectric material. And today what we're going to do is to put all the things we have learned together and see if we can actually explain a very interesting phenomenon. So before I start, I will show you a demonstration, which I'm not sure if I will be successful. It's very difficult, actually. And of course, during the break, you're welcome to come over and play with all those demos. And here, I have two sticks. And I am going to create a soap bubble from this soap and water. And let's see if I will make it or not. So basically, I put this into the soap water. And I will try to open it to see if I can create a bubble. Yeah. You can see. You can see that there's a colorful soap bubble created. You can see that it is not always easy. Oh, it's getting very messy now. I'm trying to destroy the classroom. But it's OK, because we are MIT. You can that it's really beautiful. It's colorful. It live for a while, then it breaks. And of course, during the break, you are welcome to do this. And it's actually non-trivial to create this size of bubble. So the success rate is like 50%. So as you can see from this demonstration, we see something really beautiful. This bubble is colorful. And I didn't actually shine this soap bubble by all kinds of different preset colors. So it appears automatically and just shiny with all kinds of different-- whatever, wavelengths I get from the lights that are in here. Pretty bright light, there, on my face. And you can see that it becomes colorful. And we are going to understand what is going on and where this color is coming from. And the good news is that, based on the knowledge we have learned, we are in a very good position to understand this phenomenon. So before we start to explain this phenomena, I would like to talk about a phenomenon, so-called interference. So suppose we have two electromagnetic waves. We can actually add them together because of superposition principle. So what we can do is that, suppose I have two electric fields. E1 is actually defined as A1 cosine omega t minus kz plus phi 1 in the x direction. So by now, you should know that this is actually the electric field propagating at angular frequency omega, with a wave number k, going toward positive z direction. And the electric field is perpendicular to the direction of propagation in the x direction. And also, this electric field have a phase of phi 1. So that's actually what we know already by now. What does this mean, this expression mean? And it's actually the harmonic oscillating electric field. And of course, since I am talking about interference, basically, I can add this, the first electric field and the second electric field together and see what will happen. So now, if you define the second electric field to be A2, which is the amplitude, cosine omega t minus kz, basically, they have the same wavelengths and also the angular frequency-- plus phi 2. But they have different phase. And of course, in this setup, I asked them to be pointing to the same direction, which is the x direction. So we were wondering, what is going to happen if I consider the superposition of these two electric fields. And the total electric field, which is called the E vector, is actually E1 plus E2. So before that, I would like to remind you about pointing vector and also the so-called intensity. So pointing factor is actually defined as this S vector, pointing vector, is equal to 1 over mu 0 E cross B. So this is actually the directional flux of energy per unit area. So that should be the pointing vector which we have been using for a while. And also, another reminder is that, given the electric field, which is actually a harmonic progressing wave, the corresponding B field would be equal to 1/v. v is actually the speed of the light in some specific material. And k hat is actually the direction of propagation across E. This will give you the magnitude and also the direction of the corresponding magnetic field for the electromagnetic waves. So now I'm interested in what would be the resulting intensity, I, if I try to superimpose this, to try to put together these two electric fields. As you can see, these two electric field have different phase. The first one has phase phi 1. The second one, has phase phi 2. So this means that they may reach maxima or minima at different position in space. In this case, it's in the z direction. And what I'm actually defining here is two plane waves. And so it really depends on what would be the relative phase for the first and second electromagnetic wave. In order to quantify how much they cancel each other or how much they enhance each other, what I'm going to do is to evaluate the intensity of the resulting electromagnetic waves. And what is actually intensity? Intensity is actually the amplitude of the pointing vector. So I write this as the length of the S vector, pointing vector. And I can, of course, calculate what will be the value of this or, say, the length of the pointing vector. This will be equal to 1 over mu 0, based on these equations here-- just a reminder. And I would like to know what would be the length of the E cross B field. That will give you the length of the pointing vector. And basically, what you're going to get is 1 over mu 0 times-- since the B field is actually highly related to the electric field, and it takes a hit of 1/v, right, in terms of the size of the amplitude. So basically, you're going to get 1/v, E squared. And this cross product actually is OK, because it become E squared, because B field and the E field are always orthogonal to each other. And I can now rewrite this v. v is actually the velocity of the speed of light in matter. So basically, what I can rewrite is that will become 1/v will become c/n, which is actually the refractive index of a specific material. And still I have E squared here. Finally, I can rewrite this formula, since c is equal to 1 over square root mu 0 epsilon 0. Therefore, I can rewrite this expression in terms of epsilon 0. And what I'm going to get is c times n time epsilon 0, There E squared. So basically, what I do is I multiply both numerator and the denominator by c, and also I actually use this expression. Then I can actually cancel the mu 0 and then write everything in terms of c, n, and epsilon 0. So until here, there was basically no magic. Basically, it's just rewriting the length of the pointing vector in terms of n and also the electric field. So now, what I am going to do is to plug in this expression into that formula and see what we are going to get. So let me evaluate what would be the E squared, the length of the E squared. So basically, the definition of the E is shown here. It's the superposition of E1 and E2. Therefore, I can now quickly write down what would be E squared here. Basically, you are going to get A1 squared, cosine squared, omega t minus kz plus phi 1. Basically, that is coming from the E1 times E1. The second term, which I'm going to get, is actually E2 times E2. E2 times E3, you are going to get A2 squared, cosine squared, omega t minus kz plus phi 2. Basically based on this equation, and I square it, and then I get the second part here. And finally, what I am going to get is the third term, which is actually E1 times E2. Basically, you are going to get 2 times A1 A2 cosine omega t minus kz plus phi 1 cosine omega t minus kz plus phi 2, which is actually the cross term of this E vector squared. Any questions so far? I hope this is pretty straightforward to you. And of course, I can now rewrite this product with 2 cosine, cosine times cosine, right? Basically, I can rewrite this using the formula, which we have related to a cosine times a cosine. Basically, I can rewrite this as 1/2 cosine 2 omega t minus 2kz plus phi 1 plus phi 2 plus 1/2 cosine phi 1 minus phi 2. So basically, the first term is actually collecting the content of the two cosine and their length together. The second term is actually calculating the difference between the content of the cosine function. And what I'm going to get is actually phi 1 minus phi 2. Now, based on this definition, intensity, I is actually equal to the magnitude of that pointing vector. So remember, our goal is to evaluate what will be the resulting average intensity. So now I can calculate what would be the average intensity over one period. So this will be equal to 1/T, integration over 0 to T, one period, and the instantaneous intensity, I, dt. And what I am going to get is that-- so we have three terms. The first term is here, which is actually A1 squared, cosine squared. It's actually related to omega t. And the second term is here. It's also proportional to cosine squared omega t. And finally, we have two terms here, which is actually proportional to cosine 2 omega t. And finally, the last term is actually independent of time. So what I'm going to do is to evaluate the individual terms. For the first term, basically, A1 squared, cosine squared, omega t. So by now, it should be pretty straightforward for you if I integrate cosine squared over one period of time, basically, what you are going to get is 1/2. So is actually done several times in the p set. So basically, what you're going to get is-- I am going to collect all of those constants from here and copy here. So basically, you have c times n times epsilon 0, which is actually coming from the definition of intensity. And then for the first term, what I am going to get is A1 squared divided by 2. This 1/2 is actually just an integral related to cosine squared. Similarly, you are going to get the same result, a very similar result, for the second term. The second term is going to give you A2 squared divided by 2. Finally, you can have the third term. The third turn is going to give you what value? Can somebody help me? AUDIENCE: 0. YEN-JIE LEE: Yes, 0, right? Because this is actually cosine 2 omega t, right? So if you integrate over one period, you are going to get 0 plus 0. Each period will give you 0, right? So 0 plus 0 is 0, so therefore you get 0. Very good. How about the last term, anybody can help me? AUDIENCE: It should remain as it is. YEN-JIE LEE: That's right. Because it's a constant. So the average of a constant is a constant, which is actually giving you 1/2 times 2 times A1 times A2 cosine phi 1 minus phi 2. Of course, I can cancel this 1/2, which is actually coming from here, and the 2, which is coming from here. And basically, you are getting A1 A2 cosine phi 1 minus phi 2. And I need to close this bracket. Any questions so far? So what we have been doing is that I evaluated the total electric field. I basically calculated the superposition of the two fields. And then I am interested in what would be the average intensity coming from this field. And I write down E squared explicitly. There are four terms and only three of them actually survive. And basically, the expression I'm getting is like this. Basically, you have some constant multiplied by A1 squared over 2 plus A2 squared over 2 plus A1 A2 cosine phi 1 minus phi 2. You can see that the intensity depends on phi 1 and phi 2, right? So this actually would change the resulting intensity. So in order to get some idea about what does that mean and also how does the average intensity change as a function of phi 1 minus phi2, what I'm going to do is to define phi 1 minus phi 2 to be delta, which I will call phase difference. Then I would like to plot the averaging intensity, I, as a function of delta and see what's going to happen. So this is actually the result. So if I have the x-axis to be delta, which is actually phi 1 minus phi 2, and the y-axis is intensity. Of course, I would like to take out the constant, which is c times n times epsilon 0. So I am plotting the y-axis' average intensity divided by c times n times epsilon 0. What I'm going to get is something which is actually oscillating up and down, like this. The maxima value happens when delta is equal to 0. When delta is equal to 0, what is going to happen? This means that cosine delta is equal to what? , Therefore what you are going to get is A1 squared over 2 plus A2 squared over 2 plus A1 A2. This is actually when there delta is equal to 0. And the intensity, as you reach maxima, and the maxima values is actually 1/2 A1 plus A2 squared, based on these calculations. On the other hand, you can expect that that intensity will reach a minima when delta is equal to which value? Anybody can help me. AUDIENCE: Pi. YEN-JIE LEE: Pi, yes. When delta is pi, what is going to happen? Cosine pi is minus 1. So therefore, what you are getting is 1/2 A1 squared plus A2 squared minus 2 A1 A2. And that will give you 1/2 A1 minus A2 squared. You can see that, when the filter is equal to 0 or when the filter is equal to 2 pi, for example, if you increase the phase difference large enough, or the filter is actually 4 pi, all of those number will keep you maxima constructive interference. So what does that mean? That means you are adding these two electric fields in the most efficient way. On the other hand, when the value of the filter is equal to pi or equal to 3 pi or equal to 5 pi, et cetera, the intensity, the average intensity reaches a minima. That means, instead of adding them, you are actually canceling them. You are canceling the electric field of the first and the second electromagnetic wave. And now I give you a maxima intensity, which is 1/2 A1 minus A2 squared. Just a reminder, this A1 and A2 is actually the amplitude of the first and second electric field. So what will happen if I set A1 equal to A2? If I set A1 equal to A2, that means the minima would be equal to what? AUDIENCE: 0. YEN-JIE LEE: 0, yeah, very good. How about the maxima? AUDIENCE: [INAUDIBLE] YEN-JIE LEE: It will be A1 plus A2, right? So basically, you are going to get four times larger value compared to the intensity before you add them together. So individual intensity is I. And after adding them together, with delta equal to 0, you are going to get four times larger intensity if the amplitude of the first and second electric field is the same. So very good. So that's actually the result of the calculation. And you can see that the amount of intensity we can get out of this highly depends on the filter, which is actually the phase difference between the first and the second electric field. Can we actually get some more feeling about this addition? So what I am going to do is to, again, write everything down in terms of imaginary number or, say, a complex number. So if I rewrite the electric field, E1, as a real part of A1 exponential i phi 1, exponential i omega t minus kz. In the x direction. And I can also rewrite the expression for the second electric field to be the real part of A2 exponential i phi 2, exponential omega t minus kz, again, in the x direction So if I add these two fields together, what I am doing is like in the complex plane I have an imaginary number contribution in the y direction. And the real part is actually in the x direction. Suppose omega t minus kz is 0. At some instant of time omega t minus kz is equal to 0. So what I'm doing is I have the first vector, which is actually presenting the contribution of the first electric field. And this electric field is going to be pointing to a direction phi 1 away from the real axis with amplitude equal to A1. This is actually what we learned from the first lecture. And if I add the second electric field, what I'm going to get is another vector, which is actually A2 in length. And the angle is phi 2, here. So the resulting amplitude is actually when I take the real part of the first and second expression, adding them together. Basically, I am taking a projection to the real axis. And that is actually the resulting amplitude of the electric field, which is actually the superposition of the first and second field. So you can see that, when phi 1 is equal to phi 2, what is going to happen is the following. So basically, what you're actually going to get is that you are increasing the length of the routing vector, which is the addition of the two vectors. You are actually getting a maxima out of this addition. Because phi 1 is equal to phi 2, therefore, these two vectors form a straight line, therefore, you can actually add and get maximum amount of the amplitude out of this. On the other hand, when phi 1 minus phi 2 is pi, which I define as delta, when this happens, what we are doing is like addition of two vectors, in a complex plane, but they are pointing to the opposite direction. So the first one will be like this. And the second one will be looking like that. And they are actually trying to cancel each other. So that's actually how you can understand what is happening with different delta values. In this case, delta is equal to 0. The phase difference is equal to 0. And in the second case, phase difference is equal to pi. And then what happened in between is like this. You are adding them sort of together but not in the most efficient way or the most destructive way. And you are actually evaluating what will be the resulting amplitude by looking at the vector sum of the first and second field. So I hope that this will give you a some more intuition about what we have been doing. Any questions so far? So now, we are actually in a very good position once we understand this superposition of the two electric fields and the interference. Basically, the size of the resulting intensity will be highly dependent on the phase difference between the two fields. Then we are in a very good position to discuss the phenomenon which we just see in the demo. So before I actually perform the calculation and give you the explanation, I would like to take a vote, as of usual. So the question we are asking is, in addition to what we see in the demo-- we see a colorful bubble-- how thick is the soap film such that you can see color from the reflected light? The first option is maybe it's like 1 millimeter, which is possible. And that is about the size of the head of a pin. Or it can be 100 micron, so that's actually about the size, the thickness is about the size of the human hair. Or 100 nanometer, which is the size of the virus. How many of you think the thickness is roughly 1 millimeter? Raise your hand. Nobody thinks so. Really? Actually nobody think that's the case. How about 100 micron? How many of you think so? How about 100 nanometer? Me How many of you? So that is actually the vote. And we are going to know the result very soon. And how about the rest? Cool. So now we are going to solve the puzzle. So just a quick reminder about what we have learned from the last lecture. So there is a reason why we have the lecture first on the reflection of an electromagnetic wave before we discuss the color of the bubble. So from the last lecture, suppose I have two materials, which form an interface between material number 1, with refractive index n1, and the second material has a refractive index n2. If I have an incident wave, incident electromagnetic plane wave, and the incident angle is actually, in this case, 0, that means this incident plane wave is actually propagating in a direction which is actually hitting the surface directly. So if the initial amplitude is A, what we have learned from last time is that there will be a reflective wave, which is actually R times A. R is actually reflective coefficient. And finally, you have also the transmitted wave, which I call T times A, where is the transmission coefficient. From the exercise, which we actually already done last time, R is equal to n1 minus n2 divided by n1 plus n2. And the transmission coefficient is actually T equal to 2n1 divided by n1 plus n2. So basically, what I am actually talking about here is a conclusion from the exercise we have done in the last lecture, just a quick reminder. So I would like to discuss with you various situation related to R value. So the n1 and the n2 are related to the property of the first medium and the second medium. So it could be that n1 is actually greater than n2. So if n1 is greater than n2 in the experimental setup, that means that R will be greater than 0. Because R is actually n1 minus n2 divided by the sum of n1 and n2. Therefore, what I'm going to get is something like this. So basically, I'm going to have an incident wave like this, where, say, I use the notation pointing upwards. Once they got reflected, it is actually still like this, pointing upward, because the R is actually greater than 0. There's no changing sign in the amplitude. Therefore, there's an no flip in amplitude if n1 is actually greater than n2. On the other hand, the transmitted wave, if you look at the functional form of the transmitted wave, and transmission coefficient, T is actually equal to 2n1 divided by n1 plus n2. It's always positive. Therefore, will there be any possibility to flip the sign? No. You are absolutely right. So therefore, what is going to happen is that I will use this little arrow to keep track of the sign change. Basically, you'll see that after it pass through the boundary, there will be no change in sign in amplitude no matter what happens. On the other hand, if I have the situation n1 smaller than n2, what is going to happen? If you calculate the R value, it will be negative, right? In this case, R will be smaller than 0. So what is going to happen is that, initially, the incident wave has positive amplitude. And I keep track of the sign of this amplitude by this arrow pointing up. Because the R is actually smaller than 0, therefore, there is flip in sign in the amplitude. So what is going to happen? So the reflective wave will look like this. And I use this arrow to keep track of the flip in amplitude. And finally, as I mentioned before, the transmitted wave, the T, is always positive. Therefore, there will be no change in sign in amplitude. Finally, the third example is, if I have somehow two different materials, but they have the same refractive index, what is going to happen is that there will be no reflection, and everything goes through. Even if you have two different kinds of material, but if they have the same refractive index, then what is going to happen is that everything will pass through. And what you are going to get is that you will have no reflected light. Meaning R is actually equal to 0. Any questions so far? I would like to make sure that everybody understands the consequence of this calculation. So if I introduce no flip in amplitude, this means that this contribution will introduce a filter equal to 0. So basically, there will be no change in the phase, because there's no flip in amplitude. On the other hand, if there's a changing sign in amplitude, what would be the resulting filter value? Can somebody actually tell me? AUDIENCE: Pi. YEN-JIE LEE: It would be pi. Very good. So that means you are getting hit by a phase difference of pi. Therefore, the amplitude changes by a factor of cosine pi, which is minus 1. So that is actually something pretty important when we have the discussion of the soap bubble reflection. So let me give you a quick example about why is actually the amount of the reflected light and also what is the amount of transmitted light. Let me give you a concrete example. For example, if I have n1 equal to 1, which is actually the refractive index of the air, and n2 equal to 1.5 If that happens what is the resulting intensity? Just a quick reminder, average I, the average intensity will be equal to c times n times epsilon 0 A squared divided by 2, where A is the amplitude of the electric field. Just a quick reminder. And this 1/2 is coming from the time average, just a reminder. So now I can go ahead and use these two formula, R and T, to calculate the reflection coefficient and this transmission coefficient. So R will equal to 1 minus 1.5 divided by 1 plus 1.5. So basically, you get minus 0.5 divided by 2.5. And that is actually going to give you minus 0.2. Of course, I can also calculate what will be the T, which would be a 2 divided 2.5. So basically what you are getting is 0.8. So I can now calculate what will be the resulting intensity of the reflected light. Everybody's following? So what would be the intensity of the reflected light? This will be equal to minus 0.2 squared, right? Because the average intensity is proportional to A squared. A is actually the amplitude of the electric field. R should tell you what is actually the relative amplitude between the reflected light and the incident light. Therefore, you are getting hit by 0.2 squared multiplied by the initial intensity. Basically what you are going to get is 0.04 I, initial intensity. So basically 4% of the light is reflected. That may surprise you a bit, right? Because when you see, for example, the soap bubble, you see that it is still pretty bright, right? But in reality, only 4% of the light or 4% of the intensity got reflected. That is because your eyes is actually having nonlinear. Your eye responds to the-- or, say, receiving or interpreting the intensity is really highly nonlinear. So basically, you get 4% reflected. And the rest actually goes through. And just to convince you that the total intensity is 100%, we can calculate what would be the intensity of the transmitted light. This will be equal to 1.5-- this is actually related to n2, because the intensity is proportional to c n epsilon 0 A squared over 2-- times T squared. So basically you have a 0.8 squared and the I initial intensity. And if I calculate this value, basically you are going to get 96% of the initial intensity. So 96% of the initial intensity actually passes through the boundary and continues and propagates in the second medium, which, actually, in this case, is the soap. So the picture is the following. When 100% of light intensity going towards the boundary, what is going to happen is that 4% of the light got reflected. 4% of intensity got reflected. And also, because n1 is smaller than n2, therefore, there is a flip in sign in the amplitude. And the rest continues, 96% of them. And there is no flipping sign in the amplitude. Any questions so far? We're really pretty close. So now we are in a position to discuss what is actually really happening to this soap bubble. So I'm going to keep this result here. And I will now discuss a situation in which you have two interfaces. So suppose I zoom in, zoom, and zoom in this soap bubble and put it on the board. So this is actually the soap film. And I have now an incident wave, which is actually going into this bubble. So now I have 100%, which is actually going toward this film. So after this light, this plane wave hits the film, what is going to happen? The first thing which happens is that there will be 4% of the light got reflected. n2 is equal to 1.5. It's the same setup, just a reminder, just to make sure everybody is on the same page. So 4% of the light got reflected. Of course, the sign changed. 96% of the intensity actually continue. And what is actually happening is that there will be no change in amplitude in sign. And this is actually not the end of the story, right? Because the light will continue and continue to propagate. What is going to happen is that it will reach another boundary, where the incident light is you're traveling, from n2 refractive index material, to n1, which is actually the air. Now I have a situation where the light is actually going through the boundary and going out of the air. That means the light is actually going into the bubble. So this is actually inside the bubble. So what is going to happen is the following. Basically, the calculation is the same, except that now the R is actually 0.2 instead of minus 0.2, right? Because now n2 minus n2 is actually 0.5. 0.5 divided by 2.5 is positive 0.2. So basically, what you are going to get is a reflected light, which actually doesn't change. It doesn't change the sign of the amplitude. And what is actually the intensity? The intensity will be 96% times 4%, because only 4% of the light got reflected. And of course, a large fraction of the light actually pass through the bubble, 96% times 96%. And this would be, again, pointing upward, because T is always positive. Any questions so far. You can see that this actually really interesting, because most of the light actually pass through the bubble. So that's actually already one thing we've learned from this exercise. Now, what is going to happen to this light if I continue and increase the time? What is going to happen is that this reflected light, from the second surface or second boundary, will go backward and pass through the first boundary again. What is going to happen is the following. So basically, we're going to get, again, transmitted light and the reflected light. What will be the sign of the reflected light? Will the arrow be pointing up or down? AUDIENCE: Up. YEN-JIE LEE: Up, yeah, very good. Right now, if you are bored, then that means I am very successful. So that means I'm getting 4% times 96% times 4%. What would be the sign for the transmitted light? Pointing up or down? AUDIENCE: Up. YEN-JIE LEE: Up. Very good, so everybody gets it. And 96% pass through, 96% times 96% times 4% will pass. And of course, I can now continue and continue. What is going to happen is that now you have learned 8.03. You will see that this is a crazy phenomenon. What is going to happen is that there will be a tiny fraction of the light which is trapped forever between the two surfaces. They are going to be bouncing back and forth, boo, boo, boo, boo, boo, boo, boo, boo, forever. Of course, the fraction of the intensity is really, really small. Because every time you've got the reflection actually happening, you take a hit of 4%. But since we are talking about theoretical physics, so, theoretically, that would continue forever. That's actually pretty interesting. And going back to practical situation, basically, I can safely ignore any further reflection, because they are hitting so hard, because every time I get a 4% hit, right? Therefore, I can ignore all the other contribution. And what we are actually seeing is what? Our eye is here. We see the contribution of the first pass, which is actually reflected from the first surface. The second pass, OK, it pass through the first surface, got reflected from the second boundary, and pass through the first boundary, in the second round, and then, also, reaching your eye. So what are we looking at ? We are looking at the superposition of two electromagnetic waves coming from one, which is like this, and two, which is actually like this. The question now is what is the thickness of the film? Now I can define the thickness or, say, the width of this film to be d. Now the question we are actually asking is, what would be the thickness, d, which is needed such that I can have constructive interference? Now the question becomes really clear. And we can actually calculate that by evaluating the phase difference between the path number one and the path number two. So now, in order to have constructive interference, I need a specific phase difference. But before that, I need to calculate the phase difference first between path number one and path number two. What will be the phase difference? The phase difference delta will be equal to, of course, pi. This pi contribution is coming from the flip of the amplitude. That will actually give you an pi phase difference. The second phase difference is coming from the difference in the optical path length. You can see that the first path, it doesn't go into the film. It got reflected, directly. And the second path, which is path number two, it takes more effort or more time for the light to go back and reach your eye. How big is the path length difference? The size of the path length difference is 2 times d, right? Of course, I need to actually translate that back to the phase. So first, I need to actually calculate how many period. So the length divided by lambda will be the period. So lambda is actually the wavelength of the incident light. But I am missing a factor here. And can somebody help me? Because this lambda is actually inside the material, right? So which factor, I'm missing? AUDIENCE: n2. YEN-JIE LEE: n2, right? Yeah, thank you very much. So basically, inside the material, since the speed of light is 1.5 times smaller than the speed of light in vacuum, therefore, the wavelength is actually lambda divided by n2. And this is actually the number of period. And now, I need to translate that to phase difference. Therefore, I multiply this by 2pi. So you can see that now I have successfully evaluated or quantified the phase difference between path number one and two. That is there are two contributions. The first one is pi. It's related to the flip in amplitude. The second contribution, the blue one, is actually coming from the optical path length difference. And of course, we can evaluate that really precisely. Therefore, we can now quickly conclude that, in order to have constructive interference, I need to have filter equal to 2N pi, where N is an integer. And in order to have destructive interference, I need to have filter equal to 2N plus 1, pi, which is actually the result of the calculation which we have done, I think, before. Yeah, there. So this is actually based on the calculation we have done in the beginning. So we are really close. So now we have this result, delta is equal to pi plus 2d, times 2 pi divided by lambda divided by n2, right, so this complicated formula? Now we are in the position to evaluate what would be the phase difference. So the first thing which I would like to discuss is that, when d goes to 0, what does is actually the limit? The limit is when the width of the film is really, really small, it goes to 0. What is going to happen? You are going to have destructive interference. Why is that? That is because, even when you have d equal to 0, the filter is pi because of the flip in sign in path number one. The second thing is that now I can calculate what would be the constructive interference width. So this will happen when d is equal to 2N minus 1 lambda, divided by 4 n2. So basically, you can use that formula there and solve d. Then basically that's the formula we are going to get. And I will not go into detail with this. Any questions so far? So now, the third conclusion is that, if I fix d and the change in lambda, that is actually the more practical situation. Because I have the soap bubble. And it have a well-defined width, which is d. And what is happening is that I am trying to shine this soap bubble with light with different wavelengths, right? So that is actually the third situation. If I fix the width of the film, and the change the wavelength, lambda, what I am going to get is that the lambda max, which is the wavelength needed to have constructive interference, will be equal to 4d n2 divided by 2N minus 1. So basically, I can solve the lambda if I am given a d value. So actually, we already get the answer we are asking in the beginning. The first question is, why do we see color? The second question is, when I see color, what is actually the width of the soap film? We are going to know the result in a moment. So now, I have this formula in hand. If I have d roughly equal to 100 nanometer, which is the third option we were discussing, that is going to give you lambda maxima equal to 4 times 100 nanometer times 1.5-- n2 is 1.5-- divided by 2N minus 1. So that is actually 600 nanometer divided by 2N minus 1. Suppose I have N equal to 1, basically I am getting 600 nanometer. Suppose I have N equal to 2, 2N minus 1 is actually 4 minus 1 is 3. Therefore, you get 200 nanometer and 120 nanometer, et cetera, et cetera, which are the required wavelengths in order to have constructive interference between path number one and path number two. Everybody is following? If I plot the spectra of this lambda max, assuming d is 100 nanometer, what I am getting is like this. So this is a situation of very thin film. So this is the lambda. What I am getting is that there will be a maxima here, which is actually 600 nanometer. Red color is actually roughly 650 nanometer. This is red light. And this is actually roughly the range of the visible light, which is actually between lambda equal to lambda violet-- violet is equal to 400 nanometer. So you can see that the first maxima, lambda maxima, where you have constructive interference is at 600 nanometer. So that means you are going to see what kind of color in your soap bubble? AUDIENCE: Red. YEN-JIE LEE: You are going to see red, right? And then the next wavelength which you can have constructive interference is 200 nanometer. That is actually shorter than the wavelength of the violet light. It's out of the range of the visible light. What is going to happen? Your eye will not see it. So the next one would be here, whatever, blah, blah, blah, blah, which I don't care, because they are so short in wavelength. And you cannot see them. So you can see that, if I have a width which is roughly 100 nanometer, very same situation, what is going to happen? What is going to happen is that you are going to get only one maxima in the visible light range. And therefore, you can see color. Any questions so far? Now, what I'm going to do is take the same formula here, but now I would like to change this d. So now I would like to change the d to consider a situation where you have a very thick layer. So now I would like to change the situation to a very thick layer, so maybe I need to erase this part of the board to make some space. So now if I have d equal to 100 micron, what is going to happen? So I can now still use this formula to calculate what would be the lambda maxima. So lambda maxima will be equal to 600 micron, which is when you have N equal to 1. But this wavelength is way, way larger, much, much larger than the wavelength of the visible light. So it's not going to work. Therefore, you have to be patient. You have to increase the N value until N is equal to 500. So I am calculation 1, 2, 3, 4, 5, 6, until 500. Ahh, we are in the visible light range, right? Now, 5000 will give you 600.6 nanometer. Phew. Suddenly, your eye can see it. Very good. That's very nice, right? So I can now put it in my diagram. This is actually the wavelength, again. And, ah, I get one line here. How about the next one, N equal to 501? I'm going to get 599.4 nanometer. It's pretty close to this one. And the next one would be 598.2 nanometer if N is equal to 502. And what you are getting is that you can see that, no, things are not going very well. They are full spectra, all very, very narrow. Very, very large number of wavelengths can give you constructive interference. So what is going to happen? What is going to happen is that your eye will see reflection with all kinds of different wavelengths. And what color is that? AUDIENCE: White light. YEN-JIE LEE: White! You are going to see something which is white. So that is actually the answer to our question. So what would be the required thickness? The required thickness is something like 100 nanometer. So we can see how thin is the water bubble. That may surprise some of you, right? Most of you actually didn't think that's actually that thin. Secondly, if d equal to 0, you are going to have destructive interference. That means there will be no reflected light. Everything is going to pass through. And the bubble is like transparent. Finally, when the bubble is really thick, you are going to see white. So let me finish this lecture with a demonstration here. First, before I turn off the light, I would like to turn this on. So what I have here is a very complicated machine. It's not that complicated, actually. So basically, I have a light source here, which emits light with all kinds of different wavelengths. And I have this little device here. There's soap solution inside. And I can actually rotate from outside. You see how sweet is this setup. And I can actually create a soap film out of this. You can see that I am rotating and trying to actually project the result on the wall. You can see that, initially, there's nothing really striking in the beginning. You can see that the light is which color? AUDIENCE: White. YEN-JIE LEE: It's white, right? Remember, because of the optical setup, this image is actually upside down. So the upper edge of that image is actually the lower edge of my setup, which is the lower edge of my soap film. We have gravity, right, so that I can walk around. Due to gravity, you can see that it will form a thicker and thicker layer in the bottom of my experimental setup or in the upper edge of the image. On the other hand, due to gravity, the upper edge or the lower edge of the image will become thinner and thinner as a function of time. At some point, the color will start to show up. As you can see now, since we wait long enough, the soap film becomes thinner and thinner. And you can see that there are colors popping up. It's like a rainbow. Why is that? Because I am varying the thickness of the film as a function of the vertical distance. So therefore, you can see that this is actually showing you that different d value will give you very different colors. And if we wait long enough, basically what we are going to get is that the whole film will become more and more colorful. And I am sure that after this class, you can walk out of the classroom and explain to your friend why the soap bubble is colorful. Thank you very much. And if you have any questions, I will be around. And of course, if you want to make your own soap bubble, you can actually go ahead and play the demo here. So hello, everybody. So we are going to show you a demonstration, which we can see colorful interference pattern from a soap film. So basically, the experimental setup up is like this. Basically, we have light, which is trying to shine this thin layer of soap film. And the result is actually projected on the screen. And you can see, at first, you don't really see a lot of colorful pattern, because the thickness of the film is still rather large, rather thick. Therefore, you don't really see a lot of pattern. But as a function of time, you can see that this pattern is actually changing. Because of gravitational force, you will be able to see that the lower part of the film becomes thicker and thicker. And the upper part of the film, which you see that upside down on the screen, is actually becoming thinner and thinner. As we actually discussed during the class, when soap film is thin enough, there will be only one or only a few maximas in the interference pattern as a function of wavelengths, which happened to be inside the visible light range. And you can see it now, already, this colorful pattern really develops. It's really beautiful. And you can see that, in the lower part of the experiment, really have authentic color, because there are multiple maximas in the visible light range. On the other hand, in the upper part of the film, you typically have very little number of maximas or only have one maxima, in the visible light range, as a function of wavelength. Therefore, you see really, really dramatic and very, very colorful pattern develop from this experiment. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | Students_Common_Misconceptions.txt | people take a oh sweet class especially my version most of the students may sink uncertainty principle is actually related to completely related to quantum mechanics so actually it is actually another case actually uncertainty principle almost have nothing to do with quantum mechanics it has to do with just a wave description we employ when we describe the system so that's actually one of the pics in which we learn from our three the other thing which people will learn a lot more essentially that before they come to look us they may think is almost impossible to understand infinite number of coupled oscillators and it turns out that there is a very systematic way you can actually make use of simple symmetry argument and that you can actually create a simplified complicated system like infinitely long system so so it is actually another impossible task and everything can be actually understand using the concept of symmetry which we introduced in iostream |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 8_Translation_Symmetry.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR YEN-JIE LEE: Welcome back, everybody, to 8.03 Today, we are going to continue the discussion of symmetry matrix, which we started last time. And this is what we have been doing. OK? So the thing which we have been doing is to solve the normal mode frequencies of component systems by looking at equation of motion, MX double dot equal to minus KX. And in the end of the day, what we are doing is really to solve Eigenvalue problem-- M minus one K matrix Eigenvalue problem. And we have been exercising this several times the last few lectures. And the M minus one K matrix says you're describing how each component in the system interact with each other. OK? So that's actually what we are trying to do, to solve the normal modes. So we have been making progress, and we are increasing the number of coupled oscillators as a function of time. And now we finally arrive at our limit, which is infinite system, right? So basically, what we have been discussing is a special kind of infinite system, which actually satisfies translation symmetry, right? So in general, we don't know how to solve infinite system. If this system is really complicated, no symmetry, then who knows how to solve this, right? But very luckily, in 8.03 we have started to get a highly symmetrical infinite system, and in this case, it's translation symmetry. And that is really pretty nice, and we can actually use this example to learn an interesting fact, which we can see from the physical system we discuss here. So, one thing which we have been discussing is the space translation symmetry matrix. As a reminder, S matrix, as defined here. Basically, if you have a vector A, which describes the amplitude of an individual component in a system, basically these vectors have Aj, Aj plus one, Aj plus two blah blah blah. All those amplitudes are included in this vector. And what does this S matrix do? It's actually the following-- so if A prime is equal to S times A, then the base component of A prime will be equal to Aj plus one. OK, so that's actually what this S matrix does to A vector. OK? So you can think about S metrics as an operator. It's actually picking up the Aj plus one component, and moving it to Aj in the new vector. OK? So that's actually what this S matrix does. And we were talking about the Eigenvector of S matrix. For example, if A is an Eigenvector of S matrix, then we have this relation, SA equal to beta A. Now, beta is actually the Eigenvalue of S matrix. OK? And then we also discussed last time, that means, based on this logical extension, Aj prime would be equal to Aj plus one based on the definition of S matrix. And now this is going to be equal to beta times Aj, right? Because we assume that that A vector is an Eigenvector of S matrix. OK? That means Aj will be equal to beta to the j A zero. Right? According to this relation. Therefore, we can conclude that Aj will be proportional to beta to the j. OK, beta is still some coefficient, which we have not determined, and it can be anything. OK? So, in order to consider a system of little masses, which are oscillating up and down instead of going in one direction forever or the amplitude grows exponentially. And we also don't want the system to have the amplitude go to infinity when we go to very very large j value or very small j value, therefore we limit our discussion in the case of beta equal to exponential ika. OK? In this case, the absolute value of beta is one. Right? OK, and that means-- OK, Aj is actually proportional to beta to Aj, right? So if you take a ratio of Aj plus one and the Aj, the ratio is beta. If beta Is not equal to one or its absolute value is not equal to one, then this Aj value is going to be increasing according to a power law, right? So the amplitude is going to be, whoa, going to a very, very large value, right? And that corresponds to some kind of physical system, but not corresponding to oscillation. OK? And if we do this and assume that beta is equal to exponential ika. OK, if we do this, what is going to happen is the following. So again, the ratio of Aj plus one and Aj is a fixed value beta, equal to exponential ika. But what it does is, instead of changing the amplitude, it's actually doing a rotation in the complex plane. OK? So if this is Aj, J plus one, J plus two, et cetera, as a function of say j, the variable, then what it does is that this operation multiplied by beta is really a rotation in the complex plane. And while we actually see in the physical system, it's actually a projection of this complex imaginary plane to the real axis. And that would give you a sine function and cosine function. So very interestingly, if we choose wisely, the beta to have absolute value of one, then that will give you a system which is actually oscillating up and down and the amplitude is actually confined within some value. OK, so that is actually quite interesting. The other thing which I would like to talk about is-- OK, I choose to have exponential ika as my beta. OK, why ka, right? It looks really strange here. Suddenly the k and and the a are coming to play, right? So what is actually the small a? The small a is actually the distance between little mass, just a reminder. So this is actually the length scale between all those little mass, right? Therefore, what I'm doing is to factorize out the length scale, and then we suddenly found that. OK, after I do this, I define beta equal to exponential ika Instead of exponential i theta, right? So you can also do exponential i theta, right? But instead, I gave theta a fancy name, which is k times a. a is actually the distance between mass. Then something interesting happens, because k suddenly also will have a meaning. It's actually the wave number of the resulting sine wave. OK? So that's actually why we actually factor out this a factor. Then, after that, we actually found out the amplitude would be proportional to exponential ijka, and j is actually just a label of a phase component in the system. OK. So, once we have solved the Eigenvalue problem for the symmetry matrix, S, as we discussed before, if you look at the slides, OK? If S and the M minus one K matrix, they commute. OK? Commutes means that you can actually change S and and the M minus one matrix, you can swap them, OK, when you multiply them together. OK? If you can swap S and M minus one K matrix, that means they commute. And our conclusion from last time is that they will share the same Eigenvectors. OK? Of course, not necessarily the same Eigenvalue, but they share the same Eigenvector. So that's great news! Because instead of solving M minus one K matrix, which can be really complicated; depends on what kind of physical system you are talking about. I can solve S matrix Eigenvalue problem. OK? And then this Eigenvector, which I just found here, is going to be the Eigenvector of M minus one K matrix. And that's actually really making things much easier, because now instead of solving Eigenvalue problem of M minus one K matrix, what I am doing is just multiplying M minus one K times A, then you can actually obtain the normal mode frequency omega. OK? So that's the issue of the great excitement. What does that mean? That means, if you have all kinds of systems, which are translation symmetric-- you can have a line, you have however many people together, whatever a system which is so on here. They are all going to have the same Eigenvector. You see? You already know how they are going to interact with each other, and what is actually the amplitude as a function of j, which is the location label. OK? So that's actually really wonderful. So, in order to help you with understanding of this system some more, we are going to discuss another system which is actually also very interesting. It's actually a spring-- OK, last time we discussed a spring and mass system, right? And then we solved it together. And this time we are going to solve a system which is made of mass and strings. Ok? So that may actually copy-- OK, let me actually introduce you to this new system we are going to talk about today. It has many little mass here, from left hand side of the universe and right hand side of the universe. Take forever to actually construct this system. OK? Then my student actually carefully link them by strings, and we make sure that the string tension, OK, is actually a fixed value, which is T. OK. T is actually the string tension. And of course, as what we discussed before, the space or the distance between little mass is actually A. OK? So that's, again, the same length scale, which we were using. And finally, in order to describe all those little masses in the system, I label them as j, j plus one, j plus two, et cetera, et cetera. OK. So, the question we are asking is, what would be the resulting motion of this system, right? So what we can do is what we have done last time, right? We take jth object in this system, and we look at the force diagram and this M minus one-- to write down the equational motion and also the and M minus one K metrics. So what is actually the force diagram of j's component? OK. If I take this-- so first, I take my jth mass, and it's connected to two strings, right? So there are two strings connected to jth mass. OK? And of course, left hand side you have another mass, right hand side you have another option. OK? And I know the tension of this string. Its actually a fixed value, and the string tension is fixed at the T. OK? So, in order to describe this system, I need to find my coordinate system, right? As usual. So, what is actually the coordinate system I'm going to use.? So I need to define horizontal direction to be x, and the vertical direction to be y. Therefore, I cannot express this little mass to be-- the position of jth little mass as Xj and the Yj. OK? We can do the same thing for the left-hand side mass is Xa minus one, Yj minus one, and Xj plus one Yj plus one. So to simplify the discussion, what I'm going to assume is that all those little masses can only move up and down, OK, instead of back and forth. OK, so only one direction is allowed, and also I assume that the up and down motion of all those little masses is really really very small. So I can use small angle approximation. OK, so therefore I can-- this is essentially the zero of Y axis, when I actually-- before I actually move-- wind up with the mass away from the equilibrium position. So when the string mass system is at rest, OK, not really moving, then all the mass are at Y equal to zero. OK? So now, I actually move this mass to Yj, OK? Then, apparently there are two forces acting on this mass. The left hand side is string force, and the right hand side is string force. And the magnitude of the force is actually T. OK? So, in order to help us with solving this problem. I would define two angles-- the left hand side angle to be theta one, and the right hand side angle to be theta two. Then I can now write down the equation of motion in the horizontal direction, and then in the vertical direction. OK? All right. Since I have assumed that all of those masses can only move up and down, now I mean-- and also the displacement with respect to the equilibrium position, which is Y equal to zero, is really small, compared to, for example, the length scale a. OK? So therefore, I can write that condition explicitly. So I have a condition. I assume that Yj is actually much, much smaller than a, which is the distance between those masses. And that means theta one and theta two are going to be much, much smaller than one. OK? So that's actually given us a chance to use small angle approximation. So based on this force diagram, I can now write down the two equations of motion; one in the horizontal direction, the other one in the vertical direction. So what I'm going to get in the horizontal direction is M X j double dot. These will be equal to-- OK, there are two forces. Right? Horizontal direction, I would need to calculate the projection to the X direction, therefore the left hand side force will give you minus T cosine theta one, and the right hand side of this string force is going to give you plus T cosine theta two. OK? And then in the vertical direction, what I'm going to get is Myj double dot. This is equal to minus T sine theta y. Now I'm doing the projection in the y axis in the vertical direction, and minus T sine theta two. OK. And since I have this condition, all the mass can only move up and down, and also the displacement is much, much smaller than a; therefore, I have the small angle approximation. Cosine theta is roughly equal to one, and the sine theta is roughly equal to theta. OK? And I would call this the equation number one, and the second equation in the vertical direction to be equation number two. OK. So, up to here, everything is essentially exact, and now I would like to make a small angle approximation and see what will happen. And now equation number one will be called MXa double dot equal to minus T plus T, and this is equal to zero. OK, so that means we will not have horizontal direction acceleration. Therefore, in the horizontal direction, there will be no acceleration and therefore no movement in the X direction, or horizontal direction. OK, and now I can take a look at the vertical direction. OK? So basically, what I am going to get is MYj double dot, and this will be equal to minus T. Now, sine theta one will be roughly equal to theta one. So what is actually theta one? Theta one is going to be-- OK, so this is actually the Yj minus Yj minus one. Right? So now that's actually the difference between the amplitude of the displacement of the mass j, and the displacement of mass j minus one. Right? Divided by a, I get theta one. Right? Therefore, the first sine theta one, will become Yj minus Yj minus one, divided by a. OK? And of course, you can do the same thing for the sine theta two, right? Which is actually just the theta two. Then, basically, what I am going to get is minus Tyj minus Yj plus one divided by a. OK. Any questions? OK. I hope everybody is following it. OK, so now I can actually simplify equation number two, and basically, what I am going to get is MYj double dot will be equal to minus T over a. Basically, I take T over a out of it again. And I also collect all the terms related to Yj minus one, minus two Yj, plus Yj plus one. OK, I just ask you to rewrite equation number two in a form which we like more. OK, so that is actually the equation of motion, so from now on, I am going to ignore all the motion in the horizontal direction, because in this small angle approximation we have shown you that there will be no acceleration in the x direction, right? So now it's actually getting a step forward again. Basically, we have the equation of motion, and what is usually the next step? The next step is to write down what matrix? Anybody can help me? STUDENT 1: M minus one k matrix. PROFESSOR YEN-JIE LEE: M minus one k matrix, right? So actually, as usual, we actually follow the procedure. Now I would like to write down the m minus one k matrix. OK, so before I do that what, I will define-- I will actually assume my normal mode has this functional form, yj is equal to the real part of aj exponential i omega t plus phi. So basically, that tells you that all the components are oscillating at the same frequency, omega, and the same phase, phi. Yes. STUDENT 2: When there's a scenario-- PROFESSOR YEN-JIE LEE: Yeah? STUDENT 2: [INAUDIBLE] also [INAUDIBLE].. PROFESSOR YEN-JIE LEE: This one? STUDENT 2: No, there should be one [INAUDIBLE].. PROFESSOR YEN-JIE LEE: Here? STUDENT 2: Yeah. PROFESSOR YEN-JIE LEE: Ah. OK, maybe I made a mistake somewhere. Yeah I think it should be plus, right? OK. All right. Thank you very much. So now we have all the ingredients and we assume that it has a normal mode of aj, yj in this functional form. And then now I can-- the next step is to get m minus one k matrix. All right. So what is actually m metrics? M matrix is really really straightforward. It's m, m, m in the diagonal terms, and all the rest of the terms are zero. All right. And those, of course, you can also write down k matrix, right? So the k matrix will be equal to-- there are many terms, and in the middle you have minus t over a, two t over a, minus t over a, and all the rest of the terms are zero. And of course these patterns go on and on. Minus t over a, two t over A, minus t over a and zeros, et cetera et cetera. And this pattern is going to go on forever, because this is actually infinitly long matrix, infinite times infinitely long matrix. OK, so once we have this, we can now write down the m minus one k matrix. What is actually the m minus one k matrix? It has a similar structure to k matrix, right? All those are zeros-- OK, all those are the other values, but it has a fixed structure minus t over ma, two t over ma, minus t over ma, and then zeros. And this will go on forever in the diagonal term and also the next two diagonal terms. And all the rest of the terms. are zero. OK, Any questions? OK, so that's really nice. Now we have our m minus one k matrix, and the good news is that you don't have to solve m minus one k matrix's Eigenvalue again, right? Because we have solved the Eigenvalue problem of s matrix, therefore what is our left over is to multiply m minus one k by a, right? a is actually one of the Eigenvectors of s matrix. OK, so I am going to multiply that for you, and now we calculate m minus one k equal to omega square a, then I can get omega square out of this calculation. OK? If I again focus on this term. OK, so basically, what I am going to get is, right hand side, I have omega square aj, OK? Now that's actually from the right hand side, OK? And left hand side m minus one k times a, what I'm going to get is t over ma minus aj minus one plus two aj minus aj plus one. All right? Because if you take this term-- this term is actually in the exact diagonal of this m minus one k matrix, therefore this matches with j, and this will match with j minus one; match with j plus one. OK, therefore, if you multiply m minus one k and the a, you get this result. OK? And we also know that aj is proportional to exponential ijka, right? Therefore I can take aj out of this and basically I get t over ma aj minus exponential minus ika plus two. Because I take aj out of this bracket, OK. And minus exponential ika. OK. Now I actually can cancel aj. Basically, what I get is, omega square will be equal to t over ma two minus exponential ika plus exponential minus ika. And that will be equal to two t over ma. OK. One minus-- OK, so exponential ika plus exponential minus ika, you are going to get two cosine ka, all right? Therefore, you get one minus cosine ka. OK. I define omega zero to be square root of t over ma, just to make my life easier. OK? Then, what is going to happen is that I will have omega square equal to two omega zero square one minus cosine ka. Any questions? OK, of course if you like, you can also rewrite this as four omega zero square sine square ka divided by two. OK, so if you like. OK, so look at what we have done. We studied a highly symmetric system, which is as you were shown in the slide. OK, basically you satisfy the space translation symmetry. OK? Now what we have been doing is to derive the equation of motion, make use of the small angle approximation, then you will be able to find that, OK, only the y direction is actually moving as a function of time. Therefore, based on this derivation of m minus one k matrix, I arrive, and also based on the equation of motion, which I derived from the first diagram, I get this m minus one k matrix. And since we know that m minus one k matrix and s matrix will share this Eigenvector, I can multiply m minus one k matrix, and I come back to a. Then I will be able to solve the functional form of omega square, and that is actually given here. Omega square is equal to two omega zero square y minus cosine ka. OK? And is this actually telling you that omega is a function of k. OK. What is k? k is actually the wave number and omega is actually the angular frequency of the normal modes, right? So that means what we were talking about-- that means if we fix the wavelength or the wave number, k, then there will be a corresponding omega. OK? If you fix the wavelengths you are talking about, then the omega is also fixed by this omega of k function. OK, now we actually call it dispersion relation. This term may not mean much to you now, but later in the discussion, you will find, aha! It really makes sense, and that we will talk about dispersion in the later lectures. OK, so the conclusion from here is that, basically, if I have this distance that satisfies this translation symmetry, then what it tells us is that the normal modes, what looks like some kind of sinusoidal function, as we discussed last time. And also this-- OK, so this is actually the amplitude, what I am drawing here, this curve. And all those masses are only moving up and down, OK? As a function of time. And this is aj, and that is the oscillation frequency, which is actually the frequency of moving up and down, this kind of motion, is actually omega. And also, we learned that omega is equal to omega of k. And that is actually decided by the length, and how distorted is this normal mode-- the shape of the normal mode? And this is actually determined by the k, which is actually the wave number, and of course you can also get the wavelength from two pi over k. OK? In short, if you give it a specific wave number or wavelength, than the oscillation frequency is already fixed because of the equation of motion, which we did, right, from the first diagram. Any questions? OK. The last point which I would like to remind you is that, at this point, since we are talking about infinitely long systems, therefore all possible k are allowed. Right? Because, basically, you have an infinite number of coupled oscillators, and therefore you have an infinite number of normal modes. So all possible cases are allowed, and that actually because we have even an infinitely long system. After the break, which we will take a five minute break, we will discuss how to use infinitely long systems to actually understand a finite system. So you will see that, actually I can use, now, this space translation symmetry, and to solve, in general, infinitely long systems. And I can actually even go back to find to a finite system and see what we can get from there. OK? So we will be back at 12:20. If you have any questions, I will be here OK, welcome back, everybody. So we will continue the discussion. So there were a few questions asked during the break. So, the first question is related to how we actually arrive at this equation. And that is actually because-- OK, two t over ma is actually really happening in a diagonal term. Therefore, if you multiply m minus one k matrix and A matrix, which is actually shown there, then you will get this term, minus t over ma multiplied by aj minus one plus two t over ma times aj price minus t over ma times aj plus one. And that is actually why we can arrive at this expression. OK? Then what happens afterward is that we found that aj can be factorized out, and they cancel. And then now, my solution depends now upon the amplitude, and still omega is actually dependent on the k value, which we actually choose. OK. The second question is, why do I say k is the wave number? OK, where is that coming from? So that is because-- OK, so aj is proportional to exponential ijka. OK? It has a fancy name. If I take the real part, OK, as we did when we went to the description of physical systems, then you get cosine jka. OK? And j times a is actually-- j is actually a label, right? Labeling which mass I am talking about. A is actually the distance between all those masses. j times a will give you the x location of the mass. So j times a is actually the the x position of the mass. OK? Therefore, if you accept that, this becomes cosine kx, and from there you will see immediately that k has a meaning, which is actually the wave number. OK. All right, is that? OK, so that was the questions raised, which I can quickly explain. So, what I am going to do now is that-- OK, we have solved, in general, an infinitely long system. What are actually the resulting normal modes of infinitely long systems? It has an infinite number of normal modes, and we will wonder if I can actually borrow this infinitely long system and solve finite systems to see if I can arrive at the solution really quickly. OK? So the answer is actually yes. So if I consider a finite system that looks like this; so I have many, many little masses on this system and they are connected to each other by the center strings, which I prepared before, OK? And I call this the position in the y direction of this object y1, and then the next object y2, y3, etc. And I have an object in this system and both ends of the string are fixed on the wall. OK? So I can actually now argue that the infinitely long system can help us with the understanding of this finite system. Why is that? That is because, now, I can assume that, huh, this is actually just part of an infinitely long system. All right. So I construct my infinitely long system, and now I nail the yth mass, I nail the y n plus one mass, and I fix that so that it cannot move, OK? So it's still an infinitely long system, but there are two interesting boundary conditions at j equal to zero and j equal to n plus one. OK. What are the two boundary conditions? The first one is y zero equal to zero. OK? And the second condition is y n plus one equal to zero. OK? So there are two boundary conditions, so basically what I'm looking at is still an infinitely long system, but I require y zero and y n plus one to satisfy these two conditions. OK? And we will find that, huh, with this procedure, we can also solve this finite number of couple oscillators. The problem, in this case we, have coupled oscillators. OK? So the first thing which I would like to say is, based on the functional form, the functional form of omega square, now this is equal to four omega zero square sine square ka over two. OK? What we actually have is that omega k is equal to omega minus k. OK? So both of them will give you the same angular frequency. OK, therefore, what does that mean? This means that linear combination of exponential ijka and the exponential minus ijka-- OK, linear combination of these two vectors-- is also an Eigenvector of m minus one k metrics. OK, so you can do linear combination of these two vectors. OK, so if we do that, now I can guess my solution will be like yj equal to real part of exponential i omega t plus phi. I can now have a linear combination of exponential ijka and the exponential minus ijka. Basically, I have alpha exponential ijka plus beta exponential minus ijka. OK? And I would like to determine why that's actually alpha and beta which actually satisfy these boundary conditions, one and two. OK, so now I can use the first boundary condition, y zero equal to zero, right? So j equal to zero. Therefore, basically, what I get is, when j is equal to zero, then this is actually one and this is actually one, right? And this actually gives you y zero equal to zero. If y zero is equal to 0 at all times, no matter what t as you give it to this system, then basically you have alpha plus beta equal to zero, right? Because j is equal to zero. So you have alpha plus beta, and that has to be equal to zero. Therefore, you can conclude that alpha is equal to minus beta. And I've reused the second boundary condition, y n plus one equal to zero, because I nailed this mass and then fixed that so that it cannot move. Then basically, what you get is y n plus one is equal to zero, then basically you have alpha exponential i n plus one ka plus-- okay, so beta is your equal to minus alpha, right? So basically, you can get minus exponential minus i n plus one ka, right? Multiplied by alpha. And now this is actually equal to zero. Now we have the choice. We can actually set alpha to be equal to zero, but if I set alpha to be equal to zero, then beta is also zero. Then I have zero everywhere, right? Then there's no oscillation. And that's not fun, right? OK. Therefore, what I'm going to set is actually the second turn equal to zero. OK. The second turn, I can actually simplify that to be two i sine n plus one ka. And now this is actually equal to zero. OK. What is actually the condition of this thing equal to zero? Basically, n plus 1 is actually a given number, a is actually the distance between those masses, therefore, what I can actually change is the k value. Right? So I can now solve this condition, and I will conclude that k will have to be equal to n times pi divided by N plus one. I hope you can see it. Where small n is equal to one, two, three, until capital N. So what does that mean? This means that-- OK, originally, before I introduced the boundary condition, this system is infinitely long, OK, and it has an infinite number of normal modes, right? But once I introduced these boundary conditions, which I actually require y zero equal to zero, because I fixed this point on the wall. Y m plus one equal to zero because I fixed, also, that point on the wall. Something really happened. Now it actually gives us, first, the shape of the system when it is actually in the normal mode. Basically, the shape-- what I mean here is the amplitude as a function of j, OK? That's actually what I mean by shape, OK? The shape is now like a sine function. That's the first thing which we get from here. The second thing which we get here is that now, the k values are not arbitrary anymore. The k values are equal to n pi over n plus one. And the the small n is actually equal for one, two, three, until N. So now, once you actually fix this two point, you actually have only how many normal modes? N normal modes! Right? So what I want to tell you is that, in general, the sinusoidal shape is actually fixed already by this translation symmetry argument. OK. And once we nail both sides-- actually, we also restrict ourselves to the discussion of only a few k which actually satisfy the boundary conditions. And if I plot all those normal modes as a function of i, basically what you can see from here, you can see if I have n equals to one and capital N equal to four in this case. OK, so I have four-- basically, I'm going to have four normal modes. The first one will be like a really long wavelength one, when n is equal to one. And if I increase the small n value so that the k becomes bigger, then you can see that there is more distortion when this system is in one of the normal modes. And this shape is actually going to be oscillating up and down, instead of-- OK, so all those points are only moving up and down, right? Just a reminder. OK? And why do we have all those cases? Because of the boundary conditions. OK, any questions? OK, so I have several other cases, which is open end and the closed end, and also the driven and the coupled oscillator examples. Also in the lecture notes, but unfortunately, we are will not be able to go over them, but I think they are very, very detailed, the notes in the lecture notes. OK. So, let me-- before I move on to the discussion of continuous systems, OK, I would like to discuss with you what we have learned so far. So what we have learned is that, if I have a symmetry which is a translation symmetry, and plus, we only limit ourselves in the discussion of oscillation. OK, in other words, we limit the amplitude so that it doesn't explode at the edge of the universe. OK. And I will give you a beta value which is the functional form of exponential ika, and equation of motion can be derived from the first diagram. Once we entered the equation of motion, we can get m minus one k matrix, then we can derive omega square from this expression. And finally, we actually can simplify everything and then get the dispersion relation omega equal to omega k, which is a function of k, the wave number. Before we actually introduce boundary conditions to go from an infinitely long system to a finite system, all the k values are allowed. Once you introduce boundary conditions, you find that you only have a limited number of normal modes. Second, the k value not continuous at any value any more, it becomes discrete. And only n values allowed from this exercise. And finally, what is actually the most general solution is actually the linear combination of all those normal modes, which we show here. And what is actually the ratio between all those normal modes? All those free coefficients are determined by initial conditions if you are given. OK? So that's actually what we have learned so far. And now I would like to make a leap of faith to see what happens. OK, what we are going to do is to introduce you to a continuous infinite number of coupled oscillators. OK? So what does that mean? What I am going to do is to go from this-- so I have t and then a t, a lot of string and mass system, et cetera, et cetera, but I would like to go from there to just an infinitely long string with string tension t and some kind of density or mass. OK? We like to make it continuous to see what will happen. OK? So, just a reminder of the jth term of the m minus one k matrix operation. Basically, we have m minus one k times a, the j's term of m minus one k a. That is actually given by omega square aj. This is equal to t over ma minus aj minus one plus two aj minus aj plus one? OK. So this is actually just a copy of that formula here. OK, so if I make it continuous-- OK, so that means what I'm going to get is omega square a but evaluated at position x, where x is actually equal to j times a. OK? And this will be equal to t over ma minus a, evaluated at x minus a plus two a x minus a x plus a. Now I am going to make this a very, very small, right? So that, when I make a very, very small, then it becomes a very, very continuous system. OK? So what I'm going to do is-- I can now make a go to zero. I can now use Taylor's series fx plus delta x-- and just a reminder, if you do a Taylor expansion of this, you are going to get f of x plus delta x f prime x plus one over two factorial delta x square f double prime x. OK, so that means now, I can actually do a Taylor expansion of a x minus a and then a x plus a. So what I'm going to get is like this. So a x minus a will become a of x minus a a prime x plus one over two a square a double prime x. I can also do the same thing to do a Taylor expansion for a x plus a. a x plus a will be equal to a of x plus a prime x plus one over two a square a double prime x. OK. Once I have done this, basically, then, I can calculate minus a x minus a plus two a of x minus a x plus a. OK, I'm just taking the middle term and copying it there. OK? If I use, now, this expression, OK, then basically I will see that, OK, a of x terms actually cancel, right? Because I have two a of x from these two terms, and they cancel with this two a x. OK? And also, a prime terms, also cancel, right? Because you have a x minus and a x plus a, therefore, the x prime turns cancel here. This is a minus sign, this is a plus sign. You see? So therefore, what is actually left over is all those terms. This is going to give you a double prime x a squared, plus many other higher order terms, right? Because those are actually not completed, we have many, many higher order terms. OK? In the limit of x go to zero-- Yes. STUDENT: Isn't the xa prime [INAUDIBLE]?? PROFESSOR YEN-JIE LEE: Yeah. Oh yeah, you are right. Thank you very much. OK, thank you for that. So there should be a minus sign in front of it, OK. So basically what we have is a double prime x times a square plus some higher order turn of a cubed, et cetera, et cetera. OK, since we are talking about the limit of a goes to zero, we can safely ignore all the higher order terms. OK? So now, if we go back to this equation, omega square a will become, basically, t over m minus t over ma a double prime x times a squared. OK, and then plus some higher order terms. OK, now I can define rho l to be equal to m divided by a. OK. And I will I will have to be very careful when I go to the continuous limit, OK, I also do not want to make this system infinitely massive, right? Therefore, I would like to fix the rho l when I go to the continuous limit. So basically what I am doing is that I cut this system in half so that a becomes smaller and the mass also because smaller, so that rho l stays as a constant, OK, when I go to a continuous limit. OK, so what I'm going to get is omega square a will be equal to minus t over rho l a double prime x. And to write it explicitly, this is actually equal to minus t over rho l. I'll just square a partial x squared. OK? Because each prime is actually the differentiation which is spread to x, right? OK. Don't forget-- what is actually this? This is actually m minus one ka, right? Equal to omega square a. And that this is actually just partial square a partial t square. Right? Because this is actually m minus one k matrix. It's actually originally-- going back to the original equation, we are actually solving m x double dot equal to minus kx problem, right? So there should be a minus sign there as well. Right? So mx double dot equal to minus kx, therefore x double dot will be equal to minus m minus one kx. Right? So minus m minus one k matrix will be equal to x double dot, right? Therefore, what this is actually x double dot? It's basically-- in the current presentation, it's actually just partial square a, partial t square. OK? Can everybody accept this? OK, so now we have some sensibility going from a discrete system, which you have a length scale of a, to a continuous system, because a goes to zero. By a certain time, I fix the ratio of m and a so that the system doesn't grow too infinitely massive. OK, so if I do this, then in short, you get this equation. Partial square a partial t square, and that is equal to t over rho l partial square a partial x square. OK? I can now define vp as equal to square root of t over rho l. OK? And this will become the p square partial square a partial x square. What is this? This is what equation? Wave equation! OK, you see that now? After all the hard work, OK, going from infinity long systems, discrete systems, then go to a continuous limit, we discovered the wave equation. This is probably the most important equation you actually learn, until now. More important than f equal to ma, right? Because you can listen to my lecture, even, if this equation didn't exist, right? Then I can not propagate a sound wave to your ear. Right? And you cannot even see the black board, because the electromagnetic wave, which I will show in a later lecture, also kind of satisfies the same function or form. So I think this is an achievement and a highlight of today's class. We actually realize now, what we have been doing is really solving something related to the wave equation. And next time, what I would like to actually discuss with you is the solution of this wave equation. So here, I have-- again, last time you have seen this. This is a coupled oscillator system. It has 72 components. As a physicist, that's actually equal to an infinite number of coupled oscillators, OK. That's good enough. And you can see that, if I do this, it does something really strange, right? You see a progressing wave going back and forth, and it disappears because of friction. OK? If I can construct something closer to a perfect coupled system without friction, what is going to happen is that this wave is going to be there bouncing back and forth forever. And that actually can be understood by the wave equation. And also, if I oscillate this system at a fixed frequency, you will see that these become standing waves. And of course I can I do crazy things, I can oscillate and stop it and it becomes really, really complicated motion. And of course you are welcome to come here and play after the class. And next time, on Thursday, we are going to talk about the solution to this equation and how to understand all kinds of fancy motion this system can do, given by the nature. Thank you very much. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 1_Periodic_Oscillations_Harmonic_Oscillators.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu, YEN-JIE LEE: So welcome, everybody. My name is Yen-Jie Lee. I am a assistant professor of physics in the physics department, and I will be your instructor of this semester on 8.03. So of course, one first question you have is, why do we want to learn about vibrations and waves? Why do we learn about this? Why do we even care? The answer is really, simple. If you look at this slide, you can see that the reason you can follow this class is because I'm producing sound wave by oscillating the air, and you can receive those sound waves. And you can see me-- that's really pretty amazing by itself-- because there are a lot of photons or electromagnetic waves. They are bouncing around in this room, and your eye actually receive those electromagnetic waves. And that translates into your brain waves. You obviously, start to think about what this instructor is trying to tell you. And of course, all those things we learned from 8.03 is closely connected to probability density waves, which you will learn from 8.04, quantum physics. And finally, it's also, of course, related to a recent discovery of the gravitational waves. When we are sitting here, maybe there are already some space-time distortion already passing through our body and you don't feel it. When I'm moving around like this, I am creating also the gravitational waves, but it's so small to be detected. So that's actually really cool. So the take-home message is that we cannot even recognize the universe without using waves and the vibrations. So that's actually why we care about this subject. And the last is actually why this subject is so cool even without quantum, without any fancy names. So what is actually the relation of 8.03 to other class or other field of studies? It's closely related to classical mechanics, which I will use it immediately, and I hope you will still remember what you have learned from 8.01 and 8.02. Electromagnetic force is actually closely related also, and we are going to use a technique we learned from this class to understand optics, quantum mechanics, and also there are many practical applications, which you will learn from this class. This is the concrete goal. We care about the future of our space time. We would like to predict what is going to happen when we set up an experiment. We would like to design experiments which can improve our understanding of nature. But without using the most powerful tool is very, very difficult to make progress. So the most powerful tool we have is mathematics. You will see that it really works in this class. But the first thing we have to learn is how to translate physical situations into mathematics so that we can actually include this really wonderful tool to help us to solve problems. Once we have done that, we will start to look at single harmonic oscillator, then we try to couple all those oscillators together to see how they interact with each other. Finally, we go to an infinite number of oscillators. Sounds scary, but it's actually not scary after all. And we will see waves because waves are actually coming from an infinite number of oscillating particles, if you think about it. Then we would do Fourier decomposition of waves to see what we can learn about it. We learn how to put together physical systems. That brings us to the issue of boundary conditions, and we will also enjoy what we have learned by looking at the phenomenon related to electromagnetic waves and practical application and optics. Any questions? If you have any questions, please stop me any time. So if you don't stop me, I'm going to continue talking. So that gets started. So the first example, the concrete example I'm going to talk about is a spring block, a massive block system. So this is actually what I have on that table. So basically, I have a highly-idealized spring. This is ideal spring with spring constant, k, and the natural length L0. So that is actually what I have. And at t equal to 0, what I am going to do is I am going to-- I should remove this mass a little bit, and I hold this mass still and release that really carefully. So that is actually the experiment, which I am going to do. And we were wondering what is going to happen afterward. Well, the mass as you move, will it stay there or it just disappear, I don't know before I solved this question. Now I have put together a concrete question to you, but I don't know how to proceed because you say everything works. What I am going to do? I mean, I don't know. So as I mentioned before, there is a pretty powerful tool, mathematics. So I'm going to use that, even though I don't know why mathematics can work. Have you thought about it? So let's try it and see how we can make progress. So the first thing which you can do in order to make progress is to define a coordinate system. So here I define a coordinate system, which is in the horizontal direction. It's the x direction. And the x equal to 0, the origin, is the place which the spring is not stressed, is at its natural length. That is actually what I define as x equal to 0. And once I define this, I can now express what is actually the initial position of the mass by these coordinates is x0. It can be expressed as x initial. And also, initially, I said that this mass is not moving. Therefore, the velocity at 0 is 0. So now I can also formulate my question really concretely with some mathematics. Basically, you can see that at time equal to t, I was wondering where is this mass. So actually, the question is, what is actually x as a function of t? So you can see that once I have the mathematics to help me, everything becomes pretty simple. So once I have those defined, I would like to predict what is going to happen at time equal to t. Therefore, I would like to make use physical laws to actually help me to solve this problem. So apparently what we are going to use is Newton's law. And I am going to go through this example really slowly so that everybody is on the same page. So the first thing which I usually do is now I would like to do a force diagram analysis. So I have this mass. This setup is on Earth, and the question is, how many forces are acting on this mass? Can anybody answer my question. AUDIENCE: Two. We got the-- So acceleration and the spring force. YEN-JIE LEE: OK, so your answer is two. Any different? Three. Very good. So we have two and three. And the answer actually is three. So look at this scene. I am drawing in and I have product here. So this is actually the most difficult part of the question, actually. So once you pass this step, everything is straightforward. It's just mathematics. It's not my problem any more, but the math department, they have problem, OK? All right. So now let's look at this mass. There are three forces. The first one as you mentioned correctly is F spring. It's pulling the mass. And since we are working on Earth, we have not yet moved the whole class to the moon or somewhere else, but there would be gravitational force pointing downward. But this whole setup is on a table of friction, this table. Therefore, there will be no more force. So don't forget this one. There will be no more force. So the answer is that we have three forces. The normal force is, actually, a complicated subject, which you will need to understand that will quantum physics. So now I have three force, and now I can actually calculate the total force, the total force, F. F is equal to Fs plus Fn plus Fg. So since we know that the mass is moving in the horizontal direction, the mass didn't suddenly jump and disappear. So it is there. Therefore, we know that the normal force is actually equal to minus Fg, which is actually Ng in the y direction. And here I define y is actually pointing up, and the x is pointing to the right-hand side. Therefore, what is going to happen is that the total force is actually just Fs. And this is equal to minus k, which is the spring constant and x, which is the position of the little mass at time equal to t. So once we have those forces and the total force, actually, we can use Newton's law. So F is equal to m times a. And this is actually equal to m d squared xt dt squared in the x direction, and that is actually equal to mx double dot t x. So here is my notation. I'm going to use each of the dot is actually the differentiation with respect to t. So this is actually equal to minus kxt in the x direction. So you can see that here is actually what you already know about Newton's law. And that is actually coming from the force analysis. So in this example, it's simple enough such that you can write it down immediately, but in the later examples, things will become very complicated and things will be slightly more difficult. Therefore, you will really need help from the force diagram. So now we have everything in the x direction, therefore, I can drop the x hat. Therefore, finally, my equation of motion is x double dot t. And this is equal to minus k over n x of t. To make my life easier, I am going to define omega equal to square root of k over n. You will see why afterward. It looks really weird why professor Lee wants to do this, but afterward, you will see that omega really have a meaning, and that is equal to minus omega squared x. So we have solved this problem, actually, as a physicist. Now the problem is what is actually the solution to this differential second-order differential equation. And as I mentioned, this is actually not the content of 8.03, actually, it's a content of 18.03, maybe. How many of you actually have taken 18.03? Everybody knows the solution, so very good. I am safe. So what is the solution? The solution is x of t equal to a cosine of omega t plus b sine omega t. So my friends from the math department tell me secretly that this is actually the solution. And I trust him or her. So that's very nice. Now I have the solution, and how do I know this is the only solution? How do I know? Actually, there are two unknowns, just to remind you what you have learned. There are two unknowns. And if you plug this thing into this equation, you satisfy that equation. If you don't trust me, you can do it offline. It's always good to check to make sure I didn't make a mistake. But that's very good news. So that means we will have two unknowns, and those will satisfy the equation. So by uniqueness theorem, this is actually the one and the only one solution in my universe, also yours, which satisfy the equation because of the uniqueness theorem. So I hope I have convinced you that we have solved this equation. So now I take my physicist hat back and now it is actually my job again. So now we have the solution, and we need to determine what is actually these two unknown coefficients. So what I'm going to use is to use the two initial conditions. The first initial condition is x of 0 equal to x initial. The second one is that since I released this mass really carefully and the initial velocity is 0, therefore, I have x dot 0 equal to 0. From this, you can solve. Plug these two conditions into this equation. You can actually figure out that a is equal to x initial. And b is equal to 0. Any questions so far? Very good. So now we have the solution. So finally, what is actually the solution? The solution we get is x of t equal to x initial cosine omega t. So this is actually the amplitude of the oscillation, and this is actually the angular velocity. So you may be asking why angular? Where is the angular coming from? Because this is actually a one-dimensional motion. Where is the angular velocity coming from? And I will explain that in the later lecture. And also this is actually a harmonic oscillation. So what we are actually predicting is that this mass is going to do this, have a fixed amplitude and it's actually going to go back and forth with the angular frequency of omega. So we can now do an experiment to verify if this is actually really the case. So there's a small difference. There's another spring here, but essentially, the solution will be very similar. You may get this in a p-set or exam. So now I can turn on the air so that I make this surface frictionless. And you can see that now I actually move this thing slightly away from the equilibrium position, and I release that carefully. So you can see that really it's actually going back and forth harmonically. I can change the amplitude and see what will happen. The amplitude is becoming bigger, and you can see that the oscillation amplitude really depends on where you put that initially with respect to the equilibrium position. I can actually make a small amplitude oscillation also. Now you can see that now the amplitude is small but still oscillating back and forth. So that's very encouraging. Let's take another example, which I actually rotate the whole thing by 90 degrees. You are going to get a question about this system in your p-set. The amazing thing is that the solution is the same. What is that? And you don't believe me, let me do the experiment. I actually shifted the position. I changed the position, and I release that really carefully. You see that this mass is oscillating up and down. The amplitude did not change. The frequency did not change as a function of time. It really matched with the solution we found here. It's truly amazing. No? The problem is that we are so used to this already. You have seen this maybe 100 times before my lecture, so therefore, you got so used to this. Therefore, when I say, OK, I make a prediction. This is what happened, you are just so used to this or you don't feel the excitement. But for me, after I teach this class so many times, I still find this thing really amazing. Why is that? This means that actually, mathematics really works, first of all. That means we can use the same tool for the understanding of gravitational waves, for the prediction of the Higgs boson, for the calculation of the property of the quark-gluon plasma in the early universe, and also at the same time the motion of this spring-mass system. We actually use always the same tool, the mathematics, to understand this system. And nobody will understands why. If you understand why, please tell me. I would like to know. I will be very proud of you. Rene Descartes said once, "But in my opinion, all things in nature occur mathematically." Apparently, he's right. Albert Einstein also once said, "The most incomprehensible thing about the universe is that it is comprehensible." So I would say this is really something we need to appreciate the need to think about why this is the case. Any questions? So you may say, oh, come on. We just solved the problem of an ideal spring. Who cares? It's so simple, so easy, and you are making really a big thing out of this. But actually, what we have been solving is really much more than that. This equation is much more than just a spring-mass system. Actually, if you think about this question carefully, there's really no Hooke's law forever. Hooke's law will give you a potential proportional to x squared. And if you are so far away, you pull the spring so really hard, you can store the energy of the whole universe. Does that make sense? No. At some point, it should break down. So there's really no Hook's law. But there's also Hook's law everywhere. If you look at this system, it follows the harmonic oscillation. If you look at this system I perturb this, it goes back and forth. It's almost like everywhere. Why is this the case? I'm going to answer this question immediately. So let's take a look at an example. So if I consider a potential, this is an artificial potential, which you can find in Georgi's book, so v is equal to E times L over x plus x over L. And if you practice as a function of x, then basically you get this funny shape. It's not proportional to x squared. Therefore, you will see that, OK, the resulting motion for the particle in this potential, it's not going to be harmonic motion. But if I zoom in, zoom in, and zoom in and basically, you will see that if I am patient enough, I zoom in enough, you'll see that this is a parabola. Again, you follow Hooke's law. So that is actually really cool. So if I consider an arbitrary v of x, we can do a Taylor expansion to this potential. So basically v of x will be equal to v of 0 plus v prime 0 divided by 1 factorial times x plus v double prime 0 over 2 factorial x squared plus v triple prime 0 divided by 3 factorial x to the third plus infinite number of terms. v 0 is the position of where you have minimum potential. So that's actually where the equilibrium position is in my coordinate system. It's the standard, the coordinate system I used for the solving the spring-mass question. So if I calculate the force, the force, f of x, will be equal to minus d dx v of x. And that will be equal to minus v prime 0 minus v double prime 0 x minus 1 over 2 v triple prime 0 x squared plus many other terms. Since I have mentioned that v of 0-- this will be x. v of 0 is actually the position of the minima. Therefore, v prime of 0 will be equal to 0. Therefore. This term is gone. So what essentially is left over is the remaining terms here. Now, if I assume that x is very small, what is going to happen? Anybody know when x is very small, what is going to happen? Anybody have the answer? AUDIENCE: [INAUDIBLE]. YEN-JIE LEE: Exactly. So when x is very small, he said that the higher order terms all become negligible. OK? So that is essentially correct. So when x is very small, then I only need to consider the leading order term. But how small is the question. How small is small? Actually, what you can do is to take the ratio between these two terms. So if you take the ratio, then basically you would get a condition xv triple dot 0, which will be much smaller than v double prime 0. So that is essentially the condition which is required to satisfy it so that we actually can ignore all the higher-order terms. Then the whole question becomes f of x equal to minus v double prime 0 x. And that essentially, Hooke's law. So you can see that first of all, there's no Hooke's law in general. Secondly, Hook's law essentially applicable almost everywhere when you have a well-behaved potential and if you only perturb the system really slightly with very small amplitude, then it always works. So what I would like to say is that after we have done this exercise, you will see that, actually, we have solved all the possible systems, which have a well-behaved potential. It has a minima, and if I have the amplitude small enough, then the system is going to do simple harmonic oscillation. Any questions? No question, then we'll continue. So let's come back to this equation of motion. x double dot plus omega squared x, this is equal to 0. There are two important properties of this linear equation of motion. The first one is that if x1 of t and x2 of t are both solutions, then x12, which is the superposition of the first and second solution, is also a solution. The second thing, which is very interesting about this equation of motion, is that there's a time translation invariance. So this means that if x of t is a solution, then xt prime equal to xt plus a is also a solution. So that is really cool, because that means if I change t equal to 0, so I shift the 0-th time, the whole physics did not change. So this is actually because of the chain law. So if you have chain law dx t plus a dt, that is equal to d t plus a dt, dx t prime dt prime evaluated at t prime equal to t plus a. And that is equal to dx t prime dt, t prime equal to t plus a. So that means if I have changed the t equal to 0 to other place, the whole equation of motion is still the same. On the other hand, if the k, or say the potential, is time dependent, then that may break this symmetry. Any questions? So before we take a five minute break, I would like to discuss further about this point, this linear and nonlinear event. So you can see that the force is actually linearly dependent on x. But what will happen if I increase x more? Something will happen. That means the higher-ordered term should also be taken into account carefully. So that means the solution of this kind, x initial cosine omega t, will not work perfectly. In 8.03, we only consider the linear term most of the time. But actually, I would like to make sure that everybody can at this point, the higher-order contribution is actually visible in our daily life. So let me actually give you a concrete example. So here I have two pendulums. So I can now perturb this pendulum slightly. And you you'll see that it goes back and forth and following simple harmonic emotion. So if I have both things slightly oscillating with small amplitude, what is going to happen is that both pendulums reach maxima amplitude at the same time. You can see that very clearly. I don't need to do this carefully. You see that they always reach maxima at the same time when the amplitude is small. Why? That is because the higher-order terms are not important. So now let's do a experiment. And now I go crazy. I make the amplitude very large so that I break that approximation. So let's see what will happen. So now I do this then. I release at the same time and see what will happen. You see that originally they are in phase. They are reaching maxima at the same time. But if we are patient enough, you see that now? They are is oscillating, actually, at different frequencies. Originally, the solution, the omega, is really independent of the amplitude. So they should, actually, be isolating at the same frequency. But clearly you can see here, when you increase the amplitude, then you need to consider also the nonlinear effects. So any questions before we take a five-minute break. So if not, then we would take a five-minute break, and we come back at 25. So welcome back, everybody. So we will continue the discussion of this equation of motion, x double dot plus omega square x equal to 0. So there are three possible way to like the solution to this equation. So the first one as I mentioned before, x of t equal to a cosine omega t plus b sine omega t. So this is actually the functional form we have been using before. And we can actually also rewrite it in a different way. So x or t equal to capital A cosine omega t plus phi. You may say, wait a second. You just promised me that this is the first one, the one is the one and only one solution in the universe, which actually satisfy the equation of motion. Now you write another one. What is going on? Why? But actually, they are the same. This is actually A cosine phi cosine omega t minus A sine phi sine omega t. So the good thing is that A and phi are arbitrary constant so that it should be you can use two initial conditions to determine the arbitrary constant. So you can see that one and two are completely equivalent. So I hope that solves some of the questions because you really find it confusing why we have different presentations of the solution. So there's a third one, which is actually much more fancier. The third one is that I have x of t. This is actually a real part of A-- again, the amplitude-- exponential i omega t plus phi, where i is equal to the square root of minus 1. Wait a second. We will say, well, professor, why are you writing such a horrible solution? Right? Really strange. But that will explain you why. So three is actually a mathematical trick. I'm not going to prove anything here because I'm a physicist, but I would like to share with you what I think is going on. I think three is really just a mathematical trick from the math department. In principle, I can drive it an even more horrible way. x of t equal to a real part of A cosine omega t plus phi plus i f of t. And f of t is a real function. In principle, I can do that. It's even more horrible. Why is that? Because I now have this function. I take the real part, and I actually take the two out of this operation. So f of t is actually the real function. It can be something arbitrary. And i can now plot the locus of this function, the solution on the complex print. Now I'm plotting this solution on this complex print. What is going to happen is that you're going to have-- That is what you are going to get. If I am lucky, if this f of t is confined in some specific region, if I not lucky, then it goes out of the print there. I couldn't see it. Maybe it go to the moon or something. But if you are smart enough, and I'm sure you are, if I choose f of t equal to A sine omega t plus phi, can anybody tell me what is going to happen? AUDIENCE: [INAUDIBLE]. YEN-JIE LEE: Would you count a circle? Very good. If I plot the locus again of this function, the real axis, imaginary axis, then you should get a circle. Some miracle happened. If you choose the f of t correctly, wisely, then you can actually turn all this mess into order. Any questions? So I can now follow up about this. So now I have x of t is equal to the real part of A cosine omega t plus phi plus iA sine omega t plus phi. And just a reminder, exponential i theta is equal to cosine theta plus i sine theta. Therefore, I arrive this. This is a real part of A exponential i omega t plus phi. So if I do this really carefully, I look at this the position of the point at a specific time. So now time is equal to t. And this is the real axis, and this is the imaginary axis. So I have this circle here. So at time equal to t, what you are getting is that x is actually-- before taking the real part, A, exponential i omega t plus phi, it's actually here. And this vector actually shows the amplitude. Amplitude is A. And the angle between this vector pointing to the position of this function is omega t plus phi. So this is actually the angle between this vector and the real axis. So that's pretty cool. Why? Because now I understand why I call this omega angular velocity or angular frequency. Because the solution to the equation of motion, which we have actually derived before, is actually the real part of rotation in a complex print. If you think about it, that means now I see this particle going up and down. I see this particle going up and down. You can think about that, this is Earth. If there is an extra dimension which you couldn't see. Actually, this particle in the dimension where we can see into the extra dimension, which is hidden is actually rotating. And while we see that reality, it's a projection to the real axis. You see? So in reality, this particle is actually rotating, if you add the image and the extra dimension. So that is actually pretty cool, but the purity artificial. So you can see that I can choose f of t to be a different function, and then this whole picture is different. But I also would create a lot of trouble because then the mathematics become complicated. I didn't gain anything. But by choosing this functional form, you actually write a very beautiful picture. Another thing, which is very cool about this is that if I write this thing in the exponential functional form, since we are dealing with differential equations, there is a very good property about exponential function. That is it is essentially a phoenix function. Do you know what is a phoenix? Phoenix is actually some kind of animal, a long-beaked bird, which is cyclically called the regenerated or reborn. So basically, when this phoenix die, you will lay the eggs in the fire and you were reborn. This is actually the same as this function. I can do differentiation, still an exponential function, and differentiate, differentiate, differentiate. Still exponential function. So that is very nice because when we deal with differential equation, then you can actually remove all those dots and make them become just exponential function. So essentially, a very nice property. So the first property, which is very nice is that it cannot be killed by differentiation. You will see how useful this is in the following lectures. The second thing, which is really nice is that it has a very nice property. So basically the exponential i theta 1 times exponential i theta 2, and that will give you exponential i theta 1 plus theta 2. So what does that mean? That means if I have a solution in this form, A exponential i omega t plus phi. And I do a times translation, t become t plus A. Then this become A exponential i omega t plus A plus phi. So this means that times translation in this rotation is just a rotation in complex print. You see? So now t becomes t plus A. Then you are actually just changing the angle between this vector and the x-axis. So as time goes on, what is going to happen is that this thing will go around and around and around and the physics is always the set, no matter when you start counting, and the translation is just the rotation in this print. Any questions? So I think this is actually a basic slide just to remind you about Euler's formula. So basically, the explanation i phi is equal to cosine phi plus i sine phi. And I think it will be useful if you are not familiar with this. It is useful to actually review a little bit about exponential function, which will be very useful for this class. So I'm running a bit faster today. So let's take a look at what we have learned today. We have analyzed the physics of a harmonic oscillator. So basically, we start by asking really just a verbal question, what is going to happen to this mass on the table attached to a spring. And what we have learned is that we actually use mathematics. Basically, we translate all what we have learned about this mass into mathematics by first define a coordinate system. Then I'd write everything using that coordinate system. Then I use Newton's law to help us to solve this question. And we have analyzed the physics of this harmonic oscillator. And Hooke's law, we found that he actually, not only works for this spring-mass system, it also works for all kinds of different small oscillations about a point of equilibrium. So basically, it's actually a universal solution what we have been doing. And we have found out a complex exponential function is actually a beautiful way to present the solution to the equation of motion we have been studying. So everything is nice and good. However, life is hard because there are many things which actually, we ignored in this example. One apparent thing, which we actually ignore, is the direct force. So you can see that before I was actually making this pendulum oscillate back and forth. What is happening now? There are not oscillating anymore. Why? Well, they stopped being. Apparently, something is missing. When I actually moved this system, if I turn off the air so that there's friction, then it doesn't really move. If I increase a bit, the air so that the slide have some slight freedom, then actually, you can see that you move a bit then you stop. If I increase this some more, you can see that the amplitude becomes smaller and smaller. So in the following lecture, what we are going to do is to study how to actually include a direct force into it again and of course, using the same machinery which we have learned from here and see if we can actually solve this problem. Thank you very much. We actually end up earlier today. Sorry for that. And maybe I will make the lecture longer next time. And if you have any questions about what we have covered today, I'm here available to help you. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 803SC_Physics_III_Vibrations_and_Waves_Introduction.txt | [MUSIC PLAYING] YEN-JIE LEE: 8.03 is a very, very interesting course, because without waves and vibrations we will not be able to even recognize this universe. Doing this class, I decided to include a lot of demos during my lectures. Demonstrations are particularly useful, because we first introduce the physical situation we are interested. Then we compare our mathematical solution to reality, which is actually the demo. I hope you will be able to enjoy this free content provided by OCW, including the lecture videos, the lecture notes, and the problem solving video from Professor Wit Busza. Yeah, it's really cool. You'll take the course, right? |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 13_Dispersive_Medium_Phase_Velocity_Group_Velocity.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: Hello, everybody. Welcome back to 8.03. Today we are going to continue the discussion of waves. We will discuss a very interesting phenomenon today, which is dispersion. And before that, we will discuss a bit, just to give you some reminder, about what we have learned so far. So we discovered this wave equation, which is showing here, in the class, and then we also show you that it described three different kinds of systems, which we included in the lecture-- the massive strings, which are the strings can actually oscillate up and down in a wide direction. And also we discussed about sound waves. This is also discussed in a previous lecture. And sound waves can be described by wave equation. And finally, the last time we discussed electromagnetic waves. It's a special kind of wave involving two oscillating fields. One is actually the electric field, the other one is magnetic field. So that's kind of interesting, because this is actually slightly different from what we've discussed before in the previous two cases. This is actually a three dimensional wave, and also involving two different components. And we also discussed the solution, the traveling wave solution of the electromagnetic waves. As you can see from here, the electric field is showing us the red, and the magnetic field is showing us the blue. And you can see that in case of traveling wave, they are in phase. And the magnitude reach maxima simultaneously for electric field and the magnetic field. And while in the case of standing wave, there's a phase difference. so they don't reach maxima simultaneously in the standing electromagnetic field case. OK, so what are we going to discuss today? We would like to discuss the strategy to send information using waves. How do we actually send information using waves? So you can say, OK, maybe I can just send a harmonic oscillation. So If I do this harmonic oscillation, I can basically produce harmonic waves. They are moving up and down, and is actually always constant angular momentum and angular frequency. And maybe that's a way to send the information. But this kind of wave is, in reality, not super helpful, because if you fill the whole space with harmonic waves, then you don't know when did you actually send the signal. Because it's always oscillating up and down, so you don't know the starting time of the signal. So in reality, these kind of simple harmonic oscillating traveling wave is not super helpful. So what is actually helpful? That's the question. So what is actually helpful is to produce square pulse, for example. We can create square pulse, for example, in this case, I can create a square pulse here. And in the next time interval, I don't create a square pulse. In the next time interval, I don't do anything. And I create another square pulse here, et cetera, et cetera, OK. If you use this kind of strategy what we can do is to have some kind of receiver here to actually measure the magnitude of the pulse. And then we can actually interpret this data. So this wave is going to where the positive x direction or going to the right-hand side of the board. And the receiver will be able to interpret this data by appraising this ratio on the energy or on the measure of the amplitude. Then I can say, oh, now I'd receive a 0, and then the next signal I'm receiving is 1, and this one is 0, and 0, and 1, and 0. In this way, I can actually send information and that this information can be verified as a function of time. So in short, what would be useful is probably to use a narrow square pulse, and that would be very helpful in transmitting information. So if we consider an ideal string case-- if I have an ideal string, as we learned before, the behavior of the string is described by the wave equation. Partial squared psi partial t squared, and this is equal to v squared partial squared psi partial t squared. And this v is actually related to the speed of the progressing wave, as we discussed before-- the progressing wave solution. And if I have this idealized string, and it obey the wave equation, the simple version of wave equation, then I would be able to divide the dispersion relation. So I can now write down my harmonic progressing wave in the form of sine kx minus omega t. If I have a harmonic oscillating wave propagating toward the positive x direction at the speed of v. I can write it down in this functional form, where k, as a reminder, is the wavenumber, and the omega is actually the angular frequency. And therefore, if I plug in this solution, and of course, it can have arbitrary amplitude. If I plug in this solution to this equation, then what I'm going to get is, as we did in the last few lectures, there would be a fixed relation between k, which is the wavenumber, and the omega, the angular frequency. So the fixed relation is actually omega over k would be equal to v, which is actually the velocity in this wave equation. And from the previous discussion, we know this is actually equal to a squared root of T over rho L, where T is actually the tension, the constant tension, which we apply on this string, and the rho L is actually the mass per unit as a reminder. So what does this mean? What does this equation mean? We call it dispersion relation a lot of time, right? But we actually didn't explain why do I do that. So we are going to learn why this is actually called this dispersion relation. Omega is a function of k. And in this case, in this very simplified idealized case, omega over k is ratio. we know this is related to the speed of propagation of the harmonic wave is equal to v. v is a constant that is independent of k. This ratio is independent of k. What does that mean? That means if I prepare waves with different wavenumber, or in other words, waves with different wavelengths, they are going to propagate at the same speed. So the speed of the harmonic progressing wave is independent of the wavelength. That's actually very good, because in this case, if I prepared the square pulse, as we learned before, this square pulse is actually a very complicated object. Square pulse is really very complicated. You can do a Fourier decomposition as we did before. And we need infinite number of turns of harmonic oscillating waves. We actually add them together so that I can produce a square pulse. And as I mentioned here, if the dispersion relation, omega over k, is is our constant, v. That means all the whatever wavelengths pulse, which should be added together and produce the square pulse, are going to be traveling at the that speed. Therefore, if I have this square pulse in the beginning, after some time, t, what I'm going to get is that this is the original position of the square pulse, and after some time, t, this square pulse will move by v times t in the horizontal direction. And the shape of the pulse is not going to be changed, because no matter what kind of wavelengths which produce the square pulse, all the components in the square pulse are propagating at the same speed. So this kind of system, which has satisfied this kind of dispersion relation is called nondispersive media. no dispersion was happening in this case, in this highly idealized case. We also know that in case of the string, we are actually making it too idealized. So if we consider a more realistic string, then I have to consider an important phenomenon, which is-- or is a important property of the string, for example-- stiffness What do I mean by stiffness? So for example, if I take a string from a piano, a piano string, even if I don't apply any tension to the string, if I bend the string, it don't like it, all right? It's going to bounce back and restore to its original shape. So that's what I call stiffness. It's a different contribution compared to the string tension. So what we have been discussing so far that this distorting force is actually coming from the string tension, t. OK? What will happen if I introduce additional contribution from the stiffness? The stiffness is actually not completely related to the string tension, and that also wants to restore the shape of the string. OK? Before we go to the modeling, I would like to take some votes to predict what is going to happen. How many of you were predict that if I introduce and include the stiffness of the string into my equation, will the speed of propagation increase? How many of you think it's going to happen? 