Split (1)

train · 5.12k rows

playlist stringclasses 160 values	file_name stringlengths 9 102	content stringlengths 29 329k
The_Early_Middle_Ages_2841000_with_Paul_Freedman	08_Survival_in_the_East.txt	PAUL FREEDMAN: Alright, so today the question we're going to deal with is the survival of the Roman Empire in the East. Why did the Empire, based in Constantinople, survive, whereas, as we saw last week, the Western Empire based, nominally, in Rome-- at times in Milan, at times in Ravenna-- collapsed in the fifth century? We're going to take a long view of survival in the East - that is, from the fifth century to the mid-ninth century. After the mid-ninth century, the Eastern Roman Empire flourishes and has a period, that we will discuss in a few weeks, of great splendor and prosperity. But this long view is justified by the fact that for 400 years, or so, this Eastern Roman Empire faced tremendous threats of invasion, sieges, difficulties dealing with all sorts of nations and peoples, and, at the same time, internal division, because of religious controversy. Or what the people who won, called heresies. I remind you that while we call it the Eastern Roman Empire or the Byzantine Empire, they called themselves the Roman Empire no adjective, no qualification. They were the successor to-- and if they were the only successor, tough luck-- the empire of Augustus, the empire of Diocletian, the empire of Constantine. In their base, before the seventh century, they were, as you see on the map. The map really shows them, more or less, at their height. Eastern Roman Empire-- notice that it goes as far as Spain in the Mediterranean. This was the accomplishment of Justinian, and emperor of the sixth century, whose reign marks a kind of apogee, a height of power of this empire, within in this period of crisis. So while I'm saying that we are dealing with about four century's worth of sieges and crises, there is this period in the sixth century, in the reign of Justinian, who represents a kind of brief, but very important, reconquest of the West. And that's partly what you're seeing, at least the leftovers of it, in this map, that shows you the Byzantine or Eastern Roman Empire in the year 600, extending-- including Spain, North Africa, the coast of what's now Libya, Egypt, the Mediterranean Middle East-- that is modern Israel, Syria, Lebanon-- Anatolia-- that is to say Asia Minor, modern Turkey-- and the Balkans, Greece, and the Aegean Islands. This empire was held together by Constantinople, which, as you see, and as we've already spoken about, is strategically placed to control access between Europe and Asia, across the Bosporus Straits, and also between the Black Sea, which is the access point to Central Asia and the Mediterranean Sea. This city, modern Istanbul, still has the walls built by Theodosius II, in the early fifth century. The so-called Theodosian Walls-- rather nastily restored recently-- are an incredible monument, still, in their ruined state, to the power of Constantinople, as they were built on the landward side. Constantinople-- very difficult to attack from the sea, and, because of the walls, very difficult to attack from the land. Until very recently, that is, I would say, until the 1980s, the Theodosian walls were not reached by the urban agglomeration of Istanbul. That is, they were so big and so far from the main center of the city, that only in recent decades has Istanbul, which is one of the fastest growing and most prosperous cities in the region, has the city leapfrogged over the walls, and the walls are now in the kind of midst of a new part of the city. Nevertheless, extremely impressive accomplishment. And the period we're dealing with is mostly sieges of Constantinople and heresies. And if you just hold that in your mind, this, somewhat, "one event after another, that I never heard of," quality, that this will have, I think will be, if not alleviated, at least rendered comprehensible. Before we go on, let me just say a few words about Procopius. Who has read the Secret History before? OK. So not too much. You should have started it. I should've warned you. It has disturbing, even weirdly pornographic parts. It is a diatribe against the Emperor Justinian. I don't think I'm giving anything away by saying that Procopius' theory about Justinian is that he's a demon, a devil, a representative of hell. What makes this text interesting, is it's an intimate portrayal, even if it may not be an accurate one. But we will pay a certain price-- we are willing to pay a certain price for intimacy, for immediacy, for the sense of an extremely sinister court. It's a little bit like reading about Stalin, or some other capricious, extremely powerful, hard-working, but bloodthirsty ruler. I think what you have to ask yourself is, how could a ruler of this particular time and polity, not be bloodthirsty? What seems to be Procopius' problem? And we'll elucidate some answers on Wednesday. Procopius, in part, is interesting, because all of this other works are lavish in their praise of Justinian. This is an historian who knows nothing between panegyric and diatribe. Nothing between lavish servile praise and the harshest imaginable criticism. The two go together. The two are phenomena, again, all of absolutist courts from that of Louis XIV to that of twentieth century dictators. The same kind of enforced praise can create a kind of humiliation and rage that comes out in other forms. A Secret History had to be secret, because had the authorities read a few words of this, Procopius would have not died in bed, as, indeed, he did. We know this from one manuscript in the Vatican found in the seventeenth century. OK. So that's my introduction to Procopius. When we talk about survival of the East, we're talking about survival under several different kinds of circumstances. So our first concern is, how did the East survive the fifth century, which destroyed the Western Roman Empire? Part of the answer is geography. The East was easier to defend, especially, as I've just said, the position of Constantinople, both as an impregnable site and as a commercial city with very, very extensive trade, and as a base to defend the two core territories of the Empire. By core territories, I mean that, really, the essential parts of this empire, which are the Balkans-- including Greece under that rubric, for the moment-- and Asia Minor. And, of course, Constantinople is ideally placed to protect both of them. Other advantages of the East over the West-- a bit richer, more urbanized, produced more taxable revenues than the West. It's army didn't fall apart. It's civilian structure of administration remained intact. With the exception of Justinian, very few these emperors are that outstanding in their abilities. But their subordinates were very capable, the government worked well, and the East survived a number of powerful threats from the outside. "From the outside" meaning it had the same problem as the Roman Empire, in an, admittedly, smaller and more defensible space. It had an eastern frontier and it had a northern frontier, both of which were fragile. The eastern frontier with Persia-- we already talked about them-- and the Northern frontier, along the Danube River, more or less, with all sorts of different peoples, from the Avars, Slavs, Bulgars, all sorts of nations that would attack it. It also had the disadvantage of internal religious dissent. And we're going to be talking more about this. These problems, eventually, did affect the East adversely. It would have a period of pretty radical decline, not so different from that of the West. Beginning in the seventh century, this decline can be seen in the abandonment of many cities, or their much smaller population-- we've already seen that as a feature of the West-- in the loss of territory. We're going to be talking about Islam and the Arab conquests. But they begin in the seventh century, and, very quickly, result in the loss, from the Byzantine point of view, of Egypt and the Mediterranean Near East. But unlike the West, the Byzantine, or East Roman government, never collapsed in the face of these threats. Although, it is a kind of period of cultural decline. Certainly, a period of military defeats, of sieges, of political problems, and of religious dissent. Nevertheless, the Empire would survive. In general, during this period, what unites these 400 years-- we're talking about, roughly, 450 to 850-- is the ability of the empire to resist invasions, its willingness to accept the loss of certain provinces, while protecting others, and its domination of Constantinople over its region. At the opening of our period, cities like Alexandria and Antioch are extremely important. Their importance within the Byzantine Empire declines. But in order to understand that some of the internal problems, we're going to have to talk about heresies. I think I already apologized for having to talk about heresies, and I think I already explained why it's important. Questions, remarks, denunciations? OK. Representatives of the iconoclast defense fund want to claim equal time? OK. This is just a selection of heresies, right? I mean, it's the proverbial tip of the iceberg, the proverbial icing on the cake, the proverbial-- what do you call it-- crust on the chocolate pudding. But having said that, these two are what are called Christological controversies. They're about the nature of Christ. The relationship of his human to divine nature. And, grossly, to oversimplify, the Nestorians emphasize Christ's divine nature, and the Monophysites, Christ's human nature. [correction: the nestorians emphasize Christ's human nature; the Monophysites His divine nature]. The beginning of this controversy is with the Nestorians, named after the patriarch, Nestorius, the bishop, Patriarch of Constantinople. Nestorius seemed to teach -- and he's patriarch in the 420s, and the stories would be deposed in for 431, as patriarch. His followers seemed to teach that Christ was fully human and that his divine nature was either separate from is human nature, or it was nonexistent or irrelevant. I should remind you that the problem is posed by Christ being God, and yet, being crucified and suffering and dying. So this is a problem that, logically, arises out of an understanding of who Christ is and what he does for humanity. Nestorius was deposed by the Third Ecumenical Council of Constantinople-- I'm sorry, the Third Ecumenical Council, which meets in Ephesus, on the western shore of Asia Minor. Council of Ephesus, Ecumenical Council-- the third one in 431. The first two had dealt with Arianism. I remind you that Arianism is a different problem, because it deals not with the nature of Christ, but the relationship of Christ to God the Father. Here, we're now just concentrating on Christ. The Monophysites, in opposing the Nestorians, naturally emphasized Christ's divine nature, as the Nestorians had, in their opinion, overemphasized the human nature. But from the point of view of the group that we can call Orthodox, the people who believe neither in Nestorianism nor Monophysitism, both sides were extremists. The Monophysites over did Christ's divine natures. If the Nestorians taught that Christ had two nature's, a kind of fully human one and a fully divine one, that were separate, the Monophysites seemed to be teaching, or did teach, that Christ had one nature, and that, essentially, divine. The relationship of the human and divine natures in Monophysitism was denounced by their opponents as if you threw a bucket of water into the ocean. The bucket of water representing the human part. What's at stake in this, and why it's important, is how Christ saves people. If he is too human, then he's just a human, elevated by God, like some kind of ancient-world hero. And he doesn't seem, then, to have the power to save people from the devil, hell, original sin, all of these terrible things that God has saved the followers of Christ from. If he's divine, completely divine, then what's the point of distinguishing him from God the Father? And then, how did he suffer on the cross? Was his suffering real? Can God, with no human elements, suffer? Questions about this so far? We understand the difference, then? And we, sort of, understand what's at stake? Sort of, because maybe we are thinking-- I hope not, because you're not in a medieval frame of mind, if you're thinking this-- You may be thinking, though, none the less, "Well, why don't they just agree to disagree?" Or something like, "Hey, you can believe in one nature, I'll believe in two." Or, "You can believe in two separate natures, I'll believe in two natures coexisting. And God will reward your good intentions." That's really the problem, is that we live in a society in which, at least, so we may think. enlightened people don't really impose their beliefs, in detail, on others. We're not really interested in theology that much. But the Bible, I've got to admit, does say that it is important to have the right belief. The Bible, particularly, but not exclusively, the Old Testament, is very bad on rewarding good intentions. The further back you go in the Bible, the less are good intentions rewarded. Lot's wife was told not to look back. She looked back. She was turned into a pillar of salt. Nobody said, "Oh, OK, you didn't mean to look back" or you know, "human weakness." That's just it. Or the guy-- now I'm betraying my ignorance-- who stumbles as they're carrying the tabernacle back to Jerusalem, from captivity with the Philistines. Is it Usiah? Well, anyway, I shouldn't get started on things I'm not sure of. But the guy stumbles, and God strikes him dead. He stumbled. Nobody asks him, "Oh, I'm sorry, I didn't mean to stumble," or "a little rabbit ran in front of me." He stumbles: he dies: that's it. God wants you to understand what's going on. Insofar as you don't make errors. Therefore, the right understanding of Christ's nature is important. It's not just a matter of convincing other people that one band is better than another, or one kind of game is better another, or one team is better than another. It is crucial. Gregory of Nyssa, himself a theologian, writes, about 500 AD or so, that the mood of theological controversy is so great, that if you go into a shop, and you ask about your change, he says, the shopkeeper philosophizes about the begotten and the unbegotten. If you inquire about a loaf of bread, the baker will reply, that the Son is inferior, and the Father is superior. And if you ask if your bath is ready, the attendant says that the sun is made out of nothing. Now, all of this is a satiric remark about the way in which ordinary people are caught up in this religious controversy. It is not, exclusively, a matter of intellectuals or clergy. But it's a political problem as well, and that's the reason that it really preoccupies us. In the Council of Chalcedon in 451-454. So Ephesus, 431, Chalcedon, 451 to 454. Chalcedon, also on the other side of Constantinople on the Asian side of what's now Turkey. The Council of Chalcedon denounced the Monophysites. It basically says that Christ has two natures. They are both perfect, they are indivisible, but they are separate. Two natures, one person, one hypostasis. A "hypostasis" is a thing that exists in its own right. This solution was suggested by Rome, by the pope. The same Pope Leo the Great, who'd negotiated with the Huns. The West had the advantage of not experiencing these kinds of controversies. And so Constantinople, far more powerful than Rome in the 450s-- Rome, about to collapse completely-- nevertheless, is beholden to Rome for, at least what would be the majority solution, to the problem of Monophysitism. Of course, actually, it's not a solution, because not everybody acknowledges the Council of Chalcedon. It provokes a split. The Patriarch of Alexandria would be the leader of those resisting the Council, and Egypt, Syria, and, to some extent, Lebanon and Palestine, would be Monophysite, steadfastly. Indeed, the survivors of the Monophysites-- that is the modern-day representatives of this part of Christianity-- are the Copts, in Egypt, who form ten percent of the population-- Christian Monophysites-- and the Christians of Ethiopia, who form a little more than fifty percent of the population of Ethiopia. The so-called Coptic Christians are the descendants of the Monophysites. The Nestorians also have some scattered followers in the modern world. They were very strong in Central Asia. And if you've studied things like the voyages of Marco Polo and other Western travelers in the thirteenth century, the people who interpret for them, who help them, who acquaint them with central Asia and the Chinese Mongol Empire, are Nestorians. But we're going to leave them out, because they're not a political problem for the Byzantine Empire. They're, pretty much, exiled. The Copts are an internal problem. And the Monophysites, or Copts, do not like the Orthodox, the Byzantine Emperors. The Byzantine Emperors try to compromise with them. And I'll mention a couple of these compromises. The Emperor Zeno, from 474 to 491, issued a document called the Henotikon. We're back to emperors. As with-- we saw as far back as Constantine, emperors trying to intervene to solve religious controversies, right? The Henotikon says, one of the Trinity was incarnate, and we're not going to discuss it anymore. So first, it says this rather noncommittal statement: "One of the Trinity was incarnate." And then it also outlaws any further discussion. Nobody liked this. Zeno was succeeded by Anastasius, who was a Monophysite. And then, as we'll see, the great emperor of the sixth century, Justinian, who we're going to be looking at much more closely, was a fierce anti-Monophysite or Chalcedonian, Orthodox. But his wife was, sort of, semi-Monophysite. This may have been politic. Since they were both effective rulers, the people who were Monophysite could orient themselves to Theodora, the Empress, and the Orthodox, to Justinian. Ultimately, this problem would be quote, "solved," because the Arab Muslim invasion of the seventh century would take over the Monophysite territories. Again, I hope I'm not giving away a secret, by saying that the most striking, sweeping, and dramatic event of Mediterranean world or of the Eurasian land mass, of the period that we're dealing with, arguably, is the rise of Islam. Mohammed's Hegira is in the 632-633-- I can't remember. Anybody know, off hand? Anyone want to look it up, off hand? H-E-G-I-R-A. Student: 622. PROFESSOR: 622. 622. By 660, Egypt, Syria, Palestine, Lebanon have fallen to Muslim rule. And they are extending their power as far west as North Africa and as far east as Afghanistan. How this happens, why this happens, is the subject for discussion a little later. But again, if you refer to the map in 600, this is before the Islamic takeover. And again, if you look further east, the Eastern Roman Empire consists of all these parts, many of which are about to be taken away from it. And the parts that were taken away from it were pretty much the Monophysite parts. So the fifth century is the story of the survival of the Eastern Roman Empire, despite these religious controversies. The early sixth century, which we'll talk about in more detail, is the story of the expansion of the Empire to make a stab at reuniting, by conquering the West, what had been the single Roman Empire. Justinian's empire was overextended at least in retrospect. This is a reconquest that, at least, consultants from a later generation would have said was a mistake, an overexpansion Initially, the main enemy of the Byzantine Empire, after Justinian-- so in the late sixth century, early seven century-- would be Persia. But also, at the same time, the Byzantine Empire would start experiencing Danubian frontier incursions, attacks from the Balkans. And here again, as I said, it's all invaders and heresies. Invasions from Slavs and Avars in the Balkans, and the Persians in the East. OK. In 591, a revolution toppled the Persian ruler, who, peculiarly enough, fled to Byzantium for refuge, where the Emperor Maurice helped him gain his throne back. In 591, there was a peace between Persia and Byzantium, and Byzantium seemed to have come out of this terrible period of warfare of the late sixth century. This allowed Maurice to turn his attention to his other front, his Western- Northern front, where the Avars were a tremendous threat to him. The Avars, a central Asiatic people, who come in through Central Asia into the Balkans. And they carry with them, to some extent, the Slavs. The conventional portrayal used to be that the Avars sort of lead the Slavs; the latter are kind of passive. It's a little more complicated than that. The Avars had taken the great cities of the Balkans. And in 492, Maurice turns to deal with them, to push them back against the Danube. His army rebels against him, and he's overthrown and killed. The beginning of the seventh century is the period of the maximum danger of Byzantium. It lasts, with intermittent flashes, from 602, the overthrow of Maurice, to 717, the Arab Siege of Constantinople. Immediately, this new emperor, Phocas, is attacked by Persia. The Persian King claiming to revenge the murder of his benefactor, but, in fact, simply reopening the war with Constantinople. In 608-609, the Persians and the Avars are allied, and the Persians are really on the march. By 617, they have taken Egypt, they have taken Syria, they have taken in Jerusalem, and the relic of the Holy Cross has been taken back to the Persian capital. The emperor, at this time, Heraclius, whom Wickham is not very impressed by, admittedly. Heraclius leads a resistance, as does the patriarch, to a siege that is on both sides of the city of Constantinople. On the one side, the land side, the Theodosian Walls, are the Avars and the Slavs on the Bosporus. Across the city, on the Asian side of the Bosporus, are the Persians. And what Heraclius does, is to confide the city in the care of the patriarch, and go off and attack the Persians from the rear. The patriarch defends the city, not only by organizing the army, but by putting wonder-working icons on the walls, to face the enemy. An icon is a painting of a sacred figure. So then, it is not a statue, but a painting. And it portrays a saint or Mary or Christ. And in what has come to be called the Orthodox tradition, these remain today, a figure of the church, a very distinct kind of aspect of the piety of the East. The Church -- patriarch ordered that the Church melt down all of the treasures that had been given to it, to decorate it, in order to pay for troops. So the combination of the icons, the money, the spirit of the populous, and military means were able to withstand this prolonged siege-- at times a double siege-- of the Persians on one side, the Avars and the Slavs on the other side. After many years of fighting in the East, Heraclius succeeded in overthrowing the Persians. At the battle of Nineveh in 627-- this is a seventeen-year war or so. I'm sorry, Nineveh-- E-H. Heraclius defeats the Persians, and the Persian Empire is virtually crippled. 627-- Byzantium would have seemed to of have been triumphant. The first Arab attacks, however, were in 634, twelve years after Mohammed's Hegira. By 636, Syria had been taken; by 638 Jerusalem had been taken; and the True Cross, again-- in this case, we lose sight of it. Persia, itself, would collapse in 640 and pass under Arab rule. Egypt would fall in 645. What's left of the Empire, then, is the Balkans and Anatolia-- some Armenian, some Slavic elements. So weak is this empire, so beset by enemies, does it seem to be, that a successor of Heraclius, the emperor Constans II, moved the capital to Sicily, to the West. Constans II ruled from Syracuse-- Syracuse, Sicily, obviously-- the original Syracuse. He would be the last emperor to visit Rome. And he was, actually, the first since 476. So in 662, when he moved the capital to Sicily, we have the spectacle of a kind of ghost emperor visiting a ghost city. Visit of Constans II to Rome, and the severe crisis of the Eastern Empire beset, as it was now, particularly, but not exclusively, by the Arabs. And indeed, in 674, the Arab fleet appeared off Constantinople. In 678, we hear, for the first time, of the weapon of the Greeks against the Arab fleets-- a weapon called "Greek fire." Greek fire is some kind of flaming projectile. In other words, something that you can shoot with a catapult, or some other propulsion device, that will burst into flame. Obviously, you can't launch it if it's already burning. You have to have something that--This is the essence of basic bomb throwing-- you have to have something that will explode on impact. The Greek fire was, particularly, effective on wooden ships and on rigging and sails. It would set the ships on fire. And it's a weapon that seems to have been unique, at least for awhile, to the Byzantines But, parenthetically, how was it that the Arabs have a navy, in the first place? These people, who decades before, had never seen a river that flowed all year long, who had no experience with the sea, for whom the desert was the sea. It is an example of this kind of very rapid adaptability that we'll emphasize, when we come to talk about the Islamic invasion. The East did survive even this attack. The seventh century-- we will be dealing with in more detail-- is a crucial turning point. By this time, the Eastern Roman Empire we're talking about as the East is pretty much a Greek empire. Justinian would be the last emperor to speak Latin. And the truncation of the empire, with the loss of Egypt and the Near East, means that it is pretty much a Greek empire and, also, pretty much an Orthodox empire. Orthodoxy is the Christian faith that stands between Nestorianism and Monophysitism. For the time, the Orthodox world, in the East, and the Catholic world, in the West, are the same. Their official break won't come until 1054. And as you know, to this day, the Orthodox churches of Russia, Greece, and so forth, look very different. And they also have certain doctrinal differences with the West. And that's not our subject, for the time being. We do have, however, before the close of business, one more heresy. A heresy that starts to divide the Byzantine Empire in the late seventh century, and that is iconoclasm. Iconoclasm, which Wickham talks about in some detail, and which he tells us to take seriously. What he means by that, is that iconoclasm seems to be something that must not be about what it seems to be. It's got to be about something else. Iconoclasm is the belief that images, like icons, in particular, are dangerous. And that they lead to inappropriate worship of the image, rather than what the image symbolizes. So the iconoclasts believe in banning images of persons. A cross is fine but not a picture of a saint. Even, in some circles, pictures of Christ would be suspect. The danger of this reverence paid to icons, is that the icons then, becomes a sacred thing in itself, and you've fallen into idolatry. You're worshipping multiple representatives of the divine. Now it certainly seems logical that this must have something to do with Islam. Because Islam, in its most monotheist manifestations, frowns on and bans the representation of purportedly divine figures. And it, indeed, doesn't like figural representation at all, in decoration of sacred spaces. Lest this be interpreted as exalting figures, even the Prophet -- especially the Prophet himself. There are no pictures of Muhammad for home consumption, for mosque display. And so it seems logical that this is a response to criticism from Islam, that Christianity is really not monotheist, that it's a form of idolatry, because it has so many sacred figures. And that the success of Islam and the success of the Arabs against Byzantium, might be caused by the abandonment of monotheism-- the abandonment of the worship of one god and the proliferation of multiple gods. The problem is that there's no real evidence of this. And you don't have to have Islam to force this kind of thing. If you look around the churches of much of Northern Europe, you will see statues that have been decapitated by Protestants, in the sixteenth and seventeenth century, or stained glass that was destroyed by Protestants. Protestantism is iconoclastic in many of its forms, in that it believed that the Catholic Church was superstitious, paid reverence to all of these saints and human figures, and forgot, in the process, to concentrate on the single God. Iconoclasm is a crisis of the empire. It is also, like these other heresies, a recurrence of this problem of how to represent the connection between God and human beings. What connects the divine with the humans? Are there intermediaries? Is Christ an intermediary, or is he God? And if he's God, how is there intermediation? Why does God care about us? How does God care about us? How many ways are there to approach him? It took until 843 to settle this controversy. It had many periods of settlement and then a recrudescence. It's a controversy that lasts, then, something on the order of 150, 160 years. At times, it divides the Empire completely, at times not. It tends to be supported by the emperor. If the emperor isn't iconoclastic, it tends to wane. It's supported by the emperors, partly, as a way of trying to unify and mobilize the Empire around the figure of the emperor, instead of dissipating the energies around the various saintly figures. So where are we, with this empire, that seems to consist of only sieges and barbarian peoples and heresies? In the ninth century, it would seem that the cities, with the exception of Constantinople itself, had declined to become little more than fortresses. We seem to be at the end of classical antiquity, in some fundamental way, of that society built around Mediterranean cities. Society even here, as in the West, is rural. There's not a whole lot of trade. There still are libraries, with books in them, but they don't seem to be read very much. We have very few texts from this era. It's a militarized society. It's an intensely religious one. There's very little secular literature-- really at the end of Greco-Roman Pagan knowledge. As it happens, however, this period would usher in an era of surprising, at least in retrospect, prosperity for the Byzantine Empire. And we will be talking about that later. On Wednesday, we're going to discuss the reign of Justinian, through Procopius, as a thing, in itself. And then, we will turn to the post-Roman world of the West, subsequently. Thanks very much.
The_Early_Middle_Ages_2841000_with_Paul_Freedman	15_Islamic_Conquests_and_Civil_War.txt	PAUL FREEDMAN: OK, so Islam, Part Two. I know there's a lot of new terminology, new narratives. The things that I want you to keep in mind are what we're really going to focus on today and that is the Islamic conquests, which certainly take place partly because of religious motivation, but nevertheless are not accompanied by some fanatical desire to convert the world. The Muslim conquests have to be understood in terms of religious motivation but not in terms of a determination to wipe out Judaism and Christianity. What appears to be a paradox makes this era a little hard to understand. Namely, the paradox being that you would have such a rapid expansion of the Arabs and the religion that they carried, which eventually would extend from Spain to India. And at the same time that the Islamic population would be a minority in most of those conquered regions for centuries. There is not a demand for the conversion of the population to Islam, and that although the conversion does take place, in many, in most parts of this imperial caliphate. It doesn't take place immediately and it doesn't take place under great pressure. I say apparent paradox because, in fact, the two things are different. The motivation provided by the religion to conquer does not necessarily mean that you require that everybody that you conquer embrace the religion. Indeed, in part, this is because, as Berkey emphasizes, the distinctiveness of the religion was worked out over the course of its first century, beginning as we said last time in Medina but not fully articulated until the change of dynasty in 750 from the Umayyad to the Abbasids. But the other reason is that there's no logical connection between conquest and conversion. It's perfectly possible to be a motivated conqueror and not to require that other people embrace your religion and this is for reasons that we'll see. The other apparent paradox, and here I think there really is a paradox, is that the Islamic conquests are accompanied by internal division within Islam from 650 AD. By the time of the Abbasid succession, it is a century later these two parties can be identified as Sunni and Shiite. And you've read that and you're aware that this continues to be a division that defines an awful lot of the Islamic world today. It is particularly a problem in those countries such as Iraq, for example, that have both Sunni and Shiite populations. It's not a problem in Morocco where everybody is Sunni. And it is less of a problem in contemporary Iran where a very large majority is Shiite. But it is a problem that defines both Islam as a religion and the politics of many countries to this day. And so one of the things we have to talk about in a lecture entitled "Islamic Conquest and Civil War" is the origins of the split within Islam. The paradox is that the conquests keep on going even while it would seem that religious unity is falling apart. Now as you remember, I hope, after Mohammed's death, there was no clear succession. He didn't have a son, and it wasn't clear what anyone would succeed to. If he was the seal of the prophets, then you couldn't succeed to prophecy. Was he a religious ruler, was he a military ruler, was he a judicial arbitrator? His father-in-law, Abu Bakr, who we saw was one of the first of his followers, was elected caliph--, caliph meaning "successor," simply. Succeeding to what was not defined, but to some kind of combination of religious and secular rule. As we said last time, religious and secular rule are, in a fundamental way, not separated in Islam, although as we're going to start to see and as you've read, there are some ways in which they do start to separate out, particularly in the later Abbasid period. Abu Bakr was elected, that is the followers of Mohammed, the people who were thought to have some sort of original religious authority, elected him. His rival was Ali, the cousin of Mohammed and the son-in-law, at the same time of Mohammed. Ali had married Fatima, the daughter of Mohammed. But this election was not recognized by many of the tribes that had regarded their loyalty to Mohammed as personal loyalty to Mohammed, not to some institution and not to some permanent coterie of caliphs or successors. So they refused to recognize Abu Bakr's authority and there ensued what's called the ridda, R-I-D-D-A, or apostasy , where the tribes rejected the authority of Abu Bakr and Abu Bakr militarily compelled them back into submission or recognition of his authority. Abu Bakr ruled for less than two years, but he had already started on a key aspect of the ridda, the apostasy , and, that is, turning the resistance to the apostasy into a war against external enemies. In other words, the military energy that had to be devoted to bringing these tribes back in, once they were brought in, was continued to turn their military energies outward. And outward means to the north, out of the Arabian desert and to the direct north and slightly northeast, meaning Persia, to the northwest meaning the Byzantine Empire. And already under Abu Bakr , it was discovered that the Byzantine Empire and the Persian Empire were hollowed out and that what began as raids to keep these discontented tribes happy with a spot of plunder turned into a conquest. And as success breeds success,-- and I don't think there's anymore dramatic lesson of that cliche,-- the ambitions of the conquerors changed very quickly; well the ambitions of the raiders changed very quickly, from booty to conquest, from plunder to an expansion of territory. Remember that the Persians and the Byzantines had fought each other, that in 626 Persia besieged Constantinople unsuccessfully-- 626, four years after the Hegira. So from the Islamic/ Muslim/ Arab point of view, the timing was great. These two great empires had exhausted each other militarily and to some extent spiritually as well. In 634, in other words two years after the death of Mohammed, the city of Damascus fell to the Arabs. Damascus, the capital of Byzantine Syria, indeed one of the oldest cities in the world, mentioned in the Old Testament of the Bible, an extremely important center of government, commerce, and religion fell. The Byzantine Empire was defeated near Jerusalem. Abu Bakr died in 634 and again Ali was passed over in another election in favor of another companion of Mohammed, Umar, another one of those original followers that we mentioned in the last lecture. Umar would rule from 634 to 644. He was a startlingly effective ruler. In the ten years of his caliphate, the Arabs conquered the Persian Empire entirely. An empire that had lasted for centuries, that had been one of the great world empires, collapsed and was taken over by Islam, by the Arabs. The Byzantine Empire didn't completely collapse, but in this period it lost Syria, Palestine, and then its richest agricultural province, Egypt. Alexandria, capitol of Egypt at the time, surrendered in 642. We can list the factors that favor the Arab conquest, though they're mostly sort of favorable soil, as it were, not the plant itself. Weakness of Persia and Byzantium, I've already mentioned. A mastery of desert warfare. We'll see this with the Vikings at the end of the course. There are peoples who have been able to take advantage of an adverse environment that they are able easily to swim through, travel through, and that a less mobile adversary cannot deal with. So the similarity between the sea and the rivers of Europe and the desert of the Near East is that you can pick and choose your battles. You appear off the coast. "Uh oh. There's an army there. We'll just go back and then we'll raid somewhere else." The same is true of the desert. You appear out of the desert where the urban dwellers cannot easily field an army. And you discover that there's nobody defending the city and you take it. Or you discover there is somebody defending the city. You go right back into the desert; they can't pursue you there and you pick somewhere else. So the mastery of desert warfare is in part a question of mobility and the ability to move in the desert freely, easily. Another aspect of the weakness of Persia and Byzantium is the discontent of their religious minorities. Persia was ruled by a Zoroastrian elite and had other religious groups that felt, if not persecuted, at least discriminated against. And as we've seen, the Byzantine Empire had a substantial Monophysite population that was persecuted by the orthodox. These people might not exactly fight for the invader but they certainly weren't unhappy when the invader showed up. Indeed, remember that I said that in 655, there was a naval battle. How could the Arabs have sailors if they hadn't seen a year-round river until a few years before this battle? Their sailors were, most of them, from Monophysite populations of Egypt and Syria. They were able to recruit people who would fight for them who were not Muslim. The third is the channeling of a war-like society towards external fighting. This is like a problem of conservation of energy. You have a certain amount of energy that is being expended in external fighting. If you can turn all those electrons or whatever in the same direction and make them go outward, they will be extremely powerful. Limits of my scientific knowledge, unfortunately, you see displayed. But you understand what I'm talking about. That is, the internecine warfare is now turned outside because the plunder is better, the motivation is better. And then motivation is a fourth reason. Religious motivation is this thing that is called jihad. Everybody knows what this means. And we're going to have to grapple with it because our understanding of it is perhaps partial and distorted. Jihad means struggle. It is a struggle against other religions or against other tendencies within Islam. There's plenty of energy, as we will see, devoted to fights within Islam. Internecine religious fighting if not tribal feuding. So we use the term jihad with some reservations. It is wrong to think of the Arab conquest as an expression of jihad in the sense that guys with knives in their teeth ride out and offer a terrorized population the choice of death or conversion. Once again, it is possible to have a religious motivation and yet not necessarily want to kill or convert the conquered people. The Quran itself has plenty of information about the jihad but it is not completely consistent. Certainly there is a sense that the unbelievers must be combated. A sense of martyrdom even-- that those who died in the struggle to advance the religion will receive special favor. But there is also a respect accorded to people of other religions, in particular, Jews and Christians. And if you think about it, it is psychologically possible to be convinced that God is following you. God must be following you. After all, you just conquered Jerusalem, you just conquered Alexandria, you just came out of the desert and have started to a roll like a tsunami- an image I don't think is really in the Quran.-- Well, let's say roll like the sands of the desert over ancient civilization. So God must be with you. But the fact that God is with you may indicate that you're an elite and that the people that you conquered are simply going to stay that way. Or that if they want to become Muslim, that makes sense. Obviously Got favors Islam. If they don't want to become Muslim, that's their lookout. So it does not mean that you have a hostile conquest policy. Jihad is, in this context, not incompatible with tolerance. "Tolerance" is a word I use with caution as well. Because it's not as if they have a modern ideal of tolerance, of individuality, of "You have your religion, I have my religion." It is more that they are not bothered by the presence of people of other religions. And we'll see some of why that is. So, number five, a policy of allowing conquered people to maintain their religion, livelihood, and private lives. So there are other rapid conquests in world history, and there are other rapid conquests by people who are technologically or culturally or certainly economically behind the people that they conquer. The Mongols conquer an incredible territory. The Vikings, which we will end the course with, are certainly less developed, economically, less civilized, than the Carolingian Empire that they plunder. What is unusual about Islam, and I reiterate something that I've said already, perhaps more than once is that it has a permanent effect. Rather than disappearing back into their yurts, like the Mongols, or disappearing back into the tundra- well that's an unfair description of Scandinavia- but disappearing back into the north like the Vikings, the Islamic powers not only stay as occupiers but become, themselves, a cultivated, wealthy, highly civilized empire. What is unusual about the Arabs, then, is their ability to consolidate and to hold onto their conquests. OK, I think I said before there are three startling things about Islam: the career of Mohammed, the rapidity and extent of the conquests, and this business of the cultural adaptability, consolidation, of the Arab conquerors. Questions so far? I think that the conquest part of this is clearer than the internal divisions. So let's proceed with the conquests rapidly. There's no single regime, there's no rule issued by the Caliphate for conquest policy. In general, if the population surrendered on terms the way Alexandria had in 642, that was fine. Then the people were allowed to keep their local customs. In other words, they were allowed to keep their houses, their jobs, their religion, their property. The Arabs were intent on plunder, however. Why didn't they just pillage these people? Some of it is just wisdom. They are thinking they're going to have to govern these places and that they might as well harness the industry and enterprise of the population rather than kill them or disperse them. Some of it was, I think, that they had so much plunder available to them from other sources that they didn't have to bother with some middle-class artisan's wealth. They could plunder churches. They could seize Church lands. They could take the state treasury. Between them, the state and the Church held so much wealth that the Arab conquerors didn't really want to bother with mere private property. The leading nobles tended to flee. They allied their interests with the state. They were very large property owners; that land could be confiscated. And the reward to the conquerors was to be settled on lands of their own, with tenants of their own, and these lands tended to have belonged to the state or to the Church. They received long leases for these lands from the Caliphate and they paid a religious tax, a kind of tithe, as members of the umma, the religious community. Non-Muslims were allowed to keep their property, their land and other property, but they had to pay two taxes that Muslims did not. They had to pay what is called in the English-speaking world a poll tax, which is basically just a head tax. Every person or every household pays a certain amount of money. It's actually kind of like a flat tax, but it has nothing to do with income. It is simply that you as a person living in this polity pay this as a tax. And then a land tax. Land tax obviously more variable depending on how much land you own. If you own x amount of land, you pay a tax. If you own 8x amount of land, you pay eight times that tax, at least that is the theory. And given that, as we said, as far back as Diocletian, you need to have very good records to keep track of taxes, then they kept on the old officials who had those records. So the language of administration in Syria remains Greek for quite a while; in Egypt, it remains Greek; in Persia, it remains Persian, because the guys that are running it are basically the same guys who are running it under the old empire. Why would the Arabs want to get rid of them? They would want to get rid of the high officials, the nobles, but the functionaries, the bureaucrats, stayed on. Most people who were Christians or Jews paid no more tax to the conquerors than they had to the Byzantine or Persian Empire. In other words, they were conquered, their lives did not radically change, their taxes did not go up. They didn't really miss the Persian or Byzantine imperial regimes. The question, however, is why are the Arabs so tolerant? And this surprises people who assume that Islam has always been spread with a kind of totalizing militancy. In fact, for a time, the conquerors didn't encourage conversion because you can see the consequences of conversion for taxation. If eighty percent percent of the population is Jewish and Christian, then eighty percent of the population is in a high tax bracket. If you are running things, it's to your interests that they not convert to that very low ten percent tax bracket or whatever the zakat, the religious tax is. "Go ahead and have fun. It's Sunday go to church, don't bother me, pay your taxes," would be a fairly common attitude on the part of the conquerors. And of course there's a respect for Christianity and Judaism that I've already mentioned. Some of it is confidence eventually people are just going to see that Islam is more successful. Up until the Abbasid regime, 750, a vast majority of the conquered territory remained in the religion that it had had before the conquest. In other words, in Egypt in 750, a majority of the population were Christian. And indeed in Egypt, to this day, ten percent of the population is Christian. Certainly, Islam would gain. And certainly now, ironically, much more than in 800 AD or 1200 AD or 1500 AD or 1900 AD, it's tough to be a Christian in Egypt. This is a problem of modernity, not of the period we are dealing with. So the process of conquest is very rapid. The process of Islamization is not. They are not to be confused. Amidst all these triumphs, the caliph experiences divisions that culminated in a civil war between 656 and 661. And the origins of it seems to be the murder of Caliph Umar in 644. He was murdered by a Persian Christian. So it's not a Muslim assassination. But it ushered in another disputed election. And Ali, poor guy, presented himself yet again as the successor of Mohammed. And again he was defeated, this time by Uthman. Uthman, along with Abu Bakr and Umar, we mentioned him as one of the original followers of Mohammed. Uthman was a member of a prominent clan, the Umayyads, a high status Mecca family. High status, but the Umayyads had opposed Mohammed. Uthman was an exception but his family were among those people of Mecca who had been the most steadfast in opposing this upstart guy. So to some, especially the followers of Ali, Uthman appeared to be a representative of a not really staunch Islamic family. They were not fervent new followers. Why was Ali passed over so many times? It's not clear. Here again, we are in a very controversial area in which a lot of later tradition elaborates reasons for things that may not have anything to do with what the reality was in 644. You start to have pro-Ali parties or traditions. This is what would become the Shiite party and pro-Umayyad or pro-Caliphate traditions, that of the Sunnis. Neither of which is completely to be relied on because obviously they are biased. Under Uthman, the pace of conquest continues. This naval battle in 655 took place,-- the Battle of the Masts,-- in which the Byzantine navy was defeated by the Arab navy. This meant that islands in the Mediterranean start to fall to the Arabs. Cyprus was conquered in 649, Rhodes in 654. Meanwhile, in the former Persian Empire, the eastern part of Iraq, tending over towards Persia, was conquered in 651 - 653. Armenia, north and west of Persia, east of Anatolia, the area where the earthquake was recently, was conquered in 653 - 655. But Uthman was particularly disliked by much of the population. Unlike Umar, unlike the early caliphs, he was regarded as lethargic and as a sensualist let's say. Lethargic and profligate, a lover of luxury, a monarch rather than a leader, a corrupt ruler. And he was murdered by a Muslim in 656. Here we have the first assassination of a caliph by another member of the faithful. And Ali was proclaimed as caliph. The problem here is that Ali was proclaimed caliph by the people who had assassinated Uthman. Or at least he was perceived as taking the title from the bloodied hands of assassins. Whether he knew in advance of the plot against Uthman is doubtful. But he starts off in a somewhat false position as caliph. He is opposed bitterly by the Umayyad family. But more than that, his claim to the caliph is tarnished by the circumstances under which he came into it. And an Umayyad rose up against him and starts the first civil war of Islam. This is Mu'awiya, the governor of Syria who revolts in Damascus and leads a party against Caliph Ali. In fact, this gives rise to a militant group of people who hate both claimants. Ali is assassinated, and Mu'awiya is wounded. Now Mu'awiya survives but the tendency within Islam to dispose of enemies by violent means has been sanctioned by the events of this period. So 661, the civil war is over. Mu'awiya moves the capital from Medina to Damascus. He establishes the Umayyads as a dynasty, and they would rule as caliphs until 750. What does this move from Medina to Damascus mean? It certainly is a part of the de-Arabization of the definition of the caliphate. Damascus is not an Arab city, at least in its origin. It was part of the Byzantine Empire. It is more centrally located than Medina in terms of administering the Empire. It's also more cosmopolitan. It has a lot of different kinds of people. So the move is away from the Arab heartland to a place where the population is not necessarily Arab. It is part of the transformation of the caliph from what we would call religious leadership to that of a kind of monarch, king. The caliph lives in a city. He lives in a palace. He has an immense entourage. The days of the tents in Arabia or of quasi-nomadic followers of Mohammed are definitively over with the defeat of Ali. Defeat, but it's not a complete defeat. Sh'ia means party or to its opponents faction. And for a long time, the Shiites are like the perpetual losers who cannot at the same time be eliminated. They are a minority within Islam. They are, at various times, seemingly overwhelmed by the wealth, armies power of the caliphs. But they never go away and they never abandon their claims. They form, thus, a permanent dissenting group within Islam. What is the nature of that dissent? What don't they like about Islam as it's practiced by the majority? Any sense of that from this admittedly busy reading? It's key that you understand what Shiism is and what its grievances are. STUDENT: Do they reject the caliph as a religious figure? PROFESSOR: They reject the caliph as a religious figure. Do they reject him because he's not the descendant of Ali? Partly. Part of this is a succession question. They reject the caliph because he's illegitimate. So it's kind of like a dynastic question. The only real caliphs-- and they don't use the term caliph. They start to use the term "imam" as you've read. The only real religious leader is not the guy sitting in Damascus in his palace with the splish-splashing fountains and scented perfumes everywhere. But to what extent do they reject the caliphate as such apart from the dynastic question? How would you describe Shiite political theory? If the Sunnis are monarchical, if they are comfortable with a caliph who rules over an Empire of unbelievable extent, what might the Shiites prefer to see? OK, Spencer? STUDENT: The government of the consensus of the umma, the community of the faithful. PROFESSOR: And something more informal. Indeed, although I hesitate to use this term, they are republican. Republican, not in the twenty-first or twentieth century American sense. What does republican mean in this context? STUDENT: Choosing representatives to then carry out the will of the people. PROFESSOR: Yes, anti-monarchical. They regard the caliph as a sort of George III of the Muslim world. They don't want to have a single ruler who is a political ruler. They're comfortable with rulership in at least some sense. But the rulership should be either elected or inspired. They are radicals, in part because they're dissenters. They're on the out. In part because they are really angry and they countenance violent tactics of opposition. They are egalitarian and that's sort of what I mean by republican. It's not so much that they necessarily believe in a representative system as that they believe in a system in which one class of believers is not exalted over another. And one person is not ruling merely because he comes from a certain background. Now what happens when religious movements are frustrated? That is, when they are objects of repression? Because indeed the Shiites were not particularly tolerated by the caliph. Often, such religious groups become fixated on a future in which their claims will be vindicated. This certainly makes sense. The Christians persecuted under the Roman Empire wrote the granddaddy of all prophetic texts, prophetic of the destruction of your enemies, the Book of Revelations. I suggest that you take a look at that anyway as it's always interesting reading. And it is the book of the Bible that has the most relevance, for better or worse, to the current world we live in because it's the one that talks constantly about the future and what's going to happen. Is that future the Apple computer future where everybody's wonderfully connected and we all can just float in some kind of great brain that we participate in? Or is the future some terrible ecological disaster in which we'll be cannibals and stuff? Or is the future the visitation of those angels, those candlesticks, those flowing rivers of molten metal as in the book of Revelations? Trumpets all over the place. Will one-third of the population be wiped out one day and then another third the next day? The narrator of the Book of Revelations cannot wait for this to happen. It is in the nature of apocalyptic thinking that it is violent because your enemies, who are right now persecuting you, are going to be confounded. And they're not going to be confounded in the, "Oh gee, I'm really sorry I persecuted you," sense. They are going to be split apart and pulverized. And you're going to be watching and you're going to be applauding while they're split apart and pulverized and tortured. That's the nature of messianic, apocalyptic thinking. Apocalyptic meaning the end of the world in some kind of conflagration, messianic meaning the presence of a savior. The two are not the same thing, but they tend to go together because there's going to be somebody who's going to come and, amidst the bloodshed and the fire, usher in a millennial world. That is to say, a world in which bad things have been purged. And that messiah may be Jesus Christ at the second coming. It may be the messiah of Jewish tradition. Or in Shiite Islam, it may be the imam, the rightly guided imam. The Shiites have a leader. I just said that they are republican and egalitarian, but they're not some kind of Occupy Wall Street, we don't have any leaders, anarchic group. They have leaders but they are leaders who are inspired not merely administrators of a huge bureaucracy. And these imams succeed each other and are recognized by the Shiite faction until the death of the eleventh imam-- the death of the eleventh imam without any obvious successor. Who is the twelfth imam? And we enter into this period of what the book calls "occultation." Not a word that you find used. Well, it's got some sort of medical meaning too. Occultation, meaning what? Come on, this is in the reading. He's gone into hiding. Occult means hidden. There is a twelfth imam. We just don't know where he is. He's in a cave somewhere. And there are imams and imams after him. Either he is deathless or there are other imams. But they're all hidden because they're not ready yet. But when they are ready, centuries of grievance are going to be revenged. So there's a notion of a corrupt and misguided Islamic establishment and of a true subterranean occult, righteous level of the practice of the religion. So Shiism tends to apocalyptic thinking, to prophecy. It exalts Ali and his followers. And it feels that it is in touch with the original desert, austere, egalitarian roots of Islam that have been corrupted by the monarchical, suspect purity of the Sunni caliphate. Who becomes a Shiite? This is a hard question to answer because it is more than just a party or faction. If it was just a party or faction, it could not have lasted into the contemporary world with the force that it has. Who is discontent under Islam? It would seem logical that the people who would be discontent would be non-Arabs because there is increasingly, as the Islamic world takes shape, a population of people who do convert to Islam who were not Arabs. We've said that the pace of Islamization was slow but, nevertheless, it was persistent and logical. It's logical that people should have converted to Islam, not only because it is a religion that to this day attracts lots of converts because it has a religious appeal and, as I have argued, it's a doable religion. It's a religion that does not have a huge number of self-mortifying precepts. It is a way of living a righteous life in the world and performing certain duties that are not tremendously onerous or very subtle and involve a lot of mental internal dialogue. So people are converting to Islam. These people are known collectively as mawali, singular, mawal. A mawal is a non-Arab Muslim. In the early years, by definition, a convert. The day that Damascus fell, there were no Muslims in Damascus except maybe for some Arab traders. As of the death of Mohammed, all Muslims were Arabs. But within decades of this, with the conquests and conversion, there are lots of non-Arab Muslims. They may need to learn Arabic to understand the Koran. They're supposed to go to Mecca and so forth. But they are not Arabs. Are they equal to Arabs? Well, Arabs are always, to this day, going to feel themselves to have a special relationship, a special status should we say, because Mohammed was an Arab and the movement starts in Arabia. But as I'm sure you know, the largest countries from the point of view of population that are Islamic are not Arabic, almost at all. Indonesia is the largest Muslim country in the world. India is the second largest Muslim country in the world even though its population is so large that Islam is a minority there. Pakistan is the third largest, I think. These all are countries without Arabs. Iran is not Arabic. It is, as we all know, an Islamic republic. The world of Arabs is very numerous but the world of non-Arab Muslims is more so. And it is starting to become that way in the period that we're talking about. The Arabs are simply a small number of conquerors. And particularly in Persia, where the pace of conversion is faster than that of say Egypt or Syria, there are a lot of mawali. At some point, some of the benefits of conversion, the fiscal benefits of conversion, are eliminated because the state, the Caliphate can't afford to have a population that is only paying the low religious tax. So it would seem that the moment at which you say, "OK, we're happy that you're becoming a Muslim. You're still paying land and poll taxes because we can't actually aspire to make all Muslims equal from a fiscal point of view." At that point you would have some angry malawi, at least so one would think. And so, one would think, these would be proto-Shiites or Shiite recruiting grounds. There's a lot of debate about this. Berkey kind of skirts over this issue. Other scholars doubt that this is the case. They don't actually think there's such a close connection between the Shiite party and discontented people. Or at least there is a connection between the Shiite party and discontented people, but the discontented people are not discontent because of their tax position. The presence of discontent within Islam is a constant. The presence of prophecy within Islam is a constant, even though the teaching of the religion has been that Mohammed is the last prophet. It's very hard to put a stop to prophecy in the Christian religion, in the Jewish religion, in the Muslim religion. Once you have started to talk about inspired religious leaders, they're going to crop up even after you've declared an end of religious charisma. And the consequences of that and the splendor, nevertheless, of the Abbasid Empire will form our subject for the next lecture.