1, 2, 3, 4, 5. OK. So some of you predict the speed of propagation will increase. How many of you predict that the speed of propagation of the harmonic wave will stay the same? How many of you? One? OK, only one. OK, how many of you actually predict that the speed of propagation would decrease OK so all the other students don't have opinion. OK, want to wait for the answer. All right. So you can see that it is actually not completely obvious before we solve this question. And we are going to solve it with a simple model, which actually slightly modifies the idealized wave equation. So now, one semi-realistic model which I can introduce is to add a term additional term to the wave equation. So I can now rewrite my wave equation to include the effect that to describe a realistic string, and now this is your partial squared psi partial t squared. This will be equal to v squared partial squared psi partial t squared. And the additional term, which I put into this, again, is minus alpha partial to the 4 psi partial x to the 4. And this is actually the contribution from the stiffness. This is stiffness. OK, so you can see that the wave equation is now modified. And what I could do in order to get the relation between omega and the k-- what I could do is that I can now start with this harmonic wave solution progressing wave solution, plug that in to this equation, this modified equation, and see what will happen. If I plug this equation into it that modified wave equation, what I am going to get is the following. So basically the left-hand, side you're going to get minus omega squared. And then the right-hand side, you get v squared minus k squared and plus alpha k to the 4 in the right-hand side. OK, so of course, I can now cancel this minus sign. This will become plus and this will become minus. And then you can see that the relation between omega and the k is now different after I introduce this term, which is proportional to alpha. Alpha is actually describing how stiff this string is. Of course, now I can calculate omega over k, which is actually, as we learned before, right is the speed of the propagation of a harmonic wave. So basically, if I calculate omega over k from this equation, then basically what you get is v square root of 1 plus alpha k squared. So if you look at this equation, the first reaction is, oh, now this omega and the k ratio is not a constant anymore as a function of k. What does that mean? That means if I prepare progressing waves with different wavelengths for wavenumber k, it's going to be propagating at different speed, OK? Before we introduce this into the model, the ratio omega and k is a constant v, independent of k. Now, once you introduce this model into the equation, and you plug in the progressing wave solution to actually check the dispersion relation obtained from this equation, you'll find that the speed of progressing wave depends on how distorted this progressing wave is, OK? So let me compare this to situation in this graph, omega versus k. So we will see this dispersion relation graph pretty often in the class today. The y-axis is actually the omega, angular frequency, and the k is the wavenumber, two pi over lambda. OK. In the original case, in the case I have this idealized string, obey the wave equation which we introduced in the previous lectures. If I plug omega as a function of k, what I'm getting is a straight line. question. AUDIENCE: Why are you [INAUDIBLE] minus alpha [INAUDIBLE]. YEN-JIE LEE: This one, right? AUDIENCE: [INAUDIBLE] YEN-JIE LEE: Oh, maybe I made some mistake here. So this should be also plus here, right. So you have this-- OK, so this is omega squared, and I shouldn't have this minus sign here, right? So this should be minus, and this should be-- OK, let's go back to the original equation, OK. So basically, you get-- so if I plug in this equation to this equation, so basically I get minus omega squared out of it. And I get minus k squared out of this. And I'm going to get plus k to the 4 out of this partial square to the 4 psi partial x to the 4. Therefore, this would be minus. OK, maybe I made a mistake. Thank you very much for spotting that. AUDIENCE: [INAUDIBLE] YEN-JIE LEE: Oh, yeah, I'm sorry. Not my best day today. AUDIENCE: [INAUDIBLE] YEN-JIE LEE: Yeah. Well, then I do it. OK. I must be drunk today. [LAUGHTER] Thank you very much. Anymore mistake? OK. Fortunately not, right? OK. Very good. So let me do this again. So now I can modify my wave equation, right? Originally, the wave equation is partial squared psi partial t squared equal to v squared partial squared psi partial x squared. And now I add additional term, which is actually proportional to the partial to the 4 psi partial x to the 4. OK, if I add this term into again. And now I plug in the wave equation, the progressing wave solution, into this equation, and I would get this formula, OK? So now everything should be correct, and I have clear evidence that everybody's following. So that is very good. And now, I can now cancel all the minus sign, right and then it's become plus. And now I can actually calculate what would be the speed of propagation for this specific harmonic progressing wave and omega over k will be equal to v square root of 1 plus alpha k squared. OK? Thank you very much for the contribution. And then now we see that here this ratio depends on k. So if I plug this on top of the previous curve, which is actually obtained from here, then what I'm going to get is something like this. In the beginning it's pretty close to the nondispersive case. And it goes up, because of this alpha contribution. Alpha is actually a positive number in my model. And the k is actually the wavenumber. So what is going to happen is that basically after you include stiffness, the slope of this curve is changing as a function of k. OK? What do I learn from this exercise is that if I increase k, if I have a very large k-- that means I have a very small lambda, because k is actually 2 pi over lambda. OK? So that means I'm looking at something really distorted like this. Both string tension and the stiffness wants to restore the string back to normal. Therefore, what is happening is that you are going to get additional restoring force. Therefore, as we actually calculate to here if alpha is actually positive, then the velocity actually increased with respect to what we actually get before we actually had this into a model. So I think that makes sense, because the stiffness also wants to restore the distortion. Therefore, you have larger and larger restoring force. Therefore, the speed of propagation of this harmonic wave will increase. so that's pretty nice. But what does that mean to our project? OK, our project is to send information from one place to the other place, right? So what we just discussed is that we can actually send a square pulse and let it propagate. A square pulse can be decomposed into many, many pieces-- many, many harmonic waves. OK? Before the square pulse works, because all the waves with different wavelengths should be moving at this constant speed, independent of the wavelengths. Now we are in trouble. As you can see here, now the speed, which is omega over k depends on the wavenumber or wavelength. Therefore, different components, which actually are needed to create a square pulse, are going to be propagating at different speed. You can say, oh, come on, this is actually mathematics, so I don't believe you. A square pulse is a square pulse, and that's mathematics, that's math department. But we can actually really see that in the experiment. OK? So that's-- take a look at this demonstration. Maybe you didn't notice that before, but we have seen this effect from the previous lectures. OK, so I can now create a square-- not really a square pulse, but actually some kind of pulse. OK I can create some kind of pulse like this. OK? And as we learned before, when this pulse pass through an open end, it's going to be bounced back. so therefore, I can have-- I can actually show you this demo in a limited set-up. But this pulse is going to be going back and forth, because I have open end, as we've discussed before. What is going to happen is that since we have a realistic system, what is going to happen is that this pulse will become wider and wider, right? That's the prediction coming from this equation. Different component with different wavelengths is going to be propagating at different speed. Therefore this pulse is going to become wider, and we can see that. OK, so let me quickly produce a pulse and see what will happen. OK. Originally, it's actually really sharp. And you can see that really the width of the pulse become wider and wider. And at some point, it disappear. If I have a very long set-up, what you are going to see is that it's going to be propagating toward the same direction. And the width of the pulse is actually going to be increasing as a function of time. Let's take a look at this again. Now, this time we have a negative pulse. You sort of see-- very similar, see. And also you can see that there are some strange vibration actually left behind the main pulse. So that means harmonic waves with different wavelengths really propagating at different speed. And for that, to demonstrate this effect, I also prepared some demonstration, which actually are based on our calculation, OK. So you can say that, OK, now I'm convinced I can see dispersion in the experiment. How do I know this calculation actually match with the experimental data, right? How about we really run a simulation and see what would happen. So what this example actually do is, in the beginning, you would do integration like crazy in order to get all the components calculated. Then it's going to propagate all those pulses-- all those pulse with different components through the medium, OK? And then there will be two different colors, one is actually blue, which is the original shape. The other one is actually the one which is stiffness turned up. So now, in the beginning I can set the alpha value to be 0.02 and see what will happen. And I will put produce triangular pulse. You can see that now. The program is really working very hard to capture all the components from 1 to 199 and equal to 1 until 99. And then now, these individual components are propagating through the medium. And you can see that originally the shape is like-- the blue shape-- triangular shape. And you can see that is a function of time. The pulse become wider and wider, OK? Now, of course, I can increase the alpha to 0.02 and see what happen-- from 0.02 to 0.2 and see what will happen. You should expect a much larger dispersion. And you can see that now in the beginning, it's doing the integration. And you can see that this time because the alpha is actually larger. Therefore, you see that this effect, this broadening, is actually happening earlier, and it become broader and broader, and that there are a lot of strange structures, as you can see also from the demo, produce because different components are actually propagating at different speeds. So of course, we are MIT, so in this course we have MIT-- MIT waves. So let's take a look at the MIT wave and see what will happen. Now you see that there are very sharp edge, which actually require really a lot of effort to reproduce that. And you can see that MIT is kind of distorted as a function of time. We can kind of still identify the peak, but it's actually now displaced. And in the end of the simulation, you can not even recognize that's actually originally MIT signal, which was sent from your source. So what I want to say is that this effect, this dispersion effect, is really an enemy, which is actually very dangerous. And that actually will prevent us from sending high quality signals. OK, any questions about all those demos? Yes. AUDIENCE: Why do we model the [INAUDIBLE]?? YEN-JIE LEE: So this is because the stiffness is actually symmetric, right. So if you bend the string, then there are contribution from the positive and negative part, OK? If you have partial to the 3, partial to the x to the 3 component, then it's going to be a symmetric and so actually against our physics intuition. And also, in this modeling, you also match with our experimental data pretty well. OK. Very good question. And on the other hand, we now consider then the stiffness. you can also go back to the infinite number coupled oscillator case. If you instead take an example which is actually not super small displacement approximation, you take the next to leading order term. Then you will see that the partial to the 3 partial x to the 3 term as you cancel because it's symmetric, or so I argued. And then you will be able to also obtain this tern when you have slightly larger displacement with respect to the equilibrium position. So I hope that answers your question. Any other question? Yes? AUDIENCE: If you were looking at [INAUDIBLE],, for example, what would be [INAUDIBLE]? YEN-JIE LEE: When you pass through the medium. AUDIENCE: So [INAUDIBLE] YEN-JIE LEE: A molecule can actually change the speed of different wavelengths, actually, differently, right? Very good question. OK, so very good. We got two questions, and we can see that if I now turn on the alpha and make the alpha value large, then you can see that the information is distorted. And this involve infinite number of terms. And in this case, in this new demo which I show here, I have alpha value equal to 0.2. Therefore, the effect of dispersion is actually much larger than what you showed before. And then you can see that this MIT wave quickly become something like a Gaussian-like wave, right? OK, so very good. So you can say, OK, you are making an example-- it's a very interesting example, but it involve too many terms. You have infinite number of progressing waves in this example. It's very difficult to understand. How about we go back to a much simpler example, OK? What we can do is that instead of going through infinite number of harmonic waves, now we just consider two waves, and overlap these two waves together and see what will happen. And let's see what we can learn from it, because the required number of harmonic wave to describe such a pulse is too complicated. So you can say that, OK, now let's just consider two waves and see what we can learn from this. And this is actually what I am going to do now. So from Bolek's lecture I hope that he covered the beat phenomenon. So basically, what is it? A beat phenomenon? Beat phenomenon happens when you overlap two waves, two harmonic waves. They have pretty close wavelengths. OK, but they're not the same. And now, if you add two waves together, that's actually what you are going to get. You are going to get something which is oscillating really, really fast, which is basically called the carrier. And also you can see that the magnitude of the oscillation is actually changing as a function of position, and that we call envelope. So that's essentially the beat phenomenon, which you learned from previous lectures. So in this example, I'm going to add two waves together. So the first wave is described by-- OK, is denoted by side one. It's a function of x and t, and it has a function of form A is the amplitude. And the sine k1 x minus omega1 t. This is actually a progressing wave propagating toward the right-hand side of the board, the positive direction of the x-axis in my coordinate system. And it has a wavenumber of k1 and angular frequency omega1 And I can also write down my second wave, which I would like to overlap with the first wave. So this is actually having exactly the same amplitude, which is A. And it is described by a sine function, and you have a wavenumber k2 x minus omega2 t, angular frequency omega2. With these two equations, we can calculate the speed of propagation for the individual waves, right? So the first one, I can calculate the speed of propagation v1 would be equal to omega1 over k1. Very similarly, you can also calculate the speed of propagation for the second wave, which is omega2 over k2. So now what I'm going to do is to calculate a sum of these two waves. So I have the total, which is psi is equal to psi1 plus psi2. So what I'm going to do is to overlap these two waves and see what will happen. And for that, I need this formula, which is a sine A plus sine B. And this would be equal to 2 times sine A plus B over 2 and sine-- it would become cosine here-- cosine A minus B over 2. So if I use that formula, basically what I'm going to get is-- we have two times from the formula. So if you have 2A sine k1 plus k2 over 2x minus omega1 plus omega2 over 2. So basically, the first term is the sine function. The sine function and the content is actually A plus B. Therefore, you add these two together, divide it by two, then basically this is as actually what you obtain. The second term is a cosine term. You get a cosine here. But now you calculate A minus B, which is this term minus that term divided by 2. Then basically what you get is k1 minus k2 divided by 2 times x minus omega1 minus omega2 over 2 t. OK, so now this actually-- what would happen if you add these two waves together? Until now, everything is exact. And I would like to add additional conditions or additional assumptions when I discuss this solution. OK? So how about in order to produce the beat phenomenon, I need to make the wavelengths very, very similar between the two waves. So therefore, what I am going to do is that I'm going to assume k1 is very close to k2 is roughly k. And because of this, since I have a continuous function, if k1 is really close to k2, that means omega1 is going to be also very close to omega2, right? So what I'm going to get is omega1 is going to be also very similar to omega2, and I will call it omega. So if I do this, when I have very similar k1 and k2, what is going to happen? What is going to happen is that k1 minus k2 will be very small. So this very small k means larger wavelengths. Therefore, this cosine term will become the envelope, because it's actually a slowly variating amplitude as a function of position, because the k is very small. K is small means lambda large. Therefore, the amplitude is going to be having this modulation, which is actually like the envelope, that the oscillation of this envelope is actually controlled by the k, okay? Let's look at the left-hand side term. k1 plus k2 over 2 is kind of like calculating the average of the wavenumber of the first and second wave. So if you calculate our average, you can be still pretty large. Therefore, you have small lambda compared to the difference. Therefore, you see that that actually contribute to those little structures in this graph, and it's called carrier. Yes? AUDIENCE: [INAUDIBLE]? If k1 were a lot bigger than k2, then [INAUDIBLE].. YEN-JIE LEE: So they can be different. Yeah, so you are absolutely right. So you can produce something like a carrier even when k1 is not equal to k2, right? Its just a average. You're right. But then on the other hand, the difference, k1 and k2 will be also large. Therefore, it's not as easy as what we have been doing here to identify who is the carrier and who is the envelope. But you do get some kind of graph, which is oscillating really fast, but the envelope is going to be also oscillating very fast. That is harder to see all the structure. But you're absolutely right, yes. Very good question. So now I have this set-up. I assume that they are very close to each other. So now I can define phase velocity. Finally, we define what is actually the phase velocity. In The phase velocity-- I call it vp-- you can see that before I already have been using phase velocity vp for the previous discussions. In the case of nondispersive medium, the phase velocity is just a vp, which is the velocity in the equation. And in this case, vp will be equal to omega over k, as we discussed before. And that's actually the definition of this phase velocity. And I can now also define the group velocity. The group velocity is actually the velocity of the envelope. I can calculate the velocity of the envelope. in the case of phase velocity, I'm calculating the velocity of the carrier. I'm taking a ratio of the average, and actually the average is so close to k and omega, therefore the phase velocity vp would be just the speed of the propagation of the carrier, which is actually omega over k. I call it vp. And in case of group velocity, I call it vg. vg is describing the speed of propagation of the envelope. Therefore, what I am getting is omega1 minus omega2 divided by k1 minus k2. Both of them have effect of 1 over 2, which we say is canceled. And when they are really so close to each other, this is actually roughly like d omega dk. Any questions so far? So we have derived two different kinds of speed. One is actually related to the phase velocity, which is-- one is actually called the phase velocity. It's related to the speed of the carrier. The other one is group velocity, which is actually related to the speed of the envelope. So let me describe you a few interesting examples. And let's see what we can actually learn from this. In the first example, I'm working on a non dispersive medium, OK? If I have a nondispersive medium, then basically what I'm going to get is that omega will be proportional to k. If I plot omega versus k, it's a straight line. Now, if I have omega-- I choose the omega of the two, omega1, omega2, of the two waves-- to be roughly equal to omega 0, I can now evaluate the vp. The vp will be the slope of this point on the slope of a line connecting the 0 to that point, which is actually the omega over k, right? So that's actually the definition of the phase velocity. I would get this slope. The slope of this line is actually related to the phase velocity. I can also calculate the slope of a line cuts through this point. But as it cuts through this curve, and in this case, I'm also going to get a line overlapping with phase velocity, because in this case, omega over k is a constant, which is v. Therefore, no matter what you calculate, if you calculate vp as a ratio of omega and a k, where you calculate vg, which is actually the slope of the line cutting through that point, is you always get actually v. Therefore, what we learned from here is that for a nondispersive medium, vp will be equal to vg. That means both of these two curves, both of the curve of envelope, describing the envelope and then describing the carrier, is going to be propagating at the same speed. OK, any questions? So the whole thing is going to be moving at constant speed. For that, I can now show you some example, which I prepared, some simulation which I prepared. So what it does is that it really-- oh, wait a second. This is 0. OK, so this is the case when I have a nondispersive medium. if I have a nondispersive medium, what is going to happen is that both the carrier, which is the speed of all those little structures, and the envelope is going to be propagating at the same speed. So you can see the high is like a fixed pattern. It's propagating toward the right-hand side. And the relative motion between the defined structure and the envelope is actually 0. So basically you have exactly the same pattern as a function of time. So now I'm going to move away from the nondispersive medium. How about we discuss what would happen if we have considered the stiffness of the string and see what we get from there. So if I plugged omega as a function of k, and consider alpha to be non-zero. It's a positive value. So if I have alpha to be a positive value, non-zero, in this case, I'm going to get a curve like this. The slope is actually changing and it's curving up because if you have k large, then you would see that the ratio of omega and k actually increase. So this is actually the kind of curve which we would get if I set the omega of the first and second wave of interest in this study to be omega 0. Then basically, what you are going to get is that-- OK, now I have this point here on the curve. If I calculate the phase velocity-- the phase velocity, how do I calculate that? I can now connect 0 and the point by a line. And I can now calculate the slope of this line, and I can get the phase velocity, vp. On the other hand, I can also calculate the slope of a line cutting through, tangential to the point of interest. And that is going to give me the group velocity. As you can see from here, which slope is actually larger? Anybody know? Can point it out? Group velocity's larger, right? So in this case, if I turn on alpha greater than 0, what is going to happen is that, since the group velocity is larger than the phase velocity, that means, if I go back to that picture, the envelope is going to be moving faster than the fine structure inside the envelope. How about we take a five-minute break from here? And then we continue the discussion after the break. It's a good time to take a break. Welcome back, everybody. So we will continue the discussion of the beat phenomenon. So what we have shown you is that, based on those curves, actually can actually determine what will be the relative velocity-- what would be the velocity of the carrier, which is actually denoted by vp, and the what would be the velocity of the envelope, which is actually denoted by our group velocity. And in this case, what I'm actually plotting here is that, in this case, because alpha is actually greater than 0, therefore, this curve is actually curving up. Therefore, you have larger group velocity compared to the phase velocity. So what you would expect is that the envelope is going to be actually progressing at a speed higher than the speed of the carrier. On the other hand, if magically I can construct some kind of medium which can be described in this situation, alpha smaller than 0, what is going to happen? So if I plot a situation with alpha smaller than 0, so now I plot omega was a function of k. What is going to happen is that this-- so basically, you have something which is actually curving downward. So if I now, again, work on some point of interest here, you can see that the slope of the phase velocity is now actually larger than the slope, which is actually from the line cutting through the-- tangential to the curve, which is actually getting you the group velocity. So in the case of alpha's more than 0, which is some strange medium I can which I can create from whatever, plasma, or some really strange new kind of material of interest. If that happens, then that means your group velocity will be smoother than the phase velocity. And if you look at this point here, you can see that this curve actually reach a maxima here. And if you actually are operating at this point, what is going to happen? What is going to happen is that if you calculate the group velocity, what will be the value? It will be 0. What does that mean? That means the envelope will not be moving a lot, but the carriers are still moving. So at this point, you are going to get group velocity equal to 0. And finally, the if you actually going to a very large k value in this scenario, alpha smaller than 0, you will see that even you can have phase velocity, vp, positive, because it's actually a positive slope. And that the group velocity actually is negative. What does that mean? That means you are going to see a situation that the carriers are progressing in the positive direction, and the envelope is going to be progressing in the negative direction, probably progressing to the left-hand side of the board. So what does that mean? That means this wave is doing what Michael Jackson's doing. It's actually doing the moonwalk. [LAUGHTER] So this is actually the kind of thing which could have happened, that it looks like and that you are doing-- going forward, because all the carriers are moving in a positive direction. But the body is actually going toward negative direction. maybe I can also learn moonwalk at some point. [LAUGHTER] OK. So let's go back to the demonstration which I got started, and somehow I got messed up. So let's take a look at the demo again so let's look at all the different situation at once. So in this case, as we discussed before, this is actually happening in the nondispersive situation. In this situation, you have a straight line, nondispersed medium actually give you always the group velocity equal to phase velocity. So that means the carrier and the envelope is going to be moving in the same direction at the same speed. On the other hand, in this case, we can actually have a situation that the phase velocity is actually faster than the group velocity. So what I mean is actually the situation here. The phase velocity calculated from a line connecting from 0 to that point is actually having a larger slope compared to the tangential line. And you see this situation. So basically, you see that inside the envelope all those carriers are actually moving faster than the envelope. Now I can have a dispersive medium where the group velocity is equal to 0. So what is going to happen is that really the envelope is actually not moving. It's not like this. The body is not moving. So you have some carriers inside this structure is actually moving forward. But the envelope is actually not moving. So, finally the last situation is really interesting. So in this situation, this is actually having the group velocity-- the group velocity is actually having difference sine compared to the phase velocity. So you can see that the whole structure of the envelope is actually moving backwards. But the carrier is actually moving in the positive direction in this example. So this is actually what we have learned from this beat phenomenon, and then we have covered the idea of phase velocity and the group velocity. So how about bound system how do we understand when we have a bound system? And how does that evolve as a function of time? So if I have a system of two walls and one string, and of course, I give you the density for the unit length and the string tension, and also the alpha, which is actually telling you about the stiffness of the system. Again, I can write down psi xt to be the sum of all the normal mode from one to infinity, A m sine km x plus alpha m sine omega mt plus beta m. And then what we can do is that we can first get the initial conditions of this system, and those are the boundary conditions of this system. That we actually just follow exactly the same procedure to obtain all the unknown coefficients that we would be able to evolve this system as a function of time, as I have demonstrated to you in the beginning of the lecture. So in this case, you can have two boundary conditions. One is actually say at x equal to 0. And the other one is actually at x equal to L. In those boundaries, as we actually learned before, because the endpoints are fixed on the wall. Therefore, psi of 0 at that time, t, will be always equal to 0 for the left-hand side boundary condition. And very similarly, as we discussed before, psi of L t will be equal to 0 if you look at the right-hand side of the wall-- of the system. So I don't want to repeat this, because this is actually exactly the same calculation which we have done before. So with these two boundary conditions, we can actually conclude that k m will be equal to m pi over L, and alpha m will be equal to 0. So you can actually go back and check this out. So what I'm going to say is that until now, what we have been doing is identical to what we have been doing for the nondispersive media. What I'm to say is that the shape of the normal mode is actually set by the boundary condition. It's determined by the boundary condition, and it has actually, so far, nothing to do with the dispersion relation omega as a function of k. So in short, boundary condition can give you the shape of the normal mode, and that we know that the first normal mode, second normal mode, et cetera, et cetera, is actually going to be identical to the case of nondispersive medium. so that's actually the first thing which we learned. The second thing we learned is that OK, now what we see is that once the boundary condition is given, then the k m is actually also given. Therefore, since I have the dispersion relation omega as a function of k, as shown there. Omega over k is equal to v times square root of 1 plus alpha k squared. Therefore, once k m is given, omega m is also given. So you can see that that's actually where the dispersion relation come into play. The omega m will be different if you compare the dispersive case and nondispersive case. So that is actually what I want to say. The k m, which is the shape of the normal mode, doesn't depend on the dispersion relation. On the other hand, the speed of the oscillation, the angular frequency, omega, depends on the dispersion relation, which is actually what we obtained from there. If I start to plot omega m as a function of k m-- so in the case of nondispersive medium, so what am I going to get is actually discrete points along a straight line. This is actually k1, k2, k3, k4, et cetera. They are actually all sitting on a common straight line. If you look at the relative difference between k1, k2, and k3, they are constant according to this formula. The difference between k1 and k2 is pi over 2. k2 and k3 is actually also pi over 2-- pi over L. It's always a fixed number. And since omega is actually proportional to k. Therefore, the spacing between omega 1, omega 2, omega 3, is also constant. In short, omega 2, omega 3, and omega 4, et cetera is always multiple times what you get from omega 1, according to this graph and in the case of nondispersive medium. So what does that mean? That means OK, now if I have a very complicated initial condition-- this is actually what I have, an initial condition-- very complicated. I just need to wait. If this is actually nondispersive medium, I just have to wait until p equal to 2 pi over omega 1. Then the system would restore to its original shape. That's actually what I can learn from here, because omega 2, omega 3, and any higher order normal modes, the angular frequency is actually multiple times of what I get from omega 1. On the other hand, if I consider a situation of dispersive medium-- you can see that now the difference between omega m is now the constant. So what you would predict is that it would take much, much longer for this system to go back to the original shape compared to nondispersive media. So that actually you can actually see. In a real-life experiment, I can distort this equipment in this boundless system, and it's actually going to take forever or impossible to come back to the original shape, because of that dispersion. On the other hand, if I have a really highly idealized situation, if I have both ends bound, and I just have to wait until t equal to 2 pi over omega 1. Then this system will go back to the original shape. Before I end the lecture today, I would like to discuss with you two interesting issues. So many of you have seen water waves, and Feynman actually told us in his lecture that water waves are really easily seen by everybody, but it's actually the worst possible example. That's the bad news-- the worst possible example because it has all the possible complications that waves can have. That's the bad news. The good news is that you are going to do that in your P set. [LAUGHTER] So we will be able to understand the behavior of the water waves. So that's the good news. The second thing which I would like to talk about is phase velocity. You can say, OK, you say that phase velocity or harmonic waves doesn't send information, right? And how do I actually know that? Right? So what does that mean? OK, so let's take this horrible example of water wave. OK, so the black line is actually the beach, and there is a water wave from the ocean approaching the beach. And you can see that you can have some kind of angle between the insert of water wave and the line of the beach. What I can actually do is that I can now measure the shape of the water wave at the edge of the beach. And I would see that, huh, now the phase velocity which I observe there is actually faster than the speed of propagation of the water wave, because of this inserted angle, OK? I can actually make it very, very fast. I can make the speed actually even faster than the speed of light. Right? I can now decrease the theta to 0. Then you will have a phase velocity which is faster than the speed of light. It goes to infinity. But does that mean anything? Actually, that doesn't mean anything, because I don't really move the water from a specific point to another point infinitely fast. Therefore, what I want to say is that, OK, you can do whatever you want to make a fancy phase velocity. But that will not help you with sending things close to the speed of light or greater than the speed of light. So as you can see from this example, I can easily construct a simple example, which you see that is actually really not sending anything from one place to the other. But you still have really, really fast phase velocity. OK, thank you very much, everybody, for the attention and hope you enjoyed the lecture. And if you have any questions, please let me know. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 7_Symmetry_Infinite_Number_of_Coupled_Oscillators.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: So, I'm back. Welcome back, also, to 8.03. So today, what we are going to do is something really interesting. It's to understand how we use symmetry to help us with prediction of physical situations. So first, I will go through two concrete examples of symmetry, and see what we can learn from there. And also, today, we are going to go to infinite number of coupled oscillators. OK? I think we are done with finite numbers. OK? All right. So what we have learned last time when Bolek was giving lectures, I hope we have learned that driving force can excite a specific normal mode. Right? So if you drive the system at the frequency, the system like, then the system will respond, and will oscillate the driving frequency with large amplitude. OK? And also, we have learned that the full solution of a coupled oscillator is actually pretty similar to the situation we got from single oscillators. So that where you have a particular solution, and a homogeneous solution. And the full solution will be a superposition of the two component, and all the unknown coefficients in the homogeneous part of the solution. OK? And today, I hope I can help you and convince you that symmetry actually can help us to solve the number of modes without knowing the detail of M minus one K metrics. So that actually sounds really cool, and I would like to talk about that in this lecture today. So this is actually what we have been doing so far. So we tried everything in terms of metrics. So we start from the equation of motion, and X double dot, you go to minus KX. And then we write everything in a complex notation-- exponential i omega t plus phi times A-- A is actually the vector, right? So it's actually A1, A2, A3. It's actually the amplitude of the oscillation of the first, second, and third and etc. etc. it's a component of the system. Right? Then, we actually found that, in the end of the day, we are actually solving this problem like eigenvalue problem. So basically, we have M minus 1 K metrics describe how each component in the system interacts with each other. OK? Then, what is actually the angle of frequency of the the normal modes? Essentially, coming from this eigenvalue problem , M minus 1 K, A equal to omega square A. Then you just go ahead and solve the eigenvalue problem. Then you will be able to figure out why are there no more mode frequencies, and therefore, what are the relative-- the ratio of the amplitude in the normal mode, which is actually the A vector. OK? The eigenvector. OK, so that's actually what we have been doing. OK? And today, what I'm going to do is to introduce you a very important concept in physics. Not only in physics, but also in mathematics, and also art, right? So you see symmetry in art, for example. We can see here-- there are several graphs here-- and you can see that their apparent symmetry, or rotational symmetry, they are refraction symmetry. And you can see that when we build the particle detector for example lower right plot is a CNS detector in the Large Hadron Collider. We also try to build this detector symmetric, right? Because otherwise, if we get a very complicated shape of detector, then the analysis of the data will be really complicated. So therefore, everybody like symmetry, and everybody don't like, really, chaos. Right? OK? So, that's really nice. The question is, how do we speak the language that the nature speak? How do we actually describe symmetry? That's actually the question I'm asking, and I'm going to show you that, OK, we can actually use mathematics to describe symmetry. So before we go to infinite number of oscillators, let me give you a concrete example of symmetry, and then see if we can understand how to use the math to describe symmetry. OK? So there is a two-component system. Two pendulums, which we worked together in the last few lectures, that they are coupled to each other, and there's a parent symmetry of this system. Can somebody tell me what is the symmetry, you can see from this system? Somebody? Anybody? AUDIENCE: Reflection. PROFESSOR: The reflection symmetry. So if you reflect this system, as I show you in the slide, you can see that if you reflect this picture, it looks identical. Right? So that is actually really, really good news. That means if I do this reflection, XY, and go to minus X2-- you have a minus sign, because you can see that after reflection-- the amplitude changes sign. Right? X2 go to minus X1, the system looks identical, and the physics should not change. OK? So that's actually what we can learn from there. So that means if I have-- I do this reflection, then I can actually define X tilde-- T-- this is equal to minus X2 minus X1. OK? To become paired with X. OK? And this is also going to be the solution of the equation motion if the original X is already a solution. OK? So that's the power of reflection symmetry. OK? If X is a solution, then I do this reflection, and I can figure out that X tilde is also a solution. OK? So how do I actually describe the symmetry in the form of mathematics? What we actually do is to define S matrix, symmetry matrix. And in this case, when we talk about reflection symmetry, it's actually defined as zero minus 1 minus 1, 0. This is actually a two by two matrix. And if I do this operation, S operate on this X matrix, then that is actually is going to give you the X tilde. OK? So that's the nature of the role of the symmetry matrix. OK? Any questions? OK. So now we have defined a symmetry matrix. And then you can ask, why do we actually care, and why do we actually introduce symmetry matrix? Right? Because I can always write down the X tilde in that way. That is because I think by the end of this lecture, you will find that if S matrix describes the symmetry of the system, OK, that would mean S matrix will commute with M minus 1 K matrix-- which, we don't know commute yet, but I will introduce you-- that means M minus 1 K matrix and S can actually swap freely. OK? If that happens, then S matrix will share the same sets of eigenvectors as the M minus 1 K matrix. What does that mean? That means-- OK. Before we are doing this solution, right, we are solving M minus 1 K matrix eigenvalue problem, right? And then, we get the eigenvector, which is the amplitude ratio of normal modes. And that means you have an alternative way to get the normal mode. You can solve the eigenvalue problem of S matrix, then you can get the same set of amplitude ratios as M minus 1 K matrix eigenvalue problem. OK? And then usually, the eigenvalue problem of S matrix is far much easier than M minus 1 K matrix. OK? So that's actually why we're doing this. OK? So now, I would like to convince you that S matrix and M minus 1 K matrix will share eigenvectors. OK? So. Let's go ahead and prove this, or demonstrate this idea. OK? So the original equation of motion looks like this. X double dot equal to M minus 1 K X. Right? So now, this is actually the original equation of motion. And if this system satisfy the reflection symmetry, that means X tilde is also a solution, right? Therefore, what does that mean? That means X tilde double dot will be also equal to M minus 1 K X tilde. Because it's also a solution to the equation of motion, right? That's pretty natural. OK? Now. I can actually use this expression, X tilde is equal to S times X. Right? All of those things are matrix, OK? Just to be careful. That means I can write this like this-- S X double dot equal to M minus 1 K S X. OK? There's no matrix, and I also replace-- I'm just replacing X tilde by S X. OK? And also, I call this, actually, 1; I call this actually 2. OK? I can multiply X from the left-hand side of 1. OK? And see what will happen. So if I do that, then what I am going to get is S X double dot-- OK? That will be equal to S M minus 1 K X. OK? If you compare this equation, and the equation number three, these two equations, you will see that let-hand side is the same. Right? Right-hand side-- huh! Something interesting is happening. M minus 1 K S must be equal to S M minus 1 K. What does that mean? This means that they are the same. M minus 1 K S is actually equal to S M minus 1 K. So if I say, this distance satisfy a symmetry described by S matrix, that means X tilde, which is actually the transformed amplitude, will be also a solution to the equation of motion. And therefore, an inevitable consequence is that M minus 1 K S will be equal to S M minus 1 K. Usually, when you started physics, we write this in terms of commutator. OK? So we call this, these two things actually commute. OK? So commutator is actually defined as A bracket of A and B. This is actually equal-- defined as A B minus B A. OK? If A and B commute-- OK? It's this new word, probably, for most of you-- if they commute, that means A B in the bracket is equal to zero. OK? So this expression, I can actually write it down like this. Commutator of S M minus 1 K, that is equal to zero. And you will see this really a lot when you study quantum physics. OK? So I hope this actually gives you some flavor about commutator. OK? So now, that's actually pretty nice. This means that they commute, OK? If I take X of t this is equal to A 1 cosine omega 1 t. OK? So, this means that A is actually-- sorry, X is actually a solution, which is a normal mode, a solution. Right? And A is actually amplitude the vector, the amplitude vector of the first normal mode, and omega 1 is actually the first normal mode frequency. OK? If this is the case, then I will have X tilde of t will be also oppositional to A 1 cosine omega 1 t. Because if I actually exchange X1 and X2, the oscillation frequency is not going to change. Right? Therefore, since this system is in the same normal mode with angular frequency omega 1, therefore the amplitude ratio of the first and second oscillator will stay constant. Right? Because you are in one of the normal modes. Right? Therefore, I can conclude that X tilde is going to be proportional to this expression. Because they are in the same normal mode, oscillating at the same frequency. OK? Is that too fast? Everybody is following? OK. So that's nice. So this means that S X of t will be equal to S A 1 cosine omega 1t, OK? So this is actually coming from here, right? I am replacing X tilde by S X based on this definition. OK? Then again, I replace, I write, X explicitly which is actually A cosine omega 1 t. OK? Then you get this expression. And from this expression above, you see that you conclude that this is proportional to A 1 cosine omega 1 t. That's very nice. That means S A cosine omega 1 t is proportional to A 1 cosine omega t. And you can actually cancel this. And you see that S A 1 is proportional to A 1. Or I can write it as S A 1 is equal to beta A 1. What does that mean? This means that A 1 originally-- where's A 1 coming from? A 1 is the amplitude of all the components in the first normal mode. Right? That's coming from the eigenvalue problem, which it actually does in this light. Eigenvalue problem M minus 1 K A equal to omega square A will give you the solution of normal mode and their eigenvectors, which is amplitude ratios of all the components in the system. Right? So that means A 1 is not only M minus 1 K matrix eigenvectors, it's also eigenvector of S matrix. OK? So that is actually very good news. And I can also do the same thing for A 2, to prove that it also works for A 2-- the derivation is identical, so I am not going to do that again. So that means, actually, starting from here, OK-- if X and X tilde are both solutions to the equation of motion. I will conclude that S matrix and M minus 1 K matrix, they commute. OK? How to tell if a system satisfy a specific symmetry defined by my symmetry matrix? Is by this way, you can check if M minus 1 K and S commute. If they commute, that means the system actually satisfy this symmetry. And also, the consequence is that from there, you will conclude that if you have also a set of eigenvectors from M minus 1 K matrix eigenvalue problem, then that is going to be also the eigenvector of S. OK? Any questions? OK. So M minus 1 K eigenvectors. Also S eigenvector. OK? That's actually what we have learned from this small exercise. Now, you can say, wait, wait, wait, wait. This is actually not what we need, right? I would like-- we would like to argue that S matrix-- I can solve S matrix eigenvalue problem, and I can learn about the solution of M minus 1 K matrix, right? This logic is actually in the opposite direction, right? You said, OK, you solved things already, then, actually, it's also S matrix eigenvalue problem. So now what I am going to do is to reverse the logic, and see if it works. OK? Again, to see what will happen. OK? So now, I would like to prove that if I solve S matrix eigenvalue problem, I have also solved the eigenvectors for M minus 1 K matrix. Run the logic in the opposite direction. OK? So, if I were given two things-- one, S A is equal to beta A. Number two, S matrix and M minus 1 K matrix commute. OK? If those are the given conditions, then I can actually conclude that S M minus 1 K-- OK? I can actually contract this expression-- I write that S M minus 1 K A, OK? Because they commute, right? They can actually swap M minus 1 K and S safely without actually introducing any more terms. This will be equal to M minus 1 K S A. OK? And S A, from the first expression, S A is equal to beta A. Right? Beta is a number, OK? Therefore this expression will become beta M minus 1 K A. So, beta can penetrate through matrix, because beta is just a number, is eigenvalue. It's eigenvalue of S matrix. OK? So what does this mean? OK. So what does it mean? So this means that if you look at this part and that part-- you look at the beginning and the end of the expression-- you immediately conclude that M minus 1 K A, this expression is also an eigenvector of S matrix. Right? So you have S matrix acting M minus 1 K A. And that will give you something proportional to M minus 1 K A. You see? It's magic, right? It's actually not magic, but it's actually just, you know, really logical extension. Right? OK? Very cool! So that means this is also an eigenvector of S. Right? And also, another thing which is interesting is that they share the same eigenvalue, beta. Right? They have the same eigenvalue. OK? So, if eigenvalues of S-- so you can get several eigenvalues, right? In this case, two by two matrix, you will get-- how many? Two, right? Two eigenvalues. If those two eigenvalues are different, then I can conclude that M minus 1 K A must be proportional to A. Right? Because this is actually the same eigenvalue problem, and the same eigenvalue, beta. Since all the eigenvalues from the solution of eigenvalue problem of S A equal to beta A, those eigenvalues are all different, therefore I can argue that M minus 1 K A is proportional to A. OK? Therefore, M minus 1 K A is equal to omega square A. Omega square is actually some constant. OK? This is actually amazing, because that means given the two conditions-- the first one, I can figure out the eigenvalue and the eigenvectors of S matrix; second, if S matrix and M minus 1 K matrix interaction matrix, they commute-- then I can actually already figure out what are the eigenvectors of M minus 1 K matrix. OK? And another thing which we've learned from here is that, wow, that's good! Because the eigenvectors are already solved. Therefore, I just have to calculate this. It's just a normal operation. It's not the eigenvalue problem anymore. I just multiply M minus 1 K times A, then I can actually get the value omega square. You see? That's actually much easier than solving the eigenvalue problem of M minus 1 K matrix. OK? That's actually very good news. Finally, I think the most important consequence is that once we solve this system, which satisfy the symmetry described by this S matrix, we have solved all the possible systems which satisfy the same symmetry. For example, in this case, I solve a coupled pendulum problem, OK? They look symmetric. Right? And I can, of course, I can draw another one, which is like this. It's more circular. And there are two walls, which is actually-- there are three springs connected to the wall. This problem is already also solved, right? Because it also satisfy the same symmetry. And of course-- like, you know, like this, go crazy, and even more. This is also solved! Right? Because this is also symmetric. Right? I can add more. Right? Like this. This is also symmetric. Right? And this-- let's think. The eigenvector of this M minus 1 K matrix eigenvalue problem will be identical to what we have already solved here. OK? So, that is actually really amazing. If you speak the right language, and cut into the problem in the right angle, you actually find that actually, you can solve multiple problems at one time. OK? Any questions? OK. So now this is actually very nice, and this is actually a very important preparation to the next step, actually. So now, we have understood coupled oscillator, and we have learned a little bit about symmetry. Therefore, I would like to go to infinite number of coupled oscillator. OK? So that is actually the next step, which we are going to move on in 8.03 So this is actually one example infinite system. OK? I cannot write the whole universe. Why? Because it's infinite, so I couldn't include everything in the slide. But this is actually an example system. Done OK? Looks hopeless, right? In general, we don't know how to solve infinite system, because if you have infinite number of things that are connected to each other in random ways, then the problem becomes really, really complicated. OK? In general, I don't know how to solve this problem. And if you are a EE major, the first thing, maybe, you like to do is, ah, now I have this picture, and I can put everything in my computer, and see how things evolve as a function of time! Right? Of course we can rely on the computers, and see what we can learn from it. And if you made your major of mathematics, you will say, no, this is not the problem I am going to work on. OK? I don't care. But as a physicist, what we are going to do is that, huh-- we look at this infinite system, OK? It's kind of interesting, right? It's a lot of things, a lot of small balls connected to big balls, right? Super big ones, and plotting things in log scale. So those balls are really, really large compared to all the other balls connected to this system. Therefore, as a physicist, I'm going to ignore all the other balls. Oh, if I do that, then it becomes-- there is some kind of symmetry you can actually see from here, right? What is actually the symmetry? you see? There are three balls that connected to each other. They are equally spaced. We have a translation symmetry. You see? So you can see that, actually, that's how we think about a problem. Of course, different field have different kind of thinking, and different kind of problem they would like to focus on. But as a physicist, I would like to know how the system will work, and that is actually what I'm going to do. OK? So that's very nice. We are going to discuss infinite system. So what is actually the infinite system I am going to talk about? It's actually there is infinite system with space translation symmetry. So, to save some time, I have already written down the matrix involving this system here. What I am interested is mass sprint system, OK? Infinite number of mass and spring. And they actually satisfy space translation symmetry. OK? They are connected to each other by springs, with natural length A and spring constant K. OK? And there are infinite number of them, actually, lined up from the left-hand side of the edge of the universe to the right-hand side edge of the universe. OK? I've prepared this system. OK? It took me a long time. OK? All right? But it's very difficult to describe this kind of system, right? So the first thing we have learned from 8.03 is that in order to describe this system, I need to define a coordinate system, right? And also have everything properly labeled. So I introduce a label-- j minus 1 j, j plus one, j plus two-- just to name each little mass I'm talking about. OK? No other purpose. Then, once I have the label, I can actually write everything, express the displacement of little mass, as X j minus 1, X j X j plus one, X j plus two. That's just the displacement from the equilibrium position of the mass. OK? And this system will have equation of motion looks like this. So if now I focus on the little mass, Z. OK? Then I can actually write down the equation of motion. There are two springs connected to these mass. Right? Therefore, you are going to have two spring force. Right? Since this is actually idealize the springs with spring constant capital K, therefore, I can write down immediately the equation of motion is actually equal to M X double dot j is equal to minus K X j minus X j minus 1 minus-- this is actually the right-hand side spring force-- minus K X j minus X j plus 1. We have done this exercise before, right, with a simpler problem. OK? As usual, I can collect all the parents associated with X j minus 1, X j, and X j plus 1, together. Then I get this expression, which actually looks nice. OK? And I assume that this system is actually undergoing some kind of oscillation. OK? Therefore, I assume that this solution, X j will be equal to A j is the amplitude of j's mass. OK? Cosine omega t plus phi, omega is actually the oscillation frequency, and phi is actually the phase, and I don't know why this is actually omega and A j yet. OK? We would like to figure that out. And as usual, you can actually write down the M matrix, OK? M matrix is actually really simple, in the diagonal terms-- diagonal terms are all m, and the off diagonal terms are all zero. Right? And you don't really need to copy them, because they're all derived in the lecture notes. M minus 1 K matrix-- ha! I have already arranged my terms here; therefore it looks like this. It have a strange structure, you have three terms, kind of in the diagonal terms, and this actually is shifting as a function of number of rows, and all the other parts of the matrix actually zero. OK? It's an infinite times infinite dimension matrix. Finally, I would like to also write my A matrix is the vector of amplitude, right? So you have many, many numbers-- A j, A j plus 1, A j plus 2. OK? And et cetera, et cetera. OK? Now, very easy, right? The question is actually can be solved, right? You just have to solve the M minus 1 K matrix, right? That's easy, right? It's an infinite number times infinite number matrix, right? Super easy! No, actually not. Right? [LAUGHTER] So we are in trouble. I don't know how to solve this problem. OK? What can we do? Anybody have any suggestion to me? AUDIENCE: Ask the math department? PROFESSOR: Ah, yeah! Math department is coming in to help. Yes. But actually, before asking them, we learn some concept, which we just learned, right? This-- what kind of property of this system? AUDIENCE: Symmetry. PROFESSOR: Symmetry! Right? We have symmetry. OK? So this M minus 1 K matrix looks horrible. But if I write down the symmetry matrix, actually, it looks slightly better. OK? So what is actually the symmetry matrix? So one observation we can make from this system is that if I shift this system, A, to the left, OK? I shift these two mass to the left-hand side, I shift all the mass. I have to hire many, many students to move all the mass from left-hand side of the universe to right-hand side of the universe. OK? And after they have done that, the system looks the same. Right? That's very good, OK? After all the hard work, right? So what is actually going to be the symmetry matrix? OK. Now, I would like to achieve something which is A prime equal to S A. And then this S actually shift the mass by a distance of A. Right? So what would be the functional formula for this S matrix? It would look like this. It's going to be 0, 1, 0, 0, 0-- 0, 0, 1, 0, 0, 0-- looks like this. OK? So the next two diagonal term is all one. All the rest of the component is zero. OK? And this looks a lot more friendly compared to M minus 1 K matrix, right? Still, this is horrible thing to do, because this is infinite number times infinite number dimension matrix. OK? So. We would like to find the eigenvectors of S matrix. OK? So this means that if I manage to solve the eigenvalue problem, assuming that-- OK, I haven't solved it, but assuming that I can solve it, then what I'm going to do is going to get this S A will be equal to beta A, where A is actually a eigenvector of S matrix OK? And S A, we just learned from here, is actually equal to A prime. So beta is the eigenvalue, and A is actually the eigenvector. So that means, originally, I have A, which is something something A j, A j plus 1, A j plus 2, blah blah blah. OK? And A prime, after I actually multiply A by S matrix, I get A prime, which looks like this-- A j plus 1, A j plus 2, A j plus 3. OK? So what I am going to do is-- what, actually, this S matrix does is to shift the A component one row, right? OK? So then, we basically get this expression. And of course, A 1 is equal to beta, which is a constant, times A. Right? So if you compare, for example, here, you can get that-- A j prime will be equal to beta A j, which is actually equal to A j plus 1. Right? A j prime is actually equal to A j plus 1, right? It's just shifting one unique label. Right? OK. So this is actually the expression I'm looking for. OK? We don't know yet why this is actually beta. Beta is a number. Assuming that I can solve the eigenvalue problem. OK? But I do know, if I have A 0, if A 0 is equal to 0, from this expression, that means A 1-- sorry, A 0 is equal to 1. If A 0 is 0, then everything's 0, right? And it's not fun, right? OK. A 0 is equal to 1, then something will happen. A 1 will be equal to beta, right? From this expression, right? Because beta A j is equal to A j plus 1, A 2 will be equal to beta square, et cetera, et cetera. And then I can say that A j, if I assume A 0, if A 0 is equal to 1, then A j will be equal to beta to the j. OK? Am I going too fast, here? Everybody is following? No questions? No? Good. Actually, we found that we have already solved the eigenvalue problem. Right? Because I have already the expression for the A j, which is actually in the form of beta to the j, right? So beta is some kind of number, and the infinite number of beta actually can satisfy this eigenvalue problem. No matter what kind of beta I choose-- it can be 1, it can be 2, 3.14, it can be pi-- and what am I going to get is the corresponding A j, corresponding A vector, which you have satisfied this expression. OK? So that means some magic happen. We have already solved the eigenvalue problem without really deriving, you know, a lot of deviation. Right? Secondly, another thing which we learned is that there are infinite number of eigenvalue which satisfy this eigenvalue problem. The question is, does that make sense, or not? Infinite number of eigenvalues can actually satisfy this infinity long system. It's kind of making sense, right? Because we have worked on one oscillator, you had one normal mode; two oscillator, you have two normal mode; three oscillator, you have three normal mode-- infinite number of oscillator, you should have infinite number of normal modes. Right? OK, so that is actually a very, very good news, because we have already solved the problem, and we also know the function of four of eigenvectors. OK? So let's take a look at those example system, which are actually close to infinity long. So here, you have a Bell Lab machine, which actually can have, actually, multiple coupled oscillators. Each one of them can oscillate up and down, and you can see that, huh, if I actually tried to move them up and down, that a complicated kind of motion can occur from this system. Actually, if I do this, you see that, ah, they are something similar to wave is happening. And if I do this continuously-- oh, some kind of, like, a standing wave is produced, right? And this system is actually really, really hard to describe, right? If you look at how many things this system can actually do. OK? Another example is actually-- OK, so you can say, come on, this is actually not infinitely long system, right? You have some final number, right? So how about I use this system as a demonstration. This is actually a much nicer, or much better, approximation, OK, to infinitely long system. You can see that, OK, each mass, each-- OK, I can say, for example, each small component of the spring, essentially, can become seeded as a small m in my graph, right? And actually, I can, instead of oscillating them back and forth, I oscillate them upside down. OK? And you can see that, huh, they are interesting kind of motion. I can have-- I can have this, which is like a standing wave; I can do this; I can stop this system, and I produce-- woo! I can produce a wave. And then it goes back and forth. And I can, whoa, do this crazy, and then you see that, how exciting-- a much higher frequency normal mode, right? And that's really complicated. And the question is, how can we actually understand this kind of system? The thing is that this system is so much, so complicated, and have infinite amount of possibilities. Right? So how are we going to understand this? Very good news is that we have solved the normal modes of this kind of system, right? So the normal mode looks like this-- A j equal to beta j. OK? And the following lecture, the rest of the lecture, is to understand what does that mean, and also make predictions. OK? So now we have, actually, the eigenvectors, OK? That's really nice. So from our previous discussion, if this system actually satisfy the symmetry, have the symmetry that is acquired by the S matrix, which I have here, that means M minus 1 K matrix will share the same set of eigenvectors as S matrix. So what is actually part of the work is to evaluate this. M minus 1 K multiplied by A, and that will give you omega squared A. OK? So I just need to multiply M minus 1 K matrix by A. What is A? A is actually here. Now what is actually M minus 1 K matrix? M minus 1 K matrix is here, have a kind of complicated structure. OK? On the other hand, if I only focused on the jth object, the object which is named j, have a label j, then actually I can write down, OK, the right-hand side is actually just omega square A j, right? Because this is actually-- if I only focus on the j component, OK, left-hand side is actually just M minus 1 K A multiplied by A, right? OK, so basically, there are only these three terms coming into play, right? If this is A j minus 1, so anything minus 1, we are multiplying by minus K over n. A j we multiply by 2 K over n, and A j plus 1, we are multiplying by minus K over n, right? The rest of the terms are all 0. OK? It's actually not as complicated as we thought. OK? So, if I write it down, explicitly, the left-hand side part, then what I'm going to get is minus K over n, capital K over n, A j minus 1, plus 2 capital K over n A j minus capital K over n, A j plus one. OK? So this is actually the j term. Now I can define omega 0 square equal-- is defined as capital K over n. If I do that, then basically, I can see that omega square A j will be equal to omega 0 square. OK? I am taking all the K over n out of the game and write it down as omega 0 square. OK? Minus A j minus 1 plus 2 A j minus A j plus 1. OK? And also we know, from the previous discussion, S matrix and the n minus 1 K matrix should share the same sets of eigenvectors. Therefore, I can actually try to plug in one of the eigenvectors from S matrix. Right? A j equal to beta j. OK? I can plug that in, then basically, I get omega 0 square minus b-- minus beta, j minus 1 plus 2 beta to the j minus beta to the j plus 1. And the left-hand side will be reading like omega square beta to the j. OK? Questions? OK. So now, I can cancel-- I can actually divide everything by beta to the j, right? I can get rid of beta to the j, then basically, I get omega square equal to omega 0 square minus 1 over beta plus 2 minus beta. OK? And as we discussed before, beta can have any value. OK? And also, you can see from here that, huh-- once I know the eigenvalue of S matrix and eigenvector of S matrix, I also know what is actually the corresponding angle of frequency of the normal mode. Right? By using M minus 1 K times A, you can figure out what is actually the corresponding omega, the normal mode frequency. OK? So that is actually pretty nice. But on the other hand, if you step back and just think about what we have been doing, OK? So very good. You have a beta, which is a random value. You can evaluate this thing, then you can get the corresponding omega. But then something doesn't feel right. Right? For example, if you have beta equal to 2, what is going to happen? If you have beta equal to 2, what does that mean? That means A j will be equal to 2 to the j. OK? That's very dangerous. Hey? That means-- OK, so I am-- I deploy the whole system, OK, from the left-hand side of the universe to the right-hand side of the universe. OK? So that means, if I go to the your right-hand side of the universe, the amplitude explode. Right? It's actually 2 to the infinite number, right? OK? It's not a physical-- doesn't sound like a physical system to me. Right? If, actually, beta is greater than 1, then the right-hand side A of the universe, the amplitude there, will explode. OK? Doesn't sound right, right? So I don't like that. OK? Maybe you like it, but I don't like it. For the moment. On the other hand, if the beta-- OK, again, it's not 1, but smaller than 1-- what is going to happen? If the beta is smaller than 1, what is going to happen is that, huh, OK, the right-hand side of the universe is fine, is finite, because the amplitude has become smaller and smaller. But the left-hand side part of the universe, the amplitude still explode. Right? So what does that mean? This means that if beta-- if the absolute value of beta is not equal to 1, the amplitude, at some point, goes to infinity. OK? So that's actually not very nice. That's because A j is actually proportional to beta to the j. OK? So in the discussion we have here, we consider beta equal to 1 case. OK? Otherwise, it's actually, things will explode. OK? So if the absolute value f beta is equal to 1, in general, beta can be exponential i, small k A. Right? Then, actually, you can get absolute valuable of 1. OK? If beta is equal to 1, that means the amplitude of all the oscillators are the same. OK? All right, so now, if we accept this, we only limit ourself to the discussion of beta, absolute beta, value of beta equal to 1, then beta can be written as exponential i k A. Then, if I plug this back into this, basically, what you are going to get is omega square is equal to omega 0 square 2 minus exponential i k A plus exponential minus i k A. Right? Because you have minus 1 over beta, and beta, therefore you have exponential i k A, and the exponential minus i k A. OK? It's a lot of math in this lecture, but we are getting over to it. OK? All right. So that is actually-- we actually can identify this, and this actually can be rewritten as 2 omega 0 square 1 minus cosine k A. OK? We have arrived a surprisingly simple expression. So let's take a look at this expression carefully. So that means, for each given k, a small k, then I will have a corresponding angular frequency, omega square. OK? So still, there are infinite number of possible normal modes. OK? From this. So if I take a look at the amplitude, if I select a k value-- small k value-- if k is given, I can actually calculate the corresponding A j. So the A j I can actually define as a superposition of exponential i j k a, and minus exponential i j k a. And that will give you a sinusoidal shape. So if I give you the k, basically, you'll see that if I give you a k, then you get the corresponding beta. Right? And you are going to get omega, the corresponding omega square. But one interesting thing of this expression is that if you keep beta, or keep one over beta, you are going to get the same omega. Therefore, I can now use superposition principle. Basically, I can actually add these two solutions together, since they are going to be oscillating at the same frequency. Then what I'm going to get is, huh, interesting thing happen. The A j, the amplitude, as a function of j, it's like a sinusoidal function. OK? So that is actually what is really predicted to an infinity long system. For example, if I do this, you can see that, aha, indeed, I can see sinusoidal shape. OK? And you can see that the sinusoidal shape is actually oscillating up and down, like a standing wave. And that is actually exactly this expression. So that tells you something really interesting. That means the sinusoidal shape is associated with what? Associated with translation symmetry. Right? All I have been doing is to require this translation symmetry, and you already get the amplitude A j. And if you choose the physical beta value, then you already immediately arrive at a solution which is actually like sinusoidal shape. Doesn't that sounds really amazing to you? OK. So I think it's time to take a five-minute break, because I can see that you are overwhelmed by the math already, and of course, let's come back in five minutes, then we can discuss some more about what we have learned from this mathematics. And if you have any questions, please let me know. OK, so welcome back, everybody. Of course, you are welcome to come back here, and play with the demonstration. OK? So very good. So during the break, there are several questions asked, which I think, those are very good questions, and that's actually the purpose of this break. So it's a long day already, right? A lot of mathematics, and I hope everybody survived. OK? No dead body yet? You can see that here, I'm doing something really crazy, here. So, OK. Consider-- I think most of you got this point, beta not equal to 1 is not nice. Something explode at the edge of the universe. So I don't like that. Therefore, I consider only the case which you have absolute value beta is equal to 1. And then we say, OK, it can be plus 1 and minus 1, but that's actually not the whole story, right? You can have, in general, beta equal to exponential i, some number. Right? Some real number. OK? And I write, here, a very fancy expression. Beta equal to exponential i k a. Why i k a? It's a very good question, right? What is a? I think most of you actually already forgot. What is a? a is actually the natural length of the spring. OK? So I was going too fast, because I would like to get to a break to hear your questions. So what is a? a is the natural length. OK? And the k-- what is k? Later, you will figure that out. You'll find that, actually, k is a wave number. OK? So that is actually much more of meaningful now, right? After the explanation. So you can see that beta is equal to exponential i, some number, and I call it k a, a fancy name of this number, and it has some physical meaning. OK? Another thing which is interesting is that if I plug in beta equal to a, or beta equal to 1 over a, into the same expression-- if I plug in either beta a or beta equal to 1 over a to this expression, I'm going to get exactly the same omega. So that means, OK, both of them will be-- both value will be oscillating at the same frequency. OK? So if you choose beta equal to a, choose beta equal to 1 minus a, they are oscillating at the same frequency. What does that mean? That means linear combination of eigenvector coming from beta equal to a and eigenvector coming from beta equal to one over a, linear combination of those eigenvectors are also eigenvectors of the M minus 1 K matrix. OK? And that's actually where-- OK, those are different eigenvectors for S, but the linear combination of these vectors are all the-- eigenvector of M minus 1 K matrix and always the same eigenvalue omega square. OK? So that's another thing which is important. And finally, I said that there are infinite number of choice of k. That's valid, right? Because you can choose a little number, then you get a corresponding beta, then you get a corresponding omega. So you have infinite number of normal modes. Secondly, if I give you a k, OK-- if I give you a k, or I can give you another value which is minus k, then that means you will get beta and 1 over beta. Right? Minus k will give you 1 over beta. Right? And as I mentioned before, beta equal to a and beta equal to 1 over a will give you the same omega. Therefore, a linear combination of the vectors are also eigen of M minus 1 K matrix. Though, that's actually what I am doing here, right? So in order to show you a real amplitude, I'm doing a linear combination of exponential i j k a, and exponential minus i j k a. It's just a choice. OK? Of course, you can say, OK, I choose plus, and divide it by 2, then you get the cosine. Right? But if I choose this expression, then what I am going to get is that, huh-- since both of them are-- both vectors are corresponding to the same eigenvalue omega square, therefore, linear combination of them also oscillate at the angle of frequency omega. Therefore, if I calculate this and make it real, then I find that the amplitude is a function of j. Is actually a sinusoidal function, which is sine j k a. OK? So what does that mean? This means that if I plug the a-- if I plug A j as a function of j, this is actually what I'm going to get. It's a sinusoidal shape. OK? And we know that x j is actually equal to A j cosine omega t plus phi. Right? Omega, I can actually evaluate that, right? From here, right? Just a reminder. And what we are going to get is, when this system is thinking of normal mode, OK-- actually, this system is still a discrete system, so i-- actually, would like to point out that as a function of j, only discrete location have mass. Right? So you see that those are individual mass. They are oscillating up and down. OK? And you can see that, OK, since they are oscillating up and down, therefore, the oscillation, essentially, going up and down. Therefore, what is the actually the normal mode of this infinity long system? The normal mode are actually standing waves. But they actually only appear in the discrete value of j. And it has a functional form of something like a sinusoidal shape, or cosine. OK? So that's actually what we learn, and actually, you can see that from here. So if I oscillate this at some selected amplitude-- OK? Not quite get it. Yeah. So you see that, OK, it's roughly like a standing wave. It's a fixed frequency. OK? I would like to discuss with you a really interesting selection. So if I now take a look at-- so we have went through a lot of math, right? So now is the time to enjoy what we have learned, right? So if I now take a extreme value, cosine k a, OK, equal to minus 1. OK? Then I am reaching the maximal oscillation frequency. Right? So if I choose cosine k, small k, a equal to minus 1, OK-- what is going to happen is like this. It is as a function of j, by product A j is a function of j, what you are going to get is starting like this. Those are actually the amplitude of individual mass. So you can see that if cosine k a is equal to minus 1, omega square, based on that expression-- 1 minus, minus 1, you get 2-- therefore, you get omega square equal to 4 omega 0 square. OK? And if you plug the A j as a function of j, that is actually what you are going to get. You actually have maximal stretch to the system. Right? You can see that it's actually positive, negative, positive, negative, positive, negative. That would reach the maximum speed of the oscillation. And of course, we cannot demo-- we cannot demo maximum, infinite number of oscillator, but of course, I can demo a system with 10 oscillators. So you can see that now, I maximize the amplitude of the highest frequency normal mode. And then I let go, and you see that this is actually exactly what is going to happen when I have cosine k a equal to minus 1. Then the wavelengths-- it's very small-- and you actually reach the maximum speed. Maximum speed is actually to become paired with, for example, lower frequency modes like this one. This is actually oscillating at a much lower frequency. And you can ask, OK, does that make sense? If I have this really, really zig-zag shape, why this system should be oscillating at the highest possible frequency? Why is that? It also makes sense, right? If you have that set up, then you are stretching this system to the maxima possible amount. Right? So, actually, now the springs looks like this. You are stretching this really hard, and therefore, the restorative force is going to be large. Therefore, you get high frequency. OK? OK, so I hope you actually enjoy the lecture today. It's a lot of mathematics, but what we have learned is really a lot. We learned how to actually describe system, how to actually solve a system without actually touching the M minus 1 K matrix; we can actually already get the eigenvectors. And using the M minus 1 K matrix, we can actually evaluate omega as a function of the input parameter from S eigenvalue. And the next lectures, we are going to discuss more examples, and make the whole system continuous. Thank you very much, and if you have any more questions, I will be here. I'm very happy to answer your questions. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 23_Quantum_Waves_and_Gravitational_Waves.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. YEN-JIE LEE: So what are we going to do today? So today, we're going to continue the discussion, based on what we have learned from the diffraction and also other interesting phenomena. And we are going to make connections to quantum mechanics and discuss in greater detail about this connection. And also, if time allows, we are going to cover information about gravitational waves as well. So last time, we have discussed diffraction pattern coming from a laser beam. And we discussed about resolution. And you can see that this is the graph we see, last time already in the lecture. Basically, all the point light source coming through a single slit is going to be doing interference to each other. So basically, you see interesting pattern, which you have a central peak. And the total constructing for interference happens at the center of the screen. And at some point, you have a deep-- which is actually where total destructive interference actually happened. And we were able to understand this with mathematics, which we learned in 18.03. Another interesting result we find is that, if we shoot a laser beam to the moon-- by now, you should be able to conclude that it's not going to be a point on the moon. Instead, it's going to be a spot as large as the whole Missouri state. So that's actually another interesting result we found from that discussion last time. And finally, we are able to put together all the things we have learned from the last few lectures. Basically, you can have, at the same time, the effect of multi-slit interference and also the effect of a single slit diffraction-- all then put together. Then you have this complicated but also beautiful pattern, which you will be able to observe on the screen. And basically, the point is that you are going to have, for example, in this case, five-slit interference pattern. But that is actually modulated. The intensity is modulated by the pattern from a single-slit diffraction. OK, so that is actually what we have learned from the last lecture. Coming back to the original question, why do we study 8.03? The reason is that we would like to understand-- we would like to hear from that universe. So we cannot even recognize the universe, without using waves and vibrations. So that's the course in which we have been doing here. And we have seen waves of matter. So for example, here, we have this water wave generator. You can see water waves. We have this Bell Lab machine. Because you can see the coupled oscillator-- a multiple coupled oscillator. And they are doing their job together to form beautiful waves. And you can see those beautiful results from there. Last time and also including the last few lectures, we have been using this laser to produce interesting interference patterns and the diffraction pattern. So that's the second kind of wave, which we encounter. The first kind is the waves of matters. The second kind is waves of what? Waves of vector fields. It's not matter anymore. Because this field, this oscillation field, can also travel through vacuum. So that is actually the second kind of wave, which we should learn for 8.03. They provide a pretty adequate description of the nature, description of the phenomenon, which we can actually measure, and see from the experiment we went over. So what I would like to say in the lecture today is that there are two kinds of completely different waves, which we haven't talked about. The first one is the probability density wave, which I will cover that in a few moments. The second one is gravitational waves. This is actually a space-time distortion coming from the motion of massive objects. And we would like to see what we can also learn from there, using the existing knowledge of which we have learned from matter waves and the vector-field waves. And that they are, actually, pretty similar to each other if you look at their behavior. So the first thing which I would like to discuss is light. So far, what is light? Light is like electromagnetic waves. So that is actually what we have learned so far from 8.02 and 8.03. So they are like waves. They are waves, all right. On the other hand, in the 20th century, there are many, many crises going on. So the first thing which is happening is photoelectric effect. So this experimental result was actually first discovered by Hertz. So he found that, if you want to kick one electron out of some material or some charged material, it is easier if you use a high-frequency light compared to low-frequency light. So that's the issue-- really strange. Because based on waves and also the intensity formula-- while we really care, intensity is proportional to the square of the electric field amplitude. So that's actually what we learned from the previous lectures. But what Hertz was saying is that the frequency also matters. OK, so that's really a bit strange. And Einstein actually came in and explained this photoelectric effect. So what we found is that this effect can be explained by viewing the light of small quantas. And light is actually not like waves any more, but like quantas-- the small quantas-- discrete ones-- with energy proportional to the frequency. All right? And basically, the energy of those little quanta-- or we now call them photons-- is actually equal to h, which is some constant-- relate the frequency and the energy of the quanta. And with this explanation, the view is that the photons are like particles. And therefore, he can actually explain that, OK, if I measure the kinetic energy, the maxima kinetic energy of the electrons, which are kicked out from this photoelectric effect experiment. I call it K-max. What you are going to get is a formula like this. The maxima kinetic energy of electrons will be equal to h bar mu minus phi. Phi is actually some kind of threshold, which you need or, say, some kind of energy, which you need to overcome to kick one electron out of the material. So you can see from here that, if the frequency of the light is too low, then this will never work. Because the maximum kinetic energy will be below 0. Therefore, you cannot kick out a electron. But if the frequency is high, as shown by Hertz experiment, it is possible. And also, you can create energetic electron, have them kicked out of the material. And this is actually verified by experiment. And that's essentially why Einstein should get the Nobel Prize in 1921. So let me tell you what the feeling here-- the feeling here is that, now, things are really becoming more and more interesting. Because first of all, we see really well that the electromagnetic wave describes the behavior of the light. We see diffraction. We see interference. All those things can be explained by the beautiful mathematics, which we have been employing to explain all those results. But here, you can see that, at the same time, the photons are very good tool or very good viewpoint to explain the photoelectric effect. So that's actually really surprising. Because that means you have, suddenly, both kinds of explanation of light, which should be describing the same thing. So now, one idea is to describe them by waves. The other idea is to describe them by particles. And also, at the same time, as we actually discussed in the previous lecture, we can do a two-slit experiment with billiard balls or with bullets. Suppose we do this experiment. We fire the balls or bullets through some source. And we have some kind of two-slit set up here, so that the bullets or balls can actually pass through. And then we were wondering, what will be the pattern which we see from the detector in the right-hand side. And basically, what we see is the following. So basically, we have a distribution of the balls coming from slit number one. And we have another distribution of balls, which is actually coming from slit number two. And I can call it P-1 and P-2, which is actually the probability density distribution of the experimental result. And the final result, or say, if you just look at the distribution of balls without separating the balls from slit number one and slit number two, basically you get some distribution like this, which is a superpositional P-1 and the P-2 distributions. All of these things doesn't surprise anybody. The experiment one, which we perform-- now, instead of billiard balls, we perform the same experiment with electrons. And again, we have all those electrons pass through this two-slit two-slit experiment. As we see before, basically, again, we can actually separate electrons from the first slit, which I called I-1, and the intensity of electrons coming from the second slit, which I called I-2. Then, basically, if you can identify and make sure that the electron is coming from one of the slits, you are going to get distribution like this. OK? And of course, I can always write these I-1 as a sine wave function, psi-1 squared. And I can always write this I-2, which is the intensity as a function of position of the electron coming from the second slit-- I can always write it as psi-2 squared. In the case of light, it's actually just proportional to the electric field. So if you accept this, and now you actually don't measure where the electron actually pass through when the electron from the source passed through this experiment-- we now don't measure if it passed through one or two. Then, the pattern becomes like this. You have something like this which, essentially, is very, very similar to the two-slit interference experimental result of the laser experiment. As you see from this experimental result, you see some kind of pattern. You have the peak. You have the valley, as a function of position in the detector. And we can actually call this I-1-2, which is actually when you don't measure or you don't identify which slit the electron goes through, then you have the intensity, which is actually called I-1-2. And what we actually found is that I-1-2 is actually not I-1 plus I-2. What we found is that I-1-2 is actually psi-1 plus psi-2 squared. So basically, we see interference pattern. And this will be equal to I-1 plus I-2 plus 2 squared root of I-1 plus I-2 and the cosine delta, where the delta is coming from the path length difference. So based on this experimental result, this is actually really surprising. First of all, electrons are arriving like a particle, right? Because we can see from this slide, if you look at the upper left figure, you see doo-doo-doo. Every time, you have something hitting the screen. And what is actually left over? It's a single hit on the screen. Therefore, the electrons are arriving like a particle, producing a hit in the detector. On the other hand, what we are saying here is that, before they hit the screen, they are behaving like a wave. It has interference with itself, like a wave. All right, so is electron a particle? Or is the electron a wave? Strange. The answer is electron is actually neither of them in reality. So how about we actually do some more experiments to convince ourselves what is actually really going on. So what we could do-- as I actually mentioned. I can still have the electronic gun. I have electron source in the left-hand side. Again, I have this two-slit experiment here. Then what I'm going to do is to produce a light source here. OK, I put a light source there to shine the whole experiment. Then, I was wondering what is going to happen to the distribution. So if I first close the lower slit, slit number two, and only measure the intensity coming front slit number 1, then this is the distribution I get, which is I-1. If I close the upper one and open only the lower one, I get a distribution which is I-2. And this light source, essentially interacting with the electron-- when electrons pass through this slit, what is going to happen is that you'll see some scattered light coming from the slit. Therefore, you can know which slit the electron actually passed through. And if I do this experiment result-- if I block one of the slits, this is the distribution, I-1 and I-2 and now I'm going to open both slits, and you will see light coming out of the slit when the electron pass slit number one or slit number two. You can identify which slit fora all the electrons passing through this experiment. And the resulting distribution of electrons on the screen is actually like this. It's actually like I-1 plus I-2. There will be no interference. Why is that? Now, this because you know very precisely which slit the electron actually passed through, this experiment. And also, we can say that, huh, the electrons are actually disturbed. Therefore, they now behave like bullets or like billiard balls. So this is actually a bit strange. Maybe it is because the intensity of the light is too large. Therefore, it's changing the behavior of the electron. So what are we going to do now? Experimental result number three is to lower the intensity of the light. So what will happen if I lower the intensity of the light source so that we would like to see the behavior, as a function of intensity? So at some point, we will find that some of the electrons are not heated by a photon. Or say, there will be no scattered light of the electron when it passes through the experiment. Because the intensity of the light is too small. And we already know, from photoelectric experiments, light is, essentially, also like quanta. So when the intensity is low enough, the effectiveness of the light source decreases. Then the experimental result would be like what? Can somebody actually give a guess? Is that going to be like experimental result number one? Or is that going to be like experimental result number two? Anybody want to get-- AUDIENCE: [INAUDIBLE] YEN-JIE LEE: Very good. So the result-- as I mentioned before, sometimes the electrons are detected by the light source. Sometimes the electrons are lucky. They pass through without getting heated by a photon. Therefore, you cannot know which slit, actually, this electron went through. Therefore, the experimental result is that, if I just lower the intensity of the light source, then what I'm going to get is a mixture of experimental result number one and the experimental result number two. When I have the intensity low enough-- going to really, really low intensity limit-- the result will become experimental result number one. Because then you are not really impacting the position of the electrons. Finally, you can actually suggest something else. So OK, now I have low intensity of light. One way to lower the intensity is like what I was saying. The rate of the photon emission-- I can make it lower and lower. All right? There's another way to do this. Experimental result number four-- so what will happen if I use this formula E equal to h bar mu equal to hc divided by lambda? Because mu is actually just c over lambda. What will happen if I, instead of lowering the rate of photon emission, I lower the energy of individual photons? How do I do that? What I could do is to lower the frequency of the electromagnetic wave of the light source or, say, increase the wavelengths of the light source. OK, this is very nice. Because now, I can keep this in, right? So that I make sure all the electrons are bothered by the photon. Because I can emit very high rate. But at the same time, I can also lower the intensity, so that the intensity is very, very low. Can anybody guess what is going to happen? With a result like experimental result number one, when I go to extremely low intensity? Or my result will be like experimental result number two? Because each electrons are bothered, are heated, by the emission from the light source. Anybody want to try? Just guess, no? One or two? Or a mixture of them? AUDIENCE: Be like two. YEN-JIE LEE: The guess is that it's going to be like two, which was actually well-motivated. Very good try. What essentially, happens is that-- OK, I can say, oh! Each electron are bothered by many, many photons. So those are disturbed. Therefore, it has to look like experimental result number two. The answer may surprise you. The answer is that, if I have the limit lambda goes to infinity, mu goes to 0, what is going to happen is that, no matter how high frequency of photon emission I have, I am going to get the result of experimental number one. Why is that? Now, this is because when the wavelengths of the electromagnetic wave or the photon is going to infinity, that means you cannot resolve which slit, actually, the electron goes through. Because if I draw the wavelengths here, it's going to be like this. If you observe some kind of scattered light from the electron, it could come from both slits, because the wavelength is too long. So if you go to infinity, then it's like you have a constant electric field there. It doesn't really actually help you to identify which slit the electron actually passed through. So therefore, the interference pattern reappears. So this is really crazy thing, if you look at all these four experimental results. The conclusion from these four imaginary experiments is that it is not yet possible to tell the position of the electron and also, at the same time, do not disturb it. If you were able to tell the position of the electron, then there would be no interference pattern. On the other hand, if your experimental set-up have no ability at all to tell if the electron's coming from slit number one compared to slit number two, then you are going to get interference pattern. There's another thing which I would like to make connection to the Uncertainty Principle, which we actually learn from waves and vibrations. So we have learned that Heisenberg's Uncertainty Principle-- this is essentially purity coming from the property of the wave, if you actually remember the deviation which we have done in the previous lecture. So what is this uncertainty principle telling us? Is that the standard deviation of the position times the standard deviation of the momentum is going to be greater or equal to h bar over 2 some constant. And how do we actually understand this from the electron experiment. That is actually highly related to the single-slit experiment with electrons. So what we could do now is to have a fifth experiment. I have electron source here. And I have a single slit. And the width of the slit is capital D. And we were wondering, what is going to happen? What will be recorded by the smoke detector in the right-hand side? And by now, it should not surprise you that this would give you some kind of diffraction pattern, which you say should be very similar to what we actually observe with laser experiments. So you can see that. The electron-- the momentum-- now, I would like to actually define my coordinate system. The vertical direction, pointing upward, is my x direction. So now, take a look at this experimental result. So what this is actually telling us is the following. We know the position of the electron to a accuracy of the width of this slit, which is D. So that is actually telling you about the uncertainty over the position in the x direction. Now, this electron goes through. And they actually hit the screen. And each electron is having a single path. If I look at one of the paths, the upper one, what I'm getting is that there must be a momentum quintessentially in the x direction, when this electronic goes through the slit and hits the screen. One interesting thing we learned from the deviation from last time is that, if I just look at the slide here-- if I look at the left-hand side slide-- if I have a very small slit-- D is small-- what does that correspond to? That corresponds to delta x goes to very small value case. We have a small delta x value. You are really sure where is the electron at some instant of time, when it passed through the experiment. Then what is going to happen? If you look at the right-hand side, the distribution on the screen, you have a wide distribution. The central maximum peak will be very wide. So what does that mean? That means you have a wide distribution of momentum in the x direction. Therefore, that will give you that is actually consistent with what we've actually written here, Heisenberg's Principle. Delta x times delta p will be greater or equal to some value. On the other hand, if I increase the width of the slit, the D is now large. As you are making a D larger and larger, what is happening is that the central peak, the width, is actually going to be narrower and narrower. Now, this is actually also consistent with what we have learned from Heisenberg's Uncertainty Principle. When delta x become even larger, then the uncertainty or, say, the distribution of the momentum in the x direction, becomes smaller. So now, we actually also understand a little bit more about what the single diffraction actually means. And this issue is really closely connected to the Uncertainty Principle Heisenberg actually proposed. And if we use the mathematics which we learned from last time, the C function is going to be proportional to integration from minus D over 2 to D over 2. dx exponential as ikx times x. And if I have D goes to infinity, which means that you have an infinitely wide slit-- based on the formula which we have derived last time-- basically, we will see that C function is a function of kx. It's going to become a delta function. And this delta function is delta kx. So that means, if you have absolutely no idea about the position of the electron, you are going to get very, very precise information about-- the momentum in the x direction is actually going to be equal to 0. Because it's a delta function. It's only nonzero at kx, which is the directional propagation equal to 0. Any questions so far? OK, so from those experimental results, we've found that the probability of getting heat on the screen is proportional to psi-1 square, if I only have the first lead there. That means the probability, p, is proportional to psi squared. And this is actually probably one of the most crazy results in the physics we learned so far. In some sense, it's kind of sad as well. Why sad? This means that, OK, I can calculate those wave functions. And the probability of getting an outcome at a specific position is proportional to this wave function squared. But I feel, maybe, demotivated, right? Because originally, we are like god. You can predict-- OK, I have this thing, this object. And I have force. And then it goes like-- oh-- like this way. I can calculate the trajectory of this chalk thing all over the place, as a function of time. And I know what is going to happen. I have the full control of all the objects which I have in my hand in my experiment. But now, quantum mechanics or this experimental result tells me that we can only predict the probability, the odd, instead of the outcome. You see my point? I can only pretend the wave function, the distribution of the wave function. And the probability of getting a result here is proportional to the wave function squared. But I cannot predict the outcome before I do the experiment. That's really a big change in your view or, they say, in our current understanding of the physics. You can say that, well, maybe Yen-Jie's not working hard enough. Maybe all those electrons which are emitted from the electron source already made up their mind where this electron is going to. For example, electron number one is doing this-- rrrrr-- and going to here. And electron number two already made up his mind. He's just going to do this. And the electron number three is-- uh-- maybe do this-- vwooo-do-do-do-do. And then all those trajectories are already determined. And they are heating variables which Yen-Jie doesn't know. Therefore, he screwed this up and said, oh, come on. We can only predict the probability. But the thing is that, from the experimental result number two, experimental result number three and number four, you can see that the electrons cannot make up their mind when they are emitted. Because when they got heated by that light-- electrons cannot know in advance that it is going to be heated by a light. And the light can be a very, very mild, very, very small energy. So that it should not affect the predetermined path of the electron. Do you get this? So that doesn't makes sense. So it is not because Yen-Jie is not trying hard. It is really because nobody can really tell before the experimental result is actually shown or the measurement is already done. If you can find any case, maybe you will win another 100 Nobel Prize. Because you are showing that the whole understanding of quantum mechanics is not correct, really. Please tell me when you actually have done this experiment. I will be very proud of you, for sure. So now, we are entering a position to discuss this result. So now, actually, we can also make use of this understanding and predict what would be the particle probability distribution in a potential well. Suppose I have an experiment, which I have a well, where I have potential goes to infinity in the left-hand side or right-hand side edge of this well. And I will define my coordinate system so that the well is actually equal to 0, or x equal to L. So by now, when you see this, this looks really familiar to you. In the center part, you have some kind of translation symmetry. And the boundary-- those are forbidden regions. You cannot actually have particles there, because the potential is infinity. Therefore, this is actually giving you boundary conditions of the wave function, describing the state of the particle inside this box. So the boundary condition would be psi 0. It will be equal to 0, because it's actually at the left-hand side edge of the well, where you have infinite potential. And also, you can have psi L. This will be equal to 0, because the right-hand side edge, you also have infinitely high potential. Therefore, when you see this, your immediate reaction will be, how do I know what is this? This is actually psi m. The solution to this problem must be something like psi m of x should be the normal mode of this system. And it's going to be A-m sin km-x, where km will be equal to m-pi divided by L, where m is a number. It can be 1, 2, 3-- it goes to infinity, right? By far, you have actually learned all these practical calculations from the previous examples we had. Therefore, what would be the psi m, x as a function of time? Then what I am going to get is A-m sin km x exponential minus i omega-m t. Of course, we can also really plot all those results. So for example, n is equal to 1. Basically, what you are getting is like this. Doesn't surprise you. This is actually psi as a function of x. And n equal to 2-- this will correspond to the situation where you have one node in the middle, et cetera, et cetera. You can't have many, many higher m value solutions. And what would be the probability to find the particle in a specific location? That's why we mentioned before, the probability is proportional to a wave function squared. Therefore, the probability will be proportional to sin squared k-m x. And what we are going to get is like this. If I plot m equal to 1, using P as a function of x, the probability of getting a particle at a specific place, if we are looking at the situation in normal mode number one, that is like this. You are much more likely to find a particle in the middle of the box. On the other hand, we can also plot the probability as function of x, where m equals to 2 k's. If we are actually operating in a second normal mode, then basically you have some distribution-- looks like this. In this situation, it is forbidden-- or say, there's zero probability you will find the particle in the middle of the box, et cetera, et cetera. You can actually calculate all those corresponding probability distributions as a function of m value and as a function of position. OK? Sounds like a very good story. But there's something missing, right? What is actually missing? You have the normal modes. You have the k-m. What is missing is the wave equation. The wave equation is missing, right? You don't have the dispersion relation. This solution is incomplete. You don't know what is actually the omega value. Because you don't have dispersion relation. So what is actually the wave equation for the quantum mechanics? So it is actually Schrodinger's equation. So Feynman once commented on the origin of the Schrodinger's Equation. It's from where? It's not possible to derive it from anything you know. It's just coming out of the might Schrodinger, actually. So there's no reason. And it works. That's the beautiful part. So what is, actually, this equation? So this is the equation Schrodinger actually writes down. It's like i h-bar-- Plank's constant, partial/partial t, psi xt. And this will be equal to minus h bar squared over 2m partial square, partial x square, plus v xt, psi xt. So this is really nice. And it works and matches with experimental results. And now, I have already the normal mode. I can plug that into this equation to see what I can actually learn from there. So what I am going to do is to plug in psi-m xt into this equation, to get the dispersion relation. So what this issue, the dispersion relation. So here, I have partial/partial t. So I extract one omega minus i omega out of this. Then, basically, I get h bar omega-m psi-m xt in the lambda psi. OK, plugging in psi-m into this equation and see what happens. Then this will be equal to-- I also know that, in the middle of the box, v, essentially, the potential-- the potential is 0 inside the box. The potential is infinity at the edge of the box. Therefore, I can safely ignore this term, to be equal to 0. So you have a free path to go inside the box. And what, essentially, this term-- this term will give you minus h-bar square over 2m. OK, I have a double differential of x. And therefore, I get, basically, minus km squared, right? Because it's psi zeta, right? So basically, I get minus k squared. So therefore, I cancel this minus sign. I have km squared out of this calculation. And I still have psi-m xt. I can cancel this too. Then, what I'm getting is that omega-m is equal to km squared, h-bar-- I cancel one of the h-bar here-- divided by 2m. This-- essentially, dispersion relation of the wave function. De Broglie proposed that wavelengths of the matter wave, essentially, highly related to the momentum of the matter. So basically, he propose that p, the momentum of the particle is actually equal to h-bar k, where k is the wave number of the matter wave. If you accept de Broglie's interpretation, basically what we are getting is something really, really interesting. If we put together this dispersion relation and the de Broglie's interpretation of matter wave-- what I am going to do is to calculate the group velocity of this dispersion relation. So I can now calculate-- group velocity, V-g, will be equal to d omega, dk. And I know that omega is equal to h-bar k squared divided by 2m. This is essentially equal to h-bar k divided by m. Everybody is following? OK. And this is equal to what? This is equal to p divided by m, if I use de Broglie's matter wave. Therefore, you have p equal to m times ng. Wow! Look at this. What are we getting here? What we are getting here is that the group velocity of the wave equation of the waves is actually the classical velocity, p equal to m times v. Now, everything actually is becoming more and more clear. We know and we learned already, from 8.03, what is the meaning of group velocity. The meaning of the group velocity is the speed of the propagation of a wave package, right? Remember our discussion before about a AM radio? So what is actually the speed of propagation of a wave packet is the group velocity. So now we have solved the problem-- why electron can be a particle, at the same time, also like waves. It's essentially described by wave functions. The classical behavior we see on the electron is because it is, as you described, by these wave packages. It's pretty localized. And the motion of this wave package in a free space is actually the speed of the propagation-- is the group velocity. Therefore, there is no contradiction between the classical calculation and the wave interpretation of the electron. So that really surprised me very much. And you can see that, given the dispersion relation, also, this is a rather dynamical result. The real part of the wave function is actually blue. And the imaginary part is actually red. It's actually oscillating up and down. And the oscillation frequency, by now, you know is governed by that dispersion relation. OK, now actually, everything seems to make sense now-- really, really, very cool. So on the other hand, we also have to live with probability density. So you cannot tell the exact position of a particle any more. You cannot tell the exact outcome of an experiment anymore. And that is actually to do with this interpretation. And all of those phenomena, at a very, very small scale, is actually described by quantum mechanics, which we will learn some more in 8.04. And also, in the future, you will be governed by the quantum field theory, which is actually a father future. And what is actually the life living with quantum mechanics and quantum field theory? So this is a very simple-- [LAUGHTER] --Lagrangian of the standard model. And it describes everything except the gravity. OK? And it's really simple. It's called Standard Model. And look at this part. This is governing the Higgs decay to Z boson. And the experimental result-- we don't really know what is the mass of the Higgs. It's a missing observable before. And on the other hand, as a particle physicist or as a high energy nuclear physicists, I have no idea about what will happen in the next collision. Why is that? You know the reason now, right? Because we cannot predict the exact outcome of our experiment. It's all governed by wave functions. Therefore, what we are doing is the following. We are doing the brute force. So we collide like crazy-- collide, collide, collide, collide like crazy, until something interesting pops out. That's actually what we're really doing as a particle physicist. And this is your beautiful event from proton-proton collisions at the Large Hadron Collider-- is a Higgs to the boson event. And one of the Z bosons becomes the two red lines. It's actually the two muons. And the other decays to electrons, which are detected by the kilometer as the two blue things there. As a high-energy nuclear physicist, I am interested in the production of quark-gluon plasma from lead ion collisions. So I am now putting together two ions, have them collide. And I hope that, by chance, I can deposit a huge amount of energy in a very small volume. And then I would like to see this crazy matter, actually, gradually expand and become a lot of particles. And I study those particles to understand, what would be the nature of this material, which starts to exist in the very early part of the whole universe history? Just one microsecond after the Big Bang, we have the whole universe filled by this crazy material. And we are creating this in the experiment. And we will only be able to hope that, OK, by chance, I have the collision happen. By chance, I have a very high-density environment. Somehow, multiple quanta decide to scatter on each other. And they deposit the energy in a very small volume. And then we collect all those spectacular events to study the properties of all those little Big Bangs. So that is actually the consequence of this wave function interpretation. So now, coming back to the Standard Model, this really simple one, you can't see, that is a theory of almost everything, except the gravity. Really sad. So if you can actually put them all together, then you will also win the Nobel Prize. And giving you all those ideas, so that I can have a very good student winning the Nobel Prize. Of course you will. And now, I would like to discuss and use the remaining, maybe, 10 minutes to discuss with you the gravity. So here is actually something related to gravity. So Einstein actually predicted that the distortion of the space-time generated by objects can travel through the space. I don't have the derivation here, because it would take another, maybe, two hours to do this. But I would like to ask you to trust me. This is actually a result coming from general relativity. And you can see that we can actually generate gravitational waves. And I can actually do the generation here, like this and rotating. I'm generating gravitational waves. And that student in the back is also generating. Yes, you are. Yeah, you are generating. Everybody's generating. Ah, you are also generating. Yeah, very good. But the problem is that the space-time distortion is really small for people who are not very massive, like me. So that's a problem. So I can generate. I'm doing the demo here. But it doesn't help. You cannot really detect them. And even Einstein himself thinks it's impossible to detect them, maybe, in our lifetime. And what would be the outcome of the calculation? The outcome of the calculation-- if you have gravitational wave passing toward you-- so what it does is the following. So basically, the space is distorted in a way such that it first expands in this direction and then expanding the other direction, perpendicular to the original distortion. And if you put a ray of particles, the circular array of particles, and look at what is going on, when the gravitational wave pass through it, it pass through the array in this direction, what you are going to get is effect like that. Of course, this is actually highly exaggerated in this set-up. You don't really see this kind of sizable distortion when Yen-Jie is dancing around. OK, so how about we actually visualize this thing. The problem is that we cannot really see the space distortion. But what we can, as you see, is the light which actually pass through those little distortions. So this is a stimulation from LIGO Collaboration. They are simulating the merging of the two massive black holes. And you can see that they are rotating with respect to each other. They are radiating energy out of this two-body system. Let's take a look at this again. So this is actually a simulation of the event observed by LIGO. So both black holes have a mass roughly 30 times of our sun. It's very massive. And they are rotating with respect to each other. And that generates space-time distortion. And you can see that the space-time distortion stops after they merge each other. And we were hoping that we can detect those. How crazy is that? So how do we detect them? Actually, you already have the knowledge to design the experiment to detect this kind of effect. So remember, the effect of the gravitational wave is like this. So you have distortion like this. What we actually-- MIT and Cal Tech and the many other collaborators designed the LIGO experiment. Are what is, actually, LIGO? It's a Laser Interferometer Gravitational wave Observatory. It is actually always good to have a very good name of your experiment. So this is actually LIGO. So what, actually, it does is the following. So basically, it emits a laser. And you split the laser into two pieces. And there were mirrors in the very far end, reflect those lasers. And they come together. And there is a photo-detector, which detects the interference pattern of these two optical path lengths. Wow! Sounds familiar to you, right? Hey, you already know how to explain this to your friends already. Really cool. And in order to have redundant management-- for example, if you only have a single experiment, maybe one graduate student is like, oh, doing dancing next to a detector. Then you see some fake signal. And that's not going to be helpful. So what it does is that-- basically, we have two experiments. One is actually in Hanford. The other one is actually in Livingston. And they are actually 3,000 kilometers away from each other. So that there should not be any correlation between the signal coming from a earthquake or dancing of the graduate students or whatever. So they can you use that to suppress any coincidence which is actually not related to gravitational waves. So what does this do? So now, we have, oh, the knowledge to actually explain this phenomena. So what this does is the following. So you meet the laser. And when the gravitational waves come in, then it does this space-time distortion. And then the interference pattern of the waves going through different optical path lengths is going to change. So you can see that, originally, the experiment is designed so that you have complete cancellation. But when the gravitational waves is hitting the side, you will be able to see that. Really, you have constructive interference at some point, because of the movement of the mirrors. And those mirrors are really, really far away from the sources. Each of them is, like, four kilometers away from the mirror. And due to the incredible precision which were achieved by this experiment, we will be able to detect this signal of gravitational waves. So you can see, again, from here-- so basically, when the gravitational wave comes in, first you split the light source into two pieces, have them hit the mirror, which is actually four kilometers far away from each other. And they come back. And initially, the experiment is designed so that, very precisely, there will be no amplitude detected by the photo-detector. And when the gravitational waves come in, you actually really change the length between a splitter and the mirror. Therefore, you see light, constructive interference even, from the photo-detector. So that is really cool. And this is actually the experimental result. Look at this. You actually can see that light actually achieve the sensitivity. The gravitational wave was first observed on September 14, 2015. And the LIGO is actually announcing that February 11-- earlier this year. And what we actually see from here is that this is actually-- as I mentioned to you-- there are two measurements, two sides. The left hand side is actually the measurement from Hanford. And the other one is actually the measurement from Livingston. So they are two different curves. And they all have almost exactly the same pattern. Of course, there's time has actually shifted, because they are in different places on the earth. They are 3,000 kilometers apart. So therefore, there will be a shift in time. And this is actually a time-shifted result. And you can see, also, the calculation below, which is actually what you should expect if you have the merger of the two massive black holes. So you can see that they are actually rotating with respect to each other. One of them is actually 29 times larger than the mass of the sun. And the other one is 36 times larger than the mass of our sun. It's not precision. And they generate, theoretically, this kind of pattern. And this is actually really detected by both LIGO experiments, which lay at 3,000 kilometers apart from each other. So I think this is really a historical moment-- that we actually were very lucky to live in this moment. What does that mean? That means we have a new way to really hear about what the universe is actually trying to tell us. We have a new way to detect phenomena, which is actually really happening very, very far away from the Earth. How far is, actually, this event? This event, according to calculation, is actually something like 1.3 billion light years away from the Earth. And we can detect that. And we even know the mass of the two black holes. Wow! What does that mean? This is really crazy to me and really exciting, because we are opening up-- OK, I have two ears. And it's opening up another ear in my brain. And that is actually the way to hear the gravitational wave with the experiment we've performed on Earth. So I hope, until now, I have convinced you that this is really not the end of vibration of waves, which is actually the end of 8.03. Instead, this is actually just the beginning. You have a lot more to explore when you take general or special relativity course. You have a lot, really, more to explore when you take quantum mechanics. And I hope you really enjoy the content of this course. Personally, I really enjoy that very much. I love this course. And I hope you also love it and understand something from my lecture. And thank you very much. And the next time, we are going to have a review of all concepts we have learned from 8.03 next Tuesday. Thank you. [APPLAUSE] Thank you very much. |
MIT_803SC_Physics_III_Vibrations_and_Waves_Fall_2016 | 15_Uncertainty_Principle_2D_Waves.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MITOpenCourseWare at ocw.mit.edu. YEN-JIE LEE: OK, happy to see you again. Welcome back to 8.03. Today, as you see on the slide, we're going to continue the discussion of dispersive medium-- how the waves and vibration should be sent through this medium. And also, we will learn about uncertainty principle today. Kind of interesting. That is connected back here to what we discuss here. And finally, if we have time, we'll move to two-dimensional system and three-dimensional system to look at two-dimensional waves and three-dimensional waves. OK, that's the plan for today. Just a quick review about what we have learned so far. Last time, we discussed about shaking one end of this dispersive medium which is actually a string with stiffness. And basically you would see that the strategy that we have been following is to do a Fourier transform to actually decompose the motion of the hand, which is actually holding one end of the string, and then decompose that into wave population in frequency space. OK, so that's what we have been doing. And then, we know based on the property of this medium, the dispersion relation, which is omega as a function of k, we can propagate waves with different frequency at different speeds. Then we can see how this system will evolve as a function of time. That's the whole idea and the strategy we approach this interesting problem. Last time, we also introduced AM radio. As we discussed before, if we have a very simple-minded strategy to just send the pulse-- which is containing information-- directly through this medium, due to the dispersion relation which we have this medium, different component would be traveling at different speed. Therefore, the information is smeared out after it travels through a long distance. OK? That's the problem. And then the solution was to use this approach, which is amplitude modulation mixer. That's actually how AM radio works. So basically, we have a slowly oscillating message or signal like music or voice which we want to send, and then as we multiply that by a really fast oscillating cosine tan. If we do this, assuming that omega of 0 is actually much, much higher or larger than the typical scale of your signal-- which is omega s-- then, what is going to happen is the following. Up to all the calculations we have done last time, we found that the resulting wave which is the amplitude as a function of time and space, you can see that this can factorize into two components. The first component is virtually the original signal you are trying to send. Since you're traveling at the speed of group velocity, and finally, the right hand side-- the second component-- is actually the contribution, the really small structure of these high frequency oscillation. We call it carrier, and the carrier is still traveling at the of face velocity. That's how we actually finally understand what is the meaning of group velocity and the face velocity through this example. What I am going to do today is to guide you through another example which will ensure we can learn some more insight from this calculation. Today, we are going to have another test of function, which actually I can do Fourier transforms really easily. And this function I'm trying to introduce here, I have this functional form exponential minus gamma times absolute value of t, OK? The reason why I choose absolute value of t is because I would like to make it symmetric around 0. I can now do the usual Fourier transform and then to extract the wave population. The function of angular frequency, c omega. c as a function of omega. And according to the formula here, which we introduced last time, we can quickly write it down like this. Basically you get 1 over 2 pi integration from minus to infinity to infinity integrating over time. This is the original function, f of t. And multiply that by exponential I omega t. And that's the way we extract c omega. OK? Since we have this absolute value here, basically the trick is to change the interval, split the interval into two pieces. So, y is actually the negative t part, therefore, you get the exponential plus t here, and the other part is from 0 to infinity. Then the absolute value doesn't change side. You have the original exponential minus gamma times t. Then you can go ahead and do with integration, and you get the two turns and you get the functional form, which is c omega equal to gamma over pi times gamma square plus omega square. OK? From this simple exercise, they are interesting things which we can learn from here. If I go ahead and draw f of t as a function of time, this is what you will get. Suppose I set gamma to be equal to 0.1. And I would like to visualize this function and that's what we did here. You can see that from the left hand side here, is f of t as a function of time. And you can see that this like exponential of t k but symmetric that mirror at the t equal to 0. And with a small gamma value I choose, that means this exponential decay will be really slow, therefore, you have a pretty wide distribution as a function of time. However, if you look at the right hand side, what did I show you in the right hand side? Right hand side is c omega, c as a function of omega, it's the population in frequency space. And you can see that, if I plug in gamma equal to 0.1 into that equation, then you would get a distribution which is actually pretty narrow, around 0. That's actually quite interesting. And now, if I change gamma, I increase the gamma slowly so it changes to 0.2, you see aha, that's what I expect-- the f function graphed in the coordinate space becomes narrower. But, on the other hand, you pay the price that the wave population in the frequency space becomes wider. OK, the distribution become wider. I can increase and increase. Now it's gamma equal to 0.5. Gamma equal to 1. And now I have a rather large gamma. Now it says 2.0, and you can see that as a function of gamma, if I set the gamma to be 5, and you can see that the wave, or say the waves of the wave in the coordinate space, becomes really small. But if you look at the corresponding c function, you can see that waves becomes really large. This seems to be telling us something interesting. It seems to me that I could not choose a gamma value which simultaneously make waves in a coordinate space narrow and those wave populations in the frequency space narrow at the same time. I cannot actually do that based on this simple-minded exercise. And what you are going to do in your p-set is to go through another parameterization, which is a Gaussian distribution. And you will see very similar, hope for these very similar conclusion from your exercise. So what is going on? And how do we interpret this result? And why is this result actually related to uncertainty principle? That's the first part of the lecture, which we are going to discuss today. We can demonstrate this in fact by one example of f of t, which is showing here. And we go through and change the waves of this distribution. Of course, we can also try to show this in a much more precise mathematical definition. That's what we are going to do now. The first thing which we would need to do is to define how to quantify the waves of the distribution in frequency space and in coordinate space. First, we define that the intensity of the signal is proportional to f of t squared. OK, that is the to estimate the size of the intensity. It kind of makes sense because, for example, the energy of the electromagnetic wave is actually proportional to the wave function squared. That's kind of reasonable to choose this definition. And then, once we have that the definition of intensity, then I can now calculate the average of some operator function. For example, I can calculate g of t is a average of the g function. And in this definition of intensity, how to calculate the average is to do integration over minus infinity to infinity over t. And this g function is put right there and all the components are weighted by this intensity estimator, which f of t squared. Of course, since we are actually calculating the average, we need to take out the sum of the intensity. So, the sum of all the intensity is an integration from minus infinity to infinity-- dt f of t squared. With this definition, we can calculate the average. OK and don't forget our goal is to have an estimator estimate the waves of sum distribution. Therefore, you are probably very familiar with that. We use standard deviation. So basically that's also usually associated with the exam, but this time it's associated with some physical quantity. what is the estimator of spread of time? Right. We can actually make use of this definition and I can write this notation that t-squared to be a quantity which is associated with the size of spread in time. And now as you define to be the average of t minus average of t squared. Basically you calculate that difference with respect to the mean value, square it, and then do the two averages again. All right, everybody is following? Any questions? OK. If I have this so-called standard deviation or spread of time definition here, then I can write it down explicitly, and this will become minus infinity to infinity, to disintegration over t, and I have t minus n value of t, half of t squared. And of course I would take out that normalization, which is a minus infinity to infinity dt f of t squared And I can also do a similar exercise for the frequency space. Basically, I can define the spread of the frequency spectrum. And that I define it to be delta omega squared, and this will be defined as the average of omega minus the mean value of omega squared. And with this definition, we have an estimator of this spread of time, and we have an estimator of spread the frequency. The phenomenon which we see from here, from this exercise, going from low gamma value to a large gamma value is that it seems to us that the spread of the time or in coordinate space and the spread of the distribution in the frequency space cannot simultaneously be small. OK. Therefore, based on this mathematical definition, our goal is now to show that we can prove that delta omega times delta t will be larger or equal to 1/2. That is an interesting consequence based on this definition of spread. We can actually achieve the lecture today. That's our goal. And we are going to try to achieve this goal. Before we go ahead and prove this relation delta omega times delta t greater or equal to 1/2, we also realize that when we discuss this spread of the frequencies spectrum, if I write it down here, if I try to calculate the average of omega, then what I'm going to do is to do the integration from minus infinity to infinity, d omega. because now I'm trying to calculate the mean value of omega. I have the omega times c omega. And the exponential is i omega t. If I go ahead and evaluate this integral, I integrate over omega, and I have omega times c omega times exponential i omega t. And you can see that this omega can actually be extracted from this exponential function. If I do differentiation, which is spread through time, then I can actually extract one omega out of the initial function. Therefore, what I'm going to get is this will be equal to i partial t minus infinity to infinity d omega, c omega, exponential minus i omega t. So you can see that this is the design if I do a partiality relative to with respect to t, then I take minus i omega out of this exponential function and this i will make minus i become 1. Therefore, you can see that this integral, which I construct, is equal to i partial, partial t. This function. OK, and you can quickly realize that we know what this integral is doing right. According to the form which I just did here, f of t is equal to this integral which I actually just highlight there. Therefore, this is just f of t. that's kind of interesting because that would give me i partial, partial t, f of t. Basically you can see that I don't need to deal with omega, I can actually do a partial relative with respect to time, then I can take one omega out of the function which I have constructed. Any questions? All right, now I can calculate what will be the mean omega. What would be the mean omega? The mean omega, according to this definition here, this is how we calculate the mean of some quantity, mean omega will be equal to minus infinity to infinity, tt f star, t i partial, partial t, f of t. OK sorry that this is kind of close to here. The original definition I should put omega got here, right? But instead of putting omega there, I used the trick that this i times partial partial t can generate an omega for me. Therefore, instead of putting omega explicitly into the integral, I put i partial partial t into the integral, then I get 1 omega out of it, and that's equivalent to the calculation with g of t equal to omega. OK, everybody's following? Therefore, I of course still need to normalize the calculation. This is the denominator, which is minus infinity to infinity, integral over tt f of t squared. OK, you can see that instead of using omega directly, the I used this trick to use i partial partial t to extract 1 omega and I can calculate the mean value of omega. Therefore I can also calculate explicitly what would be the delta omega square based on the definition which I outlined before. This would be the average value of omega minus mean omega. Mean omega is a number, and if I'd write it down explicitly I get minus infinity to infinity, tt, i partial partial t, minus average value omega, f of t squared divided by minus infinity to infinity disintegration over dt f of t squared. The take home message is that I'm using this trick to replace all the omega by i partial partial t. Therefore, in my formula, you will see that originally, this is supposed to be omega and now we were using that trick. Therefore, it can be written as pi partial partial t. And you'll realize what this is used for afterwards. All right, so those are just preparation. What we have done is that my goal is to show that delta omega times delta t is greater than or equal to 1/2. OK, that's my goal and I'm preparing for that. And I have that definition of delta t and delta omega. Yes? AUDIENCE: What do you think [INAUDIBLE] YEN-JIE LEE: Oh sorry, there should be-- it should be like this. So I am taking partial partial t out of f. OK, sorry. Good question. Any other mistakes? Very good. Not yet? All right. So now you can see that I have the definition in my hand, and I am almost there to show you that delta omega times delta t is going to be greater or equal to 1/2. And what I'm going to do after this-- maybe you will be even more mad at me-- is to use exactly the same trick which would be used to show Heisenberg's Uncertainty Principle in quantum mechanics. basically what I'm going to do is to consider a function which is r of t. r as a function kappa and t. and the definition of this r function is like this. I define this r function to be t minus average t minus i kappa i partial partial t minus omega. f of t. If you don't know where is this relationship coming from, don't be worried because you don't really need to. This is just to guide us through this mathematical calculation. But if you can see directly how this will help, the maybe you are Heisenberg. Maybe. So that's very nice. It's a test. What I am going to do is to employ this r as a function of kappa of t. And the 2 for our purpose to show that the delta omega and delta t greater than 1/2. And first, to make my life easier, I would define this to be capital T, and I would define this thing to be capital omega. So that my mathematical expression doesn't explode. Now I can consider this ratio function r of kappa. This is defined as minus infinity to infinity integrating over t r kappa t divided by minus infinity to infinity dt f of t squared. This is r function which is the ratio of the area of r function and the area of the f function. You may say that, professor, this is really crazy. Today is telling about all the crazy things, but that is because I would like to let you know that we are going to see a very interesting result. So that's why I'm doing this. And if I construct this r function, this r function will have an interesting property. What is the interesting property? I entered an integral over something squared in the numerator and the denominator. Now it means, what would be the value of this r function? The r function would be always positive. Right? Because this is a square, this is a square, therefore, r is going to be positive. That means r is going to be greater than or equal to 0. That's why we have this r function. And the miracle will happen because if I go ahead and calculate this r-- before I calculate this capital R function-- what's the function of kappa, I need to actually deal with this small r as a function of kappa and t squared. If I extract this component and then calculate that, r kappa t squared. What I am going to do is to use this expression r is equal to t, capital T minus i kappa omega times f of t. So that my life would be easier. Then basically you get t minus i kappa omega f. And then you need tje complex conjugate. Basically, you get T cross i kappa omega star f star. You can have T star, but T is a real number. Therefore, it doesn't do anything. Then, I can now go ahead and collect all the terms. Then the first terms which I can collect is everything related to T times f. Then basically you get the T f squared. That is coming from this T times f times T times f. This term times this term times this term. to give you the first term. And you also you can connect another term which omega f squared. Right. Basically, you can find that contribution. Use should have a kappa square in front of it. Any questions so far? Basically, I collect the terms related to omega times f and put it here. Finally, you have the third term, which is i kappa T f omega star f star minus omega f T f star. Basically, this small r function squared can be written in this functional form. We are almost there. What I'm going to discuss first is that now I have these three terms. Number one, number two, and number three. I can now attack number three first. Number three, I'm going to get i kappa Tf minus i partial partial t minus omega f star. Basically what I'm doing is to take this omega here. This is omega star. And then use that definition, write down the expression for omega-- typical omega-- explicitly. Since I am writing omega star, therefore, you get a minus i partial partial t minus average omega out of it. That's why here you have this expression and then multiple it by f, which is the original expression. I also write this omega capital Omega explicitly. I partial partial t minus average Omega. f t f star. And you can immediately realize that-- OK, this whole thing is multiplied by i times kappa. You can immediately recognize that this term actually canceled because they are-- actually they are literally the same. And then what is actually left over is the two terms, which is in the middle. So basically, you are going to get now I can multiply i and cancel this minus i. Basically what you get is kappa time T equals-- both terms have a T, so I can extract this T out of it. f partial f star partial T cross partial f partial T f star. After all those works, you can see that this one looks pretty nice. This says what? This is not bad at all after all those calculations basically these will be equal to kappa T partial partial t f f star. Everybody's following or everybody already lost? We are almost there. All right. Now, we have these three. Three originally is a beast. Looks really horrible and after I write it down explicitly, it looks OK, not perfect. Yes? AUDIENCE: [INAUDIBLE] YEN-JIE LEE: The complex conjugate of the f function. All right. Now I can put one, two, and three into this integral. Then we are done. Now let's put numbers 3 into the integral first. I do a minus infinity to infinity, number three, dt. What is going to happen? This will give you minus infinity to infinity kappa T partial partial t f f star. And I can use integration by parts so what I'm going to get is kappa T f f star evaluating minus infinity and then plus infinity minus kappa minus infinity to infinity f square partial t partial capital T partial t d t. Let's look at this. Basically, what I'm doing is to put in the numbers written back into this integral and then use integration by parts. Basically you can see that this is what you would expect. The interesting thing is that this function is evaluated at crossing at infinity and minus infinity. If you assume that your f function is localized-- it's confined in some specific range of time, instead of spreading out over the whole universe. That means this term will be equal to 0 because it's evaluated at plus infinity time and minus infinity time. If the f function is localized, then at the boundary of time, you are going to get 0. This term disappears. Very good. We've solved one problem. And this looks horrible, but partial capital T, partial t, what is capital T? T is small t minus average of t. Average of t is a number and t is just t. Therefore, partial t partial small d is just 1. You can see that there are hopes, things are becoming simpler and simpler. Therefore, what I'm going to get is this-- minus kappa minus infinity to infinity t t f squared. And then if you divide this by this term, you can see that 3-- number 3 term-- will give you a contribution of minus kappa. That's all. Because once you plug this integral back into this function, the third term contribution gives you minus kappa. That's a very good news because it's actually pretty simple. Any questions? AUDIENCE: [INAUDIBLE] YEN-JIE LEE: Oh, you mean this one? AUDIENCE: No. YEN-JIE LEE: This one? AUDIENCE: To the left. YEN-JIE LEE: Oh, yeah. You are right. I missed a dt. Thank you very much. Very good. Yeah. Basically what I'm trying to do is plug in the expression here into the integral. You can see that the contribution from the third term that number 2 is rather simple. It's just minus kappa. Let's also take a look at the computation from the first and the second. Wife Number one, will give you minus infinity to infinity t minus average of t squared f of t squared dt. And this is divided by minus infinity to infinity dt, f of t. This is not crazy at all because this just the definition of delta t squared. Just a reminder that the definition of delta t squared is written here. Therefore, this is just delta t squared-- the first term, which looks really strange there, but in reality, it's actually very simple. Let's look at the second term. This is kappa squared minus infinity to infinity i partial partial t minus average of omega f of t. And then square that. Divide it by minus infinity to infinity dt, f of t squared. And that will give you kappa squared delta omega squared. Basically, our conclusion that this r function is a function of kappa. Essentially equal to the first terms here delta t squared, the second term is plus kappa squared of delta omega squared . And finally, the third term is there. Minus kappa. And this would be greater or equal to 0. Because what I am doing is just summing all those positive functions. Then, take the rest. . Any questions? AUDIENCE: Why does the integral from negative infinity to infinity dt f squared equal? YEN-JIE LEE: This one? This one? This is equal to zero, right? Oh, here? AUDIENCE: Yeah. Why does that-- YEN-JIE LEE: Oh, I see. I see your point. This is an integrated minus infinity to infinity number 3 dt. It's the contribution here. Then, if I take a ratio between this term and that term, then this is canceled by the denominator. Therefore, what is actually left over is minus kappa. AUDIENCE: OK. YEN-JIE LEE: This 3, the contribution of 3 in green is already taking the ratio when I evaluate the capital R function. Good question. Now you can see that you can safely ignore what I have said so far. Everything you can ignore. Those are just mathematics tricks. But what is very important is that now I have this relation-- delta t squared plus kappa square plus delta omega squared minus k. This is a function of k. And I can actually minimize it. I can minimize R if I carefully choose a kappa value. This kappa equal to kappa mean value which makes the minimize the R function is equal to 1/2 delta omega squared, which I would not go over this calculation because this is just a minimization problem. That means if plug that in, what I'm getting is R kappa min will be equal to delta T squared minus 1 over 4 delta omega squared. That is greater or equal to. 0. We arrive there. If I multiple both sides by 4 delta omega squared you get delta t squared delta omega squared greater or equal to 1 over 4. If you take the square root of that, the you get delta t delta omega greater or equal to 1/2. That's actually what we started to try to prove right? You can see that after all those works a lot of complicated mathematic calculations, you can see that we make no assumption, we are just using the definition of the spread of time and the spread of frequency. We follow that definition and the use of mathematical trick which we used to prove Heisenberg's Uncertainty Principle and we arrive there. This means that this is an intrinsic property of wave function. Intrinsic property means that it's a mathematic property of wave function. What do I mean by this equation, which we finally did right? After all those hard work, we have to enjoy what we have learned right from all of those crazy things. What do we learn? Look at this function. Delta t times delta omega, greater or equal to 1/2. That means if I construct a function, which is how I oscillate the stream as a function of time, if I construct a really narrow one to this very fast and then I stop-- very narrow-- then you will have a very small delta t. Now it sounds really nice. I produce a delta function, delta t, but the delta omega space is going to be a mess. It's going to be a super wide distribution because delta t is really very, very small. That means you have to compensate that by a rather large delta omega because if you multiple delta t times delta omega, that is going to be great or equal to 1/2. And is the consequence of this, for example, for the discussion of AM radio. If I have an AM radio with bandwidth delta omega. This is 2 pi delta nu and that is something like 3 times 10 to the 4 Hz. If I have some kind of bandwidth which is actually roughly this value. I can now immediately calculate what will be the resulting delta t. The resulting delta t will be a few times 10 to the minus 5 seconds based on this equation. This means that if I'm trying to send two signals in sequence through this AM radio. that mean if the delta t-- the time difference between the first and the second information-- if the time difference is large, if that delta-t between these two much, much larger than 10 to the minus to the minus 5 seconds. Then I can actually easily separate these two signals. On the other hand, if I send then really, the two signal really close to each other, if it looks like this, then the receiver, the ones who will receive the signal, will not be able to separate, if this is just one signal or two signals, or one pulse or two pulse which you are trying to send. Any questions so far? So you can see that we can actually quantify what will be the limitation in the resolution, tiny resolution, due to the limitation of bandwidth delta omega. Before we take a break, I would like to make a connection to quantum physics. So if I look at this delta t times delta omega greater than or equal to 1 over 2, this expression, I can rewrite it. I can multiply t by velocity v. And I get v times velocity and I can have omega divided by v. And this would be better or equal to 1 over 2. So I just multiply v and divide by v, then actually you can solve. And that means this will become delta x. And that, the second term, will become delta k. And that would be greater or equal to 1 over 2. In the quantum physics, momentum is equal to h bar times k. Momentum will be equal to h bar times k. And h bar is actually the Planck constant. So that, actually you will see that a few times in L4. OK. So if I have p equal to h bar times k, that means I have delta x times delta p greater or equal to h bar over 2. That is exactly the uncertainty principle, which was actually introduced by Heisenberg. And what is actually the meaning of this? So if we describe all those particles we see by quantum mechanical waves, if I have momentum p, now it corresponds to a wave function, with wave number k. And the constant, which is associated with p and the k is the Planck constant. So this means that if I measure one particle really, really precisely in a position, due to the nature of wave function that means I will not have a lot of information about the momentum of that particle. And where this uncertainty principle is coming from, it's coming from purely the mathematics related to waves. As you can see there, there's really nothing to do with quantum so far. Quantum I'm saying actually only goes in after we prove the uncertainty principle, delta omega times delta t. You can cannot have a very precise frequency and a very precise position in a coordinated space over time at the same time. And that actually has direct consequence. That means if you are considered in quantum mechanics, that is essentially the limitation which will be posted, the uncertainty principle. So we will take a five minute break. And we come back and we take a look at 2-3 dimensional waves. And let me know if you have any questions. So welcome, back everybody. So before we actually moved to 2-3 dimensional waves, we will discuss a very interesting topic, which is related to the dispersion relation of the light actually. So if you use spatial relativity, basically you can relate energy to momentum and the mass. So E square will be equal to a p square c square plus m square c to the 4. And you actually interpret light as a photon, then basically E is actually equal-- to the energy of the photon will be equal to h bar times omega. So we are actually really going really forward a bit. Because maybe some of you actually haven't seen this before. But if you just believe what I have said, basically you can actually divide everything from the first formula, which is the spatial relativity formula, by h bar square. Then you will be able to derive and arrive the second formula, which is omega square equal to c square k square plus omega 0 square. And the omega 0 is actually defined as mc square over h bar, just for simplicity. So if we look at this equation, this is essentially a dispersion relation. Now you have seen this so many times. And this omega square equal to c square k square plus omega 0 square, this formula is actually reminding you that this is actually a dispersion relation. So what I mean by a photon having mass here? That means the m term in this special relativity formula is not 0. Therefore omega 0 will be non-zero. What is going to happen? That means the space of velocity of light is going to be different. It depends on what value of k you choose. That's kind of interesting. Because that means light with different frequency or different wavelengths is going to be traveling through the vacuum at different speeds, if that's true. Everybody get it? Very good. So how do we actually test this? So that means I need a light source, which are very, very far away from earth. Then I would like to measure the delta t as a function of frequency, for example, and analyzing. So how do we do that? So this is actually possible if you actually use a natural light source, which is the pulsar. So what is actually a pulsar? So what we actually use, essentially a millisecond pulsar. So those are actually coming from rapidly rotating neutron stars, and that those rotating neutron stars will emit pulses of radiation like x-ray and radio waves, at regular intervals. Because it's essentially rotating, rotating, rotating again and again. Based on this movie, basically what it's showing here is a very old neutron star. It's actually in a binary system. And this neutron star can absorb the material from the other partner. So that actually is-- the rotation speed actually increased. And finally at the speed of a millisecond per turn. So this actually really happened. And we can actually observe this. And if we are lucky, the earth is essentially somehow in a spatial direction such that the emitting radio wave actually pointing from the pulsar to earth, then I can see the pulsar, the amplitude of the light from pulsar essentially changing rapidly as a function of time. And another very good news is that typically those pulsars are really far away. For example, in this example, pulsar B1937+21, this is essentially a pulsar with rotation period of just 1.6 milliseconds. And this is actually something which is really happening really far away from the Earth, which essentially is 16,000 light years away. And that we can actually observe this. This is actually pretty close to Sagitta, and you can actually see this pulsar. And how does that actually associate with the original question we were posting? The original question is, does the light with different frequency travel at different speed. And this is essentially a very nice tool. Right? Because it is emitting the radio wave. And now I can just measure the spectra as a function of time. And I will be able to see if we actually can observe different speed. Because we know the rotation in the world, and et cetera. And it also emits a wide spectra of the frequency, the light frequency. Therefore, I can use this as a light source far, far away from the Earth, to see what will happen. So somebody actually did this measurement, and this is that what they found. They found a non-zero omega 0. A non-zero omega 0 was found. So that means the mass will be 1.3 times 10 to the minus 49 gram. That sounds really small. But it's not small at all. That's actually destroying the whole understanding of light. What is going on? So we are in trouble. So after all this discussion, et cetera, and also other measurements which are sensitive to photon mass, they actually threw out this possible contribution. This is essentially is just simply too large based on, for example, measurement of magnetic field in the galaxy, et cetera. It doesn't really work. So what essentially is really happening? The explanation is that the path from the pulsar to the earth it's really not vacuum. There are a lot of-- not a lot, but we have very few or very dilute electrons, very diluted free electrons all over the place. And that will change the frequency and the speed of light slightly. Therefore you observe the interesting-- observe the effect. And we are going to actually also talk about how the material actually changes the behavior of the electromagnetic wave in the coming lectures. I hope you find this interesting. Any questions? All right. So we are going to move on. So far what we have been discussing is always 1-dimensional waves. So for example, a string, and also the sound save in a tube, et cetera. We always discuss things which are in one dimension. But we are actually not one dimensional animal. We are 3-dimensional And of course, for example, these objects the surface is 2-dimensional So there are many, many things which are more than one dimension. So can-- the question that I'm trying to ask is, can we actually understand this kind of object, and how actually to understand those objects and how do we actually derive the normal amounts, and how do we actually write down the general solution, which describes a 2-dimensional or a 3-dimensional wave. That's actually the next topic which I would like to discuss. So that's actually gets started with a plate like this. So basically that plate is actually a 2-dimensional. And assuming that this plate is infinitely long, for a moment, very, very long. So what does that mean? This means that if I define my x and y-coordinate, which is actually used to describe the position of a specific point on this plate, then basically you will see that they are beautiful symmetries, which you can actually identify from this simple example. What is actually the symmetry which we can identify? Can anybody help me with that? AUDIENCE: x and y. YEN-JIE LEE: Yeah. So yeah, x and y are symmetric, yes. And the other function of x, what kind of symmetry to you have? AUDIENCE: Reflection. YEN-JIE LEE: Yeah. Also reflection, and what I'm looking for is if I change x and change y, what kind of symmetry do you have? AUDIENCE: Translation. YEN-JIE LEE: Translation symmetry. Well, all of you are correct. But what I am trying to focus on now is the translation symmetry. So if I use translation symmetry, what I'm going to get is that I can already know the functional form of the normal mode. Because essentially if it's translation symmetric, as a function of x, it's translation symmetric as a function of y. Then I can say is in the x direction will be proportional to exponential iKxX. K underscore x is essentially the wave number associated with the wave in the x direction. So that's essentially one consequence which we actually learned from the discussion of symmetry. And in the y direction, I can conclude also that the normal mode will be proportional to exponential iKy times Y. Therefore, I already know what will be the function form of the normal mode of this highly symmetric system. What is that? The psi xy will be equal to A times exponential iKx times X, exponential iKyY. So you can see that. And also I need to take the real part. Something like this will be possible in normal mode. Therefore without going into detail basically, we will see that the expected behavior of psi as a function of x and y will be something like a sine Kx times x, sin Ky times y. So that's actually the kind of normal mode, which we will expect based on the argument of translation symmetry. And of course if I now go back from infinitely long system to a finite system, then you can use the boundary condition to determine what would be the K value, Kx value, and allow the Kx value and allow the Ky value using boundary conditions. So actually without doing any calculation, we can already find that, so now if I have a plate with finite size, basically you expect that I can have some kind of normal mode, which this is the amplitude, a projection in the x direction, it can be a sine function. And that it can become 0 at the left-hand side edge and the right-hand side edge. And in the y direction it has to be also some kind of sine wave as a function of y. And of course it goes to 0 at the edge. Because if those are actually the fixed boundary, for example. And if those are actually not fixed boundary, then you expect that-- like open-end solution. So you expect that the distribution will be more like a cosine function for the first normal mode. And if you look at this, the structure of this kind of solution, it looks really complicated. Because you have x direction and you also have y direction. Both of them are actually sine functions. And how do we actually visualize this kind of sine function? And here is a demonstration, which I have prepared. It's really a 2-dimensional plate. And as you can see that under this plate, I have a loudspeaker which actually produces a sound wave to try to excite one of the normal mode. And the one I am going to do is to turn on this loud speaker. You can hear the sound. And I would like to see the normal mode. But it's very hard to see that, without doing anything. Because it's vibrating, but its so fast that it is really very difficult to see it. So what I am going to do is to pour some sand on the surface, and see what is going to happen. And if we look at this, I am putting sand on it. And you can see that, there is something happening. If I change the frequency to one of the normal mode frequencies, you can see that now we are reaching some kind of resonance and exciting one of the normal mode. And you can see that the sand actually it doesn't like to stay on some of the plate. Because it's vibrating like crazy and it's not very comfortable to sit there. So the sand, where will the sand actually sit? They will set at the place where you don't have any vibration. Because what we are talking here, is essentially some kind of sine wave times sine wave or cosine wave times cosine wave. That means there will be nodes on the plate. And those are 2-dimensional nodes. In the 1-dimensional case, we are talking about nodes, it's actually the place where you have zero amplitude. And now I have cosine times cosine. Therefore, there will be a complicated pattern appearing which is essentially the place the plate is not actually moving at all as a function of time. And you can see that now I can actually excite one with the normal node. And you can see a really beautiful pattern. And allow me to do this and increase the frequency. So that if we see if I can excite another normal mode. Look at what is happening. So now you see that the number of lines actually increased. So this is actually so-called Chladni figures. Basically those figures are actually produced by this trying to excite one of the normal mode. And basically the sand will be collected in the nodal lines. And you can see that this higher frequency input sound wave. You can excite the higher frequency in normal mode. And of course I can continue to increase and see what happens. Now I'm increasing the frequency even higher and higher. You can see that now the sound is actually rather loud. And I am actually putting more sand. You can see that there are more and more patterns. Because now I am increasing the frequency, so that actually the higher frequency normal modes are excited. And you will expect more nodes for higher frequency ones. And now I can even go even higher to see if I find success. It's not easy now. Look. Probably this is a very good way to design the pattern of your t-shirt. OK. So how do we actually understand all those patterns? And we have already started. This is actually something related to cosine and sine multiplied to each other. And the next time we are going to do a more detailed calculation and show you a few more demos and see what we can actually learn from the 2-dimensional case. Thank you very much. I hope you enjoyed the lecture today. And if you have any questions, let me know. And you can actually come forward and play with those demos if you want. |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH7_SLAM_for_Robotics_Mapping_Extended_Kalman_Filter_EKF_to_SLAM.txt | actually okay hello everybody good morning hope all of you are doing well so uh today we have short lecture for uh continuation of the extended Kalman filter and later you have one in class practices so if you have any question about previous topics feel free to ask okay so let's dive into the course for today uh we have mapping of the extended carbon filter EKF so today we want to see what is the column filter first we will have a short Brief Review of what we studied then we talk about the quickly what was the column filter shortcomings then we talked about the extended Kalman filter actually kind of reviewing what was happening then most importantly today we want to see how we can apply extended Kalman filter on the Islam last week we talked about the localization only we saw how we can how we can solve localization problem with extended Kalman filter we mostly focused on calculating when the robot is moving in the environment find the pose of the robot with eka but today we want to extend it more make it bigger it's also include the landmarks into consideration too so that our extended Kalman filter can consider also the landmarks and also map them so that we can map them on the map that we have so meanwhile we want to solve all together so uh historically one of the most influential uh Islam algorithm is based on the extended cloud map filter so that uh it is kind of father of all algorithms of the Islam that we are going to see later on also extended Kalman filter uh uh is uh is applying on the uh like we've seen that we can apply it in form of the online so that it means that without having whole poles of the robot that's moved in the environment he can we can in online form update the uh belief that we can say where is the horizontal location of the robot or location of the landmarks that today we are going to see and it's one of the great algorithms for industrial users because uh it has high certainty and since in industrial environment we can also uh put everything as we want today also we are going to talk a little bit about it uh since uh for example when we are talking about known landmarks so finding Landmark is not easy job and maybe because of uh some some exterior features like changing of the light you cannot detect same landmarks but in Industry the error is is not acceptable you should say 100 the same Landmark robot goes 100 times can see because of that we can put known landmarks ourselves we can say okay this is the landmark that robot knows in the industry no one can change it because of that we can use uh we can use more reliable algorithms in order to affect those instead of for example if we use state-of-the-art algorithms maybe with some some errors the missiles that uh that that can be problematic so how we uh mathematically represented the problem we said we have 30 of the series of the observation that uh that starts from one to T then we say we have series of the control commands that control commands are are are helping you to control your robot then we have the map then we have the robot locations as we showed that we showed them with the poses and it starts from x0 to X to T so we said that we start with zero here but the other ones with one because we initially we say robot is somewhere after moving we start to uh observe the environment of course the control command comes from uh that second point then what we've done we've uh we've shot the distribution of estimation by probability that we set probability of the poses of the robot x 0 to T given uh this is an m we want to we want to estimate these given by the observation and control command so these are inputs to our problem and we want to construct the map and we want to find the poses of the robot so in last lecture we didn't have this M over here but uh because we wanted to localize only but when you hold on to solve all Islam problem you also want to construct the map too so I've also noted that it's it means probability distribution of the pass and map given by the observation and control that you can read it more easier so but before that what was the base filter uh we said that we want to mount most of the algorithms that we're studying on the base filter it was a general probabilistic approach that known as base filter and it is principle algorithm that calculates the belief in the robotics it was meaning that so every time a robot believes only just only previous step and all the calculation is like that I believe that my previous calculations was correct based on this concept we were we were using the base filter and and continuously we were updating uh uh the position of the robot that where is the belief over there but now today we want to take the consideration of the landmarks either and and have a belief for each one of the landmarks and say okay when I I Robot has the belief of the previous calculation we can have a belief of the previous calculation for each one of the independent landmarks too so that with the same concept we can apply the extended column filter on all of these parameters together so that we already discussed that or we can show base filtering probability distribution probability of the x given by all and uh that is general form that later we applied the uh common filter and extended Kalman filter only also this uh this presentation this equation over here this probability distribution over here known as kinematic modeling too think why also we can call it as kinematic modeling we can say why yeah exactly uh actually this is representing the kinematic model and modeling of the environment what is happening in the environment is more simplest form so that uh so that like like where is the robot based on these parameters so we can call it as kinematic modeling tool so known as that if you somewhere see that uh you can think about the base filter and you can demonstrate it like this into but mathematically this one you can prove it mathematically with Exact Solutions too that that in control theory usually we do that foreign estimation we want to have a recap what was happening so we had the belief of txt that is equal to this term over here that we were calculating this term uh in recursive form that later we break it down into two steps but what this is saying to us in first uh first part we have the current observation and second part is the current motion command and the drilled part is the belief on the previous state so that observation given by XT and here probability of the post given by previous pose and control command times the previous belief that we have so combination of the if I if the job if if we are talking about only localization robot is in this port combination of the previous belief and whatever I'm running as control command can be come to the form of the recursive phase a base estimation so that based on that I can calculate new belief foreign what we studied already and I noticed the explanations over there that we break it down into three steps how uh first we said we have the motion model in motion model robot moves whatever the robot is is flying underwater water robot whatever it is whatever uh um because we are talking about robotics application what kind of robot you have we have the first step prediction that that Tuesday predicted leave calculation that we saw that we can calculate it by combining the probability of the the robot pose given by the previous and motion command times the belief so here we have initial beliefs at the beginning got them okay so here we have the initial belief at the first stage that that if we don't know we said we can distribute it over uh over all probability that we don't know where is it it may say okay I don't know where the robot is in the environment he said we can put the distribution like this then later we can update the new position so predicted belief after we calculate the predicted belief based on the motion command we have the observation model that based on the observation model robot sees the environment and based on the seeing the environment we can update the uh updated belief so this belief over here that x t minus 1 is calculated over here that's why we call it Legacy because every time this uses itself and new belief will be calculated over here that just one ETA normalization Factor times the probability of the observation and updating the predicted belief predicted please calculated over here based on the motion command then based on the observation we correct it foreign gain we also were able to adjust how much this is important in base scene 30 doesn't matter it just multiplies but but extended Kalman filter and Kalman filter the most important part The Beneficial part was kind of finding the gain how important each one of these are that automatically updates that for us and that comes from the arrow and the calculations were coming from the noise that we have based on the observation model and motion mode foreign so far be very clear for you guys so later we moved to Kalman filter and applied Kalman filter on the base filter that we said it is uh one optimal linear estimation for linear systems and the column filter assumes that everything is caution the error is gaussian and normal distribution then uh then updating the gaussian distribution finally gives us also gaussian whatever we're doing finally we have gaussian distribution as output for Kalman filter features then we said okay what is the problem of the uh called not filter the problem was the same thing that we had the only gaussian distribution so we say Okay mostly many times in the scenarios that we have the error is not caution and arrow is not linear and it's very rare to have it solve this problem uh we said okay we need to take into consideration of the non-linear or non-gaussian observation from the model that we have so this is non-gaussian model it's not caution anymore if we fit this to the column filter the output will be wrong so to deal with this problem he said we can linearize the non-linear model that we want to fit to the column filter that we we saw how we can mathematically whatever is as input transform it to kind of caution linear linearize it then later we can use the same procedure then we can get here So based on that we introduced the extended Kalman filter in Excel in Kalman filter we say we have a kind of implementation of the base filter again it is it is non-linear version of the Kalman filter as I explained and it is estimation of the current mean covariance again so that we said uh robot calls or any Landmark position can be shown as a distribution we should throw this out in so everything can be shown as distribution and we can show everything with mean and covariance of the uh the the error that we have how certain we are for example if this is X Robot position so we say most probably robot is here and most probably robot is somewhere around here so this was making everything easy for us but later on after extended Karma feature next lesson you will see that but problem that it has and and how we can solve that too so uh so we said we just simply add the non-linear functions G and H that are were two variables helping us to linearize nonlinear function in mathematical form so uh in online Islam we said that it is only based on the observation of the current position and latest control commands uh sequence of the localization and accumulated error is not important over here then we say that okay the uh uh the the online Islam were looking like this that we have the uh map constructed map we have the observation of the environment that can come from the robot pose and can come from the map itself then then motion command change the photos of the robot and correspondingly uh uh the the observation will be updated too so in in full Islam we showed that this graph is bigger but here in online slab we have just one line of this presentation for the uh Islam problem we have the linear mapping model for observation and motion commands in Kalman filter how was it we want to quickly see what what what was it looking like in yeah in formulation Port so same as base filter here we have motion model that we updated to this term over here that we said the the XT the new state is equal to the The Matrix n times previous x t minus one added by The Matrix M based on the previous uh the control command added by some noises so that these these Matrix is very linear functions that were were kind of helping us mapping uh what is happening in control and what is happening in observation uh in order to bring it to the system so nnm was uh were uh were for motion model but on the other hand we had the same for observation model that in observation model we use the Matrix W that we used it and based on the poses added by some again error of the observation that we've had then after after we modeled the column filter based on the base filter and applied on it we saw that okay we can have the uh General uh uh algorithm structure like this that we have the prediction step the same prediction step that we discussed in in form of algorithm and we had the collection instead but the most important part here that we have predicted me and predicted covariance that were calculated based on the control command so that the control command were helping that's us to do that but here the difference is that since we have the extended carbon filter we have the G instead of uh instead of Matrix so that we already applied the first tailor expansion to uh to uh to to be able to also give the non-linear uh input to the algorithm that we have so uh we have the prediction stage got predicted uh the the mean and covariance then we collected it how we collected it first we found the Kalman game after calculating the Goldman gain we updated based on the Kalman gain here that the Coleman gain was telling us how much observation is important and how much control command is important for us to update the uh the new observation then then after prediction we calculated the mean and covariance that these are output and final stage that we have so each time new data comes prediction then collection so that a collection these two line five and six so simply what we've done so this is for example the control command observation count and columns into you saw that can for example say this is correct based on the error of the observation and the control commands so UT and OT foreign I I also added the things over here again if you needed to recap you can have a look for example most important part is the non-linear model of the G that I explained the output of the extended column filter for previous step or predicted one and then uh do we have anything important so for example motion command noises as Matrix are over here and the Matrix q that we have over here for observation error so uh I already explained this I'm sure you know also we have the HDR Jacobian after observation function that that we discussed lastly that is over here okay I think everything is clear so far now we want to extend the same procedure for also considering the landmarks into our system what we do the the general uh procedure is simple because you we already break down everything else you just see that quickly we can understand what's happening so what is the AIM the first aim is estimation of the landmark to construct a map also not just only lookalikes so of course in addition to that estimation of the robot codes is also important because we Define this land problem based on that what are the assumptions in this regard first of all we take the consideration of the feature-based lab so we have different kinds of map I explained them to you in next lessons and future lessons we will see also for example how we can work with occupancy grid mapping how we can formulate it how we can construct it we will see in 2D if you want to extend it in 3D I will explain to you how to do that we also will see for example if you have mesh of the environment this kind of environment at time key time moves to keep added by one how we can measure them together we will see algorithms for those but for now what we are seeing what we are talking about we are talking about feature-based maps that we say Okay features already are extracted to me so uh I know this is like a chair I know this is table or I know the edge is the corners also in uh in chapter I think 12 13 I will start to explain Advanced algorithms if if talking firstly about the old feature extractions we will see exactly how you can extract all features those old features if you are familiar with keeping your mind that later can be come and sit over here too so that if if you have the frame of the picture that you can robot sees for example this scene you can extract important features that those features after robot moves most likely can be detected again the corners The Edge the the important elements so those those can be called orbic selection that is also used in one of the the best Advanced algorithms that the name of the algorithm is also based on that or orbus lab version one two three four that is continuing we consider we don't have a look closure problem it means that for now we can video Gap those features that we are extracted we know which one is which one not only but also we know which one is the loop closure it means that so your robot starts from let's say you have an environment so some of our students already did this experiment and they all know very well now what does it mean it means that like like you have environments like this for example robots start from here and just sees like this area then then this robot moves in the environment moves in the environment and look closure problem says following the same features that you first live scene after some while so that you can close the environment why this is important because if you don't do that if your algorithm won't detect that what will happen so the map that will be constructed maybe looks like this foreign observation and control commands how accurate the algorithm it is this can be low or less more but this point over here should be this point over here so these cars look closure detecting the same features that robot has seen here and and then kind of move it to to connect it this one also we have an algorithm to do this mathematically I'm gonna show you how we can do that in in future slides so when we say we don't have this problem it means that we already know these features over here what are these features and these features we don't got they don't take that into consideration as problems ah as I explained no Landmark detection problem we say already we know the landmark and uh uh also we don't have we don't have Landmark Association problem this is a big problem very very challenging problem in Islam what does it mean it means that your robot sees some features see some Corners Edge but next time how you know that which one was which one to construct the map you see like many chairs if I want to explain in that generally which child was which after 10 times of going and coming back this is very important if you miss them you mix the indexes then your map will be destroyed so so uh like like if you consider chairs it's easier but when you consider like features The Edge the the small color the small are important elements of the environment and you have dozens of those so matching them with each other is not easy problem but here because we want to focus on algorithm itself for Simplicity we say we already know the correspondences if you don't know how we do we just uh we just make guesses and again bring a probability based on that cases and consider it as error again and this will be again growing the problem so for now we also consider 2D environment uh not not through the environment so because also if you think about 2D and 3D uh you may want to localize some object that is like like a construct a map as Landmark that is that is landing somewhere is hanging somewhere so that's also another challenge but but we say okay let's talk about this simple problem so also we assume that robot equipped with sensors for measuring the range and pairing what was the engine bearing measuring the distance and Ang velocity where the robot is looking okay is everything clear here on the other hand what kind of limitations we have for uh for extended Karma filter to apply on the on the problem that we have before going to the algorithm we say for computational reasons the number of points landmarks is usually smaller than one thousand why what was the reason he knows what about rest I already also asked this once yeah because of the Jacobian matrix and because we are we have to commit non-linear models to linear models and each one that you wanna convert is is distribution so in common filter it was very easy and very nice Kalman filter is very lightweight and that's very nice to use you can use it in uh 32-bit very weak processor too but but here because in column filter we only care about two variables me and covariance or variance that's it two variables for for showing everything like if this is robot pose just two variables can show you the estimation of the red robot is in one day but when we have extended Kalman filter that the distribution can be like this anymore like like something else then we couldn't use this and we had to linearize it and linearization of this the Jacobian matrix and Jacobian matrix is huge because calculated all the possibilities and and practice to the to the one the one-dimensional Matrix that is caution again so because of that we had the problem of the uh uh of limitations of these 1000 so this is problem of extended permanent filter in next uh series of the algorithm you cannot solve this problem we will see how we can solve that issue also that we introduce unscented column filter and after uncensored Salman filter we're gonna see also there are some problems over there you cannot improve that too so uh you may also ask why we don't go directly to the end because we cannot you have to come from beginning to understand that one otherwise you you never can understand what's happening there foreign requires significant features detectors and sometimes using artificial landmarks as features are also critical uh because um because because of the assumptions that we had we said we know the correspondences right and let's say in time T I see 50 features she added by one I don't see that 50 features I see another 60 another new features then this this algorithm is going to be in trouble because I I couldn't detect those anymore I could take something else something new so uh it of course is better to have more General algorithm can detect both of those but here we have that challenge uh that that you will see that for example in a particle filter we have less problem with that issue of course that's also basically true so the EK problem that that has the computational expenses we will see how so uh fin noise assumptions for the motion and the uh Precision for the perception and posterior must be relied must be not very big foreign then it cannot process the navigation information that arises from absence of the landmarks that I explained to you just now I before these slides so it assumes that the state space is the combined State Vector as defined as following what does it mean it means that we have the uh the uh State Vector that can be showed as YT that is equal to x t and M and that this XC is representing the robot post X Y Theta so where the robot is x y and what is the heading Direction Theta okay clear and what are these ends these ends are indicating landmarks that that landmark one position X and Y and signature the index number where it is which one it is so Landmark 2 position and signature and Etc we continue up to a landmark n and signature n so that we have the stage vector that that represent this for me so think a little bit about it now yourself how does it look like because this is now we are going to merge it into algorithms so XY Theta and the landmarks I also indicated over here based on this representation we can say State Vector size is 3n added by 3. why because this added by tree is this tree over here and 3n is the three it's n times 3. how many landmarks I have times the uh the size but there is some tricky point so this tree and add it by three can be reduced r u r programmer you should quickly be able to answer it oh okay now we can reduce the size of the tree and add it by 3 over here very simple use programming skills data structure interview for company this can be a question from me no answer so we have the signature and this signature indicates a number for me I can remove it and put index index of the vector Matrix or whatever it is simply just use the index and don't distort it right you don't need to definitely store this because this is in Matrix or array and you know where it is right and you can throw it out and just store these two did you get it did you get it no so so how you how you get get access to a data in Array you have the index right so this this can be like they are these are not changing these are in The Matrix and these are in the array and you can send the the index and remove this say okay this is like I know in this is like in point one one so zero one this is at zero two then you can say the same number of index can be the signature I don't need to find for signature right huh I don't know just you mean you win memory but you know the index of the where it is right you can use the same that number instead of using directly this signature if you want to reorganize it and make that makes it mix it shuffle it yeah you're right then this can be still still you can use the index but this can be useful then but since you don't need it you know where is the index whatever the calculation is how how many you have you can you can use same in the indexing instead of signature it's like it's like it looks like stupid if you want to kind of remember the story because it's like these guys already finished it's like we say Maybe like a store uh instead of so I'm not writing these three here so if I like write like like 20 20 this is like X Y it's right in writing indexing of one over here true then 10 30 35 so this is X1 y1 X2 Y2 again again writing this is signature for example then X2 Y2 this signature over here can be in a state index 0 1 2. you just need to start from Two and add it up by two and you know based on the index not you don't need crystalline and why this is also can be important in embedded systems because when you have this presentation each one of the signature each one of the landmarks that you are seeing every time at each frame you have 100 right you need to match it you need to search inside and to see where it is you have a for Loop in very big table each time to find the signature right that's that's problem but instead you can use the index and you can just quickly quickly go to the index if you use the indexing system instead of putting signature there to find it this can be useful but also it has some shortcomings and problems what is the shortcoming and problem here if you have Dynamic signatures and they are that you don't know they are increasing decreasing increasing decreasing that can be a little bit problematic you can still manage it in this way but but your programming system should be able to allocate dynamic uh array for you for example or dictionary that you can add it so it could it should not be fixed fixed array that we have in C sometimes C plus plus and it's a little bit difficult to change after a definition of the array it's not like python in embedded systems basically program so based on what we discussed now we have this again super big algorithm that is a little bit bigger than previous one so but but we already discussed all of these elements you're gonna see it's very easy nothing is special so first of all we apply the motion update here same as before just we have big matrixes over here that calculates up to D up to uh here mean ankle Warriors then this part all of this part calculates the measurement Vector that this time we have measurement Vector it means that we're gonna have considerably all landmarks into a form of Matrix let's have a look how does it look like so uh we have ethics Matrix that is nothing 3D dimensional State Vector into the uh tree and added by three Vector that that we discussed but in if you look at the book also it is stated as to end over here because as I said you can consider the X Y as deposed and consider the Matrix indexing to in order to access to the data then what we have here here we have the same calculations we don't we don't have anything specific just new ethics that these Matrix now considers the landmarks because when we have motion update now we should consider the landmark student the landmarks ex the the poses will be engaged will be will be inserted here then the same update of the mean and same time take off the coverings so velocity-based motion model again comes here we discussed it all in details and put it into the Matrix so we have zeros here to make it make it in shape of the The Matrix effects that we have to make them productable so that's it same observation model just be considered in Matrix form and added the landmarks over there in first stage so so how this is this was coming this was coming from first degree Taylor extension we discussed it already so that we said we want to linearize the matrix by by considering GEOS that means there's the control UT and the and this time instead of a previous post we have U T minus one that that becomes a little bit vector so the vector of the UT that we declared over here because we now enter the uh included the uh the the position of each one of the landmarks the whole calculation this time only considers the Y T minus 1 and y t so after applying we have the GT we got this GT after applying the first Taylor expansion we have this equation and we plugged it over here that's it nothing nothing almost so in secondary stage what we had after motion model we had the observation model that that observation model should have been updated and and now what we need to do we need to just rewrite the algorithm that considers those two so uh it looks a little bit different but nothing is special here we have a for Loop that considers this time for each one of the features update what does it mean it means that the observation comes from range bearing and signature right so this range bearing signature can be used here so that we can say J is equal to CIT that we are taking the signature that we have which Landmark we are going to update actually and if Landmark already has not been seen and this is the first time that we are seeing first what we do we calculate this term over here that is the observation location of the landmark will be updated by the stimulated robot pose added by the relative measurements so this related measurements come from the range and bearing of the observation it means that so robot moved to some location so I'm talking about one of the landmarks because we are in the for Loop for each one of the landmarks we are doing so that Landmark it is first time that I'm seeing if this is first time the parenting based on the robust polls and the observation arrange and bearing I'm going to initialize it okay after initialization but we do we apply the uh we apply the observation that we've had how it looked like exactly remember observation was including the range pairing and the signature that we've had I already discussed it in details for example this is including distance based on this observation chapter that we've had added by noises and this end was the gaussian distribution noise that for each one of the range and bearing and signature we said we can have a gaussian distributions but because like the error of the range can be different than a roughly bearing so how much the error is in life here and how much unit or your orientation has errors independently can be considered as error so what this calculation looks like complex no it's exactly the same thing that already we've studied we know that just writing in algorithm form for example like if you look at observation I at time t i transition two of these like this line you look that line is this line that here m i g m j y subtracted by y already has been done here I'm just using this variable for the square velocity Q so include the understands you can do subtraction over there that comes from square and the power can be can be done over this just writing the this term in the in the form of the algorithm simply that's not that's not really complex algorithm and uh and of course the Matrix Force so since we break it down already uh understanding it should be clear and most importantly what we have here now we have a big Matrix of the ethics that includes all the landmarks observations in order to update the Kalman game so the Matrix grows why because in last chapter The Matrix will be smaller because we've just only considered the robot location but here we are considering the uh all Landmark locations tools so that the landmark locations helps us to calculate the Kalman gain and based on that update the predicted the the actual final mean and covariance okay so I put some points here that the Matrix is nothing low dimensional Matrix of the h i t into the Matrix of the proper Dimension h i t was the uh The Matrix that was helping us to linearize non-linear function and we applied the first order Taylor extension over here I think in next slide I'm gonna show you but if you are interested in for example why these are like this looking like this how exact precise calculations comes in writing form refer to the book chapter 10.23 that you can see also details of explanation of the how in detail is coming and you can make it more clear for yourself if you have problem but as I mentioned to you there is nothing special just considering all the Matrix is two times n that shows uh number of features that I extracted from environment and and calculation and taking into consideration of the same uh extended column filter calculation so here just if you want to have a look recap we say first degree Taylor extension same as last week but this time based on the observation and the differences that we are applying based on the YT the vector of the robot pose and all landmarks position okay so here here we can write this hit as this term over here that h i t is equal to h i t times FX this FX is the Matrix that I have that includes only all of it then uh we can calculate the derivatives of the H respect to the to the the state Vector to the state Vector of the Y over here if you calculate that and apply first degree Taylor then finally we have this term over here this is the output of the hit so this Hig times FX Matrix will give me the hit that is linearized that is linearization of the non-linear model so so just plug it here one time a representation of how this is looking like then plug it over here then this hit comes to the common gain calculation and the common gain calculation will give me the carbon gain but now it considers all the uh all the metrics all the all the landmarks into consideration in order to update all of it in Matrix form so again if you have like already I discussed how first Taylor expansion is coming from scratch and and explain how that is working generally but if you have again any uh interest to see more in detail just refer to this chapter and have a look at details how that is working now let's have a look at visual example what is happening with extended columnar filter for uh for Islam problem so let's say you have the robot here so you can see the robot paths as dotted lines and this is robot poses that robot is moving so I've written like estimation of the robot's own position is shut it early ellipses so then these ones the red ones so what what is what is this so landmarks of the location is Dimensions yes are the red ones so your robot is moving with startup lines in different poses and based on the observation that it sees these are landmarks these blue ones and based on the observation that it sees of course there is a belief of where the robot is robot location is unbelievously uh what are the uh the uh uh the the Distribution on gaussian model of the position of each one of the landmark right so for now for example the robot has been seeing this this and why why the the error is increasing over here because of course uh as you know we have the error that integration here error will be like QT observation error and here RT uh at the beginning here RT as the motion command error will be increased by time and this is going to increase if you continue a little bit more you see that robot is like let's consider the trajectory is like this robot is moving moving and of course the error of the very location of the robot is getting bigger while the error is like this because the error of the rotation here uh were bigger than the auroras the moving forward so that's why the distribution goes like this in uh in multivariate gaussian distribution this is multivariable because we see it in 2D and of course the error on the landmarks again a few and we continue more robot comes and the error is increasing increasing increasing and the landmarks also you can see that the error of the variance increasing it means that so the landmark is over here our our observation model and our the extended carbon filter says maybe maybe this Landmark is around hole this circle but most likely it is here in Center that's not very bad as you can see then what is interesting point that is happening is over here so when robot comes to this point sees this landmark The Landmark this Landmark was the landmark robot has seen at the beginning and here look closing or Loop closure happening and since Loop closure happening you can see that the error decreases too much because the uh The Landmark that has been seen uh the the makes gift very high certainty that uh that's where we are now where the robot is now and the whole Matrix for for each one of the observations also is decreasing you can see that's why Loop closing is very important error is increasing increasing increasing during time and gets very bad now when you see where it is then everything can be more certainly so clear so this is the output of the extended Kalman filters that we studied in one simple any stats foreign so let's have a look at the uh uh the The normalized covariance Matrix that shows the robot like let's say robot is over here stairs and the uh and the robot sees the uh sees the landmark and based on the landmark we have the distribution gaussian distribution of the landmark and if we show The covariance Matrix of that of course we have just one line because number of landmarks that we've seen just is uh for now one and uh and of course we should know we should have the data Association if robot continues movement in the environment from there and moves in the environments you can see for each one of the landmarks we have we have multivariate gaussian distribution again some black shadowed points around these blue ones of course for example this has high error because it is over there but our estimation is somewhere bad this one is also not good but this one is very nice so if we want to also show the uh the same plot you can see that based on more uh much more number of landmarks that we've seen we have we completed that and if we continue robot moves around the environment that sees more it will be correlated completely and so that so that's we can we can kind of if we know correspondences based on this we can see that how uh how uh did we did we estimated all of the landmarks or not visually so we say in practical application extended call monthly can apply successfully in large range of navigation problems including Airborne underwater indoors and values other vehicle and different problems of the real applications of course as I mentioned there are some challenge some problems that we will intend to improve it but uh but it's not mean that it doesn't mean that nowadays we don't use extended column into things this still is one of the best algorithms and it still is very applicable especially if you look at the most advanced algorithms these extended Kalman filter is part of that algorithm usually like uh my friend from Technical University Munich he proposed a new Slam algorithm that is Lola Islam if I have it I show you that's 2022. also it includes the extended Karma sister as part of whole solution for commentary for for the for the Islam problem if you look at the orbis land one of the Benchmark really nice algorithms it has also partly a common feature an extended carbon filter in order to update the beliefs and the calculations so let's have a look at this simple video so that this is a example of implementation of the column filter that robot moves based on the velocity-based motion model no landmarks and you can see visually what is happening you can see the automatic calculations you can see the map and you can see the observation that robot moves in the environment and and plot the construction of the map you can see it indicated different features and really at light on the uh unreal environment you can do the same experiment after applying if you have any robot in your access you can try to use the same implementation similar thing with the extended Kalman filter and try to construct this map over here you can see that based on the observation it shows and estimates the robot the each one of the landmark location here also let me see if it was with you I don't remember also yet here also TD two-dimensional representation of the robot moves in the environment you can see based on the limited Range View robot moves is landmark and based on each one of those multivariate gaussian distribution can be represented where the each one of the landmarks is how which how many certainties and and How likely how certainly robot location is so this is also life's output of the extended Selma filter so we have uh we have the challenge of we have the challenges also in addition to Extended carbon filter column filter navigation problem that in navigation problem we say so okay let's say we have very nice algorithm for Islam but how about the how about the robot how to know to automatically moves in the environment that generates the uh generates the path in order to construct demand so in order to do that we have different techniques also different algorithms so one of them is uh rrt rapidly exploring random tree that you can see here that we can construct a rapidly exploring random tree robot is over here for example and this is generate the passes that your robot needs to move in the environment in order to make sure that all environment map will be constructed if you let the robot randomly move maybe robot never goes to that Park of the environment but this makes sure that if you want to have slam automatically then this map can be generated during the slam the navigation so that this this can be useful you can see over here that for example robot is there and then the the passes be generated like that rrt then then moves they get the the construction of the map becomes bigger and then then you can you can do this lab but the size of these can be changed depending on the range of the sensor you may be robot is like very strong from here can see everywhere then just one movement is enough then your rrt will be smooth in order to understand this also let me introduce you two things first of all I'm gonna introduce your navigation stack so navigation stack is very uh very famous for navigation problems in robotics |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH4_SLAM_for_Robotics_Kinematic_Configuration_and_Motion_Model_Odometry.txt | so then let me start from first slide so we are talking about the in this chapter we are going to talk about the kinematic configuration and the motion model first I will be talking about the velocity-based motion model because when you have a robot that that robot you cannot read the odometry commands as I a little bit explained already and for example you don't have vehicles robot anymore your robot is flying or you have a humanoid robot that humanoid robot is uh for any reason the calculation of the automatically are from from work engine is very inaccurate in the case that it can be possible then we can read the velocity based motion model and we will see how to formalize it how to calculate it then we talk about the standard automatic based motion modulus mobile robot kinematics and already we've seen the the base structure but we want to bring it in the form of probability in this chapter today uh so why we are talking about these because we are going to feed these into the base filter that we've seen so the UT that we've written there simply motion command we want to really bring it from really robot and feed it to the uh to the algorithm that we've had at the beginning base filter later we go to Kalman filter extended column filter Etc so what is the kinematic configuration we say it is the calculus the calculus describing of the effect of control actions on the uh on the robot or the configuration of the robot and the common configuration of the mobile robot is six variable that these six variables can show as the as the external external coordinate system x y z and the rule PTR that will be the angle of the robot is Cartesian code coordinates and three eular angles that we can show XY Theta also as Alpha Beta comma then uh if we simplify the problem for now and we say Okay calculating the 3D and all those and presenting them is a little bit complex let's talk about uh 2D environment and if we have 2D we have robot codes that we mostly assuming and talking about then we have X Y Theta as the always I I refer to the robot code and explain like XY Theta for Simplicity in 2D but of course if you have drawn then you most probably need to calculate and estimate all in 3D like the pause is not like robot is like looking with this because it can be in any direction and in mapping we talked a little bit about it so for thematic configuration what we have are the essential rule that we have a state transition probability that the probability says probability of x t given by x t minus 1 and motion command so for now you should clearly understand it so from previous pose we run motion command and we get the new Post in form of probability and this is essential in base filter that we've seen when we are using it in the calculation that we have in previous slide uh of course if you want to say okay what about the observation how it looks like it looks like this here probability of the observation given by XT here we don't have motion command anymore because robot just observes a robot observation comes from the new state that robot it is a new state I mean the current state here is coming from previous one but observation comes from the same state that it is happening at the same t so uh what about robot Dynamics here we talked about kinematics what about robot Dynamics it is still largely open and is not sold completely yet and if we want to bring the Dynamics indication there are some approaches and if you are interested in think about it and see how we can update this to also include robot Dynamics so in coordinate system we can show the robot position like this robot pose like this that this is the robot this is the orientation of the robot where it is looking like that also we call it as bearing and heading Direction in different books and different references can be different sometimes you may see bearing sometimes see the the orientation or heading Direction I sometimes also reference angle of the heading of the robot and here uh um X Y of course is clear and we have Theta that Theta is the uh related to direction of the X as initial zero so we can assume that it robot is heading here like heading to the x-axis and Theta indicates how much rotation we've had based on that zero assumptions is it clear everything here okay so we say a motion model plays rule of the state transition model in the mobile robots what is the state transition also we are talking about reinforcement learning if you have the same thing from one estate moving to next state the probability form of the what is the probability from one state to move to the next state that here comes from where a motion command that we are run uh if you are clever you can connect these two if you some of you I think most of you have the reinforcement learning class too you can see that there we have observation and this can go also fit to the algorithms over there maybe to and of course then that can be nice but of course actually there we are we are trying to learn this one and and reinforcement learning tries to learn so uh what not I put it here x t and XT minus one are both robot poses and not just the x coordinate so I think this is clear so far formalities model describes the posterior distribution over kinematics in also books you will see that it is called as posterior distribution over kinematics so when you face with this posterior distribution is it it means the same term that is probability of x t given by previous 60 and UT the control command that we run to come to XT and the distribution that this probability if we want to visualize uh you can see that okay robot moves from here to here straight line then the distribution can be looked like something this why it is like distribution like this because like here we can say Okay moving straight line for the robot was more accurate the rotation was was less accurate so that distribution this is not limited to straight line robot can move any trajectory it can run any trajectory on the path and also different passes then then again we can have the uh posterior distribution over kinematics that you can see or similarly the same probability distribution I want to clarify for you when we are talking about localization when I'm moving from there to here it is like I'm going to predict the probability where the robot is because I cannot say exact X Y I want to say somewhere around this circle and this circle can be distribution like this shapes here that says okay more likely robot is here but maybe here maybe here maybe here less likely here in this distribution but if it was gaussian then everywhere it was like the same probability in one circular uh on the X Y so uh what about the velocity based and auditory based models we say in practice automatic models tend to be more accurate than velocity why what do you think automatically these tend to be more accurate than velocity model why not really yeah I I know but exactly exact answer so now you need to load what was the odometry and load what was the velocity model then why do you think that odometry model is more accurate than velocity various models that we are going to break all of two of these down today in Mass form no idea that simple no yeah how okay exactly so actually in odometry model we have sensors and we can read it your robot has wheels moves you can read it right how much resistance robot is moved but in velocity what you have it's just velocity of the what robot is moving you cannot read anything and based on developed based on that you need to kind of uh kind of estimate it kind of say okay if my speed is this my angle robots angle is this and moving in this direction that we will see if it's rotating also how we can calculate it but here you can read it I Can Read My Views if it's a new manual robot working you can read it in your step sizes and accumulate what are the step sizes and finally what was the rotation and where I ended because of that this is more accurate but many in most of applications we don't have access to these and we must we have to use it and in advance slam algorithms both can be used and this one also is very the velocity model is also very common to be engaged for example we will see later on one advance from the basic concepts of the orb slam so that there you will see that also we have we can have velocity models as input of the algorithm also one important point that in Kalman filter also we will consider velocity models as input because it's easier to plug in the occasion so very small most of the commercial robots do not execute velocity commands also this is another reason and also odometry is only available post effect it means that you should run whole procedure then you can calculate it this is also uh critical not in velocity you can say okay if my velocity is this speed is this you can kind of people running you can estimate it that's also kind of tricky and useful point that makes it more kind of interesting to consider as as at least one element of the prediction step so usually the the automatic models are apply for estimation whereas velocity models used for probabilistic motion planning mostly but they can also be used in both of them but this is kind of General things that are we can consider so first of all now we want to talk about the velocity motion model we say it assumes that we can control robot through two velocities a rotational and a translational velocity so you remember we studied about the rotation and translation and rotation means the translation means that a point in 3D or 2D we want to directly move wherever we want move rotation means that we want to rotate it simply so the translation the translational velocity at time T we can show it by VT and the rotational velocity we will show it with WT that can be can be shown as this term over here the control command u t is equal to VT and WT translational and rotational so now think the base filter we were talking about the UT u t call through the door is like the push do nothing so uh in previous slide chapter we discussed like up here we want to replace it with velocity motion model that the motion model UT that we have in the base filter algorithm that small term there can be shown by the translational and rotational movements of terrible in the environment we can Define some rules for it also we can say for example if the WT rotation is greater than one rotate to the left is a smaller rotate to the line right and if it's zero to now rotations for forward the same it is greater than one move forward and and the zero is doing nothing and the negative values move backward also this is very common in this form to be used in implementation of the humanoid robot.ng it usually uh I'm gonna recap there like your robot is working you can do apply the velocity of moving forward and rotation by control connects if you are familiar some of you are familiar with few managed robots but later on you will study you will work with Advanced robots you will see that even in drone let's say similar to drone so you can adjust the control commands motion command as velocity of moving forward how much move forward and how much rotate and combination of those can give you the final end point that you want to reach whatever it is clear so okay now uh we say okay Noise free robot moving with constant velocity V and W if you want to show can be can be generally look like this that uh when the bearing of robot is like this robot based on the V and W that we are giving can move around one Circle and this circle will be very helpful for us if we can find the uh the center and where it is we can use that to predict where the robot is moving to what does it mean it means that if you have a V and W the velocity of the moving forward translation and rotation two parameters two values for those then based on those two values I need to hum somehow try to find where this circle is find the circle and where circle is an estimate where the robot is moving and say okay robot will be here for example will be here we'll be there will be here clear based on two velocities that that its radius can be shown as this but but we will calculate it so in this year just simply if we know x y uh the radius can be R but uh we will see that in next slides how much magical League calculate it and we talk about it so what we need to do at the beginning let's assume that from x t minus 1 from x t minus 1 that robot is in X Y Theta as initial Pole we want to have constant velocity VW for some time at delta T delta T time robot moves we want to find the way find out where the x t robot is based on this one the velocity given and delta T time given uh the the main objective is okay let's say uh find out where robot can be in extreme to to do that as I mentioned uh we need to find the center of circle what's the center of circle the circle that this V on W are are causing the circle that this like if you have robot here based on the BMW robot can like go this Arc robot can go let me draw this Arc or Tango this up what's the the what is the idea the idea is if he can if he can say okay this is a circle because it is circular movement on delta T time then if you find the center we can mathematically calculate it based on the delta T that we have very these estimated for this circle we have bigger Circle then we should find this point the center critical point and based on that then based on the delta T that we have we can say where the robot supposed to be based on the V and W uh translational rotational values that we have for our velocity based motion mode so what we do for XC and YC mathematically we can calculate it as you can see here with sine and cosine rules that X is equal to the X the very very poses the the X and and based on the subtracting of subtracting it with the with the velocity over the translational over rotational times the sine of theta we can calculate it based on the sine of theta and the deposition of that we can calculate the XC in in Mass you've done that many times even if you have computer Graphics you need to like construct 3D 3D circles you can use this term over here to calculate the value price draw the 3D points on the mesh or to the environment by calculation of the XC finding the center and drawing the points then later then for the Y we can take it with cosine y added by this term over cosine that we determine XC and YC by by distance from Mass simply then after uh delta T time of motion our idea as I mentioned is to find out where the X Prime y Prime and Theta Prime is unext how we can do that we can write this term over here that X Prime y Prime Theta Prime is equal to uh this term over here XC added by what we've shown how to calculate the uh the center and this term and YC calculating this this velocity over cosine and the and Theta modified W delta T so what does it mean it means that we have new poles of robot is equal to the old pose X Y Theta added by the calculation of the the uh uh translation on the X Y and the rotation again XC and YC came from this time over here that here XC and YC just replaced by those and we put it largely the term over there so that we can calculate the uh we can calculate the if we have the uh if you have the X Y Theta based on the X Y Theta and based on the w and V velocities two velocities we can calculate the X Prime y Prime Theta Prime by using this thermometer and the idea was first we found the center then we calculate the where the robot is good so now uh so I also included some explanation this comes from telegonomy uh try try your geometry that after Delta time the robot progresses V time delta T along the circle resulting heading out W Times delta T that's V delta T so so this density this calculation over here just shows how much how much robot moves on the circle how many times robot moves on the circle and calculates its time based on the center and we can have it over there then uh they say at the time at the same time it's an Y coordinates given by the intersection of the circle about xcyc based on the center that we have and the array starting from xcyc and this is like that we can have like this so now one thing is remaining one important element is that this equation if you write it simply just plug the values over there based on the previous polls and the things will work but what's the problem the problem is that okay we say the control commands are not accurate robot cannot run it accurately most of the time we have error over there but here everything is exact so I said I have the robot pose and I said I have VW the velocities rotational translational and I show you exact calculation that how we can calculate red robotics but what about the error now so then exactly we know where the robot is in the velocity motion model right so due to that we need to also apply error on this on this term here that error as it is also well explained in the book that you you can study so and also we discussed multiple times robot starts from this bearing rotates to go there at the velocity then error can be looked like this can be looked like this and you see sampling from those errors because these are Infinity number of points in distribution in probability distribution form we can also sampling those that we can have error like that and the different noises can be different over there now we need to the idea is find somehow in the calculation that we have at also the uh the arrow in order to add in the nose let's see what we can do first of all we say okay this VW we had already the velocity of the translational and rotation some values now we want to add noise we can say okay now we can write V hat on W hat new new variables like based on VW we have new variables we have W hat that also includes the arrow that also includes the noise just by adding some notes simply for V we can add this noise over there that is Epsilon alpha 1 and Epsilon Alpha 2 based on the V and W based on the translational and rotational error that we have so Epsilon usually we use it in everywhere usually we use it with small amount of value of error for example then then we have the arrow for what error for translational that is can be different also with the error width for this rotational movement of the room that we can add it on the translational and we can add it for rotational and in the rotational uh error again we have both the transitional and rotational error it means that although your robot also just only rotating maybe it is moving also in some Direction not only error is under rotation but also error is on some some forward direction to that we can add so now [Music] um what are these parameters where does these can come from you answer oh where we can find out these parameters over here this vmw is clear the control commands we say robot move forward with velocity of the translation of zero point for example two let's say let me allow the clarify this year like let's say you have a robot um what kind of robot maybe draw Flex this is drone for example that is flying okay then uh you can have uh V and W so let's say it's Z on the range of the v's on the range of the minus one to uh to one maybe use it with column and again W is -1 to 1. one is maximum speed so if we put one here is the maximum speed of moving forward if it's minus one maximum speed of moving backwards zero is like being stable and W based on the rotation to the left and right is maximum or meaning we have these values that already we know we send to the robot to run and based on that we saw that how we can calculate on this circle where the robot is finally and now we are adding the arrows and adding error on V and W adding error over here and over here and the Very doors coming from yeah again we need to test it simply your robot you test your robot from here you run motion camera move forward if it's completely straight that's nice but it ends up a little bit in the right or a little bit in the left you add the arrow you adjust the parameter here for uh for moving forward what is the error of the uh it's right it's right movement or rotation so what does it mean straight movement and rotation your robot may go and hit like this like a little bit moving forward let me sample again so your robot may move and end up here that is the error that you have on the uh straightforward movement and your robot may have error on the rotation end up from there come here but end up like this and that's the error that you have on the rotation and just control command that you're saying okay my robot goes straight and for the rotation again if you have some rotation you may have the error for moving straight and rotation again that you find it on your robot and plug it over here any question so now let's say okay come on choices for uh how we can show those errors like how you may think okay I know that if some value how to add it to my equation uh is like you can use the probability density function with somebody on speed that shows how much error you have if you want to add the error to the system in probability form that's very simple you can use for example normal distribution with zero mean zero means that is like and we don't care about the mean but the variance how much is bigger my error is bigger how much is smaller shrinks my error is shrinking and and the error that we are talking about is for is in form of the uh like the Epsilon B that the Epsilon that we discussed here the Epsilon if you consider whole D all this term as B we can plug it out for example if our distribution is normal in normal form and increase the uh being unlikely where we are supposed to run another race triangular distribution that you can see both of equations how we can calculate it this term over here this term over there and density of the distribution function uh is shown by uh zero mean and variance B so um okay like this I have some implementation examples that I will show you soon for those because some of you have some uh small problems over here now uh the better model of the actual pose x t equal to X Prime y Prime Theta Prime after running the motion command V and W at the time x t minus 1 on the XT and WT can be this time over here but what we studied simply everything is same we just change the V and W to V hat and VW that includes noise too same equations same term that we calculated for the prediction of where the robot is moving only based on the motion Commons of rotation and translation because the rotation and translation also this time include the error how here be sure we have W hat is equal to VW that we have added five error an error can look like this and we have finally got the remover clear one thing is remaining and what is it ah the thing that is remaining is final orientation if we want to generalize the the solution that we have for velocity motion model it means that okay now I exemplified this year robot bearing is looking like this and we have the VW some constant value some some values then robot let's say move this green line and if it based on delta T that we have if robot ends up here what will be the bearing based on calculation that I have the bearing will be this right so robot moves from here and comes and into and bearings but what if what if if I wanna generalize to show other bearings if if I want to use the same term to show if the robot is moving but bearing is not there is here or is here or whatever it is so to generalizing to representing that one I can add one more parameter that is called Gamma Delta t to the calculation of the orientation that I had so here we calculated the X X Prime here we calculated the Y Prime the position here we added the additive data the orientation or the bearing of robot if this term over here but now if you want to add that we just simply add Gamma Delta T that this Gamma Delta T represent the final rotation of the robot that we may have and of course that final rotation again may have error and that error can be also included by Epsilon Alpha 5 and Alpha 6. we had alpha 1 Alpha 2 for these two Alpha 3 Alpha 4 for the second one and now for gamma Alpha 5 and Alpha 6 because they are different values that we can adjust for the final error that we have on the rotation of the robot and final pose and that's since it is included the noise too we we I've written uh also in the book it's written as gamma hat if it was gamma then it had no error just the rotation and that rotation also can be depending on the time that amount of time that we apply the additional voltage okay so any question I'm losing my view now you wanna see the algorithm of what we studied uh calculations of the uh algorithm for computing probability of the XT given by previous X and motion command so the pools of robot given by previous pulls and motion command that people based on the velocity information that's given and velocity information that's given for this position and the uh and the velocity of the transitional and rotational movement at during density so here we just want to print it and show it in probability form that how we can show the probability of the if robot moves from initial Force to X Prime X Prime y Prime with these parameters then how we can calculate the the general algorithm will look like this first of all I Define the some some notes and I explain what are the notes there then I break it down a little bit I'll explain what's happening over there so first of all we say it's T minus 1 is the vector the pose of the robot XT is again the vector new pause after robot X Prime y Prime Theta Prime from here robot moves to there u t is the velocity Vector V and W that we indicated clearly the probability a of B we will have a function probability of a of B that is here and also I will open it how it can work I will show it the comp it computes the probability of the its argument a with a zero Center distribution variance B so the distribution zero centered and variance B how much the error is and it brings it to the form of probability then we say control can be computed uh in during delta T type delta T constant time uh there is a reason that I put it here because we say okay when robot is moving of course speed can change too right and here we are not talking about the change of the speed we're saying if the robot is moving and we are predicting over here they speed is constant because of that delta T is constant if that moves we need to also also consider that one and if changed I mean we say okay the the BMW are constant during delta T they are not changing because if they're changing it ruins everything and you need to include it or you can break it down to a small uh tile steps so that you can calculate between those time steps that the speed is not changing any kind of discretible and parameters Alpha One Under 12 Alpha 6 are the robot specific motion error parameters that we explained exactly for at the beginning we explained and two later on the final rotation that were indicated all Alphas now let's uh break it down first of all we want to find the center of circle so what is the center of circle when I'm referring Circle I mean this circle and I want to find this Center here over here we want to find it out how we can find the town in practice so we can have this three times here Center of circle that the center of circle can be shown as X star and Y star finally we want to hear written xcyc is the same X star and Y star so uh we say for the robot that move from this point to X Prime y Prime we want to find the X star and Y star we don't have Theta anymore of course because we don't care about the the angle here we just want to find two points in order to do that we can write this term so I'm explaining What's Happening Here the for the center of circle we can calculate in general in mass x star y star is equal to X Y of the of the point that we have and the Lambda scientica and Lambda cosine Theta that that is equal to another term here and this this first term means that uh uh Circle Center this Circle Center is orthogonal to the initial heading of direction of the robot that that we want to calculate later so oh that that this orthogonal means this minus and positive because of that it is our token and why that's happening that comes from Mass how we can uh find it I'm not going to prove it exactly and and based on that what we want to do we basically want to calculate the halfway of the calculation and adding halfway means that um if we if you have a line here for this circle we are talking about finding the center circle and this is in the middle of it right because of that we can write this term is equal to this one over there but one very very mu is coming and how so this division by 2 is X added by X Prime divided by two it's simple and why same you just add it and divide it by two to find the center but how the MU is coming for uh for for adding this term over there it comes from here and this is a unique solution to find it out and it is already proposed to you in Mass so uh this mu can be calculated by this time here I'm not going to prove if you are interested in go study why that's cosine this term like 1 over 2 why this is happening over there and finally if you plug it back into mu then we have this big term over here for calculating the center of circle and if you want to write it in form of code we can write it like this finding a meal based on the parameters that we have X Y X Prime y Prime and detector first initial this data initial bearing of the robot then based on the calculation of mu then we can plug the same uh the same term over there this one put it here and calculate it we can get the X star and Y star less central circle so if you find the center of circle the event uh most of the paths here then defining the other things will be easier how let's go step by step first of all uh we need to find the radius after finding here you can find the radius here you represented as r but what is it it is simple occlusion distance between differences between x and x Star Center of circle and the X the point that robot is and the the differences between y's and uh if you get the square root it becomes including a distance and this gives you a value that shows a distance simple okay clear after that what we need to do calculate we need to calculate now the uh the amount of change of heading direction of the robot so from here the heading Direction Change to there right this heading Direction how we can calculate it but this line over there that is uh arctangent two of the uh the differences between the center and the a d y and x the center of the circle and center of the very robot poses and Ultra engine two of these over there uh like like the differences between the um the prime ones and the previous one the differences between this one and this one for each one find the the alpha Engine 2 and find out the uh differences then you will have the change of the heading Direction how much it is changing uh so for our tangent 2 we already have seen but our tangent 2 if you have like x y a point on the coordinate system you want to find Theta you can write data is equal to our tangent the velocity Y and X so be careful Y and X then if you calculate our tangent 12y and X you get this Theta and based on this we can of course find out the the first one and second one first one second one and finely change the amount of change that we have so these are tangent 2 also implemented in most of the programming languages and it looks like this because we don't have archangeline mass so it can be written as our tangent two of Y of X is equal to our times if the x is greater than zero the this element is greater than zero we use the arcangent of Y divided by X if it is smaller than zero we use this term if it's uh x equal to Y and both of them are zero we we put 0 there and if x is x is 0 and Y is not 0 we just can uh sine of the uh uh y so so that's how we can calculate our tangent and our tangent can be applied on this then we have finally Delta Theta that Delta Theta represents the changing of the heading direction of the robot then now finally we can not finally but now we can calculate the velocity V hat and W hat from D distance and the Delta w Delta Theta we found it over there so Delta Theta we found it over here the amount of change and now we want to calculate the velocities two velocities how much are they based on the this calculation over there uh what we need to do we need to do uh calculate that one over there this Delta distance so Delta distance can be written as distance times Delta Theta what does it mean it means that the amount of movement that we've had if we multiply this with delta T the amount of change then using that amount of movement and amount of change if we multiply that we can we can use our we can write our motion command our motion command is our motion command is equal to V hat W hat equal to uh delta T transpose times Delta distance and Delta Theta this Delta distance is this term over here we place it plug it here then if you time it on this we can have this term over there so this one times this one if you plug it here get the distance that comes from times of these two can be R star times Delta Theta over delta T that gives us the translational velocity and for rotational velocity what we do here again delta T uh uh transport times Delta Theta that becomes Delta Theta over delta T that this gives us all the orientation the velocity of the rotation actually and particular final rotation that we discussed we need to add don't forget it the the gamma the gamma can be written as the as the differences of the are the differences of the Theta Prime and Theta the the differences of the rotation subtracted by W hat that will be defined over there exactly it just Rose comes here so then finally we calculate the rotation and we can show them in form of probability how we can return probability of these differences of the V and V hat so the command that I send to and the command the the velocity that have we sent and the velocity that we calculated all these efforts here and and the error and represented in the form of a probability this function here this function gets the mean and variance and mean and variants are like we can this mean and warriors the differences and the errors of V times the probability of the differences of four translation for rotation and four final rotation of the uh comma then all these can give us the probability of the Velocity motion model by calculation that we've shown if I want to show the normal distribution function how we can implement it you just need to write algorithm probably normal distribution A and B A and B are coming here this one's a and b then A and B can be you can implement this code over there if you have normal distribution if you have triangular distribution we can write this form over there calculation of the return of this term or that one then then that's it a means the mean and P standard deviation year of how each observation value can be changed over there I also uh show how you can do that in in form of probability I've written a function for normal distribution not using the library that you can for example if you want to implement this over here you can use this function normal distribution function to to generate this or just calculate the value without generating all all of it this gets all X's as all the points and calculated each one one by one and here just calculate the final result and I printed it so uh for example here two two after calculation bring it and make it in form of probability I show that because these are simple maths you can you should not have any problem but I see many students have finally problem of how bring it to form of probability the values this can come to form of probabilities like this simply okay I think uh I think I'm not going to continue automatic motion model because you can get exhausted I'm sure because also we have lots of maths here too but that's very simple the hardest one we went through okay any question this is also assignment for you but you will have long time because you have already one just you need to uh coat these uh but you will have long time to do that why why laughing yeah I know if you want to learn you need to implement otherwise you you don't learn you just go through the a general example I also have many implementations of these but uh if you do that you have to do that because there is a reason because all these is just UT and that UT goes there all that equation we just calculated one so far so this is Islam welcome to Islam environment and and for for the observation we have something similar that's those two and based on the sensors that you have if there is no way you have like laser scanner lighter you have a vision you have whatever it has it could it should be modeled to be come into the what we are wanting to feed it into base filter and make it more complete later then so that uh that can really work and in industry in Real Environment and really you can make it use and if you implement this small component you just plug it together then you have finally a big very nice algorithm to be engaged in in any any problem that are state of the art now so for now uh I think that's it we can finish the class no need to because we don't have grid of course I don't use those bricks and I terminate classes any question X star is the center of scent Circle yeah this is the exist star and Y star no no no sorry not that one here exist star and Y star Center of circle X Y is this one and X Prime and Y Prime is this one any other questions so you're running fancy algorithms you're seeing on the YouTube that this is like very nice algorithm and localizes very well and and our professor is not teaching that so that comes from here this is just UT that blood block that goal finally that makes it fancy algorithm otherwise we can go directly around download from GitHub and run it and that's as it works very like I'm running Islam algorithm changing some parameters and I'm running Islam algorithm so that's not how it works this is how it works and this one of course go to Advanced algorithms like we talked about velocity motion model we have very nice algorithm orbis lab and that uses the initial and that uses the velocity of the IMU to improve the improve the uh monocular visual slab and to increase increase that this velocity motion model goes plugged into those Advanced algorithms not only this will be useful for our all algorithms called 950 extended column non filter particle many are algorithms that we are going to study but also Advanced algorithms are using because of that it is important and I think I clarified everything like Crystal I think you just need to a little bit look at the mass and what is happening what what they are coming and try to implement it to make it concrete for users any other question okay good so I dismissed the class thank you very much see you next week so today we are going to talk about the automatic motion model what does it mean again so in velocity motion model we said that we just want to uh since we cannot read any sensor so we have the Velocity parameters and robot is moving in the environment and based on that we wanna uh estimate or calculate where the robot is going and what is the uh what is the prediction for uh for input of the base filter but here uh we say okay if you have odometry and we have sensors that we can read and based on the robot that we have uh then uh then what we need to do first of all before entering to the topic I need to clarify this for you guys that now we have two elements like imagine one vehicle robot that moves in the environment what are the two elements one is the sensor reading that we have I call it as odometry the the one that we were talking all the time about was control commands and control commands were like you're saying okay move forward one meter 10 meters five meters right that's the control command that you send and you supposed to end up after like when you say okay move forward your robot's supposed to end at five meters but okay this is useful information right this is our knowledge that based on that in Islam we can say okay we know that our robot was supposed to move five meters we are expecting that robot is after five meter based on the control command that we are sending on the other hand second uh element that we have all the metric reading that is automatically reading reads some values for us and says okay uh how much we move so we have two parameters that these two parameters are useful for us to to consider take into consideration how uh we will uh dive in soon so we say it is also uh common to Simply consider the audiometry uh as a control signal and the resulting model is a core of the many probabilistic robot robotics systems that we have so of course if the amount of movement and sensual reading by audiometric reading if it's equal to the control command that we have it's the idealistic and that's the best then we don't have error actually but of course robot sleeps the videos is sleeping the error that is happening in the robot then we don't have a fixed coordinate transformation also and and and physical world changes the everything works if you want to have a quick recap we already seen how to uh how to calculate this so we said for in simplest form of odometry in simplest form let's consider just robot moves straight so first of all we say Okay robot is in some some pose then robot rotates then moves forward then rotates again so with this presentation we were able to uh to talk about robot that moves in the environment anywhere and we said that okay here we can find the alpha one here we can find the difficulty and distance the distance that robot moves and here we can find the alpha to how much final rotation has been done now and bring the audimetry reading and control Canal reading and show it in probabilistic form of the error how uh what is the the uh the probability of the error that we have based on the based on the control commands and automatically so consider this again keep load it in your mind but here the the the name of variables are a little bit different that the same concept and the calculations the same calculations just the variable names are a limited if you want to bring it in algorithmic mode what we need as input the pose the uh the control command and the previous pose as input and what we can do we can first of all calculate the automatic reading so what does it mean it means that based on the parameters that my robot as automatically reading have like robot rotates moves and rotates in the environment then why sensors reading some values and those values are showing with these hats like y Prime hat X hat so these X's are the initial pose then then robot moves then we have the prime ones and Theta Theta Prime are also indicating the amount of rotation in the mind first rotation and second rotation so that I can calculate this one Delta rotation one over here then then second row here this one I can calculate it and this final rotation I can calculate in third row very simple exactly what we've studied but as I mentioned to you now we have automatic reading calculation and we have three values per each one of these that they are indicating okay uh what was my sensual reading and how much robot moved but we have another important element that I told you and that is the motion commands parameters and that motion command parameters are the parameters that I telling to the robot from here to go there and based on that I can do the same calculations right the same things can be calculated based on one control command because I'm telling okay rotate 45 degrees move 5 meters and again rotate 30 degrees then based on that I can calculate the same um same same scenario for uh motion and after this of course I think it's very clear that how we can bring it to probabilistic form so we simply need to use the same function that we had in previous example the probe so that I can calculate P1 p2p3 3 probability probabilities that indicate the differences between these two parameters that I have these are with hats that you can see the difference and here the difference and they're just ah just the same Alpha One to Alpha for the amount of error that I can also add to the system based on the um based on the error that I know that will be applied on my control command to increase accuracy I can consider not only the pure control command of course I know that my plus my control command I have another arrow and that's that's um that's very optimistic if I wanna directly say okay my control motion motion parameters and control command is 100 accurate directly bring it to the uh the probability so I also can add my error on the control command and say okay I tried already 100 times and I know robot error is like that and add the parameters here then match these together with the auditory reading over there and finally finally merge all together and return uh the uh P1 P2 P3 that they are multiplied to each other and one probability can show me the uh the very robot for example what is the final error of the robot that is moving after after running this such a trajectory for me so of course for example uh if robot has more error on moving forward and if you go very far the probability distribution over there will be increased uh on on contrast it can be uh smaller on the ear if it's for example the error considered as gaussian distribution and we we plot it as normal vcd so now uh the question is okay let's say if robot moves on curve like this how we can consider that do you think because this is the simplest form of very simple we calculate everything like rotating move forward and rotate again now if you have like robot moves like curve based on all the material reading what they need what we need to do that's that's one one discretization approach that we can do but it still has error because how much we make it is smaller we still have error and we're losing like we have integral and we discreticize it and we're losing something there so same problem will happen here any other answer I think it should be very clear now based on last week and this week's study yeah exactly we can bring the parts that we studied last week about velocity motion model and we saw how we can calculate on Circle and we how we can find the center of circle we said okay robot is is here and moving we can find the center of circle and based on this we can estimate okay where the robot is with some calculations we can do the same thing here but we need to bring the parts that we need in those calculations to considerate inside here instead of for example these three lines of the calculation for example for control command motion parameter control commands you say okay my my VX if I consider V8 v y v Theta uh that robot moves in the environment this is like if you consider control Canal instead of velocity then then uh then where the robot ends ends you need to uh you need to deform the calculation in order to be able to do that yeah question okay needs Mass Fork needs you to uh to engage how to formulate it but you can also bring it into calculations or also as your friend mentioned you can sacrifice some some data and do some math work to also consider the circular movement of the road so now I would like to talk a little bit about the humanoid robots because also that's very useful for you for now are all considerations were like based on real robots I'm not going to show all calculations because this takes like three weeks of teaching a minimum then because I need to explain all the details but I want to give you a general concept if you already work with your manual robots you're already familiar with but let's see what's happening here so uh I'm I'm gonna explain okay if you wanna have automatically output from a humanoid robot what does it mean it means that first of all you have a robot in any configuration that it can be and that robot has kinematic chain kinematic chain means how the arms and robots legs and body connected to each other in simplest form then based on that you basically have implementation of the control that can be like inverse kinematical for working event what does it mean it means that uh let's say okay I'm humanoid robot and I want to control my arm so if I wanna grasp this object over here with my right arm what I should do as programmer so put each one of the joints that I have I need to send some position so that my arm reach here right but isn't it too hard because in 3D workspace even you don't know like how what what should be how you can say what is the position of this joint and this drone to be to be there too many parameters and and if it's just one time that's okay you can find it for position of each zone or angle of each joint but but if you want to do lots of things then then that's very complex right not only the arm you have legs of robots right left and everything and the sending exactly the position for each one is very difficult because of that you can have some Mass calculation uh that based on that mass calculation you can Implement Investments for example one of the examples there are many approaches also of the inverse cinematic so for example if I wanna briefly explain like analytic one what happens you write some equations so that you say okay I have the x y z of this object on 3D environment on my workspace then I want to have a function that if I consider my right arms in the vector end point and send send where x y z I want to be then that function calculates all values of these for me I Implement one time that it's very complex if you want to implement from zero yourself you're gonna suffer a lot but that's worth a lot too because you one time implement it the next time you said you you function okay go to XYZ then it calculate calculate how angle of each joint should be to be there and not only x y z you can have rule PTR rule PTR of R should be the angle on the end effector which is the uh heading direction of that the the the the end effector to that object so now we extend this knowledge to robot humanoid robot we have on same scenario on the leg so for example I'm I wanna say Okay robot brings his uh uh food or end effect or an end point of uh the feet to the forward like right foot to the forward without that so you can increase the X and robot should be able to achieve these sticks you increase the Y for example you increase the Z then you can achieve any 3D coordinate with robot leg that is achievable for your kinematic chain that you have because like if I want to say okay nothing else is moving right foot go exterior impossible right I have some limitations like this this is the end of the point that I can achieve and then you can calculate so this is the meaning of inverse kinematic we have some functions for each independent for example arm and foot then then you have some functions that can give you the answers the second part is trajectory planning trajectory planning means that okay now I have it I can have control of the each one of the end effectors endpoints of my robot legs and feet uh legs and arms so I want to say now how uh how they should move to be able to walk in humanoid robot so what do you think what is your idea how it can be possible imagine a little bit you have Humanity robots so far we implemented everything and we got to the point that you have control of each one of these then we for example XYZ will pick you up for each one of these four elements then how you can Implement work engine or trajectory for Network engine there are different ways if you think okay I can say this is robot leg then I can say okay this is x y z then this is x y z this is x y z this is XYZ I can't I can generate work like that but that's very difficult right if you wanna do a game manual same as what what I explained here that in analytical form we had it better for instead what we can do we can say okay we have for example sine and cosine right and what if I my robot for example write food if we look at from site like look at me like this if robot right foot follows this sign that's very interesting so because I have invested cinematic I can't send the position and if I generate this this part of sign and robot food follows this then I'm generating this trajectory and the other food can be on cosine for example on a movement like this just just consider offer but sorry just just you can generate this simple shown that but of course it's not that easy you need to do a lot of things a lot of things on the center of mass for example you if you if you robot like do this then of course files to the right so you need to uh generate trajectories on like uh swing then then lots of additional parameters on the Z and and maybe you need to add 10 of these combine 10 of these per arm per for each one of the joints then you achieve steady work engine but the idea the whole concept comes from here that if you understand this everything becomes much much sweet and simple then you can say okay now I can like what about my arm I can also my arm can follow the sign like this right but but if you don't do that your robot is like this okay now uh Part B finished now automatically how we can achieve automatically now uh so when you generate these step starts from here so we we say this is support slide and get support again support means on the floor and then slides on the air so if I measure the distances of between the uh the two supports per each one of the feet then if I simply talk about moving forward then I can calculate my Optometry just the distances for each one of the legs how much it is moving that can be the uh the the automatically reading of course for rotation uh also you need to calculate it or you can calculate it you need to consider calculation of the rotation of the food on the Theta then then you achieve a chieve automatic reading from the molecule so this whole procedure uh I also uh written on one of my Publications that if you are interested in you can read you can see how kinematic chain and implementation of inverse kinematic Works how you can generate trajectory based on this simple trajectory and how automatically can work on there but here we've done like learning based techniques how how we can learn this neural network that that this output of course we have error because of slippage and because of the uncertainty on the environment and and this is this contains a lot of around in different environments because like on the on the tile and on the grass and different environments it can be vary and and of course this can be trained by some neural networks to estimate the error and reduce amount of error that so if I want to summarize this uh this chapter the the most important things that we studied is a velocity motion model that we saw how we can from uh how we can calculate X Prime y Prime Theta Prime neopose of robot based on old posts that we added the amount of velocity control commands that we have and later we saw that okay this velocity control command is not enough because we have the error and we added the error by replacing V and W by V hat and W hat and we saw how we can or how each one inside of each one of these is and replace the equation then add final error for final rotation then we achieve the velocity motion mode so now after work when we are talking about the control cannons uh in different algorithms that we're gonna see so we can instead of UT fit the uh the velocity reading or automatically reading based on what kind of robot we have and what we are going to do any question here or here |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH13_SLAM_for_Robotics_Course_ORBSLAM_algorithm_details_Pose_Graph_Optimization_SIFT_ORB.txt | thank you okay hello everybody good morning so today we are going to talk about the different topics first of all posetgraph optimization then second we will talk about the visual feature extractions like surf brief and orb then finally we go through the orb Islamic cells of course all Islam has too many components that that are not coverable in short time and it takes long but we will try to cover the basic elements that are needed in order to understand the basic concept but of course you also need to study much more to make sure that you you understand it well but of course we try to clarify the small elements one by one so first of all we will start today with mapping we talk about the mapping with on the when we don't have any uncertainties then we talk about when we have certainty for now everything is clear to clarify what's happening then as I mentioned we talk about the pulse graph optimization we will understand how how we can improve the the performance of mapping using posegraph optimization then we talk about the visual feature extraction shift brief and orb then we talk about also bundle adjustment what is the main concept and what what what is it what what the rule is playing in the orbis lab we talk about also visibility and core visibility graphs what they mean and what are the what are the motivation behind then as I mentioned we went through all this land but before continuation do you have any question about previous topics and courses or any question about anything okay good so then fasting your belt that let's see what's happening first of all we said that in Islam we have two generals class of algorithms one class is online Islam that in online Islam we are doing the filtering like like we we've learned extended Kalman filter on the ended Karma filter particle filter that they are mostly are for State estimation based on the current measurement and previous belief so so this was mostly our Focus but on the other hand as I mentioned at the beginning we have full Islam problem too in full Islam problem we want to use full trajectory or full path of the robot that is moved in the environment in order to construct the map not only relying on the previous belief to do all calculations and and and predictions of the map so of course in online Islam we have real time more real time and more lightweight approaches and techniques that can be onlinely predicted but here we have for example techniques like post graph optimization that that as you know optimization techniques are also costly and Main may take longer depending on the performance that we want we have gritty techniques to solve it but but we still are more much more costy but what's the reason that we go into our repost graph optimization and fully slam the reason is that we want to don't throw out all the information that we already have like robot moves in the environment we have some poses where I don't use them that the the reason is over there so also this is knowing that as a smoothing that that is like a name given that says okay how the full Islamic can do the smoothing of the estimation of the robot post then we are following Islam problem so let's start is the mapping without uncertainty it should be very clear that if we have robot and this robot automatic model is very accurate or or we can call it also as dead recovering that depth recognizing means that the counting number of steps also is famous in Publications I mean the the name that has been used in research studies and Publications and we say that data programming is equal to automatic and on the other hand if you consider our observation model has no error lighter exactly can measure the distances of the any any obstacle and landmark that we have let's see what is that happening so we have the robot over here and robot observes so if this is field of view of the robot whatever the scan it has if this is the filter View and these green ones are the observation of the robot catches the environment based on that we can construct a map save a map on the on the 3D Point cloud or 2D or whatever we want then continue robot moves in the environment we run a trajectory it scan again so we add new part of the map that robot has seen but since be considered by default that if we consider by default that robot trajectory has no error observation has no error of course this is easy then we continue robot moves a little bit more we have like a amount of translation rotation of the robot based on the automatician observation then we construct it we continue robot rotates is that screen part and we add it in the map robot moves robot moves robot moves and we continuously do that so this is very easy no problem at all but the point is now that of course that's really ideal we have the problem that whole class we were trying to solve that first of all we have arrow in automatic models and also we have error in different different sensor models we can say lighter almost is accurate but still there are lots of noise inside and we need to do some filtering and of course we is not 100 accurate now let's see if you run the same scenario what is happening to understand whole idea so robot again is here and sees the environment as observation robot moves this time and after robot moves the new data that is coming based on the error of the model that we have estimation will be wrong robot our estimation if we don't want to apply any algorithm thinks that this this file over here now is it it is there or this obstacle Edge over here that robot was measuring is now here and there and if he construct without doing any any Improvement or anything we have the we have like observation like this then the the map construction will be left if you continue what happens again we have more error and odometry a new line becomes something like that if you continue more then you see that like this time this this wall estimation comes like that if we continue if we continue if you continue and if we continue so what you can see really if you want to implement it looks like something like this so so this is the problem that we are trying to solve but now today we want to more focus on the visual part of the how we can deal with this problem so far we basically try to focus on the algorithms that are first of all online Second double although to be extracting landmarks and features by default we said that we know the features we know the for example correspondences but today we want to first of all more Focus how really from visual information we can extract first create landmarks how we can match the features together as first step then bring it to the another like big algorithm so we say one of the ways that we can do and represent the Islam problem is use of the graphs so we want to say instead of okay for example occupancy grid mapping and having all this Dimension based on the previous predicted belief the belief and predicted belief what we can do we can say okay let's consider each one of the nodes of a graph corresponds to the pose of the robot on the other hand the edges of the exhaust between notes is the is the relationship or the constraints between the robot movement so that we can say okay my my robot control command is I'm running and I can I can connect two nodes together based on that constraints so that after extracting these nodes and X we can save combination of those and we can construct the postgres what does it look like so let's have a look at the same example to see what is happening we say the robot is here again the observation so I have a point here that this this this wall that you can see here that can be Point Cloud that can be laser scanner we scan scan then we have points over there but here I didn't represent the nodes so after moving the robot now in post graph estimation what I want to do I want to create nodes so we can call these guys over here nodes and we can create Edge between those of course maybe robot from here to there move like this path robot can create any any other trajectory but in post graph optimization for simplicification we want to create relationship between current posts and the next post and and make a graph based on that so as I explained we have node we have link or constraints and another node over here so now idea is if you look at the animation on the slides both rotation and transition can be can be applied to improve the the error that we've had there how so let's say this is the distance that the robot has been moved and now I can use those information based on the amount of movement and the the amount of error that I I estimate my movement has then I can move hole to the to the better estimation to have better estimation based on this this amount of movement on the link so now let's let's say robot again runs the same trajectory of previous slides and if we want to construct the posegraph in in during time so robot was here rotates moves there rotates moves there so this is like the trajectory and I'm creating just links between those nodes observation is of course the same so I'm just showing the same observation without without improving it we are only just creating the the the creating the post graph then we continue robot is there then we continue robot is there now the point is after arriving here a robot moves over there and see this Frame but this Frame if you have a look this Frame supposed to be this one over here the green one ready to show it in this side when we are here the scan the information that comes from environment supposed to be similar one that than this one that we know it as Loop closing and we need to detect it in order to detect it we will discuss a little bit more but if we consider that we can detect it now what can happen so look at our posetgraph and look at the robot trajectory real trajectory this is circular but there we have error so what we can do now we can say Okay using post graph optimization we can say that okay this position that robot is supposed to be this one now I can move this this point to there and with chain rule or optimization techniques that I will mention some we can then adjust all of these connected like it's a chain I can connect it together then hold will be reshaped together foreign how that's happening you can see that okay we detected the lock closing we shifted that one after shifting that one we can adjust it by any optimization technique that we know then we can form the posegraph optimization this technique is very useful one of the elements of the open slab one of the most advanced technique of the slab that so far we have of course we have improvements during time but but this this is one of the elements that we have there we have some notes here that I stated for you that we keep the relative distance and adjusting the loop closing problem and we can in the optimization parts we can use different techniques for example list the square error minimization can help us to do that and here I stated I put some Source or original paper that you can study to see details of how you can implement it during this chapter I will have a lot of these if you want to see more details of the calculation proof or something you can refer to the original paper and and see what is happening in details much more so what are the advantage now you can say yourselves we say we have better robot pose estimation of course because previously so far before this today what we've studied we studied only relying on the previous one then we were throwing up this this will becoming belief and next one previous belief but now we can use