The_Early_Middle_Ages_2841000_with_Paul_Freedman	12_Britain_and_Ireland.txt	Today we're going to talk about Ireland and England, predominantly England not because Ireland isn't important, but because we know less about Ireland. The reason we know relatively more about England in its Post Roman period, that is to say after 420 is because of the historian Bede writing in the early eighth century, a monk at Jarrow which was a part of a twin monastery in Northumbria. You can see on your map the Northeastern part of England before you get to what's now Scotland. Bede wrote among other things a history of the English church and people, which is full of miracles and very pro Christian as much as Gregory of Tour, but is a much more easy to follow narrative and a narrative with a certain kind of point. It's about the conversion of England and the establishment of the church. The other advantage for England over Ireland in terms of evidence is archaeology. A lot more has been done with excavating sites in England, and by England we mean literally England, the part that is not Wales, not Scotland, not Ireland, the part of the British Isles, the ensemble. Essentially the two islands are referred to as the British Isles. Britain is England, Scotland, and Wales, Ireland is Ireland. The Britons however, B-R-I-T-O-N-S, are the collective term for the Celtic population. Celtic is both a linguistic group and a somewhat vague ethnic term. It means the people who were there in the British Isles before the Romans came, and who were there afterwards fighting invaders from Europe. These invaders who come in the 440 is known as the Anglo-Saxons. Bede tells us it's the Anglo at the Saxons, excuse me, the Angles, the Saxons and the Jews. The Angles give their name to England, Angle land, the Jews we know nothing about. So a certain kind of medievalist will go on about funding a journal of jute studies and inviting contributors to something that we really have absolutely no idea of it being in that league of smallest thinnest bond [inaudible] at least in terms of three-dimensional books. The Saxons come from there is still a very large part of Germany called Saxony. What the nature of these peoples are, how they were differentiated among themselves is a source of a lot of real or at least it looks real scholarship as opposed to studying the Jews, but we don't have to go into that. But you need to get the cast of characters. Celts, Anglo-Saxons, the Anglo-Saxons conquer much of the island more or less what would become England but not all. They do not conquer Scotland, they do not conquer Wales, and they don't really conquer Cornwall. So the Western part of Britain remains Celtic and to this day Wales and Scotland considered themselves different from England. You can get into a lot of trouble by calling that area England with the people there and particularly in Scotland there's a possibility that they may separate from the United Kingdom at some point. Ireland, Ireland was never occupied by the Romans. Ireland was chaotic, was in contact with the Roman Empire, but was not part of it. This makes some difference and we'll talk about it when we come to talk about conversion, but it doesn't make as much difference as it sounds because the thing about England or Britain is that the Roman impress there would be almost wiped out once the Romans withdrew. So in contrast to what we saw with Gregory of Tour and Merovingian Gaul, Merovingian Frankish kingdom, the Roman influence in Britain is almost wiped out. Recall what we saw as persistence of Roman practices in the Merovingian kingdom, bishops, cities, the Latin language, tax records, written legal codes, that is not to say that the Merovingians weren't as I said before to be described by technical terms like thugs, or that this was a sleek well-functioning Kingdom, you landed at the airport and got the train immediately and everything was sleek and nice like Amsterdam or someplace like that as opposed to Kennedy. But that the Roman inheritance was visible and influential. In Britain when the Roman troops withdrew to fight the invaders in Gaul, this ended Roman society in Britain. The reason for this is partly that Britain was a frontier, viewed from the point of view of the Mediterranean the center of gravity of the Roman Empire. The frontier symbolized most dramatically by walls the most famous of which is Hadrian's Wall, a wall that separated out the Barbarians. But since you didn't have a river like the Danube or the Rhine, there seemed to be no natural frontier. Remnants of Hadrian's Wall are the largest souvenir of the Roman era, a wall to keep out the Barbarians from the North because in fact the Romans didn't conquer the entire island. They conquered the parts they thought were worthwhile, and they did think it was worthwhile. Frontier or not, we know that the Romans built villas, might be a little cold the somewhat open-air Mediterranean plan things, but Mosaic courtyards, drank a lot of wine, much of it imported, built cities, walls, other fortifications, cultivated land. So it's not as if there wasn't a serious Roman province of Britain from its conquest in the late first century, until its abandonment in the early fifth century. But here the invaders tended to obliterate much of what had been there in Roman times, and the Celtic population who had been Romanized at least at the elite levels, the Celtic population didn't really save very much from the Roman Empire. The Celts might remain Christian whereas the invaders were Pagan. But the Celts tended not to have cities or at least large centers, and they tended not to have or retain Roman forms of government. The one kind of, if not literally interesting at least weird aspect of Celtic Roman Resistance is the figure of King Arthur. I'm going to bring him up now and then I'm going to drop him. King Arthur belongs properly to the continuation of this course because his legendary status starts really in the world of romance, of French romance and then of international romance chivalric literature. By romance we mean, not only love stories but novels of chivalry, of knights, of battles. He is a figure who is 99.9 percent legend. Whatever the remainder of that 0.1 percent real. So far as he's real, he may be identified with Celtic resistance to the Anglo-Saxon invaders, Celtic Roman resistance in the late fifth, early sixth centuries. But the proportion of art to history in this is, if not 99.9 at least very, very substantial. The original setting of the Arthurian stories is that of the resistance to the Anglo-Saxon invaders. The Arthurian romances do have a Celtic beginning, well not a kind of, they have a Celtic beginning, and then they are appropriated by people in the Romance language tradition, French, first of all. So as Walkom says on page 151, nowhere else in the Roman Empire was the collapse of culture, economy and urbanization so complete. He uses that wonderful phrase again, radical economic simplification, ie, there's no more plumbing, there's no more of what we would consider to be affluent civilized society. The ceramics don't come from Africa anymore, the wine doesn't come from France anymore, people are reduced to a kind of subsistence or at least most people because as we'll see, some of these kings actually are able to get some luxury goods from abroad. If it were just a story of barbarisation, it would be less interesting then. In fact, the peculiar nature of England in this period, which goes from being a contested territory between the Germanic invaders and the Celtic population, to a kingdoms slowly converted in the course of the seventh century to Christianity from paganism, to the leading center of culture in Europe. Bede, who lived from 673-735 was the most cultivated scholar in Europe of the early eighth century. The most cultivated scholar in Europe of the late eighth century was also from England, Alcuin, counselor and adviser to Charlemagne. How do you go from being a barbarian enough area to having the largest libraries, the most cultivated scholars? Now, it is true as I think I've said before that any time you can say that such and such a person was the smartest person in Europe has got to be a fairly bad time. In the 19th century, you have your choice from all sorts of scientific, literary, other kinds of intellectual experts who would even dare to say. But we know that Boethius and Cassiodorus are the smartest guys in Europe in the sixth century because they have access to stuff that almost no one else does, because their writing about classical authors that almost no one else has in their libraries. We know that Isidore of Seville is probably the smartest guy of the early seventh century, and Visigothic Spain. Because we have his works, we have an idea of what he's read, we know his sources and again he's got the biggest library. Biggest library may mean 100 books, but 100 books in 700 AD is a serious collection of knowledge. Now, this is not easy knowledge, this is not as if everything were like Wikipedia five years ago, elementary and often wrong, these are very different kinds of works from what might interest us. Certainly a lot of biblical stuff, but also for example a lot of computing of time. Bede would be remembered for the history of the English church and people, but also for a lot of his works on figuring out time. He is credited, although not uniquely credited, but as an important person in the development of the BC, AD scheme. Believe it or not people are not born into the world calculating according to BC, AD, lots of people calculate according to other systems, how did they come up with this, and moreover how do they then fit the calendar into it? How do you keep time when you don't have electric or battery operated clocks? How do you know what the seasonal changes are? But in fact the most troublesome problem which had been particularly controversial to the conversion of England in the generation before Bede, in the early seventh and mid seventh century was the calculation of Easter. Easter is a real problem. Now, naturally it's not a problem if someone else tells you. If in 1970 you open up a little pocket book calendar and it says, okay, Easter is this day, you trust them, or now, if you have some feature on your iPhone that gives you Easter for the next 3,000 years, in case you want to know when Easter is in 3500 AD, no problem. But if you're out there in Northumbria or anywhere for that matter, in a monastery somewhere, where it's really crucial to celebrate it on the right day. Remember what I said about dogma and religious observation, God doesn't want you to say something like, "Dude, I don't really know when Easter is, but I think I'm going to celebrate it now." You can't do that, you can't just decide, I know it's sort of in the spring, nobody around here for miles and miles and miles knows how to calculate it, so what the heck, we'll do it on a Tuesday because I'm busy on what I think is Easter. That's not the way monasticism works, and we'll talk about that next week. The schedule is really, really important, but it's also difficult to figure out, and people disagree about it. To this day, the Eastern Orthodox churches celebrate a different date for Easter than the Western because they operate according to a different calendar. All right. Well, I'm not saying that this is the kind of knowledge that you ought to drop everything else to pursue, but it is a knowledge that requires a sort of observation that in fact we do not have. Most of us unless we're astronomy majors have no idea what the sky looks like at night. A, because we can't see it because of artificial light, and B, because we're not very curious. We cannot track animals most of us, and those of you who can, I'm interested in your knowledge. Most of us haven't the faintest idea how things grow except because we'd been to the Yale Farm, and "Oh my gosh look at this stuff." That's part of the reason for it because we're not very close to nature. I think that environmental concerns notwithstanding most of us have a huge investment in not being too close to nature, but the observation of phenomena is something that is much superior in so-called indigenous, primitive, traditional or historical societies. So the story of England and Ireland, centers on conversion and the reason this is so, is because conversion represents a change in orientation. A change in orientation towards a larger world. Instead of a tribal and fragmented identity. I'm not making a statement about the truth or non truth of Christianity. But about the sense of belonging to a larger world whose purposes encompass not only your group but a larger group of people out there. I think we can get a feeling for this from a famous passage of Bede's Ecclesiastical history, written in 731. He is describing events of about a century earlier, when King Edwin of Northumbria summoned the council to decide whether or not to accept the Christian God. The chief of the Pagan priest's speaks in favor of embracing Christianity even though you would think that he would be the defender of the old faith, he in fact, speaks to this assembly according to Bede in favor of Christianity on the grounds that it tells us what went before us and what will come after us. The passage goes like this, "And one of the King's Chief men presently said, thus seems it to me oh King. The present life of man on earth against that time which is unknown to us is as if you were sitting at a feast with your chief men and your Thanes", nobles in winter time, T-H-A-N-E-S. "The fire burns and the hall is warm, and outside it rains and snows and storms. There comes a sparrow and swiftly flies through the house." The installation is not great in these halls, right? "It comes through one door and it goes out another. Low in the time in which he is within, He has not touched by the winter storm. But that time is the flash of an eye and the least of times. He soon passes from winter out to winter again. So is the life of man revealed for a brief space. But what went before and what follows after, we do not know. Therefore, if this teaching can reveal any more certain knowledge it seems only right we should follow it." Now this is not why people necessarily converted, because not everybody's really bothered by that. But most people figure, "Wow, I'm in the hall, it's warm. It's great. I'm having such a good time." When I have to leave brief though it will be I'll deal with that. But, it does explain some of the appeal of Christianity and why the invaders who were Pagan converted. Indeed why people tend to convert to world religions like Christianity and Islam to this day, a local religion. I'm calling tribal only because by that I mean confined to a people whose identity is caught up in their religion. A tribal people or a tribal religion has trouble surviving extensive contact with other people. Because it's uniqueness is threatened by the realization that there's a huge world out there of lots of other people and when you start interacting with them, that is when you're no longer isolated, you will tend to seek an explanation for things that is grander than just, this Gods protect my sphere. This God protects my heart. This God protects against accidents in childbirth. There are exceptions. Judaism is one of the most obvious. Here is a religion of a small group of people that survives over the centuries. But it is not exactly a tribal religion in the sense that it's monotheistic and historical sense is very strong. This is what the priest means, or this is what I mean in interpreting the priests words as reported by Bede, by historical sense. A sense that God rules over the world even if I'm not in it. That there is something to come, not necessarily that there is an after-life although that obviously is part of the teachings of Christianity, but that there is a purpose to life. So conversion. The conversion of Ireland and England are different. The process of converting England begins in 597 with a missionary known, unfortunately, his named is Augustine. He's Augustine of Canterbury not Augustine of Hippo The Confessions Augustine. He is sent by the Roman Pope Gregory, the first Gregory the Great. Bede tells us that he was motivated to do this, it's very strange thing to do there had not been missionaries sent by the Pope before, that he was motivated to do this by seeing British boys for sale in the slave market in Rome, and asking who they were? He was told they were Angles, A-N. Angls as an Angle-Saxon A-N-G-E-L-S, and he is reputed to have said we should make them Angels not Angles. Angenly known Angle or Angels not Angles. Whatever the story Augustine arrived around 597 at an island that had some remnants of Celtic Christianity, but is basically a Pagan and barbarian. He landed in Cant in the southeast corner of the island closest to the continent, and on this map what I'd like you to know particularly are Cant with Canterbury as its capital in the south east, Westx in the west, I think I've helpfully underlined, Mercia towards the center, Northumbria northeast. The most important kingdoms in England and Wickham has emphasized how fragmented this territory was. The most important kingdoms would be at different times Northumbria, Mercia, and Westx. But the first place to convert is Cant. It faces the continent, the pagan ruler of Cant had actually married a Christian princess from Merovingian Gaul. Augustine established the first bishopric in Cant at Canterbury which would be henceforth, the major ecclesiastical center of Britain it's Archbishop wreck. Bede tells us about this, but he also tells us a lot more about Northumbria which is where he lived. Here you can see the off again on again pace of conversion. The pious King Edwin who had that council that we just described, converted his people after a vision, but after his death in 633 his successor went back to the old traditional religion, renouncing Christianity. Then the successor to that king, a man named Oswald, re-established Christianity. But he was killed in battle by the pagan king of Mercia in 642. Only in the 660s, 670s is England pretty definitively converted to Christianity. We can see this kind of transition in two of the most famous sources of information about this world. The poem Beowulf, how many people have read this? Yeah, everybody's read this at one time or another. Beowulf does have some little Christian themes and there is some debate as to what extent the poem is to be understood in Christian terms, but in its atmosphere, its rituals, the burial and the ship, the burning of the body, the devotion not only to war but to feasting and two gold, ring giving, it evokes, not merely evokes. It is a description of a warrior society in which although it is written in old English, remember that it actually takes place in Denmark. This is a north sea world in which the communications patterns are such that you could write an English poem about someone who goes over to the mainland for adventure. The other source is one of the great archaeological triumphs of the last 100 years, the so-called Sutton Hoo treasure which is in the British Museum. In East Anglia close to the water, actually close to the sea, a burial ship was found in 1939. Probably the king buried here was Raedwald, a king of East Anglia, who died in 627. Now it's a pagan burial because of all the grave goods, all this stuff is in there or so it would seem. But it's hard to tell just as in Beowulf, is it pagan? Is it Christian? It's hard to tell about this burial scene, because he's got a lot of stuff from what might be called foreign gifts or maybe plunder. Foreign gifts. He's got two Byzantine silver spoons. So two silver spoons made in Constantinople or [inaudible]. He's got gold coins. They're mostly from the Merovingian kingdom and they're different. They're all different. This is not an economic thing. This is a treasure thing. The difference between economy and treasure is that treasure is just for hoarding, and economy is fluid and transactional. The hoarding of course we see in Beowulf most obviously with the dragon. The dragon is not accumulating the treasure in order to safeguard his retirement or trade up in caves. He just sleeps on this treasure. The point of that is of course that people accumulate treasure for non-economic reasons. For reasons that have to do with their own satisfaction or their own anxieties. The utility of treasure is generally overestimated. Nevertheless of course at the same time this is a world in which gold, treasure accumulation is what men do. So what else is at Sutton Hoo? A wonderful helmet, unique because these things tend to disintegrate. A sword, a male shirt and then all sorts of paraphernalia. Some of it with Christian symbols like crosses, some of it very much in the pagan world. Beowulf and Sutton Hoo go together. They both show us a world of treasure, of weapons, of drinking halls, of palaces, isolated. The drinking hall is important as you know from Beowulf, it is the manifestation of civilization. It is that protection from outside that Bede describes in the little sparrow anecdote, but it is also the center of government. We're back to the ruler and his entourage or comatose, his gang, if you want to put a more cynical coloration on it. So the conversion of England is completed by the late seventh century, but it is a more complicated story than just monolithic Christianity versus monolithic paganism because there are two kinds of Christianity that seek to convert England. One from Ireland and one from Rome. Ireland, let's just pause over Ireland. Never part of the Roman Empire, as I said, but it's also the first place outside the Roman world to have been converted to Christianity. The first place in Europe actually. The first place period is Ethiopia. Ethiopia of course in northeastern Africa would be converted to Christianity very early, fourth century AD probably, but within Europe, Ireland was converted to Christianity. By the British or English missionary, St. Patrick, this is a little embarrassing but in fact, the Apostle to Ireland is one of those British Celtic Roman fourth century figures, Patrick. So in 600 AD, Ireland was largely Catholic while England was mostly pagan. Irish Christianity had certain peculiarities, some of them related to its lack of a Roman past. Thus, for example, it did not have bishops really or the bishops were weak. Because there had not been cities in Ireland on the Roman model. Therefore Christianity didn't have an urban background but rather a very decentralized and rural background. The most powerful institutions in Ireland were monasteries. Because these were great rural centers and so the monks ruled over the bishops generally. Irish monasticism was very austere. The Irish monks were more ascetic than the monks we'll be meeting next week from the Benedictine tradition started in Italy. They also were less fixed in one place. In Benedictine monasticism, you're not supposed to move, you're supposed to be stable, you're supposed to go through the same routine everyday. The Irish favored a more wandering existence and the establishment of little communities or colonies far away. The Irish form of piety emphasizes exile. It might be exile to a scary and almost unimaginable kind of environment. There are, for example, lots of little islands in the Irish sea that seemed to be uninhabitable. That is, if you look at them from the tour boat, you see a lot of birds and it's birders paradise. But in the middle of July, it's overcast, raining and the sea is pounding. Then you notice, there are little remnants of houses. Yeah. Question? Little caves where people in the sixth and seventh century lived or the island is tiny, smaller than this building. It looks like 20 people were living there. What are they living on? Well, poultry I guess. But this is a very severe form of asceticism. The wandering also can mean, just holding up on some island or wandering around the European continent and converting people. The Irish were great missionaries both to England and to the continent and we'll be talking about that some more. What about the Irish as the saviors of civilization? A book published about eight, nine years ago, How the Irish Saved Civilization, is like most such popular books, kind of overdone and reductionist. It's not literally exactly true. But here again, as with England, we have a society that had no Roman influence and yet had a highly developed tradition of learning, preservation of Latin. In part, very good knowledge of Latin because they didn't think they spoke it. Remember, we said the people in the former Roman Empire, it's hard to date the point at which someone in Spain is no longer speaking Latin but is speaking something that we can start to call Spanish. In Ireland, the distinction was quite clear. You had to learn Latin in lessons. You had to go to class. You had to be taught Latin. So the Latin that was taught was bookish. But for that, in many respects, correct. Finally, the Irish celebrated Easter according to a different calendar. So we refer to the Irish or the Celtic church. We mean this more decentralized church. The somewhat more wandering, missionary church. A church that was less hierarchical and less organized around bishops than that of its rival Rome. The story of the seventh century in England is therefore partly the story of competition between paganism and Christianity and flip-flopping between them and competition between Irish Christianity represented by, for example, the Monastery of Iona in what's now Scotland, I-O-N-A. The missions of St. Aidan, A-I-D-A-N, whom Bede describes with great sympathy even though he doesn't agree with him. But the controversy really centered ultimately or at least in an immediate sense over Easter. At the Senate of Whitby in 664, it was decided to embrace the Roman calculation of Easter. With that, bishops, hierarchy, a more organized church. I have a lot of trouble with this Easter problem and you will have noticed that I've evaded telling you exactly what the calculations are. Some of you may know much better than me. But the Jewish Passover is established by lunar months. Christians wanted to break with Jewish tradition and celebrating Easter according to a somewhat different calendar. So it combined lunar and solar methods of calculation. Very complex operation therefore. In the year 455, Rome, that is to say the papacy, under our friend Leo the first, mission to the Huns, definition of the two natures of Christ. Leo the first and Rome opted for a 19-year cycle of calculating Easter. But the Celtic churches cut off from the continent, remember we're in this post Roman world of very little contact, kept an 84-year cycle. So in the seventh century when the Roman missionaries had arrived again, you have two conflicting dates for Easter every year. I mean, occasionally just as with the Orthodox and Catholic Easters, they come together. So every so often they will actually be the same Sunday, but generally speaking, different. So you get these ludicrous scenes like King Oswiu of Northumbria celebrating Easter according to the Celtic tradition and his wife, who was from Kent, celebrated it according to the Roman tradition. So one Sunday was Celtic Easter and then the next Sunday was Roman Easter. So it's not so much that Easter is so important intrinsically but it is a symbol of the embrace of the Roman form of Christianity and the bringing of England into an orientation more towards the continent than towards the Celtic west. What is amazing, as I said before, is how quickly once the conversion takes place, England becomes not only integrated into the continent but a place of great cultural accomplishment. The great archbishop of Canterbury of this post Whitby era, Theodore, Archbishop of Canterbury, 669 to 690, established bishoprics, monasteries and endowed them with books. Theodore is an interesting character. He is actually from Syria. How somebody from Syria becomes Archbishop of Canterbury, something that would be very unlikely now, in the seventh century AD is an aspect of some preservation of the outlines of the cosmopolitan Roman world that we began the course with. There are a lot of Syrian Popes at this time too. Syrian and Greek popes from the Eastern Mediterranean. The first manuscript we have of the Bible as a single manuscript, in other words, where all of the books of the Bible are contained in the same volume is from this place and this era, the so-called Codex Amiatinus. A magnificently decorated Bible, sent to the Pope in 716, written at Bede's monastery of Jarrow. Now in Florence, at Lorentzian library of Florence. It is decorated in this very distinctive style that you all know, if not from courses, from Christmas cards and stuff. The Book of Kells is the most famous example of this. This is the so-called insular style because it's shared by both Celtic Ireland and Anglo-Saxon England. Lots of intricate curlicues, complicated animals, magnificent contrast of color, a kind of abstraction when you first look at it. It looks like an oriental carpet. But in fact, if you look at it a little more closely, you can see that all sorts of little intertwined animals or fantastic shapes and colors within it. Questions? Problems? We could spend an entire semester on England but I think we've had at least a taste of its significance both in its own right and as one more and rather different aspect of the post Roman world that we've been occupied with. I'll see you for the exam on Monday.
The_Early_Middle_Ages_2841000_with_Paul_Freedman	11_Frankish_Society.txt	PAUL FREEDMAN: So today is an exciting day, because the papers are due, because the midterm is soon, but most of all, because we're finishing up our talk on the Merovingians. Questions? Comments? Cat names? So the Merovingians. Remember that the reason we're studying them is as an example of barbarian kingship, barbarian states, and the post-Roman world. "Post-Roman" meaning that the Roman Empire is gone, but the society is not completely severed. Its connections with the Roman tradition are not severed. This is most obvious in the Church and the survival of Latin learning, bishops, Christianity, literacy. But even though we seem to be in an environment of rather primitive, and even, we could use the word loosely, barbarian kings, I hope that we'll see that within Gregory's narrative, there is evidence of a kind of royal administration and a certain sense of purpose. We are entering a period in which we have to start asking, "what held society together?" This becomes a question when two things start to fail. One is the government. Where it's really not clear that there is a government, other than powerful people plundering less powerful people. And the other factor is when the people themselves don't really believe that there is any force holding their society together, anything that they unconsciously give deference to. So we're all familiar with what are called now "failed states." That is, polities that have an official existence, but that cannot seem to keep the most basic form of order within their borders, whatever those borders may be. So unfortunate states like Somalia, or no longer, but ten years ago, Liberia, Sierra Leone, were examples of failed states. And this is a phenomenon that has grown in the contemporary world. In the Middle Ages-- and here we're talking about the period from the collapse of Roman authority in the West in the fifth century until at least the twelfth century-- there are various kinds of societies that are held together. They're not as anarchaic as Somalia, actually. But they are not held together by government in the sense that we understand it. They are held together partly by informal social networks and ties. Things like kinship, family, private vengeance, religion. But by having to ask the question "What holds society together?" you are already making a kind of statement about the sort of society you're talking about. I would say that the United States has, for most of its history, been a polity in which this kind of question didn't have to be asked. It's not that people loved the government, or even particularly deferred to it. But that in their everyday life, in their everyday gestures and in their everyday assumptions, they assumed that were protected. They normally did not have to go out with a weapon in order to feel that they would not be robbed. There are exceptional communities where that's not been true. But generally speaking, you could assume that the police or the police forces intimidated criminals or potential evildoers. You would, you know, send your bills in by mail, assuming that they would arrive, that a government agency would take care of the transport of them. You might try not to pay as much taxes as you perhaps owed, but you wouldn't really try to just be under the radar of the government, because you would assume that you couldn't do that. You would have to make some kind of tax payment. And on and on. Educating your children, signing up for Social Security, being part of a community. The mark of privilege, then, historically, is not having to think about the ties that hold your society together. If you had to come up with a standard with which to measure human happiness, that might not be such a bad one. Now, there are other forms of human happiness. Total independence. The idea of the person who lives out somewhere on the farm and is completely self-sufficient, has all of the food that they need, either that they catch or cultivate, lives in some kind of wonderful climate in which the food grows on trees. Dreams of authors of the nineteenth century in Europe and America about the South Sea Islanders. So we have in our imagination the idea of living a blissful life without any particular social ties, or only the most casual ones. But I think we all know that usually, such an existence, when it, in fact, exists at all, is an invitation for someone else to plunder it and to steal it. Part of the reason for social ties is company. Part of the reason for social ties is protection. So when asking what held Barbarian societies together, we're asking something that's more than just a banal question of medieval sociology. We're asking a question about the fundamental nature of a society that is not so unsuccessful as people think. You know, again, nobody wakes up in 560 AD saying how unfortunate it is that they're alive in the Dark Ages. They didn't call it the Dark Ages. They didn't think it was the Dark Ages. And it wasn't the Dark Ages, I hope to show. Now, Gregory of Tours is a great source because he gives a lot of very miscellaneous information. He's perhaps a source who likes violence, though. He likes violence for reasons we were talking about last week. He wants to show that on the one hand, the life of human beings is terrible and full of outrage and violence, but that it is redeemed by God's solicitude. And that those people who recognize God's power, as manifested through bishops, saints, the rites of the church, will, if not prosper always in this life, at least receive a reward that is commensurate with their loyalty to God. Gregory is a pessimist. One of the reasons-- one of the themes that guides this work-- I was going to say one of the reasons he wrote this work, but I don't want to kind of venture that far out. One of the aspects that unites this work is a sense of the decline of the Franks, from the model, Clovis, to the fools that he feels he has to deal with, like Chilperic. Three generations-- the generation of Clovis, the generation of Clovis's sons, the generation of Clovis's grandsons. Each one worse than the one before it. So if he had grudgingly acknowledged that the sons of Clovis fulfilled, in some sense, a mission in accord with God's plan, he was much more clearly hostile to this third generation of Merovingian leaders. He says at one point in a part that is not in Murray, "To this day, one is still amazed and astonished at the disasters which befell these people." And I think I mentioned this little passage before. "We can only contrast how their forefathers used to behave, and how they themselves are behaving today." So he is scolding the current generation and exalting the older ways. He is scolding them for their violence. But what about the fact that, as we emphasized, Clovis was violent? What he's really scolding them for, then, is not violence as such, but violence channeled to unproductive ends. Violence is inevitable, in Gregory's world. Violence in defense of the true faith is not only acceptable, but necessary in order to defend that. And Gregory's interest, as I hope I'll show, in the true faith, is not just a defense of Christianity as a religion, but Christianity as the thing that holds society together. If you asked Gregory what holds society together, he would give some kind of answer on the order of the bishops, the saints, the supernatural, the Church. And then if you said, "Well, what is the role of the king in this?" It's basically to terrorize people. To make sure that the mere threat of divine vengeance is backed up by threats of a more immediate sort. Throughout the history of the Franks, although not excerpted so much in the edition we're using, there are examples of people who hold God, Saint Martin, or the bishop, or some other saint in contempt, and who pay for it, often with their lives. So in Gregory's official presentation of events, any defiance of God is met with a thunderbolt. But he's not actually a fool. I know in the dark moments of 2 AM, reading Gregory, that thought may have crossed your mind. And I know that you repressed it very quickly, and it's evil of me even to raise it. But lest you think that he's just a credulous guy who lived in the sixth century AD and whatever, he is perceptive, and he understands that most people, most of the time, thunderbolt of God notwithstanding, need something a little more immediate to whip them into shape. That is, to follow a kind of basic civil order. And that is supposed to be the ruler. So it's fine for the ruler to be violent. And it's even OK if some people get caught in the jaws of the state, if we can call it that, or let's say, the jaws of the king, who should not have been punished. But look at the people he's dealing with. He's dealing with people who were violent, as well as kind of silly and quixotic. He has this little conversation with Chilperic that reminds one of pseudo-learned people, bloodthirsty dictators with pseudo-learning, on the order of Muammar Gaddafi. People who sort of study some stuff, and decide that they're experts on it because they're able to terrorize their population. "So Chilperic issued a circular"-- this is on page 111-- "a circular to the effect that the Holy Trinity was to refer not to distinct persons, but only God. That it's unseemly for God to be called a person, like a mortal of flesh and blood. He also declared that the Father is the same as the Son, and the Holy Spirit is the same as the Father and Son." Well, you know, people had died, and they certainly had written huge controversial works, and had lots of councils over this issue. And this is not right. Nobody actually really believes this in Christianity. "This is how it appeared the prophets and patriarchs, he said, and this is how the law itself proclaimed Him." Meaning Christ. And he then tells Gregory, "OK. This is the law I want you and the other members of the church to believe." And Gregory said, "Give up this false belief. You must observe the doctrines passed onto us by other teachers of the Church, who followed in the footsteps of the apostles, the teaching furnished by Hilary and Eusebius, and the confession you yourself made at baptism." He's got to say this. I mean, he is very courageous to say this to the king. But the king-- it is like somebody who is extremely powerful denying very basic scientific facts. Stalin tried to impose the biological theories of Lysenko, which basically went against the consensus of evolutionary biology at the time. So this kind of pseudo-learning is a feature of people who, since they're being acclaimed as geniuses and as leaders, assume that their expertise carries over to all sorts of fields. Well, the king grows angry. He says, "It's quite obvious that I regard Hilary and Eusebius as my bitterest opponents on this issue." Not only have Saints Hilary and Eusebius been dead for years, but they're saints, they're theologians. You know, it would be like me saying, "Well, obviously Charlemagne and Clovis are my enemies." A statement that is ridiculous. And note Gregory's response: "It would suit you better to watch out you do not make God or his saints angry." And that could really serve as one of the themes of the entire work. "For you should know that the Father, Son, and Holy Spirit are all distinct in person." And then he goes on to the theological justification. And then the king's response is, "I'm going to find some people smarter than you are." And Gregory says, "Such a person will not be smarter, but an idiot. Anyone who wants to follow what you propose would be an idiot." "Grinding his teeth at this response, he said, no more." And another bishop is consulted. So the king gives this up. And then he starts writing a treatise on the alphabet and wants to add some letters, and tells the teachers that the educational system needs to be modified to include these letters. Well, I go into this digression to show you, first of all, Chilperic actually is literate. He is actually educated. He's at least educated enough to have half-baked ideas, and that's more than some kings of this time and later will be. He tried writing poetry, as well. He also tried to depose Gregory as bishop, which is in some later books. Who are these people, then? What is the basis of their power? The kingship is, in large measure, based on inherited status. The Merovingian family had an aura of sacredness and prestige that made it impossible to conceive of anybody not of their bloodline ruling. This power is partly the prestige of Clovis, who is seen as really the father of his people, bringing them into what would become France, or the Land of the Franks, and converting to Christianity. But a lot of the prestige is what might be called "pre-Christian." The long hair. The riding around in carts, four-wheeled carts. And we've seen that the long hair is quite crucial. Once it's cut in a humiliating manner, the representative of the family loses some crucial kind of prestige. Remember that choice presented to Queen Clotilde: the scissors or the sword. You want your grandchildren scalped, or at least, given a military haircut, or-- actually, a monastic haircut, in this context-- or do you want them killed? And she is so angry at this that she, in fact, says "killed." That shows you, at least, the humiliation that is involved in this haircutting. These kings also practice something on the order of polygamy. They are Christians, but they are still tribal leaders in a society in which the possession of the women, in the plural, is a sign of status. One passage that describes a number of different things fairly usefully is on page 58. And this is the marriage. And again, it seems random when you're reading through it, but then that's the point of lecture, is to highlight the seemingly random, isn't it. On page 58, Chilperic's wives. "Chilperic asks for Brunhilda"-- this other, Visigothic queen of one of his brothers-- "asks for the hand of her sister, Galswinthe, although he already had several wives." OK. So he promises the envoy he will put away the other wives. He will renounce them, and he will be married only to Galswinthe. And so with these assurances, her father sent his daughter, as he had send the first, along with a great deal of wealth. This is what's called a dowry, D-O-W-R-Y, a payment made by the bride's family to the groom. "When she came to King Chilperic, she was received with great honor and made his wife. And, for the time being, his love for her was considerable, for she had brought great treasure." OK. It's not a, you know, a "we both like horseback riding" kind of relationship, although they probably did. "But because of his love for Fredegunde"-- who is another wife, a low-status wife, a wife who didn't bring him much money, but who was mesmerizing, or beautiful, or certainly had a hold over him. "Because of his love for Fredegunde, whom he had before, a disgraceful conflict arose to divide them. Galswinthe had already been converted to the Catholic creed." That is, she had been a Visigothic princess raised as an Arian. She's now been converted. "She complained to the king of the wrongs that she constantly had to endure, and said that he no respect for her. Finally, she asked him to give her her freedom to return to her native land if she left the treasures that she had brought him." Which seems like a reasonable deal. "But he made up various excuses, he mollified her with sweet words, and in the end, he had her strangled by a slave, and he himself found the corpse on the bed." Why didn't he just let her go, keeping the treasure? Um, humiliating, probably. Better to kill her. Why didn't he do what he said he did? You know, he's a barbarian ruler. "After her death, God revealed a great sign of his power. A lamp burned before her tomb, suspended by a cord. Without anyone touching it, the cord broke, and the lamp fell to the pavement. The hard pavement gave way before it, and the lamp, as it had landed on some kind of soft substance, was buried in the middle and not all broken. To those who saw it, this did not happen without a great miracle." Well, as miracles go in Gregory of Tours, this is pretty pedestrian. A freak accident. The lamp breaks, the exterior breaks, but the actual lamp part does not. But it is a sign in Gregory, and these things don't happen at random in Gregory. "The king wept over the body, and then after a few days, took Fredegunde back again as his wife. When he did this, his brothers attributed Galswinthe's killing to his orders and toppled him from power." The editor points out that probably they didn't, actually. This is a little bit too pat, and it may be a case of Gregory arranging the world so that the evil get punished in ways that they ought to, rather than in the ways that they do or don't. But nevertheless, the portrait is of a polygamous king, a king who accumulates treasure, a king who is unscrupulous enough to kill his wife, does not seem to hide it very much. However, vengeance is taken on him both by supernatural powers and by natural forces. So in talking about the bases of kinship, we have blood, and then war leadership. I have tried not to overemphasize the violence of this society, but it is a society in which war leadership is one of two major criteria of political leadership, the other being spiritual leadership, that we're going to talk about towards the end of the lecture. The loyalty of the king's entourage was based on his ability to reward them with plunder. Remember that King Chlothar goes out to fight the Saxons, but the Saxons actually give him a good deal, and offer to give up a lot of their territory. And he says to his men, "I think this is a reasonable thing. The Saxons are pretty well armed. They're going to negotiate with us." It's on pages 50-51. But the men won't accept that. They haven't come on this military expedition for political reasons. They want plunder. And so they force him, they threaten to kill him if he doesn't lead them into battle. So in certain respects, we're back to the situation of Clovis. On the one, hand he seems very powerful. On the other hand, he seems intimidated by his followers. And this is an accurate picture of the position of rulership at this time. The king has to reward his followers. Because they're not following him for reasons of abstract political loyalty. They're not Merovingian patriots. They don't have a national anthem. They don't have a flag. They have a pledge of allegiance, but it's a private pledge of allegiance, of warrior to warrior. He has two ways of rewarding them-- plunder or land. He can't pay them a salary, because the economy does not produce revenue in quite this way. It does, but it doesn't produce enough to reward soldiers in the way they want to be. Therefore, a successful leader is one who leads his troops into victory in battle. If he doesn't expand his possessions, if he doesn't lead them successfully, he's going to have to start giving away lands that belong to the king, or to the state, if we can call it that. And once he starts doing that, he's going to start having an erosion of his own revenue to the weakening of his dynasty and his power. For the time being, in the world of Gregory of Tours, the kings are wealthy. There is a description of an extraordinary dowry sent with a princess named Rigunth, beyond the page assignments that you read. And there was so much stuff that "it took fifty wagons to carry the gold and silver and other ornaments." "The Franks offered many gifts, some giving gold, some silver, many giving horses, and most garments." "The mother of the princess brought so much gold and silver and garments that when the king saw it, he thought he was left with nothing." Ha ha ha. In fact, the quantities of gold, silver, silks and other fine fabrics are quite impressive. Kings are very wealthy. And they're wealthy because of plunder, but also because of taxes. If you read Gregory carefully, you will see that the kings are collecting taxes. In order to collect taxes, you've got to have some sort of records. You've got to know where people are. You've got to have a kind of a register of property. I'm distinguishing taxes from plunder. You can plunder your own people. That is, you can just ride around and take cattle that happen to be passing by, or burn people's farms, or shake them down, you know, threaten to cut off their ears if they don't cough up a certain amount of money in treasure. The problem with that is, of course, you start killing your own economy, and even Barbarian kings recognize that. But they do then have a kind of administration. And here again, we have an interesting interaction of what might be called the practical and the superstitious. The death of Chilperic's son by dysentery, described on page 105. There's a serious epidemic. The epidemic is, of course, announced by portents. Whoever heard of an epidemic disease that wasn't preceded by coments, or eclipses, or, you know, heavenly phenomena? "While the kings were quarreling again, dysentery affected nearly all of Gaul. High fever with vomiting, extreme pain in the kidneys, headaches, and neck pain, saffron-colored or even green vomit. Some people thought it was a secret poison." Blah blah blah. It affected children. "We lost children so sweet and dear to us, whom we sat on our laps, or carried in our arms, and nursed with such care." Chilperic's younger son became sick. When they saw that the end was near, they baptized him. He was doing a little better when his older brother named Clodebert was stricken by the same disease. Now, these are the children of Fredegunde, the lower-status but extremely powerful concubine, wife, whatever you want to call her. "And Fredegunde, seeing that they were in danger of death, became repentant." And she says, "For a long time, the divine goodness has endured our evildoing. Often it has rebuked us with fevers and other afflictions, and repentance did not follow. Look, now we are losing our sons. The tears of the poor, the laments of widows, and the sighs of orphans are killing them. We are left without a reason for gathering up anything. We pile up riches and do not know for whom we gather it. Our treasury will be left without an owner, full of plunder and curses. Were our storehouses not already overflowing with wine, were our barns not already full of grain, were our treasuries not laden with gold, silver, precious stones, necklaces, and the rest of the trappings of emperors? Look, we are losing what we held to be even more beautiful. Now please, come, let us burn all the unjust registers." In other words, let's burn the tax registers. Let's burn the records we have of who owes what. "And let what was sufficient for your father, King Chlothar, be sufficient for us." "And then she ordered brought forward the registers that Marcus"-- we don't know who he is-- "had delivered from her cities. She had them thrown in the fire and then turned to the king," who's not eager to have his registers burned, but finally he does. And they stop future assessments. And the kids die anyway. "After this, King Chilperic was generous to cathedrals, basilicas, and the poor." He's sort of learned his lesson. But it's very interesting, this idea that what is killing their children is the vengeance of God, and that the poor, the widows, the orphans, the people that they have oppressed, have a kind of power of vengeance by mobilizing this supernatural force. On the one hand, this is a regular old story. People, when they are faced with difficult situations, often pray, often promise, make some sort of deal. Get me out of this, oh Lord, and I will A) never do it again, B) do something else, C) I'll be really grateful. And sometimes it appears to work, and sometimes it doesn't. But it is a perfectly understandable emotion. But the belief that supernatural forces affect politics, the belief in the political leaders themselves, the knowledge that they are evil, and that God has, at least for a while, committed this evil is very, very powerful, and very, very uppermost in the mind of even an uneducated and, as Gregory himself demonstrates, normally thoroughly unscrupulous character like Fredegunde. So what makes a good ruler, according to Gregory? Not peacefulness, since he believes the job of the ruler is to inflict fear, at the minimum, and damage, more likely. At one point, he describes Theudebert, one of the sons of Clovis, one of the members of the second generation, the closest thing he has to a good ruler. He says of Theudebert, "He ruled his kingdom justly, respected his bishops, was liberal to churches, relieved the wants of the poor, and distributed many benefits with piety and goodwill." So he is a just ruler, and an effective one. But after that, all of his good qualities amount to treating the Church well and treating the poor well, and the Church is supposed to represent. So in the remainder of the time, we should consider, what is the Church? What do we mean by the Church? Any questions so far? The Church in this society is represented by bishops and monasteries. We will be talking about monasteries next week. The difference is that bishops rule from the cities even if they are just a little shell remnants of Roman cities. Nevertheless, they rule from a population center. They are involved with ordinary people, or at least their administrative apparatus deals with regular life. Monasteries are more a retreat from regular life, where monks, as you'll read in the Rule of Saint Benedict, live in a kind of isolated community, renouncing the world. Now, in actual practice, there would be more similarities than differences, particularly as these monasteries were involved with the world quite a lot. But it is the bishops that represent, to the extent that any aspect of society does, a continuation of the Roman order, a continuation of the notion that there is a kind of educated ruler of local society. So the bishops are members of prominent families. They're often members of Roman prominent family. Remember that Gregory was Bishop of Tours? The great relic of Tours was the cape of Saint Martin. His family had been bishops of Tours because they were locally prominent under the Roman Empire, and continued this prominence under the Merovingians. Not necessarily peacefully or easily. As I said, Chilperic tried to have him deposed, and you've seen the episode in which they don't get along very well. But nevertheless, his family, of what he calls senatorial rank, even though there's no Senate anymore, were locally quite prominent. This relic that they guard is not the only reason for their power. But bishops, as well as monks, are associated with some kind of saint protector. And the saint protects churches that have relics of the saint. A relic could be a bone, like an arm or a jaw, or it could be a piece of clothing associated with the saint. In the case of Saint Martin-- Saint Martin it was a military figure, whose most famous act of piety was he was stopped by a beggar while on horseback, and he split his cloak with a sword, and gave part of it too clothe this beggar. And this relic itself, the cloak, or a cappa, was held by the church of Saint Martin of Tours. And indeed, it is thought that the word "chapel" comes from the word for "cape." It's sort of a sacred space within a church where, in this era, relics would have been kept. We'll talk a lot about relics and why they are powerful, but for now, I do want to talk about the mobilization of sacred power. Because we don't have to ask the question, well, did it really work? Did this really happen? Did Saint Martin really revenge himself on people who plundered lands belonging to him? The important thing is to realize that the conception of the saint is not merely that of a pious respect, but of fear of a living presence. Somebody who, although dead, is not dead in the normal understanding of the word "dead." The bishops and monks mobilize a kind of locus of sacred power. Now again, at 2 AM, after you were done thinking that Gregory was a fool, it may have occurred to you that this sounds a lot like polytheism This seems to multiply deities. It seems to multiply the sites, the places where the sacred has an effect. And shame on you for such a thought. How can this be polygamous, just because there seem to be a bunch of different people wielding sacred power? We don't have to deal with this. Certainly, there seem to be a lot of people, most of them not alive, wielding sacred power. And it's a rather threatening kind of power, at that. The bishop is a religious leader. Some of them are religious leaders in the sense of powerfully religious forces, but most of them are more squires than preachers. That is, they are landowners, patrons, more or less generous to the poor or to the people of the area that they rule. It's not a religion of deep introspection. We don't have a lot of mystical thinkers in the sixth century. We don't have a whole lot of ethical concern, except for the notion of the poor as a collection of people with certain rights to the ear of God. The poor does not mean exactly what it means now-- the marginal, the people below some kind of income level. It means basically ordinary people without any particular unusual power in society. In certain respects, the Church is an aspect of the power of the king. In certain respects, it defies the king. Gregory himself, and his work is full of other examples of bishops who stand up to the ruler and remonstrate with the ruler. That is, scold the ruler. But they can't really do this by themselves. They have to mobilize at least the potentiality of a kind of power that goes beyond merely the prestige of their family or the prestige of their office. So for example-- and again, this is something that's not in the Murray addition-- an example of the power of Saint Martin. This is at a monastery, the Monastery of Latte where some other relics of Saint Martin are kept. "A force of hostile troops approached and prepared to cross the river which runs by, so that they might loot the monastery of Latte." L-A-T-T-E. Latte, but I think it's pronounced "lot." "'This is the monastery of Saint Martin,' cried the monks. 'You Franks must not cross over here.' Most of those who heard this were filled with the fear of God and so withdrew." Oh, uh, I just thought it was a regular old monastery. Sorry. "Twenty of their number, however, who did not fear God, had no respect for the blessed saint, and they climbed into the boat and crossed the river. And driven on by the devil himself, they slaughtered the monks, damaged the monastery, and stole its possessions." They made the, you know, gold and silver chalices, all of these properties that they had taken, "into bundles, and piled on their boat. Then they pushed off into the stream. But the keel began to sway to and fro, and they were carried round and round. They lost their oars, which might have saved them. They tried to reach the bank by pushing the butts of their spears into the bed of the river, but the boat split apart. They were all pierced through by the points of their own lances. They were killed by their own javelins. Only one of them remained unhurt, a man who had rebuked the others for what they were doing. If anyone thinks this happened by chance, let them consider the fact that one innocent man was saved among so many who were doing evil. After their death, the surviving monks retrieved the corpses from the bed of the river. They buried the dead bodies and replaced their own possessions in their monastery." OK? So this is what happens to people who plunder monasteries. On the one hand, the story is useful for the fact that they plunder monasteries anyway. And without asking the question, did their boat really sink? We can see a notion of the violence of society being directed to illegitimate ends, and then being punished by the Church. In terms of the question that we have been asking, what held society together, a lot of the answer has to be the church and its perceived mobilization of spiritual power. It's not the only answer, but it is an important aspect of the cohesiveness of a violent but not completely unstable society. Let me give you one more example. "Palladius inherited the office of count in the region of Javols." J-A-V-O-L-S. A quarrel ensued between him and Bishop Parthenius, in which this count insults the bishop, abuses him, accuses them of all sorts of crimes, and seized the property of the Church, which is, of course, what he really wanted to do. They both go to the King's court. Palladius accused the bishop of being weak and effeminate. "'Where are your darling boys,' cried he, 'with whom you live in shame and debauchery?' The vengeance of God soon brought an end to these attacks." The following year, Palladius lost his countship and became terrified that King Sigibert wanted him killed, and eventually he commits suicide. "I find it hard to believe that this horrible deed could have been achieved without the help of the devil. For the first would was enough to kill him, unless the devil came to his assistance to give him strength to carry out his terrible plan through to the end. He stabbed himself twice. His mother rushed in, beside herself with grief, fainted in front of her son. The whole family bewailed his fate. He was buried at the monastery of Cournon, but not in Christian ground, and no mass was sung over him." Moral of the story? And Gregory is great at telling you the moral of the story. "It is clear that this fate befell him only because he had wronged his bishop." OK? Message of the book-- don't mess around with these bishops. This is a world in which spiritual power is effectively mobilized to social cohesion. Gregory dies in 594. I just want cast an eye forward, because we're going to pick the story up with the successors to the Merovingian dynasty, the Carolingians. Carolingians, retrospectively named for their most famous member, Charlemagne-- "Carolus" in Latin. The Merovingian-Carolingian transition is in the middle of the eighth century. So this dynasty had another 150 years or so after Gregory, and they continued to be involved in civil war. Eventually there was a terrible feud between our friend Fredegunde, wife of Chilperic, and Brunhild, married to Sigibert. Brunhild was sister of the murdered Galswinthe, whom Fredegunde had basically gotten murdered. So Brunhild tries to avenge her murdered sister. Sigebert makes war on Chilperic. Fredegunde hires assassins to kill Sigebert. And you've seen that Brunhild married the wayward son of Chilperic named Merovech. Merovech eventually commits suicide. Brunhild, eventually after these guys pass from the scene, rules, and so does Fredegunde. Chilperic is assassinated. Fredegunde rules in the name of her son. And so, in fact, in the late sixth century, the rulers are these two powerful and feuding women. In 613, Chlothar the second, son of Fredegunde and Chilperic, capture the aged Queen Brunhild and had her torn apart by wild horses. What is happening here, behind the unedifying drama of violence and feud within a dysfunctional family-- dysfunctional, a word unknown in Merovingian Frankish, I'm pretty convinced-- is that certain regions of the Frankish realm are identified. If you look on the last of the maps in the appendix to the Murray addition, you'll see reference made to the two regions that don't really correspond to today. One is Austrasia, which is a kind of land that encompasses the Rhine regions, Belgium, a bit of Holland, Northeastern France, and Neustria, which is more the heart of France. Paris, the Seine. These will become sort of two subrealms of the Merovingian Frankish kingdom. And our people that we're going to be following towards the end of the course, the Carolingians, will be associated with Austrasia. We turn to England for Wednesday. If you still have your papers and want to give them to us, please do so. I'll see you on Wednesday.