whole information that we have from the environment that's that's that's then we say we have we need to have a pass instead of having only one one trajectory and it can result to have better model of the environment in general so we have cups also here we say data Association is important what does it mean it means that so our robot was here let's say we closed the loop and if robot moves and moves again can see some features of the environment then again we can perform that that already have seen and again for example here they takes this corner over here that maybe can be detected of course this is not very good example because this part is similar to that part if the observation is like this and here like this but anyway let's say it is detectable so we can run rerun the loop closing problem to again adjust the whole trajectory that we have but point is so you can see in the in the in the animation here that we have so let's say we improve it much more but the challenges here that okay if we iffy in the posegraph optimization if the robot instead of detecting this feature over here was thinking that observation is from this feature what would happen if we wanted to reshape the link then we would destroy it almost because the whole graph will be trying to shift from here to for example here instead of here then we are kind of reforming whole and destroying hole because of that we need to be very careful with posegraph optimization to have many samples and try to have outlier try to detect many and and only pick those ones that high have high confidentiality that they are correctly the ones that we want so data Association is important very important for posegraph optimization is not like a predicted belief you you do just one wrong estimation then in future with seeing the features it can be quickly recovered to what what is the correct position here we can destroy so I stated some points here that that Association is very bad and we need to discard it by by feature outlier detection and remove the bad candidates from what we have in posegraph optimization so is it clear so far any question okay so what about the optimization part optimization part can be done with any online or offline technique for example some of the optimization we have seen ICP we've seen like five six five six different techniques after iterative closes close point so that so that we saw how for example in simplest form calculate the center of mass rotate and align them on the other hand we usually use a list Square errors of the minimization technique so that what is the motivation motivation is that if you want to find the error of the for example prediction or the or the alignment we just find the distance of the residuals of the this line with each individual one and then and then sum them up to have the general error of the r plus optimization so list the square root minimization is a technique due to that least square error that we can we can use the mathematical regression analysis and determine the the best fit and and detect the um did they try try different different methods like ICP also was using in some parts that how to minimize the error report it should be colleague now the question is okay so far we know that posegraph optimization idea what to do after after doing the area doing the photograph optimization how we can map it so the answer is we can use in a different techniques one of the famous one that also has been used in Orbee Islam is binary occupancy grid mapping so that how does it look like we already have a study in details how we can map it how we can update the beliefs of the each individual grid cell so we can say same example that we have robot moved in the environment and these are the vault at robot observed so what we need to do based on the based on the how how many times we see and based on the observation error that we have we also can use the base filter in order to represent the map that we have for example here if we have like high on high high centerity of the observation and multiple times of observing that this cell is occupied that cell is occupied with the updating the base filter we've seen that how we can increase the certainty here and for example here you can see that robot many times has seen error and this is like grayish with different colors that says we are our our map is less certain that this is well here or one of these representing wattage so any question so the thing is like the obstacle that we had there just here we have the h not not the obstacle behind because we are not observing what it is over there so Paul graph optimization then mapping and after mapping I have some some exact some points here here in posegraph optimization we're using fully slab that that that not only belief on predicted beliefs that we can have also much more accurate one a practical and exact implementation in this stance you can see here that we have a corridor that the robot has moved in the in the real environment and constructed demand but this constructed map you can see we almost don't understand anything everything is like yeah this is from MIT the code then after optimization if we apply the optimal the optimization and construct the map if the occupancy grid mapping you can see that posetgraph optimization helped us to reconstruct the not pretty nicely and and create probability that these white bones are free points black points are filled and the gray scales are like 50 50 that we don't know the observation what it is there so if you also want to see the details of how this is happening and how they conduct it experiment you can look at this paper over here that that's how it is working any question so far okay now we want to talk about a little bit more and open the visual feature extraction we want to see when we are talking about the observation from environment what how exactly this is happening that we can extract features of course based on the different observation sensor models I'll be different between different sensors that can be valid but but here we want to try focus on only camera because it's much more first of all accessible for us cheap and also is like more understandable because we already talked about like glider scanner kind of mapping with with constructing the point clouds and and running ICP to constructing so to understand this we will see a different algorithms these algorithms are very common and famous in matching Vision robot Vision techniques we have algorithm like shift surf brief and all why we don't directly go to the orb because to understand the orb we have to come from here we have to understand what is happening here almost what is happening here then we can talk about the old featuring section but finally after understanding this I will show that there are of course many libraries and implementation examples that already did it for you you just need to call and it will run for you but we want to see really what is happening not just using what is existing we have to understand what is happening in order to extract the features and if you want to do research of course we need to improve this by knowing what is happening on the on the background so these techniques have two steps these two steps or two elements first of all is extracting the key point so that key points are extracting the location of the distinct local feature in the environment after extracting the key point so we kind of need to describe it so this is the key Point okay I found it out that this corner over here is is the feature that I'm on my camera sees and that's but but how to describe it we need to propose techniques that describe the extracted key points and why we need to describe it do you think yeah to match in the next you use it in next steps like okay I extract the feature from from here then robot is moving so just exactly the feature is useless later I need to kind of describe that feature so that if I see it in future frames I can say okay this guy was the same guy that I'm seeing feel motivation the idea of these characters is to describing the features of the hippo this is like I'm seeing you of course I see that like you where red jacket and your your face features and the other everybody I extract them and I have some information as descriptors in my mind and same thing something similar is happening here but in form of vectors not not learning technique usually but of course it can be learning technique you can when I'm when I'm going into diving into you can think about okay how we can do that in much more Advanced Techniques how I can propose new technique in order to do the same thing with the algorithms that I know so what's the idea of of firstly stage we can say finding local distinguishable points as features if I find feature from table surface over here it's almost useless because if I move here it's almost same right so if I'm looking at this wall if I try to extract feature from here if playing is useless because if I go somewhere else will be pretty similar so the motivation is kind of find the distinguishable points like I'm looking here if this is my view the the most important is like that feature these these Corner features so the the idea is try to find distinguishable features so that in new frames or different views I can I can find the correspondences here you can see that we have two image frames that that we we extracted some features over here we will discuss soon how this is happening and what are these ones but you can see that from Sky we don't want to extract any feature and if even if it's like features from clouds they're gonna move and go away and destroy our our information but the technique that we have you see that mostly the extracted features from the parks that are more important than here you can see that also also the features that we extracted are much more reliable and as a human if you can see there is no not any element from sky so in order to understand what is happening we need to dive in the first algorithm of the feature extraction shift it is scale invariant feature transformation that that his name is sift and let's see what is happening first of all we don't have only these three four algorithms we have many different algorithms that can give us features of the each frame of the picture for example we have Helix and then many others that they are not usually robust in order to extract the features or if they are robusting in order to exactly features they are like they have some problems some of them are not invariant for the rotation or scale like for example this is the feature that we extracted the same thing if it becomes bigger then our technique just like with the for example here it's just that that's the text this part this part this part this part but this should be seen as general view not not the not small elements anymore in order to match it's like you detect a feature your robot moves to the to the closer then same object will be bigger and we cannot detect so so that we say sift is rotation translation and scale invariant you can see it's in name two so scaling variant feature transform s i is standing for scale in value so and this makes it very suitable for landmark detection in the in this land problem that we have that that usually it has like the technique includes the the ways that remove the illumination of the distance that we have and of course the Escape how it is working we have some main steps first of all as we stated that all of the techniques that we are going to talk have a extracting the key Point second Computing the descriptors descriptor for each one of the keyboards let's dive in first system what is happening we are detecting corners that is including the x of the frame so we get the frame of the picture of the environment then we want to calculate the X extract the X so how we can do that we can use gradient what is the gradient gradient is big change in the brightness in the environment so when they change and the brightness is happening if you look at for example the corner of the door over here where the visual information this is like changing the color is changing dramatically there so that can be the motivation to to extract the features or here for example here and here so wherever that is happening we can say okay we want to extract the features so what we're doing in practice we are searching for intensity change so how does it look like let's have a look if we talk about um small discreetly part of the frame of image they can say okay we can have a frame a part like this like this is the part of like a frame small cube that the color inside is looking like this another cube of instance of image frame that we have looking like this this part is more darker this part is white another human being can like this upper part is dark darker Downer part is wider another one is like majority part is dark so what we are looking here we are looking for locally distinct information that that that also we can we can say mathematically they have larger hidden values so that we already discussed what is the income values So based on that we can say okay let's arrange the information that we have intensity that we have inside so if you get the average of the intensity and try to draw some arrows to represent what is it looking like here the arrow is like in the same size because the intensity distributed evenly inside the part that we have over there but here you can see arose more tending towards the lighter part that shows us information of the this part that we have and here you can see the arrow to the down is higher because the lighter part is in downside and here you can see something similar of course here here we have much more because because only the light part is in the corner much more representing that okay it should be in the corner of that that part of the image now you can imagine yourself without even moving further more if you have a frame and if we greet it and if we can calculate intensity for each one of these small parts without doing anything then we are converting RGB image to some information that that information or like for each one of the cubes we can have two values kind of re-encode all information of RGB too many to small grid cells some values that represent something meaningful for us okay so far but of course this is not the thing but generally what's up so we have couple of steps let's see how shift algorithm is working first of all we need to we need to after doing that step we need to apply different levels of this moving or bluing we can apply different levels of caution on the image frame so you have pure image frame that is completely normal then you can apply different gaussian models on that to make it more bluish so after doing this we can the the idea is subtract two of these levels that are like if you increase the level of the bluish you can subtract two two subtract two two subtract two two and continue in the set second layer so if you subtract this to subtract this to subtract these two so you will have higher another another layer that that shows the differences of the gaussian if you want to understand it we can say okay if we have this blue image and if we subtract it with another level of polar image we are extracting we are getting the information like this over here that that this is one of the elements of the shift that we need to apply we need to do in order to in order to first of all extract the information that we have from image second part is applying different scales of the image because we said shift is scaling variant it means that when when the camera is moving much more closer to the obstacle object that we have it can detect this game how that is happening the idea is looking like this over here the step that we have after applying the different level of discussion subtracting them in order to get the points now we can say and do the same job on different states make resize the image make it smaller and and do the same thing on the phrase so that we kind of saying okay if I'm seeing this in a frame then I'm considering okay make it smaller smaller smaller so that then I'm going farther then then I know what it should look like so that gives us the looking of figure all this one so we're applying the same gaussian gaussian gaussian at this size and make it smaller and applying the same gaussian gaussian then doing the subtraction in different levels and layers so after that for each one of the key points or Corners we need to find the best and the maximum value and looking like how how we can do that so after doing this scale and after doing applying the gaussian and and doing the scaling on different levels what we can do we can now find the extrema points external Point says okay in different layers of the results of the subtraction that comes from there now we can find the extrema points that is kind of saying the Computing the corners that that which one of the eggs are have maximum value in comparison if we compare these two points like corresponding points we say which one is which one is more reliable which one has higher value as maximum point then then in different layers of the in different scaling and in different layers bring the more important information out so that we have we have then then the features that looking like this doing different caution subtracting then after subtracting the defining extrema points which one are more more reliable in different views then we can extract features of image that's looking like this circular potential so now let's say we have these points what is the next step Next Step saying okay how can I say what what this picture this this point over here looking like what is this one looking like in order to do that of course I want to match the information of the left side for example with another image that time come that is coming from frame that is rotated or or from different angles or from different distance saw that in frame a I'm detecting these these features in frame B I am detecting these features that can be different now I want to say okay which which is this feature which one is this feature in that frame which one is that this feature in that frame how can I do that by describing each one independently and that description looks like something like a vector like this that that we want to extract we will see how to extract um okay what is it safe doing we say shift saves the location of the pixel of the of the feature that we extracted gets the scale information gets the orientation and descriptors itself in into as information inside what does it mean location is the pixel location of the keyframe where it is for example when you your your camera is seeing some feature upside more likely wherever you go it should be upside that's why this position is important something is on the ground some feature is not going to fly after one hour right because you mostly is the downside it's because of that location is important feature yeah it's scale you scale of the key Point that we can got from that that we can we can say how how the differences between the frames has been changed so we will discuss it how that's happening is like when we are extracting different layers and rescaling it so when we are subtracting actually also we're saying okay this feature and this feature are getting smaller or bigger so with getting differences between the rescaled one we can get the information of the scale part and put it over there then the orientation the orientation of the each key point in next slide I'm going to show how that's happening the orientation is like okay we need to calculate this this point over here of course it's circular point we don't have orientation there we will see how we can how we can extract some information in order to give orientation to to save it in the frame next slide you will see and the descriptor that is 128 dimensional floating Point numbers that store some local surrounding relations of this point not only those information like the the location scale how big the how big the scale is and the orientation we also want to describe it with some features how that is looking like let's have a look here let's say our shift algorithm detected these features some of these features are like small Corners some of these features are bigger a little bit bigger size that that can be based on the the applying gaussian and finding maximum extrema fine we say per each one of the features let's choose one of the features and and make a grid around surrounding that feature the size can be depending on the parameters that we are written so after we having this for example extracted feature from shift we detect we we put a grid around it and how that is looking like it is looking like this one we say okay we can break it into four times four cubes one two three four and each one again four times four cubes that is representing this circle here in form of Q then we can compute the gradient and and if you can put a gradient based on this what we want to do we want to say okay this part over here this small part region over here should give me some meaningful information this part over here should give me some meaning of meaningful information in order to do that we can for each one of the parts we can we can apply the key Point descriptor that that says okay what is the intensity over here you can see that like if this part is y this part is darker based on that I can bring it to the end to the eight different values that is kind of instead of in the in the couple of slides ago I just throw it with two arrows here I can show it like with eight arms in sixth we have eight arrows we can give more accuracy bring 16 arrows for whatever now what is the idea taking the taking the feature that we detected giving some neighborhood for that feature not only that feature giving some neighborhood that is bigger then create intensity then detect some some values based on the arrows and how we can now present it in the form of the descriptor we can say we can apply the histogram of these ones and say okay how many of these arrows are existing over there and say okay to the right is this side like this many to the upright is this many just content how many of these are over there and get some values based on those just put numbers so these these all values these old calculations can come to the numerical lines now you should you should the idea should be clear that that now I can describe the features so that this feature over here that I can see are is different from this feature how because of its neighbors its intensity has some unique information that this one may has know so what we do four times four times eight becomes 120 H Dimension descriptor that we added in the in the key Point frame over there so that we can use it in order to match the key points frames by in different frames that we are observing how that's how that can happen how we can match the features what do you think now simply we can find for example let me see we can find the including distance we can say okay we have one for each one of these I have this crypto and for each one of like here I have descriptor and here I have descriptor for each one of those then I can compare it by calculating equilibrium distance among all of those and all of those clear what's the problem then we have a big problem nowadays problem what can be the challenge no idea everybody is sleepy yeah this is just beginning we have today long way to go this is the easiest part yet so the problem is it slowly and distance of the each one of this descriptor let's see I have this point over here now I need to match it with this one how can I do that this point should be compared with all of these right now the second one should be compared with all of these third one should be compared with all of these that is big array and calculating the distance of the arrays that is at it very expensive to compute so that that's that's one challenge that we have we will see how to improve it the other challenge is similarity in the image that can give us more correspondences also a wrong correspondences that we say okay this guy over here is very similar to maybe I don't know which one maybe can be more so I did the three one the three one the the features from tree can be very similar to other parts of tree that that makes it also a little bit challenging over there so how we can solve that we can we can in order to not only the computational complexity but also similarity to in order to deal with it we can say choose the best matches and create threshold value in order to in order to throw out the outliers the features that are not very reliable how you can do that what do you think the simplest technique if you have those arrays the the key descriptors of these now if I ask you two some of them are that are more reliable what you do the easiest way is like choosing the ones that more value in this crypto that the differences between the the the the brightness is too much too high gradient is too high when gradient is too high you can say okay for sure this is corner or something is not like shadow clear so where can I exemplify this so the corner of this table is white I detected that feature but the corner of this this this one that is on the with right side there is a high contrast is more reliable to detect than this corner over here if this if this is black even for human the brightness is is in highly contrast you are less chance to beat it because you obviously can see that this black that is white but if they are both totally white even human it's hard to detect it you may hit it or something you don't see so although you can detect it so that's one technique of outlier detection so as I in advance the biggest challenge I explained to you the safety is very expensive to compute that I stated over here for you so in order to now deal with this challenge we are moving to the next algorithm pre-algorithm that is binary descriptor we want to see first of all what is the binary descriptor then then how we can play bring it into the game so the idea is selecting a set of pixels around the key points K frames key points of the each frame then Computing intensity using the single pattern to perform it after doing that we are we are concatenating the comparison of the results all together with some simple group to define a descriptor so we want to now say okay that big that big key features descriptors that we extracted the array is very nice but but it is expensive to calculate it is expensive to calculate the including distance now how we can bring it into the to the binary descriptor is like three steps and one rule the rule can be defined by ourselves is like one if else let's have a look in the next slide what is it looking let's say this is the same area that we choose them and this represents pixels and and intensity of the pixels we can say okay let's have some comparison between these pixels that can be random that can be on some patterns that we will see then apply some rules so I'm saying the pixel number one and five six and four eight and six three and seven I'm creating a rule what does it mean I want to compare pixel number one and five number six and four eight and six and three and seven so if I apply this rule if the intensity of P1 pixel one that is this one and pixel 2 that is second one what can I do like if this is smaller than that put 0 otherwise put one over there so that we can compare it if pixel one is it smaller than the intensity is smaller than pixel 5. is it no zero six is it smaller than four six four oh it is not clear here but right in this monitor low quality but it is so then it is one believe me so then then a can six eight and six one yes it is intensity then with three and seven three and seven it is not three is not created it's smaller and or more brighter than the seven then it's so what I've done beautifully Define a descriptor instead of instead of calculating that descriptor that we had as like big array of the information now we put 0 1 0 1 0 1 in order to describe the the neighborhoods of each one of these key points that I extracted so we had the image we have something here like some some for example building with some trees then whatever that we have then we extracted some features then we say okay for each one I'm creating neighborhoods then here I created some values but instead I can put them at zero one zero one zero ones the final descriptive clear what is the main advantage it's clear that this computational complexity compact descriptor to store the data it is smaller requires less memory and has to compute the differences between two descriptors because this binary value is like like very easy to compare with in comparison to that part now based on that idea so what why we understand binary descriptor because we want to use it in brief that brief is kind of tries to improve the sieve technique and it's like binary robust independent element features it's like standing for binary robust independent element features and how that is looking like it is using 256 pairs of descriptors that is based on the binary descriptor what does it mean it gives us some patterns of of any region that these patterns are using the same binary descriptor idea in order to say okay each one of these lines this pixel should be compared with this pixel if you have uniform distribution of the the binary descriptors this one should be compared with this one so we have a pattern to do that another pattern is gaussian pattern you see the center is more dense the corners is less dense we have another one is like this this one that's that is like this critical caution that is that is less less dense with less features so we have we have something like discrete location one that a little bit we have also pattern over there we have polar that in polar like everything comes from Center or or crossing from Center to compare the pixel colors so what does it mean it means that we want to use this idea of the binary descriptor and use some predefined patterns in order to do so you see that the idea is very simple and the algorithm is very famous if you go study the paper it's simple but too many citations that this guy I think this has come from original paper presentation that he did this experiment and with this patterns for first time and you can see that the feature detections are working but the problem is that here it is not working very well with the rotation so it's not very clear in the image frame but with the experiments that have been done I also will show the comparison after finishing the part we will we will show that it is not a very rotation robust in the rotation part but but we still can work pretty fine so you can see the original paper has been proposed in 2011 just giving some this idea combining with binding description and it is still one of the good algorithms for feature detection from from frames any question okay so now we want to talk about all feature detection the orb stands for oriented fast rotated brief so that we are going to take the brief technique and and kind of bring a technique in order to solve the rotation problem just we have SIMPLE a simple idea to merge it to the brief in order to improve so we have the shift binary descriptor brief now we have org that tries to improve the latest algorithm so the idea of course it is covering the shortcoming and always performs as well as the shift technique if it is as good as Swift why as good as if because shift was proposing a big Vector of descriptors and it should be the most accurate one because when we are doing this we are losing data actually but in comparison we will discuss it so although it is performing as well as shift but also in feature detection tasks is better than sir and which is fast so this side orb Islam builds the key key Point detectors are similar as brief and let's have a look what is happening so here you can see two frames of pictures this one and this one same image that we have our camera detected from the information so what is happening with the orbus lab is considering the rotation for whole image so the idea is kind of thing okay I have this Frame and neither or during time this Frame is coming if something is rotated in the frame is not the pixel solely if the environment if I'm like looking at the environment from here and I'm coming here actually it is rotating the frame and the idea is okay if from there on here we have frames of the frames of the environment if you want to rotate something or just something whole should be rotated together because maybe if a guy is doing that in the middle but that whole scene is not doing that whole scene should be rotated all together so the idea is simple but very strong and robust and works perfectly fine what is happening how you can guess it what we can do here so we don't have the picture so we already performed the featured selection part then after feature extraction part we have some some points and descriptors what we need to do the idea is calculating the center of mass of the this detected point and based on that Center of mass of the detected points that that can be calculated with simple equation over there based on the intensity the intensity and the pixels that we have so and I'm replacing with it as like zero and one making us binary descriptor then after that actually here we can put the the moment that this moment is the differences between intensity using that moment we can calculate the center of mass that this calculation is is here we have the mass of the image block with m00 then then these two M10 and m01 is the centroid of the image block then after doing this simple calculation we can get the orientation but by getting the r tangent we can have detector an amount of data and the place of center of mass can be give us the rotation that we want in order to in order to when we are calculating the first frame and second frame the points all will be based on that that intensity and calculation of the intensity of the center of mass is kind of finding this and what is the intensity what is the intensity here based on that rotate it first then we start to match based on how lightly it should be rotated to to bring intensity more closer to this one of the distribution of the points then after you do that then you start to match it of course we may have still error but but rotation makes more sense to to match before before doing anything else in if you want to see more details of how this equation comes almost in details I'm not going to prove or show more details but that's like also almost all of the scenario nothing very complex you can have a look at the original paper presentation of the orb feature detections so what they've done they've taken the the previous technique at calculation of center of mass rotation and compare improve it and again very famous publication that is working also nowadays in very Advanced Techniques I represented some example code here you just can copy paste it into your computer load the image put in directory test.gpg then you can exactly all features just a few lines I've got finding the key points of the orb.detic image and some input parameters that's it all the efforts can be done in one line now okay question here we have some comparison that you can see the the comparison of the shift Surf and board that here first of all first table in this part shows the time comparison what we've done with the techniques that we have [Music] the Orbee slab has the the less time consumption it is the fastest one because it will it uses the binary descriptors so the time is very important for us but on the other hand if you look at the the technique itself shift performance match rate is higher why because it uses the descriptor in form of vectors because it's like it saves more features but that's that's more than 10 times slower in terms of in Terms to computing the performance although templation is higher but is almost acceptable just 10 we are using 10 percent of the accuracy of the match rate but on the other hand we're gaining 10 times faster that's first point so you may say okay I don't have any problem in competition computational Power then I need really accurate one day I want to use this one can you can I use it I say still you should consider one more parameter and that is this one the rotation we said that the orbislam works pretty fine in rotation part and you can see that if you compare it with like directly with sift like both in zero degree rotation here the performance was like over 100 but after rotating for example 250 degrees the orbuslam works better but this is 93 this is 97. after 180 80 degree rotation works better after the other ones also are also closed I think here if we compare with with this one I I forgotten to I didn't I didn't mark it because it's not this is not a little bit worse than the another algorithm surf that that is also pretty similar but sift is almost close but if you want to conclude of course orb is more robots in if if the frames are rotating too much on the other hand faster any question now in rotation no in matching in matching it works better in matching it works better although this is like very close but when you're rotating like you rotate 100 100 degrees then that's worse yeah let me go there rotating inside the image so this the idea with the center of mass is good anymore right if if the if you are missing whole object from a more partially the object from the frame that we have yeah you're right totally different but but we say okay we are performing on the keyframe of the video stream so that the differences of that if you can calculate higher higher frame rate then you will have higher accuracy because we are not jumping like going too much then compare it just differences between two two frames continuous then that's the key point and even if you all be slam if you can calculate 60 frames per second that's the output is higher accurate than like 10 frames per second because of this old feature extraction and future matching because these feature matching now you can consider if I if I have these features and the next features next features next features I've learned pulse graph optimization and those features are creating the nodes and Links of the pose for me I'm connecting those together when video stream is like I'm detecting the features moving moving new features comes and new frames and I'm creating poles of the posegraph of the optimization based on that and and that's like how accurate I can higher resolution I can get my posegraph optimization technique will have more more notes and will be more accurate during time is like oh I think it's very clear but let me also visualize it here so you have so instead of having like robot is moving with these peaky steps of seeing the environment the field of view fov that it has then you have more instead of course then you have more robot causes and how much more of course better and you don't have that problem that this chair was here suddenly is not here anymore no you still can see a new new one is coming then this one that one that one new come new information is coming and generating flow for me okay I think we can have like five minutes break then continue to the next topic did you start okay so so let's continue for now what we've learned we've discussed about the visual Islam featuring selection for visual Islam we've seen posegraph optimization and we've seen the feature extraction different techniques so that now we have the they have useful information from keyframes our camera is seeing you for seeing the environment and we can we know almost how to extract the features and how they are working and based on those features we discussed some important points that we should like have the outline selection and like the rotation already if you are using orbislam already has been done for us and try to decrease the error of the detection of the features from information from environment then bring it to the form of having having kind of useful useful key points on the Frameworks but there are a couple of other points to discuss also first of all we are talking about the camera and the camera and visual odometry and visual are visually understanding the motion of the motion in the environment is a little bit challenging and another challenge thing will be introduced what is that is that you don't know where the camera is right we we're talking about the robot when we were talking about the robot if we use another sensors or dimetri motion commands motion mode motion a model then we know those information but if we don't have it then what can we do something then what are the challenge that we have over there you have a camera webcam in your hand and you're walking and you you're trying to you're trying to solve the slam problem is it possible to do that orbuslam motivation is kind of saying yes to to also without using any sensor any IMU sensor any motion model to to be able to do that but if you want to answer that how we can do that we have a big another challenge and what is that challenge is bundle adjustment so what's the bundle adjustment we say okay you have if you have the camera over here this camera sees some features that features in 3D we can say x y z of each one of the feature we can detect it but not only the camera each one of the features position is imported now the camera position is also important that we can say the camera pose Plus the the orientations Three Degree there too 3D creating XYZ and three degree of Freedom that it has rule PTR for example then then we have also we need to add six degree of freedom more problem for the for the point that we have so here in this figure you can see the object and we have observation on the environment then if we have the camera that is moving from different angles from field of views to see the same object then we need to also kind of estimate where the camera is and where deposit poles of not only the poles but also root PTR and the and the all the orientation to to protect the object in order to solve this lamp problem actually what we are doing instead of robot we are talking about the camera location anymore in visual feature exception we are not talking about failure robotics we are talking about the cameras if you find the way the camera is actually we finally where the robot is to correct right clear so with knowing this we say that bundle adjustment is the component of real-time camera tracking system and it is a state estimation technique for estimating joint of these elements first of all 3D coordinates of each point second sixth degree of freedoms of the camera position orientation that known as a yeah ex extremities of the camera so what we want to do actually as I explained to you we want to track and say okay we have the post graph optimization based on the pause of the the camera frame that looks like the environment and and what we want to do finally we want to minimize the the error of the projection after each one of the camera not each one of the one camera that is moving but of course it can be multiple cameras too we can say we can consider also there are multiple buttons for now for Islam problem you can consider depending on application this bundle adjustment can stay for multiple camera from multiple views that is looking at the same object but here we are talking about Islam and tracking the the camera so it can be of course a complete optimization problem in 3D because because because the parameter is that it's visible and if and for example all features that are visible in order to extract that six degree ohm freedom of the camera is almost very complex problem so what we do usually we use it as least the final step of the feature-based 3D construction of the algorithm is in bundle bundle adjustment and we say the applications are the of the bundle adjustment is Robotics visualism and computer vision is in this text in this fields we are using bundle adjustment a lot and the challenge this minimization of the error of the least square error again in 3D not only for the points but also for camera 6 dof we want to again minimize the least squarator and estimate the data Association also that is the hardest part because if the data Association is only referring to the finding which point is which point to to localize the point that we have three parameters if you have six more what does it mean it means that we need to so we see this for example this object from this view now not only I need to find XYZ but also I need to detect the angular field of view off while camera that is looking there that is looking from here like this or rotate it like this and and the the position of the camera the pose of the camera so let me say position of the camera is easier but the the orientation is much much much harder because we need to detect the orientation. so also we say we usually have sparse data from different observation that this is First Data of course as your friend mentions you may lose some of the data in different keyframes the same old features are not extracted and this can also make it harder so what we usually do we want to just formalize it but but let's have a look we say considered environment with 3D points of the xjs and set of cameras or the camera that is moving during time in the environment as a camera eye at like at different times after movement it is common to formalize it with with talking about multiple cameras but as I said to you here we talked about same camera that is moving during time so we can say x i j is as coordinate of the JS Point screen by the ice camera so ice camera it means that building time is just the camera is moving in the environment and x i j represents the same point that is moving on the screen therefore what we can State we can say the given set of image coordinates that we have as x i j is solving we need to solve to find the camera matrixes of the CI and create a matrix where the camera is moving in that 3D coordinate so that we can say Okay C of the c i of the xgi is equal to x i j so that we can simplify a problem from the camera camera and the position to find the poles together in the form of peak Matrix over there so of course noise also can destroy this a lot data Association can destroy it can make more problem on there losing some data can make problem and the estimation of the when we are talking about the camera and estimation of the they are where the landmark or feature is also can be very challenging so what we want to do we want to do apply the maximum like the hood or ml solution assuming that the measurement of the the the noise that we have is gaussian so in simplest form as you know we were talking about these land problems auroras gaussian and if you consider the same gaussian error on the observation model that we have here and the observation of the environment that we have we can say for every view we want to minimize image distance between the reprojected point undetected one by this equation so that minimum of the distance of the This this term over here c i j x that is prediction here as as you know that when we had have had these are the prediction ones and this is the the the represented by the observation over there that that we want to minimize so so we say okay by considering this equation over here that we want to minimize we are involving adjusting the Rays between each camera Center and the set of the points that we have what is the race between cameras that have the points that we have we can say okay the points that we have the if you if you can calculate the ray like a line from here to the point and if the camera moves if I can calculate the array the the straight line to the moves to the to the to those points and they're all kind of straight lines So based on that straight line I can estimate the um position and even the orientation of the camera based on that rate so we can say besides equivalently between each 2D points of cloud we can we can we can consider that we are solving the problem of finding center of the the camera a field of view into the ray to the each each point so hold this procedure solving this procedure optimization problem we call it as bundle adjustment how exactly in detail we can we can solve it there are multiple different techniques that that for now because if I want to enter to that exactly will take time but but the objective is to minimize it in order to in order to do that and we call it as bundle adjustment to to see later when we are talking about orbis lab what does it mean for example orbislam propose a technique to solve this problem in other technique other algorithms we we see another optimization problem and and or maybe heuristic technique to solve it but for now you just need to know most importantly what's the bundle adjustment and what is the motivation behind okay clear we didn't talk about solution because it is depending on the application there can be multiple Solutions but we know bundle adjustment finding the camera pose and the object and tracking on the other hand as I told you there are many too many elements of the Advanced Techniques that visual slam other one one of the other elements that we need to get familiar with to know General Concept in order to later understand what is happening is the visibility graph we need to be able to have visibility graph of the features from environment and what does it mean it means that so that we can we can have like this ABC as a feature points from the environment or or we can consider where the the camera is observing the environment so that we can create a visibility graph of the how they are connected to each other like for example be connected to C and the C connected to a so this this creates the simplest idea of the visibility graph that that if the point B is visible from point A so if you can construct this visibility graph it means that there is something in middle that we cannot achieve to to to to see a from V so ah so this is visibility on the other hand we have the covisibility graph that income visibility graph the we have the map empty that is undirected graph that there are some nodes and there are some H's all notes are representing landmarks and X representing core visibility between each landmark and how does it look like it looks like this guy over here that we can see the robot see some obstacles over there and you can see the core visibility graph that we have over there and and like we can add one more feature then we can construct the conversibility graph by adding this feature and saying okay which one of these these features that I'm seeing in the environment are achievable or visible in order in 3D 3D constructed environment to each other so to understanding what is the application and where we can use it you should think yourself a little bit now because this is one element of also the algorithm that we have so we can say okay if you consider the image frame that we are talking about this image gives us some features that we talk for example as orbuslab and and these observations and this point over here that I'm extracting from environment I can create co-visibility graph and say okay is this guy over here from this point is achievable is this guy from this this feature from this feature is achievable and I can create the connection between those and connect them and based on that I can have bigger frame and bigger picture of environment so kind of active as they're applying orbuslab I am kind of reconstructing the shape of the environment with creating that okay this feature can be visible from there and connected this feature can be visible I'm forming a shape kind of creating a high level construction of observation from environment and this is called a whole visibility graph saw that if I can create this this can be helpful for me in order to solve Islam problem why because purely talking about purely talking about all all features is very nice we saw that it's working well but if I can reshape these in form of some bigger Construction and form them together then I can say okay we are we can talk and compare both bigger scale of the features together the motivation behind is like that in order to constitute but of course each one of these if you want to formulate go in detail takes long I I'm just quickly reviewing what what are the general idea to see how how that can work so we say at each image that is processed set of visual features as LTS landmarks we can call them as Landmark these are detected and represented and we can we can represent it like by one of these like orb shift and the call visibility graph will look like something like this based on the features that we are seeing and and current observation then looks like this guy over here then matching this graph by this graph is easier than just comparing identical features together so that so that these connections between X over here are in the observation is easier to match as a pattern with this this visibility call visibility graph instead of just searching okay where is this guy where is that guy where is that guy finding the patterns of the features by covers vertical clear just we are going we are talking about covisibility graph because here we don't want to just rely on each individual support feature we want to create some graph between then another graph another graph another graph and compare graphs between each other to to make it more stable and robust and that's idea that existing in the hope so we signed we can say we update called facility map based on the current observation and the vectorial description of the confidence of the all of those points together that we use it for visual localization information in visual automatically or visual slant or general pro now with knowing those backgrounds couple of maybe four five six backgrounds that today we discussed about visual information we want to enter to the general concept of orbis lab but is still the need to a little bit more we need need no more that I will explain during the explanations so first of all let's have a seat General General ideas it is a real-time Islam algorithm that that provide to bundle adjustments the following features so what is the bundle adjustment now we want to find the camera pose I told you I didn't discuss the algorithm because whole whole orb Islam is trying to solve this bundle adjustment find out where the camera location is and where the poses okay and that's optimization problem um so when you are hearing this algorithm is trying to solve boundary adjustment then you know that we have camera moving in the environment we want to find the force on the other hand like like in order to to do this in order to solve the bundle adjustment problem we need to find good features that that that these good features are kind of subset of selecting some frames that have good features it means that okay not only we want to talk about all features not only for the graphs that we discussed not only all the elements but also when we have a stream of video that is coming better to find out which keyframes are more important to extract in order to also increase the performance increase the runnability of course we say um we say how accurate how much with much more resolution we can compute all features between two frames and compare them together but also we say okay in some frames so robot is like the camera is like stopping right or there is not too much useful information so better to drop it and have keyframe and and exactly keyframes to in order to construct better model of teamwork so this is the meaning of the keyframes also is not that easy it's a little bit challenging how to how to understand what is the differences and how to take the good keyframes the the elements that a bundle adjustment algorithm can can be real time and good we say selecting the uncertainty rather redundancy that I explained a strong network connections of the keyframes of the points that produces the accurate results including the value spread keyframes and and of course the features too if the if our algorithm is is spreading well in order to find better org features like what one part second part better is spread off like we have one second of video frame all the frames coming from like last moment not really good although we may say our technique the text that last last moment of one second like last two three frames is very important but they we we would like to have better spread during the time if they are talking about one second at 30 frames they need to have this distribution of the keyframes over there also not not only just not the important ones and if you have looked closer matches is of course the critical point that if our bundle adjustment can have can find a much more Loop closure matches it will be more accurate in order to optimize the posegraph that we had in the first part in order to finally localize the robot itself also the significant parallelics that parallelic says that what is the differences between the operand position of the object that also need to have good distribution we formally can call it Parallax in in image processing techniques so though in addition to those three these these three that we discussed here we have three more one is the a local map in Exploration where optimization is focused should be should be scalable that that if your map is like um scalable based on the observation model that you have especially this is becomes important in drones when robot is flying not not think about the only we are moving everything is scaling a little bit initial an initial estimation of the keyframe poles and location is very important also because that's the initial construction that that that gives us opportunity to connect everything else to the initial estimation of the keyframe post and finally the ability to find the fast Global optimization of the the process that we have so maybe our algorithm is worked perfectly fine in local estimation of the differences but globally destroys everything that's not good that that these are the features of the bundle adjustment that can work based on the monocular camera basically so now specifically if you want to talk about the orb and characteristics of the orb we say it is feature-based monocularislab but but nowadays we have different also ones but the original one that I'm talking about the original first appearance of the Orbison so feature based monocular slab system that operates in real time it covers all the slam tasks of the tracking mapping localization and loop closing we discussed this all together separate sections separate courses of this this semester tracking how nothing is working our localization can be extracted from those it solves all of them that we can call it is Islam not only localization it uses work features that today we've seen how they are working that is that that most important reason is the being real-time performance without GPU it can be performed but of course you can check it out if you have algorithms or implementation for gpu2 then it would be much much faster to do that as I know orbislam is not compatible with gpus if you can do that that would be great but don't think that's easy because if you look at the Gold the things that I'm explaining today is tremendous amount of code over there for implementation so and of course good invariance for change of the Viewpoint because of the rotation the orbis lamp characteristics it is a real timely operating in large environment and uses call visibility graphs that I I gave you the idea what is it that is tracking and mapping on the call visibility graph graph for independent global map and also in addition to that we have the real-time Loop closing based approach that is optimization of the post graph and called essential graph so there is a technique that tries to improve the improve the post graph by essential graph so I know lots of information so all of this we studied today and orbislam brings to connect all together so to understand it no way we needed to know about photograph orbits or features and all the bundle adjustments like here we have real camera we call it localized relocalization as bundle adjustment that is that tries to recovery from tracking of the failure there are some techniques that we will see in general projection of the how it's look like that tries to recover from the failure with with a significant invariance Viewpoint illumination then we have survival of the fittest approach in it that that as I mentioned it has the keyframe selection as features a bundle adjustment and the the orbis lab main design idea is to use same features in 3D in three three different parallel threads that is like tracking local mapping and loop closing so the implement in general proper proposed technique there are three threads you know all trades different coats of lines that can run same at the same time together in CPU so one is in charge to do the tracking task one is constructing the map including like post graph and everything and last one is in charge of the detecting the loop closely you see that how important it is it's it's also independent parallel thread in order to help the tracking gun local mapping of the Islam technique that we have I don't know why this is blue but here is okay but there we have blur so I take the picture from camera they did the original paper deal is fine anyway let me see let me generally explain we have tracking part one thread we have localizing and map Construction and look closing part as you can see now if you look at the details we almost discussed all the details for example first for frame is coming frame of the camera we are extracting the orbs at the beginning stage of the tracking then we are we are doing the post estimation from local frame there and then tracking Lookout map based on those or features and and UK frame comes and and then and then the the new decisions based on these features based on the the old features that we have as keyframe comes so we are actually it is generating new new frame that is that is key frame of these old features then goes to it goes to the local mapping as kind of it is working at tracking and filtering filtering as initial frame then different techniques on the local mapping that we discussed like for example keyframe insertion the recent map point cooling I will explain now what it is the new points creation local bundle adjustment and local keyframe cooling that this is like the I have it here yeah this is a retaining only high quality points that is like kind of um outlier detection a technique of course if you want to discuss exactly how it is in detail you should have a look in the in the paper itself so for look for the for the loop closing they propose a technique that in this technique they are calculating the Symmetry that is like applying some transformation constraints that tries to detect the loop closing between the the features the the visible visibility graph that they constructed so if some some constraints based on the century technique so we have keyframes we have covered limited graph and we have a spanning tree that this spanning tree is like kind of a kind of brief version of the Culver's ability graph that is for for for creating minimal number of eggs to make it also much more lightweight and online that again is like applying some some like when when the discoverability graphic rolls tries to extract the important elements of those correspective graph and try to use it in whole scenario that is happening and lastly in addition to those all elements that we have we have a visual vocabulary and the Recon recognition of the the visual vocabulary data sets that says okay not only doing all those efforts is enough but also we can with pre-calculated data we can create visual vocabulary of the image frames that instead of like like it's better to if I if I my camera I see this environment right instead of orbs if I can say that chair based on that probability graph change human human computer computer company it is nicer right if I can do that so the idea comes from there based on those orbs graphs and pre-trained pre-prepared the visual vocabulary data set then even tries to make it in higher level of the representation of the environment so that what we have here you can see the examples over there that like the camera this is the camera trajectory and the camera poses that see some features in the inside and and just just example from A to B C D then in orbit slam call this is a bit of graph specifically each node is keyframe and and Edge between two keyframes exist only we have we have a common observation or or same point observation of the time to point at least 15 it means that like frame a frame B so must be they are keyframe both of these if the differences between a and b at time t and t plus one there are some features that seeing a minimum 15 number of those features can be visible then the rule is like this is keyframe so because we discussed in general causability graph but you can see how the the the edgeland nodes are defined then water place I already explained we are it's it's training image features as well to to perform Loop detection and relocalization of the loop closing problem specifically because that's this part is mostly focused on the closing the loop by keywords because if if you have a votes instead of features it's easier to compare quickly find the idrh this should be Loop closing chair computer laptop this should be the same one that I've seen already you see for Loop closing this this part is world recognition is very useful I stated some points here visual words are just discretization of the descriptor space known as visual vocabulary and the the vocabulary are created are mostly offline because because okay we can say that we can now we can one time do it then use it no need to do it in online but of course you may think okay if you do it online it's better apply some learning technique to do that yeah it could be if the image it's the image that we are doing that in offline way are enough it can be good and the performance will be nice over there it should be fine and it builds a incrementally a database of what the features that we are seeing orb Islam and put like you can you can consider write the sentence at each frame right okay I'm seeing these moves and where I'm seeing these I'm seeing this then matching in future if I'm seeing the same things then it will be working efficiently by querying that data set of the for example board vocabularies in each thing but we have the versions are the three common measures we discussed the the first one the two is trying to also improve that one the tree is trying to improve that one make it a little bit more complex but General concept is same not too much different you can see the monocular implementation also it is rust integrated I put the GitHub link you can download and install and check it out for Islam number three I shared the code with you over there that that you can see that second version first version we mostly discussed with monocular second version says okay not only cover the monocular we want to also use the stereo camera rgbd camera so they the proposed technique generalized to also be able to use on this because this one has some problems is not working perfectly fine it's not adaptable but this one you can just take the code and change it to use with rgbt for example and lastly third one it is very important to say that it tries to use the visual initial and the multi-map concepts it means that okay we say we have camera and camera is moving but we have imu2 mostly in our robots why don't use it we have momentum of movement how how fast the camera is moving why we don't use it while we are throwing out in bundle adjustment we saw okay that's very difficult to find the six degree of 60 off of the camera where it is so we can we can use that how much is rotating we can use that information then you know about slab 3 they added some elements to integrate it with this technique over there simply not simply but I mean the idea I simply so you can see the latest paper publication or the slum tree downloaded the study you will see the same things more in details more accurate formulation and equations I have a camera I have example that works on the benchmark so you can see that this is the old feature extractions and map construction of the orbis lamp that the camera is on the car the car is moving you see the you see the frame the old features that are moving towards and they are in different frames accurately can be can be detected all the procedures that we discussed now is running in background in order to construct this map Loop closing happen there detecting the same features for example 3-3 car car cartridge with more vocabulary that there were another look closing happen at the beginning was error then quickly adjust it you see there were errors like there and after look closing it's detected and constructed and improved the whole posegraph and you can see that goes you see some features is nothing and look closing after detecting after a while struggling sees the same one and you can see 3D constructed map and the ground rules very similar this is the exact one and that is the map that it is there but now let's see another video based on the rgbd camera this is this is all the slam number two that uses the rgbd camera you can see a person takes the camera and you can see the polls of what we were talking as bundle adjustment and you can see the position of the the pose of the camera on the 3D environment you can you can download it and do it on camera you saved right you can see in 3d space not only for big Compass areas with the old detected features we can we can extract the environment like that and again trying on on this one this this result is for a stereo camera previous one was for monocular camera you can see the the data is more accurate and stable at the beginning stage in hallway because we have depths again more stable another example with rgbt rotating like there is a table and some computers like similar to this part the car is moving the camera and you can see that almost very accurate and now trying to after construct it map only running localization to see with running the same trajectory to see how I create this almost you can see this Green Point almost accurate with the same cars and the location but here there are some errors it went inside too much and 3D construction of the map because we have rgbd then we have the dips we can just we can just plot the depth on the on the 3D mesh then we have this it has the features if you enable in the orbital entry you can you can do the same thing with output and one more example no before that let's have a look at the comparison tables of the recent slam algorithms on visual so these are different all different techniques that has been proposed for Islam but just a small part there are never too much more I know like five six not five three to five different also improved versions of the slums that I've seen recently just one also I reviewed myself so for a journal paper so here you can see different techniques like mono Islam like ptam and comes to the to the Orvis land here orbuslam number three that is latest one you can see the if it's visual odometry or not that is like this is folding fully slam problem Islam Islam this is like visual automatically visual automatic that is like localizing we usually camera is moving and we want to localize not construct the map and do all the other things the types that you can see different this one or the slanted Islam the pixels that they are used you can see for example these are like fast this is like orb this is another technique and orb this one is orb that we studied together because we were focusing on the best latest one data Association part here is descriptor we now know what does it mean I clarified for you what we have as estimation we have local bundle adjustment for orbislam you can see different techniques for example this guy over here have been used it here now you know so this one over here used posegraph directly purely not not local bundle adjustment then then I move to um to this part over here you can see the features that we have so for example multi-mapping if it's covering or not monocular stereo monocular with IMU is it is it covering or not Fusion fisheye lens camera is it covering or not and what is the accuracy so you can see orbus lamp 3 has all of these features together in comparison to different ones and the accuracy is excellent as they claimed and it is excellent for the others they've written good good very good but this one is also excellent here orbital number two if you come it's like same family then then robustness like Fair on excellent they compared and they finally the the paper that you can go download and study so this gives us very clear image of the residential studies that if you want to do Islam go work on this guy over here but of course I would don't go to the Google Scholar see who cited this guy and see what are the recent works and who try to improve it recently because for example one of the improvements is like outlier detection if removing dynamicity of the environment like detecting orbs after taking orbs we are we are extracting all the features but but if we say these are humans that maybe they go away after some time and we remove them as outlier and rely on more reliable objects or or detect the dynamicity of frames between frame A and B something is moving you you are moving there so you are going out for example then I know that that's moving in the frame that that that's not reliable feature as orbs then I cut anything that is moving in frames then those are those techniques are now there is Improvement of this guy over here so we have one more example from the laboratory you guys mostly have seen it from previous semester one of the students did it in campus lab the orbuslam tree you can see the output of the orbuslam tree in the campus with kokoro project the constructed map before unco came here we were struggling with that one Sun did it one of the students on the line you can see that Loop closing problem happened there and pretty accurate construction of the campus and and you can see that the location of the Verdi Google is based on molecular camera is still accurate and those are all features over there that you can see and very accurate output and what we discussed today we discussed the mapping without answer 20 first then with our certainty first we understand the main concept with introduce the posegraph optimization we talked about the feature extractions techniques like shift brief and org then we talked about the boundary adjustment technique and what is it that that said that we said that whole orbuslam technique want to solve this we talked about the visibility and coversability graph General concept and we talked about the general construction of the how orbuslam is working of course if you want to go detail in detail you need to study more and that's it for visual part of Islam for today any question from anything yeah you can use yeah can we can give yeah it will improve the accuracy at the beginning stage for you and I told you you can use it um it depends on your if you're a fan of Elon Musk yeah if you're not fan of Elon Musk it's like yeah for me for me it's like um for me using more sensual information that is useful is better than give you more reliability yeah because that's big project expensive project I would say it like that but if you want to say no we are we are going to propose a technique that is generalizable and is not expensive everybody can put a camera and do this job then the camera is better yeah definitely depending on motivation but for now if I if you ask me I would say which one is working better use that one to do the job then later we can like replace the one that is not working better and try to improve any other question so today course I think is very useful for future carriers also I highly recommend to study the more details on the references that are given to you with the Publications and papers and I think this brings us to the end of this semester because next week is the final exam date that you will have final exam and you know the regulation I already stated what are we are the requirements and what are the points that you have the marks don't forget your project a new project as I told you must have been stated in the Moodle so far what you are going to do then next week exam then later for the for the project I will give you as much as time as I can that I need to put in the system but there are there is limitations then I will cut it there then try to don't miss the deadline any question so thank you very much good luck hope you learned useful information from this class this semester good luck |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH8_SLAM_for_robotics_Unscented_Kalman_Filter_UKF.txt | you kind of stuff okay okay hello everybody good morning hope all of you are doing well and you are fine staying safe uh do you have any question about last classes and last week course okay good you may found uh you may find exercises hormones a little bit challenging but that's very nice practices for you no worry too much about the marks just worry about the course itself and learning because when you're doing that you're you're developing your different skills problem solving understanding the course and programming that all of these are crucial for your carrier for your future so how much you dedicate time that's that's the best for your future no worry about the challenge that you're dealing with if you're not understanding you're not successful completely still that's fine no worries do your best so uh and this course of course implementation understanding is one of the hardest ones so I understand that too and if you are not completely successful that's fine uh don't be disappointed no worries okay foreign filter that is development of the extended Kalman filter we will again have some mass in some parts you may find this a little bit challenging but I will try to break it down as much as possible to make it understandable as much as possible today's course so what we are going to talk first we are going to say okay what was the challenge in extended Kalman filter and it in its linearization so that we can improve it with another algorithm named unscented Kalman filter and in this chapter we're gonna see how our challenge existing in linearization of the extended carbon filter and how we can improve it by seeing new algorithm and new technique so if you want to talk about the objectives we say in common filter we only was able to use linear models what does it mean it means that we only were able to feed gaussian distribution Tower algorithm to be able to solve the problems so we consider that noise discussion and noises are uniformly distributed so when the noise is like this so it means that like your sensor your model has a noise that is formed in normal distribution but later we saw that okay the noise can be different the noise can be cannot be always in gaussian form because of that we introduce new model that was extend the Kalman filter so that only thing that we did was mathematically converting this guy over here to this guy then feed it to algorithm that output again will be this one so we all the things all the efforts that we've done converting that to this one in extended cosmicity of course we saw mathematically how we can do that and how we can bring it from a non-linear model to linear mode and we use Taylor expansion but now we want to see okay what are the challenge and how we can improve it in with as unscented Karma video the general idea is very simple you're gonna see soon but but making that General that simple idea to work is a little bit challenging especially mathematically so uh what was happening if you wanna see if we wanna have a look at Taylor approximation in extended Kalman filter algorithm so we said that we have this term that we are kind of uh with uh with G we are trying to uh linearize non-linear function that we mathematically saw how we can first tailor expansions always put solve this problem anyway this is like a standard approach that we can just just one time Implement and always use and what was visually happening visually was like we had the gaussian distribution in a multi uh multivariate or two Dimension here that's one dimension here the same in two Dimension the arrows then we have the mean and we were trans transferring this gaussian distribution and mean to another gaussian distribution that means that we have a non-linear function in Middle kind of transforming the uh the distribution to another another distribution so visually if you want to see uh it looks like this in extended Kalman filter but now we have unscented transform unscented transform says as like Duty says instead of uh considering only the mean and covariance to do that we can find some Sigma points and use the sigma points to transfer our gaussian model distribution with some non-linear function so we have two steps First Step Computing in unscented column filter first this step is Computing the sigma points that uh that uh that that will give us opportunity to transfer this model to another distribution with function G that that this function G helps us to uh to again solve the non-linear problem solve that that transformation over there that we have that Network so gaussian distribution we find some Sigma points we will discuss how to find it then in in second step we transform each Sigma Point through non-linear function G to to another four after we did that we again need to recompute the gaussian from transformed uh transform points with some weights it means that we can calculate this distribution based on the points that we have and find also the mean so whole idea of the unscented trans unscented Kalman filter is based on this three steps that two of them is basically important G is the non-linear function that tries will give us the opportunity to transform our gaussian distribution to another form that this G includes our noise and error in a non-linear form any question is it clear for everybody so far so when we are talking about unscented uh Kalman filter you quickly should imagine this this example finding Sigma Point transform them with function G and reconstructing the sigma points again we are going to discuss it we have long history too lots of math then the function G for function G we also we're gonna find some weights so in order to be able to move it to to another distribution okay any other question so now uh we want to enter to talk about the how transform each Sigma Point through non-linear function G so the main idea is looking like this visually that we have the mean we want to find some Sigma points and transform so uh simplest function that we can have to in order to do this is identity Matrix if you have identity Matrix exactly whatever is happening over here will be copied over here right exactly transformed whole gaussian distribution so uh meanwhile we are doing this in order to solve the problem and finding some uh weights and selecting the the sigma points that that this number of Sigma points also we can discuss in in simplest form if you have 2D we can simplify find four uh four plus like if you want to consider also the mean itself to five uh but we can have more Sigma points in order to bring more accuracy in order to convert all distribution to new distribution so uh meanwhile we have some limitations uh limitations uh will uh will kind of uh make a platform for us in order to uh in order to say how to do that first of all we say that when we are looking for debates the sum of the all of the weight should be one in in form of probability uh the weights that we are going to transform these Sigma points to another gaussian distribution then second limitation or constraint says that okay we need to also after trans transforming the first distribution to second one the the mean that we are calculating from weighted Sigma points should be the same as the first one so it means that you cannot like you cannot transform this from A to B then the mean is something different you should maintain same mean with the sigma points that you have it means that you can distribute your uh your uh your data points but after transformation it should be at the same so that we want to find somehow the weights that this Sigma points should lead us to the same mean that we have at the first distribution okay and the third constraint says also the covariance should be the same so you cannot also change the covariance so if you because if you change the covariance you're missing as much as possible you should keep keep the same mean and same covariance after transformation because whole idea is linearization of the non-linear function that we have and we want to keep everything same if you have like non-linear function then the mean and the the covariance we try to keep it same so that's the whole idea of after transformation in gaussian food okay clear so how we can do that we can calculate the covariance uh here just calculation a covariance is simple uh the differences of the uh the each one of the sigma points with the mean uh and that that it will come from the weights that we can calculate for each one of those Sigma forces so now uh we should answer how to select each one of the sigma points X's at first this day so you can think how how this can be possible what do you think what can be the idea you have a distribution and this distribution has a mean we want to choose some Sigma points so the the simplest form can be like going to the axis right going to the left going to the right if you want to choose four additional ones or if you consider the mean itself it can be considered two so the idea is this and we simply want to see how we can mathematically do that now and after after doing that uh we need to also answer as step B how to find proper values of the each one of the weights that we want to do the transformation so uh meanwhile that we are doing that again we need to respecting the the constraints that we have you cannot find the weights that are exceeding this or change the mean or change the code values you should have find some proper values for those that we are uh we are limited to the constraints that we have to to do that uh of course there is no unique solution because you can choose hundreds thousands of different forms of Sigma points that that can do this satisfies these limitations and do the same thing but there are multiple approaches that today we are going to see what are the most common way to solve the unscented Kalman filter so uh uh not to choose the sigma points X's so first of all the simplest thing that we can consider is the as I mentioned is the mean so mean itself is very clear and and this can be as the most important Sigma point that we have so we can consider first x0 Sigma point zero as the mean that already we have in order to do transformation then uh then in order to find another Sigma points that you can see visually here like these points we can have a term that this term mathematically can help us to do this so X I can be can be equal to the mean that we have the reference point kind of added by some value and if I want to show you the next two to understand it better and subtract it with some value so that we can calculate the uh the the additional Sigma points that we have but but what are these now of course we're gonna discuss uh in in details uh first of all we should say that the end that we have here n 1 to n is the state dimensionality then we have Lambda that this Lambda is a scaling parameter how how much we want to scale and also uh so we can say kind of distance from mean and the I is just the column Vector that that is based on the state time manuality that we have so we have some some equation that that with this simple equation we can find the mean and the the uh the the other Sigma points and we will discuss also how to adjust the properties like n is clear State dimensionality you put the value over there and and uh this is the covariance the covariance that existing over here we can put it there and the uh and that this Lambda can be adjustable but the problem that we have here the the difficulties that we have here is this square root of Matrix because this covariance is here the form of the Matrix and if we want to get the square root of the Matrix but we have a challenge what's the problem over there straight off Matrix is it easy to solve not really because we don't have one unique solution for spread of the Matrix and there are different mathematical approaches to the LED because you can find multiple different answers for for form of Matrix for multiplication so that's the challenge that we need to First also see how to uh how to solve this problem but but the rest has some values to uh replace there and find the sigma points proper Sigma points that we want so any questions so far is it clear so same thing for the uh um for the subtraction of the the mean with the same equation and here we say okay if we can consider if you want to consider two dimensions two n per each Dimension we can consider so that uh in 2D we need five Sigma points one plus two of the uh two of the sigma points we can consider more and increase how much more you have you can increase the accuracy of the transformation in the end of this slide we will kind of see visually how it's happening also that you can you can understand it bit now uh in order to deal with this square root of Matrix we should have a look at some Mass a little bit and have a look at linear algebra so what is happening over there we have a uh we have solution for square root of Matrix that is kind of um uh it is kind of changing the the square root numbers to matrices and a matrix that have several square roots and can be calculated by diagonalization so this is one of the approaches that we've done diagonalization we can solve it if we say we have Matrix a that is equal to uh LL then we can write L is the square of the Matrix a so how how this can be possible it is like uh the linear algebra Solutions we have diagonalization that we can say scale with a square root of Matrix is equal to for example here covariance is equal to l The Matrix L times The diagonalized Matrix of the date the the the data that we have in the Matrix that are are in diagonal form times the The Matrix the inverse of The Matrix then ah then is kind of this D can be represented is two of the two times of the Matrix D that is uh that is half of the half half of the value of the Matrix that we have so then that can be considered as a as true diagonal matrixes that they are timing to each other so I think I have the example here here uh here you can see this D to the power of one over two that that you just need to in order to solve this problem with linear algebra you need to uh deal with this prop that this this term over here that that uh that in order to find the sphere and instead of this D over here we can replace t to the power of Y uh one over two two times and since this is diagonal and multiplication of those two can that that each one can be squared each one of the data that we have then can uh can help us to solve the square root of square root of all Matrix here so of course this is Mass problem but this solution has some difficulties because uh it cannot find it is not stable for all these scenarios because of that we are going to see the uh the another approach that is more common so the problem that we have we say first of all real Matrix is made fail to have a real square root here and the sum of the match the the matrices uh have no square root with this approach that we have so because of that that's not stable and that's the reason that I'm not showing examples implementations and all the calculations but if you are interested in of course have a look it's very simple you can just even study the Wikipedia to see how that's happening just this D will be times 2 these two and this is the Matrix that you have you want to get this curved so uh in order to deal uh with this problem with linear algebra we have trolesky factorization or decomposition approach that that deals with this problem uh easily so again the whole idea is finding Sigma points we are going to calculate the the equation that we have here uh that those are just simple values that we put replace inside but here we have the Matrix that this Matrix since it is under square we cannot find easily the solution we are looking at the mass to see how to solve that problem so second approach is a trolesky factorization that um that says or we say it is another definition of the square root Matrix is numerically more stable and in you unscented Kalman filter it is very common to use it because it's more stable so considering again the a equal to LL and then the L equal to square of the hey what we can do we can do calculate the the form that this form that you can see here so uh what we do uh we need to calculate we need to uh first of all find this Matrix second find this Matrix then then the the the multiplication will give us the uh this symmetric Matrix that that helps us to find the solicit factorization approach so before going in detail how this is happening I'm gonna show you how this is happening uh we say that okay every real valued symmetric positive definite Matrix has Unix has unique cholesterol decomposition so symmetric is clear I think you all know but positive definite also uh who knows okay uh I'm gonna show you also how we can say if it's positive definite Matrix uh so consider we have the Matrix a the uh in this form and we want to solve it with the with the square root what we do first of all we need to uh bring it to the form of the a equal to LL into two form uh lower triangular Matrix and upper triangular Matrix so that if you calculate it we will have a symmetric Matrix look looking like this over here this Matrix is a uh is kind of mirrored and the diagonal is uh the the the the main diagonal is the same and it is mirrored on the top and down and if for example if you want to like see an numerical example like he's like this for symmetry like 6 36 96 that if you see this is the copy copy it copied over there how that is happening let's move forward oh before that we need to see some some also definitions and limitations uh uh first of all the as I mentioned how we can say we have a matrix that is positive definite uh because if it's not we cannot use the cholesky method but but basically you may ask okay if it cannot use it then what to do with uncensored Kalman filter we designed the algorithm at the beginning so to to don't fall to this scenario simply but you need to know how positive definite definition is looking like we say if the Matrix a with multiplication of the vector v as follows is positive for all real numbers it's at zero it looks like that so we have a vector v times the The Matrix that we have a times the vector v is greater than zero where we have the v as real numbers all possible ones that we can find out what to place there and the uh and the V is not equal to zero so it looks like this if you for example If he if he I want to check the identity Matrix and replace it as Matrix a holder here then per all the values of the V1 to the power of 2 added by V2 to the power of 2 is greater than 0 and this is always positive because this is always positive we say it is definite at the positive definite Matrix for example identity Matrix is positive difference so you can you can now uh consider this to say that the Matrix is positive definite but how we can do it in Python is it complex no already well known problem in mass and you just need import numpy and with numpy just you need to find the eigen values uh to to tell that if it's a positive uh definitely so uh if all the eager values of the linear attack that is coming from linear algebra of the Matrix a are positive we can say that it is positive division so who knows what's even values okay you don't know anything about algebra and maths like this so that's that's what we need all here in the okay that's not useless oh we have any slides but uh for that I will Define it in details but I can say like if I wanna simply show it on distribution so this is gaussian distribution so the relation between this uh eigenvectors we call them as eigenvectors the ratio of the change between these two how how much they are like it is like this or it is like that the real the ratio of the how what are the differences between the scale of the uh for example one distribution so this is used over there then that this ratio can help us describe the distribution basically here right because because okay before this we were talking about the mean and covariance right but the co-wariance here and here is different right eager values can help us to describe that too what is the this one and what is the that one because covariance in one dimension is okay but in two-dim multivariate then not anymore that's that's why we need the economics as you can see here uh you can like import metrics create a matrix then calculate the uh the eager values numpy dot uh linear algebra dot you can values of the Matrix a will give you the Ecom values that I showed you over there uh yeah here I thought I have it a couple of slides later so uh I defined that when a linear operator is applied to a vector the vectors line of action is unchanged first of all because because of the definition so so when we are linearly changing this to to some other form of distribution so we should maintain this ratio right if we change it then that's totally differencing the distribution is changed we should maintain the ratio maybe it can be bigger but the ratio should be constant so that's the that's what does this mean then we have the uh we say okay you can values used to identify features of large data sets and Performing dimensionality reduction because like if you say if we say this is data set and there are millions of points over there instead we can say Okay ratio of the data the relation between data on the X and Y then with two values you can reduce the dimensionality of the data that you have a lot dramatically with the calculation calculations of the eigen values and as I draw there you can see that we have some definitions eigenvectors the main diagonals vectors these two are eigenvectors and each each eigenvector has eigen value for each one of these we have even value and and the ratio between those are are the most important thing that is between two this and I explained for you already any question clear okay now let's go back here to the to the discussion that we've had let's see how this is happening simply in order to understand this uh the square uh cholesky factorization or decomposition approach here that we are calculating this Matrix how that's happening if you have a look simply to calculate this column over there you can say okay the calculation of the so we want to find the square root of the a right and we want to find out this this calculation based on this term over there then we can say the a a a is equal to l112 to the power of 2 this this guy over here that that we can actually rewrite it in form of l 1 1 is equal to a square of the a11 so we are actually we calculated the squared uh the the square root of the A1 one is it clear so again look at here a11 is equal to this term over here okay this this guy over here so that we are actually calculating the L1 ones the square root that a11 is square root of the A1 so uh and if we continue that like for the second term over here a21 um a21 from this Matrix is equal to l21 times l11 l21 times l11 over here that we can write it l21 is equal to a21 R over the l11 to calculate the uh to calculate the uh the square root of Matrix that comes in this form for the whole symmetric Matrix that we have for a31 we have h31 we have l11 times to the l31 so we can show you that so for l31 this one times this one that that that comes from there also and now if you continue like for second column you can see that for calculating a22 on the uh on the main diagonal we have the calculation of this term over here like this comes to there directly because we are on the main diagonal that we can rewrite it as l22 this is the square root of the a22 minus subtracted by the L to the power of two of the one and we can continue that for the a32 to calculate the third one over here so this is like kind of the Matrix calculation that represents how cholesky approach is is mathematically finding the the calculation of the Matrix that we have over here for square root so is this clear just Matrix calculations if you just look at the map this multiplication of this symmetry symmetric calculation over here then replace it you will see that uh simply we are achieving that and if you continue even for the the third one you can see that a tree tree that is like again on the same column will be will be this guy over here uh this guy over here a33 is this one then that's it no need to simplification and lastly as an one example can be written as since these are to the power of two we can we can write them all in form of the square so but but how we can okay let's say you completely understand this is simple math simple math of the Matrix calculation how to implement it in the uh in the computer and in the program code that we have I've did it for you guys to make it clear so we need to uh to to uh uh two for Loops indeed that uh that we can find out exact first of all the pattern of calculation based on what we see here based on what we see here we can we can find out the the form that we need to have two nested Loops first of all first like I I from uh J and for when when I is not equal to J we can calculate this term over here and this term over that the calculation of the L of the IJ is square root of the IJ subtracted by some of the uh k equal to 1 to J minus 1 then sum of the each one of those so what is this uh this is representing this is representing the calculation all the calculation that we have here just with the pattern four then then the for the cases that I is not equal to J we do this one so here the I is the inner loop four rows and here J is the alternator Loop four columns calculations so if you run this simply you see that we have previous example implementations exactly this is just pattern off or we did that is like simply matrix multiplication that that glues the calculations in in make of the in form of the algorithmic presentation then even we can also I also stated for you that this is for main diagonal update basically calculation of midnight well it is is in charge and this is the under the main diagonal update so uh I've placed the example implementation here both in two languages that the implementation of these four Loops you can see the for Loop J equal to in range of N and I equal to in range of J and n and it's like if the I is equal to J D if the term that we have here can be placed here otherwise the other term we have there over the over here simply so what is this implementation doing exactly implementation of the cholesky approach in order to in order to solve that square problem now that square problem can go back to the term that we have the term to find the sigma points clear so this shortest key let me see if I have it next slide not here let me go quickly back here to make it very clear for you guys so all efforts comes to here comes to solve this square root Matrix problem here policy method deals with it clear any question so of course today I also will give you some time after finishing the topic to have a look at the implementation and see double check and run it to see what's happening and maybe calculating to make it 100 understandable for yourself now uh we need to move to Second Step what is the second step how to find proper values for each one of the weights that we want to find so let's say that equation already sold we found the sigma points now we want to do Sigma points transform them to the uh to the new distribution how that is working uh there is uh the the term that is uh doing this for us so for case of the w0 the weights for the zero that is the weight for mean uh can be written by this term Lambda over Lambda added by n that is again the scale Sigma point spread how much we want to spread and this term helps us to find the w0 weights at zero are still mean so you just give this scale you give the dimensionality and this gives you the weights that you want how much display on the other hand when we want to find the covariance of the the same uh the the the the consider the weight 0 based on the covariance that we have we can consider this term over here that the w0 and covariance that already we had is added by this term over here one subtracted by a square of the alpha added by Beta so what are these value these value these values already uh are calculated by mathematical guys if you want to do Define and find the values proper values for these guys um you need to familiar with exactly the specific problem and the distribution that you have maybe based on different distributions that can be vary but already this is solved in unscented Kalman filter even if you have a look at the book it's already proposed the values best values for these and everybody just simply use it don't need to reprove and go all in the math but you need to generally know how that is happening but so uh I will I will show you in these slides what about the the rest of the things this is for w0 and W uh w0 mean and covariance and that that is for me for for the mean this point over here as Sigma point for all other Sigma points we can for both of the mean and covariants it will be same we can use this term over here one over two times F Lambda added by n that is the n is the state dimensionality again this is the how much spread that we want to have and simply we can calculate it so the values I I've showed to you that Alpha is between 0 and 1 usually and you can like change it to C uh to see the accuracy that I will show you the results after the implementation of the whole trolesky method and the optimal value for caution distribution that we have is two over here so uh Y2 they already tried it different values and they found out that two is the best value over there simple not specific reason you can change it even based on the distribution that you have you may have like in future very big complex problem you want to say Okay I I now I know that this beta over here can be changed I want to change it to to make to increase the accuracy that I want in our centered Cloud Market okay so uh I also explained that you need to uh have extra information of the problem and increasing of the alpha Lambda increases the just spread how you increase the value between 0 and 1 you spread it more and spread it less this is like general rule that you have over there so uh how does it look like I I presented here that also in interactive book you can see the implementation of the what we explained exactly the same terms and same implementations if you for example put the alpha as 0.3 you you will find the these points Sigma points and and here Alpha is equal to one you can see that the spread is much more much more spread for the uh 4D transformation approaches that the transformation that we want to have but now uh last lastly what we need to do as I told you we need to after finding Sigma chords and trans uh transforming them and if you want to write the uh the transformation in form of this this is like I'm let's see transformation is like if you write it as G uh the the function G so we need to reconstruct the uh distribution that we have precaution distribution if you want to reconstruct it what we need to do simply finding the mean the new mean the mean here is the sum of the weighted the the sigma points that we have so we found some Sigma points already this G is non-linear function that we cannot uh that denial is the model that we have we're gonna apply and the weights that we have found then we just find the the uh the sum of all of them then we can find the uh uh they knew me what about the core Warriors the covariance calculation is the same that we showed at the beginning but here we have Gene instead and this G uh this G that that applies on the sigma points will give us the new covariance like we can call it the covariance prime and mean Prime as new calculations so to make it more understandable let's move a little bit to here this this figure will clarify everything what we will study look at this this guy over there so we have a non-linear function we have a non-linear function that looks like this this is a distribution that is not caution and you can consider like this is the noise of the sensor model that we have or something this is the mean over here and this is the distribution itself so what is happening uh now we want to find we want to have the function FX in order to transform it to gaussian distribution how that's happening like V the uh per each one of these points over here if you match it like draw a line from there to down here and for each one of these draw a line from there over here that for example for mean you can see this red one that comes from there to here and plotted to this one like after applying whole of that over this guy and the the the the the things that is distribution you will have like this so you see that this non-linear model converted to linear mode by just just each one of the points you draw a line match it and Patch it on the distribution what is happening visually looks like this guy over here is it clear this is very important figure to understand just you can imagine like this guy this guy you plot a lot plot and over here because this is like these points over here not a lot and comes to uh format the gaussian distribution then uh let's have a look at the so let's have a look at the real example of the and comparison of the what is happening with extended carbon filter unscented Kalman filter so I'll have a comparison over there like uh now if you want to see and discuss that okay hmm this model that we have this distribution that we have here we apply this function JX that is non-linear non-linear function and we do the same based on this distribution that we have applying non-linearity function to kind of revert it to see what is happening we are actually kind of reverting what's happening but there we are trying to do this to give it to the algorithm to work to make it revert to what's happening if you look at extended common filter we have the uh the um uh discussion and extended Kalman filter gaussian comparison here so this is what the red one is is what extended Kalman filter tailor expansion calculation is doing for us you can see and this is the blue one is gaussian of the function that we have and this is like the model of the noise that really is existing we applied a Taylor expansion to to make it caution so this is really what is happening in the environment the noisy environment with applying Taylor expansion whatever is happened uh with extended condom filter we achieve this red one okay we solved that problem in order to be able to deal with the problem the red one and the blue one is the what is what is really this what should be supposed to be really in extended Cardinal filter you see the error but with unscented Kalman filter the red one is more close to Blue more accurate why more accurate because tailor expansion is only using was only using relying all the old calculation is relying on the mean and covariance it means that it was taking into consideration of the mean and covariance only but here we are kind of giving more Sigma points in order to help it with unscented Kalman filter and this Sigma Point give us more accuracy so that you can see the noisy model the noise that really if it's considering me this is this is the blue pouch into the real version of the py the unscented Kalman filter is more accurate and how this is happening again here for each one of the points just put it there and plot it here it's like this this is like one example if we put a point here it comes here and plot here so if you do for each one of those you will achieve that thread that red one for unscented colonosity especially because the other one comes directly from Taylor expansion mathematical calculations any questions is it clear so the most important one is the motivation of the and general concept of the unscented cognitive if you understand it the rest is implementation now let's have a look at the uh uh algorithm I'm not going to explain all details because that will be we want to just compare with extended carbon filter see what is happening and what we adding inside because we already also have seen and that should not be very complex to understand but generally what we are doing we are trying to do this slide over here and to see how this is this is happening and all the calculations so we had the already extended Kalman filter just load it up in your mind again we had the function G as Taylor expansion that we used on matrixes we will use some Jacobian matrix in order to find the mean and covariance as prediction step then we applied the correction step and return the new mean and covariance that was the whole idea with unscented column filter so so the most important thing was mean and covariance that we have now uh if you have a look at the unscented Coleman filter of course it's again bigger and more complex looks like you can see from line one that we continue to line 12. uh whole motivation again is that the the the previous mean previous call variance and observation comes to the algorithm and finally new mean and new covariance will be returned the whole idea but let's have a look in details what is happening generally we have these three lines at prediction step that works based on the observation but now we know that we need to find Sigma points the same equation XCS and same term that we've seen we saw that for example to solving this we need cholesty approach then uh we we calculate the um the the the mean based on that the calculation of meat is weighted weighted the function G that is non-linear function that that is like the Tuesday plotting and and applying this non-linear function on the x t minus ones the sigma points that we have so visually here here we have the gaussian distribution we find the sigma points X's we apply the G and we find the new one and G is RG is this guy over here then then finding after finding the predicted mean we find the predicted covalue of the same finding the covariance approach just here we act again the G plus the weighted keys that we have finding the covariance is the differences between the mean and how how it is distributed over there simply and the weighted one of those and finally adding some noise and this noise is observation noise that we have same as extended combat filter so we already broke down this study in these slides broke down this is like this and it's broken slightly study just we have the G here as kind of a little bit new I made it as blue for you then we have the correction step in the collection step what is happening let's see in line four to six here you can see that we have the uh we we calculate the predicted uh predicted transformed axis based on the transformation that we have and here we have transfer Sigma points through through function H because we have two one for control commands one for observation in collection step and automatically that first calculation so since we are in Second Step here the the function of course will be different variable G here is that one for observation one for for example motion model so for correction step then again we calculate the uh in the collection step uh the predicted observation from Sigma point based on the vision that we have then it goes to calculating the Kalman gate and for the calculating the common gain we have couple of steps first of all we calculate the some some points St and based on that predicted predicted covariance and calculations of the Kalman gain and based on that Kalman gain we're gonna see again how much the motion model how much observation model should be applied on it so I put some points over here for example uncertainty QT again another answer 24 observation model we have our keywords was for uh uh was for motion model QT this is the error that we have in the observation model exactly same as extended Kalman filter and what we have here using Sigma points uh propagation to Kalman gain calculation in fact process of replacing H ink AF so uh there we were like using Taylor expansion and calculations of the H in order to find the Kalman gain here we do this one finding the debated the covariance of the sum of the weighted covariants like this is the covariance calculation that's over here in order to say uh the Kalman game the Kalman gain based at least Sigma points and covariance how much should be applied on the observation or control command if you have a look pretty similar kangman game so the the predicted mean that comes from motion model here added by the observation Kalman gain says how much observation should be affected an observation is the differences between observation T and uh predict the observation that makes the differences so the same the the whole scenario and whole idea is same just the calculations becomes based on the unscented Karma filter then what we have here we have the uh update of the a new mean and new covariance finally after the calculation and Kalman gain the Kalman gain helps us to calculate the new mean new covariance and return them so for here I've written that output of the sigma point from observation function that Kalman gain do that and pretty similar that what we've had in extended Kalman filter if you remember in extended Kalman filter the camera looking like this here we just have that one instead that's it so now let's compare them if we run different these different techniques what they are looking like this this is coming from your book I think or a paper I think I bring it from a paper I don't remember exactly but anyway this is the resource so uh if he uh if you use the extended condom filter so this is the distribution that we have and this is the and we apply the tailored expansion if you remember the first Taylor expansion algorithm then this distribution this is the this is what we have the new mean and new covariance that is kind of you see that in extended Karma Festival dot we said that's good algorithm that's nice but it has a rule and and this is the error then uh what if we apply the unscented Kalman filter so we find the second Sigma point based on this distribution and we apply the function ethics that is a non-linear function on it and you can see this green one that is unscented uh transformation result that is much more close to the distribution the the first uh gaussian distribution that we have why this is happening because here just mean and covariance has been used but here these points are helping us to do the transformation through that non-linear noise that here so what do you think if you want to get 100 accurate accuracy of the transformation how we can achieve it so let's say if you if I ask you transform this gaussian distribution from nonlinear function and get 100 very accurate very high accuracy although this is accurate but there are some errors too how you can achieve very high accuracy yeah we can use the infinite number of points to generate it and that's what you see over there you can generate millions of points transform them and it will be exactly overlapped on it that's called sampling also we will have some techniques that is based on Sample for example particle filter we will study and see how particle Filter Works based on the sampling and how can help us in this scenarios so we kind of seeing algorithms to improve it but sometimes after improving I will tell you that or that Improvement also has lots of problems also because of that you need to choose what which one which one you are using all those we are improving but you may study recent papers that they are still using standard Karma filter and propose very nice technique or unscented Kalman filter very strong approach so that's that's why we are studying this otherwise you may say okay come to the end one and study directly that one we don't need to know this there are two reasons first of all you impossible to understand that last one you have to come from scratch to see what's happening second reason is that not we are not concrete we can say this is the solution for everything so because you should be able to develop and understand different techniques and based on the water you are doing to choose and apply on the problem that you have so what about the implementations what about the examples that we can have of course you can have a look at the interactive book again there is like pretty nice example that how you can Implement interactively and on the other hand you can refer to the python robotics I think let me see if the link is working and start is better to follow so for today as exercise you need to do generating 10 random multivariate two-dimensional gaussian distribution randomly and generate 10 of those and uh that they have random mean and covariance then generate 11 Sigma points for each one of those and fluff them so just first step of the what we studied today generating of the sigma points to to uh on the each one of them of course part of it also has been shown in the book you can have a look but you need to do it today as exercise and if you wanna have a summary of today's course we discuss the extended Kalman filter challenge then we discussed unsensitive transformation how it works how unscented transform works better than Taylor expansion and how EKF uses unscented Transformers so uh now you can start to uh work on this assignment and see what is happening in details any question okay good |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH12_SLAM_for_Robotics_Iterative_Closest_Point_ICP_Algorithm.txt | okay so everybody are okay our second part of class uh we are continuing with the algorithms that we can use in visual Islam and visual information of the environment how it can be used so one of the techniques that we have and very very famous in visual construction of the map is iterative Clauses Point known as ICP it means that let's say we have a lighter scanner and we have 3D mesh and cloud of the environment so you scan the environment then you have 3D mesh and point clock now how we can use this 3D Point clouds in order to construct the map in simplest form we will see the basic technique and algorithm to to understand it for example at time T time time T I have a scan then time moves T added by one new scan comes then I don't have any more the the features and landmarks that I detected to match them and update my map then it's like everything is point and pixels in 3D what we can do with those kind of situations uh today we will we want to talk about uh ICP creative closest point and different techniques so that we will start with introduction to ICP algorithm we talk about the known correspondences we will talk about the unknown correspondences and we we will talk about different techniques of ICP for example ICP algorithm for rejection the outlier and here you need to uh uh basically know what's happening in visual uh mapping for uh in in form of 3D construction of demand it is not only limited for 3D we can use it for 2D construction of the map too what does it mean it means that if you have a map like this and this is like in like something like this in 2D so how you can match that one with this one so in time T you get this point to the 2D map of this kind of the environment it's lighter scanner and he added by one you get that one then how we can know that these are the same and how we can put them and have one single identical map as output so today in this chapter we want to see General procedure about how this can be possible and how this can be happening visual automatically what is the visual element automatically it is the process of determining the position and orientation of robot by analyzing the visual data it means that we don't want to rely on automatic and up to counter and motion commands anymore we want to say okay I'm moving visual information is coming to me and I want to using the visual information no the robot location to so so that the algorithms that we are going to learn today not only can can give us the output map of the constructing mapping these together but if I'm at time T here and robot moves here this can give me some meaningful information what is the uh information that this can give me translation and it can give me the rotation if I can detect it right but this is visual information so that I can remap it to the from visual information if I can extract these translational rotation and remap it to Real Environment I can understand how much my robot moved in the environment so we have some definitions that we need to have a look at the first so first of all we have the definition of the ego motion then we are talking about the visual audimetry so Echo motion means we have 3D motion of the camera with one environment for example you can see an example here that this draw light lines show that the for example the car with the camera that is moving in the towards the straight away and here for example rotates to the right and and and this calculation of this movement is called ego motion that that is usually and basically is coming from rigid scene calculation and and it is one of the most important visual automatic element of the robot navigation because uh because if you want to have robot navigation with Visual audimetry and visual movement visual exact and visual information to control robot robot movement and do the navigation for example there is the interaction that robot is moving Eco motion is one of the important elements that we have there on the other hand what is the ego motion estimation we can Define that it is determining the most likely transformation between previous and current sensor reading so that the same thing the definition we we only want to estimate it on the other hand uh transformation in Geometry can be called as rotation and translation that we already discussed it in separate chapter in detail how we can do it in mathematical form we don't need to discuss it anymore the same rotation in calculations that we did there now can be used for all one of these these points that we have here the mass already we studied so so let's say what is the iterative Colossus Point ICP algorithms so it is introduced by bazel 1992 is a well-known standard algorithm for visual audimetry and is most often used to construct map of the library scans so if you have Library scan the robot is moving in the environment if you want to construct 3D map is very common to use ICP but we will have different techniques we will see which one is how generally and how they can work so input is the sensor reading can be as Point cloud or vision and the other one can be environment model again at Point cloud and lesion so not only the sensor reading can be as input but also my constructed map can be input of the my algorithm in order to do the calculations too okay clear what is the output article transformation that minimizes the distances between two point clubs transformation includes translation and rotation so I want to calculate some matrixes that minimizes the moving to mesh Point clouds in order to merge them to one identical map that I can have how generally it is happening in the the general layer of explanation we can say iterative iteratively adjust the transformation so that we can converge to local minimum and uh we can calculate the gradient descent or it's credible to do that but we will see how so for whole for students who are static reinforcement learning now know how what is the gradient design and what is the statistical gradient descent but if you don't know just have a look at the how we can optimize it this is optimization technique that we can optimize at ways to uh to do that so so we say okay let's let's break it down a little bit if you have two corresponding corresponding Point sets or cloud we can represent as points at Cloud p and Q that these are representing P1 to p n that each one of these P's are for example a point in Cloud that can be in three dimension XYZ we don't have orientation for each point just x y z if it's 2D XY so P1 has x y z up to p n x y z and Q is also same so we have lots of points lots of points in two different clouds we want to see how to find out uh those bunch of XYZ that we have in La we can deal with it because then it's visual you see I look look at the visual data you can understand this is the map for example but in computer in algorithm it doesn't it doesn't know just bunch of points over there you have no idea what's happened so as I told you output is the translation and rotation T and R that minimizes sum of squared error to the point to point can be considered some of this created or what was it we just want to put each one of these like if you consider this point it corresponds to this point we can calculate the errorable distance right what is the B of this distance and this is the uh we can say this is the error between these two points what about next point the error and some of the square root of all will be error of this and this matching so how we can represent in an equation form we can say the error of the rotation and translation is equal to 1 overlay of this sum of the square root of the uh including distance of these at these points considering the rotation too so when we write in this form it means that we have in Mass we can write it in this form two to the power 2 that it means the square of the distances between each one of the identical points that they are they have translation and they have rotation this is point set one on set one subtracted by rotated rotated second clot point and translation so first point set rotated second second cloud and the translation the distances can be give us the error of the rotation and translation of two 3D Point clouds I noted some points for you here that uh the the we can Define index I with Point separately two but the point is here you should quickly realize that this I these are separate Point clouds right do we know this I so if they are separate Point clouds even though if you if they are meshed together if you don't know these are and there's a meshed like these are um these are like randomly in the point Cloud then the difference is still the error will be high although you may have a map like as P here and the Q can be like this and if you don't know that I it means that although the map that really you have is looking like this but the point that the error that you're calculating if you don't know the I then they may be this point of blue one instead of be compared with this one will be compared maybe with this one over here and this can happen all the all the time over there and that can be problematic also so that's one point that we uh for Simplicity we can consider we have we have known correspondences first on the other hand we also can activate to the correspondences in each one indeed and we can say How likely that correspondency and and the difference is more important what does it mean it means that how certain I am that this point is this point over here not this point the features the point clouds that are more I'm more certain that are the same I can say it has they have more way to measure my error clear with adding weights to the point group so we Define the rate Matrix of the W's and we can put it on the uh on the calculations so here the main the main objective is find the best parameters for transformation that is that is for best alignment as we said in order to do that we need to also have a look at we have different techniques one of the techniques also that is common to use in iterative Clauses point is SVD that that with known correspondence is how to calculate the transformation and uh and it is actually estimating if you don't know the correspondence is how to calculate the transformation but let's have a look at the uh at the first level known correspondences for ICP creative closest point so we say if we know exactly which point is which point if I know the correspondence is which point is which point then I can do just Mass calculation to minimize the error how I already learned how to do transformation and rotation you know already then you can do apply if you know which one is which one then you can you can move it right move it put it there mathematically one of the ways also to do that is SVD that we will see so what happened here here okay so we say then correct correspondences are known rotation and transformation transfer translation can be in close form so that we can do it it is called closed form and the and in order to do this for make it faster we can yeah we can apply uh calculation of the center of mass of post Point Clause to make it simpler and do the rotational transformation it means that if you have if you have Point Cloud a and point Cloud B the easiest way to match this together first of all is to calculate the center of mass if you calculate Central first of the point Cloud a and center of Master Point Cloud B then you can move translate Center of mass of Point Cloud instead of moving each one of the particles each one of the point clouds then you can move Center of mass but they are they will be like not not much together then you can rotate it so how we can do that mathematically if the point Cloud P can be calculated the center of mass this is simple equation to calculate the center of mass one over the average of the weighted sum of them then times the sum of the each point Cloud Times the weight loss we calculate Center of mass for p we calculate for Q by the weight because in center of mass debate is also important right if you want to calculate my my center of mass my weight is important W is important over there two because of the weight of the each element so that what is happening we are minimizing the differences between the the that P and the Q of center of masses minimizing the distances between these so that it means that if this is point cloud considered this is just one point cloud and like scanning of evolved in 2D there is a there is a vowel or a shape like this A and B then what's happening we calculate the center of mass and we would like to uh translate it uh to uh to have it uh but this uh this uh this translation is simple we can translate but we have a technique called as I mentioned SVD his name is a singular value decomposition that helps us in order to do that