The_Early_Middle_Ages_2841000_with_Paul_Freedman	22_Vikings_The_European_Prospect_1000.txt	PAUL FREEDMAN: It does seem as if we are back to invasions again. We end the course the way we began it, except they're different invaders. One thing that I'm sure Professor Frank will want you to get out of the Vikings course-- and not all of you are going to take that, obviously, so I will mention this-- is they did not have horned helmets. The horned helmet idea-- actually, Roberta Frank has researched where this totally inaccurate idea comes from and why it is ineradicable. But if there's one thing you should come out of the second part of this course knowing, it's that. So we're discussing people from Scandinavia, different parts of Scandinavia, who had different destinations. So different parts of Scandinavia: Denmark, Norway, Sweden. Different destinations: the Frankish Empire of Charlemagne for which they bear some responsibility for unraveling, Russia, the British Isles, Iceland, Greenland, the New World. They certainly got around. They're not always the same populations. And they have different ambitions in different places. Basically, those ambitions can be divided into raiding, trading, and settling. These are not mutually exclusive. Although usually they began by raiding almost always if they were dealing with a place that had people. Thus obviously Iceland when they came didn't have people at all. So they came there as explorers or settlers. The crucial changeover is in their attacks on the British Isles and on the Frankish Empire. They begin as raiders, that is as seaborne warriors who would plunder opportunistic targets-- monasteries, for example-- and then leave with their spoils. They also, however, were traders. And I don't want to make too much of this as if it were a timeless statement, but in the period we're dealing with, raiding and trading weren't all that far apart. When the Vikings in the east, mostly from Sweden, were dealing with the Caliphate in Baghdad or the Byzantine Empire, they found these targets too well organized with too overpowering a military presence to intimidate in the way that they were able to do with Britain and the Frankish Empire. So here they were more traders. They brought various products, particularly slaves and fur, to the Caliphate and to the Byzantine Empire. And they came back with a lot of coins, among other things. 80,000 coins from the Caliphate have been found in Sweden alone. So here they're traders. Settlers. They would eventually settle in the Frankish Empire and in the Anglo-Saxon kingdom of England. They would settle in Ireland. Indeed, the city of Dublin was founded by the Vikings. They would settle in Iceland completely. That is, the people who live in Iceland now are the descendants of mostly Norwegian, some Danish settlers of the tenth and eleventh centuries. They would even try to settle as far afield as Newfoundland. There is a place in Newfoundland that it is unmistakably, by the archaeological evidence, a Viking site. This doesn't ultimately work. So it is wrong to think of them exclusively as savage warriors, as barbarians, but then again, we've seen that it's wrong to think of most of the invading peoples of the period we've been discussing as just totally savage raiders. These are extremely skilled raiders, and as I've just gotten through saying, they're raiders with several different possible agendas. They're very adaptive. The question remains, what made Scandinavia so powerful in the ninth and tenth centuries, especially since Scandinavia tends not to be a major actor in European politics. The two periods in which it is are this one-- basically the ninth, tenth, eleventh centuries-- and the seventeenth century when the armies of Sweden under Gustavus Adolphus terrorized Central Europe. That effort was ultimately ended not in Central Europe but in Eastern Europe by Russia. And the Russians defeated the Swedes sufficiently in the early eighteenth so that they basically never got themselves very heavily involved in European politics again. Part of the answer of "Why Scandinavia? Why now?" is that we're dealing with another savage or certainly less civilized population who erupt from their homeland and devastate a weak but relatively rich society. There's nothing very unusual about that. We have seen it with the Roman Empire, and you can see it later with such successful campaigns as those of the Mongols in the thirteenth century. So the other reason besides opportunity is tactics. The Vikings were masters of the sea. If you ever do go to Denmark, Sweden, or Norway, you must go to the Viking museums there. They are absolutely enthralling. And you see these ships that seem unbelievably flimsy for the voyages that they undertook. On the other hand, by reason of their small size and particularly shallow draft-- that is to say they're able to be stable without being so deep underneath the ship, having a keel underneath-- that they can sail up rivers. They can both, therefore, go in the Atlantic and be stable enough to make the journey and go up rivers that are no more than five or six feet deep at points like the Seine in France or the Loire in France. And so they could raid far inland with these ships. And as masters of seas and rivers, they could easily outrun the clumsy, slow Carolingian armies. They could raid a monastery, check out another monastery the same afternoon. "Oh, there's an army there. Well, we'll just get back in the ship, and we'll go further down. And then we'll look for more tempting targets-- palaces, towns, monasteries." They were not good at fortification. If a place was fortified, they tended to pass it by. They were not siege masters. Their control, therefore, of the water is not dissimilar to the Arabs' advantage in the beginning of the Arab expansion that we talked about with regard to the desert. The desert functions the same way. An environment that these people controlled in the sense that they could maneuver easily in it, and their more civilized opponent with larger armies could not. The Persian and the Byzantine armies couldn't really go very far into the desert. They had supply line, water problems. They actually didn't know the desert. It all looked the same to them. So this is the same or at least a similar advantage for the Vikings. The Vikings are different from other raiders partly in their ability to construct governments, not only to settle lands, but to create governments ranging from the what advertises itself with some accuracy as the world's oldest democracy, Iceland, where tourists are still pointed out the place where the kind of parliament of all citizens took place as early as 2,000 [correction: 1,000] years ago. And they're also the founders of Russia, probably not to be advertised as the world's oldest democracy. Certainly not a country that's had a whole lot of experience with that particular form of government. But in fact, the first Christian rulers of Russia, the same Vladimir and his successors, who were baptized and crowned under Byzantine auspices were Scandinavian. And the Scandinavian groups are called the Rus. They quickly lose their Scandinavian language and identity, but nevertheless that is the founding dynasty of the first Russian rulers. So the Vikings have a fascinating culture and literature, amazing sagas mostly preserved through their Icelandic versions, very interesting art, very interesting forms of decoration, and then these magnificent ships. Their major contribution to the history of Europe may be geopolitical in the sense that they connect parts of the world that were otherwise minimally or not at all connected. So from Central Asia to Greenland, they build various kinds of cultural and particularly commercial networks. They also contribute to the destroying of the Carolingian Empire, the destroying of what we were discussing before the vacation. They're not the sole cause. We talked about weaknesses within the Carolingian Empire, but certainly the Viking invasions have devastated it during the ninth century did not at all help. Where did this drive for expansion come from besides opportunity? And there's not a tremendous agreement on this point among scholars. Overpopulation and land hunger are possible. To this day, these are not densely populated countries. And in the pre-modern period, they could not support anything but a very small population given the fact that most of the land is not capable of being cultivated. So you can get to a point of over-population pretty quickly. Opportunities afforded by the weakness of others-- I've mentioned this. Internal feuding and the creation of exiles. It's hard to separate legend from history, but the legends about the founding of Iceland and Greenland in particular involve people who were too rowdy for the Vikings. I pause on that, because it's a little hard to imagine what such a person would have been like. Nevertheless, these sagas tell us that various people were just too mean for quiet, civilized old Norway or even couldn't get their energies fulfilled by plundering the Frankish Empire and went off to Iceland and places like that. The climate conditions may have been favorable. It may have been relatively warm. There's a lot of debate about the settlement of Greenland in this regard in particular. We know that by the twelfth and thirteenth centuries, Greenland was becoming too cold for the Scandinavians and not for the Inuit, who were better adapted to real polar conditions. But this is something that is of crucial importance in tracing the history of climate and is hotly debated. But it certainly looks as if it gets colder in the thirteenth, fourteenth century-- fourteenth century particularly-- throughout Europe and the Atlantic and probably warmer in the tenth and eleventh centuries when this expansion is taking place. And then finally, there's a cult of personal valor that is even stronger than that of early medieval Europe. A male cult of violent military bravery and the opportunity to demonstrate that was a kind of competitive sport. The Viking raids in England and the Continent begin around 800. One of the first stunning events is the sack of the island monastery of Lindisfarne on the eastern coast of northern England. The monastery of Lindisfarne was sacked by the Vikings in 797. Charlemagne was able to repulse these raids and the English as well. But the civil wars that we were talking about among the sons of Louis the Pious started to encourage the Vikings indirectly by the disunity of the Frankish Empire, the wasting of military resources on what was, in effect, a kind of civil war. But also the Vikings just got stronger and more ambitious, because their raids on relatively well organized Britain start to reach their height in the 830s. So you start having the abandonment of monasteries, for example, the abandonment of Lindisfarne and the moving of its relics. So the relics of Saint Cuthbert of York move around a lot. Monks on the western coast of France abandon their monasteries and move their communities and relics further inland. The Vikings seem to jockey between emphasizing raids on the Frankish Empire and on England, but basically they're doing both. They start to spend the winter, what's called over-wintering in the late 830s, early 840s. And that's a sinister sign from the point of view of the English, Irish, and Franks, because that means that they're going from raiding to some form of settling. If they can spend the winter and not just the classic raiding season, why not just stay permanently? So they start coming up the rivers. They start plundering cities that are not sufficiently fortified. A monk in the 860s writes, "the number of ships grows every year..." The feeling of just this complete takeover. Now, that's the monastic point of view. The monasteries were ideal targets, because they are rich, isolated, and minimally fortified. But nevertheless, the Carolingians have no fleet to match the Viking ships. The way to stop the Vikings-- and it was only really implemented in the 870s and 880s. The way to stop the Vikings was with fortified bridges. If you built a bridge that the Vikings could not go past without fighting and fortified it sufficiently and had sufficient numbers of troops, you would stymie them. And this is eventually what happens. In the late ninth century, the Vikings are defeated at the gates of Paris in 888-- 885, 886, rather. And they start accommodating with the European rulers. That is to say they are given lands to settle and then made to promise to stop raiding. And in effect, they start to settle down towards the end of the ninth century, beginning of the tenth century so that, for example, a treaty in 911 with the West Frankish ruler, the ruler we can start to call the King of France, allows them to settle in northwestern France in a territory that henceforth was called Normandy. Same in French. Normandie. The territory of the "Northmen" is what they're usually referred to in the sources rather than "Vikings." The territory of the Northmen. So Normandy in 911 was a province settled by Vikings nominally loyal to the King of France. The Vikings very quickly lose their language. By the time of the Duke of Normandy, William the Conqueror 150 or so years later, they are Norman. They speak French. They are more French than anything else, although a bit different. Their ships still look a bit like Viking ships. If you know the Bayeux Tapestry, which is this embroidery that shows the history of the Norman conquest of England, their ships look very much like our image of Viking ships. In England, the 860s are the zenith of their destruction. They actually in effect partition England between an eastern and a western part. The eastern part becomes a territory called the Dane law, the place where the Danes have settled. And their indirect effect on England is to force the Anglo-Saxon kingdoms to unify. So rather than the multiple kingdoms that we looked at at Bede's time-- Mercia, East Anglia, Northumbria-- we have the western kingdom formerly called Wessex, which under King Alfred in the 860s to 880s becomes really the sole Anglo-Saxon kingdom of England and gradually defeats the Vikings, eventually kicking them out of the British Isles altogether by about 930 or so. So the conquests in the Frankish and English realms are not permanent in the sense that there's minimal Scandinavian impact of a permanent sort on these places. There are not a lot of people speaking Old Norse in either place in 1100. But their impact is tremendous in terms of organizing these places, creating networks, founding cities like Dublin, reorganizing kingdoms like Ireland, creating Normandy, and really kind of throwing the puzzle on the floor and reforming it. In the East and in the Atlantic. Here you have to imagine or sort of visualize Scandinavia sitting on the top of Europe. The same effect that encourages airlines to use polar routes as a shorter way to cross the globe also allows the Scandinavians in effect to choose their targets. Some of this is logical. Norway is much easier, much closer to the British Isles than you might think. It sort of sits on top of them. And Sweden is much closer to the East via the North than one would think. But even Norway, for example, the modern kingdom of Norway, has a border with Russia. It goes so far north, and then it has this very little, narrow piece of land that is only about thirty miles from the important Russian port of Murmansk. And all of these places are relatively warm given how far north they are because of the Gulf Stream. So just as London is surprisingly warm considering that it's on the same latitude as Newfoundland, so these northern parts of Scandinavia are the equivalent of polar wastes of northern Canada. And yet they are-- they're cold enough. The problem with them is they're really dark. So they're dark for months at a time, but they're not all that cold. From this vantage point then, the East would be a tempting source of enterprise for Vikings, particularly but not exclusively from Scandinavia, especially in the tenth century. They would go via the Baltic Sea and the Gulf of Finland down the Russian rivers like the Dnieper-- Dnieper with a D-- to the Black Sea and the Volga to the Caspian Sea. They used to these rivers as ways of reaching territories of Byzantine and of Caliphal influence. They traded, raided when possible. A lot of our descriptions of the Vikings by outsiders, our most accurate descriptions, are from Muslim travelers who describe who these people are, what their products are even though very little remains in this region to attest to the Vikings. The main evidence, as we said, are really coins taken back to Scandinavia. Their base-- that is the Viking base in this eastern area-- was what would become Kiev in modern Ukraine. And Kiev would be the first Russian Scandinavian kingdom ruled by a tsar. They had ambitions to take over Constantinople, a city they called in sort of Tolkien-esque fashion "Mickelgard"-- "Gard" meaning city, "mickel" meaning powerful. "Mickel" still in Middle English, in Chaucer's English, means "impressive," "powerful." Their attacks on Mickelgard didn't work. They attacked in 860 and 941, and we've seen that Constantinople was able to fight off more impressive enemies than this. They therefore were dealing with wealthy and established states, well-organized states, better organized than the Carolingian Empire or the Anglo-Saxon kingdoms, and so states that were capable of defeating them. They therefore came to these areas controlled by Baghdad and Constantinople more as traders than as raiders. What did they bring to trade with? They have certain classic products, things from the North Sea, like walrus ivory, very highly prized, amber from the Baltic Sea-- amber used in jewelry and medicine, a stone that's not really a stone, a thing that's much lighter than it looks like credited with various kinds of mysterious or at least medicinal properties throughout the formerly Roman and Islamic world. Arrows and swords. The West was very good at metalworking. Honey, hunting falcons, wax. But as I said, their two great commodities were slaves and furs. Slaves-- these societies of the Byzantine Empire and the Caliphate always wanted more slaves. They had plenty of unpleasant labor as well as domestic service shortages. And so many of these slaves were Slavs, that is Slavic populations rounded up by the Vikings and then sold in Constantinople or Baghdad. Furs. On the one hand, furs like sable, marten, mink that bounded in the eastern Baltic regions and in what's now northern Russia were tremendously prized in a world in which central heating was nonexistent. And although we may not think of modern Istanbul as particularly cold, it's quite cold and damp. One can certainly understand the practical desire for furs for well-off people in the Byzantine Empire. In the Caliphate, it may seem a little stranger. Baghdad is more noted for unbearable heat than cold. On the other hand, the Caliphate includes territories like Afghanistan, eastern Iran. And also, keep in mind, as is the case with Palm Beach and Miami Beach even as we speak now in late November, that for certain people, the prestige of the furs transcends any need for practical warmth. So these are the two great products. So they're plunderers and extortionists, but they're fairly creative plunderers and extortionists. They create a number of trading cities, not only Kiev further south, but the great city of Novgorod sort of between the Baltic and the more modern city of Moscow. These cities are fortified, leading one to assume that they weren't just free-trade zones, that other people raided them or that the Vikings expected other people to try to revenge themselves on their kind of raiding and trading. So anyway, as we've said before, trading and plundering are not necessarily totally distinct. So finally, the West. The Vikings begin to explore the Atlantic mostly from Norway and beginning after the maximum period of raiding of England starts to tail off in the 860s. These lands were uninhabited, Iceland, or minimally inhabited, Greenland. They were very attractive for hunting and for pasturing. Where the Vikings found a fair density of people, they tended not to stay. This is their problem with Newfoundland. They have a settlement in Newfoundland at a place whose modern name is somewhat confusing way called L'Anse aux Meadows. So you have a French and English compound. L'Anse aux Meadows in Newfoundland, one of a number of certainly the most best-known Viking sites. But there were Native Americans who drove them out, not necessarily because they were superior in armament, but it just wasn't really worth it to the Vikings to stay. So their staying in Newfoundland is relatively brief. In order to go from Norway to Iceland, it's about 800 miles, and it took anywhere between one week and one month. The island is not as cold as its name suggests. It has glaciers, but in the parts that don't have glaciers, it's not all that cold. Again, the Gulf Stream. Most of it is uninhabitable, but that's because of volcanic rock. I don't know how many of you have been to Iceland, but even the drive from the airport to Reykjavik is intimidating, because it goes through the stuff called "tufa". And there are no trees, and there's sort of no prospect of anything growing there. But on the other hand, there are plenty of nice coastal strips, mild climate, great pasture. There are almost no trees now. And there's a lot of debate about whether there were trees, whether they just cut them down, and they couldn't be re-cultivated. But in fact, this is a very hospitable place: rich pastures, sea mammals everywhere. Until Iceland completely lost its mind in the speculative atmosphere of the decade preceding 2008, their main industry was cod fishing. They then went into banking in a way that just staggers the mind and have gotten back into cod fishing, my understanding is. But they had lots and lots of other things. Lots of seals which they killed for fur, walrus skin used for cable for ropes for ships, walrus ivory, another little creature called an narwhal that has a tusk that looks like a-- well, it was taken for being a unicorn tusk. There's one in the Cloisters, for example, that some of you are going to see on the seventh of December. So the colonization of Iceland begins in 870, and by 930, the island is basically full. It's habitable land, again. A very, very small percentage of the land area was fully settled. We know a lot more about Iceland than any other part of Scandinavia because of the extraordinary quality and quantity of poetic stories, sagas in which honor, treasure, and love of mayhem dominate. These are very violent and until a certain point were taken to be realistic portrayals of life in Iceland just as if, say, 1950s and 1960s TV westerns were assumed to be a totally accurate portrayal of life everywhere in the United States in the nineteenth century. So these are, like Westerns, wonderful stories of male violence with a certain amount of exaggeration, but nevertheless the reflection of customs, ways of speaking, and social values. Towards the end of the tenth century, Greenland was explored under the leadership of Erik the Red, one of these renegades so difficult and violent that he was exiled from both Norway and Iceland. He is the one who seems to have dubbed this new territory Greenland, a pioneer of deceptive advertising, I think it's fair to say. Because warm as it may have been in the tenth century, this is like calling some housing development Warbling Acres when in fact you've just bulldozed all the trees in order to create the development. So the western coast of Greenland had rich pasture. The West is warmer than the East. Settlers came beginning in 986. There was even a bishopric established at a place called Gardar, another sort of Tolkien-esque name. We don't know very many bishops who actually went to Gardar. Most of them ruled from Denmark and sort of basically told their flock to get in touch with them if they needed them, gave them their office hours and had a phone that took messages. But this settlement did not last. Greenland was more or less abandoned by 1400 and then would later be, in modern times, resettled, but this time by Denmark. And then finally, Norwegians from Greenland settled what's now Labrador in Newfoundland, late tenth, early eleventh centuries. They even wrote a saga called the Vinland Saga. The Vinland Map that's in the Beinecke Library that purports to show both the Chinese Mongol Empire and the territories of Vinland in the New World is unfortunately a fake. But as I said, these archaeological finds in Markland, as the Vikings called Labrador, or Vinland, as they referred to Newfoundland, are real. They were settled about the year 1000 and abandoned in 1020. So here we are, 1020 or the year 1000. And I know that you will be asking what has been accomplished since we began with 284. And this is a fair question, because at first glance, it would seem as if we're still in a world of declining population, a rural society with very few urban centers, a society of relatively little literacy, relatively small amounts of commerce, lots of violence, lack of governmental order, militarized society, all developments that we have been tracing since the beginning. The optimistic take on this is that beginning with the material covered in the next course, there's a very rapid ascent from 1000 to about 1300, a tremendous growth of the European economy and a tremendous expansion of both population, artistic, political, and intellectual creativity that is the central period of the Middle Ages. The real mystery behind this, the sort of historical problem, is what explains the domination of Europe in the second millennium AD? The first millennium, most of which we've covered in this course, the dominant areas are the Mediterranean at the beginning, which includes Europe, but also includes North Africa, Egypt, the Middle East, and modern Turkey. And indeed, those latter regions would outpace Europe, properly speaking. The first millennium is something of a catastrophe for Europe, at least by measurable statistics of a per capita GNP, population, population density, urbanization, nature. What then explains the domination of Europe after 1000? In some ways, it's a slow process. The first European colonies don't really get established until the aftermath of Columbus' voyage in 1492. And then they get established incredibly rapidly and with surprisingly little effort, right? Mexico and Peru, these huge empires of the Aztecs, Mayans, and Incas fall to a few hundred Spanish troops. And the Spanish and Portuguese between 1492 and 1520 are all over the world, from Malacca in modern Malaysia to India to the Persian Gulf to Mexico and Peru. Well, we don't have to explain that. That's for another time. But suffice it to say that already in 1095, the European Christian population is capable of putting together an army to conquer Jerusalem from Islam, a seemingly impossible job, and certainly one that required more than logistics and resources but also a certain kind of if not fanaticism at least a real motivation, religious motivation. But nevertheless, it is a sign of a certain kind of European power that one would not have thought in the year 1000 was possible. In the year 1000, the smart money, the Brookings Institute, think tank, kind of RAND Corporation, Bain Consulting, all the smart people would have said, "Don't put any money into Europe. You've got to be kidding. The coming regions are the same as over the last couple hundred years. Maybe Byzantium, a cautious buy. Definitely the Islamic kingdoms, even if the Caliphate is having some problems, qua Caliphate, their successor states, Fatimid Egypt-- awesome, awesome. This is going to dominate for the next millennium. Our algorithms agree on this." And all sorts of promising signs in Eastern Europe with the creation of Russia to your more prescient younger, hot-shottier consultants would have identified that. But Germany, Italy, France, the British Isles certainly would have seemed discouraging. Yet there are some promising signs. As it turns out, the Vikings are the last invaders. The Vikings coincide with invasions from the Magyars. Magyars, that's what they call themselves to this day. They're known as the Hungarians to the outside world out of a confusion between them and the Huns. They actually have nothing to do with the Huns. But they were quite frightening land-based raiders of the tenth century. And there were also attacks by ships from Muslim North Africa against Europe, what the sources refer to as Saracen pirates. And they plunder Rome in 843, for example. So Europe is certainly in the tenth century faced with yet another wave of invasions. And I think I warned you at the beginning of this course that it was basically about invasions and heresies and that you'd do well if you just concentrated on those things. So we're heresy-free at the moment, but in the tenth century, we certainly have these invasions. As it happens, they're the last that Western Europe would experience. Not Eastern Europe, because Eastern Europe would be subject to the Mongols who would, for example, score a tremendous victory over the armies of Poland, armies of the Christian king of Hungary as well in the thirteenth century. But this seems to be the end of invasions, the beginning of a period of population increase, better nutrition, better harvests, perhaps explicable to more settled conditions, perhaps explainable by improved climate, perhaps just explainable by human determination and enterprise. The Christianization of Europe is one of the tremendous phenomena that characterizes our period. And while as a religious movement I have no investment in saying that Christianity is either an advantage or disadvantage, in terms of creating settled, organized polities, the Christianization of places like Scandinavia, Iceland, or Bohemia-- the modern Czech Republic more or less-- or Hungary or Russia, all of which take place in the tenth or early eleventh centuries, all of these Christianizations, conversions bring these polities into a kind of European cultural area, political alliances, trade networks. So Christianization is as much a sign of civilization or at least of a kind of economic development as a thing in itself. So between 200 and 1000, what are the big differences? Whether these are accomplishments or not is debatable. Certainly the population has declined. Over an 800-year period, the population of Europe is considerably less, not only in towns like Rome, which has gone from something on the order of over 500,000, perhaps as much as a million, to 30,000, maximum. It is a much less Mediterranean-centered world. The sort of geopolitics have changed. The Mediterranean has broken apart into Islamic, Byzantine, and Latin regions. It is Christian, most of it. Most of Europe apart from Spain is Christian. And this entails all sorts of cultural as well as religious changes. It is also less learned. And the learning that there is is a monopoly of the Church. There is less lay, or secular, learning than there was. There are some continuities, however. The dominant language of learning and administration remains in 1000, as it was in 200, Latin. Roman culture is still the ideal and still, in effect, the practice, even though it may be adapted to things like churches. But what has been called Romanesque or simply Roman architecture particularly that of the eleventh and early twelfth centuries will indeed be based on Roman principles. And as we saw with Charlemagne, the idea of Rome, the idea of the Empire is extremely durable. And although Charlemagne's empire is dissolved in the course of the late ninth century, it is at least partially revived in the tenth century under a new dynasty whose first ruler is Otto I, Otto the Great. In 962, he's crowned Roman emperor in Rome by the pope. His empire does not include the West. So it's not France. It's more Germany than anything else. But this empire would endure until Napoleon, until 1804. In other words for something on the order of 850 years. So to some extent, what we have accomplished is we have arrived at the point of the emergence of something that can be called Europe other than a geographical term, something that can be called Christendom, not using that in its triumphalist sense but simply as a kind of cultural description of a certain part of the world. And we've reached the point where we can start to talk about the West, this very funny term still used, particularly in popular geopolitical tracts like The West and the Rest, these kinds of statements of the West or the decline of the West. We're at the point of the rise of the West. And that's where I am going to leave you. Thanks for your participation in this course. Thanks for making this a wonderful semester for me. I hope a lot of fun for you as well. Thanks a lot.
The_Early_Middle_Ages_2841000_with_Paul_Freedman	16_The_Early_Middle_Ages_2841000_The_Splendor_of_the_Abbasid_Period.txt	PAUL FREEDMAN: OK, in 743, civil war started within the Umayyad my family over the caliphal succession. This war broke out in Persia, which is a little unusual because until this point the subversive, discontented, proto-Shiite region had been what is called Kufa, basically southern Iraq as it now is. It's thought that this revolt against the Umayyads had the support of the mawali. And it makes sense that if it was in Persia, the largest non-Arab Muslim country, it makes sense that you would have the most concentration of non-Arab Muslims, that is to say converts or the descendants of converts, who might feel that the egalitarian promises of Islam had been betrayed and that in fact the religion was an Arab one in which non-Arabs were in a subordinate position. The non-Arab Muslims of Persia had converted, some from Christianity, most from Zoroastrianism, a religion of central Asia. Wickham takes issue with this. If you go back to your reading, pages 292-294, he says that he doesn't think that the discontent was related to somehow the Umayyads, being an excessively Arab, rather than Muslim, dynasty or that they provoked discontent among recent converts. So this is an open question. I think there's got to be some Mawali discontent, but as we've seen already there's plenty of discontent; Shiite-Sunni being the most obvious, inter-tribal, regional, problems of holding this empire together. At any rate, in 749-750, the Umayyad caliph was deposed by a member of another family known as the Abbasids. This new caliph, Abu'l Abbas, Abbas- the Abbasids. The Abbasids were early followers of Muhammad, although not particularly heroic ones. The family had been supporters, but hadn't taken very many risks. So the Abbasids are not heroes, though they are an old family. The Abbasids came to power with support from the Shiites. This is what Wickham means by what he calls their "salvationist theology"; salvationist meaning that they were going to restore the religious fervor that the Umayyads had dissipated. So that they were originally supposed to represent a return, a reformation, of Islam to its austere roots in which the caliph was a modest, clean-living, austere figure. They very quickly, if that was the hope of the Shiites, the Abbasids very, very quickly betrayed this. They moved their capital from Damascus, the Umayyad capital, to a new city that they constructed in the desert, Baghdad. A city built in concentric circles as a planned round fortress city, but also a commercial city and, of course, predominately city of administration. It was located thirty miles from the old Persian capital. The Persian Empire was ruled from Ctesiphon. Relocating the capital of the caliphate to Baghdad has a number of obvious implications. While most historians would not be quite as confident as Peter Brown, whom you're reading for Wednesday is, that this represents the Persianization of the caliphate, it is certainly true that moving the capital to modern Iraq, to the Mesopotamian part of the former Persian Empire, orients the caliphate further to the East. It changes the center of gravity of the caliphate from the Mediterranean, as in Damascus, basically to Persia, India, the lands between them, modern Afghanistan, Pakistan. At least those are as important, if not more so now, than the Mediterranean. Even though the empire stretches from the Indus River to the Atlantic, its center of gravity has clearly shifted This has implications also for culture, as we'll talk about in a moment. The accomplishment of the Abbasid caliphate in terms of culture is to bring together realms that had not been in very much contact with each other, certainly not in terms of ideas, namely India, Persia, and the Roman Empire, the former empire of the Mediterranean East. Persia stands in the middle between India and the West. To the extent that Persia is not an isolated empire of its own but a crossroads, this means that there's all this exchange of information, techniques, science, art, and culture. But most of all, the establishment of Baghdad clearly means a different kind of rulership. One that it does not break with the Umayyads, but rather, to some extent, elaborates on it. This is an empire. It is not a kind of sacred kingdom of people living in tents. This is an empire more open to Eastern influences. That is to say somewhat more Persian in its style. Less Mediterranean and originally more Shi'ite. So the significance of the Abbasid takeover is really basically twofold. One is this move east to Baghdad with all that it symbolizes that I just got through saying, the influence of non-Arab Muslims, and the creation of a complex administration, an even more complex administration than that of the Umayyads. And then, two, it shows the influence of the Shi'ites. This begins as a Shi'ite victory, but very quickly the Shiites, as I said, are disillusioned, and so it also shows the limitations of the Shi'ites. The Shi'ites don't just want a non-Arab dominated Islamic world, they want what we called last week a "republican administration", a non-monarchical polity. And the Abbasids are monarchical if they're anything. Until the early tenth century, when the Abbasid caliphate starts to break up, the world of Islam was splendid, rich, cultivated, and scientifically progressive. There would be no more great conquests, particularly in the West. Already, before the Abbasids took power, we've pointed to two moments in which the Arab expansion, or the Islamic expansion, was stopped. One in 717 before the walls of Constantinople, in the failed Siege of Constantinople. Two, the battle of Poitiers, not that far from Paris in northern France, in 733. A battle at which the Merovingians, or really their high servants, the so-called Mayors of the Palace, defeated Arab raiders who then retreated basically back to Spain. To some extent these defeats in the West were not so much defeats from the caliph's point of view as a reorientation. In 750 moving the capital to Baghdad from Damascus also means less interest in the West; less interest in trying to take over France, if that was ever a serious goal; less interest in the besieging Constantinople. The Abbasids begin by inviting all of the Umayyad survivors to a banquet supposed to be a banquet of reconciliation. And instead they had their servitors kill all of the Umayyads at the dinner table, spread a leather cloth over them-- some of them were already dead, some of them merely wounded-- and with the leather cloth over them set the table again and banqueted on their dead and dying enemies. Satisfying, definitely. One Umayyad escaped. Not from the banquet, but he had the foresight to say he was busy. And he escaped as far as he could go in the Muslim world, namely Spain. The last Umayyad, then, Abd al-Rahman, came to Spain and was acclaimed by the population, or got himself to be acclaimed by the population, and ruled in Spain as the first Islamic ruler to defy the caliphate. Thus the first independent Islamic kingdom, we can call it-- although they don't use that term-- the first independent Islamic kingdom, independent of the caliphate, would be Spain. The Umayyad ruler actually recognized Baghdad. He did not proclaim himself a rival caliph. It was easy for him to recognize Baghdad 3,000 miles away, or whatever it is, they weren't going to come and get him. He took the title of emir, a ruler who is more like a title of a governor than that of a king. Nevertheless, as I said, Islamic Spain represents the first piece of the caliphal empire to break off. When the Abbasid caliphate ran into trouble in the early 10th century, then the Umayyad ruler of Spain proclaimed himself caliph. In 929 he proclaimed himself caliph of Cordoba. Cordoba was the capital of Umayyad Spain. So at this point Spain becomes the most splendid, most cultivated part of the Islamic world. So if the period of the maximum power and splendor of the Abbasid caliphate was roughly 750-910, the period of maximum splendor of the caliphate of Cordoba in Al-Andalus, or Spain, was about 850 to its sudden collapse in 1009. Questions? Problems? Lot of names here. We don't have a final exam, so what do you care? But I realize it is a dramatic story, but one with a large cast of characters. By now you're used to this in history. Whether these are good cat names or not, I'm not as sure as I am with the barbarians, but worth experiments. As Wickham has described, the Abbasid caliphate was based on tax collection and administration. And your response to that may be, "Yeah, well so what?" But that's not true of all the states that we've been studying. If you take something like Merovingian Gaul, even though in the early period they're still collecting taxes-- remember Fredegund tells Chilperic, "Let's burn these tax records and maybe our sons will be cured of their disease by God."-- but you'll have scene in Gregory of Tours, that basically the Merovingians are rich because of plunder, military expeditions, and land. Land, above all, is the source of wealth in the kingdoms of Western Europe. Land, and the peasants to till it. Obviously it's no good if it's just empty land. Usually not, at least. It's productive land, and this is the source of wealth. Therefore the state gains its wealth on the basis of things like land, military power, and not on the basis of taxing an economy that is more sluggish, has less trade, less income than in the cities of the Muslim world. The caliphate was a tax-paying state with a central army. Therefore the nobility, as such as it was, was not a group of local potentates, as they had been under the late Roman Empire, great landowners for example. Nor was it a military elite quasi-independent, whose loyalty to the ruler was conditional on their own interests, as we've seen with the Merovingian knights. Rather, it was a complicated administration, served as a structure of a vast empire, and the tax revenue came into the caliph, whose administration, whose civilian administration, was supreme over army, over local elites, over great landowners, at least for a time. The Abbasid Empire was the greatest state in the world at that time. Its only rival might have been T'ang, China, but this is the period of the decline of that empire. Baghdad was the wealthiest and largest city in the world. Among the programs of the Abbasids, in addition to building this planned city, creating a certain kind of military structure, consolidating their conquests, among their plans was a cultural program. The cultural flowering of the Abbasid caliphate is, in part, a planned flowering. Not just a spontaneous one. The caliphs funded translations into Arabic of Greek and Persian texts dealing with science, geography, mathematics, philosophy, and medicine, in particular. In 830, one of the caliphs established in Baghdad a kind of combination of library and research institute, called the House of Wisdom. The House of Wisdom, in the first place, paid for and sponsored translations, but it also conducted research activities. Things like an effort to measure the circumference of the earth. The kind of thing that-- you know, how do you actually do that without modern instrumentation? A lot of the material that they translated was from Greek scientific works. Where did they get these? In some cases, they got them from Byzantium, from Constantinople itself. It's said that one treaty between Constantinople and Baghdad called for, among other things, the Byzantine emperor to lend to Baghdad a copy of Ptolemy's geography. Ptolemy, one of the great geographers of the ancient world, author of a book called The Great Geography, known in the West later on when it was translated into Latin from the Arabic as the Almagest, which is a Latin garbling of an Arab garbling of the original Greek title of the work. So this was known in the West, even when it was translated into Latin, as the Almagest. And it was just one of many works that, when they finally reached Western Europe in translations from the Arabic, kept a kind of version of their Arabic name. But the idea that, as part of a treaty, one of the things was you lend us this copy of Ptolemy so that we can translate it into Arabic, shows the commitment of the rulers to the expansion of practical knowledge. What Islamic scholars, scientists, and policy makers were most interested in from the classical world, that is from the world of the Greek and Roman civilization, was science. Broadly speaking, science. They were less concerned with Greek plays, Greek poetry, Greek literature in general. This is partly because they had their own poetic tradition, in Arabic, and partly because their real source of inspiration for literature would be Persia. The stories, as in the Arabian Nights, and the kind of lyrical poetry of the Arabs, like love poetry, or sensuous poetry, is either home-grown or Persian. So they translated things like Euclid on geometry, or the physician Dioscorides, who wrote, not the only, but the leading pharmaceutical manual. Pharmaceutical manual, a list of drugs, their properties, what they come from, what they can cure. However, although they concentrated on science, they also were interested in philosophy. They were also interested in propositions, the nature of reality, metaphysics, and the major project in this realm was the translation of Aristotle. Aristotle is someone who wrote on everything: on drama, poetry, politics, metaphysics, ethics, animals, physics. And so his influence would be tremendous in all three religions that we are concerned with: Islam, Christianity, and Judaism. His influence tends to be in two related realms, or factors. One is its comprehensiveness. They didn't translate everything of Aristotle's, but all three civilizations were aware of Aristotle as a universal thinker. That somewhere, in the work of Aristotle, there's something about everything that's worth studying. He is then, an encyclopedic thinker in a way that Plato is not. Plato is not interested in the natural world. If you go to Plato for information about animals, or plants, you're going to be out of luck because Plato despises things like that. Plato is very interested in ethics, in how to live life, in reality, in the relationship between matter and spirit, but he's not a scientist. He-- to put it mildly-- he's not interested in the material world, whereas Aristotle believes that the material world, although not necessarily the be-all and end-all of everything, is reliable. That our senses can give us decent information, that observation of the natural world leads to more than merely practical knowledge of, say, how to plow, or how to plan things, but leads to knowledge of what creation, what nature, is. So Aristotle is encyclopedic and he's also rational. This is the second contribution that Aristotle makes. Rationality, that anything from plays to rocks can be understood in terms of logical analysis. This is fine when it comes to plays and rocks, but what about metaphysics? What about the world of religion? Aristotle has a profound influence here, again not only on Islam, but on Judaism and Christianity, because he essentially encourages a rational view of God. Now Aristotle is himself not much of a theist, that is to say, Aristotle doesn't go on about God very much, and whatever God there is in Aristotle is not a personal god to whom you would pray on the assumption, or in the belief, that he was interested in your well-being. The closest Aristotle gets to God is the notion of a kind of Great Mechanic. The Prime Mover, as he would be called in Western philosophy. The guy who makes the mechanism, sets it going, and maybe, every so often maintains it. Maybe. A little oil here, a little bit of timing there, but he's not the God of Gregory of Tours. He's not the God who is inspiring saints to get revenge when their powers are questioned, or when somebody steals hay from them. This is not Aristotle's god. Aristotle's god is not concerned with our little petty squabbles. It's not Muhammad's God exactly, either. It's not a god who brings a victory in battle, who's interested in a new prophecy that will seal all the previous prophets, it's a somewhat mechanistic god. It's an eighteenth-century god, even a sort of deist god, for those of you who have studied that. The notion that the world must have been created by God, because it has a lot of design in it. It works. One animal gives birth to another animal just like it, the tides go in and out, the weather is usually rational: winter is usually cold, Halloween is usually crisp. That's imposed by some kind of original order. Just like if you went and found a watch on a deserted pathway, you wouldn't assume that nature had constructed the watch, that it just was growing there the way the ferns were growing by the path. You would assume some artificer had made it. But that doesn't mean that the artificer is still alive, still interested in the watch, inclined to take care of you. I go on this detour, or seeming detour about Aristotle, because he's important to everything in the period that we're discussing, and also in the period that is concerned for the West in the continuation of this course in History 211. There are three thinkers, just to take examples, the most famous thinkers in each of the Jewish, Christian, and Islamic traditions, who embrace Aristotle and in doing so embrace the idea of god as a rational companion to man. These are the Arab philosopher, known in the West as Averroes. Here again, as with Almagest, we're using his sort of Latin-garbled name. Averroes, active in Spain, 1126-1198. Maimonides, perhaps the greatest Jewish philosopher. A rabbi, a physician, a courtier, and a philosopher, also active in Spain, but also in Egypt 1135-1204. And Thomas Aquinas, who spent most of his career teaching at the University of Paris, 1225-1274. All of these thinkers embraced Aristotle. The Latin ones, like Aquinas, via translations from the Arabic. Aristotle was known in the medieval West, not from the Greek originals, but from translations made from Arabic into Latin. All believe that reason and faith are compatible. All based their outlook, not only on nature, but on God, on an Aristotelian form of knowledge. Interesting, in that Aristotle knew nothing about Judaism, Christianity, or Islam. So, what is it about Aristotle, what is it about Diascordes, what is it about Ptolemy, of all of these scientists and philosophers that is of such fascination to the Islamic world? All of this emphasis that we've made on Islamic culture and its openness to other influences may seem strange to you in light of the reputation Islam has in modern America, or at least in many circles of modern America and Europe, as being obscurantist, or anti-modern, or religiously inflexible. I teach a group of retired people where I live, just outside New York, and we're studying Islamic Spain. And they are astounded at what I've just described, at the openness of Islam to other civilizations, at its tolerance, at its curiosity about classical and Persian science. And I was surprised because this is not new information. This is not something that historians have just come up with and just discovered. If you read medieval history textbooks of a hundred years ago, it's in there. Everybody knows that Aristotle was translated from Arabic into Latin. "Everybody knows", everybody who studied the Middle Ages knows. And I said to them, because you can't say to older people, "Oh, well you know your education is actually not very good," the way we say to you all the time. Or, "Your attention span is not very good, because all you're doing is you're plugged in to your social world". No, these people went to college in the tough old days, allegedly, and they're like, "God, I thought Islam was just this sort of frozen religion that had never changed." So you don't have that disadvantage. You don't have that idea, and so I'm not going to browbeat you with it on the basis of the experience of teaching seventy-year-olds. But there it is. I do not accept the notion, well with one exception, with of one honorable exception-- STUDENT: I'm forty-nine. PROFESSOR: Right, me too. I don't want to go into a long discussion about, "Islam, right or wrong?" Or, "Islam, progressive or regressive?" I will say this: there are those who believe, wrongly in my opinion, that there's always been this "clash of civilization", as it's sometimes called, between the progressive Christian West and the obscurantist Islamic East. I don't accept that, in part for reasons you've just heard. There is no consistent Islamic tradition of the maintenance of dogma, or the conversion of the world by force. Insofar as that exists now, it is, in my opinion, a modern phenomenon. It is a phenomenon that results from an encounter with the West beginning around the time of Napoleon's conquest of Egypt, perhaps. It's about two centuries old. There's another kind of belief that at some point things changed. There's a book by Bernard Lewis, the most eminent Western scholar of Islamic culture, called "What Went Wrong". And so Lewis' assumption is that the world that I'm describing, the Abbasid caliphate, is an open society and at some point and for some reasons, the Islamic world closed itself. It became less susceptible to outside influence, more suspicious of it, more dogmatic, more anti-modern, more fixated on literalism, what in the Western Christian tradition would be called fundamentalism, and on tradition. I don't really like this either, because it sees all progress as the property of Western civilization. And it's not that I am not interested in Western civilization. I've taught it. I've taught it because I liked it. I'm not somebody who believes that it's all a tale of oppression, but I don't think that anybody who diverts from the path of Western civilization at some point is going off the cliff, or off the trail, and into the woods. There are a lot of different civilizations out there. There's a third related idea that the Arabs are just intermediaries. Yeah, it's great, they translate Aristotle so that the real guys who can really use Aristotle, Thomas Aquinas et al, can get started. I don't accept that, either, because they do more than that. They do an awful lot of original research in medicine, in mathematics, in philosophy. But, within all of this, to my mind, fruitless speculation, there is a kernel of what is an interesting problem. And the interesting problem is, why were the Arabs so much more successful in assimilating conquered cultures than other invaders were? Say, for example, the Germans. You don't get this kind of efflorescence of culture under the barbarian occupants of the former Roman Empire. We're talking, not just about cultural survival, keep in mind, but about an expansion of science and allied arts. I'd say there are maybe four factors that encouraged the Arab conquest to absorb these new influences. They're not in themselves explanations, but they are certainly background factors. The fact that the conquest was quick and relatively painless, and that it was not really a religious war. Two, and I think here very important, the elimination of frontiers. I mentioned this briefly before. You get Persian as well as Greek astronomy. From India you get things like chess, so called Arabic numerals, which actually, as we all know, come from India. These things come into the Arab and Persian worlds from India and eventually to Europe as well, in a world in which there are no frontiers between India and North Africa. They could go these thousands of miles peacefully. The elimination of linguistic boundaries. Arabic becomes the language of learning, as much as Latin would be in the European Middle Ages, much as English has tended to become in our era. So Maimonides, the great Jewish philosopher, wrote largely in Arabic. The Christians of Spain, so called Mozarabic Christians, studied Arabic, fought in Arabic, wrote in Arabic. And finally, number four, the attitude of the conquerors and the conquered. The attitude of the conquerors was what Peter Brown in the reading for Wednesday will call, "a garden protected by our spears". This is a quote from one of the conquerors. The Arab conquerors considered these to be wonderful civilizations that they were not going to pillage or destroy, but rather protect. "A garden protected by our spears." But they were planning on enjoying the garden, not merely standing on the outside defending it for other people to enjoy. The conquerors were confident in their religion, so confident that they didn't need for others to recognize it or convert. It also gave them the confidence to accept new ideas from Greek civilization, from Persian civilization, from India. But there's also the attitude of the conquered. Brown says that, "as the storm of the Arab armies rolled over the horizon, the population of the Near East sat back to enjoy the sunshine." The Islamic conquest was of benefit, and perceived as of benefit, by most of the people who were conquered. A kind of counter example, in a way, explains this. In Cordoba, the capital of the Umayyad caliphate, or soon-to-be caliphate of Spain, a group of Christians around 850, were so upset at the contented attitude of the Christians of Islamic Spain-- who were, if not a majority, probably about fifty percent, close to fifty percent at this time-- these more fanatical, or at least more serious Christians, were so angry that all of their compatriots seemed to be just fine with Islamic rule that they got up in the marketplace of Cordoba and denounced Muhammad as a charlatan, as a false god, and as not a prophet. And while Islam is tolerant, that is something that you couldn't do. So they did the thing that was most defiant of the regime, really the moral equivalent of burning yourself in the marketplace, and indeed they were imprisoned, told to recant, and when they didn't recant, they were executed. There are about fifty of these "Martyrs of Cordoba", as they're called. But they have to seek martyrdom because they have to look for it, they have to create it, because almost all the rest of their compatriots are perfectly happy to be Mozarabic Christians, practicing the freedom of their religion under a beneficent regime. Beneficent in the eyes of these Martyr Christians, but nevertheless the regime of the devil. This shows you something about the nature of the Arab conquest and occupation. Let me just speak briefly about a couple of aspects of what the Islamic world was interested in studying, and we may continue over into next time since the lecture on the seventh century is actually rather short. Let's start with mathematics. The great accomplishment of this time is the introduction of Arabic numbers, which if you've ever tried to multiply or divide with Roman numerals, are superior. Arabic numbers come from India, and along with this system of numerals, they imported zero-- both the number, or the non-number, and the concept. The concept of zero allows for things like decimal places, which are also developed at this time. From India the Arabs get the kind of very basic ideas of trigonometry, the sine function. But it is their own researches, their own progress, that leads to the discovery, or development, of the five other functions. And here I'm on kind of tricky ground, because despite what they tell you about math literacy and how important it is, I haven't used this since tenth grade. But I do remember the cosine, the tangent, the cotangent, the secant, and the cosecant, right? All of these are discovered by the Arabs. They built on an edifice who's foundation is Indian mathematics. In the early ninth century, a scholar attached to that House of Wisdom in Baghdad, named Al-Khuarizm, in the early ninth century, Al-Khuarizmi writes a book with the title that can be translated as something like, The Book of Addition and Subtraction According to the Hindu Calculation. And this is what incorporates zero and decimal places, and interestingly enough this book is known only from its translation into Latin. The Latin version survives, whereas the original Arabic does not. Within a century of the publication of this book, decimal fractions have been developed, square roots, the value of pi to sixteen decimal places had been calculated. Al-Khuarizm is also the author of a treatise on algebra. The word "algebra" comes from al-jabr, which is sort of restoring, restoring something that has been imbalanced and that you're now going about to balance, which of course is, in a way, the visual nature of algebra. Al-Khuarizmi was also an astronomer. He developed star tables that allowed one to locate the planets and stars at different times of year and at different latitudes. This is what allows the making of things like astrolabes or, later, sextants. These are things that describe the sky at a particular [correction: place]-- that allow you then to keep time; and also to navigate; to calculate time for things like prayers, or feasts, celebrations; also to cast horoscopes. I'll work a little more with you on geography, medicine, and then summarize the Abbasids at the beginning of our next class. So I'll let you go for now. Thanks.
The_Early_Middle_Ages_2841000_with_Paul_Freedman	19_The_Early_Middle_Ages_2841000_Charlemagne.txt	PAUL FREEDMAN: Today, ladies and gentlemen, we move back to Northern Europe to the northern part of the former Roman Empire. And since you've done the reading, I won't be giving anything away by saying that the culmination of what we're talking about is Charlemagne and Charlemagne's coronation in Rome at the hands of the Pope in the year 800 as emperor. We'll talk about what that title means, a title that had not been seen in 325 years in the West, at least not agreed upon by everyone in Western Europe. Charlemagne, at this time, didn't control quite everything in Western Europe. You have a map in the Wickham book of his empire, bequeathed to his successors in the year 843, the year that it is partitioned. This does not include the British Isles. It does not include most of Spain, which was in Islamic hands. But it is a pretty convincing effort at the restoration of the Roman Empire, even though its base-- in other words, where Charlemagne and his ancestors' lands were, where their wealth came from, where they lived, where their followers came from-- was at what had been the borders of the Roman Empire, what's now northeastern France, Belgium, the Netherlands, west northwestern Germany-- a territory known at this time as Austrasia. Charlemagne's ancestors were great men, major nobles of the region of Austrasia-- again, eastern France, western Germany, the Low Countries. They were nominal servants of the Merovingian rulers and rose to prominence with a title of maior. And Wickham preserves just the Latin, maior-- major, larger, great man. The maior of the palace-- "the mayor of the palace" is how this is usually translated. And of course, our word mayor applies to a municipal official. So mayor of the palace is a rather funny title. But it's really a kind of prime minister or leader of the soldiers-- prime minister and defense secretary or minister. And this title tended to be hereditary. One of the problems of rulers in Merovingian world, in the Lombard world, in all of Western Europe, is controlling their mighty servants. Because these people were not just easy to fire, you couldn't just cut their salaries or stop their paycheck, because they're not getting a paycheck. They are the leaders of soldiers. They own castles, fortifications. But most of all, they own land. And as landowners and as established powers within the society, their power rivals-- and in the case of Charlemagne's ancestors-- would exceed the power of the king. So these are not people who are easy to dislodge. And they are people who tend to want their power to be not appointive but hereditary-- in other words, to bequeath titles like mayor of the palace to their sons. I mention this now because next week we'll see this is a problem that Charlemagne's descendants would have. They would have the same problem. How do you make your officials that you've appointed listen to you, obey your orders, if you don't have sufficient coercive power to remove them? And the reason you don't have sufficient coercive power to remove them, again, is because they are military officials, they have their own followers, they are well-established in various territories, and so they're hard to tame. They are becoming little kings themselves. And a key aspect of the ability to become a local ruler, even though officially you're subject to the real king of a large realm, is because it's become hereditary. It's become a family property. This tendency to decentralization, inheritance, and weakened royal power is often called "feudalism," a word that you may as well write down-- you've heard of it-- but which we're not going to use. And we're not going to use it for a couple of reasons, one of which is nobody uses the term at the time. It carries a lot of other overtones that are not relevant to us, and really insofar as it has use, it describes a later period, a History 211 kind of reality, a post-year 1000 reality. But what is to be recalled is that, once you no longer have an official state apparatus with an administrative structure or bureaucracy like Diocletian, like Constantine, like Justinian, or even like those Byzantine emperors we were talking about, or like the Abbasid Caliphate-- all of those are complex structures of state bureaucracies funded by taxation. Here we have something that is not that sort of polity. It is more personal. It is more military. It depends more on plunder, on expansion, on charisma, that is, personal ability to get people to obey you. It has a very rudimentary structure. And the success of a state is judged on the basis of its ability to survive, even if the ruler doesn't have charisma, even if the ruler's not all that great. Because people obey the state, they obey its officials, they obey the idea of the state, and not the individual personality. So we're going to talk about Charlemagne's ancestors and how they got into power, how they went from being mighty servants, but servants nonetheless, to kings of France and eventually, in 800, emperors. What happened to the Merovingians? Last time we checked, the Merovingians were certainly kicking people around Francia, warring with each other, occasionally regretting it and burning the tax rolls, but pretty quickly returning to the old plunder, and killing people, and having fun kind of barbarian economy. The Merovingian dynasty lasts to the mid-eighth century. But for its last hundred years, roughly 650 to 750, its rulers are ineffective. They have the title "kings." They have great prestige. But they are weak. A lot of our understanding of their position really is simply a gloss, or an elaboration, of a few lines of Einhard, the biographer of Charlemagne, whom you've read. "The family of the Merovingians," he says on page 16 of this book, "From which the Franks used to make their kings, is thought to have lasted down to King Childeric whom Pope Stephen ordered deposed. His long hair was shorn, and he was forced into a monastery." Remember, one of the symbols of Merovingian familial prestige was this long hair. But Carolingians had short hair and wore mustaches. They kind of broke with the Merovingian look. But of course, this is not just a male fashion statement. "Although it might seem that the Merovingian family ended with him, it had in fact been without any vitality for a long time." The Merovingians were just given a little shove, because they were already basically finished. "There was nothing of any worth in it, except for the empty name of king. For both the riches and power of the kingdom were in possession of the prefects of the palace," this is how he's translating it, "who were called the mayors of the palace, and to them fell the highest command. Nothing was left for the king to do except to sit on his throne with his hair long and his beard uncut, satisfied to hold the name of king only and pretending to rule. Except for the empty name of king and a meager living allowance, which the prefect of the court extended to him, he possessed nothing else of his own but one estate and a very small income." Now, so much depends on these words of Einhard, who then goes on to describe them going around in these ceremonial carts, people acclaiming them. But everybody knows that if they want anything done, the person to talk to is the mayor of the palace. It's to Einhard's interest, or at least to the interests of the Carolingians for whom he's writing, to make it appear as if the Merovingians were already finished. But nevertheless, it's clear that they were much weaker than the people we've been reading about in Gregory of Tours. What happened to them? Well, one possibility that Einhard, in effect, sort of encourages is that something happened to the family. They were weak personalities; maybe they had some hereditary degeneration. Or, they ran out of money. They did not have lands to reward their followers anymore. Remember that in this economy, this is not something in which tax revenues are funding the state. Up to a point they are, because we saw that Fredegund and Childeric had tax revenues-- at least, tax records-- to burn. But as the inheritance of Rome-- Roman administration, Roman literacy, Roman organization-- frayed, as that inheritance became further and further degraded, the ability to tax the population-- rural, dispersed-- dwindled. So it's not only a question of the administrative decline but of the economic decline, or at least the economic decentralization of the way people lived. The Merovingians had depended an awful lot on war and on the plunder received from war. You'll remember that when we were talking about Clotar, the son of Clovis, that his men rebelled when he didn't want to fight the Saxons. That's not just because they're warlike savages, or insofar as they're warlike savages, they're also in it for treasure, plunder. Beowulf is a plunder-driven world. The author of Beowulf is well aware that this is stupid, in a way. Right? The dragon has all this plunder. And what does he do with it? Dragons are not consumers. He lies on beds of gold coins and beautiful armor and all sorts of things that have been seized. He has absolutely no use for all of this stuff. And yet, stealing just a little tiny ring or a little bit of it enrages him. And so he starts his depredations out of anger at that. The Merovingians, once they stop expanding, don't have the opportunities to keep their economy going, their source of income going. And in particular, they lose the ability, so it would seem, to reward their followers. Their followers, their knights, to call them that anachronistically, their military entourage does not flourish by being paid because there's very little in the way of coinage. There is very little in the way of revenues. They benefit from things like land, but as you are running out of plunder and giving away land, then sooner or later you, yourself, the giver of land, will not have anymore to give. That's another hypothesis about Merovingian decline. In fact, there is an effort by a mayor of the palace of the late seventh century to depose the Merovingian king-- a man named Grimoald, who is an ancestor of Charlemagne. But this is unsuccessful. He tries to depose a Merovingian ruler. And even though the Merovingians are weak, their other followers prevent Grimoald from succeeding. And indeed, he's executed. The prestige of the Merovingians was such that even if they were not effective, they were still the kings because the blood of Clovis flowed in their veins. And this was symbolized by their familial distinctiveness, which included the long hair, the uncut beard, the traveling around in carts. This is important because it means that you could not succeed by direct action against the Merovingians, at least not in 661, when Grimoald was killed. In order to make this happen-- in other words, even though he was killed, his successors remained as mayors of the palace. They were tightly enough ensconced or inserted into the structures of power and successful enough as a family that they were able to survive, but as mayors of the palace. Looked at from the long term-- that is from the perspective of 751, the year when Pippin declared himself King of the Franks and deposed that last Merovingian ruler-- looked at from that perspective, the strategy of the dynasty which we can call Carolingians, even though we're not yet at Charlemagne, the strategy of the Carolingians was to come up with another rationale for why they should be kings and not the Merovingians, what we can call "legitimacy". Legitimacy in politics is the sense that the people who are ruling are ruling for good reason, that their rule is legitimate. This can be on the basis of an election: "I may not like the president, but he was elected in a fair election, therefore I accept the fact that he's president." It may be triumph in war: "This emperor came to power, deposed his predecessor, and got the Bulgars off our back, therefore his rule is legitimate." It may be economic benefit: "This guy has made my life easier economically or I have the feeling that things are going right." It may be dynasty: "This is the oldest son of the former king." The British rulers just changed to end discrimination between men and women in the succession. Obviously, Britain has a queen rather than a king and has for the last sixty years, but the favored candidate would be a male child. The circumstances of Elizabeth's succession don't need to detain us, but she was not the logical eldest-- obviously not the eldest male child. So there are all sorts of ways of having legitimacy as a ruler. The challenge for the mayors of the palace was to create this legitimacy. And they did it by several different means. It's not that there's this project where they set out in year 662 and say, "Within ninety years we're coming to power, and here's how we're going to do it." It is historians who impose that rational strategy. But nevertheless, it is discernible. In fact, they are mayors of the palace of several different pieces, because the Merovingian realm was not unified. It was in particular pieces. So these guys are the mayors of the palace of Austrasia. So their opponents include the other kingdoms, particularly Neustria which is more or less the region of Paris, the Seine, the central to northern part of modern France, but further west than Austrasia; So Austrasia is northeast. Neustria is more central and slightly south. So there are lots of rivals. It's a very dangerous situation. It's a very violent world. But this is their plan. A lot of what they, that is the Carolingians, the ancestors of Charlemagne, accomplished was military. This is the bottom line of leadership in the period we're dealing with. Without military prestige and military success, it's very hard to craft a polity, let alone hand it down to your descendants. What is more unusual than military leadership, however, is that the Carolingians allied themselves to the Church. Their legitimacy as rulers would be based very much on an alliance with the Church, and in particular, with the papacy. The Bishop of Rome is someone whom we haven't talked about very much. We mentioned Leo I back in the fifth century, who was responsible for negotiating with the Huns in the absence of the emperor and who also upheld doctrinal orthodoxy against Monophysitism. But the pope was not inevitably the sole ruler of the Church in the way he would become in the modern world within the Catholic Church. The pope was the Bishop of Rome. He was the guardian of some of the chief relics of the Christian world, the relics of Saint Peter and Saint Paul, the apostles. He was the inheritor of the aura of the city of Rome, the imperial city. He even had appropriated some titles from the Roman emperors, such as Pontifex Maximus, an old pagan title. So the pope is the inheritor of a lot of Roman imperial prestige, but he is a beleaguered inheritor of that. In fact, the pope's life in Rome was dangerous. He was often eclipsed by or threatened by the Lombards. The Lombards, a barbarian tribe who had invaded Italy-- we talked about them last time. They invaded in 568. They took most of Italy from Justinian's heirs. They were Arian for a longer time than other barbarian tribes. And even when they ceased to be Arian, they were eager to seize Rome. They weren't overwhelmingly eager to seize Rome because they never did it, but they threatened the pope. During the seventh century, the pope considered himself the ally of the Byzantine Empire. The emperors continued to intervene, to debate various doctrinal things. But as the Lombard threat grew, as the Byzantine emperors were iconoclast, the pope cast around for a new protector, beginning in really the 720s, 730s. And so the alliance between Carolingians and popes is natural, in the sense that they both want something out of the other. The Carolingians, the mayors of the palace, want legitimacy. They want to be sacred figures within the Christian world, to trump the pre-Christian aura of the Merovingians. And the pope, out of the Carolingians, wants protection from the Lombards and a sense of rule over most of Europe that will favor the Church and allow the Church to advance its work. The means of cementing this alliance, however, are interestingly enough monks. The people who are the shock troops of the Christianization of Europe, the expansion of Europe, of the Church, and the furtherance of its mission are monks, many of them from Ireland and Britain, who would try to convert the countryside, either those places that were minimally Christian or, beginning in the late seventh and early eighth centuries, extend Christianity to places like Holland or central Germany that were not parts of the Roman Empire and had never been Christian. So these monastic settlements not only converted the countryside, but they served as foci for economic and social development. There was an alliance between the mayors of the palace and monks such as the English monk, Saint Boniface, Apostle to the Germans. Saint Boniface, in the eighth century, would convert a lot of the Germans in and east of the Rhine. He would receive support from the mayors of the palace of Austrasia, because this is east of where they are, and they're interested in expanding and settling there. And he received support from the pope who is interested in the conversion of Christians. And so it's through intermediaries like Saint Boniface and other monks that the countryside gets converted and that the Carolingians and the pope approach each other. Why monks? Who are these guys? When we looked at the Benedictine world, it seemed as if monks were supposed to be enclosed in their monasteries and not wander around? These are somewhat special monks. These are wandering monks. The Irish tradition was different from the Benedictine tradition and encouraged wandering as a form of penance. If you wanted to do penance or to experience the power of God and randomness in the world, which would you rather do-- pray seven times a day in the same place for decades, or just kind of like wander around, try to convert people, and see if you could get martyred? Certainly, the latter is dangerous. The latter is truly dangerous. But these are very enterprising guys. We just have this idea. Oh yeah, monks pray or they copy manuscripts or they wander around and convert people-- all of which are insanely difficult things to do. You really have to admire these guys. So many of them are from Ireland, or from recently-converted Anglo-Saxon England. Anglo-Saxon England combines a Benedictine structure with some of this inheritance of Irish wandering. But it is these monasteries that are founded in the countryside of Germany, of the Netherlands, and the alliances between the mayors of the palace and the papacy that are key in creating the Carolingian dynasty. The mayors of the palace of Austrasia come to preeminence in the Merovingian realms in the early eighth century. One of the key events here is one that we've looked at from several sides now and that will be, I hope, familiar to you. And that is the Battle of Poitiers in 733, also known as the Battle of Tours. This is the battle in which the Arabs were defeated in northern France, and eventually retreated to Spain. 733 marks the high water point of Arab incursions into Europe and is, in a sense, a parallel to 717, the defeat of the Siege of Constantinople. The victor at Poitiers was the mayor of the palace of Austrasia, a man named Charles Martel, "the Hammer." He doesn't have a last name. It's sort of a [clarification: a sobriquet]-- Charles Martel. And he gained tremendous prestige from this. That legitimation that we said comes from military leadership certainly was his. The Merovingian king was nowhere to be seen at that battle. It was led by the mayor of the palace. Charles' son, Pepin the Short, started really to put together these aspects of rule. Pepin the Short, 741 to 768. Now there's something going on here that I don't have an explanation for. If he really was short-- yet we know from digging up his body that Charlemagne was on the order of 6' 7". Charlemagne is really tall for pre-modern people. He's really, really tall. And Einhard describes him as tall. Einhard says his voice was kind of squeaky and high, given just how huge he was. I don't know how that works. Many of you are more advanced in science and genetics than me. But my pet theory, since Pepin's body hasn't been found, is that actually he was really tall too and that he's called Pepin the Short as a kind of joke; you know like guys nicknamed Tiny are often 350 pounders. I'm just saying. Pepin the Short is the person who crystallizes this potential alliance among papacy, missionaries, and mayors of the palace. And in doing so, he transforms Europe. He favored the Church. He could mobilize his new power and legitimacy through this alliance with the Church. He encouraged various kinds of monastic reforms urged by Saint Boniface, which meant better discipline over priests, more councils of bishops, the restoration of lands to the Church, and a role for the king as the guardian and protector of the Church. It may be at Boniface's instigation that Pepin wrote to the pope, Zacharias at this time, asking, "Is it right for the man who holds the power not to wear the crown, while the person who wears the crown does not hold the power?" He asks this as if it were a hypothetical question. "Oh, you know, we were just discussing this last night and wondered what you think." But of course, the pope is quite aware of what's at stake and says it is wrong for the person who holds the power not to hold the crown; whereupon in 751, Pepin had himself elected king of the Franks, deposed and put in a monastery the last Merovingian king, and by his being put in the monastery, he was tonsured, that is to say much of his hair was cut off, desacrilizing him. And unlike Grimoald's failed coup d'etat, this was totally, peacefully, no problem, greeted by everybody, successful. In 753, two years later, the new pope, Stephen, made an unprecedented-- literally unprecedented-- journey across the Alps. No pope had ever been in northern Europe until this year. And he crowned Pepin. He was desperate over the situation with the Lombards. And in return, Pepin led an expedition that, although not the definitive invasion of Italy that Charlemagne would undertake, at least gave the pope some breathing room and defeated the Lombards. At Pepin's death in 768, he was succeeded by his son, Charles, and his other son Carloman. Charles-- the future Charles the Great, Charlemagne. Carloman died in 771, maybe naturally, maybe not, leaving Charlemagne as the sole ruler. Charlemagne at this point is king of the Franks, inheritor of the title and accomplishments of his father. He was the beneficiary, then, of well over a hundred years of Carolingian ascent. And let's just review the factors that had aided his predecessors-- the weakness of the Merovingians; their position as mayors of the palace; the activity of monks, missionaries, to Germany and the eastern part of the Frankish world; Byzantine weakness and the Lombard threat; and, of course, Byzantine flirting with heresies like Iconoclasm. The result is then a kind of geopolitical shift of the papacy towards the North. Another chapter in that long book of the end of Mediterranean hegemony. Instead of looking to the eastern Mediterranean for protection and for the ruler who was his natural ally, the pope now looks to a northern transalpine ruler. Charlemagne you've read about. And you've read Einhard's biography of him. It is, in some sense, at least a seemingly artless biography. He obviously likes him, admires him, but he describes him as a real person. We learn that he liked baths and roast meat, that he had a high voice, that he loved having his daughters around him but probably kind of mistreated them by not allowing them to marry. And then Einhard is scandalized that since they couldn't marry, they had all sorts of guys hanging around. We get a sense of Charlemagne's personality. Charlemagne is a man very much at home in his time. He is comfortable with being a warrior. He would lead campaigns year after year after year. At the same time, he is a person of learning, or at least a person who believes learning is important. Einhard tells us that he never quite really learned to read and write, that he tried, that he slept with Augustine's City of God by his side, which is an impressive thing to do as bedtime reading. And we also know that he is pious. His piety does not interfere with his enjoyment of life or with his harsh prosecution of military campaigns. He's not a sensitive person. He's not a self-examining kind of character. But very important is that his notion of leadership combines what might be thought three available forms of legitimacy of this era. One, and the most important, is military prestige and power, war leadership. And he conquered lots of peoples. It was not just a question of war leadership with no results. He had tremendous results. He conquered the Lombards in Italy in 774. He conquered the Avars in the 790s. So much treasure did he seize from them-- remember we saw the Avars as besiegers of Constantinople? By this time, they're in more-or-less modern Hungary. He seized so much treasure that the entire economy of his empire basically was financed on the basis of this plunder until his death in 814, so for nearly twenty years. He conquered the Bavarians. He conquered the Saxons in northern, eastern Germany, a very, very difficult series of campaigns from 774 to 806 that involved large numbers of civilian casualties, virtual exterminations of peoples, and forced conversion. It was the first real, sustained campaign of forced conversion to Christianity in European history. Brutal, but successful, opening up really the definition of modern Germany. Much of what the modern German state is, in its central and eastern parts, in the north, is Saxon. There is a part called Saxony still, a province of the former East Germany. But in fact, a province, or a land as they're called, of the former West Germany is called, Nieder-Sachsen, Lower-Saxony. So the Saxons are spread throughout northern Germany. And by Charlemagne's death, Germany or the eastern Frankish realm starts to look like something familiar. He conquers a bit in Spain against the Muslims. His forces would seize Barcelona in the year 801. But he does not get as far as he had hoped. In particular, he had hoped to take Saragossa. His army was defeated by, actually, Basques. But their defeat leads to the literary triumph known as the Song of Roland, one of the great works of the Middle Ages in which the enemy are Muslims. And the Song of Roland is a great sort of Crusade ideology text which shows, in its own words, that Christians are right, pagans are wrong. Of course, they call the Muslims pagans. They depict them as worshipping Apollo, and Termagent, and other gods. They know that the Muslims are not literally pagans. But it has higher rhetorical value. Charlemagne is tremendously successful as a war leader then. His second form of power and legitimacy is as a Christian ruler. He is a man with a vision of a Christian polity, of alliance with the Church, and as seeing himself as responsible for the spiritual health of his people. This is important, this latter responsibility, because it has a lot to do with the program of education that we'll be talking about next week, the intellectual air of his court. He believes himself, therefore, to be not just somebody who is supposed to convert the Saxons forcibly, but is supposed to educate his population into becoming Christians of a real sort. This also means that he is allied with the pope and believes that the pope is capable of aiding him in more than merely symbolic ways. The third aspect of power and legitimacy is the legacy of Rome. It is the thing that unifies this entire course. Charlemagne, according to Einhard, went to Rome to rescue the pope yet again, not this time from the Lombards in 800, but from the Roman factions. Pope Leo III was rescued by Charlemagne, put back in Rome. Charlemagne, Einhard tells us, went to Saint Peter's on Christmas Day to pray. And lo and behold, the pope jumped out from behind a pillar and put the crown on his head and he was acclaimed Roman emperor. And Charlemagne said later, he wouldn't have gone-- even though it was Christmas-- he wouldn't have gone to church at all if he'd known this was going to happen. We can be cynical about the surprise aspect of this, or about Charlemagne's uncharacteristic modesty. Nevertheless, we have to think about the implications of the pope crowning the emperor. Constantine wasn't crowned by a pope. The problem with having someone crown you is that it could be implied that he is the one who bestows the crown and could decide not to crown someone in the future. It looks as if he's the more powerful one. He's standing; he's putting the crown on you; and you're kneeling. Indeed, as an evocation of this, almost exactly 1,000 years later in 1804, when Napoleon had himself crowned by the pope, Napoleon seized the crown from the pope's hands and put in on himself, put it on his own head, in a direct reference to Charlemagne. So Roman, Christian, and military leadership. Of these, the Roman is the most impressive and the most sort of historically dramatic, but probably the least significant at the time. Charlemagne did not consider his empire to be exactly the same thing as the Roman Empire. He would divide it. The fact that he handed it over to one son is that he only ended up having one surviving son. But he had plans to divide it. It's not clear if he regarded the imperial title as anything that would really survive. Nevertheless, he was an emperor; and an emperor meaning that he ruled over many peoples. He was more than just the king of the Franks because he now ruled over Barbarians, Avars, Visigoths, Lombards. He had made a good stab at restoring the Roman Empire in the West. But it's a different Roman Empire. Its base is not really in Rome nor even in Milan or Ravenna, the late Roman imperial capitals of the fifth century. It is in Aachen, a city in Austrasia where remains of his palace chapel still stand. His lands, influence, cronies, family, political base, economic base, military recruiting base, are all in northern Europe. Charlemagne is, then in some sense, the reviver of the Roman Empire. But he is also the founder of Europe as something not just a geographical expression but a cultural expression. Whether it is a socio-political expression, time will tell. When the European Union, the Euro, and all these things that are sort of semi-unraveling now were cemented in their current form in the early 1990s, the treaties that established that were deliberately made in the territories that are neither French nor German entirely, but are really part of the old Carolingian patrimony. The treaties in places like Maastricht, the location of Brussels as the capitol of the European Union, all of this is really evocative of the empire of Charlemagne. These are the lands of the Carolingians and this is, in the next thousand years, in certain respects the center of Europe. We'll talk more about the Carolingians next week.
The_Early_Middle_Ages_2841000_with_Paul_Freedman	21_The_Early_Middle_Ages_2841000_Crisis_of_the_Carolingians.txt	PAUL FREEDMAN: We're going to talk today, now, about Carolingian decline. It's not just that we're compressing lectures or in a hurry. The empire of Charlemagne is an empire that does not last that long. So when we say that it has certain flaws, like size, well, we already said that the Roman Empire had this flaw. We've already said that the Abbasid Caliphate has this flaw. But those empires are able to manage with this weakness for quite some time. Part of the problem with the Carolingian Empire is its size. Part of it, however, as you will have read in the Fichtenau reading is its lack of infrastructure and economic development. Infrastructure in a sense of not just towns, roads, communications, but social infrastructure, the lack of an idea of obeying the state or obeying the ruler, and a tendency, therefore, to mix private and public interest, and to the benefit of the powerful. We'll talk more about that. There are also external problems. The beginnings of the Viking invasion, which we will be talking about after the break, occur before Charlemagne's death in 814. Nevertheless, there's no sense hastening the signs of decline. We always can see signs of decline coming after. But Charlemagne's rule had been so successful, so full of accomplishments, he was a ruler such prestige, that even the difficult last ten years or so of his reign can't quite eclipse that. In 801, there arrived an elephant at the court of Charlemagne, a gift from the caliph of Baghdad, Harun al-Rashid, the caliph who figures in the Arabian Nights entertainments. This is a link between two very powerful and very distant empires, the two of the three that we've described as, in some sense, heirs to the Roman classical empire and civilization. There was a tentative thought of, perhaps, an alliance between Baghdad and Aachen, the capital of Charlemagne's empire. At various times, there had been negotiations between Constantinople and Aachen discussing the possibility of an imperial marriage. The Carolingian ruler was contemptuous of Byzantium because it was ruled by a woman, the Empress Irene, a rather exceptional figure. But neither the alliance with Byzantium, at least not at this point, and certainly not the more far-fetched alliance with Baghdad came to anything. The elephant was certainly the first one seen in Europe probably since Hannibal and his invasion of Italy. And how he got there, what the logistics of his transport were, how he got to Baghdad in the first place-- it's not as if they have elephants in the natural habitat of Iraq either. Nevertheless, here's this elephant who lives for about ten years. One of the signs of things starting to unravel in the Carolingian Empire, so some historians say, is the death of Charlemagne's elephant, which Einhard talks about, actually, in his biography; that is, it is an event that's worth mentioning. But pets, they don't last forever. As someone who lost his cat within recent memory, you've just got to get over it. On the other hand, I can get another cat. And Charlemagne, presumably-- well, not presumably. We know he didn't get another elephant. The high watermark of his reign seems to be the year 802. This is arbitrary, but this is shown by the energy of his quarrel with the Byzantine empress over his arrogating to himself the title of emperor. This is the first person in the West claiming to be emperor, and the Byzantine Empire doesn't like it. By 802, he is done with his two campaigns; one in Spain, and the other in Saxony and the regions of the Danube. He had pacified the Saxons after a nearly twenty-year effort. And while he hadn't achieved his ambitions in Spain, he had seized territory in the northern part of what's now Catalonia. He attempted to address the problem that I've just identified, namely the tendency of powerful people to take over and rule localities not as government servants, but as noble rulers. He, in order to combat that, tried to get every free man in his realm to swear an oath to him personally, that is to make sure that they understood that their prime loyalty had to be to the emperor and not to the count, duke, local ruler, bishop, whoever he was. And the instructions that he gave to the men sent out to try and to administer this oath show you some of his idea of rulership. We've talked about this already, but since it's a fairly complex idea, it's worth emphasizing. In the instructions, it says, "Let each man keep himself in the sacred service of God, following the divine commandment and observing whatever promise he may have made fully, to the best of his understanding and powers. For the lord emperor cannot exercise his vigilance or powers of correction over every man." So the notion that the emperor is supposed to be responsible for people behaving themselves, is responsible for not just what we would call political order, or peace, but for the salvation of the people, for the spiritual as well as political health of the realm, is typically Carolingian, and, in a way, typically medieval. There's a sense of imperial responsibility before God for the behavior of the emperor's subjects. But already, a few years later in 806, this idea has been weakened. In eighteen 806-- if you take a look at the first map that I've given out, we have a partition in 806, an agreement at a place called Thionville. I guess this is going to have to be spelled out, since we don't have chalk. T-H-I-O-N-V-I-L-L-E. And it's written on the first-- well, no it just says, proposed partition. In 806, he came up with the idea of dividing his realm among his three children. His son Charles would get the north, his son Pepin would get Lombardy and Bavaria, and his son Louis would have Aquitaine. In this document, there's no mention of the imperial title, leading one to surmise that maybe he thought this title was just his personal accomplishment. Maybe he didn't really envisage the reestablishment of the Roman Empire in any kind of permanent way. Here, we just have a kind of splitting up of land. Louis gets the southwest; Charles gets the lion's share, the heartlands of the Carolingian family, the parts of Germany that the Carolingians controlled and northern France; and Pepin gets Italy and the Alps. So here you have a contrast between 802, this grandiose imperial idea of unity, 806, just like the Merovingians, partitioning out the lands for the successors of Charlemagne. Aachen is a long way from being another Byzantium Constantinople or another Baghdad. And in these capitularies, the documents that are issued by the court of instructions to the administrators, we do see, as Fichtenau emphasizes, a sense of unease and of problems. Again and again, the capitularies lament corruption, maladministration. They start to mention the Vikings as more than just a minor, mosquito-bite-level distraction. But most of all, they emphasize usurpation of royal authority. Usurpation meaning, again, that the people, such as the counts or dukes or the nobles who are supposed to be servants of the crown, supposed to be his chief servants, are taking over for themselves things like taxes, revenues, the right of judgment, the right to punish people. And people are tending to look at them as their rulers. The count of Flanders, the count of Barcelona, the duke of Aquitaine, these are people who are starting to think of themselves as potentially, at least, rulers who might transmit their office to their children. And it then is not an office, it's a possession, if you have a right of inheritance. In other words, I could transmit to my children my ten-year-old car, my silver butter dish, all of my treasured possessions, but I cannot transmit to them the professorship that I have. I can't just say, well, my eldest son is going to be a professor of medieval history at Yale, whether or not he has any interest in doing that, because I don't own the position. It's not my property. It is my office. We're so familiar with this that we don't even think about what it would be like. Well, we actually do, because there are some things that people do tend to start to own that, originally, were not supposed to be that way. But in the medieval world, it is a problem to dislodge people from property, because most property is in land. All Yale has to do is stop paying me, and I'm no longer benefiting from this office. On the other hand, if I had a castle across campus and stored some boiling pitch and some followers, naturally, some trusty drinking mates, and had this a little moat and bailey establishment right outside of Harkness, I could terrorize Yale and extort from it. That picture is not so far-fetched. Where the picture is really not far-fetched is if you imagine Yale in ruins. People pasturing sheep on Cross Campus and wondering "God, what were those buildings, anyway? They're really huge. And all those funny little blackboards, whatever they were for." And then using WLH to build fortifications. Why build a new castle on the lawn when you've got building materials that somebody else left for you? So WLH 117, 116, 115 are one person's fortress. And that auditorium at the other end is somebody else's. And here I'm getting a little bit ahead of myself, but this is what's going to happen once the Carolingian Empire dissolves, essentially. When I say to people usurp or arrogate or make hereditary their possessions, I'm talking about something that sounds abstract. But if you think of it in terms of what it means to defy people, basically, you're talking about building castles. And this has to do with the nature of warfare. This is all a subject for the course that succeeds this one, but it has to do with the nature of warfare, in the sense that, once you have that castle, it's very hard to be dislodged from it. The advantage is with the defense. Catapults, trebuchets, all these interesting weapons, actually, both require an insane amount of mobilization and organization and are not as effective as artillery some centuries later is going to be. So the problems of Charlemagne's empire-- despite the invasions that will be our subject for Monday after Thanksgiving-- the problems of Charlemagne's empire are essentially internal, as was the case of the Roman Empire, only moreso. These internal problems, what I've called the lack of infrastructure, which means political and economic infrastructure, make it very difficult, effectively, to resist the Vikings. And there are other invaders whom we'll have to mention as well, later on, the Hungarians and invaders and raiders from North Africa. The empire was too large, given the nature of communications and the mechanisms available to impose order. The same thing that made it an empire made it have some disadvantages: diversity of population, ethnic loyalties. So you have revolts of Aquitainians who are not Franks; of Bretons, people of Britanny, who are not Franks; Bavarians; Visigoths. All of these people are not necessarily overjoyed with Frankish rule, not necessarily immune from the possibility of seizing on the weakness of the Franks to rebel. These problems become more manifest in the reign of Charlemagne's son, Louis the Pious, who rules from 814 to 840. My hesitation in using the word rules is that he is deposed once and forced to undergo public penance twice. One of the problems of the empire was obviated, however. When Charlemagne died in 814, the succession was just to Louis because his brothers had died. So the 806 deal, or 806 plan, was not implemented and became moot. Charlemagne was succeeded by one sole ruler over the entire empire, Louis the Pious, because Pepin and Charles had died. Louis is often seen as inept but well-meaning. His sobriquet-- and a lot of the Carolingian rulers now have less-flattering than Pious Charles the Bald, well, that seems a little unfair. Charles the Simple, Charles the Fat, Louis the Stammerer, Louis the Child. You get the idea. Not an imposing group of rulers. But pious, shouldn't pious be a complement? And indeed, it could be. And, as it happens, he's not known as Louis the Pious in every language. So in German, he's referred to as Louis the Pious, but in French, he's Louis the Debonair, the Imposing. He is an imposing figure, actually. He's not as weak as what I'm going to say in the rest of the discussion about him is going to make him look. He was a very effective general. He did a lot of wars in southern France. He was the effective ruler of Aquitaine. He conquered Barcelona for Charlemagne. He suffered from three problems, however. One not at all of his own making, the second certainly exacerbated by his vacillation, and the third is just who he was. The first problem is the invasions. The Viking invasions, in particular, begin during his reign, first part of the ninth century. So it's an external problem. On the other hand, the lack of an effective response does have to do with flaws in the nature of Carolingian rule, flaws in the nature of Louis' rule, in particular. The second problem is his sons. His sons fought against each other and against their father. This is not something that's new to us. We've seen this with the Merovingians. But in order to maintain control of sons who expect some kind of rulership and who are jockeying for power with their siblings, Louis made it worse, in part, because he had sons by two marriages and tried to carve out another realm for his youngest son, Charles the Bald, Charles the future the Bald. I don't know that he was called Charles the Bald when he was fourteen. I actually don't know when that title starts to come into effect. Not title, nickname. As we'll see, these civil wars have greater significance than mere civil wars, because they're at the origins of the breaking up of the empire into entities that we can just about start to call France and Germany. So we're at the kind of crucible, or moment of creation, of the European order that will exist for the next more than 1,000 years. Louis had very sophisticated ideas about imperial rule. Perhaps even more sophisticated than those of his father, because Louis was quite a bit more educated than Charlemagne, quite literate, one might almost say an intellectual as well as an effective general. But he was less pragmatic, less realistic, less flexible than his father. Even more than Charlemagne, Louis believed that the emperor must answer before God for the conduct of his population. Even more than Charlemagne, he believed that he ruled over a sanctified state. In other words, he was not just a political ruler, he was, in some sense, a religious leader that the religious and the political were not to be distinguished. If the state is a religious entity, does it mean that the state rules over the Church? Or if it's a religious entity, perhaps it means that the Church rules over the state? It can go either way. When Charlemagne was crowned by the pope, he certainly indicated a conception of rulership sanctified by the Church. He was not at all worried about the pope dictating to him. He had rescued the pope from the Roman mob. The pope was utterly dependent on him. But that is not necessarily the way things would be. And Louis had less to worry about from the popes than from his own bishops. Taking his rulership as a sacred trust seriously meant that, in 822, he appeared at a place called Attigny. A-T-T-I-G-N-Y, Attigny. In the Church of Attigny, covered with ashes and dressed in sack cloth, which the Bible describes, and which, I guess, burlap would be the best modern equivalent, so dressed in rags, literally, covered with ashes to ask forgiveness for the way in which the rebellion of his nephew, Bernard, had been suppressed. Not only were his son's restless, but his nephew had rebelled, been captured, been blinded, and died. The blinding-- maybe they knew how to do it better in Byzantium-- was supposed to be a more humane alternative, rendering him unfit to rule but sparing his life. But, in the end, he died. Louis was full of remorse for this and did a public act of penance. And we know from the experience of all forms of leadership, including modern, that there are ways of saying you're sorry and ways of not saying you're sorry. The problem with a political officer or ruler saying they are sorry is that it may make them look weak. It may make them lose their aura of leadership. The problem with them not saying they're sorry, in the modern world, of course, is also very great. And it's very tricky to negotiate a line that preserves command but also gives, at least, the impression of candor. Louis does not have Charlemagne's instinctive charisma of leadership. The penance at Attigny resulted in his loss of prestige and a great increase in the power of the Church. So there had always been an implicit danger of this once Frankish and Christian ideas of rulership were merged. Charlemagne, as I've said, had no problem with this, but Louis did. Already in 829, Pope Gregory IV would claim, "is not the authority over souls, which belongs to the pope, above the imperial rule, which is of this world?" The implication here is that because the spiritual is superior to the material, in moral terms. And why is the spiritual superior to the material? This is a sort of Plato's Republic kind of question. I'm just saying this-- Yes? STUDENT: It's morality over the pressures of lust or something like that. PROFESSOR: And not merely morality over the pleasures of lust. What's the problem with the pleasures of lust, from the killjoy, Plato's Republic point of view? STUDENT: They end. PROFESSOR: They end. Right. They end. They are mortal. They die. And so is all matter, by definition. All matter fades. So which is superior, the spiritual or the material? The spiritual doesn't die. The spiritual is immortal. That's what makes it spiritual. That's what the Forms, or reality, or the higher, the invisible, invisible-but-real. To put ourselves in the mindset of 829, of course we have to admit that. You may not feel that. I'm not urging this upon you as a world view. You may think that there is no such thing as the spiritual. Or you may think that the spiritual is as mortal as the material. But in 829, people would agree, "Yeah, OK, the spiritual is superior to the material, because it's immortal and the material withers and dies." But does that mean that the spiritual has got to rule the material? That's the question for the ages, at least for the medieval ages. So Louis the Pious and his sons. In 817, Louis issues an order, map number B, to divvy up the realm in the event of his death, an order called the ordinatio imperii, the ordering of the empire. This, unlike Charlemagne's division, really expresses an idea of imperial rule. Louis associates with himself his eldest son, Lothar. And look at how big their territory is. First of all, it's huge. It encompasses the Carolingian ancestral lands. And basically, the other sons, Louis the German, Bernard, and Pepin, are given a bunch of adjunct lands. And in fact--I'm sorry. Bernard is not his son. It's his nephew. And this is what Bernard rebels against-- the rebellion that will cause his blinding and death-- is this, what he regarded as a few crumbs from the table, rather than a full share. The real problem begins, however, even after Attigny in 825 when Louis' second wife gave birth to a son named Charles, thus complicating the succession. His second wife, Judith, urged him to fit Charles into the succession, and this enraged the older sons from his first marriage. In a 829, a council met at Paris. And while Charles was given a share, the bishops of the realm also claimed a right to judge the king by his performance. In 831, a rebellion, a second or third rebellion, broke out. The sons of Louis the Pious, although fighting against each other, allied. The Church regarded Louis, now, as hopelessly ineffectual, incapable of bringing order to the realm. And Louis was captured by his sons, forced to abdicate both by the Church and by Lothar and Louis, his older sons. Lothar was so arrogant, however, that by 834 Louis had been restored. I won't go into the complexities of this. Suffice it to say that the hapless, or at least unlucky, Louis the Pious, when he died in 840, provoked another war of succession among his sons. Keep in mind that, meanwhile, the administration of the empire is dissolving, and the Viking invasions are occupying ever more attention, ineffectual attention, and plundering even more. After a series of battles and campaigns, in 843, a third partition took place. But this one is really important. This is the Treaty of Verdun, V-E-R-D-U-N. And that's the third one on your map that I have bold or, at least, felt-tipped lines showing the division. And then, on page two of the handout, on the upper part, is the division of Verdun. The Treaty of Verdun divided the empire among the three sons of Louis the Pious, three surviving sons. The western part went to Charles the Bald. And you see that in white, Neustria, Aquitaine, Spanish March. It is what can start to be called France. The eastern part, which is the darkest-- Saxony, eastern Austrasia, Alemania, Bavaria-- went to Louis son, Louis, also named Louis. Louis the German, as he's known to historians. And he's known as Louis the German in part because his sphere of influence was the East, which we can start to call Germany. The eldest son, Lothar, got the middle part, which stretches from what's now the northern part of the Netherlands, Frisia, all the way down to Rome, and even a little south of Rome, Spoleto. This is the most prestigious and, in some ways, richest part of the Empire. It has Aachen, the imperial capital, and it has Rome, the old imperial capital. It has the lands of the Carolingians, most of them, in the region of Aachen, in the region of the Low Countries, modern Belgium. What's the problem with this realm? Or what's the obvious military, political problems? Spence? STUDENT: The shape would be exceedingly hard to defend. PROFESSOR: It would be very hard to defend. It would be easy to cut off and invade. And if we say that the western part is France and we say that the eastern part is Germany, using these terms anachronistically but not inaccurately, what is the middle part? The middle part is all that part of Europe that has been fought over. All of World War I [correction: that] takes place on the Western Front. Most of it takes place in the northern part of realm of Lothar. The places where, like Belgium, which this day, now, is bitterly divided between French-speaking and Flemish-speaking. In other words, people who speak a Germanic language, descended from some ancestral Germanic language, and those who speak French, descended from Latin. That line runs right through Belgium. And the same ambiguity pursues this whole realm of Lothar's down into Switzerland, a modern polity-- well, modern, late medieval and modern-- where they speak four official languages and are so unsure about which is the official one that their stamps give the name of the country in Latin and their airline gives its name in English. Their stamps call themselves Helvetia. There has not been an entity called that, really, in real life terms, since the Roman Empire. But that's better than having all four language on there. It's more convenient. So there's a linguistic ambiguity, there's a cultural ambiguity, and there's a political ambiguity. Because, of course, the realm of Lothar didn't hold up very long. Its strategic flaw was very quickly manifested. It was divided, but never permanently. Part of this realm would be called what in French is Lorraine but in German is called Lothringen. Lothringen named after Lothar, L-O-T-H-R-I-N-G-E-N. Alsace and Lorraine, these two provinces, are now France. In 1870, they were taken by Germany. After World War I, they were taken back by France. Under Hitler, they became annexed to Germany. After World War II, they're back with France. A substantial proportion of the population of Alsace still speaks German. And until about the seventy, eighty years ago, a fairly significant proportion of Lorraine did as well. The same kind of ambiguity as to what are these territories. And in our world, they either are neither France nor Germany-- hence, Belgium, Netherlands, Switzerland-- or they've traded hands. It is not exactly accurate to say that the political, military history of Europe since 843 is simply the unwinding of the consequences of the Treaty of Verdun. But it's not completely inaccurate to say that either. That doesn't mean that events like the Reformation or the second world war don't have significance well beyond that. But just in terms of border shifting and maps of Europe, the legacy of Verdun is tremendous. If the legacy of Charlemagne is, in some sense, the creation of a cultural realm that can be referred to as Europe, the legacy of the sons of Louis the Pious is the ambiguous division of that realm. What this really means, then, in ninth century terms-- since nobody said, wow, we're signing the Treaty of Verdun. This is going to have consequences for centuries-- the immediate consequences were the decreasing relevance, the decreasing importance, of the imperial title. When Lothar died and his eldest son died soon after, Lothar's realm was divided between Louis and Charles. Then, Italy was left to a son of Lothar's called Louis the Second. He took on the imperial title. But under Charles the Bald, the third and much youngest son of Louis the Pious, for a little while the Empire was reunited. For a little while meaning, basically, two years. When Charles died in 877, the Empire would not be reestablished as unified for almost a century. And when it was, it would really consist of, basically, an enlarged Germany and a portion of Italy, not France. And Charles, although he bore, between 875 and 877, the grand title of emperor and was unchallenged within his own family, his rulership was already severely undermined by the intrigues of his nobles and the Vikings. By the time of his death, many of the counties that had originally been administrative divisions of the Empire has become almost independent. So for example, Barcelona, conquered by Louis the Pious, was now ruled after 868 by a count who paid nominal allegiance to the ruler of the western kingdom, but who was the founder of a dynasty. Up to 868, therefore, you have counts of Barcelona who are appointed by the ruler. After 868, the ruler has very little to do with it. It is a local ruler. And the count is no longer an office holder but a ruler in his own right. Similar with Aquitaine. Similar with Bavaria. Similar with Poitou, Toulouse, Flanders. The reason that the counts are able to do this is the weakness of the central power, not only because of the personality of the ruler, but because of the inadequate nature of the administration. When Charles died, he was succeeded by several rulers in the West: Louis the Stammerer, Louis the Third, who had the good fortune of just being Louis the Third; and Carloman In Germany, the ruler was Charles the Fat. And he was elected is emperor for, again, four years, but was pretty utterly ineffectual. And not because he was fat, I hasten to add. The Middle Ages did not share our prejudices in this regard. So Louis the Fat, in the twelfth century, was a very effective king. Fat or not, Charles, this particular Charles was not an effective ruler. All of these rulers, as I said, suffered the depredations of the Vikings. But once again, I want to emphasize that the problems of this empire, or the problems of these separate kingdoms, or, indeed, the problems of some of the counties ruled by independent counts but affected by the Vikings and other invaders, were internal. The Vikings were opportunistic raiders, not the cause of the dissolution of authority. The dissolution of authority didn't mean that the Carolingians come to an end. Because by this time, in the late ninth century, they have some of the prestige that the Merovingians had in their decline. In their veins flowed the blood of Charlemagne. They were a sacred dynasty. They had a certain kind of prestige. So for example, they would be kings of France, with some minor interruption, until 987. In Germany, the family ends in 911, and a new series of dynasties comes into effect. In 987, a new dynasty comes into rule of France called the Capetian dynasty, C-A-P-E-T-I-A-N, which technically runs out in 1314, fourteen but which is related to the French kings since. And indeed, when Louis the XVI was guillotined by the French Revolution, he was referred to in the court documents as "Louis Capet." In other words, they gave him a kind of artificial last name and regard him as descended from this ruler Hugh Capet, C-A-P-E-T. Thus, a member of the Capetian, C-A-P-E-T-I-A-N, dynasty. But the reality of France, and even of Germany, in the 10th century would be as a series of nearly independent principalities feuding, only nominally controlled by the kings. The ruler, Hugh Capet, who succeeded in 987, basically, he seems to have controlled the road between Paris and Orleans. But in places that are now public parks in Paris, like Vincennes, there were castles not loyal to the king at all. So my little fantasy of a fortified Cross Campus is not so far-fetched, at least not so far-fetched in terms of what really happened in places like Paris, and indeed in, for example, the city of Arles in southern France, there's a wonderfully preserved Roman stadium, Roman sports arena that was fortified. That is, one family had the bleachers and fought against the people who had the boxes behind home plate. Not a classical term, but behind what might have been considered home plate, anachronistically. And indeed, there are towers built on top of this structure that were then demolished, because they were medieval and not classical. But they made use of these materials. So we have a society in which the power of the ruler has literally dissolved. Not dissolved into water, but certainly crumble into much smaller components. Those components being, essentially, a castle, or a few castles, the territory around it, the right to exploit the peasants around it. Maybe you would have an effective regional ruler, like the count of Barcelona or the Count of Flanders, who would tie to himself these castellans, the people who own or run the castle. But it is a society that has become fragmented. It's not a barbarian society. These are not nomads. They're violent, but then again, lots of societies run on violence. It's a controlled kind of violence. They want to squeeze the peasants, even occasionally, perhaps, plunder them. They don't want to have them go away or exterminate them, because they don't have any wealth otherwise. It is an exploitative society. But that, again, is not entirely new or entirely unknown in other historical periods and places. What it does bring up, however, and which I'll try to address in our last class once we've talked about the Vikings, is what's been accomplished. Here we are, from 300 AD to the year 1000, and we're still talking about invasions. And we're still talking about polities falling apart because they're too large. We're still talking about the lack of administrative control over powerful individuals. So I promise you that something was accomplished. And I will try to describe that next time. But you're forgiven for thinking that that, perhaps, we have wandered around and not come very far. Have a very good Thanksgiving, and I'll see you soon.
The_Early_Middle_Ages_2841000_with_Paul_Freedman	10_Clovis_and_the_Franks.txt	PAUL FREEDMAN:Gregory of Tours. Here we enter further into a stranger world. As I told you at the outset of the course, it begins fairly reasonably, as if it's another history course with great powers, states, recognizable theories of government, and practices of government. Now we're into what certainly seems like a combination of thugs and miracles. And I hope that you'll see, if you haven't seen already, that far from being contradictory, thugs and miracles go together, historically. We've already entered into a somewhat strange realm with Procopius. Procopius' Secret History certainly is a strange story, with strange theories of causality and a strange cast of characters. But it is narrated in a high classical style. Insofar as the pieces are a bit jumbled, it's because it wasn't completed. But as you will have seen, if you think about Procopius, he is easy to read because he's leading you on. He has several points to make, and he makes them with great rhetorical power. His Secret History is in the classical tradition of the invective. And in a way, we are better able to understand this because our own political discourse has gotten much more crude and extreme in the last thirty years or so. So political invective, historical invective, stylistically well - composed, is not unfamiliar to us. But Gregory of Tours is. In a way, I've cheated by giving you the assignment from this edition of Alexander Murray, because he rearranges and excerpts things. The full work is much fatter, and Murray tries to make the story fairly coherent with headings, grouping things together, explaining a little what's going on, to say nothing of the nice maps and genealogical tables in the back. But that loses some of the random quality-- or seemingly random quality-- that Gregory has. He has this funny way of seeming to move from one thing to another without any kind of transition or for no apparent purpose. So in one of the little sections of Book 3 that's not in Murray, he's telling us now we have a miracle. "There lived at the city of Langres, Saint Gregory, that priest of God famed far and wide for his miracles and virtuous deeds. While I am talking about this bishop, I thought you would like me to tell you something of the town of Dijon, where he spent his youth." Well, wait a minute. Did I ask about Dijon? Do I even know where Dijon is? Weren't we talking about Theuderic and Chlothar and their feud? How have we gotten into, first of all, a story of a saint, and second, a little travelogue about Dijon? So that is Gregory. You've got to like this. And I think we are better equipped you, especially-- because we're not so linear as we used to be. You know, magazines used to be just a set of articles, and that was it. And then about twenty years ago, they started just breaking up into these miscellaneous things with little observations, and here's what's happening in Wichita Falls. But, you know, I don't live there. But so what? You know, food festival in Colorado Springs, and what about this train trip in New Zealand? Well, I'm not in New Zealand, either. You know what I mean. This kind of little offers from all over the place, little possibilities, observations, wit and wisdom. This is the experience of modern media. So I wouldn't say that Gregory is ahead of his time, but I don't want you to complain to me-- well, I mean, you can, but I will not be incredibly sympathetic with, "Wait, I don't know where this stops and begins." Or "Wait, are we responsible for Theodebert versus Theuderic?" The answer to that is "No." I'm not going to give you a short answer about which of these names is best for your cat. PROFESSOR: Or, you know, name at least five of Clovis' grandchildren. But the rhythm of this, the power of these rulers, their thuggery or their violence, their internecine violence, their respect for miracles, Gregory's sense of God's intervention, is very important to grasp. And we will talk about the actual historical importance of this people that Gregory chronicles, the Franks. The chief thing about the Franks from Gregory's point of view is that they are Catholic Christians. They never-- unlike almost all other of the invaders of the Roman Empire-- they never go through a period of Arianism. Clovis converts from paganism to regular-guy Roman Christianity. And from Clovis' point of view, that is what is of chief importance-- from Gregory's point of view. Gregory of Tours, the author, is writing in the late sixth century. So around the same time, a few decades later, perhaps, than Procopius. Gregory lived from 539 to 594. In his time, there was still a distinction between Romans and barbarians, and Gregory was very conscious of himself as a Roman. He was from a distinguished Roman senatorial family. Note that he uses the word "senatorial," a rank of the Roman Empire, even though the Roman Empire, from our point of view, certainly hasn't existed for a hundred years or so. He notes that eighteen bishops of Tours, his see-- of the eighteen bishops of Tours, all but five were related to him. That shows you that being a bishop was a Roman office, an elite Roman office, even in the barbarian period. And also you'll see that Gregory's behavior shows us that the bishops, to some extent, have inherited Roman offices and Roman responsibilities. They are part of the government, and in a sense, opposed to the more brutal aspects of Merovingian, Frankish government. Gregory became bishop of Tours in 573, and so he was bishop for twenty-one years. He probably began writing this book-- which is actually just called The Book of the Histories-- shortly after his election. So he's writing in the 570s to early 590s. He begins Book 1, which we haven't read, with the story of creation and takes it to the death of Saint Martin, the great patron of Tours. And then he begins, properly speaking, with at least the legendary history of the dynasty of the Frankish kings, the descendants of a certain Merovech, hence Merovingians, the name for this dynasty. Gregory also wrote a number of saints' lives and martyr stories. He was very attached to Saint Martin. At one point, in one of those episodes not in Murray, he says, "If you celebrate the feast of Saint Martin faithfully, you will gain the protection of the saintly bishop in this world and the next." And indeed, that's very important. Remember when Clovis-- and this is in Murray, on the page 17-- when Clovis decides he's going to attack the Visigoths? Now, he says he's attacking them because he can't stand to have Arians occupying Gaul, which is on page 16. "Then Clovis said to his men, 'I take it very badly that these Arians hold part of Gaul. With God's help, let's go and conquer them, and bring the land under His authority." And a soldier seizes hay from a poor peasant. This is just the way soldiers are. They need that hay, the civilian has the hay, they're on the march, he grabs it. But this peasant is on the lands of Saint Martin, of land belonging to Tours. And the king, thug though he is, has issued an order saying the troops were not to take anything except fodder and water. And in fact, sort of hay is fodder. Nevertheless, "the king, who quicker than it takes to say it, had him put to the sword." Guy, you've made a mistake. And he's killed. And Clovis says of this incident, "How shall there be hope of victory, if we offend the blessed Martin?" So you've got to take seriously, if you want to call it superstition, fine. But the Frankish rulers are at least amenable to influence from the priests, bishops, guardians of the saints. And notice-- because we're going to come back to this a lot. You're going to see it everywhere in the early Middle Ages, post-Roman world-- the saint is not dead. It's not like Martin is some just kind of presence, the way, you know, the happy dead who are indifferent to us. Martin is an angry saint, or potentially angry. In fact, all saints worth anything in the early Middle Ages are very touchy. If you seize hay from land belonging to their church, they'll strike you dead, or they will see to it that you die in battle. And Gregory is indeed full of incidents in which holy figures, alive or dead, have this kind of ability to mobilize supernatural power. What is his historical model? I mean if Procopius, in The Wars, models himself after Thucydides, and if in the Secret History he models himself after a tradition of invective, what is Gregory's model? We don't really know his sources. One reason why he's so important is that for an awful lot of the history of the Merovingians, he's about all we have. And although disorganized-- quote "disorganized"-- from our point of view, he's very detailed. But he does have a model, and that model is the Bible, the Hebrew Bible or the Old Testament. If you read the Old Testament, it is, as I think I've said before, full of violence and full of miracles. And they are sort of jumbled up. The hand of God is very apparent in the Bible. And generally speaking, those who disobey God are punished. The same is true in Gregory, although the hand of God is a little more mediated by those holy figures-- saints, hermits, bishops-- that we just discussed. There is a little bit more of a priestly power, but then again, the Bible has figures like Moses, who are able to-- Joshua, who's able to stop the sun. Priestly figures, indeed. So from Gregory's point of view, there is a continuity between biblical history and the history of his times. He describes, in the prologue to Book 2-- which is not in Murray-- that his plan is to describe the holy deeds of the saints and the way in which whole races of people were butchered. OK, you got a problem with that? At least the second part we all know is what history's about. It's the first that's a little tough, the holy deeds of the saints. And particularly as they're not off on the side. The popular imagination loves what might be called "holy deeds of the saints." If you look at gossip magazines of the lower sort, or kind of internet folklore, weird births, raining frogs, space aliens all sorts of supernatural events clog them. Along with stars-- that is, movie stars or media stars gossip, and a little bit of history, a little bit of current events. This is not so dissimilar, in that sense. Gregory is both a historian and a political actor. He does not have either the luxury or the irrelevance of most historians now, who sit comfortably-- or in my case, not very comfortably, since I'm in an unrenovated office-- but comfortably enough. PROFESSOR: In universities and maybe comment on what's going on. No. Gregory is very, very involved with the Merovingian rulers. And he has to display courage. He refuses to surrender fugitives who have sought asylum in his cathedral when they are demanded by royal officials. He defends his fellow bishop, Praetextatus, who was accused by the king of treason. You'll be reading about this for next week. He'll have arguments, again in your reading for next week, with the king himself about the Trinity, and has to defend himself against the charge of slandering the king's concubine-- really, here, the word "concubine" isn't quite right, because these kings are kind of polygamists-- against the king's favorite, Fredegund. And Gregory is tried for defaming her. He resists taxes. He seems to have been a small man. He suffered ill health, or at least he took an inordinate interest in his own health. He was a great believer in potions made with dust from the relics and tombs of holy men. A medicine prescribed as potio de pulvere sepulchre, a potion made from sepulcher dust. But it's got to be of the right kind of people. What is his attitude towards the Franks? I've said he regards them as thugs and barbarians. But at the same time, he regards them as the people of Israel, reborn as a race favored by God. The Franks claimed-- or at least their spokespersons, their learned spokespersons-- claimed to be descended from refugees of fallen Troy. Thus, like the Romans. In fact, we don't really know anything about them until they appear in Roman sources in the third century. We don't know what held them together. We're back to this problem of ethnogenesis. Do they speak a common language? Do they just travel in a pack together? Do they regard themselves as a people having a common ancestor? Well, we don't really know. Constantine's father, at the end of the third century, dealt with them and settled them in what's now the Low Countries, Holland and Belgium. They were federati, which you remember means allied armies of the Empire. They served the Empire actually fairly loyally in the early fourth century, and they became rich doing so. We don't really know if the supposed ancestors of Clovis-- Merovech himself, for example-- were real or legendary. Supposedly, Merovech is Clovis' grandfather. We don't know if he existed. But we do know something about his father, Chilperic. Well, it's a chalkless day, so the guy's name is Chilperic. C-H-I-L-P-E-R-I-C. We know about him because his grave was dug up in the seventeenth century. Unfortunately, all the stuff that was in his grave, most of it was stolen in 1831. But drawings had been made before that, and they show that he owned or was buried with a cloak embroidered with cicadas, a crystal globe, a gold bracelet, a Frankish amulet. His horse's--we assume it was his horse's head buried with him, and it was covered with precious metal. He was also buried with 100 gold coins and 200 silver ones. And a signet ring that shows him with long hair, and the ring is inscribed-- in case we wondered who this was-- King Chilperic. The long hair is important. It is a symbol of the power of these rulers. It is a kind of dynastic charisma. And indeed, one of the best books about these rulers, by an English historian is called Long Haired Kings. What is all this stuff? The stuff that's buried with him? A lot of it comes from Byzantium. A lot of this would have been bribes or goodwill gestures by the emperors interested in keeping some nominal loyalty on the part of the barbarian tribes in the collapse of the Western Empire. Clovis succeeded Chilperic, his father, as the head of this federated tribe of now a nonexistent empire. All that remains of the Empire is a Roman commander. Remember we mentioned, in the life of Saint Antoninus of Noricum that an emissary was sent from the Roman army to try to get paid and discovered that the Empire no longer existed. That there was nobody to pay them. Syagrius, S-Y-A-G-R-I-U-S, is a little bit like this. He's a general in northern Gaul of the Roman Empire, and now that the Roman Empire ceases to exist, he's on his own. And he is a rival for Clovis, and one of the first targets of his expansion. Gregory calls him "king of the Romans." What does that mean? Rome didn't have king's. We don't really know what title he used. We have no documents from him, no coins. Probably Byzantium, the eastern Roman Empire, didn't like him, and probably they supported Clovis. At any rate, he was killed in 486, and Clovis' next target of expansion was the Visigoths, those Arians that Gregory tells us about in the passage that I mentioned to you just a little while ago. What kind of personality does Clovis have? Have we met his type before? Is there any difference? Anybody have a sense of him? How does he strike you? Just another one of these characters of the early Middle Ages, or is there's something unusual? STUDENT: Killing off everybody, including his family members? PROFESSOR: He kills off everybody, including his family members. Yeah, yeah. This is, unfortunately, not unusual. And why? STUDENT: He doesn't want any family member to lay claim to-- PROFESSOR: Yeah, wouldn't you think he'd be dynastically conscious? Constantius, the Emperor in the fourth century, did the same thing. Only his nephews, Gallus and Julian, survived, and indeed, Julian defeated him. Is he, then, just the same kind of violent character, or randomly violent character? Is there a plan besides expansion? At least in Gregory's portrayal? STUDENT: Christianity. PROFESSOR: Sorry? STUDENT: Christianity, forcing conversion. PROFESSOR: Yeah, yeah. He is Christian. Christianity. He doesn't force conversion, but he himself converts, and his men with him. We know his piety even before the conversion, because of this incident with the silver liturgical bowl, or ewer. Right? On page seven and eight, in 227? STUDENT: The story seems dubious. PROFESSOR: The story seems dubious. The story being that they plundered this church, the Church of Rheims The bishop asks Clovis for this silver bowl to be returned. Clovis says he's got to consult his men, because they have a kind of booty splitting muster. Notice that this shows a certain leader/follower relationship, rather than absolute ruler/follower relationship. Clovis says to his men something on the order of "me hardies," or "my good men." "Me hardies" maybe is a little too pirate-like. "So," he begins. "So I want that ewer to return it to the Church in addition to my share of half." And one soldier says, "No, you get half of that, just like everything else. Takes out his axe, one of the important weapons of the Franks, and splits the silver thing in half. And Clovis doesn't do anything immediately. In a later muster, he says to the guy, recognizing him, your kit is a mess. "Your shield, you call that a shield?" And he knocks something down, and as the guy picks it up, Clovis takes up his own axe and splits the guy's head. Saying as he does so, "Thus you did to my ewer, or my basin, in Soissons." Yeah, dubious story, but interesting because it shows both the power of the ruler and some limitations, as well as his type of piety. Power-- actually, you know, the president of the United States actually does have the power to kill people. We've seen it in action. Though at a distance and under certain, very special circumstances. But basically, it takes a certain kind of ruler to be able to kill someone outright like that. It still happens, but we're talking about people like Qaddafi or despots. So certainly, as with killing the guy who stole the hay from Saint Martin's land, Clovis is following a certain set of leadership tips that basically amounts to winning by maximum intimidation, I think it's fair to say. But he's got to do this in a careful way, because his followers are very important. They are powerful. He does depend on them, and he's got to give at least the impression of being the leader of a band and not the kind of ruler of the state that we might be more familiar with. Leadership is personal but there's a kind of tribal sense, or tribal sense of democracy. The other thing about the story, of course, is once again the controversy is over piety towards things of the Church, even before Clovis has, at least according to Gregory, officially converted. It's not that you should be nice to the Church because it's good to be a nice person. It's that you've got to be nice to the Church because the Church is in command of supernatural weapons that will overcome the weapons of this world. The supernatural interpenetrates the physical or historical at every point in Gregory's narrative. So the overwhelming fact for Gregory, as I said before, is that he is orthodox, or Catholic i.e., not Arian. Clovis is, in Gregory's eyes, the new Constantine. Someone who has miraculously been turned, thuggish though he is-- and Constantine was, as well-- to advance God's work. Of course, Gregory regards him as a barbarian, and he shows him as a barbarian. He portrays him honestly, or at least unflatteringly. As was said, he murdered his family. And then moreover, if you remember on pages 19 and 20, he pretends to be really sorry that he can't find anybody that he's related to. He's searching findmyfamily.com for a genealogy or high school classmates. Anybody who could be his friend. But in fact, he is just searching them out to kill them. And he's got all sorts of tricks to kill his relatives. Nevertheless, in the same chapter that describes his trick on Cloderic, Gregory tells us, "Having aquired the kingdom of Sigibert and its treasury, he also received those people under his dominion. For daily the Lord laid his enemies low under his hand and increased his kingdom, because he walked before Him with an upright heart and did what was pleasing in His sight." Right? This is just after Clovis, after the death of Sigibert, calls all the people together, says, "I don't know what happened, but the sons of Sigibert seem to have died as they were showing my envoy's treasure. Here's my proposal, make me king." And they say, "Oh, OK. Great, yeah. Step on the shield and we'll lift you up, just like the Roman emperors." Is Gregory a comedian? Or is he saying-- and I think this is more likely, although he is hilarious to read. I mean, I hope he's amused you. I hope while you were cursing me for giving you this assignment, or at least praying to some saints to strike me dumb or erupt in boils or probably not anything very strong, like you'll notice that occasionally people lose their intestines when they go to the bathroom. Probably not. The heretic Arias, for example, and others who betray the saints. Anyway, whatever curses you were summoning up to me, I hope you actually found this fun. This course is fun, as I think I told you way back in the beginning of September. So apart from the fun angle, people are instruments of the Lord, and they walk in the sight of the Lord even if they are not themselves good people. The Lord makes use of instruments, of people who are forceful. It's important to be forceful. If Clovis was a nice guy-- and we'll see, and have already seen some examples of rulers who were nice, often intellectual, and ineffectual. Gregory prefers effectual with some violent touches to ineffectual, because being a ruler is a hard job in a barbarian world, in a fallen world. Gregory, in this sense, is like Augustine. The world has fallen. The world is corrupt. There are no good people in power. And if they are in power, it is either unusual or they're not going to be in power for long. Therefore, it is important to be violent. It is important to be able to intimidate your troops. It is important to seek out those who would oppose you. And if they've got to be killed, they've got to be killed. The reason for this is that the work of the Lord has to be advanced, according to Gregory, and the Church has to be protected. For Gregory is exemplifying what I said would happen as predicted by Saint Augustine. The Empire might cease, but the Church would not. The Church would deal with whatever successors came up, be they Arian, or preferably not. Be they cultivated, or more likely barbarian. And as barbarian leaders go, Clovis and his sons were not so bad. We're not really sure how Clovis converted. Because Gregory is invested in a story that likens Clovis to Constantine, we have the same kind of thing. Before a battle, he makes a deal with God that if he wins the battle, he will convert. We don't really know if he was converted before this battle in 494, as Gregory reports, or maybe in a battle against the Visigoths in 506. But it doesn't really matter. It's very important that the Arians be defeated. He's got a story that's not in Murray, in Book 2, Chapter 23, in which an Arian bishop named Cryola. C-R-Y-O-L-A. Cryola, not crayola. Cryola. Cryola is angry because he sees the Catholic bishops performing miracles all over the place. So he pays a guy to pretend to be blind, and then to greet him as he comes to Church, and beg him to heal his sight, and then to say, "Oh my gosh, I've been healed. I can see. But God punishes this by making him actually blind, at this point. And then the guy, very helpfully from the Catholic point of view, said oh, I wasn't blind. This evil bishop, Cryola, bribed me in order to pretend to be blind, but now God and his saints, Saint Martin in particular, have punished me." And so that it takes a Catholic bishop to heal him back to sight. So this is Gregory's attitudes towards the Arians. On the other hand, he does report that the Franks besieged Saragossa. This is on pages 41, 42. The Spanish city of Saragossa. They've gotten that far in their attacks on the Visigoths. But the Arians were able to fight them off. "They circled the walls carrying the tunic of Saint Vincent and singing psalms. With the women dressed in black, their hair hanging loose, covered in ashes, lamented. Seeing the situation, Theodebert returned. He gave up the siege." The Arians may be heretics, but they've got the tunic of Saint Vincent. And the power of that relic is so great that even in the hands of miscreants, it's not to be opposed. Saint Vincent, a very important saint and the patron of Saragossa. So the Arians are fakes, but they are not completely without spiritual power, either. And this is a kind of universe in which there are natural and supernatural forces. And it's not that one trumps the other, exactly, but that they both have to be taken into account. So, Clovis consolidates a large kingdom in most of what would become France. Roman Gaul, medieval France. France named after this group, the Franks. The Visigoths now were pushed out into Spain and just that part of France bordering on Spain. Clovis received the favor of the Church because he was Catholic. His conversion, let's say around 500, is ninety years before the Visigoths become Catholic. And this aids him greatly, because the Church is in possession of learned people, financial resources, and spiritual power. So we follow the Franks-- and we will follow them up through Charlemagne and his successors-- because they are successful, and because their own self-consciousness is as the rightful rulers of the former Western Empire. A claim that in various generations is more or less of a reality and that is by no means inevitable, but is something that they will eventually make good on. For the time being, Clovis considers himself a representative of the Byzantine Empire, but a representative who very conveniently doesn't have to do anything. The Byzantine Emperor sends him the title of consul. He's very pleased at this, but it doesn't bind him, really. So much for Clovis. Establishment of Frankish hegemony. The prominence of the Franks in the post-Roman West. The first Catholic people among the barbarian invaders. Now we turn briefly to his sons. He divided his kingdom equally, and you have a map in the back that shows the division of the realm under Clovis' sons. Chlothar, Childebert, Chlodomer, and Theuderic. This practice of division is dangerous. It is usually a better idea to give it to one son, because then you don't divide the kingdom. On the other hand, if you have four sons who are all militarily competent, they're going to fight with each other. And in fact they fight with each other, as Gregory describes in Book 3, even though they've been given divisions. The violence of Clovis' sons is crude and even ludicrous. So for example, this awful incident of Chlodomer's sons being protected by Clovis' queen Chlothild And her sons, the boys' uncles, Chlothar and Theodoric, invite the boys to come for a visit. And Clotilde, who seems rather credulous, says, "Great idea!" Once they are in the power of these two brothers, who of course like Clovis want to kill their relatives, particularly their younger relatives, they send a sword and a pair of scissors, right? "Which will it be," the messenger asks the queen. "Cut off their hair or kill them?" Cutting off their hair will symbolize that they're no longer eligible for rulership. And it may lead to them being put away in a monastery or something like that, but they're taking early retirement. They're twelve, fourteen years old, but they've had it. And Chlothild is so angry, at least according to Gregory, that he says she'd rather see them die. And then they kill them. They kill them in this ludicrous way, because one of them gets cold feet, and the other is furious and takes up the sword, and just kills them. Even though they're begging. I mean, it's a rather gruesome scene. Meanwhile, in a scene that we haven't got in Murray's edition, Theuderic attempts to kill Chlothar. He invites him, and he's got men waiting to ambush him, but the cloth isn't low enough down. They're sort of behind a partition, a cloth partition, but Chlothar can see their feet. And so he kind of turns back and starts to walk out of the hall. And then Theuderic says, "No, no, no, I just invited you to give you a gift." And he gives him a silver goblet or something like that. So, Chlothar escapes from this, but Theuderic is so angry at having been tricked that he then sends a messenger saying it was a mistake to give back the goblet. So, I mean, these guys, what can I say? Yet beneath the barbarian acts is a society that is still being governed fairly closely. There is a fairly sophisticated administration still. There's a gold coinage, which takes a lot of resources to maintain. These rulers are collecting taxes, and they are collecting taxes according to written records. There's public land. There's revenue from land belonging to the king. The kings are reasonably conscientious about the appointment of bishops. What is Gregory's attitude towards these sons of Clovis? He certainly portrays them as fratricidal. Nevertheless, on page 26, he tells us that the brothers were endowed with great courage and had considerable military resources. Once again, their power is directed more for good than for bad. And a lot of their power for bad is merely directed at each other. He considers them, in other words, appropriate rulers for savage times. At one point, two of the brothers make war against a third. Specifically, Childebert and Theuderic against Chlothar. Chlothar is the guy who has just been depicted by Gregory as the tough one, the one who killed the two nephews. He's also an adulterer. And yet, faced with his brother's armies, he prays to God. And his mother, Queen Chlothild, prays to Saint Martin. So powerful are these prayers that the two brothers are unsuccessful. A hailstorm pelts their troops, spares Chlothar, and Chlothar is victorious. The brothers do not succeed in dislodging him. Here then, we have the power of the Merovingians and the limitations on that power. The limitations are partly military, partly that of fratricidal intrigue, of people getting killed. But they're also partly supernatural. And as you read further into the grandsons of Clovis, people whom Gregory himself has dealings with, particularly the wayward Chilperic, you'll see rulers that Gregory considers to be evil and rulers who are really falling away from the example. But what interests us in our readings for next week is the nature of this society. What's holding it together if it's rulers are so violent? Why is it not just falling apart into fragments and shattering? How could this dynasty rule over a polity for something on the order of 250 years? Have fun with the papers, have fun with Gregory, and we'll talk next week. Thanks.