it is a standard mathematical procedure for decomposing Matrix in three different matrixes and as you can see here we can do the process like this from this shape from this one we want to achieve this one so H is the what we want to achieve from this to this to applying the rotation and and even we can do this scaling too but for Simplicity usually we say okay let's ignore this game so what we can do we can mathematically decompose it to these three steps be transposed Sigma and U that each one is in charge of doing different things for example this is simple rotation at the beginning and this is like doing this scaling and this is final rotation so we say okay we have an initial Vector VT this one then scaling of the sigma as I explained and final rotation so this is called singular value decomposition that uh that's what we do first of all we find out the H that what we want to achieve from here to here we want to find the edge that that finding the edge can be the differences of this you can consider this is a point Cloud this is another Point cloud and to calculate the differences what we want to find this is the H that H can be calculated as a cross covariance Matrix simply that is the differences of these two point clouds time the rates that can be called cross covariance Matrix that finally this Edge indicates what we want to what we want to go from here we want to go there so that we can write svdf h now svdf H should decompose it to three to achieve it got it first find the difference then apply SVD of the difference then this can be shown in 3D 3D Matrix use Sigma VT music mavity so that so that we can achieve the rotation the optimal rotation can be r equal to UV transpose uh basically for Simplicity we ignore the scaling then we can scale it too translation of course is simple for translation we don't need to do something complex we can like the uh Point Cloud subtracted by rotated Point Cloud then you have the translation then you can translate it I put the uh I didn't prove this how much magical it can be proven for SVG for example I put the original paper that is actually transaction of pattern analyzers that shows how it proves exactly how this mathematically can be applied but in Python we have libraries that can do this already implemented in one two lines all the calculations can be done for us so so as I explained to you let's say the uh let's say we have Point Cloud a like this shape and point like B like that chill so what is the objective they are they coordinate the positions are different we are matching them together like as you can see here with applying translational rotation of course there is not there is no optimal solution to do this because this is NP heart problem lots of lots of Loops should be done to uh to do this but the basic idea the simplest idea find the center of mass move it then rotate it by finding the differences by knowing correspondences of course you need to know the correspondence find the differences calculate the SVD then rotate it is it clear so far General flow okay so whenever you're hearing about the we are talking about the ICP creative closest point in the simplest form consider we have two point cloud two d o 3D find the center of mass then then bring it translate to Central Mass then rotate it to match it this is the simplest understanding I will also run some examples for you today if yes time so now uh we can say the idea is generating this dimension of its Dimensions or gases kind of to make this procedure as accurate as we can if we don't know correspondences what does it mean it means that okay if we know correspondence as I told you calculate Center of mass move it rotate it but if you don't know correspondences then then how how you want to uh uh calculate the error how you want to calculate this over here this calculation where was it how you want to calculate this H over here because this says okay the covariance Matrix of the differences of the ice elements and you don't know it then then how you want to calculate it that's that's difficulties with unknown correspondences that what we say okay we say the idea is guessing kind try to guess which one is closer and with ICP it creatively guess it guess guess and try to move get smooth gas to finally to have some result uh and then after you guessing actually kind of I'm guessing that maybe like this point is related to this point this point and if I move let me remove this is a bit complex now here okay the idea is consider this is just one I'm not removing the other one so the blue one if I guess this one that is this one wrong right that should be this one but I'm guessing that one and if I move it it comes closer right kind of a step forward it is better than the current current one although this map will go somewhere there but if I'm I'm not doing just only one guess I may do many guesses and by average if I bring it closer then if I do that in iterative yes yes it may can finally give me what I want and let's see what techniques we have to do that so as I told you iteratively can do that we and we assume that the point clouds are in the same coordinate system because you don't want to make it complex for example robot is moving or something so now we need to find correspondences how how to do that cases so one of the technique is as as its name over here iterative closest point is find the closest point we have this Point Cloud a and this is point Cloud p robot is move and scan a is can be okay then the closest point says okay for this point over here what is the closest point of other cloud minimum close point maybe this point for this point what is the closest point of the other Cloud you measure the distance this is the most closest for on the on the purple one this one what is the closest point maybe this one this one this one this one you calculate by all of them or some of them that we will also discuss there are different techniques for that after you're calculating these minimum distances now if we calculate the SVD to just translate and move it rotate it by these ones at these points that we find are guesses that we have and the guess is to in order to do uh do magic so now let's have a look at the pseudo code how these steps are looking like our algorithm step a associate points to the nearest to near neighbor calculate then the uh information that the transformation of uh minimizing the error then transform points using the estimated parameters then if you stopping criteria are satisfied then return the calculations because at first step you may apply this guesses and do the translation rotation but maybe uh still you will have error at First Step did this move closer but not match completely then you guess it again then you put each some of these points you say okay find the closest Point again then you will see that it is adjusting and with some threshold that you say okay this is that threshold then I don't need to do continually move this is called iterative closest point and one of the strongest algorithms that can give us chance to yes two point clubs and move them and adjust them question any question the fellow all of you at least should know now okay the idea is simple now uh visually let's have a look how it looks like so if you have that one has two point clouds we guess then we come here at iteration one so we apply SVD to translate and rotate we achieve this one by these matchings after that I do guessing again and finding that lines again which one is which one which one is that iterate one more time a little bit closer do it again matching matching matching do it again and you see that it is much for example in this example 100 iteratively finding Lotus point and match it match it to finally uh achieve the file and in 3D how it looks like in 3D we can do this example as you can see here we have Point Cloud a we have Point Cloud b as an example of for example a chair part of environment then after some iterations and final iteration is completely matched it creative closes point and I think I can show you over here some implementation of that guy that I have in my slides uh with open 3D let me see I run it to today I guess in the morning for you ready yeah we have the 3D point class you can see Point Cloud a point Cloud B they are randomly rotated and randomly translated so these are same point Cloud because I didn't want to use two separate ones same one but I randomly moved it in the environment they can be separate scans of the environment but after applying iterative closest point give some time to my computer then you can see that we have matching like this so I did it by purpose adding some changing some parameters that is not matching complexly because it's that visible but yeah you can see that uh after applying some iterations it came closer and if you continue iteration with uh with good thresholding we can achieve High accurate uh uh Point cloud matching so that your robot is moving scanning in the environment every time one of these ones come you have one as reference as map that you have new new one comes you merge it new one come you merge it new one come you made it then you can construct the map of environment in 3D but the resolution is very important because this is custody if you are calculating many points the accuracy is higher but but but then it's slower then you need to sample how many guesses of the point Cloud to take and based on how many guesses then do the iteration trade is closest point and we will see today some techniques that make it faster so yeah here second iteration not too much differences because I make it not too accurate but in this slide you can see that here I I showed the accurate of it this is also uh very applicable in different applications like you can see this is like real sense and it can be used in cat models in this video that they are using for scanning solid object 3D shape sensor by 2D shape sensor so they have this camera which gives the depth and this is the object that they have with ICP let's see how they can uh how they can have the shape of that that object I mean we are not limited only to have it in Islam also can can use it in different algorithms so that's the scan that the it is the output of the sensor then ICP matching you can see that when it shows it again it matches to the to the map that it has already you see this is the this is the general map that this news can take out will be plotted and mapped on the on the previously known with the same idea and here you can see another representation form of the same idea and even with the rotation you see that constructed map is the same it's it's it's perfectly doing the uh algorithm putting some marks to make it more difficult I mean the scan will be changed and you can see that in heat plot that part is a little bit not visible over there and the point is the distance wherever it is the rotation wherever it is it can plot it map it in online form quickly as it is possible then they compare two different ones they are different a little bit in time of shape you can see and they saw that they show the cad model of the objects for for applying ICP and now they apply for both both together and they are different model you can see that says here and here this part are different and and after applying the uh that one you see that this one is also there or clear the other parts can be matched because very similar the parts that are similar can be matched but this part over here you can see that is also identical and uh is not is not matching that well this one is matching very well but this one is not matching very well but the parts that is matching wall still moves to the shape that is no and here I guess new unknown one is coming then a couple of examples to see if how are ICP is working okay I put the link you can watch the something similar but what are the important elements that we need to know about a performance of the ICP is like speed and stability is important trade-off between the stability and speed if you use more Point clouds we have more stable construction after that but we lose this speed and tolerance on the noise how much it is that is related to that and how far distance is between two two points Cloud can be can be depending on the data and application that we have on the other hand we have different variants of the ICP not only the one closest point one is like a selecting selecting and waking Source points B is finding corresponding points another is rejecting rejecting certain outlier correspondences another is choosing uh an error metric and finally minimizing that quickly we will look at each one of these now how they look like in briefly so first of all if we talk about the selecting and making Source points Technique we say that we can use all points or we can use random sampling if you if you use all points of course it's clear that's very heavy but random sampling says okay uniformly randomly sample from your point Cloud depending on how many how much accuracy you want you can see the density here that like to do that the the steps is especially uniform sub sampling and steady out or type these feature-based sampling for for these two we discussed it this is clear random sampling is there but what about the tree specially uniform sub sampling especially uniformed uh uh sub sampling means that the there are some some challenges also for example density of Point clouds are different so the the scan that you have the density here that is closed is higher than the density that is far from your object and when your robot is moving or if you have a car or robot whatever that is that is it and moving then you have a different set of Point clouds with different densities that you don't have uniform distribution anymore to use the uh the technique that we have there on the other hand uh that you should you should consider it's like like here you have less Point clouds and here you have more and your robot from there moves here then from same scenario you have more so that it is like uh it is like then also that the scale is different you you see this one in point cloud from far when you come here it is the same but that everything is changed so that's called the special uniform sub sampling that we need to also be aware that is uh it is existing but ICP usually is doing well uh if you if you tune parameters then we have the feature-based sampling that we already I think discussed it well but uh next lesson we will also see one Advanced technique to do that using additional information like Edge curves colors of the environment that can increase efficiency and accuracy and requires pre-processing technique for example we can see this video over here that is kind of similar to what you do as homeworks or projects that you can see in this video uh this is the robot that's moving in the environment and the library scanner The Stance comes from the environment and RCP has been implemented when like in 2D you can consider this is the this is the point class that is coming and all in online form the the same example code that I run you can run it a similar idea and match the environment and you will have online construction of the map in this form so that uh so that you can manage it to General general map but of course you will have challenge of like closing Loop you have challenge of the the error on the on the control command that that that also should be dealing with but still now we have very strong tools to to deal with the uh um 3D image cloud so that was number one the number two is finding correspondences of the points that uh we have closed this point matching technique that is like uh the idea is finding closest point in the other point set that is uh uh we can say we have uh we can have thresholding that it means that if you have a point a uh you don't match it with very far ones match it with somewhere close by so that um [Music] kind of so before making it complex let me tell you this idea also used in some other ones but says okay thresholding says you have a map like this and you know that Nexus scan is impossible to jump somewhere far will be somewhere around here right you scan a Time increases impossible basically by default we say impossible to jump to another building or somewhere else I am somewhere around here I'm moving somewhere around here then I can I can put a threshold that say okay when you're matching the features match features the nearby nearby code Point cloud the idea is coming from there and this is called closest point matching technique that uh that that this technique can be boosted because it has uh speed problem and to deal with the speed problem we can create dimensional tree that is is known as Peggy tree that is based on the binary surgery that we say each one of these points can become from the form of the kdg that this kg2 is famous how to construct it you can you can use binary search construct it after you construct it the searching and matching the correspondences is very fast later after constructed this KB trick and it's a technique to stop your uh you're finding correspondences another technique is for finding correspondences shooting based approach that shooting-based approaches okay if you if you want to have a guess if you want to guess this point shoot but does it mean shoot it means that shoots a line whatever it is although it is wrong should then it should like many of these then try to match it so although we may have lots of error what how we can shoot like but that true thing is like a spider monkey then bring it closer then do it again bring it closer then this is a technique called uh shooting based approach of ICP so we are looking at different techniques of the ICP not only the closest one other one is the projection based for finding correspondences projection based matching technique projection base says that okay if you lighter scan is in point a and move to the point B the the linear projection that moves you not moving like this then the projection should be the guessing should be in the same direction you can you can construct a visual visual line that there is the moving Direction and there is the moving then you can continue that one on the con on the matching then all of these lines should be matched like this because I have this information then more likely I have better guesses so this is called projection based matching technique for ICP uh we have third element third one that is the ejecting uh a certain outlier correspondences that is ignoring some of the points based on different techniques one can be distance one can be debates one can be uh different elements that even we can use learning algorithm to find it what does it mean it means that we have Point Cloud a we have Point Cloud B here you can see in point Cloud B this part is missing we don't have it we call it outlier and we want to drop it don't guess from this part because if we guessed it from this part since we don't have it in the second second Point plot this will error right if you guess from this one we cannot match it we should match it to something wrong most likely and if we can put outlier it means that if we can understand and remove these information then our guesses will be more likely correct for iterative Clauses point and bring it to the matching so that so that one is thresholding with simple distance another one can be like learning algorithms and techniques and there are many different research on this and this is also open problem that you can choose as continue to work even can be a helper publication you know if you can do it well and I think Hugo is doing something similar for his research this outlier detection for orb Islam that kind of trying to do this but this is for ICP so the fourth one is the error metric that the aromatic of the ICP can be point to point we discussed already it's just error of the distances of the two point clouds uh Square level but also we can have point to plane errors that is very nice idea instead of point-to-point matching we can assign individual covariance for each point to the to the plane of the other Cloud if this is the one one point one Cloud then if I pick one point then I can find the error not only to one point that maybe I have lots of error I can I can do calculate the error based on this plane not not just one point so that how can it possible if you can do that this is the paper that compared this I found out I I was searching for for this part of class to find implementation that compares these two techniques and says okay if you have point two plane and if you have a standard ICP and if we have the point-to-point calculation you can see that the the point to play is green one is doing better than is doing better than the uh this red one that that is point-to-point calculations and the the blue one is the technique that let me see the blue one or green one standard yeah this is errors so the green one is the point to plane this one is point to point as a standard ICP and this one is the generalized ICP that they propose a technique to also improve these two and publish it over here I'm not going to explain it if you're interested in goals to study the paper how you can even improve this point to play technique of in order to calculate it we have minimization that minimization says okay using non-linear minimization algorithms can be useful over here for example gradient descent if you remember in for example neural network gradient descent for helping us to calculate the ways to minimize the error and we here we have something similar problem then gradient descent for example can be applied to to the same thing over here so so fancy imagination of the bringing another algorithm From Another World to solve this problem and gaussian Newton is another technique that if you are interested in you can study how it is working it is like solving some problems of the uh uh non-linearity over there with some mathematical equations uh the question is does the automatic have advantage for visual Islam to be used there of course it is we can use automatic pause estimation to improve ICP by giving the knowledge of movement of automatically to the uh to the virtual automatically to improve it but of course it can also calculate it itself so that if robot from a moves to point B this is robot I I better to put the lighter scanner on top of it but this is lighter scanner then moves two scans then this line this automatic information can be helpful for me to also construct the map as we saw some algorithms and if we want to summarize and conclude we say ICP is powerful for calculating the displacement between point clouds ICP speed is depending on the uh number of points that I'm choosing and how to match them together and basically rcps locally optimal because if the math is too big just calculating the center of mass is not enough maybe maybe it rotates it but wrongly in wrong direction with some mismatching so that it is locally optimal okay so that's it for today if you have any question you can feel free to ask |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH5_SLAM_for_Robotics_Kalman_Filter_and_Extended_Kalman_Filter_EKF.txt | all right hello everybody good morning I hope you are all doing well and and everything goes fine so today we are going to continue our topic with the Kalman filter first of all I'm going to quick review of the what we've talked about the Kalman filter then we will see what's the problem of the Kalman filter then we extend it to the extended Kalman filter to overcome the issues that come in there have but later I'm gonna also State the problems of the extended Coleman filter what is the challenge over there after Improvement that we have and later on in continuation in future we will see how to improve that one also but we have a couple of other coffees in Middle to also discuss it we will see what are those so in this chapter we have the common filter algorithm an extended Kalman filter algorithm last week we talked about the some introductions about the normal distribution how they are physically working and what are the concepts so I still see some of you have problems with it because of that today I may give you some some practices here and I will introduce some resources and textbooks that you you need to have a look at it because these are the fundamental the most important things that you must completely understand in order to understand the topics of the course otherwise that's very hard so we talked about the covariance and what how we can discuss the relationship between two random variables and how we can talk about with increase in one how it can affect with changing the other variable then we talked about the normal distribution individual measurement the average of measurement and we talked about the variance the standard deviation and covariance how we can calculate based on the samples or number of the points that we have in different problems and we stated that we can compare them to distribution together so we said Kalman filter is an implementation of the base filter we already have seen how base filter is working and we wanted to plug it and we said it's come from 1960s and and depicted the the main idea is having the update of the base filter based on the data that we have in real-time fashion so basically as I mentioned you in this class we are talking about localization and slam mostly Kalman filter is not limited of course for this application but basically all the examples that we are talking is about the location of the robot and robot is moving in the environment either localizing each one of the landmarks or features that we are seeing in the environment or robot itself can be looked at as the Kalman filter or the algorithms that series of Kalman filter family algorithms that we are gonna study we said this can be including position velocity temperature or whatever we want to measure we said that it is good linear estimation model and produces accurate estimation of the on unknown variables new data that are coming in online way to update our belief of what what the what data should be calm down filter works with gaussian distribution it's very important because we're gonna later see how we can change it the assumption that we have and and the and all the calculations that are based on the gaussian finally results output as classroom model for us still so this is also a key element and why why this is beneficial so far you should be easily able to discuss it why everything in gaussian is better for us to to discuss is that so the probability of the the event that is occurring can be distributed by just two variables the mean and co-workers the mean move and the covariance or variance so everything in probability can be represented by only two variables mean and covariance and what does it mean if you remember these are very crucial to to understand the concepts so like if you are talking about robot localization if this is the X in one dimensional and where the robot is we can talk about the mean so most probably where the robot is or whatever the data is if this is the measurement of the sensor the weight the temperature or whatever the sensor is what what's most probably our our sensor our our machine is reading or if you have IMU what is the value that it is reading for balancing so all those can be shown as mean and covariance shows how much error we have how certain we are that our data is accurate if we are very certain our gaussian distribution will be something like this Maybe if you are not very certain it will be less like this distributed more widely so so that's the very critical point that reduces our computational complexity and with just only two values we can represent demonstrate our our calculations and our predictions in in the form that we discussed and as we as this is very the most popular algorithm especially it is using it has been used in Apollo program I'm not going to explain it again and if you want to like visually see what's happening we have a bunch of data what does it mean during time you have you have data that's reading from system in this particular example are we see the temperature so you have one temperature sensor so at time T you're reading you see this one a little bit time goes you're reading you see another temperature and these are the data that you're reading and lots of Errors of course so in order to but what's the ground truth ground truth is this line and in order to based on this data in order to estimate what is the accurate value we are going to we saw actually how we can use column filter in general perspective and we are going to see algorithms how to find this line that this line tries to predict based on the data new data comes says okay what is the prediction of the what supposed to be the correct value that we have so by understanding this you see that okay Kalman filter is very important and applicable algorithm for robotics so or or reading any kind of sensor in most of the applications we have such data and we need to filter it even if you have very good image processing algorithm you're finding distance of the landmark then of course still there you have some noises you your calculations and robot shake or the parameters that have will look like data like this in X Y then you can apply the same algorithm in order to improve the estimation of the reality objectives so the the simplest way is like you may say okay I can get average of data and plot it but if you get average of data and plotted and you compare it you see that that's very bad estimation the simplest and the the the kind of the the most basic filter can be the average but that's not accurate of course and common filter to use prediction then we discussed one estimation that we said estimation can be can come from the filter so we have again the data here we have the truth actual value this line over there and based on that data we can have the prediction and the prediction prediction comes from the filter that we have estimation comes from the filter that we have and prediction comes from the previous previous data that we have so for example in this particular example that comes from the book that today I also show how you can see implementation code so if you have a scale so you're measuring your weight every day and you know that you're gaining weight every day and you can know that okay I'm supposed to be at like higher rate tomorrow and the day after tomorrow higher rate you can guess it and this guessing in this example is scale rating but in our example we talk about the what can you guess it we talked about the control commands so matching these is a little bit confusing yeah of course if you can do that you understand what's exactly happening so in robotics application we say Okay based on here in this kind of if you are reading IMU kind of sensor data we say Okay prediction can come from our expectation of what is going to happen in future but that expectation of what is going to happen in future in our basic applications in robot localization for example we are talking as control commands so based on this knowledge and after learning Kalman filter extended carbon filter then you can use it in different applications not only robotics you just need to plug what you need as a prediction over here and try to estimate it this prediction is not limited only to control commands this can come from any resources of any sensor reading or or the or the prediction that we have based on the data that we have so another example I'm not going to explain it again some applications you've seen we've talked about the navigation control time series analysis robot trajectory optimization noise filtration and the estimation of the current of the for example a motor system that is is getting feedback from environment and we want to compensate compensation is like um for example you need your motor needs to lift this okay how much torque you need to add to the motor to lift it and and based on the reading column filter can give you better estimation of how much torque you need because if you give more it goes higher right you need exactly the correct amount to hold it like this my brain does it for me for now my finger I I have enough Force to to hold it like this in this angle but if you want to do that without position control with torque control if the motor that you have then for example you have simple DC motor you don't have position like Servo motor that you can say exactly go stop here then you need to actually that Servo motor in inside already implemented this for you that how much how much force needed to be applied to exactly to stay over here based on the based on the external weight that we have so that can go on Kalman filter or extended Kalman filter that later on we will see can do this job for us any question so we said that um we considered as observation and motion models and but we consider they are linear for Kalman filter then we indicated and declared the motion model as XT that that we set new state is equal to x t minus 1 times The Matrix n added by the mode control command and Matrix M added by the motion model noise that we have in the environment and we discussed as this in an M are are kind of mapping of the how motion model can be applied on based on the previous pose and control commands that we have kind of linear matrixes mattresses then for the same thing for the observation observation whatever can be is a lighter scanner or image processing whatever it is you have some observation that can that can that observation still has some error and mapping a matrices a matrix that that can be kind of scale our our observation model so what are the important elements I'm not going to re-explain it again we just want to have a quick recap then then some elements what we have here okay then the explanation that we discussed in detail last week later on I started to talk about the the basic probability Concepts in the Robotics and we talked about the how for example tossing a coin can work and how we can how we can bring it to the the precaution function form so that that gaussian function form in the probability can be moved to the multi-gaussian distribution so that so that if we have one one one variable one one one D is like this but if you have two Dimensions it looks like this and because of course Kalman filter can work in multi-dimensional scenario we need to consider the multi-dimensional or multivariate gaussian distribution we discussed how this can come to the inform of the multivariate gaussian distribution I'll explain this last week I'm not going to redo it again so that because this this equation here the aim of the Kalman filter was using this term over here and combining it with these two I want to show together motion model an observation model we want to plug this over that term in order to have the update rule of the Kalman filter that that we just cut the kind of plugged them together that that we had the kind of a big term in order to do that so we saw that okay the same multivariate gaussian distribution we plug the the part that we have for motion model into it to doing this we said we have motion model discussion noise so it means that we actually bringing our motion model that that robot is moving based on the control commands in the environment and we want to also consider the noise that we have over there so we've written this rule then the same thing with the same combination and the term what we've done last week we discussed that we can write the probability of observation given by XT with this term over here that's what we did multivariate gaussian distribution combined with the observation model that we discussed with the matrixes that the W that we have and I stated that this Q is for the the observation error and here we have R for control error so it is still this the gaussian noise that we have our in our in our control commands and observation that we have and usually that's with zero mean and the covariance indicates the amount of Errors what does it mean it means that like so if if I say my my robot is over here with some certainty with some belief so I cannot know it here so if I want to add noise here I have another noise that that this mean indicates some x's like from zero for example to 100 some values here but I want to add some some error over here so I don't need the mean basically so when I don't need the mean so I have like you may say this is my error so mean is not important because I don't care where it is but the the covariance is important for me I plug it to it and this will be like move the shape just make it wider if you plug it to this guy over there how you can plug it over there so of course you need to know how to add to probability distribution function or multiply them I know you have still some problems because of that I'm gonna give you some practices based on the questions that you've had since last week now for example if I want to explain the ad of course it's easy you can add the mean of two probability distribution functions if you can sum them we have two values and for the covariance you can sum them right then then you can shape new new this probability distribution function so that's that's very simple now you can like if you have two another one over here you can sum the mean and you can you can sum the covariance then you can measure them but basically we don't do that we just use the sum for managing the adding the error but but of course for multiplication today you will see how even in Python you can implement it based on the things that I'm gonna Define for you then anyway let's continue quick review of what we've discussed because we're gonna need them then we move toward the so we saw the basic intuition of the Kalman filter then we said that we wanna plot that term that we achieved together into the bayes filter what was bayes filter bayes filter had two steps prediction in the prediction we were calculating predicted belief based on the probability of the XT given by previous it's the unmotion command times the belief that we have and that the belief is related to previous belief that we calculated over here so after prediction listing at the first first starting run so it is the initial belief that we have so when I'm parking in the initial belief if you are talking about localization I'm believing that I'm somewhere in point zero zero how certain I'm believing based on this covariance that I have if I'm quite certain I can say okay it's very sharp caution distribution now if I'm not certain even at the initial belief then I can I can plug it there that you've seen example implementation for example the the chapter that we were discussing about today's history if you remember so after doing the prediction predicted belief we have predicted belief means that very important again so my robot is over here I'm running all two three meters for example then I know this control command then I want to calculate the predicted belief that I am based on the control commands previous pose that where I was and previous belief that where I was okay and don't mix this is the belief of the calculation Kalman filter and this is the pause if you are talking about the X Y and orientation or Perry then second step about the correction so in the collection we were trying to collect this estimation that we've had what does it mean so I was here I moved and calculated my belief where I am that is like again gaussian distribution then I say I need to correct it because I have lots of error on the control commands motion commands that I moved over here and how I can correct it I just can look around with observation get information I have another model then then I can't improve this that that if you can see predictive Leaf can be improved by the observation the probability of the observation then just normalize it so that you can you can plug them two together this was bayes filter that we studied but now we studied also Kalman filter and what's the objective we saw two super big equations that we want to plug it over here instead of having the probability of the the the x txt minus one UT that comes from motion command we want to plug that big term over here and here for observation we want to plug that big term over here to to use the bayes filter in order to update my my predicted belief and belief Affair the robot is in online fashion so everything clear so far I'm just reviewing what we've studied so far okay now what we've done we said okay instead of like plugging there to have very big equation directly we went to see the algorithm and we saw that we can have a Kalman filter algorithm that gets the MU T minus one mean and covariance mean and covariance at the beginning will be initial belief initial belief where I was at the beginning I told you where I'm where the robot is can be indicated by two values mean and covariance that says where I am in the environment so to make sure that you get the idea 100 so ah let's say this plot shows my whole environment X that is continuous of course can be continuous because we are talking about discussion distribution and you can say my robot can from here 0 0 up to n part can go to the dash this is whole my environment and what can I do I can say very very robot is what's my initial belief I I'm believing robot is here I'm drawing a small here and we say okay with mean and covariance I indicate the initial belief is there that comes to the algorithm in the Kalman filter and of course and of course the control command and observation also is an input for the for the Kalman filter that that can be in online way that each time I'm sending to the Kalman filter or or if I have all send it to the depending on implementation that we have send it to it but still in the in the loop that we have we will update it each time just predicting predicting and updated two steps so what we've done we first calculated the prediction the prediction came for the predicted mean and predicted covariance so this predicted mean and predicted covariants come from where was the initial robot and what was the control command that I've had and what is the observation observation will be used here for now control command reviews and we've used the matrix's linear matrixes to update the mean and covariance that I'm not going to again explain very in detail lastly we did it in correction step first we calculate the Kalman game and we said that Kalman gain is indicating how important is the control command and how important is the observation model that I have so again my robot from here moves here sees in order to update I'm saying now observation is more important or that one that I claim is more important that Kalman gay was was helping me to calculate it that this Kalman gain if you look at here indicates that observation or control connect so here we have predicted me predicted mean is where the robot eats me so predict this is new me is equal to the the in the left part we have the predictive mean that calculated directly from motion Command right and in the right side of the term we have Coleman gain that is multiplied by the observation that if I last time also showed some examples and discussed it together in Nexus slides that we have that if we can if we can change the amount of accuracy on the on the observation and on the control command how it can affect the change of the updating based on the observation or predicted motion command predicted mean that we have is kind of adjusting the value but what was the benefit the benefit is that you don't need to do anything you don't need to say okay my robot is um my robot is like you can of course put some weight over here but Kalman gain all already calculated automatically but for you based on the amount of error of the control command and amount of the error of the observation model that you have automatically adjust it adjust it if you have very accurate observation model then it ignores especially the control command says seeing is better than anything else have more weight more weight I need to predict where the robotics they mean like this one that is moving then then that's it this was the whole structure of the Kalman filter last week we discussed I'm not going to go in detail again we saw some notes for example hard collection how the Matrix operation can be done yeah here I showed that if you don't have error in observation it means that QT is equal to zero what was the QT the observation noise the observation noise that we have so if it's zero what is happening we discussed that then observation will dominate the output and it is already proven by the Kalman filter and I also replaced if you replace your cells again you will see that the how in Matrix operation this Kalman gain will give all the weight to the observation because this becomes zero over there then we saw the example and how it's working so we have in this class more than 14 chapters mostly I in all chapters we have this robot over here but lastly I saw that you have some problems in visual understanding for future iadities now you can use this one too so that we had the initial belief what does it mean it means that our robot is over here this can be any kind of robot I put you manage robot mostly so humanoid robot is here and my belief based on the mean and covariance indicates that I'm there then what is happening is Kalman filter so robot measures the environment uses any kind of sensor that it has measures the features from environment and that means German says okay robot is like over here not there me German says this so what does Kalman filter do wants to based on the calculation of common gain and based on the certainty of each one of these that is now really clear to update the belief of vague robot is how that is happening so it is happening like this over here that the belief is changing based on this new black curve gaussian distribution then we are updating where are we are believing that the robot is then we said that okay we're running control commands motion commands robot moves from there to here so after robot moves from there to here of course our our belief is moving based on the first step of Kalman filter that we have moving to the right but we have the noise based on the noise that we have that's the reason why this curve that is sharp here becomes uncertain more uncertain here so this one becomes more our Center because of the control command or or or automatically or the the motion model noise that we have so we move more this becomes more uncertain because noise becomes bigger accumulating of the he said okay if your robot is going a little bit to the right there will be very like if you want to go there you end up there this creates curve and more uncertainty during the movement and because of that in Kalman filter observation tries to correct our beliefs based on that okay we say after some movement robot against these and after the scene we have another curve this one over there and and Kalman filter again updates the um updates the new bit for us so this was recap of all what we've discussed last week of course if you want to implement we have implementation notes that that we will see next chapter first we have couple of new topics there in order to be able to go in details of how implement it but but directly we will go to extended Karma filter and next chapter I directly go to implementation of that one I will open it later the whole equations to to how we can really bring it to the practice in in localization probably so what was the shortcoming over here if you remember we said that we have all the time linear measurements and error will will be considered as caution distribution and linear let me try it because but but is it realistic is it always happening in Real Environment and all all the errors that we have also always is linear of course it is not in some applications we do but in many applications we don't have linear error in our system so so non-linear model can cause us non-gaussian model of the noise or prediction or whatever we have now the challenge is if you have a look we were talking about mean and covariance then we don't have it anymore can you show this with mean and covariance no so this is if I wanna considered non-gaussian model of course we will be happy because we have more accurate prediction of the data that we have the error that we have than the our final prediction will be more accurate but but we cannot do the same thing with mean and covariants what to do to this problem issue we have extended Kalman filter and we will see how to deal with this problem so is everything clear the challenge that we have the main concepts are clear for everybody what happened in this case okay so the the idea behind is simply trying to use Mass the power of Mass to somehow convert this non-gaussian model to gaussian modeling the whole idea is this try to use Mass to connect to this to the gaussian of course we will lose some but still we will be able to deal with non-linear model of the environment because if your sensor noise is non-linear non-gaussian or better to say nangation then you cannot use Kalman filter anymore if you feed it to Kalman filter the result the prediction will be totally wrong in order to be able to use it we have extended Kalman filter and we will see how we can linearize non-linear function like that in order to be able to do that we should have a look as a at some Mass background then quickly see how we can convert it but the most important one is the how we can how we can finally convert the text so extended Kalman filter is again as one implementation of the bayes filter it is a non-linear version of the Kalman filter everything else is same almost we just want to bring non-linearity so again we have estimate of the current mean and covariance be after conversion an assumption is that next next state probability and measurement probabilities are governed by non-linear function G and H and we are going to see how we can calculate G and H so if you have a look here the idea is the XT and the OT as like observation than the pose we want to rewrite them in a form that we don't have linear matrixes that we want we used in in Kalman filter so if you remember we used the matrix's n and M and w in order to have presentation of the linear estimation of the environment now we want to replace it with a function G that this function G do the same thing do the exactly same thing but can can get the non-linear model can get the non-gaussian distribution so that we will Define we will talk about how this G is can be implemented can be can be declared and how this Edge can be declared so G is indicating getting the control command u t and XT x t minus one so gets the pose and gets the control command exactly the same input but this time none gaussian so that g can model it and we add some error to the to the motion model that we have at the Epsilon T for example the same scenario is for the observation model too we wanna indicate and declare function H that that will be replaced if the W Matrix W that it gets the XT and we add some noise and we have our observation so we say eks calculates an approximation and replaces this approximation by gaussian so we that this D and H is doing that so so we are kind of in extended Kalman filter approximating based on these functions we don't have exactly the precise value if you are familiar with like normal Network already we have very similar concept over there we have model that our model is trying to predict the output so so but but here we are not going to use that complex models we are going to use Simple Math to to achieve so what is happening let's have a general look at the differences we have Kalman filter and in Kalman filter we were calculating the x t by by matrix and and Matrix m based on the control command based on the previous pose for motion model and for observation model we were doing the based on the xtwt Matrix W to get the observation based on the error that we have we already seen this so far for bayes filter now what we are doing we are just replacing the function G if UT x t minus one so this is the UT and this is 60 minus 1 and here XD for observation with the with the function G and H so in order to achieve this we are going to use first order Taylor expansion to linearization of the non-linear mode so what is the first failure expansion it is constructing a linear approximation to a function G from G's values and slope it uses the G's values and its law what does it mean it means that if we have a non-gaussian model then the idea is use the for example if you have a point here use the use the slope and the value where it is in order to linearize non-linear gaussian model that we have so in order to calculate the slope we are going to use the partial derivative as you know I already mentioned in the class how you can do that also I think I will include it in these slides so that you can see here especially visually yeah I added recently that that you can see how with calculation of the partial derivatives based on the given slope we can we can use this to to calculate the G Prime of the UT and XT minus one based on the control command and observation that we have so keep this keep this in your mind that we have the concept of derivatives and the slope of the slope and value in order to achieve it now based on using that we are going to define the tail or first first order Taylor expansion so first order Taylor expansion is a polynomial linear approximation of the function that it says we can have the the The Intercept of the line with the model that we have in order to calculate in order to calculate like kind of if you have this model we can model it to the to this line over there linearize the non-linear model that we have at each point and of course each one of these four time that we are going are non-linear right so we can kind of the idea is okay for each one of these points if I can draw this for each one of these then I can kind of linearize non-linear model that we have so this is in one dimension like like it's simple that that if we want to do that we can calculate the Jacobian matrix and how Jacobian matrices is working Jacobian matrix is like n times n Matrix that has all its partial derivatives so all of the possible partial derivatives for the model that we have can be included in form of the Matrix that that indicates what we've seen in previous slide it generates the high dimensional space it kind of linear approximation of the so let me bring the model so linear approximation of the the non-gaussian model that we have for example if you consider in 2D for each one of these single points we can calculate the line and the slope of that line and if you want to calculate for whole model and for each one of those independent points what we can do we can linear we can we can approximate linearly with this plane that we have kind of we are we have the model that we are flattening to the to some prediction over here and and in order to do that we are using Jacobian matrix that this Jacobian matrix do this for each one of the the points that we have over there in form of first Taylor expansion so so we also also this is like known as generalization of the high dimensional space into the linear approximation of the function that we've seen so the general idea so now you can see that okay if you have non-gaussian model like this the general idea comes from this based on using Jacobian matrix so by knowing that now let's use it to to plug it into the Kalman filter based on that knowledge that we have from this but we had we had the observation model in Kalman filter means that robot we have the motion model sorry we have the motion model that robot can move in the moving environment and we had the prediction now we said that in EKF extended Kalman filter we want to write it in form of G so that the inputs can be non-gaussian the control command and XT minus one so but but this is non-linear now in order to linearize it in Kalman filter extended Kalman filter what we do we use the same concept in order to achieve it so we replace this term over here by writing it in linearized form how that is happening so it is happening by changing this x t minus 1 to the G of the U T minus 1 that is the best previous estimation that we have added by this term over here that actually do the um linearization that that this G Prime is Jacobian matrix that tactical Matrix that is flattening is applying on the model that we have how that's happening also it has the term here what we have x t minus 1 and the differences of the deposed and the mutif the previous belief and the previous pose that we have differences of the linearized so that I think I've written here yeah he came this term can be written in form of the Jacobian matrix and the same same input that we have and this is the GT that is partial derivatives of the all possible states that that function can be linear use so the idea is simple but but maybe looks a little bit complex what we need to do in fact in fact the XT for motion model as G can be written as this part over here simple so only you need to consider that okay instead of the matrixes in Kalman filter in extended Kalman filter we are going to replace it with G of the control column x t minus one that this term is equal to this term over here that hold the discussion background is using the Jacobian matrix in order to linearize it so now we did it for motion model what about observation model for the observation model that we had collection robot see something we are doing the same thing same linearization but this time instead of instead of the Matrix W in Kalman filter we are replacing with hxt and this is non-linear really linear linearize it by the same scenario over here that we are adding the HT here each of the predicted mean added by the added by the the Jacobian matrix of the XT minus predicted me that these differences of differences of like my predicted my predicted my my predicted mean and the difference is with the XT and how this can be plotted to the non to the non-god to the gaussian model to the linear model that I have if they are non-linear as input so the same the same Jacobian matrix over here that that can be correct our observation model so with using this idea for observation and replacing with this term we can achieve linearization of non-linear mode but so far we've seen just general concepts and general idea of what's happening in next chapter also I'm going to go a little bit more in details of how this is happening over there now let's have a look what we've had in Kalman filter look at the term that we have here we have the predicted belief of XD and whole this big term to calculate right with Matrix is n and n and M so in akf what we do we replace the Matrix n and M with the G that is linearized form of these matrixes so if you remember these matrixes were kind of helping us to mapping the the pose and control Command right but here now we are using the same we want to do the same thing with g and Jacobian matrix but this time I can fit non-gaussian model inside and this is happening with first order Taylor expansion and if you think that you need to understand it more deeper over there you need to also have a look more in depth of what's happening over there write some calculations and the examples that we will have you will see how really it is happening of course we will have also implementation later you will do some practices also in order to understand it better so this dkf for only motion model and what about the observation model with Kalman filter we have the Disturbed right that later we write we wrote the algorithm also and now with EKF we have this term over there what we do instead of the Matrix w we are replacing with the h this Edge and this Jacobian matrix that calculates and linearize our input for us in observation now let's have a look at the algorithm directly how does it look like so hope you don't have any problem in Kalman filter because we are going to compare it now and see what is the idea over there so in Kalman filter algorithm we had the mean covariance control command and observation and we use the matrixes NM to First predict then update using column again but let's have a look here what we have in extended Kalman filter we have the same prediction step over here and we have the same correction step over here and we have the Kalman gain again right only thing that we are changing replacing this Matrix n and M with the what we've achieved with Mass replacing with g g of the control command and mu T minus one here four the mean predicted mean and for covariance we're using the Jacobian matrix of the calculations that we have Jacobian matrix of the a previous covariance added by some error so simply we replace this n with G here that is accepting non-gaussian mode so after calculating the predicted mean and predicted covariance what we supposed to do we're supposed to do calculate the column again in order to see is this part important or is this part important to up to update my prediction and again here Kalman gain can be Rewritten by there if you have a look at the Kalman filter we have Matrix W's that I discussed explain in detail about why those are there and how we can like with replacing how that's working we just change it with Matrix h that Matrix H is again non-gaussian and this is the Matrix of partial derivatives that accepts non-gaussian of the observation model for my filter that I have then after calculating the cost now we need to update this predicted mean and predicted covariance by observation that again the same thing with replacing h mean t and the The Matrix of the HT dot that can accept non-gaussian model from so with having a general look we see that we've used the mass we've used first order Taylor expansion the idea the concept of using partial derivative Matrix now I can give non-linear model as input and and my algorithm now is just replacing is just converting the the long version model to gaussian model and solves the problem but who can say now what's the problem here so we achieved something with extended Kalman filter but what we are losing now so first one point so can we implement it now first question can you write the code do you think no not yet we have a lot to do still we have some to do next chapter we are going to study its component and later I'm gonna open it like you will see we have super big yeah super big algorithm and lots of equations inside that's why you have like oh I don't understand what's happening like what so we are seeing for now General concept of the extended kalman filter we're going to open it and also for example we've seen the within the the motion model right by velocity based motion model for example we've seen the implementation so that's one one component that we're gonna plug it in but but we haven't discussed about observation model right what what can be observation model I'd plug to here so next chapter I'm gonna explain how observation model can come here then we put all together and we will have a big algorithm over there so still no rush you cannot think about implementation so far because last week some of you were mentioning we can implement or have practice so not yet the okay now let's go back to the question what is the what we are losing here no idea we are losing something very important I mean it's kind of drawback of the extended kalman filter that later also we are going to improve it with another algorithm time I think I've shown the complexity okay so here before before going to also clarifying exactly what is the cost over there but we are losing the the time and our algorithm is more complex here I've I I've added some notes for you guys for later to read and understand that algorithm better for example G is here a non-linear model I already explained all of these so for example the the mean t minus one is output of the extended Kalman filter from previous step that shows how this one there it is so this one predicted that the previous mean and for example we have predicted belief that predicted believe is equal to predicted mean and it means that where the where the prediction and I might believe that I am we have the covariance Matrix of the of the prediction belief and previous covariance Matrix and GT and RT is the the the motion the Jacobian of the G and the motion command noises that later when you are studying you can you can understand exactly what's happening without going too back to the slides to understand what was it so I added some notes for it for here I explained all of this today for you oh yeah yeah here we say okay in in extended Kalman filter billionaires or non-linear functions and added linear approximation of the nonlinear function so that the time complexity is the OD 2.8 added by and N squared so what does it mean it means that so for D 2.8 we need to have Matrix operation that this Matrix operation in size d d p times the cost of this t to the power of 2.8 if you want to have a proof just check it yourself and and this is added by the the N dimension of this data space so State space if is this n Dimension and that can that can also cubic cost that we have the cost is kind of is still acceptable but this is you see 2.8 is quite High and that kind of limits Us in using the extended Kalman filter everywhere previously because if this data space and number of for example objects that we have is too much like features you have on thousands of features that you want to localize in the problem after next chapter you will see that this is big problematic situation that we we go toward the unscented Kalman filter and we will see how unscented Kalman filter can fix it so here are the things that I explained to you so we have point and slope and linearize it and during time and we need to do it for all of these and that's that's why the calculation is very costly so in this chapter what we've seen if you want to summarize we discussed the Kalman filter first we then solve a demotion model with caution noise general concepts we reviewed with we've discussed observation model with gaussian nodes how it looks like we will see later in details we discussed Kalman filter shortcoming after we discussed it that we saw the the problem is that it cannot accept non-linear non-gaussian models and what we've done we introduced extended Kalman filter that can solve it with linearization of the gaussian distribution a non-gaussian distribution then finally we linearize it and we solve the problem that that this is the end of this chapter so that if you have any question you can ask. okay |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH10_SLAM_for_Robotics_Occupancy_Grid_Mapping.txt | foreign okay hello everybody good morning again hope you are doing well and you are good so uh today we are going to talk about the occupancy grid mapping but before that if you have any question about previous course and or uh your topics about the project you can feel free to ask so for for this course you don't need to uh present your project in class you just need to send me final topic that you are going to work and if you think that you have any question about your project or about the topic that you're going to choose you can directly talk to me it's fine okay no question good so uh today we are going to talk about the occupancy grid mapping we already seen uh how how grid mapping is looking like in previous course a little bit General we want to see more in detail how we can use the concept of occupancy grid mapping with base filter and how we can update the map Construction in our localization algorithm so whatever the technique that we are using finally we need to construct the map and let's see dive in how we can work with it so first of all we will talk about map in measurement models then we will talk about the occupancy grid mapping then we will talk about the Sensor Fusion and if you have multiple kind of sensors what are the general topics to fuse the uh different kinds of sensors together in order to be able to use them for uh uh constructing the map and we will see general idea of the learning inverse measurement model we will first formulate what is the inverse measurement model then we will see how we can engage learning techniques and algorithms in order to use them to construct the map so ah first of all let's have a look at what was the map if we talk about the map we can say we have feature-based Maps that in feature-based maps uh our sensor model extracts features of the environment for example you have camera robot camera looks at the environment and with that camera you extract some features or you have lighter scanner you scan the environment or rgbd camera that both can have the pixels and the distance of each pixel then you extract some features like the corner apes or some identical uh features that can be later also matched with the next frames during time so this is called feature basemap that that we have lots of different algorithms and techniques that works with this technique based on this technique later on we will going to uh see on the other hand second type of the map that we can build and construct for our slam problem we have occupancy grid mapping that in our capacity grid mapping the general idea is that the discreticize the environment to the required resolution that we want then we say okay if robot is somewhere with the existing sensors that we have robot senses the distances and we occupy the locations that this robot sees there are some objects over there exactly the environment that we are here that if you look at the tiles and look at the objects just we need to find out which one of the tiles are occupied and and put some occupation there but today we want to see in details how how we can use the base filter and probability concept to to fill this year how certain we are that there is a obstacle here or not it's not like zero and one always because if you are that certain the problem is like very uh okay and solved but we have error and based on the error maybe one time your sensor module says that here there is obstacle next time says there is no then what you want to do you want to occupy it or not occupy So based on that we want to bring the probability and the mass inside in order to be able to say How likely there is object over there so if you want to construct 3D model of the occupancy grid mapping at the beginning May looks a little bit complex but if if we uh in simplest form if we just give the Z to the occupied location that mostly whatever is in the environment somehow goes and and has like a standing point it's not on the air usually because after that we've got something simply use the 2D model and give the Z to have the 3D model like if you're detecting the wall then you can you can extend it to three dimension but on the other hand realistic form is like there is a window and of course if you have a window maybe the robot is drawn and can fly outside of the window then you need to have 3D model of the environment really based on the 3D construction that comes from for example laser scanner then what you have you have a cube that that Cube will be occupied will not automatically if the same concept you just have a cube of these then each one of the uh each one of the elements that we have we can say okay if it's occupied or Not by scanning the environment and the sensor that we have for example rgbd or lighter scanner AK on the other hand we can we calculate that next chapter we also will see how we can deal with it if you have visual information from environment uh and uh a Time key your lighter scans the environment then you have Point Cloud it means that for each beam like this is one beam that you're measuring so you have millions of or hundreds thousands of these points that that gives you in pointer pixels in in environment than in 3D model then these pointer pixels doesn't make sense for you for your robot you don't know like those are just pixels on the 3D construction you don't know what is the wall what is the chair you just have a bunch of points so these bunch of points at time T add it by time t plus one then another bunch of points come and these this is like series of millions of points that are coming how we can bring them to the form of Point clouds and how we can measure them together also next chapter we will talk about but today our focus is based on the occupancy grid mapping how we want to make a grid of environment and work on it so so so far we know three different types of uh environments I did the mapping mapping for Islam of the environment is it clear any question here so for example for feature mapping how we can do that uh of course we need to use um different techniques of image processing robot vision and all the techniques that we can extract the features of the environment there what we can use for example we can use again the different kinds of sensors the most common one is lighter scanner that in next slides we will see so uh we say the basic idea is that we want to evenly uh spread it field of binary random variables can show us which one of the uh grid cells is occupied or not occupied so this is just general idea and and they are representing presence of obstacle in in one location simply they are basically non-parametric model they already have defined and if you want to visually see what's happening we want to say okay uh we have like probability of the being obstacle or not I don't know how likely this is visible here these are darker colors these are white these are black so uh for darker colors we can say okay we didn't see we don't know robot doesn't scan but this area that is white it means that we scanned like I'm scanning when I'm scanning there is obstacles here of course the the line in Middle there is no obstacle because of my sensors the measurement the distance gives like one meter so among these one meter it's free so I can use that technique to say this cells all are free and this one is occupied so when you do the scan you can free free up to obstacles then put the obstacles over there but the other parts for example in probability form we say that those are free and random variable you know that if you talk about the tile if you can have a head and tail of the coin then we can consider that is positive form for example negative one and if if you bring it to the probability form then we have 50 percent of having the chance to that this coin is uh head or tail so that we want to bring that form to the probability of each one of these grid cells to say it is occupied or free is it clear okay uh one of the benefits that we have here we don't need feature extraction because feature extraction already is difficult and we have some Challenge and errors there later we will see but of course like we have different techniques if you study different papers we send papers some of them are still based on the feature extraction but some of them are based on the occupancy unit mapping they are like competing against each other so what are the important elements that we need to consider if we talk about occupancy digit mapping of course the basic and the first one is the map size and the grid cell size we need to think and we need to uh uh kind of decide how discrete our environment not construction should be on the other hand we have the noise in perception so this noise in perception should match this guy over here usually because uh if your noise is very big then your grid cells is like the size can be effective on the on the amount of error based on the grid size that you have uh we usually here we uh for Simplicity in construction of the map we say that already uh we are talking about the mapping part of Islam not not localization so we consider that localization already sold by for example command filter extended column filter whatever it is now we have the information and based on that information we want to focus to talk about the constructing the map as one of the important elements so so basically we consider we have the uh uh we have the output of for example EKF UKF or whatever the algorithm is as localization and we're gonna construct our map so other important parameter that we have is the perceptual ambiguity that how frequently one location is looking like to another location in that environment so if you have like Corridor environment that that there are 10 corridors that they are exactly similar and they look like just respectfully the empty corrid so constructing map in such an environment of course has higher difficulties because they are very similar to each one and and even though if you have a feature extraction of the environment the other type so the features are pretty similar then then that that is the one challenging one of the important challenging uh map construction like you have for example this environment then robot is somewhere everywhere is looking like identical there is no feature so this is called a well-known ambiguity of the environment then we need to rely on control commands motion commands mostly to or automatically mostly in order to be able to construct the map and of course we have more error than uh there are more challenge over here on the other hand the cycles Cycles also are also very difficult to uh to talk about as as we know formally it has Loop clothing problem that like if you robot starts from here moves and then comes back from here this is easier than if you make a loop why because because after making a loop we need to identify same location that we started robot starts from here identifying the same location that robot is dark because we don't have any idea this is it it will take one minute or one hour of the rotating then coming back we can see it now we can say okay that's easy but but in the algorithm we have no idea maybe a robot starts from here five hours later comes back or five seconds later comes back and maybe they can be very similar environments because of that detecting the loop is harder than uh just going like and turning back and kind of leaking so uh we have the environment map of the occupancy grid mapping you can see this kind of the environment this comes from the book that we have they cons they've they've implemented the occupancy grid mapping and constructed the map and you can see that occupied walls the free environment and the the surrounding environment that we don't know what what is there robot doesn't know what is there so these are darker grayscale colors so uh foreign mapping as you can see here so we have here lighter scanner in the middle and there are some obstacles and that obstacles like the lighter scanner scans the environment and based on the based on the distances that we have you can see that we can put directly 0 and ones on the grid map over here in this part so that we have the simple map of the environment by saying that okay these are free these are occupied ones so by looking at this map you can see that okay using occupancy grid mapping looks very interesting because we are doing any calculation we can achieve this this map construction just with having the range of the range and bearing of the sensor model that we have so if our robot moves uncontinuously we can do that with applying the localization of the robot then how accurate we are we can we can construct our map over towards each one of the individual grid cells that we have but what is the challenge why today course is coming up because when you robot moving based on this sensor of course we have error and these are moving and we have error there and again as I mentioned to you we don't know like How likely this should be occupied or How likely it is because the multiple times we will see that this is occupied or not occupied based on the error that we have on our measurement photo if you don't have error then that's it you have sensor robot moves you exactly say okay this sale is occupied or not occupied how much time removing my sensor is accurate I can say it is occupied or not with zero one I can work and that there is no need for probability model again so now uh let's gradually start to dive in how we can bring Mass Insight in order to solve this problem it will be a little bit complex in middle but I will try to break it down as much as possible as we already discussed we can show the occupancy grid mapping like this we can say the hour map m is equal to lots of grid cells so that we can split our map to the eye I number of grid cells and and indicate them with the index I that that they are we are going to show the binary occupancy value inside each one of these that finally if like comes if you consider zero and ones inside all of these if whole map is occupied should be some of them represents our map so and the resolution of course is important but if we want to bring it to the form of the occupancy probability same as previous we can write probability of Mi that that says each each one of these grid says should come to the form of probability of How likely it is occupied or not how how much certain I am I am that this is this grid cell for example is occupied or not so I have a question for you guys that uh States why only occupied so we said this term over here refers to the probability that ice grid cell is occupied so why why only occupy simple question yeah what so here the probability of Mi we say shows How likely this grid cell is occupied right now we say y we say only it is occupied while we are not saying for example for example it is not occupied yeah because its probability is different because if we because we are going to use it in later in the mass because uh probability of this grid cell if we talk about occupation occupied is 80 the number is 80 but not not occupied is 20 right so that if you want to calculate in probability form then we should all the time talk everything about the occupied form okay not not we can talk about not occupied then then we should say everything is not occupied over there so this is the point that uh you should take into consideration first of all of course that's simple and clear so uh we say occupancy probability is the distribution of all states of the environment and we can also represent that okay if then we can write if he in previous slide we showed probability of m i we can show the probability of M itself whole map is equal to probability of each one of the individual items that here I is equal to 1 to n so formulating whole constructions of demand on the other hand the golden standard that we have for occupancy grid mapping by giving Delta data can be calculated by posteriors over map that we say the probability of M map given by observation 1 to T and the the sequence of the all poses that robot has as excess so what does it mean it means that we want to construct the occupancy grid mapping today by observation and robot poles so of course we used it already many times but for localization for example we used it for EKF UKF different algorithms but here today we have M here not not the pose or previously we had the X here or the robot puzzle depending what we are going to do but now we have the map that we want to have it as output by observation series and and the robot poses that can come from any algorithm so now we can also State the note that we don't have UT anymore here control commands because as I mentioned we are not solving the localization problem it already has been solved for us we don't take any more the the control commands into consideration control command already has been used to have the observation that we have from really from the environment and the control command already called us the robot pose that we have so it is second layer of algorithm that we are talking today is it clear any question so as I mentioned uh the the common domain of occupancy group mapping is a 2d floor plan map because it's simpler and we can simply construct 3D based on that and 3D representation uh also can be uh can be can be done but of course it increases the computational expenses if your robot is not flying usually we don't need 3D construction of the map if you want to solve this land but unless you have some specific tasks for example if your robot is like working in the environment is humanoid robot or whatever it is needs to if a screwdriver is screwed screw something open something work inside one of the topics projects for Islam is that robots are are going to work inside airplane inside airplane there are like I don't I think millions of meters of wires that that takes years to people to wire them inside one airplay and that's like brutal and one of the uh projects that nowadays is one of Hot Topic Hot Topics is that robots can do the same job inside airplane but of course you cannot program it like exactly the position everything still Islam should be worked there uh maybe mapping part is not necessary constructing the map again is not necessary but localization is very important there so that so that there then you have 3D Construction in math in detail whether are the roles there are the wires and robot needs to do this and there are like big projects ongoing on this and there are many research papers that you can study also there we have optimization problem which order which one should be done first and those topics are coming also uh to becomes more bold to be sold optimization techniques to to have Optimum solution for those so four occupancy git mapping if you want to talk about decomposition we can say Okay probability of the map given by observation and uh and robot poses can be written also as probability of each one of the grid cells given by the observation and poses by decomposition simply but we are showing in a formal way so instead of math now constructing whole map we want to consider constructing a talking about probability of each one of the grid cells that that looks like this we have each grid cell and probability of each one of them and uh um and binary estimation problem can can help us to solve this by bringing it to the probability and recursively we can update each one of these by base filter so that if you remember we were talking about base filter that were bringing us to the point that we could calculate the belief and that belief was in form of probability but now we want to bring each one of these grid cells as as if as in a form that we can solve this with phase filter in form of probability independently so each one of them also can be called binary random variable that I stated over there as we discussed that observation if you have the map like this then at the beginning we have initial uh probability that how much is likely occupied for example 50 percent we don't know if we don't know 50 50 0.5 after observation comes observation can tell us if we basically uh for for this chapter let's consider like uh lighter scanner only because because other sensors is a little bit difficult to uh imagine and talk about but anyway but there will be sensor that you are measuring the distance and then your sensor robot from here measures the distance the observation can say okay this is this cell is occupied or not occupied and give us uh give us zero and ones as observation model so as you can see I I stated some Mass forms here we can say this this for example one here indicates probability of this grid cell is occupied one generally whole map can be written as probability of Mi given by observation and series of robot poses then here again probability as 50 but now we also talk about the uh the point that I mentioned to you we can say for example this grid cell the probability of this grid cell Mi we can write it in this form P of m i is equal to zero or in a in another form of representation we can say probability of not m i is equal to 1. subtracted by probability of Mi that is equal to one but basically these are different presentation so these three former presentations or four points where we can we can show the uh yeah treat actually three form of representation um can be used in our calculations and maths but basically we will try to keep on the first floor so especially with base filters and applying base filter calculation on the grid cell we will need it so now we want to see how we can bring the base filter to the gate we have pre-order map then after pure map that we have we have measurement models measurement model we already seen how we can represent it but in simplest form we can write probability of observation given by n Annex so so far we know it now what we want to have now we want to have posterior map after period 1 that that gives us probability of each one of the grid cells that we want to take into the consideration consideration we have the of the observation so here measurement model says that observation given by map Annex here map given by observation and the poses so they are swapped so uh how we can achieve this uh and and at the same time how we can bring the base filter inside first of all we need to have a look at the base theorem again that with base theorem we said that we have probability of the a given by B is equal to this form of probability that uh the distribution of the B given by a times probability of a over probability of B so this is like the the simple and very famous base theorem that that we can uh we can apply on to bring this calculation to the posterior map how that can uh can be applied let's have a look so we have the posterior that we says okay if we want to get the probability of Mi given by observation and poses that one over there we can apply the base tail room on this measurement model then we have this big term so so uh by by by applying simply of course like the term looks looks a little bit big or complex but if you look at this term over here we just apply the base theorem on this form to calculate the probability of measurement model but the calculation of these in Mass has some difficulties and challenges that what we need to do we need to do apply the log old form of representation to calculate this term over here I'm not going to show details of the uh how this can like we can achieve it there are lots of calculations you can have a look if you want how we can apply this over there in the book but but let's see how we can um we can bring it to logout representation to be able to uh solve it so first of all what is the log out representation we say it is uh it is simplification of the calculation in math that that we use it in probability form so that uh so that we can say each probability value is converted to corresponding lot old values of the internal storage for that value then then we can efficiently update the probability value in fuse operation so first of all we need to convert it to logout forms then after doing the calculation of the probability then bring it back and we will see how we can do that just just all those efforts is from prior observation to come to the uh come to the construction of the map by applying the probability of cases also the point is that we have unstability of the numerical and stability sometimes in the probability form so that log out can help us to avoid that for example in cases that the probabilities are near to zero or so one more point that uh you can quickly integrate sensor data into the map based on using that form so how it looks like let's have a look we say first of all we can represent the order of x as probability of X over probability of not X so probability of one event is happening probability of one event is not happening so in other representation other form of representation as I mentioned we can show it like probability of X over one subtractive type probabilities it is the same meaning on the other on the other presentation we can say if it X happens if it X not happening so this is like Road this is called peace representation's old call odd ratio knowing that we have the old ratio now we can we want to bring that probability in form of the old ratio if you remember we had the probability of the Mi for each one of the grid cell observation and and exists so so that that that representation of probability now wants to come to the form of both how that is happening it is like looking like this then we can write probability of this happens or not happens so probability of Mi given by X and poses and not happening of these then it is looking like the form of or odd representation odd ratio of the uh each one of the grids on the other hand what we need to do now now we need to apply the same base theorem so if we apply the base theorem what we will have we will have for this part over here we will have this there and for this part over here we will have this step so we do the same job of the base theorem in previous slide but but for happening one time here and not happening one time here again I'm ignoring representation and proving how this is happening you just can uh like we just need to apply the uh uh base theorem on this term over here then we will achieve finally this calculation with simplification uh some lines of mass then for not happening this one over there after doing this so what happened we both applied the base theorem and we both also bring it to the old ratio for so now again after putting these terms over here and doing simplification what we can have we can have this term over here some Mass again I'm I'm not going to also show uh exactly how that's happening uh with with some it is like some Mass you need to write it and and simplify so the odd ratio of the probability of this grid cell is occupied over not occupied can be represented in this form that says the applied the base tournament now is it clear generally what is happening here so we apply two things rod hold ratio and seconds base theorem first in the in the in this part and second in this part then we calculate it then we simplify this clear I just didn't show the just the calculation of the how this is happening and simplification okay we can do that but I think not necessary now uh this is in form of old ratio what about log out now we need to bring it locked out as as a solution to solve it we just simply need to convert sums to the log oats what does it mean it means that so now log out can be written as log of the same equation here equal to adding by each one of these terms by log of course bring it into the uh a lot of form first of all not adding the log per each one of the probability forms but also we need to convert it to the sum of the logos over there so that generally we say it is learning of ratio of probability of happening over not happening to 10. but what we've done put each one of the grid cells instead of directly applying base filter in order to calculate probability we bring it to the large odd form with some math calculation to make it stable for calculate first second easier or or uh or not easier uh most most importantly less computationally and more stable solution for that in the Islam problem so now if you want to bring it to the form of algorithm you may say okay this looks like a big term how we can implement it in code and how we can bring it to the algorithm form first of all we can say let's have some definitions and simplification of writing we can say Okay logout form can be written as l x equal to logarithms probability of X is happening or not happening it means that this elix represent this term over here for me okay then based on that the the updating rule of the that big equation that I I achieved in form of logarithmic presentation of the each cell is occupied or not can be written with this form how I just like we just like replace this term here with the L of the X then we can write the L of the MI given by observation annexes is equal to the uh this term over here L of X instead of x i i put the term over here added by the so this L also represents the logarithm then then the same term over here so this one subtracted by the logarithm of MI so generally what I've done this term represented by simplification of the elix and written in this shorter form so as I stated in the uh in the many references for Islam this term first term is called inverse of the sensor model y Interceptor sensor model because this comes from observation and robot pose that that based on that we want to construct the math that we have So based on that we call it inverse modulus the probability in log out forms on the other hand second part is the previous observation or or posterior that is recursive term and comes from the if you uh if you have a look at the slides here here the posterior calculation that that we calculated in this part and this is the prayer and why prior so if we want to generally after applying base filter uh understanding what we are doing actually we have grid cell each one of the grid cells should update it by probability form that we say okay if we want to apply the base filter actually during the time that time is increasing each one comes in new probability so that is one imposterior one is prettier so the calculation of posterior per year should finally lead us to achieve the update of probability for that one informal base filter so that so that this becomes how we can do that now uh let's bring it more to closer to programming or an algorithmic form what we do uh so here if you look at this term I I have more more detailed explanation so here you can see that we can say uh the Ella of the logarithm of the Mi the each one of the delete cell is the probability of the occupancy represented by logout ratio that already we've seen logarithm of The Happening uh uh happening of the the map that that is occupied or not occupied also can be written in this form at the same form so that we can we can consider this L of M I can be represented or also as l0 because also it is referring to prayer of the map that we have so why we didn't keep that LMI so uh we could keep that too but but in the reference books usually uh they try to simplify to bring it to more more closely to the uh to the algorithmic form because of that instead of uh this term over here that represents the logarithm for happening or not happening we put s0 over there I try to keep it instantly with the uh resource book that we have now what we can do uh this term over here can be named as inverse of the sensor model a function that is doing this time over here by giving we send parameters the map poses and observation added by this term over here by by same definition can be written as LS of TI minus 1 and this term can be written as s0 so l0 is clear this is posterior then this is the inverse of the sensor model that gives us update of the each one of the grid cells that we have now [Music] um based on based on this representation now we can say finally we can uh we can bring everything back to the probability form because those are in lot art forms and if we want to do that we can write probability of the Mi given by observation x t equal is equal to this term over here that we have LT and I so this calculation here that is in log out form after all those mass that we first bring it from probability to make it stable stable to log out forms after doing all calculation and make it bring it to the form of even algorithmic form then we can return it by this term over here to the probability one subtracted by one over uh one added by exponential of the logite the logarithmic form of the TNI calculation so now let's have a look how it looks like we say algorithm of the occupancy grid map is is given by the this log out form of inputs of the ti minus model x t and observation observation robot pose and logarithmic probability of the previous one comes as input and for each one of the cells for each one of the cells if Mi is presented uh is is a perceptual field of the observation T if like in is it is in the observation field that they are like that robot sees that area then we can calculate the form that the the old calculations that we've done in log out so this is same term that we calculated in previous slide otherwise the previous one goes to new one whatever it was there as black art form goes the new one the minus t minus 1 comes to T1 otherwise uh in this test uh otherwise if if it's like the sensor is measuring this all these grid cells will be in this line and will be calculated by log out observation and update based on base system but but of course so what about everything is clear in except like inverse sensor model over here I think I have it in next slide yeah so how this inverse sensor model looks like it looks like this what does it mean it means that we want to from observation bring everything into the consideration and calculation and return the the uh the L of if it's occupied or not so we can say first of all [Music] um the the inputs are coming which one of the grid cell we are talking about the pose and observation and if we consider X and Y A Center of mass of m i what does it mean for Simplicity we can say each one of the grid cells we can calculate the the uh the center of mass of it then calculate the range that we already have done in Mass not like the the X and Y and calculate the bearing of which like this is the distance that I'm getting distance of the obstacle or object that I have then bearing the angle that I have range bearing calculations then calculating k that this K is uh is helping me to calculate these IFS that is ifs uh represent different things one is like uh let me see uh this is like whenever the cell is outside of the measurement range or behind the detected range this this if over here says just says like the range the range is greater than minimum of because this calculation that calculates the center of mass and the measurement that we have as it is after that and and if it is like that we return the the uh the l0 but but if it's on the otherwise if it's like not not that one like uh we can say if the uh the observation T and K is is among these values it means that it means that I'm calculating the like the calculating the each one of the grid cells minimum and maximum if it's after that I say okay use this thing if it's in middle I say okay return the occupied because because like the object is inside that grid cell otherwise then it means that it is closer to me and put it as free these three ifs represent that three conditions again I'm measuring that substacle there so everything after that is free first time then that that obstacle Itself by calculation of the grid size because that grid size is like over there under under that and that can be partially covered by the obstacle that whatever it is I'm calculating if it's inside that with this if over here if it's inside that grid cell maybe can be here and can be here if you consider it is grid cell so if it's inside that area I can say it is occupied otherwise all the grid cells that are in the bay to achieve that are free we have some parameters I stated for you that for example Alpha is the thickness of the obstacle beta is the lead of the sensor beam so bit of the sensor beam is like like from here is like very tiny but it can be like big scan so you can you can adjust the parameter of the scan size that you have because if you have video scan size and your grid cell is too small or let's say whatever it is the size of is this one is the your grid size is very small then this this measurement is gonna occupy many grid cells not only one what will work with one beam but not anymore we say calculation will be zero uh for for up to the obstacle but also a multiple of them will be occupied and uh and the LF occupied and free are amount of the evidence of the reading of the carrier that that they are uh they are occupied or not and this can come from the uh also the applying the sensor noise that we have also How likely How likely I can say uh the the my sensor observation model is like scanning accurately then you need to calculate it and bring it into the game so now let's have a look what is happening if we bring the if your robot is over here and there is obstacle and if you apply log out then your robot is here then obstacle is here then these grid cells will be free and not occupied and if we want to show it in probability form for example to understand so initially they are 0.5 then then for example here these ones I didn't write again they are they haven't changed but here these will become zero zero zero one so uh so after like highly certainty of the update but but that one what is happening that one is like calculation and updating uh online robot is moving in the environment measurement model comes with emails sensor model and we update all the time the probabilities over there with the base filter then these fees are becoming uh with increasing gradually so that I will show you soon an example but before that let's talk about the uh this this technique over here so we say okay let's let's say my scan if if considered the peso again here my scan if it's not straight to the to the lines parallel to the lines and if it's like in in angle then how can I say which one of the grid cells are covered by my beam by by bearing that I have so so for example you can see here that robot is there and this beam that is scanning up to so far this obstacle over here is crossing some of these grid cells how we can detect which one of these are covered with this pin so we have different techniques for do doing that one of them is present homes technique that present harms technique says okay you give the start and end of the line for me and the grid cells that you have then it returns you which one of the grid cells are crossed by this line a simple algorithm that gives you like you give Stark n then in Grid cells as which one of those cases are crossed by this line then you can know that okay these grid cells should be updated by invest mode love by applying this this this one for which one of the eyes this eye before already we had this poles already we have this observation but you may ask okay where does the icons this eye comes from here so you give the algorithm then say okay this this this should be updated this next time the next thing next uh ranges scan comes you should say this this this should should be updated clear so you can have a look at this I didn't show because it's like simple for loops and simple calculation of how how this can achieve but after doing that after calculation of the occupancy probability grid mapping so here we have a architectural blueprint of the environment and here we have our capacity grid mapping by applying the same implementation and calculation from book we can have a reference book that we have we can have this one that robot is moving and you can see that this darker darker points are more likely to be obstacle and wall these ones robot never seen and these ones are more whiter but we have some some gray more gray colors maybe it's not very visible here but but it's not like three colors there are there are more grayish or more lighter colors that they are representing just probability that for example they take black one is one the white one is zero and everything is scaling between zero and one in order to say How likely the obstacle is overtake so all those efforts were four five for what because we didn't have we have the error on the observation and the localization and when your robot is moving in the environment we wanted to update the occupancy of one grid cell so that we couldn't put simply zero one we brought it into the form of uh a base filter and we saw that in probability form we have a problem that that is not stable mathematically uh to bring it more stable we apply log odd form then the uh the adopted observation model inverse observation model done that with with visibly seeing that what's happening then we achieved this map over here so now we say if we don't have the robot pose then what happens if you don't have the robot pose of course after robot is moving in the environment then the map can end up something like this why because if if you don't have robot codes or your robot pulse has like some errors then even though we are using base based on the base filter and probability form of the updating How likely this cell is occupied or free but but but it is not accurate robot is moving rotating and one time constructing map like this second time constructing email second time like like then then that map looks like something very wrong and this is really problem in Islam and this is a big uh Big Challenge over there we will we will see how we can solve this in next week we have iterative Clauses point that there are different techniques and algorithms how we can mathematically understand these constructions and maps how we can match them together there are different techniques we will study together how that can work so I mean not only we can use these techniques in 3D and visual slam based on 3D Point Cloud but also after localization you say okay I did my best with localization I implement it I tried a lot implemented unscented Kalman filter or extended columns I learned the math I did everything as much as I can but it still and I I did a lot to understand all these mapping and I constructed them I finally but output is like this or my professor is going to be angry why the output is looking like this is not working so but after that is still if you have problem this is common we had more layer to also try to match these construction of the map together so so usually if you look at the commercial or big or recent algorithms of this lab is like thousands of codes and many different different layers in order to improve it it's not like you can say okay I just Implement EKF then it works accuracy 90 85 percent no after even doing that even doing this construction even not only considering uh we we did a strong job in in first layer of like considering control commands considering observation bring everything to probability bring everything to Improvement and and after all those efforts is still in second layer of mapping still we add another layer of base filter to still bring it in the probability to improve it but still you may end up here then you need to again add some more layers of algorithms to also match it and cons and and and understand how exactly the map is and make it more accurate is it is there any question is it clear okay so also we have like check uh a chicken egg problem already we stated you know right chicken is first or egg is first on the other hand uh leave talking about the observation models and with the observation models uh sometimes we also have multiple sensors you have laser scanner and you have camera or you have rgbt sensors so how you can melt these together so we call it a field of Sensor Fusion Sensor Fusion again is a big field of study is not like small at all and there are you can search about like Sensor Fusion algorithms in Google Scholar and you see like after 2022 how many papers just published for this topic so what does it mean it means that you have two different kinds of sensor how accurately understand this this changes over here to to increase the accuracy of the detection so this integration can come from not only visual information can come from imu2 for example how what is the field of your robot what is the tint of camera in order to uh in order to scan the environment so one example here you can see uh we have the camera image here that is stereo that comes from the stereo camera and here in the middle we have the sparse display map that this is part of this neighborhood is famous in computer vision and machine robot Vision that you can extract it by calculating the differences of two to image frames so you have two image frames from two independent cameras then then the sparse display disparity map you can search there are also I think libraries to do that so you can have achieved this one then based on this uh this image and this uh sparse disparity map how we can kindly do something for uh for example occupancy mapping localization but we don't have slider camera or something we can do or we can do like you can merge these together in order to save which one of the cells most likely is occupied so this is for example one so estimation of the wall over here this also is possible of course looks more complex looks more harder and it is so when you have a stereo camera and based on the history camera you can bring it into the form of occupancy grid map one of the technique is like well-known technique that you have camera image then you create a sparse disparity mask the disparity map then then construct this by merging them into the probability so do we have any important Point here I've written that project in disparacity image into 2D plane and convolving the result with caution over here so that I forgot to mention that this is also coming from applying gaussian on grid map that we can do that too so after this criticizing the environment not only we can apply the probability form we can have applied gaussian on the distribution that over here detective probability that is increasing over here can be can be affected by the other cells with today's scores we directly only talked about occupants occupied or not occupied as one cell we didn't say that okay if we can we can apply gaussian model over here that not only change the probability over here change the surrounding grid cells too so that that can be called as applying the gaussian on the occupancy unit map too we have many different techniques of course we try to focus on some of them important ones but but when you hear caution so just updating each one of grid cells but by gaussian probability that more likely the probability that is in Center highly will change these are like less Lee change [Applause] so now we have a question you can think a little bit we say what if multiple sensors detect different characteristics so you have a camera and you have a lighter or rgbt sensor or or whatever stereo camera they are detecting different character characteristics of the environment then what you do for we are talking about mapping and Sensor Fusion imagine you have robot you have two cameras and for example project no no different okay yeah managing to put both of them together you mean or or using one which which one is more likely you want to use or uh-huh more accurate merge them together based on probability yeah this can be one technique that came to your mind so there are different ways to do that of course uh uh one of the like two of the most important ones I'm gonna introduce here so one is replacing the function of the inverse model but what your friend mentioned so by replacing image model it means that whatever comes from observation and my inverse model calculates it I can merge it for example with extended Kalman filter in the probability form which one is more likely or update based on those of both of those so that's one second one the the challenge that we have is detanging different types of obstacles on different sensors that this makes what you said challenging for example uh so when you your different sensors sees totally different things then you don't have this matching to which one is more likely to to apply on it so that's difficulties that we have over there also like if you consider so we have two sensors over here right so partially conflicted objects so one of your sensors partially sees this one the other one like sees all of this but this sensor also sees another object obstacle and and you don't know like this is like covered by that or not so these are challenges that overlapped objects and partially see invisible objects are making challenge for us so what do you think we can do with those cases of course this depends on the error that we have uh and how maybe you for example you have two kinds of sensor sensor a as like 30 error sensor be a 20 error that this also makes uh inaccuracy over detection of this whole area and error over here then uh so one of the way is replacing investment second one is kind of constructing separate model for each sensor so you can say I have two maps one is coming from lighter that I have one is coming from our GPD sensor the Techno constructing totally separate Maps finally try to match them together after construction because after construction so you can see that okay your your lighter says uh the map that I have is looking like um maybe looks like this and the other one looks like something similar but different like this like maybe this so you have two maps based on the Arrow then try to merge them together and we will see later on how if you have a uh those um occupancy give it map output or mesh in 3D or 2D we can match them together how we can do it so any question is it clear here so now we want to talk a little bit about more interesting topic here based on the challenge that we've seen and the calculations that we've seen how we can bring learning techniques into the game we say if we can Generate random triple of the poses like the poses of xdk and K is the each one of the sensor type the measurements also will become with the observation and the map occupancy value with M case for each one of the grid cells now you can think what we can do with these guys so different sensors like three different sensors for example lighter camera and an rgbt for example then then for each one we have the X you have the observation and we have the authority map map that comes from previous one one is current and pose is current and the map that is also the grid cell that I have already now think a little bit about how you would bring learning algorithms into the game here as a problem so you can think okay these are input parameters for me kind of and based on input parameters simply I can say okay let's say these input parameters the poses that I have the observation that I have for each one of the things so I can feed it to the neural network or deep deep learning techniques then this guy over there can give me the output as math or ought to have pulls off the each one of the obstacle and pulls off the uh and the pose of the robot position of the obstacles and pulls off the robot if you can if you have a robot right and robot has two types of Central and if you let train and neural network based on thousands of times of trying so the error on the observations is static in the sensor model that you have right so it's not going to change like too much like your lighter as some predefined error your um uh your your camera of the detection the rgbd has some errors right based on those pre pre-owned almost error that is very hard for us to extract it if we just put like a camera at Ground roofs on the top and let the robot move in the environment too many times based on those observations and all the parameters as input then your neural network will be learned based on true ground through data then will be you can have probability of occupancy of each grid cell by that input is it clear this one do you see is there anybody who thinks that it won't work so if you like this can be your project too it is a little bit big I know but can be so it looks maybe complex but then you don't have all those calculations and masses you know you just give the give this input parameters and you want to throw out all those calculations that we've done in this class and put the observation and all inputs inside and finally construct the map Okay so uh I explained that we can have a function approximation that can give receive the input size parameters these inputs not only limited time like these poses still can come from Kalman filter extended Kalman filter to make it accurate observation can be pure but but how much accurately we can give it to neural network if it comes from the techniques that we've learned of course it will be able to do the job better here you can see the uh the output of one learning technique with neural network you can have a look at the book already have these have been done on this lamp Problem by the also reference book that we have so this is the the blueprint of the environment the robot moved in the environment and you can see the output of the environment but uh so here we have the uh uh the point is that of course for neural network you need to uh for calculation back propagation it means that you push forward the data and back propagate to update the weights afternoon Network you need to calculate the loss function loss function can be calculated by the differences of the map that you have and the blueprint directly here it should have been here so you need to have a reference point to say how accurately my prediction is and what this is the prediction as output and how I create it really is then you can calculate the loss function and error and based on that based on different techniques for example statistic ready and descent SGD update debate certain Network and it will be trained for you and of course its challenge is that training neural network in Real Environment is very hard takes lots of time and that's the reason that is uh is not that easy to bring it to the game so if you want to like really put the camera and train neural network in online environment it takes very very long that's the biggest problem uh uh so here now we have some questions that says okay can we learn the can we make the learning independent of the robot puzzle location so here we have the I said that the post comes as input right to the learning to neural network can we remove it do you think as input then do the same job now you should look at this problem as researcher and find an idea again I have neural network and I said that the pause and data and observation comes then I have the map as output the question is can I remove this post as input power the answer is yes how yeah very close attention to the course and uh yeah this is one of the Advanced Techniques and the recent also recently there are many studies on this topic that Google mentioned correctly we say okay let's of course if we have the poses for example it output of command filter or extended comma that's great then we can have our accuracy but let's talk about only if you have only observation as input then then you should understand this point very accurately then what we have you robot doesn't know where is this then of course you cannot have the output as a map anymore first of all then output is not complete map because we don't we do not network doesn't know where it is but what it can give you the the scanning surrounding obstacles and environment and learn that my sensors my scan says the abstract obstacle is here is it really there scans and says which one of them is it really there and actually learns the error model of the environment and then the output is local map instead of global map and says uh okay uh the locally wherever the robot is can more accurately give you the map of that that part only it means that so in first example we say robot is here robot moves in the environment and the pose of x T is given at the first first example then when you give the polls then if there are some obstacles anywhere then robot can give you the probability of each grid cell so I'm not going to make a grid and can can null Network can give it even for this point for each one of these right but when you remove the pose then you don't you're not network doesn't know where it is anymore only thing that you can get as output is only the range that robot can scan the map of that area only did you get it then we don't have the map just just the map is local anymore with removing that course but still they can have it because this this this constructed map can be learned and robot says okay I'm seeing that one I'm seeing that one I'm seeing that one how I created this when when it comes here again doesn't matter so it can save the probability of okay what is this one what is this area again moves a little bit more for example here then what is this area so you still can have it but we have one more step again how to match these together outputs of each one again should be if you remove it now you can as a researcher think okay but we can fit more data based on problem that we know if you have if you want to solve Loop closing problem we can instead of neural network put deep learning here we can filter apply some filters hierarchy here for example let's say I put unscented Kalman filter a year in observation model I put another filter here to make it more accurate I make it as deep learning one specific characteristic with convolutional layers then the output what should be like let's say I want to not only the map I want to for example detect the velocity of the robot 2. then I can train my model to detect the velocity of robot 2. and whatever the problem that I want so then I become researcher then I become the who can place in this problem then propose a solution to that problem you are working industry in real robotic problem then you say okay I I know no I I exactly know what's this land problem I know the parameters I know different I know I know no different tools then let's see how I can put them to finally achieve what I want for example I can let's say how we can merge IMU over here in one of the latest research on Islam we will discuss it one of the input elements is IMU that goes uh goes for our measurement model and gives the gives us more opportunity to calculate it so what if I give IMU here what does it mean it means that I have one more element to Velocity model that I can say how fast my robot moves in the environment then I can construct map more accurate right if I can train my non-network then you see you can based on the tools that you can have you can choose what should be input what should be output and middle log I need to do any question this one here here at the first stage let's say robot has these poses as input okay so one input says where the robot is exactly if we know where the robot is it means that robot then moved in the environment can update all grid cells don't consider these circles so it means that since I know where it is that the robot is I can say that this obstacle is over here right because I know the coordinate here clear I know the coordinate I can say the obstacle is over here based on this coordinate my neural network output says the out the coordinate the coordinate of this obstacle the coordinate of the other obstacle when I have the robot pose when I don't have it then I have no idea I don't have no idea where it is and I cannot see you know little cannot say where the coordinate of exact position of this robot is this is relative the code the coordinate will be relative to robot pulse dynamically that you can consider already zero zero if you remove the post if it's zero zero just says distance and angle is the range and bearing range and bearing always then then those range and bearing that is without X is as output then you should match them together because you have bunch of them I said you still didn't understand so if I know coordinates I know my position my neural network can say exactly where the objects of class are right but if I don't know I just can't say the distance of this with me I cannot say where they are in the class correct I move I don't know where they are I just think they say this is like one meter far from me that's it then you need to you need to again merge them together to say where they will and they how they are related to each other this is artificial Network example by lighter scanner from the book that you have it's applied for uh it's applied on the invest measurement model that you can see that they what they've done there is a lighter scanner this is the robot and these are the beams that has been presented and you can see the constructing of the this one look like that one and this one look like that one here there's the model uh haven't trained well no no no uh this one is like the the noisy environment you can see that uh the the teams scanning like this and noisy but here the robot is in the corridor and based on the measurement that details output gives the output of each one a probability for each one of the Mis How likely there is obstacle or it is sorry so why this is thick because because the arrow is too big here sometimes it stands like this that then then it become thick wall over here otherwise it should have been narrow that shows the amount of error of training or network for the measurement model based on the laser scan so is it clear question so what we studied today we studied the map in measurement models first then we talked about the occupancy grid mapping how we can formalize it bring into logout forms to in order to recalculate our probability and then bring it in the form of the uh algorithmic form then we talked about the Sensor Fusion Concepts general concepts of course this has like one semester of course if we want to go into details but general concepts are important and finally we talked the budget about general idea of how we can bring and engage learning techniques into our only mapping part but of course that that can be engaged into different parts of the slant too we just only talked about how we can use it for occupancy grip mapping so any question from today's course |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH1_SLAM_for_Robotics_Introduction_to_Mapping_2023_class.txt | okay hello everybody back uh today we are going to continue the uh the general introduction to the slab quickly I will discuss what we've seen last week then we target more in uh today we are going to talk about the important challenge that healing during whole semester we're gonna solve first we discussed what are the real challenge in the uh Islam algorithm so uh we discussed that the topics that we have are introduction then uh we will talk about the localization and mapping then we dive into the different algorithms we start from base filter we talk about Kalman filter extended Kalman filter unscented Coleman filter particle filter and continue with occupancy grid mapping the graph based approaches ICP creative closest map that we use it for 3D construction of the map in the environment hierarchical approaches audimetry based approaches and we will move towards the optimization and more algorithms like orbislam that is one of the famous and most the most strong algorithm that we have in hmm Islam Islam area simultaneous localization and mapping so we introduced three books but also I forgot to mention there is one useful book that later I will introduce and talk about it in detail when you're gonna implement decode the examples whatever I'm talking in the slide the equations the algorithms that I'm explaining mostly are implemented already here it is pretty decent uh step-by-step book that that um for example we will study the Kalman filter then after you understand what's happening there you will move to the book and same example very similar example already implemented there you try to re-implement it first plus uh there is python code plus then later I will give you some assignment that you need to work on it so as I mentioned last week you need to know programming topics you need to know the you need to have some massive skills and know the basics of the mobile robotics in this chapter we are talking about the basic introduction we talked about the what's the robot what's the mapping what's the mobile robot what's the fixed robot we talked about different uh famous robots and uh General introduction of spot and stretch and simple robot that we said doesn't matter which kind of robot we have if it's just mobile then we need Islam algorithm to solve the problem different kinds of robots that we have and we can apply Islam algorithm like flight uh walking robot swimming robots running robot whatever the robot that is mobile and in the environment we talk that we can have two types of environments indoor outdoor because of that challenge because of the scenario the challenge can be different of course we would like to have general purpose robot that can work in either environments but usually for now they are splitted into two in different Challenge and competitions so um different kinds of sensors we will dive in in some types of sensors we will also try to formulate it in Mass form in order to be able to use it in our algorithms but we have vision and and we have some sensors tactile sensors for sensors and distance sensor that I last week generally described it we had a look at General structure of a robot whatever the robot is we said that we follow the essential electronic mechanic and controller that you basically already knew in advance we saw the hierarchical level of the how robotic system is working in a driver layer platform layer algorithm layer then UI layer that these are all connected together to uh to launch a robot that robot performs in the environment but why we discussed this because we wanted to see where the Islam is the Islam is located in this part here and we are going to dive team one of the algorithm layers in robotic system so then we answer the questions where am I robot asks himself or itself velamar that the answer is robot localization so imagine here robot is somewhere if asks where am I he said the the answer is the algorithms in area of robot localization then where am I going the goal determination and again localization and how should I go there the answer the answering this question was motion planning so all these and the answers moves toward too show the importance of the Islam that we discuss and we said for understanding Islam there are multiple topics that better to know and we need to know actually uh one is current state estimation that we have the state space we discussed and based on the state space uh robot tries to guess where it is so current state estimation we talked about localization the same and we said there are two types that today we are going to clarify them then we have the mapping uh mapping means that when robot is moving in the environment we want to construct the map and today we will see what kind of maps we can have and and what are the applications are we how we can use them based on those relevant topics we said we have the Islam that Islam uh is trying to do both together uh simultaneously localization and mapping meanwhile we have some topics that also we discussed like navigation and motion planning there are relevant similar topics that we need to know and we need to be able to distinguish when studying and reading different papers and understanding them uh navigation and motion planning we discussed that our robot is trying to do but generally as we said Islam is most importantly focusing on localization and mapping and finally we have the Islam you can see the robot there that moving in the corridor and localizing different uh landmarks or different objects where they are based on that robot can say okay where am I answered where am I and I'm constructing a map of the environment so uh we discussed quick what is the background and we saw the uh the evolution of the robot control why because it was very important for us because we are going to use the probabilistic robotics at the last stage that is the most advanced stage that currently we are and we will see what it is we try to actually involve course we try to formalize it we try to First bring it into Mass form then try to engage some algorithm to solve it then uh the the definition of in the definition of problem we say we need to clarify the objective of the mapping and localization why because the objective can be important if we have a robot that is moving into detail environment on the surface on the floor and we need to construct 2D map of the environment that's different from the flying robot that is flying outside so and and landmark can be different too so a humanoid robot a mobile robot inside uh like when it's on the floor and walking and moving uh the kind of map that we can have and the kind of localization that we have is different from the robot that is flying because uh you don't like the object from these features perspective that you see can be totally different from Uptown view so the the goal should be determined based on the what we want to do then apply the localization or if you are going to basically in this course we are focusing on robots not the unmanned vehicles and there can be some small differences some different challenge too because in in unmanned Vehicles you have pedestrians that working and those are very crucial to take care of four nine robotic systems we have slow robots basically I mean they are not go as fast as the car and some kind of challenge are a little bit different General thing is the same but we need to determine the goal and specify all our limitations same as solving any problem we need we have some in our environmental limitations and we have some uh robot limitations that based on those we need to take it in consideration what does it mean it means that like what is the robot limitation so imagine you have access to different kinds of robots and based on the robot that you have you have different capabilities different sensors different architectures based on those you need to solve the problem of Slam so that can make a lot of differences in the algorithm that you are gonna sold and work with it and today we will see how in order to present these points uh we should have a look of course at the taxonomy of the solutions taxonomy means like kind of classification of the solutions in the world what kind of algorithms we have if you just search on the internet the research studies there are different types and they are totally different with each other so we should we should have a look at those and of course the most important part is to know the challenge if you don't know the challenge solving the problem doesn't mean too much we need to know uh what we are facing with what kind of problems we need to deal with in underlying level of the developing algorithms for Islam so now uh I wanna introduce two major classes of the algorithms for Islam one is visual second is odometry we have implicitly third one that is combination of these two and we will try also cover all of them what is the visual visual says okay use the landmarks and different objects try to localize or construct the map of the environment by so what kind of sensors do you have for that of course the obvious one is camera second fund can be lighter scanner and any visual information that can be gathered from environment can lead us to have visual localization for example here we have a robot that moves in the environment and Gathers different features from environment and finds out and localize itself on the other hand we have the odometry what is the odometry odometry is using the uh amount of movement in the environment by the kinematic model of robot what does it mean it means that okay if I'm human or robot let's say I don't have any camera if I close my eye then if I move one step to the right second step to the right I almost know where am I right if I knew where where I started after some movements I can guess where am I so doesn't matter which kind of robot we have automatically says use The Locomotion use the movement estimation in order to say where the robot is so sometimes this is very difficult to achieve sometimes not that hard we will try to formalize everything what does it mean why it can be difficult like this is this is top down you have a robot that it has two vehicles so we can have the Contour on each vehicle then we can count how much robot is moved in the environment and some is with some Mass we can calculate where the uh how much robot moved in the mind how much rotated how much how much uh translated in the environment so but what about the humanoid robot for example as one of the complex robots that we have so calculating the step size is a little bit more challenging then because if you have only directional lock it means that robot can walk freely in the environment to any direction and meanwhile also rotate so I'm doing this all motions but I need to have an accurate calculation of the what is happening in order to say from there to hear what was the distance that I moved and you have too many joints that is affecting these movements in the environment so I will also clarify what's happening how we can also calculate that one to achieve it in simple or complex robots but what about the Drone then we cannot count the steps there how we can use automatically for flying robots Jesse GPS so if GPS is accurate GPS is one parameter we can use but basically we never use in Islam because well let's say it's indoor built and can be can be but not really because you say okay we tilted the robot like this direction but you don't know how far it goes because it depends on the The Immortals speed too if you are your robot is like this it can go 100 it can go 10. any guess Ingram any guess we will see velocity based modeling we can calculate the velocity of the robot based on different sensors and based on the velocity we can estimate the movement of robot and that's also one of the elements of the most advanced algorithms for Islam for example you have IMU everybody knows that's IMU is there anybody you don't know you know what stadium you who knows what I am you raise your hand who knows what's the IMU Ingram you don't know what cyan you oh okay so we have IMU sensor in robots that is very common to use what does it mean it means that so you can if I want to explain in simplest form you have IMU that is like kind of essential uh let me say this is the so consider this is the IMU sensor okay so you can understand amount of the angle of the uh sensors based on degree we can read it in x y and even rotation Z this is three-dimensional IMU that is very common to be used in different kinds of robots and plus those three that we have this x y z we can have amount of the velocity of movement per x y z so 3 4 angle 3 for velocity for now so far six we have nine degree of freedom I am used to that gives you more information more parameters but for now just consider the six so whenever I'm talking about IMU we mean that so that in in many of the robots we have it and and then robot is moving in the environment and if you have IMU that can be made with like IMU can be a third element that can be merged with audimetry and visual and all three of these can help us to localize and map the environment so nobody uh we will break it down one by one how how the metric can be worked out this can be work and how the model of the Velocity motion model can be presented in Mass form then later we can match them all together any question so far no so I'm explaining some Elementary topics sometimes the time in my view you already know it if you don't know please ask it feel free to ask because if you don't ask now after two three lessons you don't understand anything more all the time I'm going to refer back to those and the the things that we are going to use if I wanna every time explain it takes very long because of that please feel free to ask any think that you don't know what it is so let's have a look at visual what is happening and what are the general difficulties and challenges let's say we have a robot this cute robot over there Darwin op so this robot is working in the environment and we want to say okay let's use visual information to localize Lady robotics for now we are talking about localizing not mapping because we need to split them so robot is moving how robot can localize as I mentioned last week you need to find some landmarks robot needs to see some some features from environment to estimate where it is right so these landmarks for now as assumptions say robot knows how to detect tree robot knows how to detect building everything that we robot series we assume that robot can detect for now okay now uh of course if robot is here can see these two objects can do some Mass calculation so that what is the angle of my body with my neck where I'm looking to the right left and based on that angle differences where the object is then where am I can estimate the distance almost and can estimate the angle of the robot okay so based on these two can say this is almost north of me this is the left side right side and we usually call them the different landmarks with l l one l two L three and each one for each one of them some thetas that shows what what's the angle but time moves and the robot tries to move to other location and after robot moves to the new location of course again sees maybe new landmarks may be the same ones depending on this distance that robot moves and we will now talk about this is huge challenge why because robots these two landmarks here moves there sees exactly similar landmarks and are they previous ones or new ones and you will see that we have lots of challenge like this today we will discuss them we need to understand them well then try to find Solutions so time goes and robot moves again and this time robot sees this landmark and something new and still we don't know that this was this one or this is another new person that we will clarify but whole scenario is like this robot moves see some visual information try to localize move see some visual information try to look alike and it is inside the loop again new location so but what is the problem here main challenge that we have we know that sensors have errors you don't have any 100 accurate sensor if we have it in visual especially the Islam problem already almost solved most of the part but sensors have error not only sensor because of the environmental condition you may have errors robot is walking if it's humanoid and his head is shaking and that changed everything all the parameters all the distance estimation everything is changing because of that we have arrow and this error is called estimation error and this is very important all the efforts that we are going to do in this class actually most of the efforts that we are trying to do are trying to detect it and reduce it in our estimations the question so when we have the robot that uses visual features in the environment to to localize 10 motions motion execution accuracy important for us do you think depending on the algorithm that we are using yes it can for example for now let's say I I explain the odometry we are going to see it soon but in visual my algorithm says okay that laptop over there is two meters far from me so I want to go one meter forward with visual information with visual automatically with visual uh localization I say I'm gonna go one meter but my motions are running wrongly instead of one meter I end up one meter 10 centimeters then that 10 centimeter is the error that I have that can affect the expectation of the visual uh estimation of the varaya so let's say again two meters my let's assume that the the distance is quite 100 accurate visual exactly can detect it but after some movements if my movements have errors then my estimation throws something wrong it is expecting like the laptop somewhere else and we don't know now now that that also makes confusion we don't know the error was from sensor division or sensor a robust from the motion execution doesn't matter about the odometry so when when your robot is moving can can ruin everything if you have error for visual uh localization any question is it clear okay so let's have a look at visual uh demonstration of the problem also we have the robot here this is the robot and this is the uh where robot is heading toward like here then uh really robot like rotates and moves here and from there rotates and moves here and moves there like uh the this is the real movement of problem but the estimation can show somewhere else based on the visual information that comes why because if we assume our sensor very are very accurate for detecting visual information 100 that is impossible but uh our visual information says that robot must be here but we have error on motion command running and robot is over there and this continues and we have all the time error of the uh localization even for visual so for visual localization we can use different kinds of sensors for example we can use single camera webcam that already you all know we have wide angle cameras fish eyes and spherical cameras different kinds of cameras that we can use we can have compound eye cameras or a stereo or multi-cameras a stereo means that um we can put two camera together but final vision is just one picture that what's the benefit the benefit is not the angular field the benefit is that you can extract the depth of the objects too there are some techniques that you can study on the internet how they are working for a stereo camera they put two cameras and based on the this distance of the two lenses through each pixel that you can see you can find also the calculate the distance of the each pixel and estimate it and now we have industrialized stereo cameras that you can buy them and they give you a distribution of the um depths of each pixel too but multi-camera you can put multi cameras and and use them as visual information as input for your problem on the other hand we have rgbd cameras that rgbd is same RGB similar to simple webcam but it has depth sensor to inside that with one single camera and some techniques depending on the kind of kind of camera that we can have also that can give you the depth per each pixel you know for each camera for each picture we have each each pixel that each pixel contains uh three colors RGB but D is related to depths and one more information of the environment that we can have and also we can have lighter as a light detection and ranging that is usually used for measuring the distance of the email so there is no color basically and you can scan the environment and get the distance of the each like if you have Ray Trace like this can one line of the environment then we have different types of lighter that can scan one one line like this depending on the angle of the uh sensor that you can have at each moment I have one slight danger I will show it's in internally structure and how it's working and how there is like uh there is a motor inside that rotates the the laser point you can you can consider like uh lighter scanner exactly similar to laser point but it it moves quickly all the time moves quickly and each time measures the distance based on this uh this red point that it is there so now if you wanna scan like environments like this distances it moves like this and if you want to scan holding 3D so we have two options if you have sensor that it is like just one linear one then we need to do it manually each time like from here to this and then next time go after do this go up or do this go up or do this and with the resolution that we move that move that line we can scan whole environment so this is one kind and they also they have 3D one that automatically does this and it stands for the environment so why we are talking about details of these because we're gonna formulate this in Mass we want to use it in uh in our algorithms in order to finally say ready robot piece you will see we have mesh of those points so let's say you you your robot scans the environment in 3D then you have mesh off those points then we want to say okay where the robot is in all the Matrix of distances we want to say very robot is so that's very interesting and that's really nice in industry and nowadays everywhere people trying to use it in high level robotic developments for visual localization we have some also topics that we need to know for example Sensor Fusion who knows what is it Sensor Fusion says okay let's say my robot have not only one type of these sensors my robot has like two of these or three of these then for example I have lighter and I have single camera how can I connect these together how can I say okay my robot vision sees sees Tony this is student over there my webcam sees him and and my lighter scanner also gives some distance from there how can I make these two combine these two information together that's called Sensor Fusion very interesting topic research study in the world also just Google Sensor Fusion go to go to the Google Scholar search Sensor Fusion you will see many algorithms over there that uh that's how we can do that how we can manage those information together so in addition to in some techniques if you study you will see that in addition to visual sensors we also can manage it with inertial measurement unit or IMU so that it can give you uh more precise vision of the environment what does it mean it means that let's say I have webcam and this webcam looks at the environment and I can move it and if I have IMU here this can give me a lot of information right based on where it is looking and the velocity of movement and if I can merge IMU information that I told you it can give you the angle of the rotation and velocity with this camera how important it can be for especially Islam algorithms because then you don't have single camera that looks around you have IMU that can give you a lot of information what is happening in the environment how we can match these together we will also discuss IMU combination with in form of Sensor Fusion or Etc the same sensor IMU can be very lighter can be rgbd or any kind of visual sensor that we can have it can be matched okay now for few moment let's forget about the visual we want to talk about now odometry second part of uh information that we can use for our robot localization first of all we need to consider the estimation error of the other battery I already explained you what is the odometry I'm working in the environment and if I can measure how much I walked I can estimate where I am this is very clear what is the problem the problem is the estimation error and this estimation error comes from there comes from uncertainty comes from easily page come from come from motion execution accuracy come from my sensor reading accuracy all these together can give me can cause errors of the of the movement so so that we see the same example here that our estimation is different but here is based on the audiometry so in previous one we were talking about the movement but here reading of the information not just specifically just motion execution that we were talking about last example here the combination of all those can cause error that the most important part is the accumulating error that finally can happen because every time the error is happening it is accumulating as it is growing and if you continue this you see that robot is here maybe the estimation is over there any question is everything clear so far so we split it Visual and visibility automatically and we understood the basics of what is happening there in addition to those uh we can have some artistic Islam that it is also open problem and very nice example of uh localization we have some kind of sensors like see the studio uh boards that they have multiple microphones in around it and it can measure uh if the sun is coming what is the direction of the Sun and if you can use this sensor inside your robot then similar to you and you can detect where the source of the sound if some of you are talking I can if I close my eye still I can say where that person is right and and this information can be used by robot in order to localize where the landmarks are is similar to you can imagine a blind person moving in the environment and here's everything and knows where the car is coming what is happening around now ah this is like open problem again open problem is a problem that is in the world is still Challenge and everybody trying to solve it we don't have algorithms that can manage this with other Islam algorithms well yet have you heard that this robot can also localize by hearing not really this is very Advanced that you can research on this topic also in future so we call it as microphone array that and the technique is Artistic Islam for example uh Fusion of the landmark then can give robot more ability that audio features for example if if robot is localizing based on the camera or lighter scanner or whatever it has limited field of view that sees just from like human but if a car comes from backside then robot has no idea mostly but human does then we can give that capability to robot by adding that sensor using Sensor Fusion and how it can happen we will try to open it later of course we have to go to mass or to go to algorithms in details how it can be come to our our system and how we can manage it to be let me see what points we have here more robust map of the environment useful for ah one important point also that we can have you can detect hidden objects so there is some some object behind the other object human can hear the sound and detect it but robots so far can so like like if something is on the table some cat is there moving I can hear and localize where it is but can robot do this not any robot can do this we can also uh try to use those information but of course if still we have problem of the accuracy of Those sensors Those sensors still are not very accurate for now we can have the angle where the sound source is coming but not very accurate and of course if you are familiar with Advanced algorithms deep learning algorithms later on that can be used as estimation of the Verdi source of the sound is so we said we have the localization that needs the map and we have the map that needs the location and this battery connect problem they need each other and both of these so that's the one challenge that we have they need each other in our course localization and method and when they need each other meanwhile also we have the error of this Dimension either in mapping either in localizing so this both of these error we will clarify later also what what's the mapping and the problem that we can have there because simply you can understand if I want to explain quickly like you have a map inside your robot like I mean the brain of the robot or the memory afterward you have the map and that map is not accurate after a while you have another map of environment and that has that is not accurate too so these two inaccurate maps how should we match together so that's the the error of estimation inside our uh the the map of the robot that knows from environment and besides all of these there is the more challenging part is dynamicity of the environment so now let's add not only the robot is moving the objects landmarks in the environment are moving to so that creates more challenging part here of course we will simplify and we also assume that we don't have dynamicity at the first but later on we will see how we can add it plus though sometimes we have safety problem that um that that is crucial in some applications for example call application or robot is moving in the home let's say you build a robot that works in the home environment and there is a kit there then they should not fight each other right if robot wanna kicked the kid then the mom comes and kicks the robot and as engineer you are Developer you will be punished because of that now you need to know that okay I'm trying a lot to develop Islam algorithm developing complex algorithms it works very fine but I didn't consider safety and my robot is doing something that kid is like big human is different from kids like he tries to push the buttons play with the robot jump down throw something then you need to consider it in your techniques and that's good uh we have general definition of Islam that we say okay the environment if the environment is unknown and we want to localize and we want to construct a map we need that's the solution so what are the applications already you know we have home robots like service robots we have sweeper robot that needs to sweep the environment like this robot is sweeper we have a entertainment robot that they try to play with other people of course they need if you have a robot that try to try to play with different people if robot is on the table you can have some sensors to okay don't fall down but it's better to have local in the map of the environment if you want to do interesting things smart things better to be able to localize where it is and construct a map then robot can memorize there while the charger can charge itself this is very nice application for example or then like there is a pen and you want to ask robot go bring me pen if robot is able to construct a map of environment then can know where the pen is this is next level of robotic applications if you wanna move to the next don't don't stay on stupid robots just if else is some distances if this is the stop or it's like like very simple robot that we have uh we need to move toward that direction I I mean from Simplicity even it can be human or robot but but if your algorithms techniques are in level that are not upgradable to Advanced topics then we need to understand and move to that direction teaching robot let's say You're Gonna replace me with another teaching robot here so better to know the location and where the robot is otherwise the robot moves is there it stands here and just starts one two three hours then it moves back or maybe a little bit of movement with some sensors if you wanna have really uh robot that can interact in the environment pretty well even is it teaching it can be used Islam uh in mining application and and so on we have many different so in indoor we talked out tour it can be unmanned aerial vehicle for different applications you can see different applications here surveillance rescue air vehicles so each one of these if you search on the internet there are different challenged and different algorithms try to solve surveillance try to solve this rescue now think about it like a disaster happens robot is going to try to help people if really it wants to happen robot needs to be able to localize and map the environment first because everything is changed earthquake came robot you have very Advanced robot and and you wanna use that robot to help people how you can do that for rescue application of course you need to be able to implement very nice slam algorithm first then say okay this is the guy that I need to help to rescue that guy needs medicine that guy needs ambulance so also uh we have space robots you can see the robonaut 5 here this is from NASA and a couple of years ago there was big announcement competition I think one two million dollars for the competition that everybody could join like you could have make a team to join that the challenge was like uh there was a simulator for nobody robot robonaut 5 that you needed to program it in order to do some missions in the space then then team was competing against each other and the winner uh had the chance to go on program directly the robot and work in NASA to test the algorithms and if it was successful they were going to use it in space applications so while we are talking about this because we have same Islam problem there too right the the environment is unknown robot needs to localize where the things are and and map the environment and then you start to do something so this show is also important and how important it is in future of course we can have different kinds of robot and most importantly that is like now uh is applicable and we are locally able to use and try is self-driving cars that Tesla and Elon Musk are doing uh a nice shop there but you still they have lots of challenge that haven't solved yet and it can be improved so in outdoor applications why not GPS because in outdoor not indoor why not because still we have error on GPS so the GPS is not accurately accurate you have meters of error but you may say okay we have very accurate GPS too but yeah they are military and they are very expensive if you want to use them because of that uh basically we are not relying on GPS and also it can it can have disconnecting problem then if your robot is disconnected what happens nothing it stays there and dies should not be so we need to have techniques to solve it uh we have note that meanwhile we are doing and solving this problem also robot needs to have robust navigation and positioning system that can can as I mentioned already of course we have the the problem of mapping and the Islam and localizing together but also robot needs to move in the environment in order to do something and construct the map and localize and that moving how you want to say to move think about it how you want to say to move at the big First beginning so you know you need to also have nice navigation technique over there that I will introduce some you will see in 3d and I will introduce some tidy algorithms that how let's say Okay I I am a robot and my localization is very nice one of Islam course students developed it and that worked perfect okay for localization and Mark and my mapping is worked very well too the other student from this class developed it and it works 100 percent but now okay how to uh how to construct a map of environment now just seeing like this is enough seeing like this is enough of course it is not maybe I'm here I want to construct all the map of the environment so I need algorithms strong algorithm to save up to do at each condition and each at each state so you can see simple examples here that like you can if you have very cheap small robot with two vehicles very very small one that it has one single camera very cheap camera you can construct the environment like this build environment sample like this wherever you are then put some tapes over here color tapes then try to use like opencv libraries to detect those lines then try to construct the map of Timber this is the the simplest example that you can do it yourself whatever robot that you have that is moving in the environment put a camera put some tapes and use libraries or develop the code to detect some lines then you start to construct them this is uh uh kind of uh very simple example of localization and mapping here we have a video of how it works with drone robots let me play it it is a little bit more complex if 3D environment you can see that drone is over there flying in uh into the dimensional in 3D dimensional and it has the lighter scanner and its discuss the environment you can see the the camera here and the camera from robot the other camera and the the uh uh Islam technique that they apply to construct the map of the environment and these green ones are the uh are the lighter scanning like this as I told you one line of the scangers so robot goes out and again stops over there if I run a little bit clarify you whatever I explained to you so far all are used here almost but of course we're trying to in this course during whole course go dive in deep and see what's happening there and as much as we can try to even understand what's happening there are many things that are happening here and if you look at the code it's like big code but anyway like here we will later see for example talk about the occupancy unit mapping techniques what does it mean you will see that okay we can greet uh make grid of environment and if he has our sensor can just measure the distance like this like this point we can construct a wall over there and we can assume okay so when you detect something over here of course it is connected to somewhere and we can say okay this cell is occupied with that one and construct 3D environments like this and simplify the problem I just want to give you intuition after what's happening in simplest form but of course we will see also much more advanced algorithms like ICP that we said and that's that's trying to merge 3D construction of the environment and make it together we will talk about any question here can we have other applications more complex applications or interesting applications all kind of let me say new ideas let's say okay if you have a robot like this that is uh uh that is trying to construct building or construct a pass for himself or whatever it is of course we can still use Islam algorithm slang techniques in such a problems too because these robot may need to in the environment like this robot cannot walk on the floor for example just needs to go with this one and and of course if the Islam can scan the environment and if the environment is challenging find the passage and use those items in order to move in the environment and the Islam can be applicable so based on this idea you can think a lot you can use your imagination to imagine very interesting applications for this for example if we had a robot that cannot swim but has some objects go on on the on the water for example or micro robots in human body or you can imagine many applications that also robot uses and other objects but Islam is also applicable there and if real-time complex tasks can be used okay let's talk about the more challenging parts of the Islam now uh I gave you a little bit of introduction what is happening but let's see in more details we have the robot this robot sees Landmark one two then robot moved in the environment and sees this one first question that I explain is okay is it L2 or not from this different perspective series and maybe looks like a little bit different not exactly the same is it same Landmark or not who knows how we can solve this if it's QR code yeah that's very simple if you can Mark yeah that's okay but let's say we wanna have real application right and robot is moving here then you cannot put mark on everything that my robot must look alike and what if I'm I'm walking there too you want to put mark on me any idea okay yeah that's a solute that's a solution that can be but the answer is like in order to be able to do this we have different courses we have computer vision we have neural network we have deep learning algorithms we have matching Vision all these different courses all these different algorithms based on the what kind of problem that we can have are applicable on this problem and is still this problem haven't solved completely yet we have algorithms like 90 accurate 80 accurate 99.95 percent accurate but it is not solved completely free we will see we will see in this course okay if you have this problem how we can guess it not just only based on visual information now you should like spark in your mind okay so how we can do that now if I'm my robot is here and move like one kilometer or move 10 centimeters Landmark like fly if I move a little bit or if I move a lot that can be changed so you can think that okay I can kind of Imagine robot kind of can imagine where it is can kind of estimate where it is and we will use it a lot so to help the vision part to help visual part what about other problem that we have robot was here moves here this time instead of this L2 sees this one L1 is this L1 the same one that we've seen all this is l23 because trees are all similar is it same as this one or this is new one a question that in Islam we will try to answer then we have okay uh two items that we need to say uh future estimations can collect our estimation or can make our estimation worse what does it mean robot was here moves here this one here shows the error we call it we will you will see we call it caution error caution estimation error effect robot is this is kind of a circle that we say Okay robot if we move from here to there robot can be somewhere around this circle based on amount of error that we have if our robot has lots of error based on the all the items that I counted you can be very big circle if we have a lot of errors but if it's a small error it can be estimation error like this and even if like you don't know where the robot is like everything is like 100 error what happens then we have a big circle around all this robot maybe we wanted to go there robot is end up here so that Circle that is gaussian error we will formalize it we try to formalize and solve it uh this is robot error it's the location error and also we have the error of estimation of the Verdi landmarks are that again we control them in gaussian model so this circle like imagine that the big circle the big circle is showing okay my my vision robot Vision can detect the object over there for example then but we have error we can we can say okay it's somewhere around there inside the circle based on error that I have I know I know my my camera has 20 centimeters error and I can put a circle that says it should be somewhere around that this is that one and we say okay if robot in next move goes there and can estimate this more accurately the circle can be shrinked smaller and based on this smaller one we can we can correct all our estimations or if it gets worse it can ruin everything so based on the these change during time this can change our localization and Market you may think oh what does it mean during time it can change any idea we will see no worries of course that's also important we will see that yeah or robot with moving during time my estimation these circles can be changed and our objective one of objective is try to make it smaller either for the objects that we detect and for the robots that we detect we have static error for sensor but we want to try to estimate to make it smaller one of the uh other very important challenge that we have is Loop closure problem Loop closure problem is very famous in the world and in Islam is playing critical rule what does it mean it means that robot is moving and seeing some landmarks and moving again seeing some landmark if if this Landmark is the same landlord that robot already seen we must detect it in order to save I was starting from here as robot moved in the class moved moved moved moved came back somewhere around here and the same Landmark that I'm seeing is very important and it is called Loop closure problem because I can close my Loop and based on this estimation that at the beginning I've seen that and after a while of coming unseen again I can collect all my estimations all the circles that I showed all the gaussian errors that I showed I can correct all of those estimations during time is like this we will see uh of course many examples I think I don't have it there okay like so robot sees this object and moves but but my estimation this is the real pass but my estimation the algorithm that we have can be like estimate like a little bit of error at the beginning of the motion Vision or whatever it is then then rotating then like this maybe then maybe like this this is very common problem in algorithm that we will develop even the advanced one but this is very important as Loop closure because if you know that this is this one then you can know what to do almost VVC with mass how we can do that how we can solve this how we can if we see this over here that was there how we can deal with it that is called Loop closure problem is still open problem you can publish papers on this study on it proposed learning algorithm deep learning algorithms reinforcement learning algorithms whatever you know you can engage here to solve it and make it better just in business and we will of course since the problem is a little bit complex at the beginning consider that we can detect it no problem we don't need to solve it we imagine okay if we see that the object Landmark 1 that we already seen we know it we can just match it but later I will introduce some techniques to also deal with platform what else has challenge the challenge of seeing multiple adjacent landmarks that is very common in real environments robot from here sees three objects together that they are adjacent in Hidden back side of each other moves a little bit and sees them from other perspectives then we say okay which one was which one and should be considered whole as one Landmark or each separately this is also computer vision Machine Vision challenge that we have and it is existing in Islam too I've seen two three minutes so let's continue uh so we were talking about the challenge of Islam and we saw okay what kind of problems that we may have we talked about the multi-adjacent problem that when you see multiple landmarks in the environment how to detect which one is which one in computer vision I will introduce you some that you can see okay instead of talking about the land Works individually we can extract some features go to our features of the environment and try to extract features and talk about everything based on the features of this information not just exactly precisely The Landmark itself uh later we will see that's kind of clue for solution to how to deal with those but sometimes still you need to detect it separately uh we have uncertainty effect of the another problem is uncertainty effect of defining Landmark so these uncertainty effect is uh is can be troublesome robot is here see some landmarks move to 0.2 and sees these three landmarks and as we saw we discussed together there can be some estimation error of the object location like these three and what what that can happen what problem that can happen is here next time like previous like this this is one time next time robot moves and comes here now the question is from robot side if robot sees two of these based on this error that we have even the based on that error robot needs to answer was that these two objects or these two objects these two landmarks or features doesn't matter were these two over these two again I'm coming from here robot comes there sees do these two even can see these three doesn't matter so when robot comes here needs to say okay it was these two or these two and why this is happening because this calcium model and the road that we have is it clear for everybody so of course we want to generalize the detection of the robust features and it's still also this is open problem to uh to find very accurate and nice features of the environment that is robust and works every time also you know we have the challenge of the environment light change the the dynamicity and many parameters that that we want to also we prefer to have it and this is also so whenever I say open problem that's a field that you can go research study for your master or even PhD and even for companies these are challenging companies big big companies like uh it can be Amazon can be Google can be uh uh whoever is working related and related topics of course we have the challenge of dynamicity as I explained robot is moving detects this Landmark or detects these features over here next time comes it's not there what to do you need to solve it give some ideas what to do if robotics was there come here and working 10 times but this one time this bus is gone laughs we need to construct same map we had we need to localize the robot that we had then of course that's also open problem not completely Soviet there are techniques there are techniques that says okay try to not use just one Landmark try to use more use more features and build your algorithms somehow that if the elements are changing inside you're not relying on just one and you can estimate all but that's not easy like like let's say my robot is seeing three Dynamic objects and three static objects how can I distinguish that's not human that that knows that this car may go robot doesn't know robot says this is something over there and next time it is not there so that's that's why also uh that's challenging if if robot understand it is mobile it is dynamic that can be helpful then we can put some weights on the like if I see six subject three of them are Dynamic I can say the static ones are important for me as robot then I have more weight to Oracle in our math calculations and estimations so and this is again open problem because of that if you can solve it if you have proposed algorithm that is robustier you can change many things in the algorithms that existing and improve them a lot and we still bought one of the world biggest challenge okay uh now let's a little bit talk about the other related topics of the course that we have we have the map that this map can be 2D sketch of the environment can be 3D model or each sketch of the environment can be 3D Point cloud so this is different with 3D model or 3D Point Cloud 3D Point Cloud can be like uh everything that you can see in the environment robot can scan and can into the environment we can pull each one of the things that you can see as distance can point a put put a point over there in 3D space and and you can imagine all of whatever see the ulterior surface of each object will be as a point in 3D Point Cloud so that you can imagine in 3D environment you have the same environment so this is basic stuff the basics of the 3D modeling the animations and of course the construction the map and the output of the library scanner some of you guys I know have it in in the lab laboratory after you scan it we can construct 3D map of the uh we can have surface just only through face of the existing objects or we can have some techniques to also give the mass of the object and what is what is the object also not just only through phase like 3D or Surface and we have feasible uh roads to move in the map that that also can be included as a part of map I know maybe it becomes a little bit complex this part to understand it but let's say you robot constructing a map only based on feasible roads that can be my objective I don't care it's easy chair or some whatever it is I just care where I can go this is very important technique in Islam just we can construct a map based on where is it feasible for my robot to go that's it so this is kind of map that we have in next slide we will see visual some examples different class of the maps that we can have and the path is list of coordinates that generated based on that map so then I'm referring to the past I mean usually that the the coordinates the points that robot can move on the map that we construct in Islam we have some notes let's see what we have all these assumptions are important to what we are we want to do you see based on the sensors landmarks what we want to do and more details of the environment usually needs more computational power too it means that I can add a map construct a map based on the tiles that you can see just just step-by-step times is much more simpler than the map is constructing 3D Point cloud of the same rule so constructing those two maps are totally different techniques and depending on what I'm going to do can be very applicable so think about it 3D Point Cloud differences with having just the 2D ties of this environment think about the sensors that we can have to detect it think about the techniques that we can use the computational complexity what does it mean it means that you're writing some code some for Loops to to understand what's the pass and if you have 3D Point Cloud it means that for each point you have a pixel on 3D environment and you have millions of those in just here then how you can understand what is the path in between those no one says you where is the applicable path you need to under you need to write some code to detected and you have Point cloud and even you don't understand the differences of the floor and the ceiling they are just points on the space plus a lot of error so uh that's the note that also we will see of course we gradually need to formulate everything not just talk we need to bring it to mass and the calculations and computer system codes even algorithmic algorithm for so there are starting point that these are the masks that you need to know the the the the basics that we will always refer to talk about to first of all we have studies of observation series that observation includes observations over time observation over time that this observation is a list of the observations observation one two up to time T it means that my robot is moving in the environment and I have my robot has each time different observation of the environment and I'm representing it as observations so you may think okay observation is at each second at each minute at each hour doesn't matter depends on us depends on what we are going to do we are assuming observation format Plus doesn't matter whatever it is just whatever robot can get we generalize the problem now observation there is a control commands we should we show it with you you want to T and control commands are uh kind of like okay at the stage one robot is here I send control command move forward how much does it matter for now we have General problem robot moves that control command is U1 and the observation that we see there is U1 usually we don't have u0 we can have this is in formulation of if you study books later you will see basically at the beginning we don't consider it although we can have it observation can be at this state zero true because without motion command we have the observation too but usually we formalize it like this in books in in all calculations so from State 0 control command observation control command observation control command observation and any question okay so then we have the map of the environment during these procedures that we want to construct it so we want to run the obviously we want to run the control commands get the observation and construct the map Plus find the robot's pose what's the pose who knows what no it is location but not not the answer close robot body what do you mean no robot pose is important to know so we have two terms position and pose they are different position means where the robot is in X Y or even that if we have 3D environment robot pose means not only XYZ but also where the robot is heading to the angle of the robot it is important very important because then you say okay move more work depends on where there is the forward for me in the environment if it's like this move forward that's the pose so what we want to do we want to based on these two also get the robot pose that we show it as X's x0 to T shows the pose of the robot so each time you're running the camera and motion commands in your robot uh you get observation and you want to construct the map and you wanna find the pose of the robot so this is whole problem that we are gonna solve in mathematical form and all these will be always using we will use this in in the master calculations that we have so as I explained a little bit about the uh the error and the probabilistic error I said that okay uh uh you running motion command and robot moves somewhere in the environment a little bit then you have estimation of the error based on the sensors from automatic or visual both of them that where the robot is you can put a circle somewhere around there and that can be shown as a probability and that probability like if the robot is here in real position can be shown like this why it is like this this is this shows more certainty like like uh like if the robot is here more certainty and how goes to the corners the certainty is decreasing and of course we wanna uh this is like gaussian model if you look at 3D version model uh we have the caution model that shows we can represent where the robot is and how far we go the probability of the uh being there is getting lower and how much we are in the center it gets higher we will also explain it soon in details much more so all the things that we are going to talk we are trying to the robot pose is to make the robot pose based on the probability form of the very robotics because let's think a little bit in math like robot is in X Y you want to estimate where it is can you estimate like one exact value that never can be correct right but instead of that exact value estimation you can say it is gaussian model somewhere around there in probability for so that this is the thing that we have so now let's show the Islam problem in math we can say okay be Saudi formulation and these are the uh probability form now we want to put it together we say we have the probability of the uh x0 to T and F given by observation and motion commands so we want to get the pause and the map given by we read this line as given by observation and motion commas that they are 1 to T and one to T so you can see here the point that I mentioned X is starting from zero because the pose of robot starts from zero but basically in formulation uh we we start from one observation one and motion command one in order to calculate the problem so we want to solve this all that we are I've talked so far we want to solve this and get the probability where the robot is and what's the map so I've written here for you guys later when you study it means the estimation of probability distribution of the person map by giving observation because why why this can be called as pass because I told you the many poses we call it as pass so that if you have all of it we can call it also the path of the robot movement in the environment so it means that if your robot moves in the map in the in the environment a long while then we want to estimate where it was and construct the map also mean by so we have we're saying based on what we want as output we can Define different techniques to solve this problem of this any question okay so how we can show it in graphical model the graphical model of this lamp can be visible like this we have the XT the current holes of robot then we run the motion command based on that motion command we get the observation an observation can come from observation can come from both the state of the environment and com can come from the map itself too what does it mean so this is the map robot is here and we have some kind of lab and this one is robot and this is real environment and robot is for example somewhere here and there is somewhere there so the observation not only comes from the real environment but also can come from can come from the map itself too right also we need to see how to use those two information that comes from Real Environment comes from map how to how accurate which one it is when we need to rely on Real Environment then we need to rely on the map if if you want to Simply say okay this is like um this is o r observation of the map and this is the observation of the real environment okay you can say simply observation of the map added by for example observation of the lead environment by some ways it's alpha beta for example which one is more important give more weight to to calculate uh varieties in simplest understanding but of course we cannot do that correctly later we will see how we can do that so this is the model of the environment and this is the robot that you can see x y and the pose but the of course if we have that in current state we have one previous state that this is this is XT the state of the reality robot is this is previous one where it is coming from and previous motion command that we run to came here and observation previous observation that we had of course then we have the future one two XD added by one the the future motion command and the observation that we may have you may say this is obvious why we need to represent it like this of course we talked a little a lot about it but we need to formalize it and bring it in the graphical mode so that when we are solving it in mathematical form you understand it what's happening better that's the reason that we have graphical representation and we have some algorithms even they are working based on the graphical representation they are relying on these and we need to see what's happened now let's make the problem more dramatic what is the dramatic part we can classify Islam algorithms into two general approaches one is online Islam second one is offline but does it mean it means that everybody listen pay attention to me so I'm here I can start to move as robot and come back here then when I finished construct the map and localize the poses that I went through this approach is called offline if I do after finishing but if I want to construct a map every time and after each moving and for a localizing this is called online Islam the techniques are quite different think a little bit about it y can be different is like one time you can see everything then you want to construct the map in offline Islam that's easier kind of can be easier but that's offline that's not kind of you cannot use the map meanwhile that your robot is moving in the environment but in some application that's quite useful because you can achieve better results but that's offline later on the contrary we have online map that online slab in online Islam a robot is moving in the mode and each step tries to construct the map and the localize the position of people that we have to um two branch and basically in this course we will talk about the online Islam mostly we move towards our land Islam if you know about optimization or the algor optimization algorithms those usually goes to offline this land but they are very strong they can be they can be work very well but also we have some Advanced Techniques that trying to merge this together they say okay I have the online but some in some points after some time I can I can apply upline techniques to improve it too and and if you want to show the online we show in this form not x one to T in previous time we saw General problem X1 to dip here we have probability of the x t and M not the pass just the post here if I go back here we had to pass General problem of Islam we wanted to find the probability of pass on the map but here we have the probability of the uh pause and the map based on the observation one to T and motion command one two t and and based on this we only have this part over here not the whole graph like this I mean I mean the calculations are mostly relying on this and in next chapter we will start with base filter that we will see the assumption is like this and goes on ah goes on just the belief that we I will introduce so offline Islam also can be referred as fully slam fully slam derives company sequence of the robot pose and estimates the entire past but online is only on the latest reward post so of course [Music] since we are going to use Mass you supposed to study many of the things that are related but I'm trying to during the course introduce and quickly refer what I'm talking about so that you can understand what's happening for example we have derivative what does it mean because we are going to use it in our situations a lot we have integral what does it mean because we are going to use it a lot you may forget it so whatever you forget it please study during weeks for next week but I quickly uh try to mention it was the General topic for example when we are talking about the derivative the part that is important for us is the calculating the slope of the uh they slope of this probability like we have for example gaussian and for giving Point like a or X here for giving point you can calculate the slope of the uh this this curve here so we are going to use it and if you've studied like other courses like machine learning deep learning reinforcement learning you may face with it and that's very useful for learning we have integral what is the integral meaning that we are going to use and this is very important for us because I told you we are we are we will our our all talks are about the probability and the estimation of based on the calcium model and when you have gaussian model we need to know okay what's the probability based on value calc bring some value based on this and and that that's how you can do that you can use it integral and in integral you can say okay uh see if we want to say the integral of the function FX between B and C shows the uh the area under this part so we can say what is the amount the value that shows the area under this and you know in Mass it is impossible to solve directly because uh because this slope should be discretized and and if you want to write the program and we usually discretize this and we can solve the integral in descriptive form and get the value of the what's the area under B and C and then based on that calculation we will use it in in for example if you want to compare to gaussian models for example simply uh of course there are many but I I want to give you the clue like what is the that one and this one the difference is what is the like the area that is covered So based on those things you need to know what's the topic plus we have the probability distribution that uh that still if you forget it just have a look the probability distribution for all uh in conditional form we can say we can get the integral of the probability a given by B type times probability of the B that it says the for all possible B's for all possible bees by giving a what is the probability so a is given and for all possible P's what is the probability that we can get integral of these term over there and you can have a video if you forgotten So based on that what we want to do in online Islam so we want to get the integral of the the probability of the xtm given by observation and motion command so convert it kind of to a value that what is the probability of the where the robot is and the map is and if we want to solve fully slam it is all of them so for each pose and the map that we have based on the each motion command and the observation so if you want to calculate all of them we have full Islam if we want to just solve one of them we have one of these parts so so this is called probability distribution and of the where the robot is and the opened it exactly what's happened so first so about that we will talk more we will extend it and use different algorithms to do that let's talk a little bit also about the maps we have different kinds of map I mentioned a little bit we have volumetric Islam like Point cloud so volumetric Islam can be as Point cloud and it shows the volume of the environment so this is the scan of the library scanner this is the robot in our lab and this is me that robot scanned amoeba by a library scanner and you can see that it is a point cloud of environment that's one kind of map that we can have in 2D form or 3D form we can have feature based map that uh the the feature based map depicts the features of the environment instead of having the the volume of the objects like like say let's say in this environment I just want to get the corners and edges of these each each object then that's feature that I can extract and construct a map like that we will also see this technique how how to really Implement and how you how you can do that uh uh so we can have no known landmarks and unknown landmarks based on the map that we want to construct known landmarks it means that we know the landmark exactly what it is and we we can detect it easily for for this class at the beginning we consider like that because we don't want to solve that problem for now in the techniques that we are using so we will assume that okay the landmarks we know at the beginning but there can be all known landmarks that we don't know what they are even a human who knows what is this no one okay I think I think I mean no one human doesn't they found it and they don't know a even scientists don't have any clue what is this right and this can be valid for a robot for everything because robot doesn't have any idea what is this chair even unless we Define it so we can have unknown landmarks we can have a static environment Dynamic environment we talked about it which one is better of course if you can cover Dynamic environment is better uh we can have real time or non-real-time environments that also this is another class of the model but you can kind of consider it is similar to online and offline one uh the online and offline Islam or full Islam or online slab then we have the control part of the Islam that is another perspective that we need to know passive control active control passive control is mean it means that like I have a robot I wanna use the uh joystick to control my robot goes and come back then I say that the what is the locations of the robot and what is the map that's called passive control but an active robot needs to navigate itself so also at the beginning we don't consider the active control that we don't take care about the navigation because we need to break the problem and solve it small by small otherwise it's impossible to solve we have the class of the geometric maps anthropologic maps in geometric map you have map like this from satellite but this is nice but it has a problem of the Hidden passes uh because uh like there can be some some passes indoor that you don't see in this current map but uh we can also have topologic based maps that show the connections those all the just the links where they are connected to each other so maybe you have a problem that you need to get the output as topologic map with robot so or maybe you have a problem that you need to construct something similar to geometric map as robot so as developer you need to decide we also can have much more advanced algorithms like Islam with single agent that we talked so far and also we can have multi-agent what does it mean we want to localize independently construct the map but finally the map is one map based on different robots that we have those can be humanoid those can be quadruped or uh hexapod or drone or whatever it is different sensors they are moving in in the environment and finally we can have one single map so how to do that is multi-agent one that is it also open problem that is uh is a challenge and this can be easily a PhD thesis for uh for who wants to study or this is open problem for companies you know and so I already talked about the related complex problems like we have planning we have design that in design you can think how Islam can be important that's using your imagination task allocation we can use in task allocation problem very diverged and big problem that I can say there are hundreds of sub problems of task allocation it can be robot to to pick an object it can be a traveling salesman problem I hope you know traveling says no problem and many many application programs that are very well known in the world and it can be used there dealing with the defects dealing with the variability and dealing with the inventory there are also some relevant ones that can be combined and usedly and the algorithms that we have firstly we'll start with base filter then that is underlying of all these algorithms then we go to Kalman filter family particle filter and graph based algorithms and all of them are going to use motion model and observation model so what does it mean we are going to use observation and motion model combine them together with these techniques in order to achieve first simply localization then later how to construct map and we we will see them separately so motion model can be seen as the a little bit different than what we've seen motion model is equal to probability of x t given by x t minus 1 and UT it means that so my current robots current polls is based on the previous pose and motion command next week we will talk about the touch base assumption I'm not going to explain now and we have the gaussian uh motion model that uh discussion motion model is the distribution estimation that I explained a little bit there these are as input the second one uh sometimes we can have like this is the gaussian distribution but in some problems sometimes we can have non-gaussian distributions then we will see what kind of algorithms also can can deal with this one why why we can have non-gaussian distribution we can say rifky any idea ilham England why we can have a non-gaussian distribution you are massive students you should be very active who can answer this will get positive Mark direct positive Market positions very close the answer is very close you're very close but explaining a little bit far but yeah very very close we have two parameters that they are different but not on the Curve on the curve but you should think 2D not one D you're thinking about this model think about the gaussian distribution in 2D very very close minus very close but I I know what you want to say but you don't know all the parameters um okay I can almost accept but let's see yeah all because you you're getting very close like let's say robot is here okay if I have rotation ability and move forward the ability that I have two parameters right if the error of both are same I have gaussian distribution there because if I move forward the error is like this amount and if I rotate rotation error is the same then it will be circled there but let's say my moving forward error is too small if I Robot move this too far forward the error is too small but by rotation error is too big then my curve becomes something similar to this move forward error is small then it shrinks and this is not caution anymore it means that this is not this form of the distribution anymore yeah yeah that's simple like let's say let's say my forward if I my I have motion commands right two kinds of motion commas move forward rotate move forward let's say for me zero I have zero error in moving forward with millimeter I can accuracy I can run it but I have a lot of error on rotation completely wrong random then what happens if I say move forward one meter and turn like turn zero even then then I maybe can be end up one meter around circle on the edge of myself right wherever I can go but one meter like here or there if it's completely error and and this is this is the understanding and if the error is lower like 45 degrees in the rotation like let's say you have minus plus maybe later write it here robot is here if the moving forward error is zero and if if the rotation Theta Theta can be completely random if you run the motion command u t equal to UT as like move uh one meter as UT equal to move one meter and Theta rotate like zero then robot can end up everywhere somewhere after one meter Earth but if the error is for Theta is like 45 degree then robot may end up somewhere around here with zero error on the moving forward with 45 degrees error on the Theta robot maybe here is end up here end up here end up here because of the arrow that we have if you have some error here for example 10 centimeters error here then this can be somewhere around here that this is 10. right everybody understand exactly what's happening so when this is happening and the error is different in these two parameters then we don't have any gaussian model anymore that's not Circle anymore this dimension of the very robot is because that can be the form of the discussion distribution says okay where the robot is if errors are safe but if they are not same this becomes some other kinds of Curves like this that uh that it is not caution and leaves the algorithms first how we can solve that problem then we will see that if if the if if the model is not caution anymore then how we can solve the next stage if they are different yeah but if they have same value even if it's 10d then that's that's still gaussian so that is so let's conclude this chapter we had a understanding of mapping of the robot we discussed the localization problem with different characteristic different types and we talked about the sum application domains for Islam with understanding the full Islam and online Islam differences as very important because we have different algorithms in this splitted directions and we discussed the general problems that we need to solve with Islam algorithms then we saw how the combination of problems can make challenge for us in Islam and finally what the techniques that generally we can solve it that are introduced for example the mathematical representation then we discussed that there are some techniques like base filter Kalman filter extended call man filter Etc that next next week we will start to start to dive in details of those with some examples simple representation and simple assumptions at the beginning so that's it this brings us to the end of today if you have any question feel free to ask so please for next week study the topics that you have problems these are the ingredients that I'm not going to explain again usually I'm just referring if you don't know what's the post for example what's the location what's the gaussian distribution what I'm talking about what's the online Islam what stuffline Islam you will have problem that then then becomes very complex to understand just have a review quick one hour review during weeks so that you can get ready for next week and we'll start to have a simplest algorithm that we can have okay if you don't have any question thank you very much see you next week |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH6_SLAM_for_robotics_Measurement_Models_Markov_Localizationand_EKF_Localization.txt | okay so sorry for the interrupt uh so this is how generally the uh lighter scanner is working and after scanning the environment what we have we have a bunch of numbers simply so for example here I have the distance here I have the distance here I have the distance and this bunch of numbers can represent the environment to the robot that I have but basically if I if I plot it in 3D I have measure points what does it mean it means that so the end point over there I can plot it in 3D I can say robot is here I put a pixel there the color or something then for each one of them if I if I plot this in 3D then kind of I have the environment so uh so that how this is working looks like that but basically uh this should be we should find a way to formalize it for example if you have a rank sensor to bring it into our equations and take them into the consideration so uh what we have here we have the observations as as we had already observation T at time T we have observation one at time T up to observation and at time t for for example range sensor that we have then how we can formalize it in form of probability uh in the simplest form in the simplest form we can write it as products of the distributions that uh that each individual beings gives it to us so probability of the observation given by x t and M is equal to the the products of the all probabilities per each one of the beans that I have so lastly if you've seen how to deal with these probabilities and how get the products of them so uh so um so if you want to understand it better kind of you can consider not holding mesh you can consider independent objects that you are measuring uh that will be our consideration for Simplicity we can say we have different landmarks or objects that we are measuring the observation Forum that that Landmark or object and we can distinguish it for Simplicity we say we can distinguish it and based on that we can show the probability of the uh value for example the objective how certain that table is over there but you may say okay how can I say that is stable of course that's another topic we will later dive into how to distinguish it in all the mesh environment but also that depends on the technique that we are using that later also we will see so observation model uh in different sensors can lead to have different models of the final estimation that we have you can now think about the different kinds of map we've had but today I'm going to also uh review it for you and and discuss about the classes that we have so we can present observation in base filter as the equation that we have here so if you remember how was it we had the belief of the XT that here we can consider ETA probability of the observation given by x times the predicted belief of the x t so uh so this is second stage of the base filter that in the page the second stage we wanted to correct it what we were doing we were getting getting the observation and and correcting the predicted belief that we have but here since we have the sensor observation we can write it in this form over here so that we can write probability of observation given by XT and M also we can take to take the map into the consideration and and replace it with products after each one of the beans for each one of the objects or landmarks that we have in the environment so we say Okay formally uh to uh to break it more down uh we have the map that can that that map can have list of objects or list of landmarks again I'm mentioning you for Simplicity for understanding the whole concept better we consider that we have multiple landmarks in the environment and landmarks already can be detected of course this is a big challenge you may say okay that's detecting this this chair over here already is difficult and we we need to have a big algorithm to do that of course we do for now for Simplicity because Mass already is complex enough so we consider that we know the landmarks and when we are talking about the map we are talking about each one of the landmarks or each one of the we can call features for objects in the environment so later I'm gonna talk more about the features it means that I can say instead of considering Landmark as whole this chair I can say the features of this object that are easier to distinguish and later we are going to see in visual Islam how we can extract some features from this this guy over here I will really clarify for you for example we can find the corner of this table over there corner of that door over there so those can be our features so those features can be also considered as this is already here not only a big something big a building as landmark so this look to present the map we can have uh to to present this map we can have two general types of presentation that one is feature based that in feature base as I explained right now uh we have n features that they are indexed already we know which one is which one um also we know which one is which one also is another challenge so let's say we have the feature we have the uh landmarks as I explained I know this chair that is stable that is another table but later after I have it in time T time elapses and after I after some time how can I understand which one of the features that I'm seeing again is the same chair over here so if we know that we can call it as known correspondences if you don't know that we call it as unknown correspondences so this is a note that keeping your mind again for Simplicity we say we know which one is which one also that's also not easy task to do like like even I I'm human there are lots of chairs right if I go a lot in the environment it's also a little bit difficult to say which one is which one maybe the end one is easier to detect but somewhere in Middle if there are 50 can you say exactly which number it is you should come from the beginning to say which one is it in the middle right if there are plenty so because of that also that is challenging when I'm saying the n features that they they are indexed so but usually we do in such a scenario we say Okay wherever the robot is I can say okay I know the pose of the robot and based on this pose of the robot I have features or landmarks that then I can just keep the position of them simply I don't need poles just the position because the orientation is that important for me so far so I saw that by default because they're like that you may think can it be useful if I know the orientation you can think this is open problem this is a challenge and and if you work on it and if you can improve the current algorithms with including the including the orientation that is new work that you can do as research for even your master thesis if you like but how to detect the polls and how to make it useful to understand the whole scenario that we're gonna talk about is kind of a challenge anyway for now because the robot hole and uh Landmark positions for feature-based maps on the other hand we have location based maps that can be taken into consideration and how they are looking like they are looking like that we have in correspondences to a specific location that say okay we have the robot we can we can have a grid and descriptive form then in this security form for example if there is obstacle over here based on my senses of the light laser scanner or lighter I can say okay this is occupied or not occupied so these kind of maps also known as volumetric that uh that they are considering the occupancy or not occupancy of the map that we have kind of you can say if you look at the class very nice uh Tails here that we have tiles that we have that you can consider each one of these are occupied or are free for example these are free this one that is chair even partially depending on this criticization that we have fully we should consider them as occupied so even a little bit object is there we can cancel it as a quite and based on that we have construct them so is it clear both of these types for you at the beginning we start to talk in this part we will go to the feature base and be diving later in other algorithms that we have for example histogram filter we will dive in to the location-based Maps but also this has kind of mass that we will see how how we can calculate for example these guys over there with the robot where it is and how that is generally worked so in basic measurement algorithms even if sensor correctly measure the range stands for are currently range to the nearest object of course we have the error if we don't have error or our tasks already is very simple as as you've seen for example in as we I'd explain it in a Kalman filter if you measure it very accurately then then you can say where the robot is based on the surroundings and there is not big problem too much you can based on the kind of mathematically can calculate everything and finally save value but even with the the most precise algorithm we have noise we have disturbances we have dynamicity different different things that predict the probability inside and we have the error on the other hand we have limited resolution of the range sensor usually so uh tall sensors that are like like very common if you want to scan this my hand over here like this so the resolution will be different from with doing the same scan over there the the distances between two senses is too high here but the the measurement is there is like jumping and how far you go it is jumping more and depends on the resolution that you have now you can understand oh how challenging it is why because if I scan for example this guy over here as as an object as Landmark I scan with my sensor over here so the mesh that I'm getting is totally different from that I scan it over there if I put it and scan it another problem what where the problem is we say okay whatever it is the problem is you scan this guy over here your robot moves there and it scan uh moves like a little bit then he scans it far from like let's say better to say the object is over there your robot is scanned from here then moves to the front and is scan it then how I understand that this was exactly the same one because of the resolution is totally different so matching the information is quite difficult over data so uh that that brings us the limited resolution range of sensor challenge we have reflection error so who knows what's the reflection error for any reason for any reason your sensor sends the variable wave after sound or wave after laser and the reflection if not coming back goes somewhere else what happens then your receiver don't receive it so this is like how uh anti-rada airplanes are working they don't reflect back to sound base they reflect somewhere else then your receiver never gets where it is and this is very common problem in in with sound waves too in laser is less this is happening very rarely but yes with the and of course you will see if you use a lighter have you ever any of you guys okay good so if you scan you say okay that's very simple I scan the environment and I should have a very nice information but suddenly you see after this scan okay there are some points over here I scan there there is nothing here but there are some pixels over here in The Matrix that I have randomly then then oh oh my God what how can I filter this how should I remove these outliers and how this is so that's the noise that we have over there so we need to understand exactly what are the challenge that we are facing with the measurement model that we have something can be atomers atmospheric on the measurement signal temperature electricity or whatever it is based on the sensor that we have so what we do exactly same as what we discussed already we want to bring everything to the gaussian distribution to pre to present the ropes and if you bring it to gaussian distribution everything is simple we have zero mean and and the error can be represented by variance or covalues so we have different types of measurement errors you can think about it how kind of measurements error we have so first one can be the small measurement error it means that you mean it in some point then you have it or some some error over there so that observation that you have this is the error of the sensor that you have how accurate your reading is like for Simplicity you can understand how we can show it is we also can show it in the form of gaussian distribution to add it to each one of the observation or means that we are reading from in mind so there can be error due to unexpected objects that is existing in the environment so if this is observation Max so you see suddenly you get something like this depending on the noise that you have and and this is unexpected object error like like as I told you for example you're measuring there suddenly somewhere in the middle maybe can be uh can be presented we have another error that is famous as error due to the failure to detect the object it means that the object is over here you're scanning this but the laser point goes and shows somewhere else instead of this point over here there is object I scan my hand instead of getting points from here I get points from there so that can be measured that can be shown like this if we consider this as observation Max you see at the end point Infinity for example he put and then another type is of course a very simple random unexplained noise that that the noise is distributed over everywhere like like we don't know what it is like we don't know uh the the probability distributed in uh like everywhere the the human says okay it can be anywhere so these are different kinds of uh four different important kinds of noise that we should know are existing in observation model that we have and basically we can merge them all together too hot a form of this notes so this includes four of those all together that basically if we want to create noise ourselves and make sure that in our simulation or or if you don't want to run really robot and we want to uh kind of generate exactly simulation of what's happening in the environment we need to consider this noise over here that includes four different types to make it more realistic so before knowing this you may would have if I asked you you may not have mentioned this guy over there there is a gaussian distribution mean with zero mean and and the error covariance uh the error variance or covariance so that uh we all may think about this but there are four types that we need to include in our measurement model to make sure that our model is accurate so any questions so far everything is clear good so now we want to formulate the observation model by lighter in simplest form that we I can have so if we say we have Landmark observation we can consider like this that we have observation I the ice landmark in time T that is equal to range and bearing so what is the range range is referred to the distance that we have if the distance of the measurement if the eyes landmark in time T and bearing is referring to the angle of Philadelphia robot where it is looking like so I'm the robot you can consider my neck what is the bearing which direction I'm looking at So based on that so this is like robot but basically we consider it on the lighter scanner itself where the pairing is like this so uh just uh just don't mix it because it's a little bit complicated if you Insider if you consider for example humanoid robot we have the bearing we have the robot pan we have the robot position and if it has like body rotation that can be too also that you need to consider all of these in order to what what we are going to do we are going to do where the land to save where the landmark is based on my my current robot position so each one of them in order to be able to say where it is so I need to say okay my scanning is like in this angle so we call it as bearing or or Pi that that comes from both of these are coming from uh sensor reading so how we can very simply include the undistance can be uh can show each one of the uh objects and landmarks that I have so you can consider the X Y as the robot position and the consider the ends as the information that comes from can be here uh come from the map or or we can really bring it from the sensor itself to depending on what we are doing so anyway we consider it as m i x and miy it means that for each one of the per each one of the landmarks the ice landmarks I calculate the distance with the robot position that I have that gives me the distance so robot is here the distance from this chair the distance from that one that one for each one of the landmarks I can calculate the distance and varying of the each one of the landmarks also can be calculated over here with arctangent to that we've seen multiple times simply so uh The Landmark position on the map can be represented in this form that we we consider the m x y the Iceland mark on the map on the other hand robot poles can be considered as X Y Theta that that can can use it to calculate these overtake so the mass over here is not complex very simple to read the information from library scan so how it looks like it looks like we have the map we have the robot the distance and of course the pi over there or bearing over there that gives me where the landmark or feature of that Landmark it is so that's just just just representation to everything more clear so there are some critical points that better to know in order to understand the uh noise and gaussian knows better let's say my robot is over there and I'm measuring this obstacle over here and my sensor my observation model says there is a landmark overview and if I time goes and robot is like at the same location or moves a little bit whatever so if I show this in gaussian distribution then the you can see how we can use that gaussian distribution if I measure this Landmark over there to element eliminate the noise kind of make use of that gaussian distribution to eliminate the nodes how the principle is it looks like this the idea says okay uh when I'm the robot here and I'm measuring this this Landmark over there and if I have the gaussian distribution then after a movement or at if the robot is the same at the same place if I measure again if I see somewhere else like like one of the error types that we have over here or or if the robot measures somewhere around here of course most likely that's error because already I know the obstacles should be around here and most most likely should be around discussion distribution not somewhere totally far not somewhere else so this is very interesting to know and very nice day of elimination of the outlier elimination of the uh the the data that you I'm scanning there I know there is a wall there suddenly next time I see some pixels over here based on discussion distribution concept I can remove all of them simply so uh so uh so this is kind of nice idea on the other hand on the other hand uh what what what else I can do so when you have the robot over there and you have multiple objects over here so robot is measuring here so the the beam is crossing some distribution over here so this is another kind that your sensor is not reading anything reads over here or reads Infinity but since we know that on the map that we have this pin is crossing over here we can kind of classify or allocate to this line to which one of the obstacles we are close to so because uh because we say okay we are measuring infinity and this line that is crossing most likely with some certainty should be this obstacle over here that that's a noise and you have lots of those then this is useful in order to detect it you may say okay maybe there is not really maybe this is from the middle and that should not be yeah of course there are some threshold that you should be considered but but this technique will help you to eliminate noise a lot in very noisy sensors that we have so is it clear any question so we've seen two types of user age for elimination of the noise and based on the distribution that we can have on the uh and the map on the 2D map for example okay so we say in many robotics applications features correspond to distinct object that we can call it as signature so as I told you we can have known correspondences and unknown correspondences since we are considering corresponding known correspondences we can call it a signature signature what's it it means that I can put numbers number one two three four five six seven eight then I can say number one is this chair and this share is one of my landmarks that I want to consider and and later in the in the algorithm implementation and details you're gonna see that that signature I'm going to use to understand and find out which one is which one so so that as I already explained that can be called for door posts Windows features or or old building as a feature so depending on what we are considering or detecting as feature or landmark in the environment so uh the most common model for processing Landmark comes from range and Berry related to robot coordinates we've seen already and now we can show it as set of features so it means that we have feature observation at currently that this includes feature one feature two up to how many features I can't take or I can have in the environment in the most advanced algorithms that nowadays have we have for Islam this part is very challenging detecting the features and how many features you've detected so let's say I have an algorithm that works in my Islam technique to detect the features first then later localize the robot so for detecting the features from environment you may think that okay Landmark is detected over here even though I know I consider that I know correspondences but next time you don't see it the feature is missing one time you detect 100 features next time there's 10 features although you know they have attendances so that's that's the challenge but anyway we are formulating so far for now and we say okay we not only know the correspondences for now let's say we can see all the features then uh then each one of these features contains what range bearing and the signature so what are those so far you should know where the robot is the range distance of the uh the distance of the robot system Landmark or uh or feature then the bearing it shows the what is the the angle of the the sensor that I'm reading it's over there that one is over there that one is over there I know the different angles for each one of them and the signature is the indicating number that this is like number one that's number ten that's number 12 that I get it so at time T I have set up these features clear indicate it with signature so if Landmark measurement in we consider it in conditional independencies that noise is not related to each other uh like like the measurement of two beans of of the environment being one being true is not uh the noise is not affecting each other we can for Simplicity we can show it in this form but but of course it's better to cancel that part too when there is noise here that may can affect the next one too uh how you can think about it how but for Simplicity we say okay let's say those are not affecting each other based on that we can show it like this for for landmarks the probability of the features of the observation T given by x t and M can be the products of the probabilities of the the features that I have the the range bearing and signature given by the XT and for each one of these uh landmarks I so again the map consists of the features from M1 to MN that each feature now we can consider like this for the signature location or transition so when I'm talking about each features afterward you need to consider range bearing signature for each one of them that we now included signature to know the correspondences how that can be calculated we calculated in the previous slide we can show it in this form range bearing signature equal to this term over here the including distance and the the orientation with Archangel 2 and finally signature that we don't need to do anything just that's the signature or number but also now we need to add the noise same as previous if you remember in motion model we added the noise and now we need to add the noise per range how accurate I'm measuring the distance can be also different how what is the error of the bearing so for each one of them I'm considering we consider Epsilon error for range Epsilon error for bearing and Epsilon error also can be for the signature we can say How likely I'm detecting which which one is which one what is my error in detecting which weak signature which Landmark is which one that can be also considered as a rural voltage but basically we are saying we know the correspondence is to make it simpler so far so clear okay I think this is very simple I should be very clear we just add the noise for the calculation that we have and each one of these are each one of the features that time T that our sensor is observing now if I want to write the algorithm that that shows the uh Landmark landmarks for non-correspondences let's see how it looks like we say we have the features uh c-i-t that indicates which uh which correspondences is for which one so this is like connecting my my sensor reading to the to the features that I know that that is because DCI that's the reason that ivr saying we know the correspondence is if we don't have it we don't know XT and M so the the uh the features that we already seen the algorithm looks like this first of all we take the J as CIT it means that for each one of the landmarks that I'm going to calculate the uh uh calculate the probability distribution we say that take the J J as indicating which one is ritual then first of all calculate the range calculation of the range looks like this range of the equilibrium distance between the the feature the JS feature of the map and the robot pose so y.js feature because I know the correspondences and I don't know which Landmark is each Landmark I just put it as index over here on the on the features that I have to edit clear simply I get which one is which one and I just take it from the index which one is which one to calculate as a range for repairing I'm doing the same calculate the bearing based on the the feature from m j and Y and feature M from j and x to calculate the base so after those calculations now I want to bring it in the form of the probability so to bring it into into the form of probability since we have uh we are talking about each landmark and we can show it a unique probability one probability for each one of them we have product of the probabilities that that each includes first part includes the range this one includes the bearing and this one includes the signature of course I need to consider the error per each one and of course I need to consider the differences between the observation and from the pose on the map so these are predicted are when we had we when we have had always in most of the courses machine learning artificial intelligence um wherever we have had mostly for the variable we have prediction so predicted r that comes from here and the distance that we have that this distance is from the pose on the map on the other hand we have the uh observation directly that can be the sensor is reading and can be the differences of those in form of the probability and and products after all can be written as a variable as product of the distribution for my Landmark model with known correspondences so so far what we have now we have The Landmark measurement based on the uh range sensor and and now we can also use it to plug it into the column filter okay so we are gathering everything so for now so we we have one more element one more uh calculation of the measurement model but before going to plug everything all together let's see the mobile robot localization based on the Markov visually understanding it is very simple then we uh we dive in the extended column field so for I wanna clarify this a little bit over here so we studied extended Kalman filter and Kalman filter but basically although I try to explain it in form of uh robot localization all the examples were based on that but those algorithms can be used for anything for example temperature reading for example whatever you want that wanna filter I also will show you one example today implementation of the cosmic filter on visual information but uh but basically specifically from the mobile robot localization we want to First also see the features uh we say Okay robot localization is a problem problem of determining the cause of the robot we know and it is can be called also a position estimation or position tracking that uh that can be uh also known as problem of the coordinate transformation of the very robot is and where it is working so in Mobile robot localization if you want to have a general taxonomy we we already talked about this but let's have a look we have the local versus global localization they are other known that in uh that in this way we have the position tracking position tracking means that we have the uh that's also known as local we assume that the initial pose of the robot is known but in global localization initial pose of the robot is not known for example if you have the map this is the map so and this is the real environment on the right side so where the robot is if you know it or we don't know it we say okay we know it or we don't know it that's that's the that's two types of the taxonomy that or class of the techniques that we have in Mobile robot localization on the other hand not only the local versus global localization that if the technique is uh local or position tracking depending on later algorithms that we are studying I'm gonna mention for example this is global or local but also we have kidnap program that that the algorithm that ivr learning together let's say is very accurate and robot is moving in the environment and I'm plotting the map and localizing everything pretty accurate but what if there is a naughty boy comes and takes the robot from here from here and place it over there somewhere else algorithm works if someone comes and kicks my robot one meter to the other side will it work if it works then we can say our algorithm is uh capable to solve the kidnap robot problem too or not okay so for any reason robot location suddenly change that is not our under our control if it works or not for example to make it very clear for you if you have automatically then the technique is based on automatically means that counting number of steps all the time and we know the initial position that is then position tracking then kidnap problem cannot be dealed there because usually step in use counting every everything it's like plan cry if you if somebody is blind and walking if suddenly remove him and put it somewhere else for him is impossible almost to understand unless meanwhile he uses other sentences to understand and localize again but otherwise it's impossible to know where where he was that's the same thing on the other hand for mobile localization uh I already explained that we have passive versus active approaches in passive approaches the the robot's motions is not animated and and facilitating localization that is like kind of robot moves randomly on the other hand the active localization control VR controlling the robot in order to minimize the error and everything what does it mean it means that so I'm gonna localize this uh I'm gonna run Islam algorithm in this class so one technique is so let's say my algorithm is very well true if if I move in the environment I can I can detect everything and localize by robot and landmarks that part is okay but the challenge and the question is so should I should my robot move randomly or they should be a technique that says how to move to improve whole process if I have the technique we call it as active localization it means that my algorithm says okay go from here to there in order to have better View and localize everything but but if you don't just randomly move everywhere to to find out what is happening clear so passive active another taxonomy says static environments versus Dynamic environments that's quite clear so you may now think oh do we have static environment at all do we have we do where in Factory in a company that nothing is moving there is a warehouse nobody enters and robots are just working inside can be okay so that those kind of environments can be considered ecstatic or is everything is on the plan like you exactly your robotism robot is moving but you exactly know that object is dynamic then that can be also considered with static still because you know that and you you can remove it from all information then your sense of reading although there are many things are moving in the environment but you can filter them because you know the dynamicity exactly so that can be considered also static um so we know everything there and in Dynamic environments that how you guys some of you guys were doing experiments to gather data and people were moving on the campus and and too many people are moving like ants in there and localization is quite difficult for uh for dynamic environments so uh I mentioned to some of guys that I recently reviewed the paper uh transaction paper that there was a nice idea don't publish this and don't develop this because it's already given but since you are my student I can give tell you that what's happening there so we have very Advanced algorithm orbislam one of the best so far like you know YOLO is best one of the best for image processing and object detection Orbee slam is one of the best for Islam algorithm as far as we have time I will also talk about that and the features but the algorithm is tremendous I will break it down and come block by block but anyway that's one of the best the idea that gives there that works there and improves the orbis land dramatically says how to remove dynamicity of the environment when there are two frames of the image that are coming from from input they detect which of the objects are moving based on calculation velocity after each feature like like if I can understand it like my motion velocity that I know how fast my my frames are moving but this guy over there is moving and I can detect the velocities different than all faster or slower than all my movement then I can consider it as outlier and remove it when you remove all dynamicity you have more stable calculation of the robot localization robot location and the and constructing more accurate map so the idea and the nice thing is that based on so sometimes I also introduce right many of the things open problems that can give you the idea inclusion how to do nice research if you remember if you go check slide chapter one I said that open probe dynamicity is open problem you can check it and meanwhile you see somebody solve that so so I should not go and change it that's not open problem completely somebody considered it pretty well on the other hand can have single robot and multi-robots that we discussed not only we should in Advanced Techniques we can have a bunch of robots that all will be moving together so should we construct different independent maps for each robot or we can bring them all together to construct one whole map that that can be called a multi-robot slam techniques that for example a drone is flying a human a dropping robot walking there another robot is crawling there then combination of the sensors can come to have a multiple boat uh multi-robot robot localization so any question up to there okay now we want to talk about the markov's localization first the idea is simple you can quickly understand Markov localization Works based on the base filter and it's just practical way of implementation of this simple base filter it is probabilistic localization algorithm that value is variant of base filter and it is destroyed forward application of base filter I explained to you and Markov localization characteristic is like uh the base filter transform probabilistic belief at time T minus 1 into time T it means that so when robot is moving I have new belief and previous belief comes to my new belief each time previously comes to my new belief and that previous belief means that as we view we say I'm believing that whatever I calculated already whenever I'm working whatever I'm calculated I'm believing that this is true whatever it is maybe that's very wrong maybe that that's very true I believe that that's true and based on that I do next step calculation so the mark of localization is global localization now you know what does it mean based on the definition that we have it can be also position tracking problem and also includes a kidnapping problem into insert itself so uh the other characteristic is that it is for static environment it's not usually working for a dynamic environment and stuff so let's have a look how it looks like the algorithm Markov localization Markov localization is very simple quite similar to what we have for the base filter if you remember we have we had the predicted belief and the calculation of probability based on the previous belief that we had so this is motion model previous belief that we can calculate predicted beliefs then based on the predicted belief we calculate we add the observation and cut the belief that we have but here what we are including now uh we are including the map into the consideration in the mark of localization so XT given by not only x t minus 1 but also m and that M gives me more information about the where the robot is M of the M1 now we say okay uh in default indicates that the position is unknown how we can start we start with the belief of the XT as one over all possible X's that I can have that this is looking like the distribution that we already have seen like we have this distribution over here and if I if I draw if you calculate this belief 1 over base the the whole state space that you have then the distribution instead of caution will look like something that we don't know which robot is the probability of being everywhere is similar that that is our initial bit fix zero here in this case so what if no one you may say okay I already know it then what you do you say Okay How likely you know this is X for example my robot is here I can say my robot is a voltage simple how certain I am I can put the distribution over there now we want to directly go to the example to see how visually it is working to make to make it understandable let's assume there is a one dimensional uh hallway environment that robot is uh is going to defect different landmarks that here in this example we have a door initially robot position is unknown we don't know and we use that probability distribution that I drawn there and the mark of localization tries to localize the robot it looks like this we have a robot whatever the robot is whatever observation model is and whatever motion model is we don't care for now we just say okay we have the robot we have some landmarks and we have one dimensional robot only can move to the uh to the right or left for example in this case for example let's say move to the right and observes the features then then how generally the distributions looks like we wanna see so as I told you if we consider that in our Markov localization robot doesn't know where it is that the probability looks like this so belief of the zero is the distribution one over the the size of the X and the robot is over there so what is happening here we can say okay we have the algorithm of the Markov localization that that I indicated there for all of the X's we can run these terms over here predicted belief and the belief predicted beliefs comes from motion model and belief comes from the observation model at first stage we had the initial belief then we say okay in this red line we have the observation model what does it mean it means that my robot is over here looks at the environment sees these three landmarks and and based on the technique that we studied the calculations that we studied for example for range or bearing calculates the range and burning and of course that has still error that we say based on the robot that is here but I don't know yet I don't know yet observation that I have is this red line This direct distribution probability of observation m x y x t so so uh now I can say if I have this observation that indicates this term for me over here and I have predicted belief or initial belief as looking like this at first stage now I can calculate this term the belief by calculating this term over there if I apply this term what I have this distribution over here that is result of multiplying this one kind of to this one that gives me this one so now I have believed at X1 x0 was that please X1 looking like this distribution so now we want to continue and uh and let's say robot from here moves to here so after robot from there moves to there now I can shift my belief what does it mean it means that I have motion model and I can say if I'm moving like one meter of course the doors that I've seen also should be shifted right because my I I'm assuming that in whole map I'm moving two meters right then based on the uh the based on the shifts that on the uh on the on the movement that I have and the and the model that I have then I can consider the multiplication of the this one with uh with new observation that I have with new observation that I have to calculate new uh new belief so uh the belief that I have so let's see if it's uh okay from here shifted believe yeah next stage is the observation so let's go observation state by state so after we moved so what we are doing now we are seeing the probability of the new observation so robot is here we see new observation where the uh robot is then multiplication of this term over here with this one over here results me this guy and you can see that the the probability that where the robot is becomes higher here why because this distribution times this distribution over here indicates that most likely robot is in front of door number two and as you can see that that distribution is increased over there and says most likely the robot location is over there based on multiplying to Distribution on the observation and belief that we have then what is happening if I continue robot moves so when the robot moves uh based on the term that we have and based on the uh motion model that we have of course we have noise and that noise increases during the time and my my probability of the of how certain I am where the robot is gets decreased if you see here we have more certainty if we move the certainty of where the robot is gets smaller and how much you move further without observation of course it's this is going to uh that the certainty goes to increase because uh because of the accumulated error on the um robot movement based on the for example year shift so this is whole concept of the Markov localization individual that that shows that this calculation of these simple products of the beliefs calculations of the beliefs and observation models that we've seen we can achieve so of course you can implement it for for your exercise so that only thing that you need to do instead of considering last week's example of the one gaussian distribution then you need to consider whole environmental gaussian distribution and bring it into form of the Marco localization over here okay I think just five minutes of rest then you go to a kind of localization explain a little bit then we go driving to how to bring everything together so first of all we say EKF localization is a special case of special case after Markov localization that gives you foreign was based on the base filter that simply you saw how distributions can make can match together the observation the the shifted control command and the belief they imagine together to believe that to bring the prediction uh the update the belief of the way the robot is and and in EKF uh really present the beliefs as you know belief of x first and second moment that is like the uh movement at the first stage to next stage with mean and co-warias that mean and covariance is based on the probability distribution that is based on the gaussian distribution or in EKF we saw that we can consider that non-gaussian distribution can be modeled too that now we are gonna see how it is happening so we have a note that we say EK localization can be a concrete implementation of EKF in context of the actual robotics problem so how it is again we have the observation one two up to observation and at time T it means that this time the observation is not only one we can have set up observation to in order to apply localization problem and localization again mean that for for now we are considering where the robot's location is we're not talking about mapping we're not talking about the localizing landmark stem cells we are talking about localizing robot itself so that we have the observation that that that some of some of the landmarks can be seen but by extended Kalman filter and based on that we have the uh the identity feature that we denoted as CRT already and we call it as correspondences variable or feature vectors of the oi key so far so as we said we consider that correspondences are known and for each one of the correspondences also we have the signature that indicates which one of the features are which one of them uh those features that are known can be shown in this form probability of the observation given by x t and CT that CT can be included the landmarks that we have so what are these landmarks can be in this example ABC so first initial belief for example if it's here the landmarks that we have that if you want to see how visually EKF basically working so we have initial belief robot moves then the belief uh becomes much less on certain where the robot is and after that we have observation probability of the observation based on the M C1 X1 that that gives me the observational need of the vision and if we can't cut if we calculate the this one as belief X1 and the observation in the Kalman filter we are going to achieve the variety robot exactly is and this becomes more certain why because more certain because this one that where robot was believing to and where the location that robot sees it is is same because of that the certainty increases if they were different depending on the Kalman gain depending on the error of the observation and the motion model that I have it could have been shifted to which one that was more accurate so this is visually how uh how everything is going on so here observation detects for example CT as B this guy over there and after movement I quoted some notes uh the the resulting belief looks like that one that is integration of the both of them and again robot moves uncertainty increases and and we can do the same routine for extended Kalman filter localization in order to find it what is happening but now let's let's mask already last week we've seen this this slide in detail and we've seen that in extended Kalman filter we applied uh linearization of the non-linear function and be exactly how in detail how this can be achieved how it can be the GCS can be calculated that we generally set in prediction step we apply a linearization of the non-linear input model for motion model and here for observation model that that we needed to collect it based on the Coleman gate so column and gain calculates based on the this time uh um non-linear model that if you remember in Kalman filter we had matrixes here we had instead Jacobian matrix that touch Jacobian matrixes was plotting whole uh whole movement of the environment into this turnover but now what we are going to do now we are going to do and see how this can be calculated and how for example the motion model can be matched here how observation model that we studied together can come into this equation so Lord is in your mind that we are going to make it super big algorithms now yeah of course uh to to use it for robot localization so at the first class looks very complicated and big but actually we already studied all elements one by one what does it mean it means that we have the algorithm EKF localization keeping your mind that known correspondencies first of all we are calculating the motion updates over here then we are calculating the measurements of the environment over there how that is happening let's see so first of all let me see what are the points that here I stated a gaussian estimation of the robot poles at time T minus 1 with the the mean and covariance plus a control command and a map and set of observations are as inputs over here that are a little bit small and output is the a new rewired mean on covariance that that finally is over there but let's see how that was happening so first of all we should have a look at the motion update how was the motion update if you remember that was simple that you understand after understanding that for simple we had the XT that was coming from the velocity motion model that we've had based on the X Y Theta we calculated what is the velocity motion modeled by X by Y and what was the Theta so here also later we added the noise and noise is already included over there with uh we had based on this table now if you have a look here looks pretty similar but but if you remember we said we have extended Kalman filter a next in extended Kalman filter we have uh we should accept non-gaussian models too so in order to do that we needed to apply first order tailored expansion we saw how that is working we saw the equation the calculations but finally we concluded that okay G mu t as control command and XT minus 1 can be written in in in linear form that is like it looks like this term over here G and Big G of this thing I'm not going to explain the all the details but now the uh the control the demotion model can be merged can be applied we can apply the first Taylor expansion on the motion model that we have that finally we can write this whole this term over like same as this G that that you can see uh all these matrixes so uh actually what we've done we have the Jacobian of the GT that that Jacobian of the GT finally can be calculated and we have these matrixes and these terms over here that represents the velocity motion model based on the X based on the Y and based on the Theta that we have so that uh that pure total rotation is included over there after just only applying some Mass until your expansion we will actually so after we will achieve it what we thought we'd have a look here in our email we have the uh predicted mean that is the previous mean added by velocity motion model and we calculate the Jacobian matrix of GT that this Jacobian matrix of GT can be calculated can be used for to calculate the covariance that is into this term we just replace the linear matrixes of the Kalman filter if you remember we said that we are mapping with linear matrixes now we have we want to consider non-linear gaussian that nonlinear gaussian is GT here based on the Jacobian matrixes that we calculated and this will be placed here and this this term that is this term goes into the G and G's are are going to be used to calculate the covariance that is non-linear so if you have understanded this part over there in this slides that we had separately there is not big problem then applying first failure equation that we studied later and another situation another slide then bring it into the extended Karma filter as a velocity motion model code so this is the first part and second we need to do the same thing for observation model observation model we've seen together today how for example for range sensor it can be work so uh we need couple of things here of course we need error Matrix of the uh of the observation there we had already included in the model that we have with the with the equation is over there with the w that you've seen in built in but here we need to have the observation error then we have a for Loop that in for Loop in for each one of the observation for each one of landmarks for each one of the landmarks we need to calculate this term this this part here an update the Kalman gain and after updating command gain for for all of the features of the landmarks that we've seen from the environment then finally update the mean and predicted belief and collected Collective motion model so how that is this part can be calculated this part can be calculated Again by linear approximation of the observation model by applying first order Taylor how that is like let's come step by step uh here I represented the observation the observation or Landmark I Iceland Mark at T so I'm representing just one that includes range bearing and signature we today studied and we saw that range can be represented as first line including understands bearing can be archanged on Two And signature comes from directly to the map added by some noises with zero mean and and like here Epsilon or uh or if I error on the on the covariance this n is also for gaussian distribution representation so we uh we represent it with N2 so for each one of them I add the noise at the noise 3D stand that for each one of the landmarks I have the noise then after that now this observation model that I understand we want to apply the tailor approximation the same equation that but this time with h if you remember in the chapter we were talking and this Edge is the Jacobian of the edge at predicted mean that Jacobian matrix looks like this and what we need to do we need to do rewrite this term over here that that gives me the uh the robot poles based on the observation that I have and replace it with the estimation so so to do that this term that we are here with Jacobian matrix uh so one point over here this this that I indicated over here is the predicted uh predicted mean that this predicted me in this slide that we've had we had a certain positioned over there IPS certain pose of the robot now since the observation since the observation is going to collect the previous stage we replace it with predicted mean so that the predicted mean will be calculated here here then we replace it on the observation that that observation is going to collect this this guy over here that is calculated with the motion model then that Jacobian matrix uh we need to calculate all derivatives from this term that is for range bearing and signature and finally if you apply it you you get this term over here that that this term is the h i t that is Jacobian matrix that I'm gonna use it over here to do that if you have a look is like first we get the signature then the the distances of the some some helping selfie helping variables that we had already in the uh in the calculations of this term we break it down already in the extended column filter already there were the calculations then observation then Jacobian matrix of the observation then I'm using it in the uh in the Kalman gain calculations with this Edge in order to in order to collect the previous stage so observation the QT the error of the observation and and finally after uh calculating that we can we can update our mean and provides this is pulling everything together everything should be very clear unless maybe you get a little bit confused with the how this can be calculated this Matrix with applying tailor expansion first photo expansion that is just math you need to if you want you need to study more to see how you can from that term over here this term over here achieve this step that's it then plug it into the uh plug it into the extended column filter he's just replacing the this all of these is replacing the this one that we understood already like for example this Edge now we calculated how to replace it with the observation model this G we saw how to uh how to bring it from a motion model then plug into there this super big big algorithm then finally the same thing Mina provides so kind of the efforts of four week coffee study comes into one chapter one one algorithm okay in this chapter we discussed the observation model for lighter we discussed the measurement model for the environment then we saw briefly Markov localization that is Valiant safety base filter that was simple then we saw how eks that also known as variance of the Markov localization but basically we refer it basically all both Works based on the base filter we side and uh and now for next upcoming lessons what we are going to do if I want to give you a perspective now later we are gonna see okay we have some problems still we've extended Karma filter who can guess what it is we saw Kalman filter we saw its problem then extend we we introduced extended Karma filter now what can be the problem of extended Kalman filter I mentioned it one time next week you have exam the Jacobian matrix I said that's costy you remember I said Jacoby and Magic's calculation is costy because because there is a big Matrix every time we need to calculate for all the things that are happening because of linearizing non-linear non-linearity we added this one that is costly why because let me show you over here that we say in Kalman filter everything was with mean and covalience everything was with just two values me and covariance two values were showing everything to me just need to update that but later we see that okay what if we have something that is none then we have beat Matrix instead of two values these two values mean and covariance instead of these two I have a big Matrix and and if I have like like 100 of landmarks just you have 100 times true in Kalman filter but here 100 times maybe 100 then that's too big and if you wanna 100 times 100 is okay but but but in simple feature detection algorithm you you get thousands of features from one frame of image then for each one of them you should create this one and that's super big calculations and that if your problem is complex then extended file monthly to get in trouble so that to improve it next lesson that we have we will introduce unscented column filter as a new technique to improve the problem okay any questions so I can dismiss today's course next week you have midterm uh that in midterm you can use these slides you can use the book and you can use the example codes and that's it no internet no communication so uh just if you practice what you've studied in the class it should be enough for answering the question okay if there is no question I can dismiss the class thank you |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH9_SLAM_for_robotics_Histogram_Filter_for_Robot_Localization.txt | foreign [Music] hello everybody good morning I hope all of you are fine so today we are going to continue with one new algorithm first of all then as much as we have time we move forward uh after today you don't have homeworks anymore but uh you're supposed to think about your projects for this course for students who has both courses of the reinforcement learning and Islam they are allowed to work on same project with one one type title but uh if it's like because in reinforcement learning we allow that you can work with two people then if you wanna like work to then work same project for discourse and that course then the project should be quite uh big because then it's like four four people project for just one uh for free with fun titles because of that uh you should be aware of that but about the details of the project I will uh post soon so that you can start to uh to do whatever you want to do or my suggestion ideas that I will give you after this chapter also I also I I discussed some open problems those can be your projects during the course if you look I mentioned multiple like I think about four open problems but the next chapter also we have an interesting title interesting topic that for occupancy delete mapping how we can solve this if for example our general Network or deep learning if you are familiar with you can move towards that that title too but if you are not familiar of course uh mathematical days of the solving different problems in the uh uh in the topics that we've studied would be very interesting to to seeing how to for example do something to improve it how to match them or or give some some kind of combination of sensor Sensor Fusion to to to plan to to to localize or map the environment anyway I will give you some suggestions uh but also you can think yourself too we do of course I know that the time is limited and based on that time that you have uh it should be sufficient to do project any question about anything okay so let's start with the histogram filter today uh histogram filter is applicable for many different applications especially in image processing it's very famous to do some uh some image processing tasks I mentioned robot Vision but here we are focusing on the robot localization we want to see if there is any way to use a histogram filter on robot localization we already know base filter and now we want to see how what is the general concept of the histogram filter and if it's possible to merge base filter and histogram filter together in order to be able to localize a room so the motivation is based on that and let's see how it looks like so first of all in this chapter we will talk about the non-parametric filters and we Define what does it mean then we move correctly toward the histogram filter localization and you explain you expect it after this chapter a small chapter to know how these concepts are working and how we can really uh bring the uh histogram filter to the game of the localization of the uh robot that we have here so keep this in your mind that we have localization problem and mapping problem so during the course you usually try to split them because they are kind of separate problem although