The_Early_Middle_Ages_2841000_with_Paul_Freedman	17_The_Early_Middle_Ages_2841000_The_Crucial_Seventh_Century.txt	PAUL FREEDMAN: So we had talked about the mathematical researches of the Arabs combining Persian, Greek, and Indian mathematics and, of course, with contributions of their own. So that the enumeration, the use of zero are from India, but the development of algebra is a unique contribution of this period and of these people. Let's talk briefly about geography. Remember the chapter in Wickham opens with the contemptuous description of Palermo by the tenth century geographer, Ibn Hawqal, H-A-W-Q-A-L. And the point of that is not Palermo or anything like that, but just the fascination that the Muslim world had for travel, for geography. Geography both of a quantitative kind-- measuring, navigation, figuring out to get from place to place-- and of a kind of curiosities of the world kind, of different customs, different peoples, different products. So these geographers were employed by the caliphs, for example, to figure out the circumference of the world, to figure out the relationship between land and water in the world. This is an interesting form of speculation. If you look at Christian maps of the world up to 1300 or so, they show almost no oceans, It's all huge amounts of land mass. This is partly, it's thought, an interpretation of something in one of the apocryphal books of the Bible that seems to suggest that seven-eighths of the world is land. Ptolemy, whom we spoke about last time, the Greek geographer, author of this book known as the Almagest or Geography, translated into Arabic as one of the first projects of this House of Wisdom in Baghdad. Ptolemy has a different picture. And Ptolemy is the first geographer received in the medieval period to suggest that there's an awful lot of water. And that you could get around much of the world by water. Although crucially, Ptolemy does not think that you can go around Africa. Ptolemy has a kind of Antarctic land mass that connects with Africa. And it was only the Portuguese at the end of the fifteenth century-- specifically in 1498, well really, 1489-- who demonstrated that you could go around Africa, and thus from the Atlantic Ocean into the Indian Ocean. Crucial, crucial discovery. But this question of how much water is there versus how much land is there-- a sense of the entire world-- is a problem investigated by these geographers. Many of these guys are indefatigable travelers. So there's this book by Al-Muqaddasi, M-U-Q-A-D-D, usually known in English as the Best Division for Knowledge of the Regions. Completed in 985 after twenty years of traveling. But the greatest traveler of the Islamic premodern world was Ibn Khaldun, who is much later but worth at least mentioning here, 1332 to 1406. And he started from his native Tunis and traveled as far as China and Indonesia. And then, finally, a scholar named al-Idrisi, another one of these travelers, geographers, was hired by the Christian king of Sicily, Roger the Second, in 1138 to put together a map of the world with accompanying descriptive texts. And it is an aspect both of the respect accorded to the Arab geographers in the Christian world, and the fact that despite our tendency to see these two worlds as opposed-- after all 1138 is the era of the Crusades-- there's quite a fair amount of collaboration, interchange of knowledge between the Christian kingdoms of Europe, and the Islamic world-- the Islamic kingdoms-- of the Southern Mediterranean and the Middle East. Finally, medicine. We're not exhausting the subject studied by the Arabs, but I wanted to give you math, geography, and medicine as three examples. The main authority for the Arabs, the person that they translated with the most assiduity and interest, was Galen, G-A-L-E-N, a physician who wrote in Greek at the time of the Roman Empire. And Galen is the person who is responsible for the transmission, if not invention, of the notion of the four bodily humors. This model of physiology dominated medicine until the eighteenth century, let's say. This is the notion that within human beings there are these four fluids that are essential building blocks of character and of health. They are both mental and physical factors in health or in illness. And they correspond both to the four elements-- the four basic things out of which the world is built according to Greek science-- and to the interaction of the corresponding four climates or four tendencies. So the four elements: earth, air, fire, and water. These climates or tendencies are hot, dry, moist-- hot, dry, moist, cold-- right. Hot, cold, moist, dry. And the four humors-- these are liquids that are inside our bodies-- are bile or yellow bile, which corresponds to fire, which is hot and dry. Blood, which corresponds to the element of air, and is hot and wet. Phlegm, mucus, P-H-L-E-G-M, which corresponds to water, and is cold and wet. And, finally, black bile, which is earth, and cold and dry. Key to this idea of the humors is the notion of balance or equilibrium. And in this it resembles Chinese medicine, Indian Ayurvedic medicine, and indeed, at least conceptually, notions that people have of their own bodies. That the experience of illness or of mental distress is one of imbalance, of the predominance of one element over another. So the healthy body is in a state of equilibrium, while disease is part of a fluctuation due to imbalance. But people are never completely balanced, at least not for long. Everybody has some, what's called temperament. A "temperament" is a favoring of one of these humors. So and we still use these terms without particularly being interested in their origins. So melancholia, or the melancholic temperament, which is associated with sadness, lethargy, what would be medicalized now as depression, is from a predominance of black bile. Melan-- black. Cholar-- bile. In Greek, melancholia. There's the choleric temperament, people who tend to be angry, irritable. And this is from regular or yellow bile, predominance of that. Or sanguine: sort of more optimistic, more risk taking. Predominance of blood, the sanguinary humor. This is the basis of an awful lot of medical theory of physiology, of understanding of disease and its treatment, as well as its prevention through things like diet. There are lots and lots of medical writings and doctors in the Islamic world. The most famous is known in the West as Avicenna, Ibn Sina, 980 to 1037. He is a Persian, active in Persia. And he, like many of these doctors, was not just a physician, but a musicologist and a philosopher. He wrote medical writings on physiology, diagnosis, treatment, and medication. His work was translated into Latin and known in the West as the Cannon. The Cannon of Avicenna was the standard work taught in medical schools until the seventeenth, eighteenth century. Again, I wouldn't say that I would be desperate to be alive in the eleventh century in order to have better medical care. There is no--the humors don't really work; it's not scientifically true, but so what? We are interested in the world views in aspects of how people look at things. Certainly, many aspects of this medical care were superior to what was available elsewhere. It was based on observation. The observation obviously couldn't be MRIs or CAT scans. The observation, however, was much closer than that even undertaken by the Greeks. An awful lot of what might be learned of disease was through urine. And the examination of the urine is almost somewhat the symbol of being a doctor, that in some Western illustrations of medicine you know that the person is a doctor because he's holding up this little flask and examining its properties. So, again, you weren't supposed to-- in some societies-- cut up bodies for autopsies. We all know things like the circulation of the blood, the role the heart in that were not properly understood for many centuries later. But this is the most elaborate and successful model of medicine and practice of medicine in the civilized world at this time. So this is a splendid civilization. I hope I've given you some slight indication of that. Why does it collapse? This is partly a question of why does any civilization collapse. Time tends to ruin everything. The Abbasids were victims of the same divisive tendencies we've already seen at work within the Islamic world right from the beginning. Religious strife, particularly but not exclusively the Sunni/Shi'ite division. Dynastic, that is to say, internal or familial problems. Resentment at taxation. In the beginning, as we said, the Islamic conquerors taxed rather lightly. But as the ability to rely on confiscated estates of nobles, the Church and the state faded as the Abbasids became the state. Like all states, they started to run out of money. They had a large army, they had a large court, they had a large administrative structure to maintain. And then, as now, people tend, rightly or wrongly, not to appreciate the role of government in everything, and to be resentful of having to pay for it. The fundamental problem, as Wickham points out, is that the Empire was too big. And here, we're back where we started with the Roman Empire. Empires tend to fall because they are too big. And being too big they tend to overreach. In other words, they're already big and they try, if not to get bigger, at least to deal with more enemies. Because as you get bigger you develop more enemies. And as you get bigger you also develop more fears of external enemies. So to say that the Empire was too big is not to say anything very innovative or unusual. The real question is why does there come a point at which this bigness is fatal? In other words, the Abbasid Caliphate does fine from 750 to 910 and then it falls apart. Why does it fall apart when it does? And I don't have a great answer for that, except to point to the other divisions, or to misfortune: having poor Caliphs, having Caliphs who don't last for a long time and are overthrown. Nevertheless, states start to split off from the Caliphate. The first, right from the beginning, is Umayyad Spain. And Wickham talks a little bit about the civilization of Umayyad Spain. But you start to have the splitting of places like Egypt, under the Shi'ite Dynasty the Fatimids by the tenth century. What's interesting is that these societies are run very much like the Abbasid Caliphate. Although they are large, they are more practical, compact, and somewhat easier to hold together. They have the same kind of cultural efflorescence, scientific curiosity, sensuality of culture, luxury products. Indeed, Umayyad Spain would have the reputation of the height of civilization in Christian Europe of the tenth century. A nun writing from a German monastery in the tenth century named Hroswitha, Hroswitha of Gandersheim, describes Cordoba, capital of Umayyad Spain, the largest city in Europe-- excluding Constantinople, the largest city in Western Europe at this time-- she describes Cordoba as "the ornament of the world". She had never visited it. She's a cloistered nun in a monastery in Germany. Nevertheless, for her this is the most splendid place in the world. Splendid in terms of wealth, population, culture, learning. And Ornament of the World is the title of a book by our colleague in the Spanish department, Maria Menocal, written about ten years ago, describing medieval Spain and its civilization. Cordoba would be a center for learning among Christians, Jews, and Muslims. So this series of cultural accomplishments by the Arabs, as I said, may come as a surprise, but it should not be. The surprise element may be, as we've said now more than once, the ability of the Arabs to assimilate other traditions and to remain as conquerors. That is, these two things are related. They remain as conquerors even though the Caliphate does not survive. The Arabs are still the dominant force in Egypt, North Africa, and much of the Middle East. And where they are not dominant, Islam remains the dominant faith of places like Persia, modern Iran, and further east. So just because the Caliphate falls does not mean that Islam loses power and it doesn't mean that the civilization of Islam fails. At least not at this point. I hope then we can see that Islam is a thing in itself, a historical force in itself, developed in our period, but also to some extent an heir to the Roman Empire. Remember I said that there are three heirs to the Roman Empire-- the Byzantine or Eastern Roman Empire, most obviously the Western kingdoms-- and when we come to Charlemagne next week we'll be talking about this much more aggressively-- and the Islamic world. It's also, however, the heir to some other cultures. It's the heir to Sassanian or Persian culture, for example. So it is not exclusively to be understood as a successor to the Roman Empire, but then again, neither is the west of Europe and there is Byzantium. And those are the things that we're going to be discussing in the future. So any observations thus far, or problems thus far? The Islamic world, these three lectures clear is as can be? Imprinted in your mind like the Seal of the Prophets? OK. So what about the seventh century? Now we're backtracking a little. Because with the Abbasids we'd gotten up as far as the tenth century. I want to go back to the seventh century because it's the crucial turning point of the early Middle Ages. Even though we're in the tenth week of this course-- is that right?-- here we are at its hinge, I think. Or at least we can get the lay of the land. This is a little bit like approaching a shoreline which you see very vaguely, and then suddenly actually you can start to see the houses and see which are the mountains that are far way, and which are the hills that are in the harbor, and so forth and so on. So I hope that--I mean, the course differs from many other history courses in that beyond just the fall of the Roman Empire, you don't have an instinctive feel for what this course is about, what its contours are. So what I'm trying to do is not just point to a turning in the road, but I'm trying to show you the road itself through the proverbial forest and the trees. OK? Partly what we're concerned with is periodization. Now what are the time periods? Is the classical world and then the medieval world? Is it something called the classical world on intermediate period called Late Antiquity and then the Middle Ages? What does the course title, "The Early Middle Ages," mean when its successor is called "The Birth of Europe"? We're going to change that, by the way, maybe we're going to combine these into one course called the Middle Ages, but that's for the future. So periodization. And then when are we talking about as the borders of these periods? It's a murky period that covered by this course, roughly 284 to 1000 or Diocletian to the year 1000. Murky but important, as I hope you see already. The development of such absolutely fundamental world historic things as state-sponsored Christianity, Islam, the ideas of political power in Europe as nations as opposed to the universal Roman Empire. All of these things take shape in our period. The traditional periodization concentrated on the fall of the Roman Empire. And while everybody admitted this was somewhat of an arbitrary date, and indeed its origins and consequences in Gibbon's Decline and Fall of the Roman Empire extend to the second century AD and go on to the fall of Constantinople in the fifteenth century, nevertheless, 476, the deposition of the last Roman emperor ruling from Ravenna by the barbarian chieftain Odoacer, who then proclaims Italy to be part of the Eastern Roman Empire, or at least loyal to the Eastern Roman Empire, that loyalty largely a fiction. In the traditional periodization 476 is then followed by something called the Dark Ages. And the Dark Ages end, depending on your point of view, with the growth of the European economy in the tenth or eleventh century, with the rediscovery of Latin classical culture in the twelfth century, or with the Italian Renaissance in the fifteenth century. Certainly, the Renaissance artists regarded everything that came before them as the Dark Ages. And it is they who call medieval architecture "Gothic", by which they don't mean a complimentary term. Because if there's one thing the Cathedral of Notre Dame in Paris is not, it's not Gothic in the literal sense. It has nothing to do with the Visigoths or the Ostrogoths. We have a few little remnants of Visigothic and Ostrogothic architecture, and it's not like that at all. But for Vasari and people like this-- Italian Renaissance writers-- all this was just junk. It was just junk of the past. It's just the Dark Ages. The sun rose in Florence sometime after Dante, is what most people continue to believe. And as a medievalist I long ago gave up fighting this and embraced it. The Dark Ages are cool. I know Halloween is over but, nevertheless, we all know that the Middle Ages is far more fun than the Renaissance. Who wants proportion and logic and severe classical lines, when you can have gargoyles and weird stuff? I'm preaching to the converted, right? You're in this class. If you didn't like weirdness, you'd be taking well, what would you be taking? I think I'll just leave that. We're not in competition in this department. So I'm trying to argue that this period is more than just a long nap for people just waiting for something like the Italian Renaissance. There is this book that is on the cutting edge of scholarship of this period that is called The Long Morning of the Early Middle Ages, which I think is not a felicitous title, much as I admire the people who put this together who are at another university not all that different from this one. By "long morning" they don't mean brunch. That's what I would have called it, The Long Brunch of the Early Middle Ages. People enjoying eggs Benedict on the smoldering ruins of the Roman Empire-- eggs Benedict, right? The Benedictine Rule. [LAUGHTER] OK. OK. So we've seen that 476 is not a cataclysmic turning point. OK. It's not a cataclysmic turning point because, first of all, the Roman Empire survives in the East as we've said. [LAUGHTER] So I think we should turn this off for just a minute or two if you don't mind. Why the seventh century, seriously? It is a better claim to the status as pivot for this roughly 700 year period than 476. It is in some sense the end of the classical world. It is in some sense the end of whatever we want to call this, Late Antiquity. This is for basically four reasons. One, and the most obvious, is the rise of Islam. The rise of Islam and its consequences. The breaking apart of the Mediterranean into different regions. Although I've stressed the ties between Islam, Greece, Persia, between the northern and the southern Mediterranean, between Islamic Spain and Christian Spain, nevertheless, the conquest of the Arabs in the seventh century and the early eighth century create somewhat of a break up of what had been a united Mediterranean under the Romans. They're different religious, cultural, and trades zones. Under the Romans, North Africa and Italy had been really very close together. Had much more in common with each other than say Italy and Northern Gaul or Britain. Augustine sails between North Africa and Italy all the time. They're quite close. But we think of them as being far away because in the modern world, and indeed since the Islamic conquests, they've been culturally and economically very different. So this breaking up of the Mediterranean creates-- and I'll elaborate on this in a moment-- doesn't create the birth of Europe exactly, but it creates Europe as a kind of separate region. Naturally, from the geographical point of view, Europe has always existed as a continent. But here we have the beginning of the distinction between Europe and Asia and Africa without the kinds of close ties that we've seen connected the Mediterranean, the two shores of the Mediterranean, which mainly because they're different continents and, indeed, the third shore of the Mediterranean in the East, technically in Asia. Now these start to fall into different cultural and political realms. So the first aspect of the seventh century is this breakup of Mediterranean unity, the breakup of this aspect of the Roman legacy. And if I've emphasized that there are three heirs to the Roman Empire, the fact that there are three heirs to one fortune shows that they are distinct. Second, and related to this, the rise of Northern Europe. What had been peripheral in the Roman Empire starts to become much more central. And when we come to Charlemagne you'll see this. Around 800-- well, 800 exactly-- is the year in which Charlemagne is crowned Roman emperor in Rome itself by the Pope as it turns out. But already, this importance of Northern Europe is evident in some things we've been talking about. The Irish missionaries, for example. The role of Ireland in preserving knowledge and in diffusing Christianity. The role of Britain. The fact that, as I said, Britain at the time of Bede, was the most cultivated heir to the Latin learning of the Roman Empire. And the fact that this should be true in the eighth century shows some kind of difference, some kind of change, since in the Roman Empire these had been peripheral areas. The further north you went, the further away from the Mediterranean, the less civilized the society was. The third aspect of this turning point, a third way in which we have a kind of shift, is the crisis and reshaping of the Byzantine Empire. The loss of Egypt to North Africa, Palestine, and Syria, which take place in the seventh century. And we'll talk about this more next week. But the decline of the cities of the Byzantine Empire, the militarization of society in the Byzantine Empire. In fact, the seventh century is the era of the Byzantine Empire that most resembles the fifth century for the Western Roman Empire. If we preserve the term "Dark Ages" reluctantly, the West goes into a period of what Wickham calls "radical simplification of material culture." That is to say people become poorer and less in contact with the wider world. And this happens in Byzantium in the seventh century. So it's not that the Eastern empire survives completely intact, but that its collapse is later than that of the Western empire. But crucially, again as we will see, that collapse is not total. It's not as complete as that of the West. The Byzantine Empire would just barely survive the seventh and eighth centuries, and by the ninth century enter into a period of efflorescence that we will be describing. But this society is not really Roman anymore on some fundamental level-- fundamental level including control of Rome and Italy. The basis of the Byzantine Empire will be Anatolia, that is Asiatic Turkey and the Balkans, modern Romania, Bulgaria, Greece, Albania, Croatia, Serbia, and so forth. Constans II, Byzantine emperor from 652 to 668, leaves Constantinople after the first Muslim siege intent on creating a new capital in the West because Constantinople is too vulnerable. In other words, he envisages a Eastern Roman Empire, but with its capital in Sicily. He moves his capital eventually to Syracuse, Siracusa in modern Sicily. He's the last emperor to visit Rome. Well, the last eastern Roman emperor actually to put in an appearance in Rome. As I've said, these emperors would call themselves the Roman emperor until the day the Turks penetrated the walls of Constantinople in 1453. But they weren't really emperors of Rome in the sense of control over the city of Rome after 664, the last visit of an emperor to Rome. And then four years later he was murdered in Syracuse. Well, the fact that the emperor is murdered is not all that unusual. A lot of these emperors get murdered, get their noses cut off in lieu of murder. The notion being that if you're mutilated you can't be an emperor again. And then one of these emperors as we'll-- again, we'll discuss this-- comes back even though his nose is gone. But what this means is the end of this experiment in moving the seat of the Empire. It moves back to Constantinople. And Constantinople, for better or worse-- and surprisingly, a lot for better-- remains the capital of this powerful, if limited, empire. The seventh century, however, should not be seen as a time when these realms are completely isolated from each other. The Islamic, the Eastern, the Western. It is still possible to travel. And, indeed, Brown emphasizes this. The archbishop of Canterbury in the end of the seventh century, Theodore, came from Tarsus in Anatolia, Syria. Many of the popes of this era were of Syriac or Greek origin. This starts to fade, however, as Islam takes control over more and more of the former Eastern Roman Empire. So not only do you get a diminution in communication and cultural exchange between the Islamic world now as it is and the Christian world, you get less between East and West. In the West people no longer tend to know Greek outside of Rome and the papacy. And by the eighth century, even in Rome, this knowledge is much, much diminished. And then the reorientation of Persia. It's no accident that Brown begins the chapter that you've read with a discussion of Persia. And, actually, we hear more about Persia now in this reading than in any other single reading for the course. And this is not just because of the Islamic conquest. Part of it is Persia's, modern Iran's position. It's modern Iran, but it's also modern Iraq. The capital of Persia is in what is now Iraq, in the more fertile part of the former Persian empire, that is to say the West, what is known in the ancient world as Mesopotamia. So Persia could be oriented towards Mesopotamia or could be oriented more towards the East, towards India ultimately. And this is partly for extraneous reasons. The rise of these people called the White Huns who press Persia from the East and take over modern Afghanistan and even what's now Eastern Iran. Persia has been a kind of off stage presence in this course. But in terms of trade, there had been a great deal of interaction. Trade and culture. The Silk Road. Traffic in spices. There have been a tremendous traffic in religious ideas, as well. Nestorianism becomes strong in Persia, the heresy of the fifth century. Manicheanism, which we discussed in relation to Augustine comes from Persia. A lot of apocalyptic thinking in both Islam and in Christianity. The focus on the end of the world and what God has planned for sinners and for the justified, comes from Persia, as well. Now, however, in the seventh century and the eighth century start to see a hardening of the boundaries. Western Europe is less in contact with the East. It's less in contact with Byzantium, with which it has religious disputes. And it is out of contact with these influences coming from the East from as far as Persia, that characterized the period that we began with and up to now. And this is reflected in the changing of the center of gravity of the Caliphate that we alluded to last time. The move from Damascus to Baghdad is not only a strategic decision or a cultural decision, but it's a de-Mediterraneanizing of Islam. Its capital is now within the former Persian Empire. And if it doesn't mean a Persianization of the Caliphate, it certainly means that Islam is not really a Mediterranean religion and certainly not exclusively. And then, finally, in the West the seventh century sees the end of a secular elite. When we began this course we talked about the Roman Empire as characterized by a civilian or senatorial elite of wealthy people of cultivation, who are not only literate but who are scholarly and artistically inclined. These people are gone by the seventh century. In their place is a smaller and somewhat different elite, at least elite understood by learning, of clergy. It's at this point that monasteries and churches become the repository of the classical legacy and are run by the almost sole literate people in society. So how do we put these things together, these phenomena together? One way of doing this that was very popular in the mid-twentieth century was what was known as the "Pirenne thesis", named after the great Belgian historian Henri Pirenne, who was active in the teens, twenties of the twentieth century. Henri Pirenne, the Pirenne thesis. And the Pirenne thesis goes like this: The Roman Empire did not fall in 476. It continued, if not as a political entity, as a sociocultural and most especially, economic entity. Because the Mediterranean and Mediterranean unity were what characterized the Roman Empire from the start, and this was not disrupted by the barbarians. Mediterranean trade continued to exist. Gold coinage continued to exist. What ended them was not the collapse of the Empire in the West, but Islam. That the Arab invasions cut off the different pieces of the Mediterranean and ended Mediterranean trade. And with the end of the Mediterranean as this key entrepot, or economic heartland, new centers were created, particularly Northern Europe. The rise of Northern Europe that I mentioned here was most obvious in the ascent of Charlemagne. Charlemagne, crowned emperor in Rome in 800, was by no means from Rome or Italy, but was from the Frankish realm. The lands of his family were in what is now Belgium, Western Germany, the Netherlands, and Northeastern France. His capital was not Rome. He went there to be crowned. His capital was rather in Aachen, a city that is in Germany but only barely. It's very close to the Dutch border. Very close to Belgium, as well. Very close to Luxembourg. And quite close to France. He is a representative then of Northern Europe. Aachen had been known to the Romans because it has hot baths, and that's why Charlemagne chose it also: natural hot springs. But it is not part of the olive oil and wine-growing regions of the Mediterranean that we saw were what the Romans loved, and what they considered to be civilization. For Pirenne then, the rise of Charlemagne is made possible by Mohammed. And, indeed, his master work was called Mohammed and Charlemagne. Here, the periodization is definitely Islam. Islam creates Europe because Europe is the antithesis to the world created by Islam. Pirenne had no ideological opposition to Islam. For him Islam is simply a facilitating factor in destroying the ancient world. And by ancient world, he means the Mediterranean. Well, this is one of those elegant theories that has been disproven. It's been disproven largely by archaeology, which has shown that there's lots of trade in the Mediterranean. That the arrival of Islam by no means disrupted trade, by no means disrupted these contacts. But it is true-- and I've just said or emphasized-- that beginning with Islam, beginning with the seventh century, there is a drifting apart of cultural and political realms. We can start to identify three different civilizations. And next week we're going to talk about the flowering of Byzantium, that is the height of this Eastern Roman Empire in terms of its political military power. And then we're going to come to Charlemagne and try to see what this landscape of the development of something other than mere barbarian post-Roman successor states means for the West. OK. It's been a lot of fun. 721 00:45:14,600 --> 00:00:00,000 Thanks.
The_Early_Middle_Ages_2841000_with_Paul_Freedman	07_Barbarian_Kingdoms.txt	PAUL FREEDMAN: So last time we spoke about the collapse of the Roman Empire. And I didn't quite definitively answer the question: External force - Internal collapse? There are other possible explanations: an eminent historian of the barbarian says that the Roman Empire committed suicide by accident. That essentially it was just a political problem. The wrong people became emperors. Some bad things happened and one day there it was, it was gone. I'm not sure I buy that; I like long-term causes more. But it is important to emphasize that a lot of this is contingency and not inevitability. Historians generally tend to make things look as if they had to happen. As if there's sort of long-term things playing out inevitably. And the longer or the farther away the historian is from the period that he or she is studying, the greater that tendency because the look back is longer. So in talking about both the Empire and the barbarians, I want to at least remind you that events could have gone other ways. There are lots of long-term tendencies, but we're talking about a series of factors that are both immediate and long term. This is relevant to talking about the barbarians and who they are. Which is more of a mystery than it might seem. Who they are as in, what does it mean to say that someone is a Visigoth? How much have I described what that means? And despite the business about plunder, that's not actually the only thing they were after. As we have tried to emphasize, they liked the Roman Empire. They wanted to share in its advantages, not to destroy it. We've emphasized accommodation rather than conquest. We've said that this is the end of a world, not the end of the world. It is the end of a certain civilization, perhaps, or maybe transformation of that civilization, but it's not the end of civilization. They're not invaders from outer space. Where do they come from? Who are they? What are these aspects of accommodation? That's partly what we want to talk about today in discussing the barbarian kingdoms after the collapse of Rome. So 476 to 530. What happens in 530 is that the Eastern Roman Empire embarks on a reconquest of the West under the emperor Justinian. And that will be the subject of our discussion a week from today. Any questions in the meanwhile? Notice that in the Burgundian Code the authors of the code, the Burgundians, call themselves barbarians. They distinguish between barbarians and Romans. Even though they use the word, it's deceptive to think of barbarians, or tribes, or Germans as if these were absolute well-defined terms that corresponded to an absolute well-defined set of realities. What do we know about these people before they enter the Empire? We know something from archaeology. But as they moved around, as I said they're not nomadic, they have settlements, but they're not very urban settlements. They have gravesites. People who have gravesites with a lot of graves are not moving around a lot. So that's one indication. And the gravesites sometimes have stuff in them, things buried with them. And among other things, they show that they had trade with the Roman Empire because they've got Roman artifacts in them. Well, OK. But we actually don't find out that much about them. The main written source for pre-invasion, let's call them Germanic tribes delicately, is Tacitus, the Roman historian better known, or best known, for his very pessimistic annals of the history of the Roman Empire. But also the author of a brief work called Germania about the German tribes. For Tacitus, the Germans- that is the peoples living beyond the Rhine frontier- are both childlike and noble. They're warlike. From the Roman point of view, these Barbarians are intent on invading the Empire and enjoying its riches. Hence the defensive kinds of frontiers we've talked about. The Rhine, or in Britain, Hadrian's Wall, which you can still see in the north of England, not that far from the Scottish border. That to guard not against Germans, but Celts, Picts, and Scots, in particular. Tacitus portrays the Germans as kind of warlike. Around the year 100 is his description. But he never visited Germania. And if you'd asked him, well, if you're going to write about them, shouldn't you do some field work? he'd have looked at you as if you were crazy. Go there? Me? Moi? You've got to be kidding. The reason he wrote the work was probably not an anthropological description of the Germans, but as a way of berating the Romans. If you describe people who are virtuous but primitive, you can use that to castigate your own people. Rousseau's noble savage where the American Indians are used to attack supposedly civilized societies is an example. Or descriptions of the South Seas, some of Herman Melville's earlier works. Or Robert Louis Stevenson. Or Gauguin's paintings. Contrast a beautiful, natural, simple world far superior to the fatiguing rat race of what passes for civilization. So Tacitus' Germans are warlike, concerned with personal bravery and honor. They have close family ties. They're heterosexuals. They treat their women well. All of these are supposed to contrast with what Tacitus, who's a bit of a scold, Tacitus sees as Roman decadence. The Romans are given to prostitution. None of that in the German realms. The Romans are given to same sex love. Oh, no, no, no. The Germans know that that is really evil. They don't practice divorce, according to Tacitus. Now this is not-- This is a moralistic rather than an ethnographic treatise. He does condemn them for certain vices. The vices typically ascribed to so-called primitive peoples by the civilized. They're lazy. They tend to get drunk. They quarrel. They gamble. In several respects Tacitus, however, describes things that are true of later German practices visible in the Burgundian Code, for example. And that he does not make up for any particular moralistic purpose. Two of these things are the comitatus. The comitatus is the important men surrounding the leader, his entourage, but his military entourage, his armed men. Not just bodyguards, but members of a gang, I guess would be the closest simile. People who are loyal to their superior, but who have a certain amount of autonomy. They're not just sort of paid, as I said, bodyguards. They are his followers. An anachronistic word would be "vassals" anachronistic because it's not used at this time. His military followers. Armed military followers, the comitatus. Tacitus describes the feud. Feud between clans. Feuds are generally characteristic of societies without a strong central government and with fairly generous definitions of kinship. A generous definition of kinship means you know who your second cousin is, maybe your third cousin, maybe your third cousin twice removed. And that cousin is going to consider your interests to be his or her interests as well. You might expect your children or parents to support you, but you probably don't expect your great uncles or second cousins to do much for you. So in terms of vengeance, which is also protection, in other words, I am protected by the fact that if somebody kills me, my clan will take vengeance on their clan. In terms of protection and vengeance, extended kinship is related to a feud and to keeping order in a society that doesn't have a very powerful central government. One way of avoiding feuds that killed too many people is compensation. And this compensation is mentioned by Tacitus and is what appears in the Burgundian Code and elsewhere as wergeld. Wergeld is the money paid in compensation for hurting or killing someone. I killed your brother. We have a drunken brawl. I don't like the way he describes my mother. And I kill him. I'm sorry, but that's just the way things go. What are you going to do about it? Are you going to kill me? Are you going to kill a cousin of mine? Or maybe you'll accept compensation based on, say, what kind of guy he was. Was he a silversmith? In which case I'm going to have to pay a huge amount of money. Or was he just some guy? Some random guy, random Burgundian? Or free Burgundian? Or freed, formerly slave? All of these are tariffs. They're sliding scales of compensation. Tacitus mentions this. So we're looking at the Burgundian Code, and there are other barbarian law codes, for clues as to how the society functioned. But of course, it's a society that's already in the Roman Empire. It looks like before they entered the empire, they lived in little villages. They cultivated grain, but they were more cattle-raisers. They're skilled at iron working. They also supplemented their income by a spot of raiding and warfare. Opportunistic warfare. Ties of kinship are very important. When we're talking about a clan, extended kinship group, we're talking about maybe 50 households. And we'll see this again. We'll see this with the Bedouins in the desert, for example. Within the clan you're not supposed to feud. Not supposed to. Above the clan level is some kind of confederation or tribe. And this is where things get kind of difficult, because we don't really know how one clan considered another clan to be part of something larger. That is, we know that the Romans call the people who defeated them at Adrianople the Visigoths. "Oh, my gosh. Here I am. Adrianople. The Visigoths are winning. What am I going to do?" But who are the Visigoths? One theory is that they're just groups of people who come together in contact with the Roman Empire, in part because the Roman Empire calls them something. It gives them a name and they develop what's called fictive kinship. From a common ancestor. They invent the notion that they all come from one place and one ancestor. This process of sort of fictitious ethnic invention is called "ethnogenesis." Ethnogenesis means the birth of an ethnicity. Rather than some kind of biological fact that you could confirm with DNA, e.g.-- all Visigoths have some sort of biological thing in common. These people are not really related, but they invent a common ancestor. And this question of who forms a real group remains both important as a real thing. For example, American Indian tribes. There are some whose claims to existence are indisputable. They have treaties with the United States. They've had reservations for many years. But now with the inducements for tribes, the tax free status, the ability to have casinos and things like that, there are petitions for tribes to be recognized as such. And here the question of ethnicity. Ethnic identification becomes extremely important. A more sinister and much more widespread modern aspect of ethnogenesis is precisely the use of the Germanic barbarians as the origins of the Germans. It's no accident that in the late nineteenth and early twentieth century, culminating but not limited to the Nazis, the idea of the Germans as a racial group; as a group with a common Aryan- with a "y"- ancestry; As manly and as pure in the sense that Tacitus portrays them becomes a polemical idea. A fighting idea. An invented idea of great force. Just because something is false, it does not necessarily lack historical importance. So the idea of ethnogenesis, of the invention of a group called the "Visigoths", is one way of approaching who they are. On the other hand, there's not a whole lot of evidence that they're doing this. There's not a whole lot of evidence that they are developing this notion of a common ancestor. Much of the evidence, or seeming evidence, for that is Roman. A lot of this ethnogenesis comes from contact with the Romans. Certainly peoples who come in contact with those who are more civilized than they are, and by civilized I mean peoples who have writing, who live in cities, who have extensive trade and administration. The so-called barbarian peoples are going to want to define themselves against the Romans. Hence, among other things, many of these invaders are Arian, with an "i." They use religious difference as part of their identity. So they have come into the empire and, as we said last time, they come into the empire first as allied troops, as refugees, as federati. Federati, that is to say armies of the Roman Empire. They are supported by a system with the bland name of hospitality. Hospitality meaning that they're settled on the land of Romans and they share in the revenue of that land. That's how the Romans pay them. They don't pay them cash. They don't pay them in plunder. They pay them in a portion of the tax revenue. So you owe a reasonably powerful but not quite powerful enough senator in Burgandy. You settle some friendly Burgundian troops on your land. And you give them hospitality, that is to say one third of the tax revenue that you're collecting for the empire. Or maybe one third of just your regular old private revenues. This is a kind of accommodation then. It's accommodation that costs money, but it is part of a set of ways that the Roman elite figures out how to deal with these invaders. Collaborate with them. So the Roman aristocratic land owners and the barbarian war leaders come to various kinds of accommodation. Now, the accommodation differs depending on where we're speaking of. And now we come to the point of having to describe the barbarian kingdoms. I've given you two maps, one of which you're not to show people who are not in the class. This one. The one with the arrows. Yale University is home to one of the great historians of our time, Walter Goffart. And I can't believe that I'm talking about all sorts of people like Wickham and Goffart in something that's going to be widely available, but, anyway let me express my admiration to him, great early Medieval historian who could certainly run rings around me. He's retired. He taught at the University of Toronto. And among his many works is one that completely destroys the notion of having invaders with arrows. This whole idea, like they've got this path; we know where they are; they come from somewhere. See up where what is now southern Sweden, Skandia? A lot of these histories, or what purport to be histories, say they came from Skandia. And you can still read in not very old textbooks, oh, the Visigoths came from Skandia. And then they went here, and then they went there, and they're migrating all round. And you have little arrows that show their progress. You're not supposed to do that. I'm not sure what you're supposed to do though, as a substitute. And as always with historically misleading things, once you get rid of the misleading thing, you're kind of helpless if you're trying to teach this. So I'm asking you to look at this really closely and not take it seriously. I'm asking you to memorize everywhere they went, but not to tell anybody. Once they enter the Empire then those arrows start to make sense. We know that the Visigoths were in the Balkans at the time of the battle of Adrianople in 278. [correction: 378] We know that they sacked Rome in 410. We know that they go down to Italy to try to get to the granaries of North Africa. We know they discover, "OMG, I can't build a boat," so then they come up the other side of Italy. They settle in southern France. They're kicked out of southern France by the Franks for the most part. And they settle in Spain, where the Arabs get them. Four weeks from now, I think. So the arrows are not completely deceptive, and that's why I've given these to you. And it's hard to tell which arrows apply to which tribes, so hence map two. Map two, a lot calmer. This is the situation in 506. Why 506? Because in that year the Franks, whom we're going to be following more closely, the Merovingian Franks defeat the Visigoths and start pushing them out of southern France. So this is a map, I guess, before that defeat. You see the Visigoths in southern France and northeastern Spain with the Basques kind of in between them. So this is the situation in 500. There's no more Roman Empire of the West. Or there is a fictitious Roman Empire of the West. All of these people to varying degrees-- well, not all of them, most of them-- acknowledge some kind of suzerainty of Constantinople. You'll read about Clovis, King of the Franks in the beginning of the 6th century, who gets some sort of gift from the emperor Anastasius in Constantinople. A letter of appointment, some robes, various trinkets, and, according to Gregory of Tours, the historian of Clovis, the title of consul And he is very pleased with this. He dons these robes. He scatters coins just like a newly appointed emperor. But is he obeying the emperor Anastasius? Did the emperor Anastasius start sending orders to him? Or have any kind of administration? No. This is really just symbolic. We will talk about the relationship between the Eastern empire and the barbarians, because it's going to change in the sixth century as the Eastern empire fends off its opponents and becomes more concerned to take back as much as possible of the lost Western empire. In the year 500, the most impressive of these barbarians would've been the Ostrogoths because they are occupying Italy, which is the most Roman, the most prosperous, the most intact economically and culturally of the former Roman Empire of the West. The Ostrogoths had been in the-- if you look at the arrows, they had been maybe in the Crimean area, around the Black Sea. They came into the Balkans. They tried to attack Constantinople in the late fifth century, and they were defeated. And they were encouraged to move into Italy by the Byzantine emperor to get rid of Odoacer, that military leader whose takeover of Italy in 476 is conventionally understood to be the end of the Roman Empire in the West. The Ostrogoths had an impressive ruler named Theodoric. And they ruled from Ravenna, the old last Roman capital in northeastern Italy. And the tomb of Theodoric can still be seen in Ravenna. Very impressive monument. Roman education survived in Italy. It would reach its last flowering with two figures: I mentioned one of them last time, Boethius and Cassiodorus. These are two key figures in the preservation of classical learning. Boethuis, not perhaps literally the last person in the west who knew Greek, but certainly the last person who tried to make Greek knowledge known to people who could only read in Latin. He conceived the project of translating all of Plato and Aristotle into Latin. He started by doing a kind of introductory textbook. Like a lot of great projects, this one was not completed. In fact, this one barely got off the ground because he was accused by Theodoric of conspiring with the Byzantine Empire, the Eastern Roman Empire, to overthrow him. He was imprisoned for a year. In prison he wrote one of the most magnificent works of philosophy, of why we are alive and why we die. The Consolation of Philosophy. And then he was executed. Cassiodorus lived to be ninety. So one of the differences between these two figures of the last gasp of Roman culture in Italy is Cassiodorus's relative longevity. They're both figures of the sixth century. Boethius dies in the 530s, Cassiodorus much, much later. Cassiodorus also conceives of a program of education, but it is more oriented towards Latin learning. And Cassiodorus in some way is the founder, or at least the transmitter to us, of the idea of the liberal arts. Cassiodorus is a religious figure. Boethius is a Christian and he wrote on Christian topics, but The Consolation of Philosophy, interestingly enough, is a stoical work, has very little explicitly about Christianity. Cassiodorus, on the other hand, is the guy who invented the idea that monks should copy manuscripts. That the preserve of culture, the place where it seeks refuge and is protected in barbarian times, should be monasteries. This seems so self-evident to us. Because if there's one thing we know about monasteries, it's guys hunched over and writing stuff and the preservation of learning. But, in fact, monasteries start out as just anti-intellectual institutions where you pray and you don't spend a lot of time reading, let alone copying, let alone thinking. You're supposed to have visions. You're supposed to be inspired. You're supposed to fast and become ecstatic. It's Cassiodorus who conceives of this as a contemplative and learned project. The liberal arts means here things that are not immediately practically useful, but that help illuminate the person seeking after knowledge. And what kind of knowledge is a person seeking after in the 6th century A.D.? They're seeking after knowledge of God and knowledge of the divine. Why not just read the Bible? I'm sure many of you have read the Bible or read parts of it. The Bible is not an immediately evident document in terms of its view of the world is total, but it's full of mysteries. It's full of obscurities. It's a strange work that requires knowledge and explication. Or to celebrate divine services, for example, requires a certain kind of knowledge. To know when Easter is. To know the phases of the moon. To know what day it is. These monks, or just anybody out in the countryside, can't just look at their phone and see what time it is. There's a need for some practical knowledge, but that involves abstract concepts like the movements of the planets. This is what the liberal arts are and this is what's being preserved in the Ostrogothic kingdom. But the fate of Boethius shows you the sort of duality of the barbarian patronage of culture. On the one hand, the Ostrogoths in Italy are as civilized as these groups get. On the other hand, of course, Boethius is executed. On the third hand, you didn't have to be a barbarian to execute people. After all, Seneca was forced to commit suicide by Nero. So the fate of intellectuals in the Roman Empire is not necessarily so much better than the fate of intellectuals in the barbarian kingdoms. The thing about the intellectuals in the barbarian kingdoms is they're very few of them. Seneca's a great man. It's too bad that he died. We could have had more works. But there were lots of other philosophers. There were lots of other playwrights. Boethuis we can say-- Boethius and Cassiodorus, maybe, are the two smartest people in the sixth century, judging by what they had access to, what they read, how they wrote. And that is scary. If you can say that Isidore of Seville is the smartest man of the seventh century. Or Bede and Alcuin are the smartest men of the eighth century. It's not just a compliment to them. If you're rated like the eighteenth best tennis player in the United States, that's a tremendous accomplishment. But presumably, there are 200 tennis players who are ranked. And behind them there are 10,000 very good tennis players. But what if you were the number one tennis player in the country, and there was no number four? No number four through one hundred million. Tennis would be an endangered game. It would mean a lot, but supposing nobody followed tennis anymore? I don't know enough about antiquated games, but some medieval game that only five people know how to play. I could be the fourth ranked. But here we're not talking about sports, important though they are. We're talking about the fundamental aspects of knowledge. Theodoric. Theodoric is a great ruler, but he had a problem that is typical of many of these barbarian groups: He had to hold his minority together. The thing that made Italy the wealthiest, the most important, the biggest prize for the barbarians, is its Roman population, its Roman wealth, the preservation of its cities. But that also meant that the Ostrogoths were a tiny proportion of the total population. He needs to hold them together, but he also needs to mollify the Romans. So it's a dangerous place for barbarian rulers. Odoacer had already been overthrown. It's too valuable to the Eastern Empire. And indeed after Theodoric died in 535, very shortly thereafter the Byzantine Empire, the Eastern Roman Empire, would invade Italy and devastate it in the course of conquering it in a twenty years' war. Now if you look at the map again and turn to North Africa, you'll see we've got the Vandals in what's now Tunisia and eastern Algeria. And then Moorish kingdom and Roman Empire. Ignore Roman Empire. I don't know what they're talking about. Moorish kingdoms, what does that mean? We don't really know who these people are either. They're not invaders. They're desert peoples who have now taken over what was formerly the Roman Empire, and they're pressing the Vandals. The Vandals were less accommodating than the Ostrogoths. They were more fiercely Arian. They persecuted the elite of the Roman population, including the Roman bishops. But they were very effective rulers. They had a navy. They were able to plunder Rome several times in the 5th century. But they were beleaguered by these Moorish groups, in other words native peoples of the North African desert. And so by 506, their kingdom has shrunk. They were also a minority in what had been a very populous part of the Roman Empire. And they tended to fight among each other. They had internecine feuds. And so we're talking about things that are common to many of these barbarian kingdoms. Disorganization. Internal fighting. Alien religious beliefs, particularly the Arian heresy. And once they've done the plundering, inability really to start making the economy work very effectively. The Vandals would be driven out of North Africa, or obliterated actually, by the Eastern Roman Empire, in the late 520s, early 530s. Now I'm not going to go through every one of these, but I want to give you some examples of accommodation. Go up to the British Isles. You'll see it says British kingdoms, that means Celtic kingdoms whose remnants would later be Wales, Scotland. And then the Anglo-Saxon kingdoms. The Anglo-Saxons are invaders who come from the continent beginning in the 440s. This is the first place that Rome abandons. Here it looks more like a conventional invasion. The invaders come and the Romans pull back their troops because they're afraid that Gaul is going to fall next. And this is an island where the Roman impress, the Roman impact, was less. There isn't a large Roman majority and a small German minority. There is a Celtic majority that blends with the invaders or that seeks refuge in these independent British kingdoms, as they're called on the map, to the west. We don't know very much about what's going on in Britain at this time because more than Vandal North Africa, more than Ostrogothic Italy, the past is obliterated. There's very little Latin being written. We have very little knowledge of what is going on. So this is at one extreme of what might be called Barbarization verses Roman permanence. We're going to be talking about the Franks later and we're going to talk a little bit about the Burgundians in closing today. But this leaves really among the important groups the Visigoths. The Visigoths, the people who in a way started this with their invasions of the Balkans in the late 4th century. In 506 they control much of France, the south and the west particularly, and are trickling into Spain. We will be following, in reading Gregory of Tours, the tremendous success of the Franks against the Visigoths. And so the Visigoths will be pushed out. What about the Burgundians? You've read the Burgundian Code-- anything strike you about it? Spencer? Spencer: Mainly it focused on differences between different classes and emphasized the free men versus the slaves. Burgundians versus Romans, et cetera. PROFESSOR: Very status oriented. STUDENT: I didn't realize there was so much hair pulling. PROFESSOR: Yeah, why? What's that all about? Yeah? STUDENT: Well, it talked about the-- in the book it talked about how long hair became like a status symbol. PROFESSOR: Yes. So the question was, what is all this hair pulling? It's a status symbol. We'll see that the Merovingian kings wear long hair, specially long hair. And when they're finally deposed by the Carolingians, that hair is cut. Now of course, all their hair is cut, they're put in monasteries. And monks are what's called "tonsured." If they're not completely bald, they at least are pretty near. Like many barbarian, so-called barbarian, people, or like many people period, they're certain signs of prestige, symbols. The Burgundian Code is drawn up between 483 and 532. It's drawn up in different stages. The Burgundians were closer to [correction: "than"] the Ostrogoths in degree of Romanization. They're a group that wants to be Roman, or at least accepted by the Romans. They write their own law code in Latin, like the Visigoths, for example. They also write a sort of law code for the Roman population. This law code is aware of disputes between Romans and Burgundians. And if each has a different kind of law, then how do you settle a problem that arises between members of both communities? The Burgundian law in itself shows a lot of Roman influence. For example, in chapter eighteen you've seen this title "Of things that happen by chance" and probably didn't seem very dramatic. If any animal by chance or any dog by bite causes death to a man, we order that among Burgundians the ancient rule of blame be removed henceforth. This is an interesting question. If my dog bites you and you die, am I responsible? Is your brother going to have to kill me? That's what the Burgundian tradition would have been. But here they say if it's an accident, then your brother can't kill me. This is the difference between -- this is a tricky problem. Those of you who have the good fortune to go to law school are going to study this first year: torts. A tort is a so-called civil wrong as opposed to a crime. A crime is where I kill you because I want to. A tort is I leave a roller skate out on the sidewalk, you trip and die. I'm not going to be considered in the same league as someone who poisoned you, but that roller skate shouldn't be there. And of course this is a crucial thing. For example, I've learned, fortunately not from experience, but from neighbors after Hurricane Irene, that if a tree in my yard falls on your house, I'm not to blame. Your insurance is going to have to cover that. I'm really sorry about that tree. But if you warned me, "I don't like the look of that tree in your yard. It's leaning over like this. I'm afraid in the next storm it's going to fall in on your house," and I don't do anything, then my understanding is that I'm liable for negligence. This was a present and obvious nuisance. It was an obvious threat, and my neighbor called my attention to it. And I didn't do anything. So next time it storms and your house is threatened by somebody else's tree, just as the wind starts to blow go next door and say, you know, I don't like the look of that tree on your property. You better do something. These are real legal questions. And they are handled in here with some sophistication. On the other hand, there is vengeance. It's OK to practice vengeance. But there are some limitations. For example, if I kill you, your relatives can kill me, but they can't just kill my cousin. This is sort of individual-directed and not clan-directed vengeance. There's a lot of talk about compensation and wergeld for victims. How much you pay. Whether you grab them by the hair. Whether you cut off which finger. Whether they were free or slave. Whether they were a skilled artisan or a serf. I love title ten. "If anyone kills a slave, barbarian by birth, a trained house servant or messenger, let him compound 60 solidi. But 200 solidi if the slave is a skilled goldsmith." 40 solidi for a carpenter, and so forth. If you cut off someone's arm, it's half of their wergeld. Wergeld is like murder. Their murder value. So I have a murder value of 100 solidi. Cut off an arm, you've got to pay me 50 solidi. This seems pretty crude, doesn't it? How does it strike you? Yes? STUDENT: Yeah, it does seem crude, but I think it gives a solution to something that could cause a total outbreak, a civil war. PROFESSOR: It is a maintenance of peace. And what about victims' compensation? In the Western legal tradition, if you injure me, it's a crime against the peace, and the state punishes the perpetrator. Only relatively recently has this notions of victims' rights, victims' compensation, been entered. Which is like a reversion back to the notion that the crime really injures not the state or the king or the peace that we all take for granted, but the individual who is affected. But what makes it seem crude is the specificity of the offenses. If you look at the Connecticut Criminal Code, it's not quite so precise about hair pulling. If anyone seizes a freeman by the hair, the fine is greater if he's seized with two hands than one. Maybe that has to do with intent. One arm might be instinct. I'm pulling your hair. But two hands argues of serious intent to do harm. Or it's more humiliating. This is a culture in which there's an awful lot of shame and compensation for public shaming. A lot of questions of personal status. In title four about theft, if a slave commits a theft he's either beaten or killed, end of story. Freemen, that is to say people who are not slaves, pay fines and compensation. It's a violent society. Course all criminal codes show various forms of violence. There's a lot of mutilation. There are a lot of assaults on women. Compensation for assaults on free women are paid to the women themselves, but a native freeman who assaults a maid-servant must pay the master. Maid-servant, as a slave, is regarded as a commodity. And then finally, it's a society in which, at least according to the official law code, men are more valued than women, or men are less regulated than women. If a man breaks a marriage, in title thirty four, he's fined if he goes and runs off with another woman. If a woman goes off and runs off with another man, she's to be smothered to death. On that enlightened note, we'll leave the Burgundian Code. And indeed we're going to leave the barbarians only for a little while. Next week we're going to talk about the Eastern Roman Empire and why it survived and even why it flourished.
MIT_ESD051J_Engineering_Innovation_and_Design_Fall_2012	Instructor_Interview_What_Happens_in_Class.txt	BLADE KOTELLY: So the class is broken up into two sessions, a Monday and a Wednesday class. Each class is two hours long. The typical class runs where at the beginning of the semester, there'll be more lecture than towards the end. JOEL SCHINDALL: Blade and I have developed a style for teaching the course which works very well for us. It's a bit like Our Town where the actors go through their paces, and every once in awhile they stop and the stage manager comes on stage and makes an editorial comment that couldn't be conveyed in a direct fashion. We evolved it perhaps because Blade is charismatic. He is very effective at the teaching of the course. He knows the material. He lives the material. But I've had a lot of the experiences in industry about how this material actually plays out. So typically Blade will do the bulk of the instructing in a very Socratic manner, which is part of what makes the class effective. Blade is very, very good at evoking from the students their ideas about what is design. Meanwhile, I will listen to the progress. And where Blade touches on a subject which can be enhanced or embellished by talking about real world experience relating to that particular topic, I'll chime in. Blade is wonderful about stopping just about in mid-sentence and allowing me to work with the students just a little bit to engage them on this, to share with them about it. And then I go back and sit down, and Blade continues right where he left off. BLADE KOTELLY: The lectures are interspersed with activities. So students will do some hands-on activities every, let's say, half hour. Probably at the limit is about halfway through, about an hour through, they'll have to do something no matter what. Because you want to keep students' attention up. There'll be some classes which are, like I said, primarily lecture-based. Some classes where it's a lot of students working in groups, and then we're stopping the work, asking a question, sharing ideas, and evaluating it. Some classes run in a very Socratic way. So we're really having them come to conclusions. So a class on ethics, for example, runs better when you teach it Socratically because they need to become engaged with the material. And if you're just saying, here are examples of ethical problems. And here are their solutions. They can check the box. OK, yes I get that. That makes sense to me. Or maybe there's something where they don't quite get it, and you could bring up some interesting discussions. But I think it's more successful to have them think about it and be able to then even argue in class. And so you find divergent points, and you have different students hash them out. And you'll find that sometimes other students will come in having turned their brain on and being sparked by an idea and say, wait a second. No, no. I think they're right. And because we use name cards that have the name on the front and the back, the students can see each other's name and can say, you know, what Joyce said was really good. No, I like that. That was an important point. Basically they can see each other. So it connects a class to be able to start learning together, which makes the learning process actually very important for those kinds of classes to be in person. The class is meant to have a lot of interaction. As much as possible, really. At the end of a big school day, from 3:00 to 5:00 PM, they could be tired. And they probably stayed up really late the night before so they're probably definitely tired around that time. So you want to make sure that you're keeping them entertained and engaged with the material. I mean, it's really-- every class has great material. Any class can have great material, but the attitude, I think, is that if you get your students to be engaged intellectually, they'll learn it faster. Then when you're trying to shift their thinking, you're not just simply explaining a concept, but having them think differently. Then you need to engage them even more, because you need to change the way their brains are functioning and get synapses to fire even differently. JOEL SCHINDALL: We bring in outside speakers for some of the talks. And the outside speakers are an eclectic mix. In some cases, we'll bring in someone from the Engineering faculty who is particularly gifted at communicating mechanical engineering design skills or electrical or chemical, because we want to give the students-- there tend to be some discipline unique ways of thinking, and we want to give the students an idea of what the broad range is. But other times we bring in someone who seems rather off-the-wall. We brought in someone who has started two or three restaurants in the Boston Area. And you say, a restaurateur? What does that have to do with engineering? And the students come to the class, but don't really expect to get anything of value until they find out that designing a restaurant is a really significant design process. You have to look at what do the users want? How do you greet them at the restaurant? What type of food do you have? How do you design the space? How do you make the patron in the restaurant feel welcome? How do you make the staff function effectively? There are many, many aspects. And to see someone in front of the room who is not an engineer, and yet who is using some of the same engineer thinking that you use to solve a problem that you never thought much about, because when you go to a restaurant you just hope that the food will come and that it'll taste good and that it won't be too expensive and that your favorite dish will be there. But you tend not to pay any attention to how were you greeted by the hostess? How were you seated? What are the wait staff doing? How is the cook working in the kitchen? And you begin to realize that there are many more dimensions in the world that you're interacting with than you pay attention to. BLADE KOTELLY: If we have a quiz in class, we administer a quiz, we swap all the quizzes, we review all the answers. Quizzes tend to have a lot of the questions repeated on each quiz so if they didn't know the answer the first time, they should know it the second time. And they'll definitely know it the third time. Because we review it in class. We'll spend several minutes reviewing that quiz to make sure students can use it as a learning opportunity, because I do want to do a diagnostic to see what are they getting? Are they doing the reading? I want them to do the reading. It's how I test for it. But I also want to make sure that they're learning. And if they haven't done the reading, maybe they learn a little bit from this, maybe they'll ask some different questions. So we'll have someone grade and then give the result to see what the contour of the grades are. Even though they've already swapped papers and done their own grading, students go through and check all of them again so they can understand what the contour is so I can understand are students not reading the book yet? Maybe we assigned the book too soon and they weren't able to get to the bookstore soon enough. Or maybe they're in a real crunch time, they weren't able to review some of the material. So we try to do a diagnostic to see what's happening. The teaching assistants will take notes, one teaching assistant will take notes during class of everything that we discussed so we can tune out the slides and topics later on. The may be an example that we haven't used before that either is topical, because now a company releases a new product that we want to be able to incorporate. Or there'll be a new way to articulate something. They'll say, oh, that's a really good way that we were able to articulate this idea. Or a really good moment that happened here in class. Let's think about how to bring that into the curriculum. So we're always taking notes about each class.
MIT_ESD051J_Engineering_Innovation_and_Design_Fall_2012	Instructor_Interview_Grading_a_Design_Course.txt	JOEL SCHINDALL: Our grading in the class is important, but it's done a little bit differently from the way an ordinary course is graded. In an ordinary course, there's a specific body of material, and so you can grade on proficiency. Can the student solve second order differential equations? So you give them some second order differential equations on a problem set, and if they solve it, they get a good grade. And if they don't solve it, they wouldn't get as good a grade. We're trying to teach a way of thinking and being innovative so we give them exercises and presentations, and then we grade them on the passion of their engagement. Some of them have better presentation skills than others. We're not looking at an absolute mark, but we're saying, did you go outside the box? Did you try something new? Given where you were when you came into this course, did you increase your skill set effectively and energetically? And if you do, that's a good grade in the course. And we actually give many-- many students get good grades in a course like this, because they've elected to take a course to enhance their capabilities. And that deserves a good grade. The ones who don't get as good a grade are the ones who simply haven't participated as fully.