we have to solve them together but to understand different algorithms we are separating how localization is working and when we are going to map it how we can have mapping parts and how we can manage them together so basically the idea is is generally elected so in order to understand the course we have some uh course of today we have some definition that you should be careful to understand that so first of all we have posterior posterior is pro is uh a probability of the assigning observation to groups of given the data so when we are talking about the posterior you should always think about that the data is given and the data groups of data is given it means that like robot is moving in the environment and we have the observation and data for the robot on the other hand we have prayer that it is like before collecting the data so uh so we haven't seen the data and we call those scenarios as clear and basically but for understanding it is like much much easier you can consider that lens like robot is here and move to the next so first one can be clear next one can be posterior state so current state and next is State kind of like that so this is very common to use it in Islam algorithms Korean posterior we're gonna also in some cases during course use it so keep this in your mind to make sure that you understand the concepts we have different non-parametric filters that uh they are basically our replacement for gaussian techniques so in gaussian as you know pretty well we have the distribution and we were talking about the mean and covariance in order to localize it but now we want to change it kind of to non-parametric filters we want to see whole game in different scenario how and what does it mean it is it is like we say we don't have fixed functional form of the posterior such as gaussian that I explained and they approximately they they kind of approximates the the posteriors by a finite number of values so that we kind of want to instead of having one gaussian distribution have many number of values in order to say where the robot is by explaining this you may think okay how that can can be happen if if you have number of values in order to say where the robot is uh that we're gonna uh see soon we can kind of say okay if I'm localizing robot I'm robot in this room and I want to localize myself instead of talking about just gaussian distribution I can discreticize the environment whatever we're doing in many different techniques and saying like what is the probability of being here what is the probability of being there instead of having just one value to showing that we can split it so uh based on that if you want to Define it in non-parametric filters we can say that uh they are like um [Music] relying on decomposition of the state space it means that we cannot kind of split the environment to many many different probabilities instead of one and now press the button and the uh the values are usually based on the cumulative probability of the posterior density in compact subregion of the state space that says very robot is so of course these Concepts will be more clear Zone with saying visually what is happening uh we say some of the uh approximate approximation of the state space and where the location of the robot is coming from by random sampling uh from the posterior distribution that we have based on the prior and posterior that I explained to you and the uh and the number of these posterior ampere approximation can vary by the uh uh by the number of splitting or number of decompositions that we are doing what does it mean it means that like if I have this state space and I want to decompose the environment how much I decompose it is smaller spaces kind of you can think about grids if I it's related to smaller grids I have higher accuracy because instead of saying I am here so moving to the next stage can be can be one big step I can split it to smaller States so that I can say I have high accuracy on the prediction of the pre-run posterior for my robot so is it clear so far to understand this better you can have a look at this figure over here that this is the uh decomposition of the environment so that it looks like exactly a grid that you know and you can see different probabilities like darker Black Point over here is like a hype robot most likely for example can be here and and less likely is here based on the the color that we have that it is representing the amount of probability that robot is there so we said the composition techniques can be ecstatic and decomposition techniques can be dynamic what does it mean it means that I can say okay this is my state space and environment I want to localize my robot I split and decompose the environment to this static number of periods then I start to develop some algorithms some techniques that today we are going to see based on histogram filter how this is work but on the other hand what I can do I can do this side If instead of decomposing the environment for a static number of uh kind of small elements or or small spaces I can say I'm gonna become posted in Dynamic way what does it mean it means that So based on the probability distribution that I have the area that I don't know the probability I can say okay this is like big space hold this area but these spaces that are smaller and I have some ideas that uh how uh what what is the How likely robot is there I can make them more precise how much I know more about the environment I can make a grid sizes smaller so that give more chances to more accurately save where the robot is so this is dynamic technique of the uh decomposition that um that we can we can uh specifically rely on the the posterior distribution of the very robot is and and work with but of course working with Dynamic maps and dynamic decomposition is harder than a static one today we are going to basically talk about the uh what happened today today basically we are going to talk about the static one but uh but we can easily beat some challenge with some considerations also move to the dynamic one is it clear so far any question here because we're gonna now uh see how this is happening how we can we can't work on it uh also I need to mention that like the figure that you see in the right side for density tree also one of the techniques that we can uh we can work to do that is uh density tree approach that is famous we can use different techniques but density tree approach is also one technique that we can achieve it so uh and resolution of the what what we want to how we want to localize it we can we can change it Dynamic dynamically so for non-parametric approaches when I'm talking about non-parametric approaches I mean that we are not talking about gaussian distribution anymore we are talking about uh kind of grid-based decomposition that we want to say the probability of each grid where the robot is okay one of the technique is adaptive approach so uh it adopts the number of parameters to represent the prayer online in adaptive approach second approach is uh recurs resource adaptive approach that in resources adaptive approach we say Okay based on the resource that we have on the embedded system of the robot that that that is like if you wanna uh basically since we are talking about localization you have limited limited amount of power that in online form you can construct the map localize the robot location based on that especially on the embedded systems we have resource adapted approach that takes decomposition is based on the amount of power that we have it can be statically defined at the beginning or it can be dynamically based on the resource that can be allocated to process it like you can say in online wave when robot is moving you are going to localize it so you you Pro your robot processor is busy with calculations or something then then dynamically you can decrease the accuracy over there make it bluish but at least you can localize it's not lagging you can blurish localization decrease at the accuracy decreases or increases dynamically by based on the amount of processing power that you have available to do the calculations of for example grid Construction maybe this is like more reasonable when we are talking 3D mapping and 3D Cloud construction that then then this concept is more understandable there because it's very costly over there so it is known that this approach plays an important role in robotics and enables robots to make decisions in real time because if your robot is like humanoid robot or or flying robot that is flying or walking then if your trades are become becoming busy to do the constructing the map and misland algorithm that control part will be in problem lagging there is unacceptable and and due to uh deal with this problem we can say okay like the priority of this threat is higher whatever resources that you have allocate to uh the second part of the algorithm that we have because if you have like if you don't use the resource adaptive approach then then you may don't don't you will not be able to process the data in online form and construct your map and you lose it if you have limited resource but if you have Dynamic then you still can deal with this problem and have some on accurate but still you have localization of your robot in the environment so to talk about directly a histogram filter histogram filter also decomposes the state space into uh finitely many regions and replace it represents the posterior by histogram so how this is happening first of all let's have a definition with the histogram a histogram as is a single cumulative probability of each region for each region of the whole Google space that we have so kind of this histogram filter we want to bring the probability for each one of the regions that we decompose from our environment in order to be able to localize where the robot so one of the uh common techniques and best approach to do this is using base filter which means that the concept of uh bringing the probability form of the histogram filter into the base into the game of the localization is using the concept of Base features so in order to do that we should first discuss that in this security spaces we had this Security based filter that we've already seen if you remember we were discussing about the base filter and said it is continuous and we said if we put Sigma in the equation it is this criticized and we can say some of the probabilities we can calculate it you solve examples and homeworks by by simply doing some of the probabilities and that that was almost discretization of the state space that we have okay so uh this one we started already on the other hand in the continuous State spaces uh for example histogram filter can be applied but in order to again apply it we should uh apply the discretization that is kind of similar concept of what we have here with disability based filter but but it comes from the uh histogram filter technique itself So based on that concept we can say histogram filter decomposes the continuous data space to finitely many regions that we have the new status space actually and the idea is that we use uh we we should be able to use the security base filter to apply what we want to do on it so what does it mean it means that let's have let's say we have a region uh and and the environment so in that environment can be splitted to range of XT so if you show a whole environment has 60 range of XD can be can be split can be demonstrated as splitting the environment to small regions for example we can say uh X1 t uh Union of the all the X ones to x k T's can represent whole my environment so each small region that we are splitting we can call them as x's and put some labels on it like based on the region X1 in time T that we are seeing you can look at details and consider these Tails as each one of the x's and Hold Us hold the XC as the um uh the environment that we have so I've noted some notes Here for readability there's state of the robot uh position based on so uh all those we have splitting the the decomposing they become decomposing the environment since we have time T also so we can consider that also it is representing where the robot is based on the time T since we are bringing the probability into the gain but but also range XD as I mentioned is uh representing the um the whole state space and XK is whole environment at the end as uh as a state space so end of the uh Vision that we have including there meanwhile we are defining this and we decomposing the environment we have some limitations one of the limitations is saying is saying that so we should not have any intersection between these areas by um by default because if we have intersection it means that if they have overlap then the calculation should be considered that too because the probability of the being here or being here can affect each other if they have overlap so because of that basically we say the uh decomposition is like drawing a line and splitting the two two areas not not having overlap on the so this is the limitation that we say okay uh there should not be any common between xkt and xit and and of course they I should not be K because otherwise it represents the same decomposed region is it clear okay on the other hand uh the union of the all should represent again the range of the XT that we discussed so the kind of we say if you do the decomposition if the environment is not like Square which is like circular after after the splitting the range should represent the same environment you should not drop anything in the environment and this is kind of also challenging especially if you don't have if you have weird shapes and there are different techniques also to do this like if you have this shape of the environment then it's not like easy to grid it because when you do greeting then you may have this over there so that that says that you should not drop this part in the environment and to do this we have different algorithms different techniques too that decomposition based on triangular technique that uh that you you will be able to decompose this part for example you have this region over here how to do that there are some techniques and and optimization techniques and also values of papers how to do that for example one of the most common ways or we can do that again decompose this area to small triangles we can do this as as smaller so then we have small regions and we can decompose it and we can consider it and bring it into the cake so is it clear yeah when you when we are talking about uh the environment like class everything is easy we can create it easily but but in those environments that basically usually is like that is a little bit challenging that we need to know how to do that finally if you consider these two limitations it should be fine for our technique that we are working on so we say decomposition of continuous State space for a multi-dimensional grid where each grid cell is defined as like this one can be shown here that you can see we have a grid and we can say X1 t x 2 T and we continue I mean continue to x x KT at the end so uh we also have a concept here that is better to know we say we have a granularity of the decomposition that we can control trade-off between accuracy and computational efficiency that that as we explained already based on the amount of computational resource that we have we can say okay it is granularity of the decomposition that is kind of common concept to know in Islam techniques but what are the steps we want to directly move to uh see how the steps of the histogram filter is the the whole idea is simple uh some some equations just uh we just we need to use in order to be able to first of all we say assign a uniform probability to each state x t within the each region X KT as initial belief so your robot is going to start in the environment and we said okay already we decomposed environment now uh as initial State we don't know where the robot is right so we should have initial belief where the robot is so since we don't know we consider that we don't know where the robot is we can say okay let's have initial belief that initial belief can be calculated by this simple equation over here that probability of x t where the location of the robot is because we are talking about localization so is the probability of KT over all the probabilities that we can have it means that we have the volume of the region X K and looks like something like this that we decompose the environment then each one of these points and this size shows the probability of the where the robot is since the size of these circles all right same we don't know where they are and it's kind of uh they are they are they are the same probability where the robot is so here is like uh putting some values in each one of the grid cells How likely robot is there and we want to with playing this and changing these in order to be able to localize the robot this of course representing some numbers also that that in exercise I think we have have one example let's go so uh uh the same thing that I explained with each region we can only uh maintain the weights for each region and then we are also when I'm calling about the weights and we are talking about the weights keep you keep it in your mind that we are talking about the probability of the where the robot is the weights for each region so weights is referring to where the uh where each one of those are and if you don't know uh the equally distributed it means that yeah over here let's say simply probability of the x t where the robot is can be defined by these two to initialize my initial belief we can say the probability of KT over all the probable all the the size of the region that I have the the size of the xkt is like since we have 25 grid cells here 1 over 25 becomes 0.04 so that I can initialize my oh my my initial belief looking like this so simply in Grid cell you put values the initial belief very robotics it means that How likely where the robot is we don't know same probabilities now we want to kind of find out how we can change these probabilities in order to say okay more likely robot is here increase the value of probability here and decrease the other ones that finally sums up to one clear now what we need to do as I mentioned to you histogram filter is going to be applied on base filter we want to use the concept.base filter and in base filter what we had we had the prediction instead we had the correction step in prediction step we have the motion model that robot is moving in the environment and based on that Movement we were we were having predicted beliefs and this predicted belief were coming from from previous belief and the motion command the pauses given by previous polls and motion command that we ran so this was one state uh multiplying by previous belief uh the previous belief we have the predicted so now you can think yourself how we can manage this concept into histogram filter vivana we want to adopt use it in histogram filter in decomposition based form not gaussian distribution anymore on the other hand for the correction what we've had the belief of XT new belief actually were calculation of the predicted belief that were coming from prediction step based on the emotion model and the observation so the observation that we have is probability of the observation given by the robot pose that is normalized and we're giving me the predictive the the the the the belief that where the robot is so motion command observation based on division were giving me base filter as recap what we've done over here we said that this integral of the belief can be written as become as as descriptive form that we can simply replace it by zigmas of the probabilities that should be one and now we want to maintain this again and use it in the histogram filter and if you want to have a look at the descriptive based filter you already did it and implement it also so for all of the case to this first step predicted uh probability of the sum of the probabilities that we have and then this is like uh the algorithmic form of the prediction step and here we have the correction steps like ETA the probability of observation given by observation times the predicted probability that comes from there exactly the algorithmic form of the distributed base filter that we have over there so clear of course must be clear for all of you we've studied it many times and applied Kalman filter extended Kalman filter on send it Kalman filter on this technique now we want to bring histogram filter into the key of course we will have prediction step and correction steps at the prediction step what we do we want to calculate the predicted belief predicted belief the of the integral of the probability of the poses given by poster motion command times the the belief that we have so what we can do is that we can write predicted so we already know that right knew it now we can write it as predicted belief of the XT that is equal to some of the some of the belief the previous belief and some weights so kind of Vedic belief of the where the robot was and what is the weight over here the weight is coming from the grid and and the grid cells that we decompose based on the histogram filter concept so if you remember I said that we have weights and represents the grid cells in previous dislike let me go here here so or here doesn't matter these weights these are called as weights of How likely where the robot is now those weights are coming into the game by replacing this part by weight and and multiply by multiply them by exactly the same concept that we already have the belief of the XT minus so is it clear for everybody base filter we remove this part and we place it with weights weights are coming from the composition of histogram filter that are indexed by time T and the ice Grill itself ice a region that we have okay in order to be able to calculate predictive beliefs but how these weights can come and mathematical mathematically calculated we can say the uh and the uh the predicted weights are some of the the uh the debates time the probability of x i and XJ given by motion command that I have it means that so I'm going to run the motion command and probability of the motion command that can be run on my technique that I have applied by weights and sum up all of them represents my weight or for the predict the belief that I'm going to calculate the predictability in base filter what we were saying in base filter we were saying so robot is somewhere motion camera we run the motion command and and based on that motion command we are updating the predicted belief right and now that is coming from here and that is coming from the grid cell that I have so whole grid cell that I have I apply the motion command and that motion command changes the probabilities over there by this equation over here how that is happening that is happening looking like this if you want to visually understand so at the beginning we had the circle sizes all same right let's say we're running motion command like this from initial release so robot is moving like in this direction One Step if robot moves in this direction in one step what happens most likely if we calculate the prediction step the grid cells should be shifted to the up left what does it mean is it means that probabilities of these being here location after here will be decreased and probability of robot being over here will be increased and it makes sense like wherever I am in the environment if I move this step more likely I'm over there not not there right whole probabilities of the grid cell will be shifted to the left up wherever I am it shows that in worst case even if the robot is here the probability of being in that cube is higher although it may be initial is here but says more likely robot is here and what happens if you continue that so if we do one more step of going there so again the probability will be shifted more lightly and let me wherever your robot is here if you always uh run the command of up left after 100 times if there are no obstacles or something certainly you are at the corner right you're just running motion commands certainly wherever you are will finally end up there so this says the same concept of the histogram filter in first stage of the updating motion just just calculation of the grid cells and updating debates after exact weights are coming from the probabilities there from initial if you want to write whole equation in one one term we can write it s predicted belief of x t is equal to 2 times Sigma I 1 to n j 1 to n that represents the uh the the decomposed grid cell there and the weights of the jst minus one times the probability of the uh the X I given by x j u t the the motion camera that I run times the previous belief that where the robot was so this is the calculation of the prediction and Visually you can see what is happening over here by shifting all this thing so one time can be then then if if like we robot move to the left then hole will be shift to the left probabilities if we run the like from here to the right then whole probabilities will be moved there and based on the motion command robot is running this will be shift and help us to make it more certain where the robot is now we should see okay after first step of the running motion command then how update is working update of the environment we can say update by uh uh by sensor or Vision or whatever robot so what was what we had we had the base filter we said that we have the belief that is updating of the predicted belief and the observation so the observation comes from environment by sensor that I have of course the sensor model that is like implemented range bearing or something should finally give me a probability that this probability comes times the predictive belief the previous slide then give me the final belief now I can use the same idea of the histogram filter to bring in the weights into game so we can write it again some of the weighted predicted beliefs this time so the predicted beliefs and this term over here is going to be debates that come from uh histography so how we can calculate the uh debates of the uh debate from there looking like this term over here so this term over here just looks a little bit complex because um because we have normalization over there through otherwise uh nothing special just wait it uh the the weighted probability of observation given by x i Dot that that shows my observation from environment times the the debates that come from grid cells then this is over some of all the probabilities of the weighted observation that I can have that is normalization of the weights that we can so observation over this one normalized and will be replaced over the term that I have over here so I noted some also points here that we have the if you want to describe it in Prior and posterior form it is the prior weight that that prior weight is this term over here times the probability of the measurement that I have over some of all that is for normalization prayer over observation and then normalize we don't have very complex things just just simply it comes from grid cell and the terms of the base filter and if you want to rewrite the equation just replacing this term over there then we have this this belief that we can write believe after x t is equal to uh equal to some of these term times predicted belief so that this predictive belief is the same belief is the same this part goes instead of base filter normalized observation you see normalized observation that observation is over here and that is normalized based on the weighted that comes from histogram filter combination of the two things weights of the histogram filter Plus uh velocity applying the base filter on the histogram this histogram filter the idea is decompose the environment yeah and with decomposition show the probability of the what is happening in that region the histogram idea is like this histogram filter idea is that and bring we are kind of bringing that into game of the localization kind of forming it to say where the location of the robot is with that idea and these are showing probabilities and where the robot is shows like more likely now my prediction says that robot is over here after some movement with observation with the update it will be like more likely and bigger Circle as you can see over here so new observation comes if the observation like robot throws over here with the calculation of the term the probability grows around here by updating that then it says more likely robot is here after after moving and more certain like more more movement more certainty on the observation and more probability come from here so more likely if you say observation these observation says probability of observation time T that I am in x x i this x i for example can be this one more likely I am here more likely the probability increase if I increase these other ones will be decreased right because some of them all should be one then then I'm doing localization indeed but of course when observation says there or or observation see some objects that says I'm here based on the Range and bearing that I'm gonna show you now like I'm here I see that landmark and I say okay more likely I'm here then that probability comes and updates the whole whole grid style then we can say we are using the base filter in order to Soul localization problem any other question is it clear everything so if you if you understand the whole concept then then you see that it's very easy just base filter change a little bit then we have histogram filter update so in order to understand it better of course we keep continue to give you some practices in class this example comes from I think I did some some some development myself but also very similar uh one is in Python robotics too that you can see here um here this is the robot location this is histogram filter and this is the robot location you should go and run it yourself today too so the robot location is here and robot sees this a landmark okay so after robot sees the landmark why we have distribution like this the probability of being here more likely the robot is high after robot sees the uh object is like that when I see that landmark I I haven't seen any other landmark and more likely I can be in circle around that Landmark because I don't have any reference point everybody understand so I see that Landmark everything is blank I don't know my probability is like maybe can be here I can be here I can be here I can be here I can rotate all around that because I don't have any reference point and and the grid cell update will looking like this but after the robot moves a little bit update of the uh motion command and uh and and observation then the robot sees like one two landmarks and when the robot sees one two landmarks then then more likely says okay I should be in middle of these in Grid cells because now I see that one and I see that one then it's impossible to be in circular form and the the concept of the update in Grid cells come from there but what's the any question very very similar you you did you a little bit deviated from what we want to ten so yeah okay uh then that's better than you can easily understand and today is easy peasy and the idea is like when you're doing practices you will see in future the other algorithms you see will become very easy to understand you you will see oh this is like and when you know the base of the uh the the course and the important algorithms the new ones the whatever the complex they are you see that with reading oh they change a little bit just the equation is changed and they they claim we did lots of like very extraordinary things after knowing the underlying Concepts and algorithms and that's the nice part of the course especially in reinforcement learning we have that now now the students know all the simple things even you go to end part you study you they will supposed to understand everything because because it's like mixture of whatever we studied that's it so 10 robot moves sees these two then the distribution is like that over there and especially when uh you see that like the red ones has more likely where the robot is and and and robot really is there but but prediction is like chain most likely is here but there can be there too but after seeing more landmarks the red part is smaller and and most likely says the robot location is here and the prediction is kind of more accurate you see more landmarks so this is happening by uh histogram filter localization that um that you can check the code over there and the example over there I usually give a practice or homework that I don't go to give you homework try with different sensor range and obstacles the example yourself you need to download it run it and change the different sensor range to see what's happening when the sensors like because the range that we can scan the environment is limited right so and it's in circular form if you decrease it what is happening and if you increase it to see very large amount of environment then what is happening then are you supposed to do that and also uh also then uh you need to draw the simple follow chart of histogram localization the core to make sure that you understand what are the steps that is happening uh to uh by looking at the slides and the code together to see what's happening so this is what you need to do so this chapter we studied non-parametric filters decomposition techniques and histogram for localization so I think you can have some time to do that then we have another chapter that is the composition of the occupancy grid map and that's also a important topic and a little bit lots of mass we have again there uh to to see to see we now talked about only localization now based on this occupancy like this map if you want to construct the map then what we need to do then you need to calculate everything the range bearing the construction math how can we happen and we will see in probability form that's hard we will bring it to logout forms then try to solve it mathematically then constructive map of really where robot is because after you now practicing you will see that whatever is happening robot is forgetting like after moving seeing the after I'm here I'm here a little bit moving far nothing or everything is vanished we don't have math because of that so in next chapter we will see so practice this let's see how long does it take we may start that chapter today too okay thank you so let me share also slides with you or you can go to python Robotics and click on the histogram filter you can directly have access to that one |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH11_SLAM_for_Robotics_Particle_Filter_Localization.txt | okay good morning everybody uh today we are going to first talk about the one of other algorithms that is famous in Islam and uh we will see uh how it can improve the existing techniques that we studied so far but also we will see that there are some problems with the algorithm that we are going to see today the algorithm is particle filter and and today we will focus on the particle filter localization because it can be used in different techniques and solving different problems but we will see how we can adapt particle filter in order to solve localization problem so in this chapter first of all today we will talk about the algorithm itself particle filter then we talk about the Monte Carlo localization that that comes from uh and basically the general idea is based on the particle filter and we also talk about the fastest land and we will see uh how we can use benefits of the existing technique that we will study with a particle filter in combination together also of course we will talk about the one of the techniques of fastest lamp for fastest land there are multiple different techniques that depending on the application we can use them so first of all let's have a definition of what we want to see we say the particle filter is alternative non-parametric implementation of the base filter so if you remember we had some techniques that they were non-parametric and it means that we are not relying on gaussian distribution in on mean on the covariance So based on that we have non-parametric technique still over here too so what is it uh first of all the the basic benefit is that we are removing linearization that we were doing in other algorithms for example in unscented Kalman filter we have to do linearization of the nonlinear function that was costly and we did lots of effort in terms of mathematical equations but luckily we don't have that complexity over here anymore uh what is happening with uh particle filter we say it is approximating posterior by finite number of parameters so it's looking like the histogram filter but but we do it in different ways in histogram filter we were making we were making a grids of the distribution and we were allocating probabilities to each grid but now we want to do something else we want to increase the accuracy with particle filter itself so uh if I wanna then uh have a look at the beginning the differences with the part if the histogram filter that we studied we say how the parameters generated are different that we will see how they can be uh they can be done and how we can distribute it in the environment so for now you can consider we have some particles that we will Define what those are and we don't want to drop them as probabilities on each one of the grids that we make rid of the environment anymore so the key idea is that we want to represent the posterior belief that we already know by set of random State sample that are drawing from the posterior itself to in order to calculate the period how this is happening uh visually we can say okay let's have this distribution or a non-linear function of if that we already know that uh we cannot use this uh this form of distribution in our algorithms like extended column filter or unscented Kalman filter by because it was not caution and what we were doing we were converting this to the gaussian distribution later we were able to use it but now here we want to kind of if you have a look here we want to kind of have the particles that they are showing the density of these probability distributions uh function that we have so how dense they are for example here the probability is higher we have more dense and much more particles over there that of course this is not directly using a particle feature but this is the idea that kind of says instead of instead of saying How likely where the robot is if you talk about the position then instead of having this probability distribution we can throw it out and we can say how dense the points are here then we can understand the same concept by number of particles that we can call here is it clear here this part for everybody so for example here we have less points less likely if we talk about the location localization less likely robot will be here most likely robot will be here because this is denser and this represents exactly this distribution for us so that without any effort of conversion of the gaussian distribution we can show the same scenario with particles but of course it's not that easy we will see uh what else and what we should do what are the procedure but this is the general concept of uh uh for example in the localization what we can do so other point is as I explained to you instead of representing distribution by parametric form we can show density of the normal distribution so that it represents distribution by set of samples drawn from the distribution that we can call them as these Blue Points as samples to so the particle filter represents approximation but is non-parametric by approximation because of course when you are converting that distribution to samples uh then you may lose some data depending on how much now how many number of samples you have because because here when you have distribution itself it means that like when you have this it means that for each one of these points you have exactly the the samples if we call and the idealistic way is like plotting all of these two two samples but but that's not uh that's that's what we want to avoid we will discuss also because of that it is uh the approximation so that we can say it can represent much broader space of the distribution uh uh one of course simplest one is uh caution but non-linear functions can be represented to as we show and in particle filter samples of the posterior's distribution are called uh particles as you will see over here so we say we have set of particles so each particle is a sample from the environment that we have okay so we call it sampler posters so we have set up samples that these set of samples includes each identical sample in the environment for example xt1 xt2 up to xtm that uh that for example these each one of the each particles can be uh can be represented the true value of the for example robot pose that robot post can include the X Y Theta for example so each of my particles now you can imagine that says like if my robot is here uh and I have I can have many particles that the pose of them are different in the environment and that that pose can be the X Y and Theta so that represents How likely will robot my robot is and what is the orientation or angle of robot heading to clear so we say m what point I have here m is number of particles in the particle set and usually is large number of these M says indicates how many particles you are if I want to have in the environment so uh the rule of the including a particle in set x t can be uh can be defined but if we say ideally the x t should be proportional to base filter posterior belief it means that [Music] um uh B if we want to if you want to like ideally present exactly what is what is the distribution we should plot and bring all the points exactly to don't lose the data and if you have gaussian distribution for example then then the the sample set or particles should be exactly representing the same uh the same distribution that is too high if you want to do that because of that what we want to do we usually have levels lower samples instead of having like millions of samples we can say okay just having like 10 percent of samples can show can show my distribution still if you could be enough to to show the same concept so that sampling can look like this we can say and in the set of XDM setup particles that I can have we can bring how we can bring particles inside the probability of the XD given by observation and control command so that generally it means that we want to sample particles with the probability occurrence that we have that can come from observation and control command it means that the distributions that I have indicates the probability of the pose of robot that that distribution that indicates the pose of robot can help me to choose the samples that I want so it means that when my observation says okay I see some environment most likely robot is here okay previously our probability distribution gaussian was like around here right so if it's 2D like around here because my observation says most likely robot will be in discussion distribution so now if we want to bring it to sample form we use the same probability concept to sample this time instead of having that distribution that can come from two sides observation or control command or automatically that they have also different distributions also but they can help me to sample from environment or better example like if I'm the robot moving in the environment and now I know the particles and if I want to sample how the sample I choose I would choose I would choose the samples that more likely says I'm here I would like to have examples or samples of the particles of the problem that indicates where the robot is and where the pose off the road so we say a sub region of the state space with more populated samples is showing higher probability of the robot through pose or state so that those particles when the robot is here if it's more populated here and in that corner there is no I can say more likely robots so all the concepts that we discussed are same just we remove the uh for example gaussian distribution as representing a mean and covariance Edge robot is the particle so far so similar to previous techniques that we've studied particle filter also is relying on the base filter technique base filter algorithm and it constructs the beliefs of the uh where the robot is in recursively form of the belief based on the previous belief on the time step that we've crossed so same concept predicted belief and belief that that we can also say the belief of 60 and belief of the XD minus one that the whole calculation it comes from here and it means that when we talk about the base filter it means that robot believe that previous calculations was correct and all calculations comes from previous calculations and we have online Islam again so all the calculations is online not in uh considering all time studies of previous occurrence of the particles where they of course we can consider those two then if you consider those then it will be it's not it's not it will not be online Islam anymore foreign as you realize so far now the beliefs are set of particles and the particle set XD comes recursively from set of previous particles so here we have the belief here then we talk about the particle set for everything so it means that in time T we have environment map of environment we have lots of particles each one represents where the robot is and very deciding and time t plus 1 we want to kind of play with those particles to see how we can we can update the new particle sets we will see how to do that it means like kind of robot is at time T something happening robot is moving observing new data then previous particle said we should sync how we can update those to new particles set to more likely say lady robotics now you want to talk about these steps of particle filter step by step is simple let's see what's happening first of all we say randomly generate a bunch of bunch of particles in the environment is like seeding like distribute particles in whole environment considering that we don't know where robot is so it can be uniform distribution of the like something similar to what we were doing in histogram filter we were giving the probabilities of uh the equal probability to each one of the grids at the beginning here also the same distribute the particles to the environment randomly so that uh if we want to solve Islam problem localization problem we have position heading and the also the weight so position says okay where's the X Y heading is like to Theta and the weight says the probability or How likely that particle is important also so that is it is also the one element that we want to calculate so after first step randomly generating bunch of particles we have a prediction of the next state of the particles that to do that we move the particles based on how the prediction of the real system is behaving for example if our robot we have lots of particles and our robot moving forward of course most likely all the robot all the particles should move to the upside because because we are we know that we know that our robot is moving one one step forward so most likely my particles also should shift to the up so now similar to uh histogram filter you can also think that if he if he put lots of particles in the environment and if if your robot is moving to this side all the particles move to that side finally they stop at the end right and if I'm moving for a long time finally also particles will be collected there so with this concept only with automatically you can see that okay this makes sense then those particles will be collected there and more likely robot is there too because all the time moving to the left so this is the uh general idea of this step so after prediction similar to base filter we have the updated step in updated step what is happening the the observation is coming from environment and the observation changes the weighting of the particles based on the measurement so here David says which one of the particles is most likely the the particle that we want we are not updating the position of particles anymore here like previous ones here we say Okay update the weights of those particles that we moved How likely which one is representative of our robot most likely depending on observation that can again rely on the pose that pose includes position and the heading direction of the road is it clear this step so here we have differences with previous techniques in all previous techniques observation we're updating the collecting the last step of the odometry so we had the motion model moving and every step we were updating the data over here to there too but but in particle filter we are updating the weights instead of correcting the pose of those particles we don't want to move those particles anymore just we give the weight so and last and most important instead is the sample the sampling says okay now we did it in one iteration robot moved at first we distributed particles robots moved we shifted particles based on the odometry or motion model then based on the observation we gave or change the update the weights of each one of them which one is more likely the particles that that that we have after that now we need to resample the sample means that uh for Next Generation or for Next Step particles which one of these particles should be chosen to move to the next step and that that's called resampling and we want to uh discard the particles or choose the particles that have higher probability to be the the robot pose that we have so if I draw something a little bit visual here we can say if you have the environment and if we distribute uniformly particles that each one has three elements of x y z Theta then after I run the motion command like move to the right all the particles shift will be shifted to the right so that I can remove for example this part over here let's say all shishu uh for Simplicity and we have more here after that uh wherever the robot is we don't know so far but it's it's like after observation robot was here and observed like some some elements of the environment then the particles inside this part will gain more weight the W of these ones at the beginning were equal but they will increase after increasement of course as a simple simple problem we can say Okay based on the observation that we have and debates that we have more likely here more likely robots should be here because the weights of these particles are more it means that more likely one of these particles representing where the robot is so because of that in next step if I draw it down I would like to resample the particles more likely around here that represents robot location so I would like to resample from here more likely and less from other ones and this is how how we can say okay where the robot is an example set will be more likely representing my steps any question is it clear so we also have one instead of computing the estimate that computes the weighted mean and covariance of the particles to sell really where the robot is that it's like at the end or if you want to really say where the robot is you can calculate the mean of all so here if you calculate the mean of all you will say okay you would say robot is here right mean of all particles for the position but here now I mean maybe is more likely closer and if we continue this motion command observation motion command up there we're gonna find where the robot is this mean mean of all particles will move towards the very really robot is yeah yeah the probability of the old particles the the Dominion covariance says the main says exactly where it is covariance is how what is the error over there it becomes like gaussian distribution again based on all all data points particles that we have so as you see the algorithm technique is looks like simple and not as complex as previous ones that we needed to do lots of match calculations but of course there are some elements that we need to see how we can bring them into into game um in order to do so we will talk about first of all Monte Carlo uh technique as as a technique of particle filter that it says using finite number of randomly sample points to compute the results in Monte Carlo method so it's kind of like particle features General model of the algorithms there the idea is same Monte Carlo is a technique to do that and the idea is creating enough points to uh it's like at a practical way of bringing the uh particle filtering to localization problem we say we want to generate enough points to get representative samples of the problem then run the points through the system that you are modeling can compute the results of the transforming point and then apply the Bayesian filter on the problem that we have uh and and and after after doing so we can say you can find the extract the estimation of the particles with the weights that we have so this idea is like representing the same thing but but as I mentioned it is a specific instance of particle filter and is applied to localization algorithm based on the particle filter to understanding I visualized it there for Simplicity but let's have a look at the directly uh how we can implement the uh in algorithmic mode so in algorithmic mode of the particle filter we have the set of particle sets a set of x's control commands and the observation as input so what we do we create a empty set of the particles at the beginning that that at the beginning predicted so this is like the current set of the particles and this one is the new new set of the particles that we want to all the time talk about like the the belief unpredicted belief in form of base filter then what we do for each one of the uh particle sets we sample based on the this distributions that we have so the the sampling from the uh it's the sampling of the XD from the probabilities of the control commands based on the previous post then calculate and update the rates that we have based on the observation then calculate the then then at the these particles these particles based on the like the set of top of the particle poles and the and the weight to the previous particle sets so previous I mean predicted particle set so we have a particle set each time we sample new sample comes with the not only particle we activate that we calculated to we find out based on the probability distribution and the other two particles there and after this is there we generate new particle set with weights of each one of them then also I put in some points here beside generators yeah the same thing and then then consider the automatic motion model and sampling from distribution comes from after applying the motion command they probably have the probability distribution that it moves and this gives us the probability of the uh the debates as a probability that we can add it to the each one of the particle and put it into two set so and I have another point at the observation over here is calculation of the weight that that is again uh the same idea but also it is called as important fact importance factor that that we will we need to discuss it a little bit in detail how we can bring this importance Factor important factor represents these W's for me this waits for me that I include in the set and it says it is the probability of measurement observation under each one of the particles that again can be represented with this equation the weight is equal to probability of the observation given by the poles of the robot that I have that this important factor calculation is a little bit challenging that we will see in next slides how we can bring it into the form of Articles why because uh the probability distribution if it's linear if it's gaussian distribution or linear we can do it simply for sampling over here but with non-linear models sampling with from non-linear model is also troublesome that that we will see what what technique we can use in order to do that so clear so far we have a for Loop to generate weights and particles with sampling based on the probabilities here I explained to add to samples for irritability for you then we have a uh for for important factor calculations we say there are different approaches that we will discuss in next slides I added for comments for you we have another loop that says for each one of the particles what to do before uh uh each step that we need to move to the to the next part what we need to do draw eyes with probabilities after the base that we have actually we are doing resampling the step here with the weight probability that we have so here we moved from particles from there to here with resampling so this is happening in this for Loop over here draw I of sample the probability of the this W for each one of the article that we have and then add it to the new set of particles so here we have the predicted set we have the new set that is the sampled so I can write kind of pieces like predictive this is predicted X and this is the X if I wanna represent it visually for you then then we can return the uh finally we can return the new set of the x that is representing those second one over there clear just now we need to see a little bit of more details of how uh importance the sampling or uh this step can be done so we say from the uh what we have here draw from the temporary set of the X predicted x with the sampling of the particles and the probability of drawing each particle is importance weight that I explained to you but how now you can think a little bit um how this can be in algorithmic form represented you can think about this so if you have the probability gaussian distribution this is simple to bring it but in order to bring the importance resampling we can use one of the techniques of the drawing Lottery that is called rolity so if you are familiar with evolutionary algorithms we say we have set of solutions for a problem so if I'm talking about a little bit evolutionary if you have set up solutions for a problem that each one have some how good they are based on the objective that we have we have some value for each one of these for example from if it's from 100 this is 90 this is 85 this is two I don't know 50. how good they are so we need to have a technique to do the resampling of course that that that brings it select which one of these to new set of population that I have a solution so similarly same concept from evolutionary algorithm can be used here that we have set of particles instead of value here how good they are as Fitness what are the weights of each particle here so how we can how we can choose these in algorithmic form not just okay we we say the probability so how that can happen one of the techniques is uh roll it wheel that is rowlet field we say you can have a distribution like this each one of the particles each one of the particles that we have can have uh like if we Define a roller field like this say particle number one two three four five and each one can have different probabilities based on the distribution that we have then we have a selecting Point simply then you just rotate it if you rotate it what will happen then you have a higher probability to the particle to be chosen that has higher weight over there so if you rotate it many times so this particle that is more important has higher probability to be chosen so this is how we can apply to choosing the particles from there for here I automatically did it by choosing this one that I said these are more importantly Firebase but but this is how we can implement it roll it is very famous of course you can have different techniques nowadays you have libraries to to bring it in form of distribution in Python simply do that but if you want to implement it yourself you need to for example create an array and inside those array copy for example this element more times number of times if you have you put one time in this one maybe two times this one in this array then for example five six times more so if you put more elements of who is going to more likely be there you're creating an array form of the particle filter that you can see like each one of these segments can represent each one that this one has more numbers then if you apply random selection from that one that that big array then since you have more number of these elements number three then you more likely will choose it and bring it to the next distribution okay clear simple and practical way of doing this so we have a problem here what can be the problem or benefit can be like both problem and benefit but do you think the problem is with the roulette wheel yeah that's one problem but that we are not exactly meaning that one here but that can be acceptable problem here but there is nothing else you can do with it that's like the competition that you need to do and that's actually particle filter problem not really feel that we will discuss it later what else can be the problem that is also not problem also benefit not only is the problem but also is the benefit with this technique if you any of you were working with evolutionary algorithms would answer it in a second because that's very common problem in Eva developing techniques for that one no idea okay the problem is that if you having if you have a look at number three if I rotate 10 times maybe all the ten times these three will be chosen then I'm losing I'm creating lots of repetitive particles from these three and I'm losing all these right I had many particle samples although these probabilities higher but maybe this is the answer or maybe this number one is the answer exactly where the robot is but but with this the sampling technique I'm losing all those particles other particles but what's the benefit why I'm calling not only problem but also benefit the benefit is looking like this then you discarding other ones then you although this this sample may be this sample may be choosing three times this sample may be chosen 10 times but it's more likely representing the robot that's the benefit that we have the idea that we have to use it but but also we may use for we may have that problem and also we will soon see in a second that how we can deal with that problem and propose some solutions for particle filter technique so resampling step is probabilistic implementation of the Darwin idea for survival of the fee test I since you don't I I so late let me explain this it's very also interesting so let's say in human population we want a specific answer like you are looking for Superman or you are looking for let's make it more meaningful so let's say we want a person who is three meter high specific red eyes red hair and skin color is I don't know yellow and and what else and bodybuilding right also can run very fast so those characteristics almost we don't have any person like that right so with evolutionary algorithms we can say okay let's say let's talk about current human population and control kind of next population based on who have more chance to be like that person then only those people will survive who has like colored eye color that is red maybe is more trans or colored or who is like taller who is who this skin is yellow or we are very specific artist that we have for then we control who survives and if you do that thousands of generations you finally will have the answer and this is evolutionary algorithms for example if you look at the families of cat let's say at the beginning there was an animal that they wanted to find lion and if the line was the objective that we want to control the whole Evolution and if we would control it we could control it we finally can end up with lying and this can happen really in simulation and now millions of problems thousands of problems that were not solvable can be solved with this technique you define your population characteristics of the problem each one represents one answer then you say okay I want these exactly end answer you define it what you want then you let it to iterate millions of times they they of course they marry each other they have children then you control that you control mutation and control Next Generation and you do the selection also selection comes usually based on the who has higher probability to closer to your answer that you write a fitness function for that then later you have the answers that you want for example we can solve a cream problem with this end Queen problem with this there is a chessboard you need to place for example if eight times eight you need to place eight Queens none of them collide with each other this is age cream problem if you try that you may think that's simple but you if you you can try these soldiers to place it that's not that easy uh to find even for human you can find one you can find two but if you don't know the technique you cannot find 26 different for example 30 different combination but evolution algorithms can find it for you that that that that eight times eight is okay but 100 times 100 for human almost impossible that's super difficult but evolutionary algorithms are able to easily solve these problems so now having this in your mind also you can kind of develop that idea to generate a slam problem and see if we have an offline Islam then of course we can find the exact solution if your robot moved in the environment for one hour two hours then you have the data you don't need to onlinely construct it then you have this you can use something like same idea to bring it to uh to Islam problem and Soulful full Islam problem as optimization problem and have the exact pose in the in the Verdi robot position was all the time so that was why I explained it a little bit but not only there in other techniques too but one point that keeping your mind this is not online basically because this needs generations to let it develop algorithms like artificial network is in online you can directly ask and give get the answer but here we should wait it usually takes one hour calculations few hours calculations in order to find answer for them so if we Rift come back to the course we say instead of keeping all particles uh the uh we actually use the one that has higher probability that we discussed on the other hand now if you want to improve the roulette wheel technique a little bit this is common to use in particles physically low variance resampling uh production that this low variance the sampling production the the point is okay instead of having one single point that then if he rotated too many times instead of having this if I rotate this 10 times Maybe maybe all 10 times I choose number three right but with low variance resampling produce production we can say okay let's put multiple uh uniformly distributed points to my view then when I'm choosing one I'm forcing to choose another sample from another locations too so that here if you choose one rotate 10 times not only you have to choose one of the particles from this guy number three but you force to also choose one particle from number one there is no way but of course it's still that one we'll choose more maybe than this one and three because we'll be choosing one two maybe three four each one of these two times more but sometimes even missing this and sometimes only can choose it with this idea this is called Low variances sampling that is very common to use in particle filter and it looks like this in implementation you have the of course we want to choose based on the W's and these W's can be distributed in this some of them bigger and based on the weight that we have done with this simple equation you can create these pointers that added by subconstant values and and distributed based on the based on the size M that we have this equation can give you the each one of the points are added by m to the power of uh minus 1 so that m is the the number of the particles that we have that each one based on the w then then we solve that problem of uh that problem of losing the particles and the implementation looks like this low variance we have set of particles you get the random number at the beginning as R then creating the for Loop that that calculates the same equation are added by m minus 1 to the power times to the power of n minus 1 then there is a while loop that says while it's is equal is greater than C do this and choose the particles up to and like moving from here to here and and get the particle and add it to DC and finally at the at that particle and return implementation algorithm of the low variance resampling so what we have important Point here we're selecting a sample with probability proportional to the sample weight is still because the as I explained the weight is higher more likely the is still the low volume sampling will choose more particles from that's it so the advantage I almost already explained it covers the more systematic function of the resampling and if all the samples have the same importance Factor what will happen then then we don't lose any sample this is also a nice nice explanation so if if all of these are same probability then then of course we should not lose any because they are same but with the other Rolex wheel we will lose some because that's just random but with lower Alliance all of the particles that if they have all them are the same probability will move to the next Generation next set of particles that we have so we say if there is no observation sampling the step estimation also can be wrong because because then we don't have observation and and of course the probabilities have been changed and if there is no observation then robot location is changed and the selection will be all based on previous observation so robot from here moved there but choose the particles from there instead of choosing giving more weights to here so that's also a point in particle filter if you implement technique robot is moving in the environment and is not observing detecting features that you want then the observation the estimation will be wrong it's not like in unscented Kalman filter you don't see it just the error is increasing nothing wrong is happening in in unscented extended Kalman filter if you don't observe just uh just you your error is increasing but here no that can be wrong so what is the target distribution in important sampling let's now see how we can choose the distribution based on the probability we say density function function f of probability distribution can be shown as this graph this F and this is the density distribution and we would like to achieve distribution that uh we want to achieve this distribution that maybe is not that easy to calculate it how would you like to uh calculate that one from the f if it's gaussian distribution we can sample from normal distribution then that's easy but from this function sampling already is there but how you want to sample that's difficult to do that's that's maybe also not possible to do because because this is a function and and sampling where where is the peak you don't know exactly is non-linear then you need to do lots of calculation mathematical find the uh and if we would solve that we could use it in particle filters in unscented filter or extended commandment there are multiple solutions to do this one of them is important sampling but with important sampling we can make two steps of localization for motion command and observation together let's see how it can be done easily we can generate particles from density such as G we know so since this is normal distribution gaussian distribution we have been python also functions and we can simply do that based on mean and covariance we can create this that's okay but how to generate if so first of all we say okay let's let's call this uh this distribution as proposal distribution that we can write numpy random normal to generate it for the prediction and I'll put the link if you want to study more about how you could do that with different ways you can have a look at this link 4G so if we consider this is as proposal distribution now we can we want to calculate if using kind of this G how we can do that we can offset the differences between those particle weights hold that now we can say based on the let's let's see how we can uh have these particles we can say okay let's say the differences of G and F gives me the weights of each one of these in order to do that how we can do we can write w of the uh W of the m is equal to the the particle that comes from distribution F divided the particle that comes from distribution G and and if you divide F over G then you will achieve these weights over the particles that that if you do that then we can say the we have the uh belief of the XT and belief of the predicted XD that here G G is the predicted belief and F is the belief itself if you remember we were saying predicted belief as first step is coming from motion command so it means that I was calculating predicted belief robot is moving I'm running motion command and writing predicted belief is equal to the motion command that I run then I was updating that so here the gaussian distribution as G can be considered as the motion command that we call it as belief of x t the distribution that represents police activity and we have this distribution over that as particles then we can calculate the weights based on the observation that observation for example can be non-linear function then this observation that is non-linear if you divide F over G then you get debates that these weights actually giving you the weights of the particles that you wanted to have in order to give the weights over here to move to the next step understanding this is a little bit challenging you need to focus and think about it because it deals with two three steps together but general idea is bring the belief and predictive belief all together in form of particles and at the same time calculate also divides so for example one run also Point here tricky Point here in implementation if you think about okay let's say this this value this this value like f of the X whatever the value is if you divide it on this one like 0.3 divided by this one has higher than if you divide this part over here or this part over here then you have lower weight over here but but if you consider you may say okay maybe these moves in next steps and they come together but if you divide that one to that one the value is lower than the value that is you dividing here in Mass and that makes confusion for you but you should consider that uh you should normalize each time independently the values in each one can be different so in time XT you calculate these weights the the values cannot be compared with the next step values that you can get from here you should normalize it also each time okay any question simply weight can come from f and g f represents blifa fix d and G belief of predicted polypha fix the that's it in implementation for well uh for uh particle filter localization now let's see a visual example uh this is the environment cuts the robot position for example and from a starting point robot has moved and they are this is representing office environment of sites like 54 meters times 80 meters then then what is happening we distributed lots of particles in the environment on the environment then then robot moves after robot moves observes the environment and you can see that we have particles over here and this is real robot position that we know uh what happened from Next Step we run the all the things that I explained to you with particle filter and the particles come to the next step that have higher probability to be here the answer is maybe robot is here here here why these are the uh these also are existing as particles because because of similarity of this area based on the error of the observation the observation model that we had says most likely this this one or this one can be the robust location or this one can be the first location and that's like kind of interesting and you see that uh we don't have known correspondences for example in here and and the particles are are are are representing the robot position and after moving more then you can see that since the observations is more identical uh features over here than robot position more likely is something in the center of the particles that we have okay clear now what problem can we have here State a problem here in these trees like A new challenge let's say we run the particle filter as I explained and robot is now here particles are create a problem also in chapter one two we I introduced the problem of the Islam that we it is valid here too make something that this algorithm won't work yeah yeah kidnapping problem exactly yeah we have kidnapping problem right we said kidnapping problem in robotic and Islam is mean we catch the robot put it somewhere else kidnap it so now if you remove the robot from here and put it here then the algorithm is like particles were there and robot is now somewhere else and is it able to to find it no what we can do now propose the solution reset the environment yeah but that that works but that's not good idea better to have better idea because maybe the observation is kind of new then although that is correct but it's resetting all the time that creates lots of another problems also better idea ilham better idea risky better idea Simon better idea kick Simon you can wash your face if you're sleepy so the the idea is okay let's say in next slides we have it but let me explain it here let's say at some time although I'm more certain that robot is here but and I can calculate the mean and covariance for robot location right that's fine but sometimes if I distribute some seeds a little bit of seeds in whole in the environment what happens most likely my mean and covariance is still the same but I give more chance to other particles this suddenly kidnap then more likely that particle get high weight and from there they will be vanish and come here like what happened here like at the beginning distributed then this one those other ones vanished because of the these ones that gain more weight because of the movement and observation so the same scenario can happen if you distribute some particles at some time very low amount but you give chance to check the other ones to waiting and if that's the case then um then this over here will have uh we'll have more accuracy if kidnap this happen so so it is called recovery from failure recovery from kidnapping problem is the challenge and particles can survive based on that we discuss it algorithms may accidentally discard also that's another problem not only by purpose maybe accidentally all of them discarded during the sampling problem sampling a procedure even if you implement low areas maybe we have chance to to lose them and and we call it we can use Simple heuristic to solve that problem not only doing that uniformly some resampling uh uniformly generating new samples in the environment but also we can use heuristic techniques heuristic in artificial intelligence means that we have a simple algorithm that is search technique and search search the environment and gives [Music] um a value to evaluate the situation this is called heuristic in artificial intelligence if you we discuss it a lot there but simple heuristic we can call also greedy technique like for Loops that search that are best optimum and puts there you can write some code examples to maybe smarter even put new particles there in the environment so that can be called as technique that can solve the problem and as as I as I mentioned once one is the heuristic adds random particles also we say even the kidnap problem if it's not happening we are sure that is not happening it's still this technique can increase the robustness of the algorithm of the particle effect so but here we have two questions now the question first says how many particles should we add at each iteration how many new particles now we need to add a new iteration something like you you want to say something like it's uh static value depending on the beginning article particles that I have yeah that's one one way to do that we can say one approach might be a fixed number of random particles at each iteration what else you use the remove ones as new ones yeah it can be that one too but remove ones may be also lost the thing randomness that's that has another problem then better to create new random one or use heuristic to add inject new smarter ones another way is like better ideas articles based on the some estimate of delocalization accuracy and based on the observation it means that your heuristic can say my observation sees environment looks like this and better than add particles around that part of environment that looks like that area like if we go here here for example like let's say so your observation see something something look like this then better to add particles around here rather than adding some random articles around here because you know that you're seeing your robot observing this area this Landmark or whatever then better to distribute new random particles around here instead of somewhere far okay clear and second question says uh so that's not very important and from which distribution should we generate these particles from which distribution we can say new particles can draw in according the uniform distribution as we discussed and new particles can be directly distributed accordingly observation likelihood that I answered already so now let's say when to use particle filter instead of unscented Kalman filter what do you think what do you think Tony so you now you have two options you learned particle filter and you want to do it as project on scented common filter but if you are interested you can do particle filter too so when to use particle filtering instead of unscented Karma filter what do you think so we had a professor who he was like if somebody is a little bit sleepy or something he was like okay I'm asking a question then if a guy is not answering that question that is related to course then all the class members will get Negative mark then that was like serious rule then no one would even imagine to get close to be sleepy because because if you lose your own Mark that's fine you that's your own own Mark right then you can give it up but you're losing a whole class mark so but yeah imagine like studying like that whole semesters and I think Hugo has some experiences he's laughing yeah I see so if there is high amount of non-linearity of course using particle filter is useful because we don't have that complexity anymore they you remember that we were struggling equations doing from linear non-linear problem to bring it to linear problem that was difficult but here it is easy we didn't do too much complexing just simple technique we've done and uh of course based on the number of particles the computational cost is also increasing here and it is much more higher than parametric technique then we need to also think if if we if you have computational limitation you are going to run your code in a method system then number of particles if increases then that's that's highly costly for in comparison to UK for example because why because there we were just keeping one mean and covariance for all environment we were keeping one million covariance large robotics but here we have like 100 000 of the particles then particle filter is not good for big space dimensions because of this problem that if the big space space is Big then you may have millions of then you run a localizing city you cannot put 100 particles 1000 you need to 1 million particles maybe even more then the big Dimension is still uh the other techniques for example UKF is useful so how we can solve this phase dimensionality problem uh if we solve that problem with particle filter we end up with new technique that is called fastest land fast Islam is very sweet technique why because instead of estimating each Landmark with particle we can that that increases the dimensionality we can use the previous algorithms for example EKF can be used how does it look like let's have a look we say okay you have particle one particle 2 particle n so uh that each one each particle has X Y Theta and the landmarks number of landmarks now we can use extended column and filter localization instead of uh instead of particle filter idea what does it mean it means that I can say I have particle number one that include this data for me X Y Theta and and robot like let's say this XY cater shows my robot is here and heading this direction and these are some obstacles then particle 2 looks like this particle 3 looks like this so I have the particles now I want to bring extended Kalman filter in order to calculate the particle 1 2 3. and then I don't need too many particles instead of extended carbon filter we're running like only one on one scenario I have a couple of scenarios for extended Kalman filter with different noise different initial poles that each one leading to solve extended column filter for this problem that looks like this for example particle 1 robot moves with control command the same control from initial different positions so say we say particle one random position we're here this one is here this one is here we run the same control command on the on on the robot but if article one moves like this particle two room moves like this particle three moves like this then what I do then observation comes then I update the observation based on the observation that I can update particle 1 2 3 then this looks like this the error for each one of these marks shows my observation so that instead of having too many particles I can have fewer but in each particle on each particle I can apply one algorithm like extended Kalma filter or maybe wiser this is called Fast slam because it makes it faster because using external code or maybe wiser I can use instead of particle one that is used by extended Kalman filter particle 2 can be solved by unscented Kalman filter particle 3 can be solved by another technique then then I am combining particle filters with all the calls that so far I've studied in order to generate and propose faster technique that is also more robust that uses benefits of EKF UKF even Kalman filter or different techniques that I can apply or for example this can come from histogram filter one of them and this is called Fast Islam and we have different techniques the fastest land that only I introduce one so if you want to conclude in this chapter we discussed about the particle filter localization then we went through Monte Carlo localization that was exactly the same but practical practical way of implementation of the particle filter and we'd introduce the low variancy sampling and finally we discussed how fast Islam is working and how we can propose faster localization and technique so if you want to see the implementation of course the best example given by the Kalman and base filter in Python book uh that that is interactive you can have a look there and and we have also python robotics that you can have a look at some implementations examples but be careful that the resampling step can be different or uh or weight calculation step can be different depending on different variations of implementation with article filter also I think as I remember in the book there are multiple ways but exactly |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH3_SLAM_for_Robotics_Recursive_Bayesian_estimation.txt | all right so last week we talked about the recursive phase filter that uh we said it is one of the basic algorithm that we want to learn and mount other algorithms on the uh base filter we said that it is based on the markov chain and markov chain probability uh that that we want to get the uh real estate from hiddenly state we don't know this state we don't see this state but the output we see from the output we want to uh detect itself and we later said we have observation set the uh control command sets and the environment m plus the x's that are showing the poses of the robot that we want to estimate so uh our probability distribution we always will show like this probability of states given by observation and control commands so uh so we said also yeah we have the unknown probability density function or named pdf that we want to find it during the course we have plus set of vectors and command vectors that later we went through two important steps continues the continuous variables we first saw how we can calculate it in uh total probability then we talked about the belief that robot believes where it is the old calculations believes that it is that that shows like we state uh all of the states during the time the observation plus the control commands so finally we talked about the base inter-general equation that we discussed this is the probability of observation over uh states that comes from the integral of the all possible beliefs and the probabilities of the control command over observation so we broke it down to motion model and observation model in motion model robot run one motion and we want to predict that motion so estimate that motion that at the beginning mistake we saw how we can do that that is the belief of the uh the belief shows integral or some of the products of the two distribution the first probability that control commands gives and second one is transition uh from xt minus one to xt that you want to calculate after prediction step we have the correction step that uh you saw how we can apply observation modeling that in there we had the terms of the normalization we had the probability of observation over states and beliefs then we saw the phase filter algorithm quickly then we set the important concepts also we later discussed that we have some algorithms that we will start to see called monthly theory extended call mounted to particle filter grid-based estimation and after that we have over hundreds of different algorithms then finally we also have uh uh we also have for example orb islam or islam one two three one of the state-of-the-art algorithms that work greatly in islam problems as long as we have time as i mentioned we will go through them too but what's the reason that we don't directly go there because uh the important reason is that uh if you don't know the basics if you don't know where the equation calculations come from it's very difficult to understand that part because of that we should in the course come from scratch to see what's happening then uh also we talked about the uh general specification specification of of the each one of those algorithms then we said that okay uh in uh we have inaccurate motion control commands that you have a robot you send go one meter instead of one meter it goes one meter and half that was the reason that we needed to uh actually that is the reason that we need to have the estimation otherwise if you want to run one meter go forward and turn left or right for specific amount then the problem already solved we don't need to do too much for specifically localization but of course for mapping and the landmark detection uh we needed to do some stuff also we talked about the accumulated error that's in odometry you have um accumulated error that during time it increases because of that we have collection step that we mount the uh some sensors on the robot that these sensors help the robot to do correction step the automatic based approach that today we will talk about and velocity that today is the main course that we will have then uh then we also will talk about the translational rotation of the odometry we will see today indeed also we discussed that there are three elements that are important alpha one uh uh delta transition and alpha two that those are triangles that are important for us to uh consider as error we talked about the distribution of the different kinds of error later uh we a little bit discussed about the observation model environment assumption for one example finally that we saw and we saw how we can calculate a robot can detect the door is closed is open or do the push command what is happening we discuss for example we come from initial belief that we don't know the door is up robot doesn't know that robot door is open or closed that we said okay it is 50 50 then uh then we start some assumptions for example our sensor error we have a camera you implement one algorithm then you say okay uh the robot detects the door is open or closed our robot your developed algorithm says that but but of course it has error so you try for example you try one hundred times your algorithm you say okay sixty percent it is successful forty percent it is not you give an assumption that to be uh the model and what about the clause if it's closed can i detect it my algorithm can detect it this time for example eighty percent uh versus twenty percent these data come plus what about push we try our robot manually well it can be manually you try a hundred times robot push the door if it's open or closed then you give the probabilities then we have the same equation they believe they calculate at first the uh belief in correction in estimation step to make it believe if it's open we calculate it together then we calculate it estimate it believe it flow then uh then we said okay what about the uh prediction what about the collection step then we corrected the prediction so that uh the values came and sat on the updated belief so that we said okay 75 percent our robot says the door is open and 25 percent says it is closed then also we said okay you can continue this so initial step state state one then we can continue to stay two this is state two we did all the calculations but this time we used x one or previous belief that we calculated already seventy five percent and twenty five percent that you can see in these |
Simultaneous_Localization_and_Mapping_SLAM_for_Robotics_NTNU_Course | CH2_SLAM_for_Robotics_Introduction_to_Coordinates.txt | so hello everybody good morning uh nice to see you again so uh last week we talked about the uh slam definition and we talked about the challenge that we have in Islam and now you all guys have General perspective of what's happening in Islam and what is the challenge that we are going to deal with so uh today we have a chapter short chapter that we are going to talk about the coordinate systems and what's the uh what's the reason that we are going to talk about it because we have the mapping problem of the Islam that if you remember for Islam problem you want to simultaneously localize and math and mapping means you need to bring everything inside to the map and if you want to be able to do that you need to know about the coordinate systems and what are the different approaches that you can work with points and clouds uh basically we will have a general and quick introduction of the how different coordinate systems are working and how how we can work with them uh so that later when we are talking about the mapping it will be more clear and easier for you and of course if we need more details uh we will discuss uh later in the course so today we are going to talk about first about the affine transformation translation by default all of you know these but we will see how it works uh we will talk about the both translation and uh rotation then we will talk about the polar coordinate system and how we can convert Cartesian to Polar and vice versa polar to cartesia and what's the reason that we are going to do that what's the benefits also we will talk about the homogeneous coordinates and basically in this chapter you're supposed to know how to work with these systems basically first of all we have a question the question says why we need to know about the coordinates that I answered at the beginning robots are visual sensors and they collect robot colleagues visual information from a surrounding environment and needs to plot it in the map and kind of sensors that we can have also can vary based on what we are going to do like you can have cameras rgbt lighter projector image of the uh lighter sensor that you want to project the 3D image into the map and of course uh points can be in 2D and 3D we need to be able to uh work with both of them and uh and we want to basically know how we can work with a single point on 3D coordinate system so what is the refine transformation uh if you want to have a definition we can say it's a geometric transformation that preserves lines in parallelism and also a function that Maps a finding space into itself that uh that that we want to also keep the dimensionality of the each one of the points when we want to apply some movements on the each one of the point on the stage space on the space of the map that we have so basically we can have translation scaling reflection rotation Shear different elements that we can apply on it and or any combination of the all of those to get so let's start the most basic uh thing that we can do transformation translation that's very clear that if you have 2D coordinate system x y and if you have a point on the coordinate system if you want to move it on the uh from from initial point x y to X Prime y Prime what we need to do we need to apply the uh TX Ty to the each element of the X and Y that is kind of adding some some value to them that we can move on the X and Y but how we can show it in a matrix form you can show it X Prime y Prime in Matrix form that that actually we can multiply The Matrix of txy TX and t y amount of translation that we want to have on the initial Matrix that we have like like you have X Y point over there if you multiply by these you finally will have this term over here after uh after multiplication so finally so ah if you implement this you will allow you will achieve the X Prime y Prime based on the txty that you want to have on the point so uh so when your robot is moving on the coordinate system and you want to plot it you map it of course you need a translation as one of the basic steps that we have what about the rotation if you want to have a rotation on the point uh of course in 2D coordinate system maybe is a little bit harder to understand but you can imagine if your robot is rotating uh but but when we are talking about the rotation you need to also be careful about which dimension and which axis we want to rotate it so let's say in this coordinate system we have a point and if you want to rotate this point around the z-axis what we need to do okay let's say we have Theta and we want to rotate the uh this point around Theta around around Z Axis or amount of theta what is actually happening actually we are a rotating whole coordinate system and and if we if we draw it again here you can see that uh we are we achieved X Prime and Y Prime so that uh after rotation uh the point here uh should be kind of if like rotating a pixel doesn't doesn't mean too much but if you considered as object we rotate all of it on the Z axis how we can do that in two-dimensional uh already uh you most probably studied it uh we have single Matrix form that we can say x Prime y Prime can be calculated by uh by multiplying the X Y on this equation and this Matrix here that that includes cosine Theta sine Theta uh negative sine data and cosine Theta that we're multiplying this uh amount of data you will arrive you will you will have the amount of rotation that you will have on X Prime and Y Prime so this should be very clear and simple for you guys so uh for example if you're gonna you're going to implement some 2D mapping and you want to rotate your robot on the coordinate system for each one of the elements of the robot or center of the robot that you have uh you can use these simple terms to rotate on two type engine what if we have 3D if you have 3D mapping then we need to do a little bit more first of all we need to understand that rotation then is not on the z-axis anymore only because in 2D it doesn't matter like you cannot rotate on the X basically we rotate on the Z in in 2D even if we need to rotate on the X because it's 2D just just the name names of the chord the axis can be replaced but in 3D we need to be aware that around each one of the axes we can have rotation and based on the uh access that we are going to intending to have rotation we need to use different form of matrixes to replace here and multiply by the x y z that we have so so here you can see that if you wanna rotate the point that we have around x-axis for amount of data we need to multiply X Y uh Z on this Matrix so these Matrix have of course proved I'm not going to do it here uh you you just multiply this and you get new coordinate that represents new point after rotation for uh if you want to rotate around Y axis we do the multiplication by this Matrix and for that one we need to multiply by the third one over here is everything clear any question if you want to study more I put a link here by default you suppose to notice and how to work with it but if you have any problem go check it it shows you how to work with matrixes and more details you can have useful in this link and of course nowadays you can find anything on the internet easily what about the polar coordinate system who knows about it any of you okay good so uh polar coordinate system is a coordinate system that each point on a plane is determined by distance of the point and reference point so actually um instead of indicating this point over here by X and Y we can say okay in polar coordinate system the distance from the uh and the center and the angle from the coordinate systems zero zero point Center can represent our system or our point on the on the map that we have so how does it look like so the point on Cartesian was like X Y but in polar we have R and Theta and that we can have we can show it denoted with different uh terms here but R shows the distance between this point and Theta shows the amount of uh the the angle from the x-axis that we have so now we how we can car can convert these terms together that's very of course simple uh polar cortesian system uh to Cartesian and vice versa and actually uh after calculating the coordinates of Point P we have the uh we have the oral Theta that let's see how it's happening here visually so uh if you have X and Y and the point over there now we want to incarcassian system now we want to convert convert to Polar what we do simply we need to calculate the r and r can be calculated by including distance that that simply you say X power 2 added by Wi-Fi 2 and then we got this square root and then we have the distance simply what else then we need to calculate the angle so here I called it Alpha of course we can call it Theta so what we need to do we just simply need to do a calculate the arctangent two of the X and Y and our our turn is on two usually and I is very common to use in uh 3D modeling and we we use it to get the the angle of the uh the the point that we have in Cartesian system so you feed the X Y and you get the alpha over here that's that's very simple so now uh now we can say Okay R Prime the the new uh after if you want to do the like after after conversion now if you want to calculate the amount of rotation that we have so the r Prime is exactly R itself that we have and Theta Prime is the alpha subtracted by Theta here what does it mean it means that the amount of rotation that we have can be subtracted by the alpha and and if you look at here the the alpha that we calculated over there and Alpha Prime this one is subtracted by Theta that that simply we can rotate the point on the coordinate system of the Polar system now what if we want to convert it back from polar to cartesia we simply can use distance over here so X Prime is equal to R Prime Times cosine of the alpha Prime so and Y Prime is R Prime Times sine of the alpha Prime so we take the R Prime and Alpha Prime that we calculate it and and then we can take the X Prime and Y Prime based on uh the the the the after conversion the phones that we have in our program the alpha Prime so now after conversion back if you want to do applied rotation back again so amount of rotation that we did here if we want to revert it or rotate it again what we do and finally X and Y can be can be shown by this term X is equal to R Prime Times cosine of t Alpha Prime minus Theta that this Theta is over here the amount of rotation that we've done subtracted by Alpha Prime Alpha Prime was the was the first one over here that we calculated converted and rotated then later we find we get the cosine and times the distance that we have a new distance that we have here so this gives us X and the 40y the same thing just the difference is that instead of cosine we got sine so here we demonstrated how we can convert first from Cartesian to Polar then how to rotate it then how we can convert it back then how we can rotate it the calculated rotations in order to show the amount of rotation that we have so before pushing forward I'd like to show the so next thing that we are going to talk about it is the projective geometry that uh we say calculation is usually uh challenged especially if you have a not just single point we have uh image for example to calculate on our presentation and projective geometry is an alternate alternative job algebraic representation of the picture in the coordinate system that we can we can use it to project it on for example other plane other axis so actually when we are using it we are not changing the uh geometric relationships we have the same geometric relationships we just need to project this project it on the other planes and actually it is dealing with the relationships between geometric image that we have on the frame so uh actually after calculation we have the the same thing on the other plane that that requires less computational complexity if you want to answer the written reason that is why we are going to also know about projective geometry and use it is that we can displace a point in Infinity on the system what does it mean it means that in Cartesian system can you show Infinity point you cannot show it because you need to definitely have some values on the coordinate system X and Y but here you don't need to have it we will see how we can we can achieve it in next slide I'm gonna show the calculations and how we can do that so uh we use it for denoting the location of the object on the including coordinate system that cannot show it and and of course the calculations is more complex in uh in Cartesian system but here uh we can we can calculate it much much faster we will see how to do that so basically we want to simplify the whole calculation for example here if you have a look at the uh this image so robot see some view of environment and this view of environment when robots is moving can change like I'm in point in this coordinate I see I move a little bit I see again everything is same but but it is changing so that we can uh uh we can instead of working with X Y in 2D we can work 50 including geometry so that uh actually projective geometry so that we can add one extra Dimension to the frame as called as W that this W is going to help us to project the same frame on different types on the coordinate system that we have so what is happening we have x y w and we add one more parameter to our X Y in projective geometry so that we can call it as homogeneous coordinates if you have coordinates in projective geometry so homogeneous coordinates are also famous uh you may have heard about it already but let's have example how this is happening in 2D calculations now we want to add one more parameter instead of Simply Having X Y we have W for example if our image is 810 by 600 we have the parameter tree here that we added in a homogeneous coordinates so that what is happening actually actually simply if you want to project our image these three represents that okay just the answer for if we wanna project this point over here the frame that the the view the picture that we have uh over coordinate system just simply can be divided by the number that we have in homogeneous coordinates w so we just simply divide it and we have new result so by adding this W if we place one then we have the same frame but with adding w we can uh we can project the image in different coordinates that we don't need to calculate it anymore because if I tell you okay this is the frame the The View that we have in the map and you want to project it in different uh different depths or or different uh different uh distances from where the robot Saudi environment so simply with adding w we don't need to recalculate it again in basic informal form of the projective geometry so we say projective geometry in two-dimensional easy to alternate identify because uh because it is a 2d and adding one is simple but when we are going to 3D then you need to uh you need to a little bit consider more parameters so let's have a look if we have any point in uh in projective plane that we can represent it by x y z if uh if you have P Prime as a geometric object we can say that the uh it is representative it is representing the same object in 3D Point uh in 3D homogeneous coordinates on the system where the W if if W is not zero what does it mean so let me clarify for you so we have P Prime that is X Y uh like like a point on the coordinate system so uh in including space actually so this is including space if you have x y and one over here that this one is a w that we added in the previous slide we can write it in in form of homogeneous coordinate system that is w x W Y and W that gives us the X Prime y Prime and W that this W is representing the uh the the year over here the value that we have and uh uh we can we can have it in homogeneous Courtney so from Nickelodeon space we come to homogeneous space is adding one more parameter named so if you wanna do the convert back the same thing from including to homogeneous we want to convert back from homogeneous to including what is happening here as we saw in the example X Prime y Prime this time we divided by it then we have we have Cartesian X Y included space so actually one time we multiply second time we divide it and come back in the in the conversion from homogeneous to uh Cartesian analysis in one single sentence if I wanna explain it we can say we usually set W1 basically we don't need to change the the scale of the image on the system that we have so have a look at the converting back from homogeneous coordinates to including M1 here is the robot and here is the Cartesian 2T so actually we're drawing a line and projecting it in different W's you can see that so that if you have W1 and if you have the size of W1 we can from the single center point of here we can project it on the uh on the depth that it grows bigger actually the calculation any question so what happens if you have it in 3D sync up single it a little about it now yourself so it is exactly the same so here we have 2D here we have 3D we just need to apply it on each one of the single points of the cloud consider instead of having the 2D pixel we have Point cloud of the data that we have then the same term over here that we have the calculation will be applied on all of the 3D Point Cloud then we have the same thing that if what is changing the w we have a scaling up and scaling down simply over there as projective geometry so therefore W is the scaling transformation in 3D so we have couple of points here that uh we say it is simpler than Cartesian coordinates why because in Cartesian coordinates if you wanna like let me I tell you if I give you a picture and you want to draw it in depth X plus one then it's harder to calculate it but here in coordinate system we have it by parameter W that is built in in homogeneous coordinate so we have infinity points that can be represented over there but does it mean infinity points that we can represent how we can do that do you think yeah we can set W to Infinity exactly by setting it to zero if we set it to zero we can say okay this is a point in Infinity why we need it why we need to have a point in Infinity foreign no no idea Google yeah it will be Infinity but why why we need to add totally do that more view but why what's the reason you are close but answer is not that huh what are you googling no it doesn't care about the resolution the reason is so you have robot and the robot has lighter scanner or some kind of scanner that measures the distance whatever it is sometimes you don't have the distance it has maximum amount that you can measure right and if it's out of the maximum you don't know if there is or not and you want to construct a map and you want to say okay that's Infinity I don't know what is it there that's the reason that we have homogeneous coordinates and that's the reason that we have W there and that's the reason that we have W as 0. clear when you have this kind of environment that it is infinity and you don't know that the measure so I know here is five meters for example but when you don't know then you put uh and that's the reason that we had so we say also a single Matrix can represent a fine transformation and projective also we will discuss it uh all objects can be rotated and transformed by multiplication with one single uh one single Matrix we will show how to do that that's the benefit and it's clever way to extend transformation matrix to be square three times three Matrix in 3D four times for Matrix that if you go to the details uh in transformation matrix we don't have a square matrixes but it is a challenge to make it Square so so with adding one more parameter we can have square matrices that that we can do calculations much much easier so uh that of course requires one more parameter that we need to add to also for a translation TX and Ty that we saw at the beginning so you can see visually here also that's what's happening so if you consider the O3 as the center of the uh coordinate system so with adding one always removing it so we can scale on the scale one point on the on the system the the geometric coordinate system that we have and and that's I think very clear for you guys so for infinitive far objects as I explained to you we can uh we can put zero over there X Prime y Prime Theta Prime as a point on the infinity we can put it as zero and and that's that should be clear uh and let's now see okay I discussed the details and the benefits of the homogeneous coordinates let's see the results what we gain from all those efforts that I try to explain we remove the Cartesian we already know Cartesian XY that was very simple for everybody why we try to learn more to come here that's the uh this is the reason that we have here so as I explained we have one single Matrix operation that can allow us to do all conversion how let's have a look we can have uh in Matrix form the point that we have we want to put a matrix here M that is four times four times the uh the the homogeneous coordinates that we had X Prime y Prime Z Prime and one this was w so for now we don't have anything like very complex XYZ in 3D coordinate system the point in the space wherever it is and one is representing that we don't have a scale W is that this can be multiplied by The Matrix that we want to have it now and this Matrix is going to give us lots of benefits so what is it uh I'm demonstrating the m over here so that I want to step by step show you all the benefits of homogeneous coordinates first of all we want to see how we can have a translation it means that point I want to move it on the coordinate system wherever I want not rotation so far so I can replace this m with this term over here this simple Matrix over here that you can see first of all when I was talking about the uh the the size of the Matrix that is four four now you can see the calculation first of all simple so in this representation I have identity Matrix over here and the translation Vector here the identity Matrix looks like something like b stand the translation Vector looks like this one that uh if you remember we have the translation amount on the X Y and Z so it means that okay how much I want to move it on the coordinate system you just place it here uh here uh we have uh zero transpose that is uh that is the the transpose Vector of zero that that is in uh in the form that we defined for our homogeneous coordinate system and here we have Delta that is scaling factor of whole system that we have so if any value we can have it don't mix it up 50 W ah that's uh that W is the so you can think about it what's what can be the difference a little bit think about it and I explained to you if someone can tell the difference there can be positive work for him too that was for projection that projection already is over here right but this one is a scale factor that scales whole or procedures that we want to do here translation only because the Matrix that I Define here is only for translation so scaling in the it's it's not not the uh not the depth that I've changed there it's it's the scaling of the whole procedure that I have so they are different first of all second simply if I want to clarify this part here for you so we have x y z and one in homogeneous coordinate system right that we see how to bring it how to find it then simply if you wanna if you wanna change the point to translate the point on the coordinate system you multiply the same points with this Matrix over here that that amount of the translation is written over here so you just like like say okay I wanna change 10 15 20 then put the values here multiply this Matrix with the points that you have then what you have as a result is as P Prime is the new point that is translated on coordinate system but on homogeneous coordinates clear for everybody so the proof why why in this form you need to have a look at the proof of the homogeneous coordinates so for now what was it oh yeah since I'm moving I don't realize it okay so again we had Cartesian systemics y simply points x y z very simple points so instead of working for a translation and rotation that first slide I showed you and I showed you some codes we wanted to make the calculation simpler because that because if you want to do uh rotation and the translation Plus the scaling it is very hard to calculate in Cartesian coordinate system to make it simpler we came and introduced homogeneous coordinates an email homogeneous coordinates we saw how we can convert it here here we saw how including distance can come from come to the homogeneous coordinate system so it's why we had we just multiply by W's and then we had the X Prime y Prime w by multiply multiplication so including space through homogeneous space then also we saw how to convert it back reverted from homogeneous to equity now we are seeing what now we are seeing okay all those things that we discussed now we are seeing how we can use it how to use it we have we Define a new Matrix that is multiplied by the point that we have then then we have the P Prime that is translated on the uh on the new coordinate system homogeneous coordinates now what if we want to include the rotation so we keep translation 0 here for now I put 0 for Simplicity and we wanna use and add the rotation Matrix same form of calculation the same Matrix times the the point that we have the coordinate then then we want to replace the rotation Matrix over here what is the rotation Matrix at second third slide we discussed it if you want to rotate a point on around the x-axis we just simply multiply that that point on this Matrix form here that gives you rotated on the X what about the Y what about the z-axis so this is the like object I want to rotate X Y and Z axis tree axis that I want to rotate you just put the point here times it and it you will get the rotation now we use the same depending on what we need which axis we need to rotate put it put this Matrix over here or this Matrix over there or that one over here clear so what if we want to do three of them all together so you have a point you want to rotate it in in three axis you just can put the merge them together we can have a matrix that includes all three rotations together so that we can write r x times Ry times are the times and of course parameters are different because the amount of rotation that you have different like alpha beta theta amount of rotation for each one of the X so actually this here is this one over here this here is this one and that one is this one and as input parameters you indicate they indicate them and you will have the rotation on the on the space that we have on the on the 3D point on or homogeneous coordinate system that we have but the point is of course the rotation the order of rotation is important so amount of like if you if you change the order of these rotations the final point that you achieve will be different think a little bit about it why so the question is uh the rotation of a point on X Y Z the order is important you cannot switch them mm-hmm so correct actually what is happening because our refresh reference point or the system that we have is aesthetic and only the object is rotating not whole coordinate system because of that if you rotate like x y then then for example Z so the object will will uh will stay like this right but if you do the same procedure with same amount with Y X Z so uh this time here here and here so I ended up here so one time like this one time like this the same amount of the rotation so because of that you cannot change the order over there based what you want the order should be so now let's get them together we just simply put the rotation Matrix here with three axis and put the translation Vector over here that uh we have three parameters for it x amount of translation and x y z so that uh we can say we have translation added by rotation that that this gives us on the homogeneous coordinate system and makes everything much more simple of course the calculation for you learning maybe seems more complex but simply you need to put the rotation Matrix and translation Vector here then we have the final Point rotated or translated or both together on the homogeneous coordinate system so the question is uh now we can use this to map the observation uh this is not this is now so uh why because when your robot is moving in the environment of course like the everything getting closer and and based on that you can plot it you can map it on based on the need 2D or 3D like if you have 3D you have this kind of the environment then go scan then go scan then go scan then you are now able you know how to do that how to uh if your automatically is accurate that we discuss amount of movement of robot let's say there is zero error and if there is zero error in observation then you should be able using this term over here exactly math team environment clear everybody but what's the problem in this course of course is that error that we cannot have 100 accurate uh automatically and presentation that we will talk about it how to fix that issue one for parameter uh here we have is the scale factor of object that that we can say okay now uh let's see if I can scale the object that is separate from this uh this parameter that we had here and the W that over there think about it what we are going to do and why we want to add one more Factor as the scale again you can see what can be the reason if you look you can so this one that was okay at the beginning and we added into our coordinate system to convert it from cartesians and it was scaling at the beginning because of we wanted to show the Infinity Point in the in the system that we have and and that is good and this one we said okay that's the scaling Factor but for what for whole conversion problem because you are you have this object here when it gets closer to me it gets bigger right so translation and rotation together can be scaled but what if when I'm rotating it there should be some parameter that I can be adjust with scaling the rotation because when you're rotating the scale can be changed too or you should have control to change it to so because of that we have the parameter M here that you can apply it again so may look a little bit confusing complex but it is not actually you just need to use all this term we have just simply points x y z and this implementation just one time you do that already also there are many but you have some assignment then then you just give the inputs as I did one example then you get the output for each one of the points if you have for one object you need to calculate for whole object for each independent point on 3D coordinate system any question so finally in general we have seven parameters three rotation three translation and uh one scale that we can we can as final Point as final uh homogeneous coordinate transformation use it so do we finished only thing that we need here is rotation not really what if we want to do something else like if we wanna share the object like cheering this one can we do that oh okay but yeah we can do that we just need to replace these are over here instead of rotation with whatever we want to have a valid transformation that we have in Matrix form how over here so uh before talking about the assignment that you have over here for example like if you want to have no change you can put this metrics if you want to translate if you want to uh scale it if you want to rotate it if you want to Shield it in each Direction in y direction shooting means like so rotation we discussed in the three coordinates so if you want to shade it in uh in each direction if you want to shade it in my direction so you just need to add it over there add it in in The Matrix that we have if you want to reflect it you can add this form of Matrix about x y and uh origin and this is the all the things that you can put it on but what you have as an assignment simple assignment that clarifies everything for you implement the transformation in homogeneous coordinates translation rotation scale that you need to implement this one simply and what you need to do write a class for it then validate with applying a reversing a point what I've done on the example like give the point as input then then apply hold the process then revert it back to see if it's working well and you're getting the same point on the coordinate system or not and of course try to visualize it to see what's happening not not too complex 3D environment just 2D uh or you can do that 3D in Python 2 up to you but uh I don't expect too much complex things for now for this example any question is it clear so for inverse operation you may say okay we didn't see how to invert it can we can we work with that simply Yes actually actually one of the benefits that when we are saying the calculations in simple if you want to invert it in a Cartesian system that's that's not easy that's very difficult you need to calculate Everything But Here simply what we do so P Prime is equal to this Matrix times this we we say okay we convert it and and we applied very complex rotation uh translation or Shear so now you can do this with simply this Matrix with just implementation in a point you can do whatever on the space you want right beside simply you can put uh reversion at and that this Matrix can be to the power of the minus one and if you do that the same Matrix to the power of minus one and times it to the to the to the points that you have you can achieve the English is it clear again you cannot change the order of transformation by The Matrix that I mentioned over here to same scenario that we had there we have for reverting operation or undoing operation either so in this chapter shortly we saw how how homogeneous coordinates are working and how we can convert from Cartesian to Polar and Cartesian to homogeneous coordinate system and the homogeneous coordinate system we saw that we can add one more parameter W first of all to bring it to the system and we saw that W can be times in The Matrix form or W can be divided by W uh the the point can be divided by W to achieve the revert then after we bring it to a new system what we've done we Define the form of the calculation that that form of calculation gave us the opportunity to do all process of the transformation and rotation together simply and even we saw how we can revert it back simply so that any time when we are going to use work with maps especially on 3D environment it's not wise to use Cartesian mostly we go to the homogeneous coordinate system and work a bit okay any question in this chapter no |
MIT_2215_Essential_Numerical_Methods_Fall_2014 | OctaveMATLAB_for_Beginners_Part_2_Fitting_Data_and_Plotting.txt | PROFESSOR: OK. Here we are. We've got our data. We've managed to plot it. Now let's go about constructing a matrix which will enable us to fit a polynomial to this data. First of all, I need a matrix. Here is a way to construct a matrix. We put s equal to-- The function zeros is a function which produces a matrix with all zeros in it, and I want this matrix to have dimensions endpoints by endpoints. So this command should produce such a matrix, and lo and behold, it does. Let me just clean up this display a little bit. At the moment, it's a little bit annoying that I'm plotting out absolutely everything that I have. This won't be too much trouble when I only have six points, but it might be in a lot of trouble if I had a lot more points. Here's how to stop our MATLAB or Octave from printing out the results of a command. All you do is you put a semicolon at the end of the line, like that. Or, like that. If I make that change, so you hit and run again, it no longer prints out x and y. It's still doing the plotting, and it's printing out s as being zeros of endpoints endpoints. That's not terribly interesting either, so I'm going to put a code on at the end of that line and prevent s from being printed out. Now, zeros is not what I want. What I want is a matrix which has the appropriate values to enable me to fit polynomials. And those values I'm going to generate by using a loop. In general, it's not a great idea within MATLAB or Octave to use loops, but it's perfectly possible to do so. Loops are generated in the following way. Supposing I choose i to be the index of my loop, I can let i range from one to endpoints by writing 4i equals 1 Coulomb endpoints. The end of that for loop is indicated by writing end. Actually, in Octave, it's endfor, but in MATLAB it's end, and so I'm just going to put end and that works in Octave as well. So that would loop over one index, but actually I want two indices. So I'm going to put another loop inside of the first loop that I had and I'm going to make its index j and I'm going to let it also run from one to endpoints. And I need to end that loop, too. Let's do my indentation neatly so I can understand this loop when I come back and read it later, and now that's a loop which will loop over all of the indices of the matrix s. To refer to a particular element of the matrix s, I write s of i and j, where i and j are indices. So I'm going to set the ij-th element of s equal to an appropriate value to use for polynomial fitting, and that value is x-- actually x I have to refer to by its index, so that's xi-- and I'm going to raise it to the power j minus 1. So if j is 1, which is the lowest element, this would raise it to the 0 power, which would just give me the result of being x to the 0, which is 1, and for higher powers, it would go on appropriately. I don't want to print this out at every time that I calculate it, so I'm going to end the line with a semicolon. And then at the end, perhaps I do want to see s, so let me just write s, and that will cause s to be printed out. So here I am. I run it again, and now s consists of this 6 by 6 matrix whose values, if I look at the top line, you can see that-- Well, first of all, let's look at the first column. The first column is all the values of j equals 1, and they're all x to the 0. And then this next column is x to the power 1, so you can see that it ranges from a 6 to 1. The next column is x to the power 2, and so it runs from a smaller value up to 1. So of course all the values along the bottom row are 1, and the values along the top row are 1/6 to the power 0, 1, 2, 3, and so forth. So that's my s and that's what I'm going to use as my matrix. Now, I can take the inverse of s by writing some new variable name. I'm going to call it sinv to remind me that it's the inverse of s, and put it equal to a function which is called inv, which stands for inverse, called s. So this command finds me the inverse of the matrix s. And when I run that, I find that s inverse is given by this matrix here, whose values will be very hard to guess. Now, the way to find the coefficients of a polynomial fit to my original data are to put those coefficients equal to the matrix product of the inverse of s, which is sinv times the y values, which we learned about in the lecture. So that would give me the coefficients. When I run that, I find out what the coefficients, or the different powers, of x are. So in other words, these coefficients-- the first line is the coefficient of the power x to the power 0, the next one is x to the power 1, and so on. So I've actually found the coefficients of the fit. For the moment, it's not obvious whether I've done it correctly. I could certainly plot out the values of this fit at various places, and that's what I'm going to do. I'm going to plot it actually with more points than I started with. So let me define a new parameter, np2. I might make it equal to, let's say, 40. I could then have a second variable, x2, equal to something running from 1 to np2 transposed, divided by np2. So that will be an x array running from a small value to 1 with, in this case, 40 steps. I'll set, for now, y2 equal to x2. That's just created an array that is of the same length as x, and is actually equal to x, but I'm actually going to end up setting y to be something else in a minute. And let me, for now, put fj, a new variable, equal to the c that I've just calculated. This won't do anything interesting, because I've commented those out, and so when I run it, I just get the same result that I had before. So I haven't actually done anything. Now I'm going to have another couple of nested for loops. I'm going to say for j equals 1,np2, and for i equals 1:np2. Let's f set the value of fj, which is a matrix of the vector, strictly speaking, column vector of the same length as c. Let's set that the i-th element of that equal to the x value, which is x2, because this is the second array that I'm creating, evaluated at parameter j to the power j minus 1. So that's actually evaluating x2 to the appropriate power. So it shouldn't have been j minus 1. It should have been i minus 1. So this is x2 j to the i minus 1. Again, I don't want to print all of those out, so I'm going to put a semicolon at the end. So that's calculated by fj value, and now I'm going to put y2 of j equal to-- Well, what I basically want to do is form the dot product between c, the coefficients, and the value of fj that I've just calculated. So I want c1 times fj1 plus c2 times fj2 and so forth. One way of doing that-- there are various different ways of doing it-- is to take the transpose of c. C remember, is a column vector. Let's transpose it. That's going to give me a row vector. I can then take the product of that row vector with the column vector fj. And so taking to the matrix product of a column vector times a row vector is equivalent to taking the dot product of two vectors. So that has produced a value y2 of j, which is equal to the sum of the coefficients times the values of x to the appropriate power. So that's what I want to form in that matrix. Again, I'm-- It seems as though I've made a mistake. And I'm not quite sure what I did wrong, but I need to find out. So let's have a look. It's saying that I made my mistake at line 29 of column 8. 29 is this, and it's saying that I have a 1 by 6, and op2 is 40 by 1. I don't know why that is 40 by 1. I'm a bit surprised by it, because-- Ah. I see what I did wrong. This should have been endpoints. So what I did was, this inner for loop shouldn't have been over all of the j values. The j values refer to the length of the new vectors that I produced. It should've been over the shorter version. So let's see. Let's save that and hope that's corrected my error. Yes. Lo and behold, it has. I haven't actually done anything to show what the result is, but at least now I've got the result. Now what I want to do is, I want to plot these two new matrices, x2 and y2, and actually I'd like to overplot them on my old plot. If I just say plot like this, save this and plot it again, that isn't what happens. Instead, what happens is just the curve that I've just calculated is plotted, and my previous plot is wiped out. What I can do to prevent that happening is to say, hold on. Only MATLAB slash Octave would have something like hold on as a command. But anyway, hold on basically says, retain the data that you've already got in this plot and add some more data on. So let's try this. So now what we see is the data that I've plotted out in my first plot, which was up here, is held and the second plot is plotted. Notice that this fit does indeed go through the six points that I originally retained, and yet, that line actually does some funny things. Particularly at the end here, it goes negative. There's another trick that one can do in plotting, and one can say things like axis manual, and I think that, if I'm lucky, that will fix this plot. No, it won't. Never mind. Anyway, there's a way-- and I'll show it later-- to prevent the plot rescaling and the required command is axis manual. But at the moment, I think, before I do it, I've got to say hold off. And then if I re-run it, I will find that lo and behold, I've got a plot of the six points and the line that I fitted, which is a polynomial fitted to those lines. And lo and behold, it fits. |
MIT_2215_Essential_Numerical_Methods_Fall_2014 | OctaveMATLAB_for_Beginners_Part_1_Starting_from_Scratch.txt | PROFESSOR: Hello. I'm Ian Hutchinson, and the purpose of this short video is to give you illustration of how to use Octave. I'm certainly not an expert at [? Octave, ?] which is an open source equivalent of MATLAB, but that's part of the demonstration. Here's someone who's not an expert who can use this routine for carrying out the kinds of exercises that we want to do. So I'm going to delete my picture from the screen now, and just show you the rest of the screen. Here I am in a directory. I'm going to start a new file. It's going to be called fitting. Let's say, fitting.m, is the correct extension for a MATLAB or Octave file. And I've opened Emax, and I'm ready to get started. Actually, I'm going to run Octave simultaneously in the adjacent window. I run Octave here. So now I'm in a situation where I, essentially, have my own IDE, integrated development environment. It's not quite the same as you would have if you're running MATLAB itself, but it's pretty similar. What I'm going to do now is develop this fitting program. I'm going to start with some parameters. Let's, first of all, define the number of points I'm going to fit. Let's make it a small number, so that it's kind of manageable. And now, let's generate some x and y values. I can set x to be equal to an array. It might be an array with six points. And I'm going to make it be run from 1 to endpoints. And so I do that by saying x is equal to 1 colon endpoints like this. I can save this file-- it's called fitting-- and then I can run it in Octave by just typing fitting. If I do that, what you see happens is, it tells me that endpoints is 6. Tells me that x is 1, 2, 3, 4, 5, and 6. Actually, I don't want it to run from 1 to 6. I want it to run from, essentially, a small value up to 1. So let's divide it by end points. And I can save that file again, run it again, and now, of course, my screen shows that it runs from 1/6 up to 1. This is, of course, a row vector. It's preferable that I have a column vector. I can transform a row vector into a column vector by taking its transpose. In MATLAB or Octave, transpose is prime. So I can say, transpose the numbers 1 through 6 into a column vector and then divide by endpoints. And if I do that and save the file, then I see I've turned it into a column vector. Let me now make a y variable. y, I'm going to make equal to x, let's say. That would just give me a straight line, if I made it nothing but x. Then I'll add to it some small fraction-- let's say, 1/10th-- not 0.1 times the sine of, let us say, 10 x. I can save that file. I can run it again. And it tells me, here's x and here's y. That's given me a start. Actually, it's a bit inconvenient to see it in quite those terms. So let's actually try to plot it. So I can say plot x y. Save that and run it. And lo and behold, it brings up a plot. The labeling is rather too small, but that's kind of built into the rather poor graphics in Octave and MATLAB, for that matter. That can be fixed in ways that I'll go into later, but we won't worry about it now. This is a line plot, which is a little bit annoying. So let's change that plot. I'll put the figure over here. I'll change that plot by telling it that it's going to have points, and those points are going to have the form of a plus sign. So let's save that and run it again. And Lo and behold, it's changed it to a plot with points. Again, the markers are rather unpleasantly small. I can actually change that if I want by telling it a string marker size. Making that size larger than it would be-- let's say, 20-- and running it again. And lo and behold, the points are bigger. So we've started, and we've made, some data. And we've used parameters. And in our next video, we'll move on to finding out how to proceed on that basis. |
Science_Technology_BBC_News | Tech_giants_harness_nuclear_energy_to_power_AI_BBC_News.txt | you're watching the context it's time for our weekly segment AI [Music] decoded welcome to AI decoded that time of the week when we look in depth at some of the most eye-catching stories in the world of artificial intelligence I am your naive Inquisitor I know nothing about it so you're in good company if you don't either this week we look at how big Tech is searching for new sources of energy to power the latest generative artif icial intelligence models it's been estimated the current AI boom could see an increase in demand for electricity so by 40% in the next decade to solve this issue Amazon Google and Microsoft are betting billions of dollars that nuclear power can help provide their AI energy needs they have revealed plans to buy electricity from nuclear power plants but what impact could this have on the planet well Tech informed says prioritizing AI over climate change could be catastrophic Recent research suggests that Global AI in data centers could need as much electricity as a small country such as the Netherlands or Sweden by 2027 so could the answer be nuclear power Tech Giants Google and Amazon have both recently unveiled plans to power their AI needs using Advanced nuclear energy as part of their efforts to become carbon neutral meanwhile Bloomberg says some of the world's biggest man managers of private Capital are also also making moves to finance and invest in nuclear power plants latching on to a Revival in the sector driven by the tech Giants electricity intensive AI Ambitions with us is our regular AI commentator and contributor Stephanie hair Stephanie I know that Bitcoin mining needs huge amounts of energy I mean what sort of levels of electricity are we talking about for AI we're talking massive as in there is not a single power grid anywhere on the planet that is ready to go where we need to go with artificial intelligence so we're going to have to completely retool the grid and that's why we're looking at not just Renewables like solar and wind but nuclear which is something that companies weren't talking about back in the spring when Microsoft and Google announced for instance that they they were not going to meet their net zero emissions commitments let's bring in Dr Sasha luchon who's the AI and climate lead at hugging face Sasha first of all just tell us what hugging face is huging face is a platform that hosts AI models and data sets and it's become really the hub for both sharing your models and finding the models you need and uh we really as spous the responsible AI approach so not move fast and break things but think about things first yeah we don't want to break things when we're talking about nuclear power do we at all I mean AI could some people say help solve the climate change crisis Sasha but it's not going to do that if it's sucking up all the electricity itself exactly I mean what we're seeing is that the climate positive applications are relatively efficient they run on your laptop sometimes on on a small computer it's really the large language models the chat Bots that are gobbling up gobbling up a lot of electricity and they're being deployed in so many different applications and that's really adding up Sasha when we hear people like Eric Schmidt of Google say that AI is going to solve the climate crisis is there any Merit to that statement at all or is that just sell-side analysis well climate change is not a single problem so it doesn't have a single solution and it's true that there are myriads of problems that from climate prediction to actually decarbonizing our electricity grids that have to be solved but AI is always only going to be part of the solution and we really have to apply it mindfully and especially with domain experts you can't uh chatbot your way out of climate change and is there any need for us to slow down unrolling out ative AI into every business on the planet if it's going to be requiring these electricity needs that we can't sustain without going literally nuclear I definitely think currently we're uh putting the the horse before the cart because uh we're focusing on getting more energy instead of thinking about why we need the energy in the first place and how whe whether we can reduce the amount of energy that AI needs and and apply it a little bit more mindfully I'm increasingly hearing the term digital sobriety and I really like that so thinking about whe whether we really need generative Ai and everything from navigation do we really need to talk to a chat bot uh or can we do something a simple Google search or do we need generative uh summaries right and and I think that currently we're just in this uh AI summer uh but hopefully an AI file will come and have us contemplate a little bit um on the applications of AI in different fields I've never heard that expression digital sobriety I I do rather like it I mean maybe it's just a little bit like you know when we we didn't used to pay for plastic bags when we went shopping and suddenly when you start to have to pay for it you start to think do I really need it I was just reading a little earlier that one chap GTP GPT query needs the equivalent electricity of powering a light bulb for 20 minutes should companies have to declare how much electricity is being required so we as consumers can make a choice I definitely think they should and nowadays people are are considering the climate in their day-to-day actions and their diets and their transportation and and digital Technologies like AI are increasingly parts of our part of our lives and we need this information in order to choose um what I don't like is is is not being able to answer the question for example how much more electricity does the new generative AI search use compared to the the good old fashion one from a year or so ago and and we really need uh opting out mechanisms and more transparency about the energy and the carbon costs of all this and Sasha one of the questions that I'm really curious to hear your thoughts on is about competition in the market because it's all very well and good for a big giant company like Microsoft or Google um or Amazon to buy a small uh reactor for themselves but most companies can't do that so could we see Regulators getting in on this and saying somehow we're going to have to diving up the resources now yeah I think definitely in terms of nuclear it's already a technology that has had its its booms and its busts as well and and for example in the United States you can have you can privatize small and medium nuclear reactors in many countries that's not the case and it is uh federal or or Regional it's government owned and so there isn't um a single solution and we're going to have to see some kind of legislation about when when you're making trade-offs between building a new data center or using that energy to power homes or uh to build new new housing or new Transportation because now more and more we're going to have to Electrify things we're going to have to have a more more robust energy grid and if that um if that energy is going towards Ai and not towards decarbonizing energy then we've got a problem and what burden is this going to be putting on all of the businesses around the world who are wanting to use AI in their processes but also have their own climate and sustainability commitments how are they going to be able to answer to how much more electricity they're using or water they're using if they're AI providers the big companies don't give the transparency that you were talking about I actually think that companies uh are the key to transparency because especially if you're using a Google a Microsoft an Amazon product and and you have hundreds of thousands of dollars of Revenue you can ask some questions you can ask questions about where is the energy coming from how is it being generated is it low carbon is there a way to make it low carbon you can really ask these questions because I think people come to me all the time asking how do I really get a handle on this how do I put add that line to my ESG report and the answer is if you're using these Commercial Services you have to ask for transparency on the other side and and you have to add that line because chat GPT is not this magic ephemeral entity uh it does it's turning on a data center somewhere and that data center is using energy and and water for cooling and and and natural resources so you we need as as customers as consumers information about all that I'm staggered that these companies are in such a position that they can be commissioning nuclear power in in in this way I was also reading that Amazon is already the top corporate buyer of solar and wind energy I is it is that scalable that green energy source it is scalable but we're going to have to see more uh Power purchase agreements which are essentially these um IUS or these promises that when a solar plant will be built that that energy will be bought by someone and actually the big tech companies Google Microsoft Amazon have been signing these agreements because it is a big risk it is a big big investment to to build these renewable uh power sources and knowing that someone's going to buy that energy in five to eight years to 10 years sometimes is is really reassuring for these providers but also I think that nuclear is kind of seen as the bridge solution because it it takes less time for example to um bring a Three Mile Island back uh back into business back into production then to build out a whole new solar power plant and Sasha one of the things I was thinking about is again the international competition angle the big companies that we've just listed that are going to be building their own reactors or buying it in are all American so what does this mean for everybody in the rest of the world we just saw you know Germany a couple of years ago decided to move away from energy could this see them needing to move back towards nuclear again remember it was in 2012 I think with the Fukushima meltdown in Japan Angela Merkel famously did the U-turn and Germany backed away from nuclear could we see AI bring countries back to nuclear who had been wanting to move away from it I mean hopefully no hopefully uh countries will be going more into Renewables uh as much as possible but I think that uh the reason why it Al it's all starting in the United States is because it's the legislation is a lot more permissive it's not a centralized power grid the US has has dozens of independent energy providers so it is relatively easy I mean it's easier uh than in a place like Germany Canada the UK to to actually uh buy up uh you know some terawatt hours of electricity but but hopefully this is is not going to set the precedent for uh just um powering up decommission power PL uh nuclear power plants but on the contrary for bu building out renewable energy and saying well actually we have a new a new wind turbine a new solar farm and and you know come build your data center here but actually that comes with its own challenges because of course it's hard to uh provide the output necessary for a hyperscale data center based on solely renewable energy because there's not always Sunshine there's not always wind and there's always CH GPD queries so it's actually really really hard to make that work you need batteries you need sometimes like diesel generators in order to be the backup and that's why nuclear has has really dominated at this point because you you flipped the switch and and you've got energy Sasha and Stephanie are staying with us thankfully because I can't do this on my own uh coming up after the break it's the 31st of October which means that many people will be putting on their scariest outfits to celebrate Halloween one of those embracing the spirit of All Hallows Eve is journalist Martin Paris who's written an article just this week on how to use AI to help make this the spookiest of Seasons she'll be giving us a devilish demonstration right after the break around the world and across the UK this is BBC News [Music] welcome back to Aid coded and as we mentioned before the break it's Halloween which hands us an opportunity to use artificial intelligence to enhance the festivities and tonight we have a special trick or treat for you let's introduce Martin Paris San Francisco based Tech reporter who writes for the BBC is a features correspondent and also is a Forbes AI columnist it's going to get quite confusing with two martines isn't it it's very unusual to have another Martin on uh just this week Martine wrote an article for fores on how to make Halloween fun with chat GP PT so we decided to invite her on the show to tell us how uh with us again is our regular AI commentator and contributor Stephanie hair and also Sasha luchon is still with us as well so we're gonna have a bit of a play Martine tell us about this new feature called advanced voice but producer I can't hear what they're saying hi she can't hear what we're saying I'm here when you're ready to start oh okay um tell us how advanced voice works how does Advanced Voice work Martin okay just stand by we're g to go on in just a second no we're struggling we're struggling with this let's see if we can establish contact with Martin um the the point is that this is a feature uh Stephanie that can make stories for us could tell us a spooky Campfire story tonight well so uh Americans are crazy about Halloween and are set to SP 12 billion this year on this one holiday alone dressing up candy stories are a big part of it so what we're going to be hoping to ask this tool is it for it to tell us something that'll scare us so I think we have to acknowledge the fact that we're using chat GPT which might be running on nuclear power for all we know to do something that's maybe a bit glow-in-the-dark it might it might be running on candle light tonight judging by the difficulty we' just had let's see Martine Paris can you hear us now yes I can hear you thank you tell us a little bit about just briefly what advanced voice does okay well advanced voice is um part of open AI Advanced reasoning model that they just released and um it's very relatable it it it's emotive it could sigh it can laugh it tells jokes it tells stories it can be a good coach some people are using it as a therapist some people are using it as a tutor to learn languages it knows 50 languages so there's a lot that cat GPT can do now and what kind of scary stories can it tell us well let's see chat DPT are you there we are okay so we've gathered the squirrels young squirrels in the forest can you please tell them a spooky Halloween story about witches werewolves and zombies absolutely gather round little squirrels Once Upon a misty Halloween night under the glow of a full moon a coven of witch gathered around an ancient Oak their High cackling voices whispered through the branches casting spells of Mischief nearby a werewolf howled its cry echoing through the forest sending shivers down the spines of all who heard it and from the Shadows zombies emerged their steps slow but Relentless hungry for the thrill of the night can you can you tell us how the what how the werewolves feel give us one of the howls as the Mist thickened the werewolf raised its head letting out a chilling [Music] howl I'd like to hear it in a kind of Vincent Price voice wouldn't you Stephanie wouldn't you Sasha Sasha throw something into the mix what can what do you want it to do I can't get how about can you hear me how about a a good witch comes and and casts a spell on the zombies okay all right so Arbor now the witches are coming to cast a spell on the zombies to save the day in that high squeaky voice can you tell us what the witches are doing in their High squeaky voices the witches chant with a flick and a swish we cast our spell to break the zombes gruesome nail with a wave of their a shimmering light envelops the zombies freezing them in their tracks and saving the forest from their Advance yay happily ever after and you've chosen a character called arber to tell this story but there are others that's right chip PT comes in nine voices two are British sounding uh the other seven are American I think there's four male voices four female voices and one nonbinary yeah and what are you supposed to use it for other than just to entertain yourself which by the way is totally fine um you know you could get very addicted to it except there's a one-h hour uh limit on use if you subscribe to chaty BT plus there's some sort of daily limit on it um but even free users get about 15 minutes that they could uh try out uh um advanced voice and it's great as a therapist I mean you could tell it I'm trying to lose weight can you coach me on my daily meal plan it could give you a daily meal plan then ask you how it's going um you know you could use it to study you could use it to audition you know you feed it the lines um there's a lot people are using it for CH there's a little bit of caution there that should be put because if people create these very human links with uh AI uh models um that can give them advice I mean recently there was a a suicide right from a by a boy who got addicted to his uh AI companion so I think it's grain of ass um with uh therapy specifically because people who are in vulnerable places and who need emotional support shouldn't necessarily rely upon uh large language models but but seek professional help I mean I'm all for having a companion or having advice but I think what especially when it comes to to the psychological part of things um a little bit of caution is good yeah just briefly Martin Martin I just wanted to ask it's therapist I'm sorry go ahead chat GPT turns two next month um what do you think we're going to see it evolve into in 2025 just briefly well we know open AI has just raised an enormous amounts of money to create agents at a chat GPT and these are um these are transactions that chat GPT can do um with human instruction but um autonomously and so agents are the next big thing uh book a flight um you know get you a table at a hot new restaurant that's that's coming in 2025 more mainstream next year it sounds like the scariest Halloween story I've ever heard more AI in your life great powered by nuclear energy trademark yes what could go wrong how often do you use it though in this form Martin you've obviously had to play with it this week would you would you use it in your spare time so I do I use it quite often um I I I actually use it um just to check in with I had covid about two three weeks ago and it kept me com when I had to isolate um and you know you can again feed it your goals um and it could just check in on you and say you know how's it going with this um so yeah I find it it's a very uh um interesting companion because it's very uh empathetic uh emotive entertaining it could give you a guided meditation it could give you a l and it'll keep you accountable which is even better Stephanie Martin Sasha great to have you all here on Aid coded we'll do it again same time next week |
Science_Technology_BBC_News | AI_robot_dogs_take_bullets_to_save_humans_say_engineers_BBC_News.txt | uh you're watching the context on BBC News it's time for our weekly segments AI [Music] decoded welcome to AI decoda that time of the week when we look in depth at some of the most eye-catching stories in the world of artificial intelligence well the AI Summit landed in London this week showcasing some of the most Innovative companies using Cutting Edge artificial intelligence we were there in a moment we'll show you what we discovered and will hear from some of the biggest names who were at the event they include Boston Dynamics that's the world's most advanced robotics manufacturer they were featured in The Internet of Things website that's after a Tik Tok video of the company's robot dog spot demonstrating its potential civilian uses that went viral online we'll hear exclusively from spot well maybe as human Handler anyway in just a moment variety magazine asks is the music industry too frighten of artificial intelligence as artists raised concerns over the changes AI could bring to musical creativity so we'll hear from one pop star and a famous music producer who think that AI will help unleash human imagination and make the music even better well with me is our regular AI decoded contributor Stephanie hair author on technology and AI commentator uh Stephanie good to see you as always um so it's been what tech week and AI Summit was part a couple coup of days of part of that wasn't it that's right right up your street you've had a great week haven't you yeah this is like Christmas and birthday week all rolled into one for anybody who's interested in technology particularly in AI so we had the AI Summit yesterday and today in tobacco dock which takes place in East London a really Dynamic part of the city where a lot of tech companies are already located and then all week we've been having this big kind of gathering if you will where lots of Scholars have flown in and researchers from North America the Royal Society giving papers sharing talks sharing best practices so it's it's really important for researchers to come together and get their research out to policy makers lawmakers and business and vice versa to kind of feed back into the labs the real world challenges and experiences with AI um and I suppose I guess the sense is when you're there you can have these conversations you can meet all these people and that's where the real work gets done doesn't it yeah I mean yesterday for me was just sort of magical because I was talking for instance with IBM about their responsible AI practices and how they're trying to use generative AI in a really ethical way and looking at cyber security because the more we're using AI the greater the attack surface so we've got to protect all that data we met with Boston Dynamics about which more in a moment I won't spoil that surprise and for me the Highlight was I spoke to a woman named Crystal Johnson who's a scientist at Nasa who was talking about NASA's efforts to get humans back onto the moon and eventually to Mars using AI as part of that it's just breathtaking uh so let's have a look at what you found out shall we yeah hello there welcome to the AI London Summit 2024 [Music] Brendon first thing I have to say is I'm wearing an IH heart AI badge you're wearing one that's slightly different can you discuss cuz it's got something to do with the little dog that's walking around behind us yes thank you I'm wearing a a pin that represents our spot robot spot is a quadruped robot that does commercial and Industrial inspection it's often used in manufacturing facilities energy plants it's being used uh here in the UK for uh decommissioning ofle sites for example at Coffield and junet now when you say it's being used who's using it and to do what like what does what does spot do is he fetching is he rolling over or is he helping people in some way uh spot typically is used in industrial facilities as an inspection robot so for example it will walk around the facility autonomously 24 hours a day looking for anomalies in the plant for example you a piece of equipment might be overheating or a bearing might be wearing out to alert the maintenance staff the something needs to be fixed before the entire facility has to be shut down so that's a way of of doing preventative maintenance and inspection in a way that's much more efficient and cost effective for the industrial facility now how is he doing that is that Sensors how many cameras does he have embedded in him how's that how does that work so so the robot has cameras around its body for navigation purposes and then as you see here there are sensors on top of the robot and those can be changed depending on what the customer wants to do with a robot so in this case there's a lar sensor there that's used to create a 3D map of the environment it can create like a like a digital model of a building or a construction site but we also have customers that do um visual or thermal payloads so a thermal sensor might be used to detect overheating of equipment um or other types of problems that might need to be addressed in the facility and is this a case of spot is doing things that are too dangerous for humans to do or simply that you don't have to pay for 24/7 Security in a facility you can simply have a robot do it for you instead that has six cameras instead of two eyes it it's a combination of doing things that are either dangerous for humans for example uh decommissioning of a nuclear site or things that are that are dull because it's a 24-hour inspection routine that just consists of walking around looking at things uh or dangerous it might be sort of a hazardous type of uh situation maybe it's an industrial plant with um with extreme temperatures send the robot in keep people safe uh keep them focused focused on more productive or more interesting tasks in the facility now you've mentioned safety a couple times in this conversation so I'd love for us to brooch the topic of safety ethics and the law how do you make sure that a robot dog is always friendly to humans and never harmful well one of our ethics principle is that uh and this is right in our terms and conditions of sale is that the robot is not allowed to be weaponized nor can it be used to harm or even intimidate any person or animal so if you buy the robot from us as a customer you are legally agreeing not to misuse the robot in that way do you have the remote capability for instance to shut it down if you were seeing you as a company that your product was being used in a way that was harmful to humans so there's two solutions to that first of all it's never happened we we haven't had to do that um but we do have legal remedies because it is in our terms and conditions of use as soon as that misuse occurs the software license becomes invalid and they no longer have legal authority to operate the product and we would we would pursue legal options in that respect um but there also is a software license on spot that expires uh every year and so in the event that we learn of misuse it's it's possible that we would not allow automatic update of that license so that's one additional way that we could take a technical measure uh to address it who would have the responsibility to police that uh you would expect the authorities starting with law enforcement and then prosecutors and of course the judicial system uh to resolve it to figure out what exactly happened uh did they do something wrong or not not and then to apply penalties if appropriate definitely part of our long-term vision for Robotics and Society is for this type of technology to be helping people who might be disabled uh who might need physical assistance who might even need companionship that's not a product we have today I wouldn't say that spot is designed for that application yet our focus is on the industrial inspection uh and Public Safety actually we we had a robot about 3 months ago that was shot during during a uh police uh encounter with an armed suspect in a sort of barricade uh scenario there were uh the robot was sent in to try to figure out you know what what's going on inside this house where someone has barricaded themselves with a weapon and that person uh sort of kicked the robot and then decided to shoot spot three times so spot took three bullets which sounds awful if you like robots uh but to us is a is a great story because that's a machine being harmed instead of a person I feel really sad for spot spot got shot uh it's definitely still with us uh I mean you got such a great insight there into how that works and the thing that strikes me watching that this really is that kind of the intersection is it between Ai and Robotics um and the two can exist on their own but this is where the two really get quite powerful yeah because we were actually able to see how spot the robot sees the world so I got down was you know looking on it and we suddenly were able to see on the big screen how spot was seeing me right and it's totally different you know machine's eye if you will sees differently than the human eye but what's really different is that it's taking and capturing all of that data along with its sensors and it's sending it back and learning all the time what is it learning from that image so that image of you is it identifying who you are or type of threat you might be you could put facial recognition on that gate analysis on that you could learn to spot um spot could learn to spot uh body temperature right so like maybe it's completely dark and there's no light but it could be taught for instance it could be given the capability to see that there's a human being hiding in the factory or um passed out in a fire in the factory where there maybe just smoke and identify it and like identify that somebody needs to go in and rescue it so it could be given all sorts of things the thing I was a bit worried about and I would urge these engineers in Boston Dynamics just to consider this is the ability to to remote disable a robot I think legal recourse but actually a call a lawyer and it'll take like two years later to get get a lawsuit filed so you'd like perhaps to see that they could remotely disable the abilities of off spot yeah if it for instance if it got hacked if it just went haywire like went rogue if there was some way you know things happen unended consequences all the time in technology it would be really nice in certain situations not just with this robot with I think with any robot that principal is there if it could be remotely disabled um Stephanie really good to you to talk to you about that and really nice to see that piece actually can it really brings it to life doesn't it for now thank you I know you're going to stay with us we'll talk some more in just a moment because still to come on AI decoded is it music to their ears or a threat to musical creativity we'll hear from the pop star Daniel beningfield and legendary music producer Fernando garbay about the future of human creativity in the shadow of AI stay with us on AI decoded around the world and across the UK you're watching BBC News welcome back to AI decoda now we've been showing you a glimpse of the future and how robots can reshape our daily lives but what about the impact on things like human creativity in areas like art literature or music what role could AI play in writing songs and making music are they a tool for creativity or simply a threat to people's livelihoods let's talk now to AI contributor Samir malel he's chief executive of creative AI company that's one day with us now Samir nice to see you um this is the common debate isn't it when we talk about AI that it can stifle all of human creativity that robots and machines can never be as creative as humans you don't agree necessarily so AI will never replace human creativity but it can expand what you are capable of it can allow you to create in a way that you have never been able to create before and the clip we're going to see is a very very good illustration of that yes and in this clip and we'll just explain what's happening talk to me about what we're going to see so we're going to see Daniel uh and Fernando and they're going to be doing an experiment so the experiment is how to make the best song using this AI toolo so they're going to take two different approaches and we're going to we're going to discover which one works best so Fernando is going to ask the audience for emotional responses and he's going to use that to prompt the AI and by prompting I mean he's going to give ideas to the AI about how it should perform and Daniel's going to take a different approach he's going to be like a curator and he's going to quickly go through all the different iterations and he's going to pick the best one and so we're going to discover which is gives you the best result so let's find out let's take a look the first ever electronic bedroom producer I should say yeah yeah scaled you scaled you make pop music probably yeah because it's the one who gets you the Finish Line first it becomes the owner of that title one of the greatest producers of all time and uh he wrote B Moss BOS at 15 he had his first number one at 15 you're going to take part in two different ways of working with the machine machine with some very exciting special guests that just thrown in and we're also going to write as a comparable well we're going to prompt uh the same platform to make a song on its own anybody like TR Bas come on London okay guys you not making a lot of noise that means you're good listeners go N na everywhere what words can you hear to na na na come on writing a song I'm putting the track that we just in there to generate new versions of what we created I'm happy through your kitchen or cook any dish Etc so I can see that so so I'm going to generate like 100 pick one in 10 minutes do is let's find the greatest human not no longer 10,000 hours to to the equivalent of Mastery of a discipline is 10 hours yeah so when you think about prompting it's important to think especially the creat a space to think about what moves you what's truly honest to you you could have one meal and only one meal as your last meal with anyone that's ever existed in history who would that be Frank Sinatra being replaced and unless we pivot as musicians it's over we all have to get used to this is a tool a tool to enable creation we have to see as our Ally at least for now not do I'm asking that you write me a song about self love feeling seen feeling free and navigating the ups and downs in life right in a first person point of view and had a lyric about loving yourself better so we're going to run that we're going to show the full emotionally affective PR it from the audience AI song it's again it's a lottery system we'll see [Music] upar the and the lows [Music] if you think that you're a Creator and that's your identity and it's based on that you're not going to have that to fall back on anymore we are creative as as a world and I think we're going to have to move into the we to get our sense of self we play again [Music] for the of your releas now releas now cut the strings of Your Love releas Me Now release cut of [Music] Youree my son is uh you know in first grade and he generates 12 songs on the weekend this last weekend and he djed them during his little lunchtime so and he learns he plays every instrument right so he manually plays every instrument drums piano guitar um and so so that for me that's the balance right it's like I want him to learn how to be able to use an instrument to express his feelings see it's a cathartic process that you know it's it's a little different from prompting that you get from actually playing expressing your emotions T you know Tak right playing picking up a guitar that there's a value to that and equally there's a extraordinary value to prompting and learning the language to better prompt to get to the the the song he wants to hear to to live in his feelings with the songs that he generate [Music] soon so whatever you think of the music uh fascinating insight into how all that works Stephan and Samir are still with us um Samir I thought it was really interesting there Daniel benningfield saying unless we pivot as musicians it is over and I wonder how you think that role as as a creative as a musician in this case will evolve because of AI yeah it's a really good question well look at the difference between Daniel's track and and the one that was produced directly in with just the AI so Daniel's like a curator and that yielded a different result it's it's track was emotional and he's still putting himself into it and and that is the role that I see us inhabiting as as creatives and we have a huge Advantage we have our taste we have our craft we have all of our experience that we can bring and we can Elevate AI in into into a whole other kind of you know collaborative medium um and Stephanie what strikes me when you look at something like this as well is that yes you may see it as a threat to you know to the very nature of what humans do which is create stuff but if we think about using it as a tool then suddenly it opens doors to people that maybe don't have some of those skills but they have different skills and and in so many different creative Fields this could open the door to a lot of people absolutely when you think about how we don't actually have a lot of funding for music education for example in so many countries now at the cost of living crisis there's a startup cost to learning how to play the piano or learn music theory really well these tools could give give anyone the opportunity to experiment and composing their own kinds of songs and expressing themselves emotionally now a trained musician or someone with that training might take it much further but it still makes it it's kind of democratizing all sorts of artistic expressions and democratizing it but is there a danger that those tools fall into the hands of big business and I mean this is a common theme isn't it is about who has the power um here who has the tools available and If that is a tool and access ability tool for whatever industry it needs to be available to all doesn't it I I totally agree with that and that's why it's really important that young people across all kinds of um you know um Spectre of society are are getting the opportunity to use this tool and to learn how to use it as a collaborator and not just get it to do things for you because that is going to create a new kind of class structure around AI right the people who learn how to use AI to make themselves do more and to scale themselves and to do things that they couldn't otherwise do those people are going to get way ahead and so we need to encourage that across a broad section of of the culture and society and Stephanie you talked about education for things like music or instruments and then having the you know the financial means to be able to afford it is there is there enough education around what these tools can do because these will be the the instruments of the future I would say not yet I think that every country that is looking looking to capitalize on AI and the opportunities of it is going to have to rethink their education curriculum starting from the age of children you know Preschool On Up you want kids playing with this learning to have like a critical constructive facility you know the the ability to sort of understand and differentiate between what is fake and what is real and how to play and manipulate with it kids are really creative naturally and I think they're going to have so much fun with this so it's for parents and teachers to get in on this too yeah and Sam what are you most EXC exced about this as being a tool and and and we have to view it as that don't we it is a supplementary tool it is not a replacement and again you know in Daniel benfield's words we need to Pivot and it's about that embracing it rather than fearing it yeah I mean look some things are going to get replaced like that is just a fact of any new technology coming in so we we can't sit around as artists and and wait for that to happen and give all the power to these AI companies and trust them when they say they don't want to replace us I I I really don't buy that and when you look at tools like Sora and and things like that I mean what are they trying to do so I think we have to get out there and and use this in our own way and do do what creatives do which is express ourselves through this technology that's what we always do and we got to find ways of doing that um it's really going to be fascinating to see how all this plays out isn't it so nice to see the pieces you made for us thank you for doing them uh so the AI Summit this week and really f get an insight into the real world applications of all of this uh Stephanie and to Samir thank you really grateful for being with us thank you uh that is it uh we are out of time of course we will do AI decoded same time same place next week much more uh on this on the BBC website of course and you can watch previous episodes of AI decoded right there but thanks to your company this week see you very soon bye-bye |
Science_Technology_BBC_News | How_AI_helps_predict_extreme_weather_BBC_News.txt | we are back with our weekly segment AI [Music] decoded welcome to the program we have had a summer break from AI decoded but if like me you were on the British beaches Sheltering from the rain then maybe you were scaning your mobile weather app to see if the sun might ever reappear which got us thinking what about Ai and the weather how do you predict climate when it is changing so fast how do you process that incredible amount of computerized data that is now being generated well you model it and that is where AI is making huge advances there is a forecasting Revolution underway so accurate says the guardian and now in much more accessible format that very soon governments around the world will be able to save lives and protect livelihoods before extreme events even occur we'll hear from the team at Oxford University who are filling in the gaps with AI and making it more readily available through Cloud computer shoting or how about this from the EU destination Earth a digital copy of our planet on which scientists are running complex simulations to predict natural phenomena AI combined with climate science powered by supercomputers a digital twin if you will that will help scientists predict the evolution of climate change with me has ever our regular commentator and colleague uh Stephanie har is here also in the studio the very well-known meteorologist Florence rabier Dr rabier director general of the European Center for medium-range weather forecast and joining us also on Zoom Professor Steven Belcher who is chief of Science and Technology at the UK Met Office welcome to you all um fla uh we're going to start with you um and the Earth's digital twin that you and your team have built in collaboration with the the AI industry so let's get a view for the viewers let's let's just show the viewers what it entails and we'll talk off the back to create a better future we must push the boundaries of today simulations of our Earth system known as digital twins will help us understand predict and plan for a rapidly changing world this twin will offer highly detailed Interactive data that can support decision making around extreme weather [Music] events this twin will show us possible Futures it simulates different climate change scenarios over many decades helping us to be ready for whatever happens wow so in simple terms you are stimulating the natural phenomena and the human activities on Earth putting it all together through this supercomputer and what putting it onto a digital twin of the earth yes so digital twin of the Earth because it's this super model of everything that the Earth is doing that we can predict through Computing equations so it's a model where all our knowledge of the physics of the atmosphere and the Earth system is encompassed in that model so it's a computer program that we put on a supercomputer and we run it but all our knowledge of the physics accumulated since Newton and all is there about gravity condensation you know storms Etc and it's a digital twin of the Earth because it's very accurate and it has a very high resolution and also it's interactive you can play a bit with it and simulate what if scenarios so I imagine that in Times Gone by you would do that at a very local level but of course we're all interconnected the world is is is a global environment our our weather systems uh and activities are all connected so so how does this enable you to improve the forecasting that you do yeah so at ecmwf what we do we run these Global model so it's really across the whole world because if you want to know the weather in Europe now you have to know what happened in the US a few days ago and in the Atlantic and even in the Pacific if you want to predict the weather 7 Days beforehand so it's all interconnected you're right you have to start with a global scale and then you can refine at the local scale as well but you really have to know what whatever happens on the world at any point in in time in order to go further in time in your predictions and that's what we've been doing for about 50 years in collaborations with our member states 35 countries in Europe supporting this work so Florence is this a uniquely European initiative or do you work with other partners around the world so there are several Global models in the world and our because we are European we are working in collaboration with 35 meteorological services in broadly Europe broad Europe but Amer model Etc ah okay but are you using historical data or like live data or both probably both I mean for the weather forecast usually we use the current data so the data we've seen in the last 12 hours but the model had seen the data beforehand and it's a sort of continuous process we combine physics and data we go forward combine again so the latest forecast uses the latest data but historically we've used the data from the last decades and rolling like this I tell you what we we've got a a real life example uh that mapped the recent typhoon typhoon G I think it was called uh in July this year so so you see all the lines around the two main lines so there's the red line and the black line which we'll talk about in a second what are the other lines that we're looking at so that's typically what we do as a forecast so we we predict the weather but in particular we concentrate on severe events like that because this typhoon G me was really uh had dire circum you know consequences with 100 people dead and millions affected so what we produce every day we produce not just one forecast but we produce actually several forecast together to to depict the whole probabilities of what the weather will do this way we don't just simulate the track of the typhoon but all the possible tracks that we think the typhoon will take in the next few days these are the gray lines so which is the AI model so the gray Line's our physics based model and the black line is the real observed track of typhoon and in the blue what you have is our best estimate that we had before AI of where the typhoon would go and would hit China he's telling me that red one is the AI that's almost tracking exactly what happened in real time in that case it is and that's incredible it is incredible but you can't judge everything on one case of course we accumulate all the these cases and we do statistics but it is true that the AI models are in general about 25% more accurate in predicting the track of tropical Cyclones typhoon and hurricanes which is huge but they are not doing everything right either so in particular in terms of the intensity of the typhoon they are actually about 20% worse so it's not all perfect you've got a real interest in this because I know that you grew up in tornado Valley in America right so Tornado Alley is the midwestern part of the United States that runs from North Dakota all the way down to Texas and then probably for 500 to a, miles on either side so I grew up just outside Chicago and routinely we practice these drills as children you get a little bit of warning we're talking seconds and you have to find the nearest basement and get underground because a storm will come through that can destroy an entire town in seconds presum this could tell you which street to go to well we're not at that sort of scale especially as we work I have big expectations but but it's get but it's getting better and better all the time it is getting better all let's bring in Professor Steven Belcher who is the chief of Science and Technology at the UK Met Office um welcome to you um so far we've talked about global weather patterns uh Stephen climate Trends mapping evolution of weather patterns but how much more precise is weather prediction getting dayto day because of this AI technology well it's worth remember remembering that there's always pressure to increase the accuracy and the utility of weather forecasts uh today's great example we've had certainly lots of rain here down in the southwest of England so with climate change making extreme events even more extreme we're demanding that our forecasts get better to uh help us understand what the impacts of those might be also we've got new applications of weather forecasts and just think about the roll out Renewables this is meaning that weather is now the fuel of the future so understanding that fuel is another application of of our weather forecasts and so to make them more accurate we need increased lead time so we need warnings further ahead of when we're getting these extreme events but we'd also like finer detail just as Florance was describing earlier I was making quite big demands of Florance but I'm going to put up an image here about just how accurate this can get so here's a here's an image of London that we'll all recognize um uh you can see the Millennium D there the bend in the River East London tell us what we're looking at here on the left and on the right right so at the Met Office we complement What's Done in Florence's organization the European Center by producing highresolution physic Bas modeling of the weather over the UK so the leftand side is showing you the grid that we divide London into in order to provide that weather so what what we're seeing now is the weather on at that kind of resolution about 1 and 1 half kilom we we kind of increment the the differences in the rainfall and the temperatures what we've been able to do in fact one of our Rising Stars Lewis blun here at the Met Office working with students at the University of reading and also at the Bureau of meteorology in Australia um has devised a machine learning techniques to add fine detail onto those routine for CS that gives us detail resolutions of hundreds of meters in the temperature so you can tell the temperature and the Heat and the rainfall literally over the Millennium Dome uh the temperature at this stage and maybe other variables in the future but but the the temperature is what Lewis and his colleagues uh worked on and the reason this is important is that we we've known for some time that uh when we have heat waves um those heat waves are more extreme in urban areas so in particular those who live in cities will have noticed that the temperatures don't cool down so much at night and we call that the urban heat island so what Lewis and his team did was to take data actually from crowdsourced data in back Gardens and uh citizens in London their data so of variable quality frankly plus five professional weather stations they Mash that together together with machine learning tools and augment the regular forecast that we produce here at the Met Office and can then produce these temperature forecasts at these very fine levels so it's another example of how AI can really change what we're doing in the in the weather World Professor beler I've got a question for you exactly about this um taking data from your back Garden sometimes when I'm standing in London I will consult the Met Office app regularly in fact and it will say that it's sunny and I'm being rained on why is that happening and second how or when will I be able to send data to you saying no no here in hatney it's raining so you can you can send data to us right now so it's called weather on the web the wow site so please do that you can Lodge your longitude and latitude and send in your data to us and as I say that's the data that Lewis and his colleagues used to produce this um I think in terms of weather forecast let's not forget that over the last 50 years through the Advent of satellite observations and other observations right around the world the Improvement of those global models that Florence was describing earlier and and the increased scale of supercomputers that we've got these physics-based models we've got the weather forecast has increas improved tremendously well and and one of the statistics we describe is that the weather forecast incre improved by one day per decade so the 4-day forecast now is as good as the three-day forecast was 10 years ago so this is often referred to as the quiet revolution in weather forecasting what AI is doing is really accelerating that Revolution so it's a loud Revolution we're going to continue the conversation we have to get a short break but we're going to see how this can be applied around the world um coming up after the break we'll bring in the climate physicist Dr shuy Nath she is part of the physics team at Oxford where they just pioneered a new approach to predicting extreme wither stay with us welcome back we are warned repeatedly that climate change will affect millions of people worldwide in fact is already affecting lives and livelihoods and particularly so in some of the poorest regions of the world where they don't have access to this realtime forecasting or the vast computer power needed to produce it well Dr shuy na is a climate scientist at Oxford University she's been working with the UN world food program to develop an AI system that is pulling together all this data current and historic and applying that to localized area that information can now be condensed and shared through cloud computing to help the governments and Aid agencies better prepare for climate disasters let's bring in our guest then Dr shudy D It's good to talk to you thank you very much for coming on the program um there were some brilliant physicists like you in the in the Oxford University Department I I want to better understand that what the AI is doing to speed up the process and fill in the gaps yeah so thank you for having me at oxid physics we're exploring hybrid modeling approaches so we're looking at how AI can best complement our existing physical weather models so as Florence says these models have all the physical knowledge that we've accumulated since Newton and we're complimenting it with AI particularly at Oxford we're looking at rainfall since this is a high impact very localized feature of the weather and what we're seeing is that when we take the best of the physical weather forecasts um we can really use AI as a data driven technique to correct the structural errors that exist in these physical forecasts um that could arise from incomplete representation of atmospheric processes to better deliver actual accurate rainfall forecasts um within the region that we work in so that's the greater Horn of Africa and um Dr n how do you see Ordinary People in the regions where you're working being able to access this very sophisticated and high powerered technology that you're working with so that's a very good question and that's actually in my opinion one of the real strengths of AI it's a very lowcost lightweight model of being able to represent very complex phenomena so we work closely with all the local mological bodies and we work with developing the model with them so they actually run the AI models um inhouse and that means that they can actually generate weather forecasts on a laptop mind you that's a laptop as compared to a supercomputer which is what typically is used to generate weather forecast can you give us an example of where you've used that a real a real time example of course yeah so we use it in Kenya so they update the forecasts every day um in Kenya and Ethiopia and the forecasts are also available on a website so um the website name is sean. pac. net and they're updated every day um from the in-house forecast generated on you know their uh equipment so it really is a way of giving these people a bit more access ible weather forecasting but presumably that I mean the Breakthrough of all this is that you can if you know what's coming and and the long range forecasting improves you can the aid agencies can can put can sort of store forward the aid that they're going to need for what's coming at them so you know so often on our programs we're we're sort of saying well we can't get to these inaccessible areas but now the stuff will already be there because we've already forecasted what's coming exactly so we particularly actually focus on linking research to actions so we work with linking these forecasts to anticipatory action and as you said we can have these long range forecasts and also chipping in on what Florence mentioned about how you know weather is quite chaotic so there's lots of possibilities that can arise from a given starting point so we have a lot of uncertainty and you need to actually generate a lot of different weather forecasts to explore that AI allows you to do that in a very lowcost way so you can generate forecasts that explore the uncertainty space in a very lowcost manner so that you can actually properly inform anticipatory action in these areas we've talked a lot about weather what we've not actually talked a lot about is is climate change and and of course there are climate deniers out there Florence uh that we must uh acknowledge I'm got to put a picture on screen do you ever remember this uh this was a a tornado that was coming at the Florida Panhandle um and also was some questions about whether it might go to Alabama and and they got a Sharpie out and they actually drew it on the end at the Trump Administration which uh which tells you that that uh you know we it clearly is something that that people try to play with when when we talk about climate the way climate's changing what weather is going to do but your your for are so accurate Florence and presumably with your digital twin earth You can predict how climate is going to evolve well into the future well exactly and we use the same weather model to to do climate models as well so they are just a bit more complicated but it it's based on the same sort of of modeling but also we can document climate change and that's what we're doing with the Copernicus program from the EU going back since you know from 1940 and really depicting what the weather and climate have been doing every hour from 1940 to now we have this picture of the Earth and we can then document how much the temperature have increased how much the frequency of storms have increased Etc so it's predicting it but there is already this reality we not we have enough information to know what has had happened already and then with these models then we can do a digital twin of of the climate as well and go forward in the future with different scenarios of course of what will happen in the reduction of greenhouse gases because of course it all depends how much we can reduce the amount of carbon dioxide in particular that we put in the atmosphere and I've got a question for all three of our distinguished scientist only got a minute left so you're going to have to make it quick go we keep hearing that we're running out of data and that this is a big problem for AI but I wonder if that's actually true particularly when it comes to weather climate change and biodiversity loss we have to fix obviously the climate change and biodiversity problem do you feel that there's a way for citizen scientists to get back into action and be submitting data to all of you scientists so that you can help us fight these bigger problems St Stephen pick that up because we've just about 30 seconds left yeah it's a great shout and as we talked about earlier we've got the weather on the web there's another great crowdsourcing initiative to look at um in and early sighting of insects around the UK which we've also connected with climate change um here at the Met Office along with many other partner organizations so I think it's a great shout for citizen science this one I could talk plenty more as I always could on this program every week we we never get to the bottom of everything but listen uh Florence Stephen Dr Nath Stephanie thank you all very much uh for your time really fascinating discussion just a reminder we are putting all these half hour programs on the BBC's Aid decoded YouTube site so you can find all our pass programs there we'll do it again same time next week thanks for watching |
Science_Technology_BBC_News | China_space_probe_returns_to_Earth_with_rare_Moon_rocks_BBC_News.txt | China's Chong R6 lunar probe has returned to Earth bringing with it samples from The unexplored Far Side of the Moon so these are live pictures of the capsule re-entering orbit Earth's orbit in the deserts or above the deserts of inner Mongolia and you can actually see it touching touching down on Earth as it descends and there it goes you can see the parachute just collapse and uh follow uh down to the ground there so this is in a Mongolia in northern China it's the northern Chinese uh region scientists say that uh they will very soon start to analyze the rocks and the soil that have been gathered from the Luna surface China is the only country actually to have landed on The Far Side of the Moon with this particular craft docking in a giant crater close to its South Pole uh whilst it was there I think it spent some 2 months uh in space well our China correspondent our beijan correspondent Laura Bier has been following uh the story for us hello there to you Laura we're just looking at the live pictures there uh on the plains of uh in a Mongolia um this is a a hugely significant uh step for for the Chinese government yes this is a world first and China hasn't just landed on The Far Side of the Moon once it's landed on The Far Side of the Moon twice the reason this is a world first is it's the first time they've managed to collect soil and rock samples now why is The Far Side of the Moon such a fascination with Scientists well first of all it's thought that The Rock composition is very very different to the side of the moon that we can see and the reason for that is the side of the moon we can see the rock samples are a bit like that you'd find in Hawaii or Iceland they're volcanic in nature but scientists just don't know what kind of rock samples they'll see on The Far Side of the Moon the other reason The Far Side of the Moon is of real interest is because it's very very difficult to get there now China launched a special satellite to allow it to communicate with The Far Side of the Moon because it faces away from Earth it means that space centers here on Earth cannot communicate with the craft when it goes around that side of the moon so what China did was launch a satellite at that time to ensure that it could communicate the third thing that China was able to do was use that robotic arm and collect those Ro Rock and soil samples and enable it to put that back on the craft and as you see they've just landed on Earth and scientists will be able to research those samples this is a major step forward to for China in its space Ambitions pre president shei has described it as a Chinese dream he believes that this is part of a space race to the moon and certainly NASA officials have said back in May that there is a new race to the moon between the United States and China um Laura it's you know it's often referred to as the dark side but it's not dark is it I mean it gets its full share of light but do we know why they chose the South Pole to land do you is there any information as to why that particular Landing site it was it's because of the crater that is there um it allowed them to land on that South Pole Basin Atkin Basin and that's because it's got a massive crater that allowed them to land there and that's where the coordinates for the satellite came from so it's one of the reasons why scientists have chosen that site it would allow the probe to dig into that crater what they're hoping is that these rocks will be able to tell scientists about how the moon and how planets are formed and that's why they want this particular rock sample and to analyze these particular Rock samples and yeah you're right uh we have been told off by the science department to not call it the Dark Side of the Moon It's The Far Side of the Moon and but when it comes to uh when it comes to what we see that's probably why people at home are going oh it is the Dark Side of the Moon okay lauraa thank you very much indeed thank you |
Science_Technology_BBC_News | Rise_of_AI_influencers_raising_ethical_concerns_BBC_News.txt | artificial intelligence influencers are a growing industry with some AI models gaining hundreds of thousands of followers and getting increasingly lucrative sponsorship deals itana is one of the world's most popular AI models known for her stylish pink hair the BBC's cyber correspondent Joe tidy reports a photo shoot with no model she's not late though she doesn't exist itana is an AI model since she was created around a year ago she's amassed a big following and is making thousands a month for her Barcelona based agency we intend to always try to make it as similar as what an influencer would do we take a picture with me in the image and we have to replace it with AI so we have to play a little bit with lights and shadows to make it as real as possible maybe the Barcelona the background is going to be more interesting touchups used to take around a day but now it's a few hours because of how the AI improved so much Here's the final product the studio says they can get thousands of pounds a month for sponsored posts and endorsements with itna her virtual life is built for her mostly male fans a key demographic for these AI models some find the message they're sending to boys and girls troubling I see huge issues with the rise of AI models and influencers I think they're setting an unrealistic Beauty standard that is close enough to being real that a lot of people who follow them don't realize they're not real especially teenagers young teen girls itan is marketed as a fitness loving woman who lives a healthy lifestyle she's even been sponsored by nutrition and sports brands is there a problem where you're uh promoting a body image of someone that is you know in many ways perfect and there are some people some of your followers that say I wish I had that body in the beginning we tried to make more curvy models for example Le or more not standardized models and clients didn't like that but you can see this everywhere in publicity comparing her to the rest of the influencers she looks the same as the rest the agency started creating more models with more diverse looks including some men too although apparently marketeers aren't as interested in male AI models the latest project is for a major car company the brief is to design an AI model to be the face for an incar AI voice assistant a very 2024 assignment Joe tidy BBC News |
Science_Technology_BBC_News | How_drone_technology_is_changing_warfare_BBC_News.txt | [Music] hello everyone Welcome to our weekly edition of the security brief a lot has happened since we last did this some of which we had anticipated in the earlier editions of the security brief the deterioration in Northern Gaza and that worsening situation in the jabalia refugee camp the time that has passed between Iran's ballistic missile attack and the subsequent Israeli response we told you two weeks ago it might be delayed until Israel's missile defense supplies have been replenished we've just seen this week the deployment with 100 US troops of an American high altitude anti-missile system known as Thad and that brings us to the other big story this week hezbollah's surprise attack on a military base near hia with a UAV a drone Four soldiers killed dozens more injured with a drone that somehow penetrated the Israeli defense system one of the biggest attacks on an IDF position in over a year of fighting with me to discuss as ever our resident analyst former senior British officer Mikey Kay who for 20 years flew assault helicopters for the RAF he is a former strategic military planner and if you followed us before you will know that we do this as he would deliver it within the Armed Forces good to see you you to um obviously we've talked before on the program about how the Israelis have dismantled the Hezbollah leadership and yet they're still able to fire these Rockets and the drones why well they're still firing Rockets which are not guided fairly indiscriminate but I think what this week's drone attack has highlighted significantly is the major threat that the IDF now face uh given this sort of asymmetric Warfare if you like that that Western forces have seemingly found quite difficult uh to counter go slide please um if we just take a look at this week's attack I think there's a couple of significant points about it uh the first one being that it was roughly 40 mil inside uh of Israeli territory um and I think that that makes it um significant when it when it comes to uh Israel defending against attacks on you know some of its elite units this was the Golem Brigade they are the special a Special Forces Unit with inside the IDF and as you say it killed four and injured over 60 so so that's significant uavs um as you call them in in the business unmanned aerial vehicle drone to the rest of us they're an Ever evolving Dynamic of the battlefield um do we know what type of drones they have what this one was and what sort of capability the group has yeah we we'll come to sort of the the breadth of the technology a little bit later on uh in the security brief but what's interesting about this is analysts are calling um or identifying this uh UAV as the as the merad one slide please so so the merad 1 is uh an Iranian uh developed drone uh it's very small and lightweight in comparison to some of the bigger drones that we'll see later on it's got a range of about 120 km uh a payload of up to 40 kg of explosiv so you can see the devastation that you know flying one of these drones into a Target can create the IDF are saying that it actually launched two projectiles on the target before actually going into the target they're calling it a suicide drone but that doesn't really make sense cuz there's no one flying it inside it um so more sort of a kamakazi style attack it does have a top speed of about 370 km but I think the important bit of that is it can also fly very low and very slow which makes it um harder to counter and the last bit of I think important information is it's got a um a low radar cross-section and a radar cross-section is the thing that any targeting radar any search radar will look at and try try to identify a potential Target now what this strike tells us which I think is is very interesting is that yes the leadership has been taken out M ranala has been taken out um but the IDF still have the ability to launch rockets and launch attacks like we've seen with this drone so they've still got intelligence uh Gathering capability uh and the command and control structure seems to be uh in place but but critically when it comes to how the Drone got through Iron Dome and the L defense system is interesting because Hezbollah uh and the idea for saying this is that the they're using a tactic where they basically overwhelm the ionome system with rockets and then place these drones underneath it which makes it harder to Target right so when they talked about altitude it wasn't per se the altitude itself it was the fact that it was coming in perhaps at a different altitude than a volley of missiles that was coming with it right with a lower radar cross-section of a missile and a lower speed of a missile which is what the targeting systems will will look for they'll look for Speed and they'll look for direction of the Target and and Iron Dome will only take out a missile if it knows that it's projecting onto a specific Target that could be lethal for the IDF that's really interesting I mean when when you look at this what what what are you seeing in terms of the development of this drone technology and in particular in the two major Wars that we're focusing on the one in the Middle East and of course the one in Ukraine yeah two of the buzzword that you'll hear when talking about drones drones is obviously a very generic term are RPS which is a remotely piloted system so um there are predator drones over Iraq that flown by US forces inside the states the US um and there are uavs unmanned aerial Vehicles which um could have a controller uh but also could be GPS guided and not have a controller and not have that ability to um to interrupt What's called the radio frequency signal between a controller that you'd see on a drone and the actual drone itself right okay um so can you give us some some examples of that I mean can you can you talk us through maybe some of the things that we've seen from from the theaters in both Wars yeah I think there are I think there are four categories that are that are really important to look at but actually this idea of using an autonomous weapon uh goes back a long long way and if we if we go to World War II for example slide this is the V1 rocket the Nazi V1 rocket and it was nicknamed the doodle bug um which was used to uh great effect and the Nazis would effectively obviously there's no GPS inside that but the Nazis would calcul how much fuel would needed to go in and then when the fuel ran out somewhere over London the V1 would just drop out the sky and indiscriminately hit what was below grandparents used to talk about that you'd hear it buzzing and then it would just stop that's right and that's when it fell yeah frightening I mean if you're underneath it um and the only way to counter this later on in the segment we will talk about the uh the conventional uses of counter drone technology and what's out there in the future but if we can go next slide please what the British Ro Air Force were doing that's a Spitfire on the right and a V1 rocket on the left and and the only way that the um the Royal Air Force um back in the day could actually counter that is by flying alongside the V1 and actually tipping the wing to put it off track and you know putting it into the countryside so that always and even today there's this lack of counter drone technology which we'll come to a bit later um the houth are using it to to quite good effect the houth are um in fact this is a good time to look at sort of the the spectrum of capability if you like and if you can go slide please this is the um this is the black hornet and you can just see how small that drone is in the hands of that operator uh it's 16 cm long it has an ability to put a day camera on it and a night thermal camera on it and this will really come into its own um when you look at Urban operations you look at look at soldiers operating in an uran environment so you know they want to clear a block of houses Apartments you can put this thing inside any room within those apartments or that building and that will clear any imminent threat before the troops go in um and then we upscale a little bit we go to um the next sort of category category two if you like slide please which is um viewers May recognize that that is a Chinese made DJI drone called a quadcopter because it's got four rotors um and this is available all over the world to commercial filmmakers to surveying capability or just people using it for their own person use this is actually a photograph taken from Ukraine and the ukrainians have actually now weaponized this quop copter as you can see and put a bomb on the bottom of it which does have devastating effect and we've got some video footage a little bit later on of that um then we go to category three let's go back to the um the merad one slide please this is now sort of you you see the RoR blades have now disappeared now you've got more of a fix wi effect yeah so um again incredibly capable uh travels at uh 370 km an hour can go up to 3,000 M you can put a 40 kgam payload in the top of it but what this does is that it gives it range now so now you're starting to bring range into it 120 km is significant when you look at the strike which is 40 mil south of the Israeli border you know that's almost double the capability of what this drone can do very low Tech very low radar cross-section and can move slow which makes it harder to um harder to uh Target and detect and then sort of the finally the the the the upscale end if you like um of drone technology slide please this is the Triton which is a replacement for uh the US Global Hawk system what's really significant about this is it's got an altitude of 50,000 ft uh which is way higher than any civilian airline that will fly at uh 30 hours endurance and what this does it does ISR and targeting so intelligence surveillance reconnaissance uh and Target tracking as well and this is currently in use uh with the uh US military for Mar anti- maritine operations so you know the the the breadth of where this capability is from right from that black hornet at the very beginning all the way through the commercially made up to you know this type of capability this this has come about in the last 10 years and it's it's you know phenomenal you said you had some video can we see it in operation yeah there's some examples uh operation let's take a look at um this video first slide please this is a warship uh targeting a healthy drone and and and the the hoies are actually using drones to significant effect uh um targeting shipping commercial shipping uh targeting destroyers Naval weapons and you can just see through that video that again you know this sort of Western lag and the ability to be able to take out drones um is is is really hurting the West at the moment someone's actually watching that this is the remote this is the remote application you're talking about someone's flying it ex exactly well some yeah someone could be either flying it or it could be GPS guided so if it's GPS guided then you don't have that radio frequency signal that you interrupt which would be a counter but you can't with these plus they're launching many many many drones so which is called swarming so if you've got you know a couple of rockets that are available then you know that's great but if you've got 20 20 drones and you only take out five it only takes one to get through and I think that is what is providing Western forces with a bit of a nightmare at the moment um there was a a writers report that we saw um I think in the last week Russia now sourcing a lot of its technology from the Chinese how much of a focus is this now for Moscow and what does that mean for the rest of the defense industry well I mean I think some some statistics coming out of Ukraine at the moment um you Ukraine have lost uh 10,000 drones alone in the month of September and again information from Ukraine the Russians launched 1300 drones inside Ukrainian territory in September so the Reliance on drone technology whether it's for intelligence surveillance and Gathering or whether it's used as a as a kamakazi style targeting capability um the Russians have now realized that actually you know they can um deter and and provide Force projection and significant effect inside Ukraine with this capability so now they're Outsourcing and it's from the European intelligence agency that the sources came from for this Roy's article uh and basically Outsourcing a weapons program for drones inside China so the Chinese are now in on this and as you go back the Chinese have got a lot of experience in this because of the the DJI drone and the technology that's gone into that and made that so prolific and I guess the big Powers who've invested so much money in their defense systems are watching this slightly aast at how fast it's advancing I mean just coming back to that B that attack in Israel in in binyamina how do you defend against against the use of drones particularly if they're coming in as you say in a swarm with great difficulty and there's been a huge lag and counter drone capability that the West are slowly starting to keep up with but it's a it's a tip for game at the moment there are conventional aspects that are being used to Target drones so for example the uh UK launched um a mission against houy targets from roal Air Force akuri using typhoons uh a very good source has informed me that two azram missiles slide please I'll show you what an aan missile looks like that's a advanced short- range air toar missile um and that has an IR Seeker head has a has a pretty good range on it two of those were launched by typhoons to take out houthi drones but as we spoke about earlier if you've got 20 houy drones in the air um then this is going to be a really difficult thing to counter those aircraft can carry I think about four as Rams and those units those missiles are north of 200,000 a pop the next layer of Defense which could be used is What's called the cam the counter rocket artillery mortar and these systems slide if we can just go to a bit of footage please oh yeah okay that's the cram in use and and they put it on strategic locations like Baghdad International airport um was used against an attack an attack in Iraq on the US Embassy for example and it works on a hose pipe system effectively so it'll just put loads and loads and loads of bullets in the air all radar tracked in a hope the slew will take out the artillery or the rocket or the mortar that has been has been fired in it's a it's a supremely advanced system but you know with the with the generic use of drones you know you can't put these systems everywhere so you are tied to strategic locations and as we saw drones can get into cafes houses apartment blocks so that's not going to be significant now back to your point on the um compact laser weapon system this is where the future is going in terms of counter drone um slide please this has been made by Boeing and it's effectively a 5 kwatt laser to defeat drones now up to 600 kg so now you're sort of getting into the merad one range um it's a layer defense system so the first thing it'll look at or one of the things it'll look at is the radio frequency so if the UAV has been controlled that will have to have a radio a radio frequency to control it can disrupt that if it's autonomous UAV with a GPS guided system then you then you're starting to look at um what's called a ATP radar which is a chir track and point that will then be used to slew a laser beam onto the Drone and what this capability can do the CWS is it can Target many many drones so this swarming capability where all you need is one to get through this is where where it really comes into its own now what's interesting about this Christian is it's got a range of 650 feet to 1.6 miles that is key because the Iron Dome system has a range from 2.5 mil to 40 miles and as we know the merad one managed to get through the iron doome system and attack its Target so with a little bit of anticipation of what we might see in the future it wouldn't surprise me if this capability which has only been deployed with the United States Marine Corps who have recently proved it in trials in Saudi Arabia it wouldn't surprise me if we see this compact laser weapon system with the IDF in the coming weeks and coming months have you asked me to got it um I think uh we should I'm not sure we'll get the answer we want it's a long step forward though isn't it from tipping the wing of a V1 my goodness um it shows you how quickly it's advancing that was an education uh and I think it will give people context for what what they're looking at when they when they hear about these attacks and particular the one we saw in the last week Mikey as ever thank you very much indeed just a reminder that all our uh editions of the security brief are there on YouTube you can watch them back uh there's a lot of good stuff there so do take a look at that and of course we will do this same time next week thanks for watching [Music] |
Science_Technology_BBC_News | Sharks_less_likely_to_attack_surfboards_with_lights_study_finds_BBC_News.txt | shark attacks have always been a real worry of course for Surfers especially around the world but uh University in Australia may just have found a solution by adding bright lights to surfboards Dr Laura Ryan from mcari University in Sydney spent nearly 500 hours towing illuminated seal shaped foam decoys around a bay in South Africa a popular area for Great Whites now she found that vertical stripes of light confus the Sharks enough to stop them thinking that the decoys were potential prey so does it work uh let's talk to a marine scientist and expert on sharks Riley Elliot also known as SharkMan um Riley what just talk us through the principles of this idea and whether you think it might work yeah good evening Ben um look firstly as you said shark attacks are tragic albeit rare um but anything we can do to reduce that risk like we do with Avalanches or car crashes is fantastic um great whites unfortunately hunt by Ambush and low light visibility and um they're looking for that silhouette of a seal and unfortunately a surfboard from below can often be mistaken for that so what these scientists are doing and I commend them on it is is a difficult task but uh is they're trying to break up that silhouette or show the shark that it is not a natural seal silhouette by Illuminating the bottom of it um there's been a lot of attempts to do things like this uh you know sea snake patterns um different kind of visual cues or colors but a silhouette by definition is going to block out any of that because the light is being silhouetted so what they're trying to do here is you know create light under that board or that seal decoy to show that shark you know that's going to come up like a missile uh that this isn't it's normal prey sharks are very cautious and calculated and will avoid something that isn't their natural prey cuz you you it's a bit counterintuitive isn't it because you would think that putting lights on a surfboard would actually be attracting shark attention um but it's kind of the opposite really yeah well in nature bioluminesence is used as an attractant and a deterrent um the behavior of sharks especially a great white as mentioned before is is they're like a mechanism if a b c d and e all add up do if you know um but if one of those things is not right they are smart enough to avoid it um now this isn't foolproof you know these things take a lot of time and effort and therefore funding and support to do and um Towing seal decoys I've done it in South Africa a lot it is timec consuming and you need large data sets for this stuff but what should be commended is effort to reduce risk because look you were talking about Ukraine before thousands of people being killed you know Chucks kill 10 people tragically on a global scale when billions of us go in the sea but the shark is the animal that's copped the most you know bad rep of anything and um unfortunately that's resulted in hundreds of millions a year getting killed so anything we can do to reduce human shark con is fantastic I I said at the beginning you're known as shark man just tell us about your experiences with sharks yeah well like Laura the scientist I'm a surfer this is my backyard right out here this is where I swim with great whites blue sharks makeer s we tag them track them learn about their behaviors all in an effort to conserve them against risks like Fisheries um but also risks that they can pose to us when we overlap and swim in what is their ocean uh and we tend to forget that um so you know knowledge is power and my big effort is to do the science lace it beautifully with imagery of Storytelling and put it in the media and persons like yourself sharing it on a global Mass because not everyone can see a shark experience a shark be exposed to a shark but we all breathe the air half of which comes from the ocean that sharks have been maintaining the health of for hundreds of millions of years so this isn't something you should shy away from these animals are incredibly important but um at the same time we want to enjoy ourselves and go swimming and anything we can do to improve you know you know should I say reduce our risk of doing that is great but perspective is key you know wearing a life jacket learning how to swim you know that's your greatest danger is drowning sharks are definitely down the bottom of the list good perspective um thank you very much indeed SharkMan Riley Elliott thank you so much for being with us thank you cheers Ben |
Science_Technology_BBC_News | Hackers_expose_deep_cybersecurity_vulnerabilities_in_AI_BBC_News.txt | you're watching the context it is time for Aid [Music] decoded welcome to AI decoded it's that time of the week when we dive deep into the most eye-catching stories in the world of artificial intelligence this week cyber security how long would it take an advanced hacker to break into the most complex most powerful AI models that we built 30 minutes as it happens this week the Ft carried an exclusive interview with the mysterious faceless hacker known as plenny the prompter he is stress testing or jailbreaking the large language models that Microsoft Chat GPT and Google have been building an ethical online Warrior who is part of the international effort to draw attention to the shortcomings of the biggest tech companies who he argues are putting profit before safety and if you think that is a risk somewhere in the future think again just two weeks ago the Russian cyber criminals killing used sophisticated AI tools to find their way into the NHS computers tens of thousands of patients here in the UK had names dates of birth and private information published on the dart web when the testing firm cinis refused to pay the ransom the hackers encrypted Vital Information which made the it systems at two NHS hospitals useless so how worried should we be what are the implications for those businesses who are turning to AI to improve their systems tonight we're bringing together a former hacker Conor Lehi now the CEO of AI Safety Company conjecture darl Flack is here CEO of cyber security company blockfish and as ever to help guide us through it our resident expert and presenter Stephanie hair let me start with you Stephanie plyy the prompter is what we call a white hat a friendly hacker yep the good guys in the shadows who are stress testing the system what have they been able to do so they're able to get large language models to do things that they should not be able to do so these are Co with guard rails they're CED coded with rules and jailbreaking a model is imagine what you would do if you had a sort of teenager at home who was trying to play with a game and see if they could break it break with the system lots of Engineers have grown up trained that way hackers love to do it they almost can't help but doing it and I I quite like plenty the prompter argument that he's actually doing work for free that these companies should be doing themselves to bring attention to the public so we're talking about writing malware we're talking about showing how SC uh scammers could create scripts that make people click on links which is a way that you can inject all sorts of very nasty code into people's hospitals as we've just seen which is a very soft target very ripe Target but it's schools its individuals and it's only growing this is only a growing problem and so we just had last month the AI safety Institute here in the United Kingdom published a groundbreaking report brand new showing that every single major llm large language model can be broken jail yeah it's quite alarming if you like the color red which I have worn tonight to you know show and solidarity with our our researchers here in this country they are trying to put out a warning to the public for all those companies that are saying I've got a bit of fomo bit of fear of missing out I really feel like I need to get in with generative AI which I am hearing with every single client group I speak with everybody's got real anxiety about missing out what we're hearing from the AI safety Institute and from the national cyber security Center here in the United Kingdom is that a lot of this technology we should really consider to be in beta it's not really ready so it's fun if you're approaching it from an engineering perspective but not if you are a CEO or general counsel who needs to protect your risk but Conor these companies they have red team hackers who were employed by the company to go in there and try and find a way through the system why are the white hats guys like you able to do it and their red teams are not well so in the hacker business you usually talk about blue teams and red teams so red teams are the people who try and break things blue teams are the people who try to defend and and the way things usually are is red team always wins red team always wins blue team can just minimize the harms and with AI systems in particular what we're seeing by people like py and a lot of other people like me my former and my old friends back you know in the in the you know Discord online days um is that AI systems are very immature when it comes to safety a lot of the stuff that we do for cyber security and safety simply does not apply to AI systems in the same way in other forms of software when a hacker finds a vulnerability you will have your programmers go look at the code of the system fix the problem and then deploy a patch that solves the problem the problem is is that AI systems are not like normal software they're not written line by line with code it's more like they're like grown they're more like artificial like huge piles of numbers that can do great things but we don't really know how to patch them we could do a little bit you know openi and all these other companies invested a lot of money into trying to tweak these things but as you know peny and other people have shown it's wildly ineffective at this point in time so darl that this jailbreaking started about a year ago and and the attacks as as Connor is describing have evolved so it's a constant C game of c mouse this what's the inherent problem with that if you're a company hoping to integrate it into your systems I think Ely it's always going to be an unknown risk um you are giving up your data your information potentially your intellectual property your brand and your reputation and you're putting it into a system that you are hoping is going to protect it and secure it and so organizations need to be aware that the risks that they're taking around that and um like we say organizations don't yet know what those risks are and because it's a new technology there's always going to be a bit of an arms race there's going to be the Defenders against the attackers has been said and so looking at that arms race everything comes down to how quickly you want to jump to these platforms and how much data you want to give them as we've seen from the um uh Institute it's very much uh early stages beta stages and so the risks of things going wrong are quite high at the moment so um taking pilot approaches with synthesized data with anonymized data would be a good start to test it to make sure that you're getting the types of outcomes that you're EXP expecting but if you jump straight in right now with all of your data trying to be sort of aead of the curve then you've got to be aware that that risk you're taking could come to fruition what's really fun about this article is it gives a bit of a heads up that California's legislature is going to be voting in August on a bill that will require any company in the state so that's open AI That's Google and that's meta to ensure that they don't develop models with a hazardous capability and plenty the prompter says all AI models will fit that criteria I I just talking um um about the NHS model Connor um what what is it what is it that is weak in the system and and and does that mean that all our systems given what you've just described are at risk of this kind of of of malign activity the short answer is absolutely yes it is a complete disaster it is a complete mess none of our methods are adequate whatsoever this is not ready for safe production whatsoever across the board to give you a a a feeling of this there are systems that are as close to unhackable as possible these are usually used in military contexts or like nuclear power plants and stuff and it's called formally verified software and to give you a feeling for this developing even like a relatively simple piece of software let's say the embedded software and like a helicopter or something which not simple but like you know it's something that usually takes like maybe a couple years to develop developing this kind of thing can take over a decade and can cost millions or even hundreds of millions of dollars and this is using techniques that we understand the best tools the best researchers were tools that we've developed over many many decades AI as it ex today has only existed really like for like a couple of years maybe a decade so our understanding of what our AI models do internally is extremely inadequate compared to our understanding of other types of software systems and even with other types of software systems our safety is like very shaky that that terrifies me I I was because I wrote a question down here Daryl earlier and I thought well if we're integrating this technology into our critical infrastructure systems then this becomes really serious it's interesting Conor used the term about a nuclear power plant but maybe that's not far-fetched maybe maybe our critical infrastructure is at risk I think with the Advent of new technology um legisl is always somewhat behind and so organizations will start to deploy it to save time to speed up operations and if it's deployed too quickly in some of those critical National infrastructure environments then there's always the risk that it will go wrong um and as Connor was saying um years and years are spent to assure products to assure platforms to assure software so that when they are placed into uh critical National infrastructure they perform as expected just just really quickly Stephanie are we talking AI developing AI to attack these systems absolutely so you can use AI both that becomes ever more sophisticated potentially the question is going to be when it's it surpasses us we won't be able to necessarily even keep up with that war that would be happening between the machines okay you think that's scary coming up the former Twitter boss Jack dorsy warns that within the next 5 10 years we won't know what is real anymore so sophisticated will the AI generated content be that it will feel he said says like you're in a simulation will those technological advancements bring us all closer to Singularity the point in our Evolution when we share this planet with entities smarter than us we will discuss that after the break welcome back to Aid decoded earlier this year during a primary election in New Hampshire thousands of Voters were sent a message by Joe Biden you know the value of voting Democratic when our votes count it's important that you save your vote vot for the November election we'll need your help in electing Democrats up and down the ticket voting this Tuesday only enables the Republicans in their quest to re elect Donald Trump again it's persuasive but anyone carefully listening to that Robo call might detect some stilted language the emphasis and pauses in the wrong places which would tell you there's something wrong with it in fact it had been created by a political consultant who'd use generative AI to influence the vote it shows what is possible and it raises some really big issues this week the former Twitter CEO and co-founder Jack dorsy warned that in 5 to 10 years from now it will be impossible to differentiate what is real from what is fake don't trust verify so even this talk everything I've said don't trust me you have to experience it yourself and you have to learn yourself and this is going to be so critical as we enter this time in the next 5 years to 10 years because the way that images are created uh deep fakes videos you will not you will literally not know what is real and what is fake it'll be almost impossible to tell it will feel like you're in a simulation because everything will look manufactured everything will look produced and it's very important that you shift your mindset or you attempt to shift your mindset to verifying the things that you feel you need through your experience through your intuition because all these devices in your in your bags in your pockets they're all floating from that image of the neuron I sent you and because all these things are on your phone now you're not you're not building those connections in your brain anymore this is one of those stories where you just wonder how Mr dorsy would like all of us to only verify by experiencing like that is not a scalable model for a tech CEO to be recommending so it's quite weird how can I know what is being reported for instance in China I'm not there I'm here in London I'm Rec the whole point of news is that we need a system of contributors who put forward evidence that other people peerreview and then it's dis it's discussed as truth I mean this is taking us back to philosophy what is reality or the study of history how do we treat sources or even the law what is evidence what is not what is admissible in court what is not telling everybody that we just have to you know go with our intuition doesn't feel great can you protect a democracy Connor if you can't differentiate what is real and what is fake I mean yeah definitely not easily that's for sure a lot of what makes a society possible is that we can agree on something being true or not if we can't fundamentally agree on what is true or not then and especially if the things that we believe are true or not is maybe selected by people or things that do not have our best interests at heart whether it's to sell us something or to make us angry or to make us do some political thing then you can't form a state you can't form a civilization in the limit it's kind of interesting darl that he's putting the onus on us because I would say if you can't differentiate then that is an existential risk for them for the social media companies why would you ever tune in if if it's just bringing you fake news absolutely I mean to to try and put the burden on the uh consumer or the user is moving the uh portion of blame to the wrong place um it's the tech companies that are providing the technology they should have the intelligence behind that technology to be able to identify if something is true or if it's false or not ultimately the the user at the end is the last line of defense if we're having to use our inition then the system has failed to get to that point what about watermarking I thought open AI were going to Watermark everything that their systems produce watermarking is often trotted out as this sort of um solution but everybody agrees it's also not a silver bullet so let's discuss that why everybody's going to have to come up with um some sort of water marking that they would all agree upon and use this becomes really interesting for things like blockchain ways that You' be able to do even like a chain of evidence how do you verify there's there's cyber security and cryptographic principles that we could use in this that problem is is it doesn't scale it's really really intensive so you know what are we going to do every time we check a post on social media we're going to have to do some sort of decryption to see if it's real like that's what doesn't work and you're right they constantly these tech companies put the onus on the users to protect their data and now to decide what's true or not based on feelings weird you know thing we thing we keep returning to in this program and is and and in mind of what we've just been discussing here is how long it's going to take before we reach this thing known as Singularity what what do I mean by that Singularity is the term given to the point in human history when the machines become smarter than those programming them so the point where they don't really need us is that really likely to happen or is it just a concept created by those who are making money from the technology of the future there's no better panel to discuss it with so let let's begin with you Connor are you are you a believer in Singularity or are you a skeptic I see no reason from any scientific evidence that we have so far that it shouldn't be possible humans are the dumbest species that can create industrial civilization we were the first ones to evolve we were the first draft there's no reason we couldn't build AI systems that use you know that are faster you know our CPUs our computers you know switch about a million times faster than our neurons do so even if we just get a computer smart as a human right now let's say it runs a thousand times faster than the human well that means it can do two years of thinking per day two years of labor per day I mean that if that exists already like and we know that this is like technically possible look there are there are so many facets that we call intelligence two of which computers have already mastered one is memory and the other is is calculus or how to calculate right what about reasoning and emotional intelligence is that innate or is that learned I mean it's a bit of both but I mean both of that you know you open up your brain there's a bunch of goop in there made out of neurons that are sending electric signals around sure it's a pretty complicated system the brain is one of the most complicated things in the universe but that doesn't mean it's not something we can do we already now have systems like GPT 4 is much better than me at writing Shakespearean poetry it's uh much it know has read much more books than I have it's really good at understanding social situations and analyzing emotions it's not perfect no sure but neither am I neither are you the concern Daryl is that the machines become smarter develop feelings of superiority and then decide that they don't want to be turned off right that's that's the concern at what point do they say actually I'm in charge and I think that's why it's really important to set the guard rails now to understand the principles of how we should be using Ai and the use cases where it is valuable and there there will be places where it's incredibly valuable to have that speed of processing that U ability to scan lots of data and to find solutions to problems that we've struggled with for hundreds of years but then equally there's things that humans are very good at um and the empathy side of things the looking after each other and that closeness and uh intimacy to be able to have that um maybe that we have to look at a different future where the workload side of the world is carried out by Ai and we have to look at other things to keep ourselves busy and to have a view to what our top level on maslin's hierarchy of self-actuation should be I was having a philosophical conversation with someone the other day about this I'm sure lots of people at home do as well about whether I mean you know machines can't feel touch or the emotion of Love or hate they can't react to a flower opening or a sunset or actually can they because that is all learned behavior well there's even this question of is intelligence also about embodiment so we exist in a physical body that has you know we sense things but also I don't have to physically touch you to sense how you're feeling I'm reading you and can machines do that really you know they can't physically exist in the world unless they're a robot which it does that has sensors and cameras Etc it doesn't know what a feeling is because feeling are biochemical Productions in a human brain or if you have pets certain animals um perhaps all animals and even plants we're still learning even about the natural world so there's a lot of this discussion you know what is thinking what is intelligence that isn't just about machines or even humans it's about what it means to be alive do you always feel that we never have enough time to get to everything in this program it just sort of flies by doesn't it every week I could talk for another two hours about this um thanks to Connor thank you Connor for joining us again it's always great to have you on the program thank you darl I hope you'll come back and thank you also to Stephanie just a bit of housekeeping before we go we will be off air next week for the election but Aid coded will be back a week on Thursday from The Wimbledon Championship uh priia is going to be going to look at how they are using AI to improve the whole experience of tennis and not just tennis see I didn't even mention v um do join us for that |
Science_Technology_BBC_News | How_AI_defeats_humans_on_the_battlefield_BBC_News.txt | it is time now for our new weekly segment Aid [Music] decoded welcome to AI decoded it is that time of the week when we look in depth at some of the most eye-catching stories in the world of artificial intelligence now last week we looked at how artificial intelligence could threaten human jobs in the future but what about those on the battlefield well the guardian is calling it AI Oppenheimer moment due to the increasing appetite for combat tools that blend human and machine intelligence this has led to an influx of money to companies and government agencies that promise they can make Warfare smarter cheaper and faster and here in the UK leading military contractor BAE systems are ramping up efforts to become the first in their industry to create an AI powerered Learning System meant to make military trainees Mission ready sooner now our BBC AI correspondent Mark chesak went to meet all those involved we will be showing you his piece in just a moment but with me I'm very pleased to say is our regular AI contributor and presenter Priya laani who's CEO of AI powered education company Century Tech now Priya this is a fascinating area but perhaps one of the most controversial and people have huge concerns about it yeah that's absolutely right because this is using AI to potentially have unmanned military drones what you're going to see in Mark's incredible piece is unmanned military Warcraft potentially and then there's you know all these questions about well hang on you know obviously it's great if there aren't humans being harmed out there on the field but does that mean that actually War could escalate much quicker a decisions then going to be made by these AI systems if both parties have ai system systems what happens then it's sort of a race as to who can escalate further and so there's all sorts of ethical considerations but you're also going to see learning systems and how BAE systems are approaching using AI to improve learning in terms of training uh the military and soldiers so it's a fascinating area and then we'll do a bit of a deep dive into the ethics a little bit later in the program lots to talk about Priya so let's take a look uh as we just talking about uh this uh report by Mark chesak and then stay with us cuz we've got lots to discuss afterwards up down flying or hovering around for 75 years the farra air show has showed off aircraft both civilian and Military often inviting Pilots to put their airplanes through their Paces to the Delight of the assembled attendees including plane Buffs even new prime ministers in recent years fber has played host to a lot more of these unmanned air vehicles or drones as they're commonly known drones with military application with fixed wings that behave like an airplane or rotors capable of hovering like a helicopter are in abundance but all have something in common a human being involved in the command and control of these aircraft at some stage it's a process that's called human in the loop it's it's critical from a a moral and ethical point of view to ensure that there is a human judgment that is always at the heart of selection of the course of action military application of AI is extremely controversial images of Killer Robots and the idea of AI run a mck are frequent additions to stories in the Press about the risks the technology poses nevertheless militaries around the world are already using artificial intelligence one area where it's particularly useful is training Pilots to fly aircraft like these flight simulators are an integral part of a pilot's training they save time and money allowing prospective Pilots to gain valuable skills from the comfort and safety of terra firma formerly with the RAF Jim Whitworth is a pilot instructor experienced in flying military jets like the hawk and tornado soon as you see that I want you to just pull the stick back set an attitude as we discussed this simulator rig is for a hawk jet the Royal Air Force's preferred trainer what sort of feedback have you given to the team developing this um in terms of its realism uh so really it's about the feedback from the controls I would like it to feel as much like a hawk as possible where does the AI come into the mix we can record everything a traine does in this environment in this simulator we can give some metrics with which to measure the performance and then score each performance and then as we start to build up data on each trainee artificial intelligence can then start to analyze that data for us and show us where our pinch points in the syllabus are and by that I mean where each traine is struggling where perhaps we might want to refine a piece of training either coare material all technique from the instructor to try and make that training as successful as possible greatest advantage of learning to fly like this is that when I need to get back down on the ground I can hit a few Keys take the headset off and I'm good to go synthetic training isn't exclusive to aircraft nearly every element of the battlefield and its surrounding environment can be simulated the software powering these tools has evolved from the same Tech as video games the addition of AI allows the environments to behave in a much more realistic way even replicating civilian activity how does AI help in simulation it's really difficult to replicate real life scenarios it's very difficult to get enough space to do the training in it's very difficult to get enough assets available particularly if they're on operations we can make them incredibly complicated scenarios and the AI can then create the the complexity that they need to train against when it comes to Aerial combat training new AI powered adversaries are proving to be a challenge even for experienced Pilots definitely puts you through your Paces it puts you in positions that you've not traditionally seen before it fights a different doctrine that we've not necessarily trained against so I think it's going to become become the Future Okay Pi's headset on and put it through his PES Pierce Dudley used to fly the F's most advanced fighter the typhoon he's about to fly a virtual version of the same jet in aerial combat against a System created by developers from crownfield University it's called the AI aided tactics engine yeah so if your opponent is also a human being there's something at stake for both of you your lives are at stake but if your opponent in the real world isn't a human being does that change things for for you as a human pilot the AI is learning as and is adapting to your reactions so therefore it becomes quite difficult to train against if you're tra if you're fighting against other other real world uh air crew you potentially know the training that they've been through you know almost what to expect whereas against this you just don't know what to expect with it the AI engine has come out on top now it's my turn to take on an AI Top Gun where did he go I lost him got to get some altitude out maneuvered at every turn the AI made quick work and this novice pilot is just too elusive Pilots aren't just learning from the AI in turn it's learning from them too it's refining skills which one day may be used to Pilot drones in real world situations a scenario that for many presents a significant moral and ethical risk yeah that risk um associated with technology is a is a a critical area um it's not new um every technology that's been deployed in defense has a risk associated with it and there's a very wellestablished um moral ethical and legal framework around how we evaluate the risk of any new capability alongside the operational capability and the imperative to use it but what what happens if an adversary doesn't play by the rules if they don't play by the The Rules of Engagement or they they don't play by the same ethical Frameworks we don't assume that our adversaries will play by the same rules that we do um but because we understand the technology we understand how you would go about deploying autonomy outside of that framework and when we understand the technology and approaches they would use we can understand the techniques we would use to counter that to defeat that threat this is a glimpse of the future it's called Tempest a joint collaboration between the UK Italy and Japan this proposed sixth generation stealth combat jet will have advanced radar and weapon systems as well as flying with its own mini Squadron of drones The Tempest acting as a flying command and control center at a distance while the drones perform missions semi-autonomously which begs the question how long will the human being remain in the loop I told you it was interesting that was Mark chesak reporting there now coming up we will delve deeper into the issues surrounding AI on the battlefield we will be speaking to Mikey Kay a former senior RAF officer in the British Military and Dr Peter azaro from The Campaign to stop Killer Robots a coalition of non governmental organizations who seek to preemptively ban lethal autonomous weapons join us for all that on aiid decoded after this short break around the world and across the UK this is BBC News welcome back to AI decoded now we just had a glimpse of how defense manufacturers are using AI powered military training tools to train the next generation of fighter pilots but are we in danger of handing too much autonomy to these relatively untested systems we're joining us now are Mikey k a former senior RF military pilot and Dr Peter azaro from the organization stop Killer Robots who's also a professor at the new school in New York where his research focuses on artificial intelligence and Robotics thank you so much both of you for joining us here on AI decoded and Mikey perhaps if I can start with you and ask just to give us a quick rundown of your understanding of how AI technology is being used on the battlefield at the moment uh I think a really good example is um the a process called the kilch um which is a a procedural uh approach to the Precision guided munition process and what that does basically it assists with the identification uh uh and selection of a Potential Threat and then the approach looks at What's called the CDE the collateral damage estimate and it will look in the vicinity of what the target is let's say for example two Islamic State snipers on the second story of a 30 story building and then it will assess um potentially what components within a certain radius of that Target uh could be or could form some form of collateral whether that is uh endangering human life or endangering infrastructure um at the same time you've got a significant amount of intelligence that is going into this process whether that's human intelligence which is intelligence you get from informance or whether it's imagery intelligence or electronic intelligence so listening tapping into phones or listening to um radio frequencies or uh looking at imagery from predators um then it will go into weapon selection and it will basically look at what type of weapon whether it be a bomb from a platform like fastjet or whether it's an artillery cell which is precision guided from a tank it will look at what type of weapon um is the most appropriate in order to minimize that collateral and various governments will have various different tolerance policies on that and then it will also bring into all of that what the rules of engagement are uh in terms of being able to prosecute that Target so um AI can across all of those areas including the battle damage assessment which is effectively taking a photograph after the bombs hit it can it can inform all of those components of what what is commonly called in military P to kill J okay let's go to Dr Peter rosaro and just to I mean your your organization is called stop Killer Robots which perhaps gives people an idea of where you're coming from in this the film that we have just seen is about how AI is being used to train uh Pilots um do you have a problem with AI being used in that sort of capacity or do you want AI not to be used at all when it comes to Battlefield training and effectiveness um yeah so I think there's a lot of valid applications of artificial intelligence across many different domains from medicine to healthcare and in even in the military for Logistics and training and things like that uh we're really focused on autonomy in Weapons Systems and ensuring that humans are ultimately making the decision to use lethal force and determining what is a valid and lawful Target in armed conflict um and we've been working at the UN for more than decade trying to get a treaty there uh but there's of course many different kinds of applications and there's been a lot of debate around exactly how to define these systems uh as we just heard from the the video and and the previous speaker the there's a lot of different ways to integrate these into the complex operations of the military which involves a lot of data a lot of computers a lot of people making decisions at different levels of command and control uh so it's is challenging to find ways to really regulate how that happens and ensure that humans remain in control so Mike I have a question for you because presumably one of the areas that the military is trying to achieve here achieve better is like less civilian harm right we know from the UN that the civilian casualty ratio is about 9 to1 so nine civilians to one uh combatant um but making Precision targeting theoretically more possible doesn't necessarily mean that the impact on mitigating risks to civilians is more probable because when it comes to using artificial intelligence it's about speed so if both parties have artificially intelligent uh trained weapons or drones and they're using this technology speed is key in the process and so we saw from for example lavender which is the AI system used by uh the IDF sources alleged that actually they increased the number of civilians that they were permitted to kill when they were targeting a potential low-risk militants to 15 to 20 civilians and they would drop a bomb on an entire house and flatten it to try and achieve their goals so what do you think about AI making War actually more destructive in this sense and not helping us when it comes to reducing civilian harm well PRI what you're talking about there is the collateral damage estimate and the collateral damage estimate varies from government to government um I think it's quite obvious if you look at the tolerance policy of the IDF it's significantly different uh from experience of what the tolerance policy was of say the UK when it was operating um prision guarded munition strikes in Iraq or Afghanistan and I was part of that kill chain process in Baghdad over three tours so I'm incredibly familiar with that and I'm incredibly familiar with the collateral damage estimate and what the rules of engagement are where AI can improve this and you're absolutely right when you talk about speed speed is of the speed is of the essence so if you do have a imminent threat uh to life or to infrastructure neutralizing that threat uh through speed and accuracy is where AI can help improvements so the collateral damage estimate for example AI will be able to speed up that assessment of what the potential collateral damage is and when we're talking about collateral damage I'm talking about a school potentially within the radius of impact of a certain weapon you know or a bus passing by at a certain time of the day and that's where what's called pattern of Life comes in which is effectively drones overhead of Target looking at what the pattern of life is of various components surrounding that so speed speed is critical selection of the weapon and speed at which the weapon can be selected from The Rules of Engagement from the collateral damage estimate is is critical so AI for me um will speed up and make that process more accurate but ultimately the very high top level tier has to be the government's tolerance policy on what it's willing to accept in terms of loss of life and at the moment we talked a lot about human in the loop so the slowest and therefore the weakest link here would arguably be the human in the loop is there then a risk that the human will be cut out of the process well you're talking about speed and potentially the human could become the slightly slower component of that but then what's a critical comp component to think about is is accuracy and ethics and AI isn't there yet will it ever get there um I'm not sure there there are those that argue it will there were there were those that argue that you will always need uh a human in the loop to give that overlay of what the ethics are what the rules of engagement are um the scenarios are very different you know Prosecuting different targets in different environments with different platforms different weapons you know I gave the example of two Islamic State snipers on a two on a second flooor of a 30 story building we the human has the ability to be able to select a weapon um through technology through machine learning but also put for example a steel tip on the top of that weapon called a penetrator so it can go through 28 floors to the second floor with a delayed fuse on it and just take out what's on the second floor without destroying anything else so it is a massively massively complex procedure of which AI will be learning how to do that but my my advice and certainly the way I would approach this is is that a human in the loop right now is imperative in order to minimize that collateral and minimize potential mistakes and mistakes do sadly happen quite a lot yeah and we haven't talked about the transparency of that either in the sense that a lot of this is classified intelligence you know W defense cont contractors be Peter I've got a very quick question for you we running out of time but war games show that the use of machines are to result in Conflict escalating quicker than it would otherwise what are your thoughts about that well as you said with the speed right uh decision making happens in shorter and shorter time frames the real difficulty is when uh more and more uh strategic decision making and engage decisions to engage a Target or initiate an operation become automated then you actually would have humans that would not be in control of the overall planning the decisions to go to war the decisions to escalate a conflict could all just sort of happen automatically and we've seen this already with online trading and Flash crashes that have occurred in stock markets where different algorithms will interact with each other and lead to uh you know a stock market crash and they have to turn off the whole system uh we don't want this happening with autonomous systems in Warfare um but I think uh to the question you asked before about Precision weapons I what we know is this is Automation and automation increases speed it also red reduces cost by reducing the cost of bombing each individual Target that means you can afford to bomb a lot more targets so if you were only killing you know a certain percentage of civilians with each strike but now you can strike many many more things you can actually wind up having a much larger impact on the civilian population uh even though you've increased Precision so it's it's not automatic that these systems will improve Warfare and any uh uh impact on civilians Dr petaro I'm gonna have to stop you there I'm sure we could talk about this all evening it's an absolutely fascinating subject we really appreciate your time Dr Peter aaro Mikey K thank you and here in the studio uh priia thank you so much for joining us that's it we are out of time AI decoded will be taking a welld deserved break for the month of August but don't worry we will be back in full force at the beginning of September so do please join us then |
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