MIT_ESD051J_Engineering_Innovation_and_Design_Fall_2012	2_10Step_Design_Process_and_Dieter_Ram_Sample_Lecture.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 view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. BLADE KOTELLY: What was the objective of the assignment? Charlotte? AUDIENCE: To test your product. BLADE KOTELLY: No. No. But I'm really happy you tested my product. That was great. That was not the objective of the assignment, though. Not 100%. Ben. AUDIENCE: To see that design is everywhere. BLADE KOTELLY: Yeah. That's part of it. To see that design is everywhere. So you can see all the things that people have done as well in terms of their critiques. Christy. AUDIENCE: To start analyzing the design. BLADE KOTELLY: To start analyzing the design. Absolutely. And what are you analyzing the design for? OK. We can do this. What are you analyzing the design for? Kenny. AUDIENCE: Do you mean for what product are we analyzing the design or are you thinking why are we analyzing? BLADE KOTELLY: Oh, let's talk about the why. Why are you analyzing design? AUDIENCE: So we can incorporate what we're learning into things that we design [INAUDIBLE] and what we design ourselves. BLADE KOTELLY: Yes. You're going to incorporate the things you're learning in terms of being able to do an analysis and work it in somehow to when you're designing. Isabella. AUDIENCE: To understand effective and ineffective designs. BLADE KOTELLY: Ah, to see what designs work and what designs don't work. Now this is interesting. You used one product. There weren't two different products. You didn't say, well this was a good design, this was a bad one. You said, within one product, what was good and what was bad? Other reasons why we might have done it? If you get really good at being able to critique other designs, you'll be able to be really good at critiquing your own designs. So what you'll do over the semester is learn a whole bunch about this. And at the end of the semester, I want you to look at the same video you've made and it see how you could make it better. Let's see what comes to mind about that. Do you have a comment, Joel? JOEL SCHINDALL: No, just watching the answers. BLADE KOTELLY: OK, so here-- JOEL SCHINDALL: But actually, I think whoever answered early in it-- an awareness of design so that as you go-- this course actually takes place not just in the two hours that you're here but in the hours in a week minus hours that you're here that you spend the rest of your lives. And we intend to project it out there and have you actually be aware during your life of what design is. That's what's going to make you a better designer. BLADE KOTELLY: OK. So, we're going to get right into the meat of this. This is the 10-Step Design Process. This is the core of what we're going to be teaching. You'll use this process over and over and over again. It's a great process to know. You might find that it appears on pop quizzes. You might find it appears on pop quizzes. And it might be something that if you wrote on a card and you put in your wallet and kept with you, you might be allowed to use on a pop quiz. Just saying. It might be on many pop quizzes. But it might not. OK. So we start with these first beginning steps. Number one, we want to identify the needs and really understand the problem. In our last class I gave you a design challenge. So this is the first step, identifying the needs. What is the problem we're really trying to solve? And if we can get underneath that we can design something in a much more impactful way. So let's talk about this interesting example here. I had a teacher as an undergraduate who designed a toothbrush. Now, I'll show you a picture. This is Napoleon's toothbrush. Napoleon Bonaparte used this toothbrush. A long time ago. If you bought a toothbrush in the '60s or something, you'd buy a toothbrush that looked like this. Does that look familiar to people? Yeah, OK. He designed a toothbrush that looked like this. That's his design, the Reach toothbrush. Who's heard of the Reach toothbrush? OK. And there are a lot of different versions that they wound up making over time. But that's the early version of the toothbrush. People brush longer and more thoroughly based on the design of the toothbrush alone-- with no instructions. Here's what happened. If you have a toothbrush and it's a flat head toothbrush like the one we showed you before here-- like that-- you hold it, you start brushing your teeth like this. And you see people can do this all day. They can watch a sitcom with doing this to their front teeth, no problem. Very comfortable. But if they need to brush other parts of their mouth-- and they do-- they do this. They take this. I'm going to represent the bristles with my thumb and hold the handle like this. They brush their teeth like this and then they get their rear molars like this on the side. And they want to get the upper rear molars on their sub dominant hand side. Which means they do this. Right? I'm writing, so I do this. So everyone, if you're a righty, put your right hand up. If you're a lefty, put your left hand up. Take your hand, make a fist like that with your thumb out, curve your wrist over, and bring it across like that. Now hold this. Is that comfortable? This is not a comfortable position for your arm to be in, right? OK. So as a result, people do this. And if you watch them do it, they do this and they go, ugh, they get bored. And they stop brushing. That's not good. So this teacher, this professor I had, to understand this, he did some studies. He had people stain their teeth red. And then, with no mirror, he said, brush your teeth. And people would brush it. And then he'd look inside their mouth and see the red was all of the front and all stuck in that part in the back. He said, that's no good. So he designed this thing. In fact, there's a ton of innovations around this. Different handle. You see this side. Your thumb sits in that groove really easily. In fact, you'll turn that toothbrush 90 degrees and your thumb will rest right there. You do it automatically. You'll do it automatically like this. And this is thin over here at an angle. So it doesn't pull your cheek out like this . That's not very comfortable, right? OK. So he did that. The head was shaped differently. Instead of doing a square head, it's now tapered, the bristles are shaped differently. So here's the question. What was the underlying problem he was trying to solve? Kristen. AUDIENCE: The fact that people weren't able to reach their back teeth properly. BLADE KOTELLY: That was a problem he was trying to solve but it wasn't the underlying problem he was trying to solve. AUDIENCE: The fact that people didn't want to brush their teeth. BLADE KOTELLY: The fact that people didn't want to brush their teeth. That's a problem that he was helping with but that wasn't the underlying problem. David. AUDIENCE: People with bad teeth. BLADE KOTELLY: People have bad teeth? People with bad teeth-- not the underlying problem. [? Cosi? ?] AUDIENCE: The design of the toothbrush hadn't changed in a while. BLADE KOTELLY: The design of the toothbrush hadn't changed in a while and we're getting closer now to the underlying problem. Because we saw that Napoleon had a toothbrush very similar to the toothbrush that you could buy in the '60s. A small difference though, his was they said silver-plated, I think. Anyone here own a silver-plated toothbrush? OK. Yes, Dennis? AUDIENCE: The functionality of the toothbrush? BLADE KOTELLY: The functionality of the toothbrush. He definitely wanted to change the functionality of the toothbrush but it wasn't the underlying thing. Louis? AUDIENCE: Was it to simply build a better toothbrush? BLADE KOTELLY: It was about building a better toothbrush but that's not the underlying reason. [? Shuni. ?] AUDIENCE: An uncomfortable toothbrush was leading to poor brushing habits. BLADE KOTELLY: Yes. But we're not getting to the underlying reason, what made him do this. Emily. AUDIENCE: Was it low toothbrush sales? BLADE KOTELLY: Well, interesting. It wasn't-- we're getting very close now-- it wasn't low toothbrush sales, per se. But by doing that he did make somebody happy by increasing the number of toothbrush sales. AUDIENCE: People have loads of cavities back here? BLADE KOTELLY: Oh, cavities. No, we're getting further away. Cavities is cooler. Sales is warmer. Patrick. AUDIENCE: The ability to increase the price on the toothbrushes that are new? BLADE KOTELLY: Increasing the price of toothbrushes that are new. That's interesting. Kind of. Kind of. It's actually-- they would have been happy if the toothbrushes were the same price. AUDIENCE: I mean, but you're like, trying to get people to believe that it's worth what you're paying for. BLADE KOTELLY: Yes. For what though? For this for that particular toothbrush. AUDIENCE: Yes. BLADE KOTELLY: Yes. It's a little bit-- it's a shade of meaning difference. I think your close. AUDIENCE: To design the best toothbrush? BLADE KOTELLY: Well, he definitely wanted to design the best toothbrush and he did at the time. But we're now getting colder. [? Cosi? ?] AUDIENCE: So they can make money? BLADE KOTELLY: Oh, to make money. Yes. To make money. Absolutely. For whom? [INTERPOSING VOICES] BLADE KOTELLY: For who? AUDIENCE: For himself. BLADE KOTELLY: For himself. No. He's a designer. Designers don't make much money, it turns out. Some do. Some designers make money. Not a whole bunch of designers make money. And they paid him a fee to do this work. They don't get residuals. Like if you make a movie and you're a famous movie star, you get residuals. Designers don't get residuals. They should. Definitely. Ben? AUDIENCE: Stakeholders? BLADE KOTELLY: Stakeholders. Yes, stakeholders, yes, that's kind of close. A little bit too far back. But if you tell me which stakeholders. AUDIENCE: Company. BLADE KOTELLY: Which company? AUDIENCE: Did he just not like brushing his teeth? BLADE KOTELLY: I don't think he cared about brushing his teeth. He was hired by a company who said, hey, John. We make blank. We want you to make something that's going to sell a lot of blank. Can you fill in the blank? AUDIENCE: Toothpaste? BLADE KOTELLY: Not toothpaste. That's a great idea. It's not toothpaste. Emily. AUDIENCE: Is it the nylon, like the bristles? BLADE KOTELLY: It is nylon. It is the bristles. Nylon is made by whom? DuPont. Nylon bristles started coming out in, I think, 1936. And they, DuPont loves to sell nylon. And they said, hey John, we want to sell a lot of nylon. Can you do something that going to help sell a lot of nylon? And they asked him to do this. So what he did is he looked around the world and he said, what in the world is made of nylon? It's a lot of research just to figure out what's made of nylon. What hasn't been redesigned in a long time that's made of nylon that I could redesign? Hey, what hasn't been redesigned in a long time, that's sold all over the world, made of nylon, has existing manufacturing capabilities, so it's really easy to make a small modification that will sell a ton of nylon. Answer? Toothbrush. So he made a toothbrush and he improved the design. And they made a tremendous number of changes to the toothbrush in the first design he made. And they kept releasing them slowly over time. So people get used to it, buy more toothbrushes, buy more nylon. Cool, right? So understand the underlying reason. If you said, I want to sell-- if someone said to you, I want to sell a lot of nylon, it's hard to figure out what to do to sell a lot of nylon. And that was his approach. So what's the real problem here? Information phase. What in the world exists that can inform us about this problem? So what kind of things might you do to understand a problem? AUDIENCE: Google. BLADE KOTELLY: You can use Google. Excellent. What else might you do to understand a problem? AUDIENCE: Talk to people who are suffering from the problem. BLADE KOTELLY: Talk to people. Do market research. Excellent. You might even look at adjacent problems. Problems that are not exactly the same. So if you're doing a toothbrush redesign, what other kinds of things might you look at to help inform you about how to design a better toothbrush? Emily. AUDIENCE: Hair brush design. BLADE KOTELLY: Hair brush design. Absolutely. Why? AUDIENCE: Might have similar problems dealing with the product. BLADE KOTELLY: Absolutely. What else? AUDIENCE: Dental floss. BLADE KOTELLY: Dental floss. So you might figure out what dental floss does well. In fact, there's a dental floss device that looks kind of like a toothbrush. It's got a handle. It's got a little small piece of floss and you use it like this. So that's another way of considering it. Excellent. Stakeholder phase. This is really important. What's wanted and who wants it? Just because you can make it doesn't mean that people want it. Who knows what a VCR is? Great. This example won't work one day. OK. So here's the question. If I made a VCR, what functions would it have to have. I'll start you off. Play. AUDIENCE: Stop. BLADE KOTELLY: Stop. AUDIENCE: Rewind. BLADE KOTELLY: Rewind. And? AUDIENCE: Fast forward. BLADE KOTELLY: Fast forward. What else? AUDIENCE: Eject. BLADE KOTELLY: Eject. That's great because otherwise the tape is sitting stuck in there. Wow, it's an awesome tape I keep using. I've watched "Tron" 145 times. AUDIENCE: Open. BLADE KOTELLY: What is it? AUDIENCE: Open. BLADE KOTELLY: Yes, so we have an eject mechanism. Pause. AUDIENCE: Power. BLADE KOTELLY: Power. AUDIENCE: Record. BLADE KOTELLY: Power, yes. AUDIENCE: Record. BLADE KOTELLY: Record. That's great. AUDIENCE: Some of them have the little displays with like the time. BLADE KOTELLY: Yes. I need a flashing 12:00. Let's do flash 12:00. OK. So, a time. Why do we have a time display at all? Why was there ever a time display on a VCR? AUDIENCE: So you know long is the tape. BLADE KOTELLY: Well, yes. So we have some sort of a method. That actually is separate. To position the tape, I just use the counter. It might go up to a thousand or something-- or more. The counter might tell me a position of the tape. What'd the time tell me? Besides the time. AUDIENCE: How long you've watched. BLADE KOTELLY: It could tell me how long I've been watching it. It might allow me to do something. AUDIENCE: Timed recordings. BLADE KOTELLY: Timed recordings. I could not have to be home and I could set my VCR to record channel four-- because back then we only had five channels-- channel four and that would record that at 5:00 PM when I didn't get home till 7:00. Big deal. It was before DVRs. Amazing. What else? OK. I like that list too. So, let's suppose I made a VCR and it had all these features on it but I took away one feature. I took away the ability for you to record. Show of hands, who thinks that's still useful? Who thinks it's useless. OK. Why is it still useful? A VCR that cannot record. AUDIENCE: Because that ability is pretty-- it's decoupled from the other-- from the other functions. BLADE KOTELLY: But why would I want a VCR that doesn't record? AUDIENCE: So you can watch movies? BLADE KOTELLY: So I can watch movies. When would I want to watch movies, but not be able to record things? AUDIENCE: When you rent them. BLADE KOTELLY: When I rent them. Or when I bring them to a ski condo or something. I go to someone else's place, we bring up videotapes and then people can watch the video tapes. Right? Great. And what's the benefit of not having that record head in the machine? Because it's a record head and a playhead. AUDIENCE: It saves you a lot of money manufacturing. BLADE KOTELLY: It saves you a lot of money manufacturing. You can pass that savings on to the consumer. Because these are two different objects. OK. What if I took out, instead of the record head, I took out the playhead. Who thinks that's useful? Who thinks it's useless? You're all wrong. No, it's you're all right, in a certain way. Why do you think it's useless? I can't play videotape. Why is it useless? AUDIENCE: Because you can record something. You can't watch it. BLADE KOTELLY: As soon as I record something, I can't watch it. Kind of a weird thing to do, right? Oh, I can't wait to watch this thing when I get home. I've recorded it. Now what? I have no idea. But think of it this way. What if I had a business and my business was a video duplication business. You gave me one videotape and I'd make thousands for you. You know at graduation they shoot people when they walk down. [LAUGHTER] BLADE KOTELLY: With a camera. They shoot people when they walk down and receive their diploma and they shake hands. So, they have you on videotape. And what if people want to order videotapes? They want to duplicate them. Or back when you used to buy videotapes, as a kid perhaps, you bought "Bambi" and you wanted to get a copy. Well, there's some room where there's a machine and it plays. And there are thousands of machines that record. Thousands. They can record and rewind. They can do nothing else. They record and they rewind. And that's all they do. That's the whole thing. And so it's a lot cheaper for people to buy thousands of those things without the playhead or fast forward or anything else. You can really make it a much less expensive product. So, just because you can do it and you can put it on there doesn't mean you should. So, stakeholder phase is also a little bit bigger. Who are the possible stakeholders? We talked about this a little bit before. I think Ben brought it up, saying that the stakeholder can be shareholders or they could be people who are related to the design in some method, some aspect. Whether it's-- in this class. Let's take this class, for example. Who are your stakeholders in this class? Who's the primary stakeholder? AUDIENCE: Ourselves. BLADE KOTELLY: You. You're the primary stakeholder. Who's another stakeholder? AUDIENCE: Parents. BLADE KOTELLY: Parents. Why? AUDIENCE: Because they're paying for it. BLADE KOTELLY: Because they're paying for it. And they want to get some value out of that. Who else? AUDIENCE: Staff. BLADE KOTELLY: Staff. Which staff? AUDIENCE: All of you guys. BLADE KOTELLY: All of us. So we're all stakeholders. AUDIENCE: You all want to see this class be a success. BLADE KOTELLY: No. We want to see you be success. It's different. AUDIENCE: Aww. BLADE KOTELLY: I don't care about the class. [LAUGHTER] It's true. AUDIENCE: I believe it. BLADE KOTELLY: The class could be a massive failure, but if you're successful, and we've helped you do that, then we've been successful. That's our job, to make you successful. What other stakeholders do you have? AUDIENCE: MIT. BLADE KOTELLY: MIT. How's MIT a stakeholder? What? AUDIENCE: They're putting us on their CW so they get more attention to MIT-- BLADE KOTELLY: Well, maybe so they can get more attention or maybe so they can share the ideas with people who can't be in this room with all of you. So maybe there are two different stakeholders. Maybe there's people that want to get money from and say, look at this cool class! I hope they think it's cool. Or maybe there are people who say, I really wanted to hear about that lecture that I can't get to. John's brother can't get to this lecture today. Wanted to. Can't do it. So he's a stakeholder as well of the recording. So lots of stakeholders and we'll be discussing this next class. Now we do planning/operational research. What's realistic? What limits us? If we want to make something, what limits do we have whenever we make something? AUDIENCE: Cost. BLADE KOTELLY: Cost. Sure. What do you mean by cost? AUDIENCE: The cost of manufacturing. BLADE KOTELLY: The cost of manufacturing. What about software? Does it cost anything to manufacture software? AUDIENCE: Yes. BLADE KOTELLY: What does it cost? AUDIENCE: Time. BLADE KOTELLY: For the-- well, yes. Let's call that the design development portion. But how about the manufacturing of it? Because if I manufacture toothbrush, I've designed and developed it and now I could have machines that are stamping out toothbrushes and putting bristles all on stuff. How about software? Any cost of software? [INTERPOSING VOICES] A lot less. There is a cost, though. Because I gotta pay somebody to host it and somebody to-- every time you download software, it costs a little bit of money and that begins to add up. So yes. AUDIENCE: Cost of memory-- BLADE KOTELLY: Absolutely. Yes. So there are costs involved that can limit us. What else? AUDIENCE: Time. BLADE KOTELLY: Time. What kind of time? AUDIENCE: When you're in the-- basically any stage, you have a certain amount of time to get this done, so you've got deadlines to meet. Plus, if you're paying people to work for you, the longer they're working on it, the more that turns into money later. BLADE KOTELLY: Yes. So there are lots of costs involved. I'm sorry, lots of time costs involved. So the time it takes for something to be executed upon to the time we have to execute it. In classes, you're often limited by time. If you had an infinite amount of time, you could learn the material much more easily, probably. What else are we limited by? AUDIENCE: Finite amount of raw materials. BLADE KOTELLY: Materials, right. And materials can come in a lot of versions. Resources can be physical resources, they can be people resources, they can be environmental resources that we have access to. Anything else? AUDIENCE: Technical capabilities. BLADE KOTELLY: Abilities. Knowledge. We can be limited by knowledge. So we have a team-- a brilliant team. You're all brilliant people. Who here knows the process of opening a restaurant that's successful? OK. So right now we're limited by a certain level of knowledge. If we all decided to open a successful restaurant tomorrow, but you are all brilliant people, so maybe we could figure it out very quickly. Maybe not. Maybe we'd find someone who's already opened a successful restaurant to let us know all the things we should know and short circuit that amount of failure time we have. OK. So, from there we go into a hazard analysis. And we're thinking about here, what's safe? Or what can go wrong? So in classical design, let's say it's a baby's high chair. I might say, well, if the baby can slip underneath the high chair, that's not safe. So you gotta keep that from happening. If I'm designing a stock trading system, where online you get to buy stock or maybe call over the phone. You say, buy 100 shares of Microsoft at the market price. What could go wrong? AUDIENCE: Fraud. BLADE KOTELLY: Fraud. What kind of fraud? AUDIENCE: Someone impersonates someone else BLADE KOTELLY: So we have a security issue there. We don't know if you are you. What else can go wrong? AUDIENCE: In terms of how you design the website or whatever else-- the interface-- if it's really easy to make mistakes. Say, an extra zero somewhere. BLADE KOTELLY: Yes. What if I put a number in and I don't put the dots and I have two zeros. It's a bit more than a rounding error. In fact, a friend of mine just made a piece of software where you can pay-- you walk into a restaurant and if they have the software running, you can walk in to say, I'm here at the restaurant. And then when you want to leave, if a bunch of you are all eating together, so we're all eating and we want to split the bill differently, and he ordered something, the very expensive caviar, and she ordered the very expensive champagne, and she ordered the very inexpensive fries, and she ordered the somewhat moderately expensive chicken, and I didn't order anything. Well, we want to split the bill somehow. Well, they make it very easy to do it. But they were just testing it in real life and for a server, the server came over said, let me see how to do this. And he said, sure let me show you. The server entered in the numbers for how much we had. But it came out to a huge number. Much more expensive. 100 times more expensive. Because servers, on these point of sale systems that they press in, they don't enter the decimal point. Because it's faster to just type in the numbers and enter two zeros. So his system required that you enter a decimal point. And he realized, oh, gotta change that behavior. So what can go wrong. We think about in this hazard analysis, which is lots of things. And so when you're designing something, you want to think of what can go wrong. In software, we have bugs. Bugs can go wrong and we try to mitigate for that. In physical design, it can be unsafe. Someone's hand could be caught something. They could pinch their hand. It could cause injury. From that, we do a specifications phase to really sit down say, OK. What is required? What's required of this design without any specific instructions of how to design it? What's required? So in this phase, we really sit down to figure out what we need to do. But we haven't said what to do yet. We go on to creative design. Who here knows how to brainstorm? Who here does not know how to brainstorm? OK. Brainstorming is really important and we'll talk about this a little bit later. How you brainstorm is important as well. This is the part where we begin to think about all the different things that are possible. And if you're working with a good team or people you like a lot, it's easier to come up with really interesting ideas. They may be terrible ideas but they may be very interesting. And that's OK. From there, we start narrowing down to conceptual design. What are the potential solutions that we can make? So we might have a few different ones that look pretty good. But they may not work together. We might say look, we go down one path, we can't go down the other path. They are mutually exclusive. Or if we try to do both paths, they're very hard to do together. So we narrow down the concepts and then we say, OK, we're going to pick something. At this phase, you might just say, let's pick whatever one we want to. Or you might have a process for picking a design. You might ask experts to help you pick which approach to take. You might do market research. You might do a whole bunch of other things to figure out which one you prototype. And lastly, the last step is verification. And I don't mean quality assurance. I don't mean does it work to the specification. Of course we expect it to work as we want it to work. But I mean, do people like? Can they use it? Do they want to use it? Is it emotionally and intellectually compelling? Does it makes sense? Does it connect with people on these two levels? And that goes right down to very small things. To parts and cars. Goes to things that are consumer products and things that are less obvious in terms of being consumer products. And we have an end solution but is it an end solution, really? What solutions or products do you know that cannot be improved upon? Any ideas? That's pretty good. Maybe there is something out there. But I like the idea that we can improve on anything. So end solutions mean if there's more room for improvement, we go back and do the whole process all over again. Let's map this to cooking dinner. Who here has cooked dinner? Who has never cooked anything in their life? Ah, it's worth cooking. You'll like. It will make you less hungry. So let's start off. We're going to identify the needs. What is the underlying reason that we cook dinner? AUDIENCE: Hunger. BLADE KOTELLY: Hunger. Because we're hungry. What other underlying reasons could there be for cooking dinner? AUDIENCE: Other people are hungry. BLADE KOTELLY: Other people are hungry, yes. AUDIENCE: Could be a social occasion. BLADE KOTELLY: A social occasion. AUDIENCE: To stay alive. BLADE KOTELLY: To stay alive, yes. Maslow's hierarchy here. AUDIENCE: Not to take the dining plan. BLADE KOTELLY: To avoid a required dining plan, you need to cook. OK. What else? AUDIENCE: To win or earn money. BLADE KOTELLY: To win or earn money. Do you mean, on a TV show? Fantastic. AUDIENCE: I like cooking. BLADE KOTELLY: You like cooking. It's an enjoyable experience. It's fun to do. It's creative. What else? AUDIENCE: Boredom. BLADE KOTELLY: Boredom. I'm bored. What should I do? Watch TV? No. Play video games? No. Cook? Great. Why else would we cook? AUDIENCE: To come up with new dishes. BLADE KOTELLY: To come up with new dishes. To create, to innovate on dishes. What else? AUDIENCE: To impress someone. BLADE KOTELLY: To impress someone. Who might you want to impress? AUDIENCE: Boyfriend or girlfriend. BLADE KOTELLY: Ah, a date. A boyfriend or girlfriend. Great. Jackie. OK. So Jackie has a date. And she's identified the needs. She's gotta impress her date. We go on to an information phase. What in the world can help Jackie determine how to impress her date? AUDIENCE: What does he like to eat? BLADE KOTELLY: Ah, yes, so she's lost her voice here. And she said, what does he like to eat? Right. What does the date like to eat? Right. That's what we want to find out. So we're doing market research to that point to figure out the preferences of our target audience. Emily. AUDIENCE: What the date's allergic to? BLADE KOTELLY: What's that he's allergic to? I would put that in step number five. AUDIENCE: Food in season? BLADE KOTELLY: Ah, food in season. Yes. We could be informed by what food is in season. And how would we find out what food is in season? AUDIENCE: Grocery store or look online? BLADE KOTELLY: You can go to the grocery store. Now, tomatoes. Have you ever not been able to find a tomato at your grocery store? But they're not in season very long. So the question is, if you want to get something that's in season and local perhaps, you can go to grocery stores, you could look online. AUDIENCE: Farmers market. BLADE KOTELLY: A farmer's market where the farmers who are local come over there and they'll let you know, we've got lots of kohlrabi. Rabi Who here has ever used kohlrabi? Who's ever heard the word "kohlrabi?" OK. So it's one of those things that farmers' markets have lots of. What else? AUDIENCE: What's affordable? BLADE KOTELLY: What's affordable. I might put that under our planning research and operational research there. Jackie. AUDIENCE: What do you know how to make? BLADE KOTELLY: What do you know how to make. Knowledge. That's what would be limited by in planned research. But what else can inform our decision can also be that. Which is, I happen to make these four things really well. So, that's part of my research. What else? What else might we look to, to help us with planning a date for Jackie? AUDIENCE: Whether he or she is vegetarian or not. BLADE KOTELLY: Whether the date is vegetarian or not could inform us. So some market research. AUDIENCE: What kind of date it is. BLADE KOTELLY: Ah, the kind of date. We're going back to step one. Tell me about this. AUDIENCE: It could be a very important occasion as far as like engagement. Or it might be like a first date. BLADE KOTELLY: A first date, an engagement. And they might be different. So the first date may not have caviar and a diamond ring. It might. Might be pushing it a little bit much, if you want the date to go more than five minutes. OK. So, yes. So first day and an anniversary date might be very different. AUDIENCE: What tools you have to cook with? BLADE KOTELLY: Tools you have to cook with. Yes. I might put that again under planned research but information phase as well. AUDIENCE: What Jackie likes to eat. BLADE KOTELLY: Ah, yes, what you want to yourself. Jackie enjoys pasta and hates hamburgers. What about some resources that are available for research? Ann. AUDIENCE: You can get a cookbook to see what types of foods go well together. BLADE KOTELLY: Cookbooks. Absolutely. And she said to look at cookbooks to see what kinds of foods go well together. Most cookbooks don't tell you this. Interestingly, most cookbooks tell you how to cook a specific dish, but don't tell you what to cook it with. Some very good cookbooks do. I recommend Mark Bittman if you're cooking and you're in college. It's a great cookbook and tells you what to pair with it. What did you say? I heard something else. AUDIENCE: The internet. BLADE KOTELLY: The internet. Absolutely. And what might we Google? AUDIENCE: The price of stuff at stores, recipes, what goes good with it, everything. BLADE KOTELLY: So we have we have recipes we could Google, the price of stuff at the store. Let's bring up Google for a second here. OK. So, let's bring this over and type in, price of stuff at the store. Just slide it over-- Great. And slide it over to the right a little bit, please. [LAUGHTER] Jackie. Do you like beer? Like beer, Jackie? Because if you do, this is a great thing to Google? OK. What else might we Google? Thomas. AUDIENCE: What does my date like to eat? BLADE KOTELLY: Let's Google what does my date like to eat? On the board, 100 people surveyed, top answers. 10 foods you should never eat on a first date. Phenomenal. The person's not sure if they can eat chorizo that is still not expired for another month. I'm glad they posted it on here and it's the second result. What else should we Google? AUDIENCE: Delicious food that's easy to cook. BLADE KOTELLY: Delicious food that's easy to cook. It's auto completing. This is great. Which I guess, John has already been to. John is in charge or does a lot of work with the food at his fraternity house, and that makes a lot of sense. What else might we Google for what you should cook on a first date. How about, what should I cook on a first date? I have no idea what's going to come up. AUDIENCE: Be careful. Be careful. BLADE KOTELLY: Actually, go back to what should I cook on. Let's go back to what should I cook on. And hit space. A, letter A. Romantic dinner, first date, and date come up at the top three suggestions by Google. That's pretty cool. OK, let's go back to that slide, please. Yes. So this is pretty cool. OK, we're getting a lot of information right now from Google. And we're up here to stakeholder phase now. Who are the stakeholders involved? AUDIENCE: Jackie. BLADE KOTELLY: Jackie. Who else? AUDIENCE: Her date. BLADE KOTELLY: Her date. Who else might be stakeholders involved? AUDIENCE: People that sell food. BLADE KOTELLY: People that sell food, absolutely. Yes. AUDIENCE: Her parents. BLADE KOTELLY: Her parents. If they don't like Jackie's date at all. Make the pineapple upside cake. But mom, I can't make that. Make the-- AUDIENCE: Maybe anybody that shares the kitchen with Jackie. People sharing the kitchen. There could be other stakeholders because maybe Jackie lives with other people. And she's like, hey can you be out of the kitchen tonight? I'm Like, no, I've got a really important date. I'm making dinner. Two people making dinner dates at the same time. BLADE KOTELLY: OK. Planned research. What could we be limited by? What could Jackie be limited by? AUDIENCE: Cost. BLADE KOTELLY: Cost. Right. So maybe the beluga caviar is prohibitively expensive for the date. Daniel. AUDIENCE: Experience. BLADE KOTELLY: Experience. Cooking experience. I can boil water but I can't make a bechamel sauce. OK. AUDIENCE: Equipment. BLADE KOTELLY: Equipment. Yes. I have a pot to boil water in but do not own a toaster. Making toast is harder. Not impossible, but harder. Yes. AUDIENCE: Time. BLADE KOTELLY: Time. Oh my god, the date's in half an hour. I haven't started dinner. I haven't been to the store. Calling Dominoes. OK. What else could you be limited by. AUDIENCE: Her date's dietary restrictions. BLADE KOTELLY: Yes, and I like that, actually, dietary restrictions in that phase. Stephanie. AUDIENCE: Ingredients that you can't find at the store. BLADE KOTELLY: Ah, yes, ingredients that you can't find at the store. So sometimes certain-- you have to go to special markets to find certain kinds of special spices or something else. And if you can't get that at your local store, then you may not be able to get it all. Or maybe you have to fly it in or mail order it or something. OK. This is good. Hazard analysis. What could go wrong when cooking dinner for a romantic evening? Rod in the back. AUDIENCE: Allergies, food poisoning. BLADE KOTELLY: Allergies and food poisoning. Should she cook the chorizo? I don't know. Looks kinda iffy. Allergies, yes. AUDIENCE: Faulty equipment. If you have a bad stove. BLADE KOTELLY: Yes, faulty equipment could cause a fire or something. That's really bad. AUDIENCE: Setting the entire chicken on fire. BLADE KOTELLY: He sounds like he speaks from experience. AUDIENCE: Personal injury. BLADE KOTELLY: Personal? AUDIENCE: Injury. BLADE KOTELLY: Injury, yes. So when cutting onions, look at the onion and don't try to make cool eyes. Stop. Bleeding is not considered cool on a date if you can avoid it. AUDIENCE: Quantity of food. BLADE KOTELLY: Yes, quantity of food, absolutely. This is a very real issue that really happens on dates. I'll tell you a story when I'm not on camera sometime. AUDIENCE: Your date doesn't show up. BLADE KOTELLY: Oh, yes. She's not speaking from experience. But yes, the date doesn't show up. That is sad. That can be a very sad thing. AUDIENCE: Or you have a pset due the next day. BLADE KOTELLY: Or you have pset due the next day. Not a good day for a romantic evening. What else? AUDIENCE: Forgetting to set a timer. BLADE KOTELLY: Yes. That's an easy thing to go wrong-- not setting timers. Yes. In fact, yesterday I did not set a timer. I put a thermometer inside the chicken and I said, great, when the thermometer reads 162, I'm going to pull the chicken out, no problem. I proceeded to enjoy the company my friends and drink the wine and went, oh my god, came back over here, went oh, 175. Darn it. Yes. I should have set a timer. That would have been helpful. AUDIENCE: Unlabeled food ingredients, such as salt and sugar. BLADE KOTELLY: Confusing two similar in appearance ingredients like salt and sugar. Thomas sounds like he speaks from experience in this one. Yes. Not so good in coffee, salty coffee. But I believe popular in some places. AUDIENCE: [INAUDIBLE] BLADE KOTELLY: I'm sorry? AUDIENCE: Fire drills. BLADE KOTELLY: Fire drills. Something's that are a little bit beyond your control. OK. So this is good. Good hazard analysis for that. Specifications. From there, we try to figure out what we're going to do. We might make a shopping list. We might make a list of what we're doing for the recipes. We go on to design it. And then we have to figure out, do people like it or not? Verification. How do we test to figure out if people are going to like it or not? Ben. AUDIENCE: Take a small bite. BLADE KOTELLY: Take a small bite. Take many small bites. Over the course of the meal, they say a good cook keeps tasting it before you serve it. What else could you do? AUDIENCE: Get someone else to taste it. BLADE KOTELLY: Get someone else to taste it, yes. When? Do you say, psst, come over here, John, come over here, I'm about to serve it to Jackie. No, when? At the time? AUDIENCE: Earlier. BLADE KOTELLY: Earlier. How much earlier? An hour? AUDIENCE: Enough so you have time to fix it. BLADE KOTELLY: Enough time so you could fix it later. What else could you do? AUDIENCE: Call mom and ask if it's supposed to be brown. BLADE KOTELLY: Mom, the chorizo's not looking very good. Yeah. Purple, green, yeah. Use it? OK. AUDIENCE: You could, if you wanted to, do like a practice dinner beforehand. BLADE KOTELLY: Ah, yes. A practice dinner beforehand. Let's see if you can make this stuff and how it tastes and if you like it. That's exactly right. OK. So I've given you a design process that I'll tell you, you can use for making anything-- anything you ever make ever, ever, ever, ever, ever, ever, ever, ever, ever, ever, ever-- ever. In all your engineering disciplines, you can use this exact same process all the time for anything you want to make. We've got it to cooking dinner. Let's have you try it on your own. Let's try this. Here's your design challenge. Map the steps of throwing a surprise party for your best friend. You're going to map the first five steps. I want you to work in groups of three-- the people in your vicinity. I'm going to give you about five minutes to do this. First five steps as completely as you can to throwing a surprise birthday party for your best friend. Here we go. All right, so right now the students are trying to figure how to map the steps to throwing a surprise birthday party for their best friend. And they'll take about five minutes to do this. Over those give minutes, they'll try to map each of the steps individually. And we're going to do a debrief and figure out what they said. But now, if you want to, try doing it yourself and see if you can come up with a really good solution. And see if they get some ones that you don't get. All right, let's find out what you said to solve this problem. So you've had five minutes to try to figure out how to solve the first five steps of this problem. To figure out how to throw a surprise birthday party for your best friend. What is the underlying problem that we are trying to solve? AUDIENCE: They don't have plans for their birthday and we want to make it awesome. BLADE KOTELLY: She said we don't have plans for the birthday, and we're trying to make it awesome. Or they may have plans for the birthday and we're still trying to make it awesome. What are the other aspects of the underlying problem? AUDIENCE: It's a surprise. BLADE KOTELLY: It should be a surprise. Stated in the problem statement but also true. What else? Underlying problems, underlying objectives. AUDIENCE: Throw a fun party for all those involved. BLADE KOTELLY: To throw a fun party for those involved. Let's talk about those involved-- who are they? Anybody. In the back. AUDIENCE: And the actual person whose birthday it is. BLADE KOTELLY: And the actual person whose birthday it is, yes. What else? That's it? No other reason to throw a birthday party? AUDIENCE: So that you get one later on. BLADE KOTELLY: Ah, it's for you to get one later on. In psychology, we call it the reciprocity effect. Good. OK. So, we've identified the needs. Information phase. What can inform us about how to throw a surprise birthday party? AUDIENCE: How old they're turning? BLADE KOTELLY: How old they're turning? What do you mean by that? AUDIENCE: Probably don't throw a clown party for a 50-year-old. BLADE KOTELLY: You don't throw a clown party for a 50-year-old. I happen to know some 50-year-olds who might enjoy that, but it'd be kind of weird, right? OK. So maybe you do. Gotta pick your 50-year-olds very carefully. [? Affinity? ?] AUDIENCE: When their birthday is. When their birthday is. BLADE KOTELLY: When their birthday is would inform it, absolutely. AUDIENCE: Just a quick question, does surprise party automatically mean it's a birthday party? BLADE KOTELLY: This is a surprise birthday party. I'm sorry, yes. In this case it did. I didn't put that on the slide. Yes, you're right. AUDIENCE: When they're free. BLADE KOTELLY: When they're free would influence it, absolutely. What else can inform us about throwing a surprise birthday party? AUDIENCE: If they like surprises or not. BLADE KOTELLY: If they like surprises or not absolutely will inform us about how to throw a surprise birthday party for someone who doesn't like surprises. AUDIENCE: What they like to do. BLADE KOTELLY: What they like to do. For example? AUDIENCE: If they like to go out bowling or something, you can throw a surprise birthday party. BLADE KOTELLY: Right. To appeal to their hobbies and likes. Great. What else? AUDIENCE: What kind of friends they have. BLADE KOTELLY: What kind of friends they have. How do you mean that? AUDIENCE: It informs who we're going to invite to the party. BLADE KOTELLY: Informs who we're going to invite, yes. AUDIENCE: Size and nature of the social circles. So you could have small gatherings or big gatherings. BLADE KOTELLY: Yes. So how big the party should be. What else could inform us? AUDIENCE: Past parties that you have been to. BLADE KOTELLY: Past parties you've been to. Personal experience, where you say, this was an awesome party. This party sucked-- we are not going to do one of those again. Right. Absolutely, past experience is hugely important. AUDIENCE: What can you do to distract them? BLADE KOTELLY: What can you do to distract them. How do you mean? AUDIENCE: You have to trick them into showing up in a room full of people at some point. You need a plan. BLADE KOTELLY: You need a plan, yes. OK, good. So that's information phase that can inform us about it. But we forgot one of our most valuable tools that we talked about before. AUDIENCE: Google. BLADE KOTELLY: Google! And what might you Google? AUDIENCE: How to throw a surprise party. [INTERPOSING VOICES] BLADE KOTELLY: How to throw a surprise party. And do you think you'd get any results? A ton. You'd get a ton. Google has all the information that would appear. OK. Stakeholder phase. Who are the primary stakeholders? AUDIENCE: Guest of honor. BLADE KOTELLY: Guest of honor. AUDIENCE: Everyone invited. BLADE KOTELLY: Everyone invited. AUDIENCE: You. BLADE KOTELLY: You. Who are secondary stakeholders? AUDIENCE: People who live in the place you're hosting. BLADE KOTELLY: The many people who live in the place you're hosting, the neighbors that call the cops all the time, and therefore the cops are also stakeholders. OK. Planned research, operational research. What are we limited by? AUDIENCE: Money. BLADE KOTELLY: Money! Great. So if we don't have a lot of money, we can't buy the expensive beer. What else? AUDIENCE: Again, time. BLADE KOTELLY: Time. When's their birthday? Tomorrow. No way. Tomorrow. What am I going to do? Going to throw a surprise birthday party in one day is going to be really hard to do. Right. OK. How much time do have exactly. What else? AUDIENCE: Your best friend's schedule. BLADE KOTELLY: Your best friend's schedule. Yes, because they could be traveling or our of the country or working night shifts or something like that, right. OK. What can go wrong at a surprise birthday party for your best friend? Veronica. AUDIENCE: The person doesn't show up. BLADE KOTELLY: The person doesn't show up. Absolutely. David. AUDIENCE: Person finds out ahead of time. BLADE KOTELLY: The person finds out ahead of time. AUDIENCE: None of the guests show up. BLADE KOTELLY: None of the guests show up. It's you and the person, you're like, surprise. AUDIENCE: Going back to the cops. BLADE KOTELLY: Going back to the cops. AUDIENCE: Having them come. BLADE KOTELLY: Having the cops come. Yes. Ben. AUDIENCE: If you scare them into heart attack. BLADE KOTELLY: Yes. You don't want to scare your friend if they have a heart condition. That's good. Cameron was that yours? AUDIENCE: Yeah, weather. BLADE KOTELLY: Weather. So don't have an outdoor party when it's going to be threatening to have a thunderstorm. Or in January in Boston. Not a good time for an outdoor barbecue-- just isn't. Kristen. AUDIENCE: You accidentally send someone to the wrong location. BLADE KOTELLY: Ah, yes, someone goes to the wrong location. Thomas. AUDIENCE: You have invited some people that your friend is on bad terms with. BLADE KOTELLY: Ah, yes. The old ex-girlfriend issue. I thought you were together. We haven't been together for months. I didn't know that. So I'll tell you a little story. So my best friend in high school-- we're best friends and I'm throwing him a surprise birthday party. And my best friend was notorious for not showing up to things. You make plans a week ahead of time, you confirmed a few days ahead of time, it's Friday night-- ghost town. Just not there. And no one knows where he is. He just was kind of casual. This happened all the time. And we all knew this. I said, OK, I'm going to make sure he shows up. So I said, look-- he's really into art and design-- there's this great exhibit coming up for an M.C. Escher thing they're doing at this museum in Boston. And there's someone speaking and I'm going to buy tickets to it for your birthday and they're really expensive so can we clear the date, make sure it's OK. He goes, yeah, it's fine. Great. So it's like two months out. Two months. So a month later, I'm like hey, looking forward to that exhibit thing? He goes, oh, yeah. Do you have it in your calendar? I do have it in my calendar. It's like the only thing he had in his calendar. It's good. It's now like a week out. Hey, dude. Next Friday we're going to the M.C. Escher exhibit. Right on. It's great. Perfect. It's Monday. Hey, Friday night, we'll get together like 6:00-ish, we'll go and get some dinner or something. Then we'll go-- yeah it sounds great. Cool. Great. Wednesday. Got two days. Two days away! Cool. Right on. Thursday. Tomorrow! Friday night, 6 o'clock, his house. I go there, what happens? AUDIENCE: He's not there. BLADE KOTELLY: No, he's there. It's amazing. I'm blown away. I'm like, he's actually there. Incredibly cool. So we do our whole thing. We go. We go to the thing. We go to the house. We walk inside, open the door. I go around the side of the door. Everyone's waiting here. He comes up around the door, everyone goes, surprise! And he's like, what? I said, dude it's your surprise birthday party. Surprise! And he's like, I thought we were going to an exhibit. No, no, that was all fake. But you bought the tickets. No, they're not real. And he was sad. What we learned from our hazard analysis, our post mortem, don't make the other event sound more fun than a surprise birthday party. OK. All true. Next. So, I've said you can map this to anything. Well, let's be a little bit more serious here. A little more serious about the engineering aspect here. You have four minutes now to map it to this. Making a car fueled by a nuclear reactor. Same groups. Four minutes. If you happen to be a nuclear engineer, you have a head start. OK. Right now, they're doing the same exact thing except for they're mapping something more engineering based. And the idea is that they can start to apply something that seemed very easy and informal to something a little bit more of their engineering curriculum. It's not a big stretch in this case here. They're going to get lots of practice throughout the whole semester being able to apply this to a variety of different environments and produce things using this process. But here I wanted to show that there's a mapping that exists between stuff that seems very unrelated to engineering, like throwing a birthday party, and some very engineering related. Let's see what they come up with. All right. Let's find out what you thought about how to solve this problem. Mapping the steps to making a car fueled by a nuclear reactor. What is the underlying objective? Or what could the underlying objective be? AUDIENCE: Finding a new means of fuel. BLADE KOTELLY: Different fuel. AUDIENCE: Building a car that never needs to be refueled. BLADE KOTELLY: A car that never needs to be refueled. AUDIENCE: Cleaner energy. BLADE KOTELLY: Cleaner energy. AUDIENCE: Job market for nuclear engineers. BLADE KOTELLY: A job market for nuclear engineers. That's very good. I like that. What else? AUDIENCE: Faster car. BLADE KOTELLY: Faster car. Zoom! What else? AUDIENCE: Cleaner for the environment. BLADE KOTELLY: Cleaner for the environment. Yes. What else? OK. Step number two, what can inform us about how to build-- where might we look to understand about how to build a car fueled by a nuclear reactor? AUDIENCE: Other vehicles fueled by nuclear reactors, like submarines. BLADE KOTELLY: Like submarines that are fueled by nuclear reactors, yes. Understand how a submarine works. Jackie. AUDIENCE: Current car designs. BLADE KOTELLY: Current car designs could inform us about what we could do. AUDIENCE: How you could research possible nuclear accidents. BLADE KOTELLY: Ah, look at nuclear accidents. I'm going to put that under the hazard analysis section. But yes, absolutely. Charlotte. AUDIENCE: Small module nuclear reactors. BLADE KOTELLY: Small? AUDIENCE: Module. BLADE KOTELLY: Module nuclear reactors. She knows a little bit about this. AUDIENCE: I just got hired to work them. BLADE KOTELLY: She got hired to work on them, great. You could actually research the thing that you might want to use. AUDIENCE: Professors. BLADE KOTELLY: Professors. Yes. You could talk to professors who deal with these things. AUDIENCE: What regulations exist on nuclear reactors in cars. BLADE KOTELLY: Regulations about nuclear reactors in cars or other kinds of transportation. AUDIENCE: Find out what aspects of cars people don't want to change. BLADE KOTELLY: What aspects of cars people don't want to change. Sure. AUDIENCE: Who will want to use it. BLADE KOTELLY: Understand the potential market of people who might want to have a car that never needs refueling, Stakeholder phase. Who are the stakeholders? Ben. AUDIENCE: Everyone who's Course 22. BLADE KOTELLY: Everyone who's in nuclear engineering. Who else? AUDIENCE: NRC. BLADE KOTELLY: The NRC who are the--? AUDIENCE: Nuclear Regulatory Commission. BLADE KOTELLY: Nuclear Regulatory Commission. So, government. Government. Who else? AUDIENCE: Everyone within a 50-kilometer radius. BLADE KOTELLY: Everyone in a 50-kilometer radius of you driving your car. Rod. AUDIENCE: Oil companies. BLADE KOTELLY: Oil companies. Yes, they are a stakeholder. Absolutely. Yes. Because if you have a really great car that doesn't need to be fueled ever, they're like, excuse me, pardon me, would you mind not making that? AUDIENCE: Countries that mine uranium. BLADE KOTELLY: Countries that mine uranium. So, they're definitely stakeholder because they've got uranium. Dale. AUDIENCE: If we haven't said it already, car manufacturers. BLADE KOTELLY: Car manufacturers. Yes. Who else? We haven't said one particular constituent group that I think are very important in this particular calculus. Maybe not. AUDIENCE: Mechanics. BLADE KOTELLY: Mechanics. Wow, yes. Boy, how do you fix that? No idea. Why not? Didn't go Course 22. Really? What'd you do? Course 18. What else? AUDIENCE: You. BLADE KOTELLY: Yes. AUDIENCE: The nature of the fact that you're designing them. BLADE KOTELLY: The designer. Or the person who's the consumer. AUDIENCE: Anyone who buys a car. BLADE KOTELLY: Anyone who buys a car. Right. Absolutely. Anyone who buys a car-- electric cars, non-electric cars. Anyone else? That's a good list. Planned research. Operational research. What are we are limited by? AUDIENCE: Fission or fusion. BLADE KOTELLY: Ah, the choice between fission or fusion. AUDIENCE: Current roads and whether we can have nuclear reactors on them. BLADE KOTELLY: Yes. Whether we can actually have this on our current infrastructure. David. AUDIENCE: Disposable spent fuel. BLADE KOTELLY: Disposable spent fuel, yes. Charlotte. AUDIENCE: Have to have low enriched-- you'd have to have low enriched uranium. You can't have highly enriched uranium. BLADE KOTELLY: OK. So we're limited by our ability to get low enriched uranium. Yes. I'm glad we have you here. AUDIENCE: What's the cost of making them? BLADE KOTELLY: Cost. Absolutely. The cost of making a nuclear powered car. Jake. AUDIENCE: Different laws on street legal vehicles. BLADE KOTELLY: On? AUDIENCE: Street legal vehicles. BLADE KOTELLY: Yes. Government laws on street legal vehicles and what you can and can't do with a vehicle to begin with. [? Yu? ?] AUDIENCE: Price that people are willing to pay for a car that doesn't refueling. BLADE KOTELLY: Yes. What would you pay for a car if it never needed fuel ever again? It's a good question, right? Would you pay a million dollars? No. Do you think you're paying a million dollars now in gas over the course of your life? AUDIENCE: Your car won't last that long. BLADE KOTELLY: Your car won't last that long. OK. Foiled again. What else? AUDIENCE: Whether people would buy it because it's a nuclear reactor. BLADE KOTELLY: Whether people would even buy it. It's nuclear reactor. I don't want to get that car. But it never needs fuel again. I don't want that car. Well, why not? Because I don't want to glow, I don't know. What else are you limited by? AUDIENCE: How available the raw materials are. BLADE KOTELLY: Yes, availability of raw materials. What could go wrong? What could go wrong in a nuclear powered automobile? AUDIENCE: Two cars crash into each other. BLADE KOTELLY: Two cars crash. That doesn't seems so wrong. So far, it sounds OK. Or are we talking about fusion? What do you mean by that? AUDIENCE: Finding out what happens-- BLADE KOTELLY: Oh, what happens to the nuclear reactor during a car crash. What was that movie-- was it the new Batman? [INTERPOSING VOICES] They had a nuclear thing in a truck and it kind of like, boom, boom, boom, boom. You're like, oh no, that seems so bad. But everything worked out just fine. Batman saved the day. OK. What else? AUDIENCE: Can it be modified to serve another purpose. BLADE KOTELLY: Such as? A what? AUDIENCE: Like a more dangerous purpose. BLADE KOTELLY: A more dangerous purpose. So yes. You could have terrorists who take advantage of the fact that you have a nuclear powered car to create a nuclear powered bomb. I saw that in "Batman." I know. I saw. Everything I ever needed to learn, I learned from watching "Batman." Cameron. AUDIENCE: If it's a fission reactor, where does the waste go? BLADE KOTELLY: Ah, waste. Yeah, what do you do with waste disposal? Right. Ben. AUDIENCE: Exposure to radiation. BLADE KOTELLY: Exposure to radiation. Yes, absolutely. Charlotte. AUDIENCE: Control and proliferation concerns. BLADE KOTELLY: Control and proliferation concerns. What does that mean? AUDIENCE: If you create nuclear waste, and you can't control it, someone can take it and turn it into a nuclear bomb. BLADE KOTELLY: Yes, OK. So how do we keep that thing from happening that could be used negatively and prevent that. What else could go wrong? AUDIENCE: Do it yourself people. BLADE KOTELLY: DIY. How to build a nuclear reactor at home. Yes this may require a few more tools than most people have. OK. So are you beginning to see how we can start applying this process to things of engineering base as well? Right, that you have to make? And now, you may not be making a nuclear powered reactor car right now, but Charlotte, you're working on these small reactors, right? And what could they be used for? AUDIENCE: So the market shares that number one, reactors are really expensive and they're very big. And if you don't need 1,200 megawatts of power and you don't want to spend $7 million, you can get 250 megawatts of power for $1 million. BLADE KOTELLY: OK. So you could make a small reactor and use it to do what? AUDIENCE: Basically, you create electricity and then distribute it cheaply. BLADE KOTELLY: So cheap electricity. And where would you want to do that? AUDIENCE: All over the world. BLADE KOTELLY: All over the world. In even a company, potentially like Apple where they have that new campus being put up. They have their own power energy place and they might, potentially, put a nuclear reactor there, right? They could power their whole thing and then supply the energy back to the grid, if they chose to do that. OK. Joel, did you have a--? JOEL SCHINDALL: Yeah. This process we're going to use again and again during the course of the term. But I wanted to just point out a few things to set a little bit of context for you. First of all, I think there's an image that designers just kind of go into this special sort of a daze and they come out with a wonderful invention, a great dress, a beautiful room layout or something like that. And I want to point out that it rarely happens that way. The design is work and effort and looking at relationships and going again and again. And looking at what's wanted and what's needed and what's the context of it. And actually what we described here is not that different from what you do as engineers when you study engineering. It's breaking down the problem into parts, looking at the relationship between those parts, and optimizing the system, just like you optimize an engineering system that's designed to generate electricity or build a bridge whatever branch of engineering that you might be involved in. So actually you've got the kind of training to be able to do good design. Second point I want to make-- the numbers, one, two, three, four, five. We all know how to count. So it sort of leads you into thinking you do one and then you do two and then you do three and then you do four. And again, not that way if you recognize that. Actually, good design, you're actually doing it in parallel. You get about up to number five and you're doing the hazard analysis, you realize some of the things, the assumptions you made early ain't going to work that way because they're dangerous to your health or other people's health. You go back to step one. So actually, this is a very good linear way of representing it. But in the actual implementation of doing it, you're going to move in and out of all those different phases. And then the third thing I want to say doesn't quite apply here but I spent a lot of time in the satellite industry. And in the satellite industry, you go through a very careful analysis up front of the design that you've come up with. Make sure that it's reliable, that everything's going to hang together. And then, later on, down around here, you wind up making a few changes. Things are just a little bit different. You modify this. You modify that. And almost every serious failure that occurs is because after you made those changes, no one kind of went back to the beginning and said, well did this perhaps change the assumptions under which we based our design and move us onto a different track? So again, you always have to be aware of those things-- just kind of a perspective to put on it. BLADE KOTELLY: Rita. AUDIENCE: So say I'm Course 20 and I was hired by a Course 22 company to be a project manager and I don't even know of the existence of some of these problems that could come up. How do you go about figuring that out? BLADE KOTELLY: Ah, yes. How do you solve a problem when you don't know much about problem space. That is a good question which we're going to hold for now because of time. But we will address it because you will all be working on problems over the semester which you may no knowledge about. And so the question is how do you acquire that knowledge and how do you figure out what you don't know. It's a great question. I want to talk briefly about innovation. This is a huge thing. The course called "Engineering Innovation and Design." I have a very particular thought about innovation that I want to share with you. This is a diagram from a very famous design consultant and how they explain innovation. Now, I think I see where they're going. They talk about the business on one side, technology and people. And they say, look, innovation happens in different places here. Process innovation occurs between business and technology. Functional innovation occurs over here. Emotional innovation occurs over here, like building a brand. And then they have experience innovation. And this is this thing that's very, very special. They say yes, when we combine understanding of the business, the technology, the people. Do we build something that people want? Is it able to be built? And will it create a business that can sustain itself? Then we have achieved great experience innovation. Now it's not a bad model. And it's not untrue that innovation occurs in these places. But I think it's not a useful model. I think in that zone here, you build things that are useful. They're useful. But they may not be innovative. So here's my thing about innovation. There's something out there. There's something. And you're required to do something and yet you have this other tension pulling you because you desire to do something else that seems in conflict. I'm required to create a nuclear powered car but-- I desire to create a nuclear powered car, but I'm required to adhere to laws of government, which is causing a lot of problems. I am required to make an artificial heart valve and I want to make that but what I realize is that there's a problem because in this requirement, I have something that spins and it creates friction. And the friction causes blood platelets to form and causes clotting. And I desire to have no clotting happen even though I have this spinning object in a heart valve. Tension. I'm required to pass the class but I desire to go out drinking with my friends. These are in tension. OK. So when you have this and you start stretching this, by resolving this, this is where innovation occurs. Innovation is the result of resolving your need to do something with your desire of how it can be done. The designer's job is to reconcile the seemingly irreconcilable. The designer's job is to reconcile the seemingly irreconcilable. It's not that you can't do it. Maybe you think you can't do it. It appears that you can't do it. But you gotta think about it differently or think about it from a new angle. Or get some new information to resolve the seemingly irreconcilable. And that is what your job is your whole lives is to try to figure out the solution to these problems. If they were obvious, people would just do them. But when they're not obvious, and they cause this tension, this pain, this is where the innovation occurs. And where you get people who do things. Like a company called Levatronix who took that spinning thing. And they said, well, we know if they're touching it causes friction. Instead, they used magnets to levitate it so there's no friction at all inside of a heart valve. Do you want to talk about the heart valve for a second? JOEL SCHINDALL: There's a small company out in Walton called Levatronics. And part of their charter was to build an artificial heart that could be used at least temporarily as substitution until a real heart was available for transplant. And you know, the usual way that you build a pump is a rotary pump that produces just a constant pressure. But everyone knows that the heart beats like this. And everyone assumed that the body needs that heart beat in order for the biological processes to work as they're supposed to. Turns out, that's not the case. Turns out that if you pump blood smoothly through the body, it works. You get oxygen from the lungs to the parts that need it. And you actually can have a working rotary heart pump. So Levatronix thought, well, this would be a great thing to build except that the spinning pump shaft has a bearing at either end of the shaft and there's friction in the bearing which creates heat, the heat creates blood clots, the blood clots break off and go to the lungs and that's an embolism and the person dies. So the question was, well, looks like you can't do it. So talk about reconciling the seemingly irreconcilable. It turns out that you can magnetically levitate the ends of the shaft so that they don't actually touch the bearing. And you have a frictionless bearing. Now, it's not stable. It takes an external electronic circuit in order to be able to sense the little latitudinal motions that come up in the shaft. But we're pretty advanced in our technology now. We can sense the position of the shaft and you can fix that. And Levatronix has actually been selling that product for the last four or five years. It's saved lives. It works. It reconciles the seemingly inconceivable-- well, inconceivable-- but irreconcilable. And that is what I would call a real out of the box innovative idea. Yeah. AUDIENCE: Is this the company that they were written about in "Popular Science?" They were having people who had these smooth hearts going in. And they were going into doctors and freaking the doctors out because they didn't have a pulse? JOEL SCHINDALL: It certainly would fit. There were a few articles about Levatronix. I don't know that specific one. But yeah, that's right, they don't have a pulse. So when you say that to be alive, they must have a pulse, perhaps that's not a necessary precondition. BLADE KOTELLY: OK. So I want you all to work in pairs for just a few minutes. I want you to come up a list-- let's see who can come up with the longest list in three minutes, what group can come up with the longest list in three minutes, of either things you've experienced personally or things that you know about where people had to reconcile the seemingly irreconcilable. To solve a seemingly impossible design problem at the time. You have three minutes. All right, let's find out. OK. Who put down one thing or more? Wow. Pretty good. Two. Three things. Four things. Five. Six. Seven. Eight. Nine. 10. OK. 15. 20. 25. OK. 21. 22. How many did you get? AUDIENCE: 22. BLADE KOTELLY: 22 things. 22. Both 22? AUDIENCE: 21. BLADE KOTELLY: 21, OK. Who only got five or fewer? Five or fewer. Tell us one of them. AUDIENCE: Portable media players BLADE KOTELLY: Portable media players. Tell me what you mean by that. AUDIENCE: [INAUDIBLE] BLADE KOTELLY: Yeah, go ahead. AUDIENCE: Basically making something that is small and functional. BLADE KOTELLY: That would do what? AUDIENCE: Playing any kind of media. BLADE KOTELLY: Right. OK. So it's like the idea of putting all your music in your pocket, right? That seems impossible to do at some point in time, right? And now you're like, of course, all my music's in my pocket, all my videos are in my pocket, everything's in my pocket. Got big pockets. OK, yes. So things like that. That's an excellent one. In the back, yes. AUDIENCE: Infrared thermometers. Infrared thermometers. BLADE KOTELLY: Infrared thermometers. Yeah. How to be able to get the temperature of something at distance. Well, you got 21 of them. We're going to work our way up to you. OK people who got 10 or fewer. Groups that got 10 or fewer. OK. Tell us, Daniel. AUDIENCE: Selling a product without a salesforce. BLADE KOTELLY: Selling a product without having a salesforce. Right, that's an amazing idea. Like, what do you do when you don't have anybody doing the selling? How can you possibly do that? And said, ah, I've got the internet. I'm Jeff Bezos. I can sell everything the world. AUDIENCE: A self-driving car. BLADE KOTELLY: A self-driving car. Yeah. It seems impossible. GM is working on this and putting a lot of effort into this. In fact I've had a conversation recently with someone who thought there's no way we're going to have self-driving cars in the next 15 years. They think well, maybe for special lanes, special places. But I think we're going to see a lot more self-driving cars with breathalyzers on them. [PUFF] You are not driving home. Get in the backseat. You pass out. You wake up at home. OK. Amazing! Who else? 10 or fewer, yes. AUDIENCE: Oh, no sorry, I had more. BLADE KOTELLY: You had more than 10. OK. Who had 10 or fewer? AUDIENCE: Nuclear fusion. BLADE KOTELLY: Nuclear fusion. Can we do it? AUDIENCE: Yeah, just can't sustain it. BLADE KOTELLY: Just can't sustain it. Interesting. So we're so close. But we desire it. What else? How about 15 or fewer. I'm sorry, were we at 15? 15 or fewer. AUDIENCE: The invention of the light bulb. BLADE KOTELLY: The invention of the light bulb. So people thought, boy, how do we get light without candles? Right. How can I stay in light without candles? Who invented the light bulb? AUDIENCE: Not Thomas Edison. BLADE KOTELLY: Not Thomas Edison. That was a correct answer. Swan did. Swan did in England. Smaller version. Swan invents the light bulb. Edison's like, ugh, you. And he spends a lot of time trying to figure out how to get around this patent. But we all call them Edison bulbs and not Swan bulbs. Do you know why? AUDIENCE: Because he made them really big. BLADE KOTELLY: Because he made them really big. How did he do it? So clever. So in this whole thing, we talked about process, we talked about stakeholders and all these different people who are involved. And Thomas Edison had a very smart staff. And the staff had a very big-- we call it systems thinking perspective. They said, well look, candles are used or things that supply light and heat, gas lamps, are used on the side of fireplaces in a very expensive homes. Particularly in Boston. They said, here's an idea. We're going to take these light bulbs things, we're going to run wires right through the tubes that currently kept gas, we'll turn the gas off, and we'll put a little meter outside of your house that will measure how much of this electricity you're using for your light bulb. It's all brand new, right? So everyone's like, whatever, OK. And so they did it. It's cool because it won't burn down your house. And they put these bulbs in and they ran the wires through. Because they, said, if you don't like it, we'll pull out the wires, turn the gas on, everything just works. So it's easy low switching costs. Easy to start trying it out. Low risk. If you don't like it, you can go back. No problem. Money back guarantee. And a way of measuring it. And that's why he became hugely successful. OK. Great. Other inventions from people who got 20 or fewer. AUDIENCE: Yeah. SR-81 Blackbird. BLADE KOTELLY: Yes. The SR-71 Blackbird. Yes. Something that would go incredibly fast. How fast does it go? So fast we don't even know! I think it's still classified. And it goes so fast and flew so high that it couldn't be caught on radar. You couldn't even see. You didn't know it existed at the time. AUDIENCE: The design compromise was about the fuel because it's not sealed at ground level. BLADE KOTELLY: Ah, yes, so the design compromise specifically here, is that at ground level, it just leaks fuel. Because when it goes so fast, it gets really hot. And we all know from your thermal class that things expand when they get really hot, like metal. And it would expand and all of a sudden not leak fuel when it was flying really fast. But on the ground it is just dripping fuel. Pretty crazy, right? What if your car ran like that? I'd love that. I could drive fast all the time. I'm sorry, Mr. Policeman. I had to drive fast. I'd be leaking fuel all over the ground. AUDIENCE: Alternating currents BLADE KOTELLY: Alternating currents. Tell us. What was the-- AUDIENCE: They were looking for a way to distribute and transmit high voltage. Enough electricity to keep the [INAUDIBLE] and direct current would break. Would not-- it wasn't-- BLADE KOTELLY: Didn't work. OK. AUDIENCE: Motion pictures or movies. BLADE KOTELLY: Movies. Yeah. Movies. I want to see in front of me, stuff happening like I'm there. How do I do that? I just have to put you there, in front of a train, speeding towards you at 100 miles an hour. Or put a camera and I project on a big thing. And it's so big, it's so exciting, that people in the audience were aghast. They gasped when they saw people moving. What else? Actually, coming off of that-- color. We don't think about color too much. All we think of is black and white. But we want it in color. And that was a huge process change. And how about 22 items or fewer. We'll give you a chance. Go ahead, Patrick. AUDIENCE: The printing press was a big one. BLADE KOTELLY: The printing press. Yeah, huge deal. What was the issue? AUDIENCE: They were having to have scribes-- BLADE KOTELLY: Yeah, you have to copy everything by hand which leads to lots of-- AUDIENCE: Carpal tunnel. BLADE KOTELLY: I don't know if they really cared about the carpal tunnel syndrome thing back then. They might have cared. But lots of errors. Lots of errors and translation errors and tons of errors. And what else was the issue there? AUDIENCE: Slow. BLADE KOTELLY: Slow. It's very limited. So if you had a book, it's a very big deal to have a book. And probably in the future it will be a big deal to have a book again because we'll all be reading PDFs. And from-- is this your group who go 22? Yes. OK, yes. AUDIENCE: Paper cups. BLADE KOTELLY: Paper cups. AUDIENCE: How do you use something that isn't waterproof to actually hold water? BLADE KOTELLY: Right. So paper will let water go through it at some point when it saturates. And The question is how do you make it waterproof. Right. So these are all incredible innovations that occurred from paper cups to something like SR-71 Blackbird. And what I want to do is show you, quickly, a short video. This is a really interesting thing because the year it was made was? JOHN: 1987. BLADE KOTELLY: 1987. Take a look at this. OK, So I won't show you the whole thing here. If you'd like, we can send you a link. This is something Apple made in when? JOHN: 1987. BLADE KOTELLY: And in it you'll see there's a date that actually occurs. And the date is? JOHN: One year before Siri is launched. BLADE KOTELLY: Yeah. OK. So it's right around Siri's launch. And now we can do almost all the things you see in this video. You'll see there's a camera up there. He has a video chat with her. They're looking up things. He's correcting his spoken spelling of something which Google does all the time. With enough context, they correct things, sometimes even accurately. He's getting his information here. He's reading appointments. This is all something that's happening now. This was the idea they wanted so desperately to create. Something that allowed you to do something in the most natural way, but with technology. And we're basically there. So for your homework, I want you to do something that maybe none of you have ever done before, your homework. No, the-- OK. I want you to design a game. I want you to make a game. There's not many requirements you have. But it's a two player game. Maximum cost of materials must be under $5.00. You can find materials. You don't need to spend any money. But the cost of materials if someone were to buy them and make your game, has to be under $5.00. It must include an element of chance. Must somehow contain chance by whatever method you want. And must be able to be taught to someone else within three minutes. AUDIENCE: Do we actually have to make it or just design it? BLADE KOTELLY: You need to design it and make it. You design it and make it. I suggest you even try it out. We might try some of them in class. We might try some of them in class. AUDIENCE: This is due what day? BLADE KOTELLY: I don't know. It's on your syllabus. I think it's due on-- JOHN: Next Monday. BLADE KOTELLY: Next Monday. It's due next Monday. Yes, I'm not going to give you two days to design a game. OK. Thank you very much, everyone.
MIT_ESD051J_Engineering_Innovation_and_Design_Fall_2012	3_Research_and_Stakeholder_Analysis_Sample_Lecture.txt	NARRATOR: 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 view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Welcome to another exciting day of Engineering Innovation and Design. We'll read some interesting things today so the pace might be a little bit faster. Here we go. Pop quiz. I've given you a piece of paper there. If you don't have that paper you can use your own paper. This is the pop quiz. It's going to be given orally. Are you ready? I want you to tell me what questions I would ask you on a pop quiz today. That is your pop quiz. Question. AUDIENCE: Could you repeat that question? PROFESSOR: I'd be happy to. It sounds a bit circular, right? I want you to tell me what you think I would ask you on a pop quiz today if I were giving you a quiz on the material that we've had so far. AUDIENCE: What are the 10 steps in the design process. PROFESSOR: You should just write this down. But I'm sure everyone would appreciate your answer because it's a good one. So write that down. You might have two or three answers. I'll give you about 34 seconds to fill that out. And time. Take your papers. Pass them over to this side of the room all the way that side. And pass them to the top down once you've collected all those papers. Now-- and let's do it quietly-- here's the question. What questions would I ask you? AUDIENCE: [INAUDIBLE] PROFESSOR: Your name. That's a great one. Keep going. AUDIENCE: Do we write our names? PROFESSOR: Oh, yes. You should write your name on your paper, of course. Yes. That's so I know who wrote this. But that would be a good question to ask on a pop quiz-- your name. AUDIENCE: What is innovation. PROFESSOR: What is innovation. That's great. What else? AUDIENCE: A few characteristics of good and bad design? PROFESSOR: A few characteristics of? Of good and bad design. Sure. What else? AUDIENCE: I believe I've already stated-- PROFESSOR: You did. And it was a great one. Could you restate it? AUDIENCE: What are the 10 steps of the design process. PROFESSOR: The 10 step design process. That's a wonderful one. Because that may even occur on a subsequent pop quiz. AUDIENCE: What makes a good design critique. PROFESSOR: What makes a good design critique. Excellent. AUDIENCE: What's the most important question to ask. PROFESSOR: What's the most important question to ask particularly when you're given a problem. Absolutely. That's a great one. Any other ones? You did a great job. You all get A's. So that's the beginning. So look for these questions that may appear on subsequent pop quizzes. Let's start in here. I want to know if anybody here knows who these two people are. Anybody know who this person is on the right? Tell me. Who is it? AUDIENCE: John Ive. PROFESSOR: Johnny Ive. Absolutely. And what does Johnny Ive do? AUDIENCE: He's the Chief Designer at Apple. PROFESSOR: Yup. Chief Designer at Apple for hardware products. AUDIENCE: Industrial Designer. PROFESSOR: Industrial Designer. Exactly. And on the left-- this guy here in the black and white picture-- who's he? Hah. Not as famous as Johnny Ive, I guess. Oh, maybe he is. Hold on. AUDIENCE: Is it Dieter Rams? PROFESSOR: It is Dieter Rams. Absolutely. Dieter Rams and Johnny Ive-- two very important people. Let's show you a little bit about them. Dieter Rams was born in 1932 in Germany. And he's closely associated with something called the functionalist school of industrial design. He made these things. Johnny Ive was born a lot later in 1967. And you're all familiar with his work from having experienced it firsthand or seen it firsthand. These are Dieter Rams' work. These are Johnny Ive's work. Let's do that again. This is what Dieter Rams made. And, interestingly enough, Johnny Ives made these. Do you notice any parallels? Let's take a look some more. Johnny Ive on the right. Dieter Rams on the left. Johnny Ive on the right. Dieter Rams on the left. And would you believe Johnny on the right and Dieter Rams on the left? Again, Johnny Ive on the right with a speaker that has an iPod on top of it and a speaker over here that has a phonograph on it. An iMac. A speaker. Johnny Ive. Dieter Rams. Johnny Ive on the right. It's like a television. Doesn't it look like a television? And here it's a television. So this interesting. That's a speaker I guess. What is this product? AUDIENCE: An iPod. PROFESSOR: It is an iPod. And what is this product? AUDIENCE: A radio. PROFESSOR: It's a radio. It's a radio. So here's the question. They didn't talk about this for a very long time-- Johnny Ive and Dieter Rams. So we're going to put ourselves back up a few months or a few years ago when no one knew what's going on here or how they felt about each other. What do you think about this? What do you think about this when you see this? AUDIENCE: Legally different. PROFESSOR: Legally different? Legally. What does that mean? AUDIENCE: It wouldn't be copyright infringement. PROFESSOR: It's not copyright infringement. Yeah, totally different. These look totally different from each other. I know there's no way you could see any similarity in this corpus of work at all. Don't tell the Apple lawyers who are suing Samsung-- or who sued Samsung successfully. What else? What else do you think of when you see this? Yes. AUDIENCE: Good design is repeated. PROFESSOR: Good design is repeated. What do you mean by repeated? AUDIENCE: Used again. PROFESSOR: That's pretty clever. Used again. [LAUGHTER] PROFESSOR: It's very-- [INTERPOSING VOICES] PROFESSOR: So she's saying that good design, you just use the same thing over again. AUDIENCE: No. PROFESSOR: No. Not quite? Am I shading it? OK. Let's see what-- go ahead. AUDIENCE: No, that's all. PROFESSOR: OK, fine. If you think of something, let me know. AUDIENCE: As long as you don't have to redesign the wheel, [INAUDIBLE]? PROFESSOR: So adapting designs for what you need, OK. What else? AUDIENCE: While the designs are very similar and shared between them, the products themselves are very different. PROFESSOR: Ah. He says the designs are similar but the products are different. Tell me. I see a music player on the left and a music player on the right. This one fits in your pocket. This one fits in your pocket. This one has a circular thing that spins and this is a circular thing that spins. This allows you to select stuff. That circle and this circle allows you to select stuff. Tell me are they different? AUDIENCE: [INAUDIBLE] PROFESSOR: A little different. Sure. Because it's a screen over here on the right. And a hard drive, yes. Actually it's kind of funny. Right now, interestingly, if you buy an iPod Touch or something, you don't have to have music on your iPod. It streams it wirelessly over the air much like a radio. Fascinatingly similar. Everything old is new again. So you say they're different, but they're kind of similar. What else? How do you think they feel about this? How do you think that Dieter Rams felt when he saw these things coming out? AUDIENCE: Happy? PROFESSOR: Happy. Why happy? AUDIENCE: He insprired a whole new generation of design. PROFESSOR: There we go. So he says, I'm so glad you're copying all my hardware. I feel like I've really, really contributed a lot more to society because of this. That's one interpretation. What if someone was sitting next to you during a test and took that philosophy? Would you feel happy about the fact that they were inspiring a whole new set of A's? I don't know. At what point have you ever made something or thought, hey, you're copying our stuff? AUDIENCE: You want to look at whoever wrote the textbook. You're reading the textbook and putting down the knowledge. You're stealing from them. PROFESSOR: I don't know. I don't know. This is interesting. So we have these things that definitely seem very similar. But what's interesting is that they both believe in the same fundamental approaches to how to design great stuff. And they might have come to similar conclusions either knowingly, because of this form factor, maybe somewhat unknowingly and they realized, boy this looks a little bit like this, what can we learn from that. What is step number two? AUDIENCE: The information phase. PROFESSOR: The information phase, yes. The information phase. So how can we leverage what's out in the world already to inform our design? And they might have looked at-- I don't know-- 50 or 100 or 200 different ideas and came on this one or a group of them that looked like this. And he said, it reminds me of this other thing that I saw a long time ago, when I was a kid. And I loved the way it worked. So yes. I think you're right about this-- that great design has a lot of similarities. And you'll see this happening throughout history. Things change very little in history. There are few changes that occur-- fundamental changes. Take a look at kitchens. Kitchens in the past-- I don't know, let's say 60, 70 years-- have only had really two changes that are substantive. One of them is that there are now-- almost always when the new kitchens are designed-- open to another room or to an area where people can entertain. People use the kitchen differently now as a way of connecting with people. Before, you'd shut off the kitchen. You close the door. And you bring out the food. And you say, look at this beautiful food and not the mess in the kitchen. That changed. And microwave ovens changed. Who here has a microwave oven? Wow. And who here has a microwave oven and doesn't have their own kitchen? So some of you don't even have a kitchen and you've got a microwave oven. Pretty amazing. That's a big change. Otherwise, we've got refrigeration. We've got a stove. About the same height as all the stoves before it. We've got ovens. If you're rich, you might have two ovens. Maybe you have a garbage disposal now, but there's not a whole bunch of changes. Things change very slowly. So we'll see this in design. And what's interesting is that Dieter Rams came up with these 10 principles of good design. So let's discuss them. I want you to tell me, for each of these principles, what you think they mean and if you think they're any good. Good design is innovative. What does that mean that good design is innovative? How about this. Who thinks good design is not innovative-- does not have to be innovative? Give me some example. AUDIENCE: [INAUDIBLE]. PROFESSOR: Sure. To prove that good design does not have to be innovative. AUDIENCE: The one you just showed us? PROFESSOR: So you're saying that this was not an innovation over this? AUDIENCE: Well, parts of it. PROFESSOR: Part of it. What part? AUDIENCE: The way it looks. PROFESSOR: Is innovative? Or not innovate? AUDIENCE: Not if you're comparing it to the other one. PROFESSOR: How come? This is made of plastic. This has different kinds of plastic. It's got a screen on it. It's got four buttons on the outside. It's got headphones that are attached to it instead of using a speaker. You think it's too similar? AUDIENCE: No, I'm saying that it's as innovative. I think it doesn't have to be extremely innovative because I'm saying they look very similar. There are innovations but they're not drastic. PROFESSOR: Would you say an iPod is not a drastic innovation over a radio? AUDIENCE: Yes, I'm saying it is, but I'm saying the physical appearance of it. PROFESSOR: The physical appearance may not be innovative. Other examples? I'm going to bring this other slide back up. Yes. AUDIENCE: Some of the things that we've been using since forever, like a bowl or something-- it's really basic but I think it's good design. PROFESSOR: A bowl is a good design. But if someone made a new bowl-- AUDIENCE: It could be a good design and innovate but I don't think it's required. PROFESSOR: You don't it's required? So a new bowl doesn't have to be innovative to be well designed or to be a good design. That's interesting. AUDIENCE: To go back to the last example, innovation also depends on the context when you're looking at the design. PROFESSOR: What do you mean the context in looking at the design? What do you mean it depends on the context? AUDIENCE: So right now, before I saw Dieter Rams, I was of the opposite position of Johnny Ives. But now I that I see a different context, maybe I see [INAUDIBLE] PROFESSOR: Interesting. That's interesting. Context. What do you mean context, now? What's your context? AUDIENCE: It's what I know about those kinds of designs. PROFESSOR: It's what you know. Context about what you know. Could it be something else as well? AUDIENCE: Context of similar designs and their past designs related to that. PROFESSOR: A broader context. What else? Yes. AUDIENCE: I would have to argue that this design is innovate because if a design is very good, then there is no reason you want to improve it. PROFESSOR: If a design is very good if there's no? AUDIENCE: There's no reason to improve it. PROFESSOR: No reason to improve it. AUDIENCE: If you come up with something that's good than from what is was before and it's selling well then there's clearly some improvement. PROFESSOR: She said if you have a new product and it's selling well then there's clearly some improvement. What if it's not selling so well? Could it be innovative? AUDIENCE: It could also be innovative because I think the innovation is defined-- well, not defined, but it about when you decide that needs to be redesigned. PROFESSOR: Innovation comes about when you decide it needs to be redesigned. Interesting. Other ideas? I think context is very interesting here and a little unusual. Context-- we look at the world in a certain way. By a show of hands here, who thinks that their hairstyle looks ridiculous? There are no hands that went up. Who here thinks that people whose-- they see pictures of people from the '80s have ridiculous hairstyles? Yeah, a lot more hands go up now. How about the '70s? So you don't think that in 20 years you're going to look back at pictures of yourself and go, I cannot believe my hair looked like that? Context, right? Context of our society. Angel goes, no way, his hair looks great. That's awesome. I'm always keeping this thing. And he may. He may keep that. Some things are a little more timeless than others. Do you know something interesting about art forgery? Anyone know a lot about art forgery? So if there's a piece of art from the-- let's say, early 1800s-- and let's suppose it's now 1920. And I have hired Jacob to forge a piece of art-- he's a great art forger. Well, if he's great, at the time when they had these forgeries, you wouldn't be able to tell that it was a forgery. But 30, 40, 50 years later, you say, oh, that's the forgery. I can tell. Because unconsciously, Jacob sees the world around him and he begins to put in elements of contemporary design into that piece. And 50 years later, the context has changed, and you can see it. You can see the stuff in there. You can see those differences and everything he's done to balance out all the small differences. And it looks like a forgery. It's pretty amazing. So maybe this is true. Maybe it's not true. How about this one? Good design makes a product useful. Is that true? Who thinks it's not true? Who thinks it is true? What does it mean? What does it mean to be useful? I want to know what it means to be useful. AUDIENCE: Satifies a need. PROFESSOR: Satisfies a need. Tell me more about that. What's a need? Do I need to listen to all my music wherever I am? I kind of need to. I get bored easily. Satisfies a need or maybe something less serious than a need. AUDIENCE: If it adds value. PROFESSOR: Adds value. What does it mean to add value? What is value? Any ideas? Anyone? AUDIENCE: Performs an action efficiently. PROFESSOR: Performs an action efficiently. Does art perform an action efficiently? AUDIENCE: It depends on how if art is useful. PROFESSOR: Well, yes. Is art useful? I don't know. Is art design? Oh, different topic. Reserved for a different day. What else? AUDIENCE: It does what it was designed to do. PROFESSOR: Designed to do. It does what it was designed to do. So good design makes a product useful because it's doing what it's supposed to do. It has fulfilled its intended purpose. AUDIENCE: I think I'd like to argue that because I think that you could have a useful product that has a purpose that wasn't intended by the manufacturer. PROFESSOR: A useful product whose purpose was not intended by the manufacturer. Let's consider this. This is risky. This is a brand new Apple Macintosh Retina Display MacBook Pro which I'm going to use as a door stop. Oh, yeah. Not int-- [LAUGHTER] Can we get a close up on that one? Can we see this over here? I don't know if you can see it down here. This is my pride and joy here being used as a door stop. Not intended by the manufacturer. Pretty useful if we need to prop open the door I suppose I could prop it open. Oh god, that scraping sound sounds terrible. Anything for you guys. Anything. So look how nice it props the door open if we didn't have something else. Again, not intended by the manufacturer who had to work on the tolerances of this device. So that's interesting. What if it didn't performance its intended action and I found a new use for it? Is it still useful? I could have an Acer or something that I would think-- or maybe a five-year-old Acer that's very, very slow and doesn't work very well and I need to get rid of it anyway. And it's broke. It's falling apart. And the screen-- every time I move it the screen falls off. And I can take it and make it a very useful doorstep. Not its intended purpose at all. AUDIENCE: I still don't think that it's a good design just because it has a use, though, because you used it as a door stop but I still don't think that is one of the best choices for a door stop. PROFESSOR: You don't think it's the best choice for a door stop? I think it's a beautiful door stop. Maybe the MacBook Air is better. It's wedge shaped. AUDIENCE: I think the connotations of design is purposeful. So if you use it for an unintended use, I don't think it's considered a good thing. PROFESSOR: If I use it for an unintended use, it's not good design. Why not? AUDIENCE: Because when a designer is designing a product, they have a specific use in mind. And they're trying to achieve that goal. If they don't achieve that goal and then achieve another goal-- PROFESSOR: What if they achieve something far better, far more noble, far more incredible? AUDIENCE: That's not what they were trying to do. PROFESSOR: I know but is it good anyway? Does it matter what the intent is is the question. AUDIENCE: I think it does matter what the-- PROFESSOR: You think intent matters. Who thinks intent matters? Who thinks intent does not matter? Who's unsure about this? Oh, yes. This would be good for a later conversation. Let's consider this. Good design-- now know we're getting really crazy-- is aesthetic. What does it mean to be aesthetic? [AUDIENCE MEMBERS RESPONDING SIMULTANEOUSLY] PROFESSOR: Pleasing. Pleasing in what way? AUDIENCE: Visually. PROFESSOR: Visually pleasing. AUDIENCE: All ways. PROFESSOR: What? AUDIENCE: All ways, PROFESSOR: Pleasing in other ways too. Not just visually but auditorily pleasing. Maybe the smell of a new car. You don't think they work on that? Oh, they work on that. In fact, Mercedes once was having an issue with some cars because it didn't quite have that Mercedes smell. So they hired a nose. Anyone knows what a nose is? It's a person who smells really well. And it's about one in-- I don't know-- 100,000 people or 500,000 people or a million people who have this great ability to smell things well. And the nose went to the car. And they took this car. They shipped it from wherever the car person, owner was. They gave her a different car. They shipped it down. And she [SNIFFING] smelled all around the car. Then she went, door, take the door off. And the went, OK. They stripped the door off. She's smelling around the door. She said take this panel off the door. They took the panel off the door. She's smelling and goes, this is it. This is the problem right here, in the door. It was the insulation. And they went to the insulation people. They said, what did you do to our insulation. They said, we didn't do anything to the insulation. Show us what happened. And they found out. In one part of this process, really early on, the insulation had been stored in sacks that had once stored tea. Oh, yeah. That new car smell, very important. So good design is aesthetic. Who thinks this is true that good design must be aesthetic? AUDIENCE: It's something that you're going to use and you want it to be pleasing in every sense of the word. PROFESSOR: You want it to be pleasing in every sense of the word? Who thinks it's not true? Tell us why. AUDIENCE: If you look at the inside of a motor or something that people aren't going to look at I feel like what it physically appears like does not matter. PROFESSOR: Great. So you're saying if you look at the inside of a motor people where people aren't going to look, you think it doesn't matter? There's a company that disagrees with this philosophy. And this company is called Apple. I bring up a lot of Apple examples because I happen to know them. And I think it's very interesting because we are all familiar with them. Apple does something interesting. With the inside of an iPhone, if you-- I'm not going to take it apart-- I'll do a lot. But if you take the iPhone apart, everything there matches a certain color chart that they have. They have a color chart. And if it doesn't match the color chart it doesn't go inside there because they believe if you start cheating on the inside, it'll begin to leak out. And that cheating will become revealed on the outside of the design. They think the parts that you never see are still important. When the Macintosh first came out-- it was a big object like this. A little small display. And if you were able to open it-- and it was only meant to be opened by professionals who are in the shop. You weren't meant to open it because of the CRT and it can be a very high voltage there. You open it and take it off the back and inside is a relief of everyone's signature who worked on that product, inside that, that no consumer was meant to see. Do you still think it's unimportant? AUDIENCE: I feel like what makes a good design would be other factors. PROFESSOR: Other factors. OK. AUDIENCE: If you're talking about like an engine or something would you count the sound of it as aesthetic? PROFESSOR: I would count the sound of an engine as aesthetic. Absolutely. AUDIENCE: So I want a car that sounds like an angry weasel. [LAUGHTER] PROFESSOR: You want your car to sound a certain way. People say, oh, the roar of the car. The roar of that V8 engine, they say. Or that distinctive Porsche sound they talk about. Absolutely. Think of the sound of the car. Good design helps us to understand a product. Who thinks this is true? Who thinks it's a lie? Who thinks it's not necessary? Good design helps to understand a product, no? We all agree on this. What does it mean to understand a product? How do I understand a paper cup or a bowl? AUDIENCE: Well, there's some cases in which you'll have something and people don't usually read manuals or anything like that. So the more intuitive you can make the design-- like make some spot for, no, this is clearly where your hand goes. PROFESSOR: Yes. Intuitive. Something where it's clear, where you know how to interact with it, engage with it. Good design is unobtrusive. What does it mean to be unobtrusive? What do you mean about good design being unobtrusive? AUDIENCE: Doesn't get in the way? PROFESSOR: Doesn't get in the way. Who thinks this is true? Who thinks this is not true? Can you give me an example? AUDIENCE: I think there are buildings that are very well designed and they're very obtrusive. PROFESSOR: Obtrusive buildings that are well designed but obtrusive. What does it mean in that context to be obtrusive? AUDIENCE: They can obstruct traffic, other buildings, other-- PROFESSOR: They could be obtrusive in terms of the visual line. Well some designs are interesting. This design is somewhat obtrusive, particularly when it's being used. If anyone here has ever been in an environment where someone pulled the fire alarm, you'll know how obtrusive a fire alarm can be. But it's pretty good because it needs to be at that time and not now, which is why it's trying to be a little bit more quiet. It could be even better maybe if we didn't see it at all. Maybe. I'm not sure. There must be a reason why they all have to be red. I don't know what that reason is. AUDIENCE: I don't think that premise applies when part of your design is to make something obtrusive. PROFESSOR: When do you want to make something obtrusive? Give me an example. AUDIENCE: When you have a fire alarm. PROFESSOR: Well we're trying to make it minimally obtrusive, right? They could've made it this big. It could be coming out of the wall. It could go off every hour just to let you know everything's cool. What if they made it half the size? Or they could make it even smaller. Wouldn't that be better? Maybe. OK. AUDIENCE: If you're Apple, yeah. PROFESSOR: Good design is honest. Whoa. What does it mean to be honest in your design? What does it mean to be honest? Good design is honest. AUDIENCE: If something looks like it's supposed to be doing a specific thing it shouldn't do something else. PROFESSOR: So something looks like it should do something, it shouldn't be doing something else. So I shouldn't walk up to this and say, oh, you got a beautiful door stop. I've been looking for a door stop all day. What else? AUDIENCE: If it promises to do something, it should do that thing. PROFESSOR: It should do the thing it promises to do. AUDIENCE: It should abide by all regulations and safety conditions so it doesn't hurt you in the process. PROFESSOR: Yes. It doesn't hurt you. It protects the user. AUDIENCE: Does that mean you should design it in an honest way, as in not steal the design from somebody? PROFESSOR: That's a good question. Should you design it in an honest ways, as in not steal the design? I don't know. We should ask Samsung. A little jab at that. It's a good question. AUDIENCE: I just don't know what it's referring to. PROFESSOR: I don't either. I think we can actually find out more information now about it. But it's a good question. What does it mean to be honest? It might mean that as well. It can mean a lot of things about what its intended use is. When I use it, does it do what it's supposed to do-- what it promises to do? AUDIENCE: It can also be adding more than it needs to be-- like making a gold hammer. PROFESSOR: Gold hammer. So that gold toothbrush that we saw from Napoleon. It may not be an honest design. Maybe it's silver. Silver toothbrush. Can we think of an example where this is not true? Where design is dishonest? Where you believe you could do something with it, but you can't and it's still good? AUDIENCE: For instance, there's iPhone cases that look like Game Boys. PROFESSOR: iPhone cases that look like Game Boys that make it not look like an iPhone. Is that dishonest? AUDIENCE: It might be dishonest but I think it's still good design. PROFESSOR: What about up there? AUDIENCE: [INAUDIBLE]. PROFESSOR: Little outlets. You can't figure out how to get this thing in til you turn it. Dishonest design. Who thinks that's a dishonest design? Who thinks it's an honest design anyway? Interesting. What about this one. What about childproof bottle caps? It looks like they could be opened, but if you are without the skill, strength, or intellect, then you won't be able to open this. Childproof bottle caps don't just affect children though. They can affect adults who simply don't have the strength to be able to open one of these things-- to push down and open. So they have other designs to get around that as well. But they're still a good design. But is that a bit dishonest? To give a whole population the idea that it can be opened, but you can't open it? I'm not sure. Good design is durable. What does it mean to be durable? What does it actually mean to be durable? For the design to be durable. AUDIENCE: It's not going to break. It's last. PROFESSOR: An object that will last a decent amount of time. AUDIENCE: I mean for the design to be timeless. PROFESSOR: For the design to be timeless. What do you mean by timeless? AUDIENCE: It means that five years from now it won't look antiquated and out of touch. PROFESSOR: So years from now, is it will still look fresh and new and novel contemporary. AUDIENCE: [INAUDIBLE]. PROFESSOR: The idea that this was the intended concept and it will still feel like it's appropriate. AUDIENCE: I feel like it's sort of difficult to do that though because-- PROFESSOR: Oh, yeah. Is it difficult? AUDIENCE: --people's ideas of what they want change a lot. PROFESSOR: You say that people's ideas of what they want change a lot. Tell us. AUDIENCE: Well, maybe not a lot, but if you look back at older shows that were predicting what the future was going to be like, they might be spot on with the technology, but the aesthetics of things-- we tend to have more rounded corners on things. We don't like the points as much anymore. Things like that, that people hadn't even considered back then, are just taken for granted now-- sort of. PROFESSOR: Interesting. AUDIENCE: Well, I mean, good design can be determined after the fact. Maybe when you make it, you don't know if it's a good design. And then after tastes change and you are 10 years down the road-- PROFESSOR: You're able to see if it's still a good, sustainable, relevant design later on. Interesting. Good design is consequent to the last detail. Who thinks it's true? Who thinks it's false? Who is unsure? Who did not vote? Let's try it again. Given your options, good design is-- Let's clarify what it means. My mistake here. What does it mean to be consequent to the last detail? AUDIENCE: Everything you put in the design has the intended effect. PROFESSOR: Everything you put in the design has the intended effect. Everything. If you were going to give me a written report-- a big one-- give me some aspects of that report that you'd be concerned about. AUDIENCE: Whether or not the content [INAUDIBLE] . PROFESSOR: Content. What else? AUDIENCE: Citations. PROFESSOR: Citations. What else? AUDIENCE: It's understandable. PROFESSOR: If it's understandable. Comprehension. AUDIENCE: Format. PROFESSOR: Format. So the-- AUDIENCE: Structure. PROFESSOR: The structure. What else? AUDIENCE: I was going to say the format. PROFESSOR: Format. What else? AUDIENCE: Font size. PROFESSOR: The font size. And therefore, what else? AUDIENCE: The font. PROFESSOR: The font. Absolutely. What else? AUDIENCE: Is it too wordy? PROFESSOR: Length of words. AUDIENCE: The paper it's on itself. PROFESSOR: The paper it's on itself. Absolutely. What else then? AUDIENCE: Does it fulfil the task and requirements? PROFESSOR: Does it fill the task and requirements? We talked about the paper. I heard something else here. AUDIENCE: Color of the ink. PROFESSOR: Color the ink. Absolutely. Color of the ink. AUDIENCE: When you present the paper-- like if it's bound. PROFESSOR: Yes. If it's bound. If it's stapled. How it's bound. All these things are details. Do you think they all matter? AUDIENCE: Yes. PROFESSOR: Who thinks if you take a paper that has brilliant content and a paper with the exact same content-- two of them with the same content-- and one is stapled in the corner and one is bound beautifully-- do you think that they will affect your grade at all? Who thinks it will not affect your grade? Who thinks it will affect your grade? That's good. Statistics show that it will affect your grade. Everyone who doesn't think that it doesn't affect your grade, you should make sure that your papers are well bound-- because it looks to someone else like you put more work and effort into it and that you believe more sincerely in your product. AUDIENCE: A lot of that depends on what the value system is that you're working on. If you don't actually have the money or you don't want to spend the money to bind that paper and you think that it's good enough on its own then maybe the best design isn't binding it. You might have a professor who doesn't care. Given it's on average you will score higher [INAUDIBLE]. PROFESSOR: So yes. You have a specific case where it doesn't matter. That's true. AUDIENCE: I think you're talking about high school teachers-- that probably doesn't apply-- but once you start going into college and you're looking at the true content of the paper-- PROFESSOR: You think it applies in high school but not in college. AUDIENCE: I think it applies less in college than it does in high school. PROFESSOR: I will tell you this is not true. I will tell you from firsthand. And when I get a paper-- and I know this to be true-- if anyone submits their midterm report-- their individual project-- and it is stapled in the upper left hand corner, you will with 100% certainly be dropping the class soon afterwards. I've seen it every single semester. Every semester, I'll get at least one person-- and I'll say, please do not do that-- and they will give it to me anyway bound like that. And I just suddenly have to count to 10 before they drop the class. AUDIENCE: But do you ask them not to staple it? PROFESSOR: I say, please don't use a staple in the upper left hand corner. And they do it anyway. There's a high correlation between this. And teachers, when you get that beautifully bound thing, you think, wow, look how cool this is. If you could sit in those rooms, you'll think there is a difference. And of course, they will read the content as well. It's not that it's going to make up for bad content. But it shows a lot more strength and structure. And their brain will start focusing a little bit differently when they review that paper. Consequently to the last detail. Who thinks that good design is consequent to the last detail? Who thinks it is not? Why not? AUDIENCE: Well, I mean, it's the same thing. It's just like, you have to consider what the audience will do. You need to knowledge the value of that extra detail. If they don't value it, like if you're just trying to feed a lot of people and they're just incredibly hungry-- if you are trying to feed a starving population, they're not going to care that you seasoned the food that you've made exactly perfectly. They're going to care once they get something to eat and they get more of it. PROFESSOR: What if you could season it perfectly? Would that be better design? AUDIENCE: Well, that would be great, but that's not the world we live in. We live in a world with limitations PROFESSOR: Yes. We do live with limitations. But the question I would ask you to think about is when are those limitations real and when do we impose them on ourselves unnecessarily? When do we think, well, we can't do this, instead of thinking, well, maybe we can't do this-- let's see if we can do it. You'll find a tremendous amount of innovation happens when we resolve the tension between what? From last class. AUDIENCE: From what we desire? PROFESSOR: Yeah. From what we desire and what we require. If we can resolve these tensions, that is where we get innovation. Absolutely. Good design is concerned with the environment. What does it mean? AUDIENCE: Good design doesn't neglect anything. PROFESSOR: Yes. Good design isn't just sitting in its own little vacuum. It works within a whole system, a whole big context of things, whether it's a physical environment, a social environment, or, like the iPod player, works with the iTunes Music Store. It connects to other things. Lastly, good design is as little design as possible. What does that mean? AUDIENCE: I think to use other things, like how Apple used previous designs. So maybe they didn't have to redesign that much. PROFESSOR: So she's saying less design. Not as much redesign. What other interpretations do we have? AUDIENCE: Keep it simple. PROFESSOR: To keep it simple. What else? AUDIENCE: Going back to the example of Apple, they try to limit the number of buttons that you have. PROFESSOR: Try and limit our buttons. Yes. AUDIENCE: And also with the mouse. Let's use the Magic Mouse for example. There is no button like there are with other mice. There aren't two buttons. It's just one click that you use. And it's very intuitive to how you're going to use it. PROFESSOR: So a Magic Mouse has no buttons on it at all and you can still click anyway. And it knows what you're doing. They're just trying to reduce that user experience. But they had a lot more complexity inside to figure out how to make that work. What else? AUDIENCE: I think the design is as little design as possible as in off of previous designs, like going back to Dieter Rams. PROFESSOR: Dieter Rams' work. Absolutely. Where he's really trying to get that functionalist-- let's think about the functions first and really build things around in the simplest most streamlined, elegant way possible. I want to consider these steps. Part of your homework will be to consider if these are all true and reflect on them and see how they can be improved and which ones are missing. I bet you're going to be able to think of ones that are missing. Design challenge. Are you ready? Are you ready? AUDIENCE: Yes. PROFESSOR: I'll take that. Here we go. Are you ready? This is what you know. The music stops. A man is dead. That's all you know. You need to solve what happened and why did it happen. And I will answer questions. I will say, yes. Or I will say, no. Or I will say, Relevant. That's what you get. And we need to do this quickly. Go. AUDIENCE: Was the man listening to the music? PROFESSOR: Yes. AUDIENCE: Was he blindfolded? PROFESSOR: Yes. If you happen to know this particular question. Was he blindfolded? Yes. AUDIENCE: Did he die because the music stopped? PROFESSOR: Did he die because the music stopped? No. AUDIENCE: Is this a human man who actually died and was living and then now is no longer living? PROFESSOR: Was it a human man who died who was living and is no longer living. Yes. AUDIENCE: Did the music give instructions? PROFESSOR: Did the music give instructions? No. AUDIENCE: Did he die while the music was playing? PROFESSOR: Did he die while the music was playing? No. AUDIENCE: Where'd this happen? PROFESSOR: Where did this happen? AUDIENCE MEMBER 1: Yes or no questions. AUDIENCE MEMBER 2: Does the music stopping coincide with the man's death? PROFESSOR: The music stopped and coincided with the man's death. What's the question? AUDIENCE: Did the music coincide with the man's death? PROFESSOR: I don't know how to answer that one. Give me some more detail around the question. AUDIENCE: Did they happen at the same time? PROFESSOR: No. Did they happen at the same time? No. AUDIENCE: Was he alone? PROFESSOR: Was he alone? No. AUDIENCE: Did the music stopping indicate something else is starting? PROFESSOR: Did the music stopping indicate something else is starting? Yes. AUDIENCE: Was the music playing in headphones? PROFESSOR: Was the music playing in headphones? No. AUDIENCE: Did the music start in relation to that the man was dead? PROFESSOR: Did the music? AUDIENCE: Did the music start in relation to the fact that the man was dead? PROFESSOR: Did the music start because the man was dead? No. The music stops. The man is dead. AUDIENCE: Did someone stop the music? PROFESSOR: Did someone stop the music? Irrelevant. AUDIENCE: Did someone kill the man? PROFESSOR: Did someone kill the man? No. AUDIENCE: Did the man have a preexisting condition? PROFESSOR: Do the man have a preexisting condition that was not covered under the health code? No. He did not have a preexisting condition. AUDIENCE: Is the music playing at a funeral? PROFESSOR: Is the music playing at a funeral? No. AUDIENCE: Did the music stop because it ended or did it stop [INAUDIBLE]. PROFESSOR: I can't answer that question with a yes, a no, or irrelevant. AUDIENCE: Was the music short? PROFESSOR: Was the music to cut short? No. AUDIENCE: Was the man's death an accident? PROFESSOR: Was the man's death an accident? Yes. AUDIENCE: Did the man die before the music started? PROFESSOR: Did the men die before the music started? No. AUDIENCE: Did the man die because the music stopped? PROFESSOR: Did the man die because the music stopped? No. AUDIENCE: Is the reason the man died also the reason that the music stopped? PROFESSOR: Is the reason that the man died also the reason that the music stopped? No. AUDIENCE: Did the man kill himself? PROFESSOR: Did the man kill himself? Ask the question differently. AUDIENCE: Is the man responsible for his own death? PROFESSOR: Is the man responsible for his own death? Yes. AUDIENCE: Was the man involved in stopping the music? PROFESSOR: Was the man involved in stopping the music? No. AUDIENCE: Did the man die before the music stopped? PROFESSOR: No. He did not die before the music stopped? AUDIENCE: Was he in public? PROFESSOR: Was he in public? Yes. AUDIENCE: Was he driving? PROFESSOR: Was a driving? No. AUDIENCE: Is the music the name of something unrelated to sound? PROFESSOR: Is the music the name of something unrelated to sound? I don't know what you mean. But I want to. AUDIENCE: Is the music a name? PROFESSOR: Is the music a? AUDIENCE: A name. PROFESSOR: A name. AUDIENCE: Of something. PROFESSOR: Of something. I don't know what that means. AUDIENCE MEMBER 1: Is it not music? AUDIENCE MEMBER 2: He means is there a track called "The Music." PROFESSOR: Oh. No. Thank you. It's hard. It's not that hard. AUDIENCE: Was the man in control of the music? PROFESSOR: Was the man in control of the music? No. AUDIENCE: Is the music relevant to the man's death at all? PROFESSOR: Is the music relevant at all to the man's death? Yes. AUDIENCE: Did someone try to stop his death? PROFESSOR: Did someone try to stop his death? Irrelevant. AUDIENCE: Did he want to die? PROFESSOR: Did the man want to die? No. AUDIENCE: Is the song that was playing relevant to the man's death? PROFESSOR: Is the song that was playing relevant to the man's death? -ish. Sorry to break the format. AUDIENCE: So is it an internal injury that killed him? An external injury would be like a trauma, whereas an internal injury would be like a heart attack. I'm trying to figure out the way he died. PROFESSOR: Ask me a very specific question. AUDIENCE: Was it an internal injury? [LAUGHTER] Did he die of a heart attack? PROFESSOR: No. AUDIENCE MEMBER 1: A stroke? AUDIENCE MEMBER 2: Something hit him? PROFESSOR: Yes. AUDIENCE: An ice cream truck hit him. PROFESSOR: No. Did something hit him? Yes. Did an ice cream truck hit him? No. But that's very funny. AUDIENCE: Was the thing that hit him intended to hit him? PROFESSOR: Was the thing that hit him intended to hit him? No. AUDIENCE: Did the music player fall on the guy? PROFESSOR: The music player did not fall on the guy. AUDIENCE: Since he was blindfolded, was he to guide himself in a certain direction? PROFESSOR: Ask the question again. AUDIENCE: Since he was blindfolded, was he using the music as a way to guide himself towards or away from something? PROFESSOR: Yes. She asked the question was the music guiding him-- AUDIENCE: Was he using the music to guide him-- PROFESSOR: Was he using the music to guide him? Yes. AUDIENCE: Is the man a performer of some sort? PROFESSOR: Is the man a performer? Yes. AUDIENCE: Was he a tightrope walker? PROFESSOR: Was he a tightrope walker? Yes. AUDIENCE: Did he fall? PROFESSOR: Did he fall? Yes. AUDIENCE: Was the man using the music to guide himself blindfolded across the tightrope and then the music stopped and he fell off? PROFESSOR: Was the man using the music to guide him across the tightrope-- AUDIENCE: While he was blindfolded. PROFESSOR: --while he was blindfolded. And what was the next part? AUDIENCE: The music stopped so he couldn't find where he was going so then he fell off. PROFESSOR: The music stopped so he couldn't find where he was going. And therefore, he fall off. No. So close. AUDIENCE: Was he supposed to jump into a net and missed? PROFESSOR: We he supposed to jump into a net and missed? No. AUDIENCE: Did the speakers fall on him? PROFESSOR: Did the speakers fall on him? No. AUDIENCE: Was he using the number of beats to traverse the tightrope? PROFESSOR: Was using the number of beats to traverse the tightrope? No. AUDIENCE: Was the tightrope the wire for the music player? PROFESSOR: Was the tightrope the wire for the music player? Very creative. No. AUDIENCE: Was the music supposed to stop when he was at the end but it stopped early? PROFESSOR: Was the music supposed to be stopped when he got to the end? Yes. And that's what happened. So he's walking on a tightrope. And all of a sudden-- he's blindfolded-- and the music stops, so he figures he's at the end. And he just steps off. But he wasn't at the end. And there was no net. And he fell to his death where the ground hit him. [AUDIENCE DISGRUNTLEMENT] You said, did something hit him. Yes. Something hit him. I didn't lie. Something did hit him. AUDIENCE: He hit the ground. PROFESSOR: Oh. I'm sorry. You've all taken physics. The ground hit him as much as he hit the ground. [INTERPOSING VOICES] PROFESSOR: He wasn't dead. He was still alive. [INTERPOSING VOICES] PROFESSOR: The music stopped before he died. AUDIENCE: Because arguably, he died when he hit the concrete. PROFESSOR: Oh. No. I answered the questions very specifically each time. In fact, we have all the questions, here, that you asked. Any ones in particular that were of note? So what's very interesting here is about asking questions. And it leads us into what we want to talk about here with research. Asking good questions is really hard. And when you ask questions, sometimes you find you're going down a path that's giving you information. Sometimes you don't. Often the first question I get asked was, was he outside? No. Was he in a building. Yes. What comes to your mind as someone said he was in a building? [INTERPOSING VOICES] PROFESSOR: You'd think an office building. Right? You wouldn't think a tent or a circus. That's a building. It's a structure. If I said no to building, would I have to say yes to tent? Like at some point if I'm being very binary. So asking questions is very hard. You see any ones that you're skimming? QUESTION TYPER: The internal injury one was really good. PROFESSOR: Internal injuries. QUESTION TYPER: That put them in the right direction. PROFESSOR: Hitting the ground. So when you said, did something hit him-- well, yes, something hit him. But it doesn't tell you about the direction. Right? And now you're beginning to think an ice cream truck struck him. And this makes sense. What you did is exactly right. All this is exactly what you should be thinking about. But it shows us, given some data-- think about when you're asking questions-- you can get the exact, truthful, right answer and still be radically incorrect about what you understand from this. That was a little induction to research here, complete with formula. So research. Just a basic thing. You want to ask questions and find out about stuff. Asking questions is important, but answers can be misleading. Academic and scientific research is often wrong. We think it's the truth when we read it. And maybe it's truthful. Many of them are very good. But often they're wrong. And we base beliefs and make conclusions and decisions based on faulty information. Which gets us back to the first thing I talked to you about on the first day, which was? To do what? The first thing. AUDIENCE: Ask the right question. PROFESSOR: To ask why. To make sure that we're getting to the underlying reasons. Because that may be wrong. Research results may be good but the conclusions may be wrong. So here we had great research. The question was, did he die of internal injuries. Yes. Did something hit him? Yes. What did we conclude? That something hit him-- that he was stationary. Easy to do. This is Fitts' Law. It's pretty cool. I won't bother explaining it right now. It's so interesting. It's used a lot in computer and human interaction. I'll give you the basic idea. This distance is D. And I think, here in the formula, this is W, which really talks about-- actually, that's Ws here and Ws here. It's a margin of error, technically. But here it's a width. And what he would do is he'd say, look, we can have people doing something like tapping. Here. Here. As fast as you can. Now if I take those lines and I change them. I'm going to make them like this. So that's one. I do this. Faster. What if I do this? Pretty good. Pretty good. And so I'm pretty good with that. But my speed changed. And if I wanted to go faster, my accuracy would go down. So what can we conclude from this? Lots of things. Somethings that are very good and somethings that are incorrect. One conclusion. If I work on a computer system that just has a keyboard and no mice at all. And it's now 1985, 1986. Should I use a graphical user interface or not? Well the incorrect conclusion might be it will slow you down. Because every time you move your hand over-- we can calculate it out. How long it's going to take you for every action that requires you to use a mouse. And so we don't want to have people slowing down. We're going to keep everything using keyboard commands. But it may not be true that it's going to make you faster. That's an incorrect conclusion-- maybe given that same system. But maybe if you redesign the system, it will actually become a system that you can use faster because you can use the mouse to be able to do things you couldn't do before. And the correct conclusion that we draw is the right click for a pop-up menu-- you right click on something and then the menu's right there. So now you've moved your hand to the mouse. You move your mouse to the target. And you right click on it. And now you have a menu that's contextual, that's short and easy to get to. Instead of moving your mouse all the way to the top to a big menu bar and having to find your way through cascading menus. That is the correct use of it. Research results may be good but conclusions may be wrong. So when you see a really good research piece like this, understand that what you do with that is really important. We design projects for people. People don't know what they want often. I could say, do you want to have a device that's this big and flat and has a keyboard on it that's virtual and all the stuff. You might say, nah, I don't want that. In fact, when the iPad came out, the week beforehand or two weeks before I had pre-ordered it because I had to be really cool and wanted it. And my classmates were saying, oh that's ridiculous. I said, why is it ridiculous? Well, it's like a bigger iPhone and you don't need that. And I'm like I think it's different. They said, no, it's just a bigger iPhone. We're not going to get one. Well within a month, of course, a whole bunch of them are ordering them because they saw it was different. But if you asked them-- if you said, would you like to pay $600 or $800 for an object like this, they might have said, no. And then they never would've made an iPad. It's very hard to ask people what they want. And if they know what they want, they often can't articulate it. They don't know what words to use to convey the idea. So as a designer when you research, how you ask questions, how you interpret people's answers is really critical. I'd like to show you this video about why it can be hard to get good answers when you ask a question. This video is for a game show called the Family Feud. Who does not know the show? Briefly, here's how it works. They have parts of the show where they ask people-- 100 people get surveyed-- they'll ask them a question like, what would you expect to find in a refrigerator? And you want to guess the most popular answer because that will be the number of points you get. So what would you answer? AUDIENCE: Milk. PROFESSOR: Milk. Milk is the most popular answer. And so this is a speed round at the end where they have two different teams. And this one person comes over and he's looking away from the board and this guy asks him these questions in a row. It's like five questions. One of them is the milk question. You're asking this person who's on a game show-- average person, answering questions. He happens to be under pressure because he's on a game show. You'll see his responses. I'm just going to roll this for a little bit and then we're going to show you the second part of this. HOST (ON SCREEN): Name an animal with three letters in its name. CONTESTANT 1 (ON SCREEN): Frog. HOST (ON SCREEN): Something found in a refrigerator. CONTESTANT 1 (ON SCREEN): Milk. HOST (ON SCREEN): A brand of gasoline. CONTESTANT 1 (ON SCREEN): Regular. HOST (ON SCREEN): Something that comes with a summer storm. CONTESTANT 1 (ON SCREEN): Snow. HOST (ON SCREEN): A sport with an all-star game. [BUZZER] Turn around. You may never be up here again. Let's take a look. Name an animal with three letters in its name. You said, frog. Our survey said 0. Two people would have to say that. Something found in a refrigerator. You said, milk. Our survey said 28. A brand of gasoline we wanted. You said, regular. That's a good brand. Our survey said. CONTESTANT 1 (ON SCREEN): It's the brand I use. HOST (ON SCREEN): Something that comes with a summer storm. You gave me the answer snow. Our survey said. PROFESSOR: So you saw what happened here. This person is trying to answer questions under pressure. He's trying to provide the best answers he can. An animal with three letters. Frog. I can see maybe-- it's a short word, right? Something in the refrigerator. We got milk. You all got milk. You were great. A brand of gasoline. Regular. He thought regular is the brand instead of Shell or Mobil or something else. That's what he associated with that area. Something that comes with a summer storm. Snow. It doesn't happen in the summer, I think, for most parts of the world. Certainly not here. But his reaction was to supply an answer that wasn't useful, even though he probably would know things. But under pressure, not easy for him to be able to come up with good answers. Let's continue this and watch his opponent. HOST (ON SCREEN): I got good news and bad news. CONTESTANT 2 (ON SCREEN): Give me the bad news first. HOST (ON SCREEN): The bad news is you need 172 points to win the money. The good news is you're the man to do it. I'm going to ask you the same questions I asked the other Bob. You cannot and you do not want to duplicate his answers. If you do, you hear this. [BUZZER] What noise do we hear? [BUZZER] Thank you. I will then say try again. You'll give me another answer. Alright? Remind everyone, to Bob's shame, the answers he gave us and give me 20 seconds on the clock, please. Name an animal with three letters in its name. CONTESTANT 2 (ON SCREEN): Alligator. HOST (ON SCREEN): Something found in a refrigerator. CONTESTANT 2 (ON SCREEN): Milk. HOST (ON SCREEN): Try again. CONTESTANT 2 (ON SCREEN): Ice. HOST (ON SCREEN): A brand of gasoline. CONTESTANT 2 (ON SCREEN): Ethyl. HOST (ON SCREEN): Something that comes with a summer storm. CONTESTANT 2 (ON SCREEN): Rain. HOST (ON SCREEN): A sport with an all-star game. [BUZZER] CONTESTANT 2 (ON SCREEN): Football. HOST (ON SCREEN): Football. You've got to give him that. Any man that says alligator, you've got to give it. Name an animal with three letters in its name. You said, alligator. Our survey said. You don't use narcotics. Do you? CONTESTANT 2 (ON SCREEN): No, but I will. HOST (ON SCREEN): I mean, I thought frog was bad. I thought frog was a disastrous answer until you came up with alligator. It's a real tough one. Dog was the number one answer. Dog. CONTESTANT 2 (ON SCREEN): Are you sure it was? HOST (ON SCREEN): Three letters in it's name. Dog. D-O-G. [CHATTERING] HOST (ON SCREEN): And we wanted something found in a refrigerator. You both had this nailed down very well. Unfortunately, you repeated his answer, which was milk. But you said, ice. That's the place to find it. Our survey said 17. Milk was the number one answer. It was the only good thing that Bob did. A brand of gasoline we asked. You said, ethyl. CONTESTANT 2 (ON SCREEN): A brand. HOST (ON SCREEN): A brand which I think you've been drinking. Our survey said. The number one answer was Shell. CONTESTANT 2 (ON SCREEN): Shell. HOST (ON SCREEN): Something that comes with a summer storm. At least you have reached. Did you see his answer? Snow! At least you said, I believe, rain. Is that correct? Well, that's good. Our survey said 9. And then a sport with an all-star game. You said, Football. It was about two minutes late but I insisted you get it. Our survey said. [BUZZER] So these people are not stupid. They're smart people. They're regular people. And they come with these answers under pressure which were just not the right answers by a long shot. So how you ask questions, who you ask questions to, the environment you ask questions-- it may not always be this extreme where someone says alligator for a three letter animal. But you will get shades of differences-- shades of meaning. Sometime who is very stressed will provide really bad answers. If you're really, really-- I get test anxiety. So when I took my tests in grad school I went to support services and got time and a half because I couldn't do it. I'd be there and I would look at these problems and the information would empty out of my mind. I just was too anxious to do it. Like other people, you will get different responses. So how you conduct your research is really important. So one of the various ways we can research. Let's talk about this. If it was 1960, and we wanted to learn to cook like a French chef, what would we do? What could we do? AUDIENCE: Go to France. PROFESSOR: Go to France? Just go to France? And you just happened to have the knowledge by going to France. Yeah. if you start smoking, you get-- [GRUMBLES] You walk down the street, and you just happened to know. No. What else do you do? AUDIENCE: Talk to the chefs there. PROFESSOR: Talks to the Chefs there. Sure. What else could you do? AUDIENCE: What about French cooking school? PROFESSOR: Go to French cooking school. AUDIENCE: Watch Julia Child. PROFESSOR: Watch Julia Child. Absolutely. Watch her show called The French Chef. Yes. This is good. 1848. The best way to conduct a defensive military retaliation. AUDIENCE: Go to military school. PROFESSOR: Military school. Yes. Look at the what's happened before in history. 1990s. The best way to clean a kitchen. We want to make the best way to clean the kitchens in the '90s. What do we do? AUDIENCE: Ask your mom. PROFESSOR: Ask your mom. If not, just ask your mom, however, you could also do what? AUDIENCE: Watch her. PROFESSOR: Watch her. Yes. 2013. You want to save money on a call center. This call center handles technical issues for customer complaints for satellite television. What can you do? AUDIENCE: Internet. PROFESSOR: What would you do with the internet? AUDIENCE: Just search for it. PROFESSOR: Search for what has been done to save money in call centers that have these issues? I don't think you're going to get a whole lot of good responses. AUDIENCE: Outsource. PROFESSOR: Outsource what? AUDIENCE: The people answering-- PROFESSOR: How would you learn though? How would you research this? Have a consulting economy. What would they do? AUDIENCE: They would go out and probably talk to other people who have done similar things in order to--? PROFESSOR: Yes. They could talk to other people who had similar problems, but what about this one particular call center for satellite TV, located in Denver? AUDIENCE: Look at its budget. PROFESSOR: Look it's budget. What would you learn from the budget? AUDIENCE: Seeing where the most money is going? PROFESSOR: Well, we know that a lot of money is going to this thing. How do we have them save money on this one particular part of the call center? AUDIENCE: Reduce the number of workers by having an automatic system. PROFESSOR: Reduce the number of workers by having an automatic system, but how would you know what the automatic system should be doing? AUDIENCE: Look at what the workers do. PROFESSOR: Look at what the workers do. By what method? AUDIENCE: Watch them. PROFESSOR: Watch them. Absolutely. Actually sit down there and watch the workers. 2015. The decision to develop an extremely new type of consumer product, like when people had to develop the iPad before they developed the iPad. What would you do? AUDIENCE: Talk to people. PROFESSOR: Talk to people and ask them what they want? What would you ask them? What would you ask people to figure out that brand new product that's different than anything ever before it. AUDIENCE: You talk about what they actually want like why they use iPads. Maybe they want something easy in front of them to touch. PROFESSOR: Yes. So to get the underlying mechanisms. Yes. So we have expert education here, as he said, correctly. Historical and cultural explanations, as you said correctly. Ethnographic research, as she said about observing someone actually performing these tasks. This is how the Swiffer was developed. They had people with cameras watching people clean and mop their floors. And they thought, oh wait, they do all these things. The water gets dirty and all this stuff. And they could develop these ideas-- the wet Swiffer and the dry Swiffer. Here, direct observation. Sit there and listen to those calls coming into the call center, which I did. And I heard them say things. I sat down next to this person. You know when they say the calls may be monitored for quality control or quality assurance? Well, that was me sitting next to her, jacked into the same box. And I said, I'm just going to hear what you do. First call comes in. I've got a problem with my TV thing. I can't get this station and she'd have a very interesting thing. Did you diagnose it? She'd work with them. 20 minutes later, it'd be done. The next call would come in. I've got this black screen. She's like, oh, we'll, can you go in and unplug it and plug it back in. Sure. Hey, it's working now. Great. Next call comes in. I've got this really strange problem. I was getting these channels but now I'm not getting anything. She'd diagnose it and send it a restart signal. It would work. The next call would come in. I've got this snowy screen. She'd say, can you unplug it. Yes. And plug it back in. Yes. How's it working? Works great. Perfect. Every other call. Every other call. Black screen. Snowy screen. Black screen. Snowy screen. Unplug it. Plug it back in. Resolved. What's going on here. I said, how do you know that's the problem. Oh, because the installers say don't turn off the box. They'd say you don't have to worry about turning off the box. Turns out if you don't turn off the box every week or two, eventually it will want an update, not get it, and produce a black or snowy screen. And so she knew to do that. They were given incorrect instructions by the people who installed the box. And she gave them better instructions. Well, kind of better. The better instructions we're actually, by the way, you'll have to do this periodically, even if the installer told you you didn't have to do. So here by observing that, we figured out that 30% of the calls to this particular part of the call center were for a black or snowy screen. Automation was introduced, as you said-- who was it? Yes. Correctly. Automation was introduced to solve this problem. The first question was, are you experiencing a black or snowy screen. No. All right. Let me give-- Yes. Great. Unplug it and plug it back in and let's see if that helps. I'll stay on the line. When you're ready, just say I'm ready. And people would do that. They'd say I'm ready. Great. Did that solve the problem? Yes. Alright. You need to turn this off, periodically, like once a week or two. otherwise you'll get the same problem, even if the installer told you you didn't have to. So that's how you solve a problem. Observation. This is the hard one. And this is exactly what you're alluding to. A deep understanding of humans. What they want. What their real desires are-- technology, culture, manufacturing, philosophy, art, design, and everything else. When you want something really radically innovative you need to understand a lot about a lot. And while you're in school, you have an opportunity to learn a lot about the a lot. So take advantage of doing that. Steve Jobs sat in on a calligraphy class. And that's why the first Macintoshes had fonts. Before, there were no fonts in computers. But he didn't have this experience of what a font can do and change meaning of something and he wanted that in that first Macintosh computer because of the experiences of sitting in on a calligraphy class. Have more experiences. Understand everything about culture, technology, art, design, philosophy. It'll make you better at designing very technical systems. Any questions about that? AUDIENCE: I would actually disagree with that last point. You get more innovation by just trying 100 ideas and seeing what sticks. PROFESSOR: You think you can get more innovation by trying 100 ideas and seeing what sticks? AUDIENCE: Yeah. [INAUDIBLE] that make great things and have no idea what they're doing. PROFESSOR: You think people who make great things have no idea what they're doing? AUDIENCE: In some cases, yeah. PROFESSOR: Can you give me some examples? AUDIENCE: Some examples. If you think of a product like Facebook. PROFESSOR: Facebook. He had no idea what he was doing? AUDIENCE: Yeah, he was doing something cool. Ended up making a lot of money later on by [INAUDIBLE]. PROFESSOR: Making money. But that wasn't the objective. The objective was to make something cool. AUDIENCE: [INAUDIBLE]. PROFESSOR: But he didn't try 100 different designs. Did he? He didn't just try a 100 designs and see what stuck. AUDIENCE: They updated code twice a day. PROFESSOR: That's not trying 100 different designs. Facebook has maintained-- its core origin, at the very beginning, was a rating. Hot or not. Right? So like, hot or not. You would just rate people. Then you started being able to post more. And it involved. And when it evolved to a certain point, then it became particularly big. But it wasn't that they tried 100 designs. No one sat there and said, let's observe 100 different things we could be doing for Facebook and say, let's see what sticks. People don't often do that. It's also very costly and expensive to try 100 different designs. AUDIENCE: If you look at how they do agent testing everyday? PROFESSOR: Yes. But that's making small decisions. But not radically different things. We're talking about technology that's never been seen before. A completely new type of user experience. Something that's never been tried before. Derivative things, absolutely. You can do ABN testing. You can test 100,000 variations in an hour and see which ones people used and which ones they took longer to use. But that's for small changes. Not when you're doing something completely radical and new and very different and very innovative. AUDIENCE: I just wanted to support his point a little bit. I don't think that anyone who designs these really good products sits down one day and realizes, given everything I know about art, technology, society, etc, this is how it should be. PROFESSOR: You don't think so? AUDIENCE: No, I don't. PROFESSOR: If you were to design something, you wouldn't think that it was the amalgam of everything you've learned in your life so far? AUDIENCE: No, no. It wouldn't just come at once. PROFESSOR: It may not come at once. AUDIENCE: Unlike the other examples-- in the other examples, you narrowed down the [INAUDIBLE] because you realized this causes this. PROFESSOR: Oh, right. It is not a good example. Exactly. That is true. But it is the synthesis of everything you've learned so far. Right? AUDIENCE: Right. But the process of getting to the design that you get to is a meandering. PROFESSOR: Oh, yes. You may take a long time to get to that design. Absolutely. Yes. But it is the idea that, if you-- I'll bring this slide up again. If you don't have a deep understanding of people, you're not going to design things really well for them. If you don't understand how the technology works, you won't be able to make something that's useful, that people enjoy interacting with that takes advantage of the technology. If you don't understand about the culture it may be the wrong time to introduce it to a certain place. If the iPad was launched in a poor country where they could never afford it, then it may not be very popular. Or a place where there wasn't internet reception for some reason. Or if you don't understand about how to manufacture something like that, then it gets very clunky. If you don't understand about art or design, how do you make something that's aesthetically pleasing and sustainable? So that's why the idea is to synthesize. And yes. It takes a long time to get there. That's why creativity gets better as you get older. The older you get, the more creative you will get. You don't get worse with creativity. It gets better. Because you know more and you have more life experiences that you can synthesize. Other questions? Or comments? AUDIENCE: I feel like it goes back to the conversation we had about intention. PROFESSOR: Intention. The idea of intention. AUDIENCE: -and what you intended it to do. I feel like it does require the deep understanding of certain things depending on what your design is. But it's like what you said, it can evolve into different things and that might mean you will look for more understanding of humans and manufacturing maybe later on depending on where the design-- PROFESSOR: So you'll keep evolving that. Absolutely. You will definitely keep evolving your ideas. Joel. PROFESSOR JOEL SCHINDALL: Just to add a little bit, I hope you're not falling into the school idea that these questions have right and wrong answers. These are thought provoking. They're to get you thinking about things. They're to challenge your assumptions. Some of them are absolutely ridiculous. But without looking at that, it doesn't give you the perspective that you're getting at. I think you've probably done this in other sorts of classes but it's a different type of perspective. And to get the most value out of it you need to set aside-- by the way, the people who are answering, I also want to really hand it to you. Put yourself out there. Throw it out even if it's-- there are not right and wrong answers. We need illustrations of the wrong answers-- we need illustrations of the wide range that people come up with answers about. I think if you're sitting here in this class, the answers that other people are giving are a demonstration of the wide range of reactions that people have to the same stimuli that you receive. And you'll receive a stimulus and you'll say, oh, yeah, of course that's true. And someone else is going to say, I object violently. Now that's worth knowing because that person's giving an honest reaction. PROFESSOR: The whole point of this is to provoke your thinking. To make you think deeper about this and to set the stage for what you will be doing over the course of the semester. It is meant to challenge the ideas. We ask a lot of questions about Dieter Rams' principles and you'll be reflecting on that. But these are ideas. And they're not meant to say this is an equation where when you put something in you get something out like this. It's not deterministic that way. Design is a very, very complicated thing. That's why we talk about it for many different aspects and different approaches to get you to think differently. Because you'll be able to soon become much better at it through that process. AUDIENCE: So I know that 2.009 is a very artificial setting because you're given a theme and you have to design a product based on that theme. But how do you think 2.009 and that process fits with-- PROFESSOR: I don't know a whole lot about 2.009. You said it's an artificial setting. It's not that artificial. There are companies that have innovation labs where they say, we do something with our product in this space. Can you do something with our product that takes advantage of it somehow? And people have to figure out, OK, what do I have. What are the resources? How much time do I have to do this? Do I have an infinite amount of time or a limited amount of time? And they do that same process, just like you do in 2.009. PROFESSOR JOEL SCHINDALL: Blade, let me comment on that also. Design takes place at many, many levels. And sometimes, you just have a group of flowers and you're trying to make a floral design and you're very restricted in what you can do, but there is a methodology, there are rules. You can put the big flowers-- I don't know how to do a good one, so I better not give you examples of that. And on the other hand, sometimes you're trying to do either a very complex technical system or perhaps a complicated political process. People design press briefings for presidential candidates. It seems amazing. It seems they're so bad it doesn't seem as if it could be designed. But it actually is very carefully researched and designed. Now 2.009 places itself kind of in the middle of the design space. It's more creative than just figuring out how to assemble an erector set. And it does encourage you to do some innovative thinking, but not as much-- we're trying to go even one level higher and something that will apply to everything you do and just, what we call, design thinking. And it will help you in 2.009, but it's not as specifically applied to-- 2.009 is a mechanical engineering course for people who intend to grow up and design mechanical things. And so it focuses on that. This is more for people who intend to deal with life issues and come up with answers. PROFESSOR: Whenever you have to do anything-- in my software company, I apply these principles to everything we do-- the ones I'm teaching you-- to every aspect of it, whether it's to hiring, to bring people on board, to figure out what they're going to be doing the next week, how we're going to communicate internally, how we're going to communicate externally, which brings us to stakeholders. Cul Bono. What does it mean? Anyone know? Who benefits? Who benefits? So stakeholder. Well the definition I get off the internet-- a person or group that has an investment share interest in something. We talk about stakeholders for your education-- you or your family, teachers, school. Who else could be a stakeholder for your education? AUDIENCE: The community. PROFESSOR: The community. What community? AUDIENCE: The one that you would benefit if you go-- PROFESSOR: The community that benefits when you go and do something. What else? AUDIENCE: Your employers. PROFESSOR: The employers. Yes. And actually potential employers. Who else? AUDIENCE: The clients. PROFESSOR: Clients. When you're working at the employer you have a client. Yes. AUDIENCE: I think the government or the president in general. PROFESSOR: The government or the president, or you could say the country. The country benefits. Absolutely. Who else? AUDIENCE: I don't know if school includes this, but your classmates. PROFESSOR: Classmates. Sure. Tell me how your classmates benefit. AUDIENCE: The more you bring to the table, the more they're going to gain. PROFESSOR: Yeah. So when you have a certain cohort in a business school, if there's people with different experiences, they can bring new ideas and formats. That's why we have discussions like this at the beginning of the lectures. You get more benefit because you hear someone's idea that you hadn't thought about before because they bring their perspective. Here's a quick sketch. Just a quick sketch of how you might go about the process of writing out the stakeholders. Flour Bakery. Who knows it? A lot of you. So this is a great bakery, very close by. And its owner is Joanne Chang, a friend of mine. And Joanne owns a bakery. So I'm going to say that this is in the center and this is one of the primary stakeholders. Workers would be another primary stakeholder of the bakery because if the bakery's selling product they get paid. There's a whole bunch of others, of course, that we can fill in. Now we go from a secondary one to the workers' banks. How do they benefit? Well, the Flour Bakery gives the workers money. The money goes into the banks. So as we go through that process, the bank begins to be able to get more money into them, particularly a local bank, perhaps, that's being used. And what's interesting about this is there's a big profound effect. What we're going to do is we're going to have you do a quick sketch for Flour Bakery. And what I want you to do is to do that system with much more detail, right now in class. And if you need to, you can use lines to clarify what's happening. Someone pays someone, like pay the workers, or the bank receives cash as a result. I want you to work in groups of three. If you have paper, please draw this on paper. And then, we'll project a few on the screen. So tidiness doesn't really count as long as you can explain it. And you'll have about 10 minutes to do it. You can work with any people you want. By now, the students are trying to figure out how to map out a simple stakeholder diagram. Now this is not a very full or robust stakeholder diagram. It's just meant to get everyone thinking about the system that's involved. In a stakeholder analysis that's done really well, you'd actually phase out all the different levels. You'd think about all the different stakeholders and where they lie in the spectrum of value, too. Here we just want to make sure that students understand the idea that things are connected and that these connections can seem very distant. But if they understand the connections and the space, it can help them make better decisions later on. And we'll be doing that in the next slides that we show. We'll show what the students have done on the screen. So the thing to look for in this is to see if the students pick up on some of the other more subtle aspects. Are they going to think about things like legal system or the accountant or people like that who are direct benefits and every store has to work with their legal people and their accountants, but it doesn't seem like it often pops in the radar. And this is where all these hidden costs occur when someone's starting a business. They think, well, this one's going to cost this much or they're making a product that's only this expensive, but there's everything else around that ecosystem. And let's see if they pick up on this. All right so let's go over your results. Why don't we take yours to start? Does that sound good? STUDENT PRESENTER 1: Sounds good. PROFESSOR: You can take care of this. Let me know when you're ready. So you're going to have to explain this because it's hard to get the catch of this on here. But it's OK. Just walk us through it. In fact, use the laser pointer-- this is the red button here at the top-- to point out. Tell us what we have over here. STUDENT PRESENTER 1: So immediately, you have the owner who benefits up here and also the employer. And so from there, their banks benefit. And that kind of leads into the economy. PROFESSOR: Tell us about just the first level, right around here. [INTERPOSING VOICES] STUDENT PRESENTER 1: And so the suppliers who supply the materials to Flour, furniture, ingredients, and stuff like-- they benefit as well. And then down here, you have neighboring stores who benefit from the popularity of Flour, bringing in more traffic. PROFESSOR: Neighboring stores. Really creative. They'll benefit from the fact that it's a popular place. Keep going. STUDENT PRESENTER 1: And so competition here, you can extrapolate, to them being driven to produce better goods. PROFESSOR: Wow, so competition. That's very creative. Keep going. STUDENT PRESENTER 1: And this actually feeds back in to customers who benefit from better quality. PROFESSOR: I guess competition is a good drive out quality from other bakeries who aren't starting to get good. Flour has to get better or lower their prices or something. Keep going. STUDENT PRESENTER 1: Right. And so the second level here, back to the banks-- they benefit from both the owners and the employers making income. And then down here, you have friends slash the community. Say you refer a friend and they really like Flour, that's a benefit for them. PROFESSOR: So it's a benefit for the customer if I refer a friend. It's a benefit to me if I refer you to go to Flour. STUDENT PRESENTER 1: It's a benefit for me if you refer me to Flour and I like it. PROFESSOR: So you get the benefit. But are you attached to me or are you attaching directly to Flour? In other words, do you benefit directly from Flour? STUDENT PRESENTER 1: That's fair. You could say that I definitely benefit from Flour as well if I like it. PROFESSOR: So maybe this kind of line would be a dotted line-- provides information to, and then directly from. Sure. Keep going. STUDENT PRESENTER 1: And so naturally, the nearby community also branches off from the neighboring stores. One more thing we have over here is the publishers because apparently Flour sells cookbooks and stuff like that. PROFESSOR: Flour sells cookbooks. There's a publisher involved. And they love it. The more Flour bakeries that are around or the more people know about it the more cookbooks they buy. STUDENT PRESENTER 1: And so this leads to the bookstores, I think. PROFESSOR: Book stores. Absolutely. STUDENT PRESENTER 1: And this actually feeds all the way back to the economy. And from the economy-- PROFESSOR: The economy "boomph." Giant. The beneficiary. That's great. And what comes off the economy? STUDENT PRESENTER 1: And so this is where we got creative and said that the government, the president benefits from the economy being strong. And then you can even pull out the political parties if you wanted to. PROFESSOR: Sure. So political party, government. This is great. So Flour makes America strong. Forget GM. Forget Ford. Flour does it. I love that. It's a great job. [APPLAUSE] Who's up next on the chopping block? Let's get this going here. You get this. I'll give you this to hold. I'll give you this to use as well. Let's talk about this. Walk us through it. At the center is Flour. What else we got? STUDENT PRESENTER 2: So we have Flour. And then it first goes to the banks and investors. PROFESSOR: Investors. Yes. STUDENT PRESENTER 2: So banks. So people who have money in the bank. So it's really important that the banks are doing well. Similarly, people who are friends with the people with money the banks who needed to be spotted for a meal at Flour also benefit. So we also have the workers. Their taxes go to the government which helps America. And then workers. Their families also benefit from the making income. And then it goes to the school system. PROFESSOR: How's it go to the school system. STUDENT PRESENTER 2: Because the children go to school. And then, thus, benefits citizens. PROFESSOR: So money goes from Flour Bakery to the workers. The workers give money to their families? STUDENT PRESENTER 2: Yes. PROFESSOR: And so how does that benefit the school? STUDENT PRESENTER 2: Because then the children go to school and get educated. You need people to go to school. PROFESSOR: How do the families pay for that? STUDENT PRESENTER 2: Through their taxes. PROFESSOR: Through taxes. STUDENT PRESENTER 2: And then the government. PROFESSOR: Before it gets to the school, where does it go? To the IRS. STUDENT PRESENTER 2: That too. PROFESSOR: And them to the school. STUDENT PRESENTER 2: Yes. PROFESSOR: To the IRS first and then to the school. STUDENT PRESENTER 2: Yes. PROFESSOR: Yes. That is true though. STUDENT PRESENTER 2: And it goes back to the citizens because then you have an educated population. PROFESSOR: So Flour Bakery educates the population. I love that. We'll tell Joanne. She's going to love this. STUDENT PRESENTER 2: Then kind of going on a more fun note-- so we also had neighboring companies, such as Novartis who's like a biotech drug development company which helps hospitals. And then the patients can go to Flour. PROFESSOR: Lovely. Keep going. STUDENT PRESENTER 2: Similarly, we have more customers such as MIT students. And so our parents benefit from us getting an education. Professors and other MIT employees who go to flour. And also the world slash everybody is invested in. PROFESSOR: The world. I can't wait til the next one that says universe. That's good. Big round of applause. [APPLAUSE] We've got time for one more example. Who-- yes. Let's take your example. Cannot wait to see it. STUDENT PRESENTER 3: So ours is similar to many of the others. We have some things that other people didn't have-- PROFESSOR: Point out the differences. STUDENT PRESENTER 3: --in local gyms. PROFESSOR: Local gyms benefit from Flour. STUDENT PRESENTER 3: They do. PROFESSOR: Tell us why do local gyms benefit from a place that sells lots of bakery confectioneries. STUDENT PRESENTER 3: Flour is really delicious. And then people eat a lot of it. And they get really fat. And then they would like to lose some of those calories. PROFESSOR: So the Z Center, the MIT gym, benefits from Flour being there because more people use the Z Center who may not otherwise use it because they're saying, I love Flour so much but I've got to work out the calories. STUDENT PRESENTER 3: Exactly. PROFESSOR: Local bike shops maybe as well. STUDENT PRESENTER 3: So their employees benefit too. PROFESSOR: Their employees absolutely benefit. Yes. STUDENT PRESENTER 3: And we also had hospitals in that similar-- PROFESSOR: As Diabetes go up. STUDENT PRESENTER 3: Exactly. PROFESSOR: Yes, they're so tasty they cause diabetes. STUDENT PRESENTER 3: Precisely. PROFESSOR: And hospitals benefit. And doctors from selling-- STUDENT PRESENTER 3: And the doctors' families. Yes? PROFESSOR: And the doctors' families benefit. STUDENT PRESENTER 3: Exactly. PROFESSOR: Now this may sound bizarre, but this is true. This is how it happens. Imagine that we had to work it out for a tobacco company. All the people that benefit from a tobacco company selling things, including people who are injured by tobacco because of cancer. So that's all true. What else do we have? STUDENT PRESENTER 4: We had aspiring chefs because of the cookbook. So they can see that. Or even aspiring restaurateurs who see how the owner set up Flour and maybe use it as an example or inspiration. PROFESSOR: Brilliant. What else do you have? What else is brilliant? STUDENT PRESENTER 5: We also have how MIT is generally affected. So if students are eating at Flour instead of the dining hall, then that's affecting MIT. That's affecting the classes and the professors and your classmates. PROFESSOR: And maybe for good. Maybe not for food. This is great. This is an excellent one. Here's a question. Did anyone get lawyers? Good. Two groups. How about accountants? One group. Excellent. Every business deals with lawyers and accountants. Lawyers accountants all the time. Every business, no matter what, deals with lawyers and accountants. It should be on all of these because, no matter what-- and particularly as a business owner-- boy, I get on the phone with my lawyers, I talk to my accountant. I can't even avoid it. It's not even possible to avoid, particularly when you have to hire people and fire people and the whole bit. That's why they're such big businesses-- why accounting and the law are such big businesses-- because everybody needs to use them. Any other people have examples of beneficiaries who we didn't list? AUDIENCE: Insurance companies. PROFESSOR: Insurance companies. Yes. Absolutely. AUDIENCE: The farmers. PROFESSOR: Farmers. People actually grow this stuff. Absolutely. People grow stuff and have more supply chains. And this is true. Flour Bakery may have a little impact, but McDonald's has enormous impact on cattle companies, and people who supply tomatoes and lettuce and all those things. Absolutely. Huge impact. Industries are built around these things. AUDIENCE: We also listed internet providers because they offer free Wi-Fi to the customers. PROFESSOR: Free Wi-Fi to the customers as well. Let's go back to slides, please. Thank you. This is excellent. You did a great job. Did we give them a round of applause? [APPLAUSE] You got that. This is what we care about though. Why do we care about doing this and why are you going to be doing this yourselves? It's starts out with systems thinking. Establishing a global perspective about the little problem you're trying to solve. If I said, make a calculator-- a calculator doesn't exist in isolation. It affects a lot of things and can affect a lot of things. We want to maintain a really big perspective over every small decision we make. Because of that, we can understand how to make good decisions and trade-offs, establish priorities or reestablish them, and be able to communicate more effectively. Not all stakeholders have the same amount of value to a company. Different stakeholders hold different kinds of value. Joanne may say, look, I really care about my customers but she may not say, I really care about the people who work at the gym. So she may not say, let me put extra fat in the products and then advertise, by the way, with these things, if you care about it, I'll give you a discount to the gym membership. Which stakeholders do we benefit more and which stakeholders benefit us more? Sometimes, in a nonprofit, we might think we really want to get the best thing out there no matter what because we don't care about making profit. Other times you think, well, we want to get the best thing out there, kind of, but we also want to make sure we're balancing that out with our stakeholders. An example of this is angel investors versus venture capital. If you're starting a company, angel investors will give you a little bit of money. It's a little bit easier to get the money. And there's far fewer strings attached to that money. A venture capitalist will give you money-- much more money, but they have a lot more requirements. And so each of them need different kinds of things. Angel investors don't need a whole bunch of return on their investment. And a venture capitalist says no, we want to make a ton of cash. So we'll give you more, but we're going to take a lot more back and have more requirements. So different kinds of stakeholders would allow us to figure out which do we use. If we understand this network very clearly, it helps us to understand priorities and trade-offs. And then, if I understand this diagram and convey this to you very specifically, it could help us align the team. So my software is sold to people at companies. If everybody in my company knows who those people are, who makes the buying decisions, who is going to use it. Are they the same people or different people. How do I make sure that the buying person gets what they need and the person using it gets what they need. They may need different things. And even though the people who use it may use 90% of the functionality and the people who buy it may use almost none of it, or 1%, do I want to invest that 1% of the functionality even if it costs me a lot of time and effort? Maybe I have to. So it can reveal hidden cost and opportunities. A cost. A student can get an easy or a difficult C. From a parent's perspective, which is better? The easy A or the really difficult say? Please pass the class. I'm your parent paying for it. I don't want to have to pay for you to take it again. So maybe they might think it's really better to have an easy A class. But maybe from the student's perspective, they think, the harder C is-- I'm going to learn a lot more in. And it's better for me and my future. Or an opportunity. If a company has enough employees, for example, a company can get better buying power with vendors or the gym or something. Because we have so many employees they say, look, we want to have our employees go to your gym or maybe some competitor's gym. If you give a bigger discount, we have more buying power. Or to the vendors like Walmart. Walmart doesn't pay much for anything because they sell so much. And it's such a valuable brand to have when you're selling something that they make their vendors cut their prices way down-- as low as they can possibly get them. And the idea is that for them is they pass their savings on to the customers. For the homework, I want you to map out primary and secondary stakeholders, and more if you'd like for two things. An art museum and a new kind of battery technology. So one's a museum and one is a technology. Starting with technology in the center. I'm thinking about that. All the different ways it connects to everything else around it. A new kind of better technology. If you have something in mind, you could use that. Just let us know what you used. And if you don't really quite know about battery technology, you could just kind of think about what it might affect. That's the objective here. Understanding your stakeholders will make a huge shift in your ability to make decisions, to think globally from a systems perspective. And if you can do that on little small projects, as the projects get bigger and more complicated and complex, you'll be able to make better decisions. And it will help you make decisions when you're not too sure what to do because at least you'll have a framework and be able to communicate that to other people on the team. And they can say, yes, we understand that that's an important feature to add-- to spend weeks or months adding because someone needs it in order for us to sell the product. Any questions about stakeholders or research or Dieter Rams or Johnny Ive? AUDIENCE: Is the homework for Monday? PROFESSOR: This homework is for Monday. In fact, I will show you on the next slide what you've done so far. We had an introduction. We went over the 10 step design process. We actually moved Dieter Rams to today. And what's due on Monday is the game design and the stakeholder analysis for games. Have a wonderful weekend. If you have any questions, email us at eid-questions. Thank you.
MIT_ESD051J_Engineering_Innovation_and_Design_Fall_2012	Instructor_Interview_Online_Student_Forum.txt	JOEL SCHINDALL: Initially, the course was taught in a more or less conventional manner where Blade and I did the teaching, and we had one teaching assistant who was actually someone that Blade new from Tufts University who came in and helped the students with some of the technical issues in the design problems. But after the first term, some of the students volunteered to be teaching assistants the following term. And they brought a whole new dimension to the teaching of the course, because the students were encouraged to-- The students don't do their homework during class, they do it typically at 10:00 PM or 2:00 AM or 4:00 AM, any time of the day or night. And it's frustrating to run into an obstacle and not be able to get an answer to your question. So we established a website where the students can go to it and ask their question. And we have three or four teaching assistants who are monitoring that website 24/7. Literally 24/7. And it's fun to watch the dialogue because you'll often-- at 2:00 AM a question will come in. One of the students will say, well, Jim is best equipped to answer this question, but he's sleeping now. I'm going to give you an initial answer. And about 5:00 or 6:00 in the morning, Jim will get back on and give you the rest of the answer. We have probably, over the course of the term, at least 1,000 question-answer exchanges that take place. The students who evaluate the course often give perfect scores of seven to the teaching assistants. A little bit humbling for us and the faculty who are getting good scores-- 6.1, 6.2-- but the teaching assistants get the best scores because they're actually one-on-one guiding the students through a problem. And they're doing it very much from the student's perspective, because this is the same problem that they had to deal with the previous year so they know what questions to ask. They phrase their answers so eloquently. You know, today's younger generation is accustomed to electronic tools, to chatting, you know, to social media, and they have a very nice deferential and yet effective style of interacting with this communication.
MIT_ESD051J_Engineering_Innovation_and_Design_Fall_2012	Instructor_Interview_Origins_of_This_Course.txt	PROFESSOR JOEL SCHINDALL: This course represents one of four courses that are given in the Gordon Leadership Program. We have a course on engineering innovation and design, a course on engineering leadership, a course on people and organizations, which talks about how to work effectively within a company, and of course on project engineering, which teaches them how to use the same tools and skills they learned when they assemble electronic systems to assemble the management system that it takes in order to run a complicated program. When we got funding for the Gordon MIT Engineering Leadership Program, we got together with a number of industry leaders, actually quite a large number of industry leaders, to look at what was engineering leadership and what were they looking for in the successful engineers within their companies. About 3/4 of the topics had to do with leadership-- decision-making, advocacy, cross-cultural communication-- but about a quarter of the topics that they really were looking for had to do with good engineering designers. And they were talking not just about being skilled in the craft, but actually looking at the world in a way where they realized what was wanted and needed, what was it the people who are using this product might require, and they actually came up with elegant, innovative designs. They observed that a small portion of the engineers that they hired seemed to have that ability, and a much larger portion of them would do competent design work, but just didn't pick up on the kinds of breakthrough designs that the smaller group could do. Rather than teach the students the design skills of a particular engineering discipline, we work to teach the students to think like designers-- to be able to get outside the problem itself and look at what is the purpose of this project or product or process? What function does it serve? What is the need that is required out in the world? And how can I innovatively and creatively use the tools that I have learned in order to design, invent, produce, and implement something that will satisfy this need? So we put together a course which is a combination of 10 design principles, Socratic inquiry, and the students themselves being engaged in design projects, and supported by some student teaching assistants, which engages and provokes the students to develop these kinds of abilities and causes them to leave the course not so much with a specific body of knowledge-- we don't actually care whether they continue doing that specific design project-- but what we want them to do-- and they do, in fact, they can't avoid it-- is to apply this way of thinking to the way that they go about solving future problems. I actually had a career in industry after graduating from MIT, 35 years in aerospace and telecommunications, but I couldn't resist the opportunity to come back and give back by helping MIT's young students develop the kind of attitude and behavior that is necessary to be effective as an engineer today. PROFESSOR BLADE KOTELLY: We're successful if a student exits the course having completely changed the way they think about the world. And I know that sounds like a strange thing. And what we mean, is that hopefully they see everything differently. When they're walking down the street and they pass a door handle, they think, why is the door handle designed that way? Does it communicate effectively to me to know how to use it? What about other people? Would they understand how to use it? What's the material made of, which material's involved in that door handle? How has it been used? Is it smudged? Is it clear? Is it clear against the background? Hopefully, they see everything differently in the vast interconnectedness of everything in the world. And the fact that everything we do is ultimately in service to people. So if you're making a part for space station, it might have to be replaced by someone or diagnosed, so that is in service to people. People to operate a bigger system that can tell us more about how we live. So if they walk out of the class being able to do that, we're successful. PROFESSOR JOEL SCHINDALL: One way in which I like to challenge the students at the end of the course is to point out to them that the course is not ending now. It's beginning now. We actually gave them the instruction set and the way of thinking. Their job now is to go out into the world and to use that thinking in order to be more effective designers. And here's a gotcha. Once your eyes are open to that, as has happened in this class, you can't stop doing it. So a year from now, or two years from now, or five years from now, I expect to hear back from you that you faced or came up with some kind of a creative solution to a longstanding problem. And I'm going to take great satisfaction in the fact that you came up with that solution, but some of the tools and the ways of looking at the world that we discussed in this class will have been the enabling or the facilitating factor in your effectiveness of doing that.
MIT_ESD051J_Engineering_Innovation_and_Design_Fall_2012	Instructor_Interview_Teaching_Design_Thinking.txt	PROFESSOR BLADE KOTELLY: I think the way that we open their thinking in the process of teaching it is to start connecting our process to everything else they do in life. So start to really make sure that they understand the connections between the design process being used for something as simple as planning a birthday party to something more complicated, like making a mechanical system, designing a phone, or something like that. We try to have them reflect on it in their normal existence. So, do a design critique of something, and come back in with that. So we can actually have them think about oh, the design of a simple object in my life, what do I like about it? What don't I like about it? And then they start thinking a little bit differently, because they realize that all the ideas they've had about certainty, these principles are true-- they realize, well, they aren't always true. In fact, they're only true in context. PROFESSOR JOEL SCHINDALL: Part of what we do in the class is to ask provocative questions. Students will give an answer that they think is the normal answer to the question. And Blade will say, why do you think that? The students are a little irritated. I think that because that's the right thing to think. But it turns out that it's not the only way to look at it. And they simply haven't challenged that way of looking at. And sometimes we have to walk a little fine line to not be too irritating with this. But the fact is, the irritation provokes the expanded exploration, the sensitivity to things around them, which is what we want to draw out in this class. PROFESSOR BLADE KOTELLY: Some of the other goals include just doing a really clean, simple design process they can apply to anything. Being able to operate as a designer does. So in the context of whatever they're doing, know how to evaluate systems. Thinking about people. Understanding stakeholders. Understanding a little bit about the architecture of a system and how to abstract it out. Understanding how to write good requirements. Being able to usability test something to see if someone actually can use it, they like using it. Understanding the psychology of human interaction with technology is really important. Being able to think that the brand of something actually affects the way someone uses it. It's not just the logo or something else, but the way the whole system feels and the identity it produces in the mind of someone that's unique compared to other systems. And hopefully they're able to see all this whenever they create anything. PROFESSOR JOEL SCHINDALL: Blade had previous experience when we put the course together in speech-activated satisfaction systems, or answering systems. There's no easy name for it in the language, or at least I'm missing it, but when you call American Airlines to get information about a flight, or when you call to order a pizza, you'll often interact with an automated voice system which gives you certain prompts, listens to your responses, and based on those responses it gives you other prompts. Most people find them very exasperating, because somehow they don't seem to be foreseeing correctly the issue that you're dealing with. And so we have the students design systems. Initially, we have them design a simple pizza ordering system or simple banking transaction system, but then as their project for the term, they will do a more complicated system. Something like, one of them did a system-- I forget the exact name-- but it was for a parent to let a child call this automated system and it would say, "Hi, this is Santa's elf. And what would you like for Christmas this year?" And the child will respond with what it would like to get for Christmas. And the system is prompted to listen for things and it will record the child's answer, say that's a wonderful thing, we'll see what we can do. And then the system actually will call or text the child's parent to tell the child's parent what the child asked for for Christmas. It was a very clever idea, and it was implemented in such a way that people who used it actually had fun and enjoyed the answers. The challenge for the students is that you'd think that designing a speech-activated system is an easy thing to do. And you quickly get humbled by the fact that the first person who you have try it comes up with a perfectly logical response that is not what you had predicted. And it forces you to get into the user's head and look at what do I need to provide the user in the way of information and what responses do I need to be prepared to respond to, so that I can have an effective dialogue with this user? It's a wonderful way of training the students in how to be methodical, how to put together a plan, how to engineer something, but how to also test it with users and deal with the issues that come up with those users.
How_We_Teach_507SC_Biological_Chemistry_I_Fall_2013	Advice_for_Next_Teaching_Generation_Focus_Curricula_on_the_Microbial_World.txt	PROFESSOR: If you're a teacher and you're inventing a course for the first time, or revising it a lot, you sit down with your teaching partners and you put on the table all the ideas. Teaching, you've got an ever-expanding universe of knowledge out there, and you have to cherry-pick the things that are going to be important. It has to hang together. One of the strategies JoAnne and I thought, when we went into the current iteration of teaching 5.07 biological chemistry, was to abandon completely, higher eukaryotes, namely us, because genome sequencing projects had sequenced so many bacteria that one could create an entire course in biochemistry that would be very meaningful, just focusing on microorganisms. We spent a couple of days reading and thinking about it. That would be the course JoAnne and I would teach, if it weren't for the fact that we actually have-- feel as though we have a commitment to students that are going to go on to medical school and therefore, if we avoided mammalian biochemistry, students wouldn't know anything about the mitochondria and organelles, and things like that that are associated with eukaryotes. We wouldn't be able to make these connections to disease, the physiological scenarios. Nevertheless, why were we so interested in bacteria? What would be an interesting story, that I might be able to tell you, if we had taken that path. So we have a fellow in biological engineering, named Eric Alm. And he is an informaticist and an engineer, and an extremely good chemist. He really knows his pathways. When he looks at a cell, he thinks about what it is, but also where it came from, in terms of how it evolved from precursors, its family tree, so to speak. One of the most interesting organisms that he's published on, not too long ago, is an organism called, Desulforudis. And this would be a wonderful biochemistry course in itself. He wondered, if he went out and dug up a cubic meter of dirt-- and outside MIT-- and if he did 16S RNA sequencing, how many living things would be there, many thousands, maybe 10,000. Then he asked the question, what if you went down 100 meters, you know, maybe you see 1,000. But what if you go down until there's really only one thing there. And that's what he did, going down two miles into the ground. And there was a single, species ecosystem called, Desulforudis. And I remember seeing this paper, and I brought it over to JoAnne. I was so excited because the last picture showed its metabolic network, its metabolic pathways. It had everything. And it makes sense. It can't rely on other things. For example, we can't make all of our amino acids. We got to get them from food that we eat, or in our co-factors, some of our vitamins are made by the bacteria in our gut. So, if all the bacteria disappear, we would too. So we rely on other things, but Desulforudis doesn't rely on anything. So when you look at it's biochemical networks, what you see is that it can fix nitrogen. It can take N2 and convert it NH3, and then put that into amino acids, and it can make all of its amino acids. It has a really good pentose phosphate pathway. It actually uses radiation in a strange way to generate some of the energy that it needs. It uses it to generate carbon monoxide. Ultimately, that CO is going to form an acetyl group that will be able to generate all of the organic material inside the Desulforudis. It's got all kinds of electron transport pathways. So it's developed enormous versatility by being a single-species ecosystem. So, again, this was a course where we had to make a compromise because of our clientele. Teachers have to think about that. We have to teach to what the people need in order to go on to the next step. But as sort of a closing thought, I think that it would be wonderful for next-generation biochemists to really turn their attention to the microbial world, to teach this vast biochemistry and understand how bacteria effortlessly, swap biochemical pathways, pick-up entire biochemical pathways without even breaking a sweat. Whenever they find themselves stressed, they just pick up a new pathway and they survive.
How_We_Teach_507SC_Biological_Chemistry_I_Fall_2013	Teaching_Central_Pathways_to_Help_Students_Understand_Metabolism.txt	JOANNE STUBBE: The way we teach the course is we show them that all of these chemical transformations can be described by 10 pretty simple steps. And if you understand the basic chemistry of these simple steps, you can really understand almost all of the kinds of interconversions you see and basic metabolism. And what you'll see is while this looks overwhelming, really, with a few central pathways, which is what we focus on in this course-- glycolysis, fatty acid oxidation, biosynthesis, sugar biosynthesis as well as degradation, the Krebs cycle, which feeds into the respiratory chain-- knowing those central reactions-- almost everything in metabolism feeds in and out of these pathways. And so then, it really is a question of what is the environment like and how do you enhance breakdown of sugar under the appropriate environment versus synthesize sugar under a different environment. So then it's a question of regulation. So what you're going to learn in this course is really focused on central metabolism. And it doesn't matter whether you study a bacteria or a human, the central metabolism is pretty much the same. The thing that's different is the detailed regulation and the complexity of the regulation. And we don't really talk that much about regulation in 5.07. What we do is introduce you to five or six basic regulatory mechanisms that are used over and over again. But then, regulation is really distinct, even between organisms. And so then that becomes much more complicated. And when you go off and become a biochemist, you've got to study your own system and figure out what the environment is.
How_We_Teach_507SC_Biological_Chemistry_I_Fall_2013	How_Can_You_Not_Think_Enzymes_are_Cool.txt	JOANNE STUBBE: When I went to graduate school, which was in the late 1960s, I didn't even know what an enzyme was, because back in those days I'd never had a biology course. They didn't do biochemistry back in those days. And I think I heard a lecture by Van Tamelen at Stanford. He was interested in steroid structures, steroids that have four rings and it's the basis for sex hormones and for cholesterol biosynthesis. They're all sort of made through a common biosynthetic pathway that we don't really talk about. These are these five carbon units to form carbon-carbon bonds that I mentioned earlier. Anyhow, what he showed was you could take 30 carbon strung together in a linear form. And then somehow these 30 carbons folded up with one enzyme to form these four rings, putting in eight asymmetric centers in a single step at pH7 in 100% yield. Once I saw that, I said man I don't want to be a chemist. If you could see how nature designed this, and what is the basis for being able to make these molecules, it was sort of mind boggling to me. And I think enzymes are like that. What they do is they've evolved for billions of years to accelerate rates of reactions by factors as much as 10 to the 20th. So that's really fast, like a bat out of hell. And so nature has figured out how to control all of this. But again, she has a limited repertoire of reactions that she catalyzes, but she's extremely good at it. And so understanding people have studied enzymes forever because I'd like to understand the basic principles of catalysis. And then if you understood those, can the chemist then take this understanding and translate it into the bigger repertoire of the periodic table you have to be able to do these transformations? So the mechanisms of rate acceleration, which we talk about in some detail in a lecture, what causes these catalysts to work, and the way you describe how these catalysts work. It doesn't matter whether you're using a small inorganic molecule or small organic molecules or a protein, the basic principles and thinking about catalysis is exactly the same, except nature has figured out how to do this better than anything man can do. But again, she's limited in terms. She's had a billions of years to evolve these catalysts, but then she's limited in the repertoire of reactions that she needs to catalyze. So how can you not think enzymes are cool?
How_We_Teach_507SC_Biological_Chemistry_I_Fall_2013	Research_Focus_Genetic_Change.txt	JOHN ESSIGMANN: I work in the field of genetic change. In a perfect world, you would say, guanine would always pair with cytosine and adenine would always pair with thymine. It turns out, however, that sometimes chemicals from the environment can react with our normal nucleotides and change their coding characteristics so that mistakes are made when polymerases try to read them. These are mutations, and mutations cause genetic diseases. My role in the field of toxicology is as a person, who is both a biologist and a chemist, who studies how chemical damage to our informational molecules is converted into changes in coding that results in genetic change. I'll emphasize, of course, this is the basis for all genetic disease, but it's also the basis for evolution. In other words, mutations happen naturally. That means that we're not all-- we don't all look alike. And that means there's diversity in a population, and that's because of mutations. And evolution is a really good thing, because if we were all alike when the environment changed, then the chance of extinction might be very high. If there's diversity in a population, that's actually a hedge that life uses in order to be able to make sure something's going to survive, because some members in the population, while they may be considered quote unquote "weaker" in the initial environment, when the environment changes-- they're the ones, for example, with hair on them, and survive the global winter that happens after the meteor strikes. So, we are interested in chemical modification of DNA and RNA as it relates to the causation of disease, but we're also interested in the rates at which genetic change happens in a population, and how that's a good thing, and that it provides for the continuance of life. One example of our work in evolution comes from recent work that we've been doing on HIV. When a virus infects one of our cells, our cells respond by trying to limit the growth of the virus. They try to kill it. And one of the strategies that used by what's called our innate immune system is to induce a number of enzymes that start to rip apart the DNA bases. They really take the amino groups off of cytosines and adenines in order to try to convert them into non-coding nucleotides or miscoding nucleotides. What happens is, if you take a cytosine and you take away it's amino group, it makes it into a uracil, and then, rather than pair with a guanine, it'll pair with an adenine. Because these are enzymes that kind of move along the viral genome, they create a huge number of mutations. The process is called lethal mutagenesis, because what happens is, eventually the number of mutations is so large that you can no longer produce a functional protein or nucleic acid. That's a natural strategy that we use. And thinking about this, some years ago, given my lab's expertise in knowing about the structural modification of normal bases that makes them mutagenic, we wondered if we could contaminate the nucleotide pool of a cell with mutagenic nucleotides that would force a virus to mutate even quicker. HIV, it turns out, almost goes extinct, but not quite. In other words, our innate immune system, in one day, creates every single point mutation in the virus, but it also creates every single drug-resistant variant. And it just doesn't push hard enough to be able to push the virus to extinction. So, we wondered whether-- if we could push a little harder by using creatively designed molecules-- derivatives of cytosine, that would pretend sometimes they're a cytosine and sometimes they pretended that they were a thymine-- that we could push the virus over the top. And we found that it did work, OK. In other words, we were able to push the virus to a technical state of extinction using our understanding of the chemistry of the molecules that the cell has the capability to use in replication. It may seem unwise to intentionally put mutagenic chemicals into people, and, obviously, we worked out a strategy to prevent mutations in people in the drug design process. Specifically, it turns out there are pathways called DNA repair pathways that repair damage in our nuclear genomes, and they happen in the nucleus. That's where the enzymes are located. It turns out that the early stage in HIV replication involved replication in the cytoplasm. There are no repair enzymes in the cytoplasm. So, the virus has no defense against the mutagenic affects of these compounds. We picked compounds that, if they were to get into our nuclei-- it turns out that our polymerases don't like them very much, anyway, but if they did get in, they're very rapidly repaired. So, it creates what we call a therapeutic index which is very favorable in favor of killing the virus but not putting mutagenic chemicals into us.
How_We_Teach_507SC_Biological_Chemistry_I_Fall_2013	Focusing_on_the_Morphological_Unit_of_Life.txt	JOANNE STUBBE: The morphological unit of life is the cell, whether you're a flea or you're an elephant. Right? And we all have water as the major solvent. We all have the same biological molecules that play a major role inside our bodies, like sugar or fat, or amino acids, or nucleotides. We all have the same ways of making reactions work fast enough so they can succeed inside the cell, and controlling the specificity, and they're conserved from bacteria to humans. We all use the same vitamins on your vitamin bottle. And those are also conserved in general from bacteria to humans. And we also all have the same major regulatory mechanisms, although as you go from prokaryotes to eukaryotes, things get more complex. And so what we cover in the course is, in fact, most of the things we talk about are bacterial systems because they're better studied but can be extrapolated between the two systems. So are these things ordered inside the cell? And how do you study them inside the cell? That's the major focus of a biochemist. You want to understand things at the molecular level, but then you need to understand what you see at the molecular level, how does that relate to what's going on inside the cell? And so you need to go back and forth between inside the cell and understanding the chemical and physical principles by which all the reactions work.
How_We_Teach_507SC_Biological_Chemistry_I_Fall_2013	Using_a_Vitamin_Bottle_as_a_Teaching_Tool.txt	JOANNE STUBBE: If you look at the vitamin bottle, you have all these vitamins you eat, like, what do they call them? Biotin, riboflavin, pyridoxal. So all of those small, organic molecules, and they all have chemical reactivity and they interact with the protein and allow the protein to do chemistry that can't normally be carried out by just the amino acid side chains of the protein in the active site of the enzyme. So the vitamins you eat are not actually what's interacting with the protein, they need to be modified. So they are the precursors to what are called co-factors that, again, expand the repertoire of what's found in enzymatic systems. So you have a whole bunch of organic co-factors that actually can be made spontaneously. If you throw in some simple molecules like cyanide and stuff, these things all self-assemble, so they're all from the primordial soup. And in fact, many of these vitamins can do chemistry without any enzyme at all. But they can't do it specifically. And they can't do it rapidly. So we have all these organic molecules that can self-assemble that expand the repertoire, but if you look at a vitamin bottle, you will see minerals. And that's one thing that I think most biochemistry courses don't talk about, is metals. And it's now proposed that between 35% and 50% of all the proteins in our body have metals that are essential for function. And so these minerals that you eat, iron or zinc or calcium, all play a central role, again, in expanding. They all help in many cases facilitate chemical transformations, and in the way we can understand by understanding basic chemical principles. So the vitamin bottle, we come back to over and over again through the course of the semester, because all the enzymes in metabolic pathways have different kinds of co-factors that are required to make the enzymes function.
How_We_Teach_507SC_Biological_Chemistry_I_Fall_2013	Motivating_Students_to_Study_Metabolic_Biochemistry_with_Oncology_Applications.txt	JOHN ESSIGMANN: At the end of the course, when there's so many pathways out there that things start to get really, really complicated, we try to increase the number of physiological scenarios, again, to try to get the students sufficiently interested in a pathway and thinking about how the whole pathway works, not just each individual step-- to get the student to like the example so that he or she will go right in there and study it. And one of the areas that I think really important these days in basic metabolic biochemistry is in oncology-- cancer biology. JoAnne mentioned that not that many years ago, academic programs wondered whether teaching metabolic pathways was really the best use of time, because so many other things were happening in the molecular biology revolution. And certainly in 5.07 we decided to maintain emphasis in this, because we-- just because these are the first pathways that were studied doesn't mean they aren't important. They're medically very important. They were originally studied because of medical or economic reasons that-- fermentation, for example-- that these pathways were right in front and center. They're always very topical. But what happened in I'd say the last 10 years is that there's been a reawakening of the understanding of how metabolic pathways redirect themselves in order to accomplish disease goals-- for example, with a tumor. And one of the things we teach is that a tumor is a lot like a running muscle. And Matthew Vander Heiden, who is here in our biology department and teaches the comparable course is a real expert, a pioneer in this area. But what we've learned is that cancer cells tend to be addicted to glucose. They would much prefer glucose over any other fuel. In fact, they-- when you think about what a cancer cell really is, it's a cell that's not terribly different from all our other cells. It's acquired some small number-- we'll call driver mutations, maybe seven or so driver mutations. There are many more passenger mutations, but maybe seven or so genetic differences that separate it from a normal cell. But among the things that has happened to it is reprogramming of its metabolic needs. And it has acquired the commitment to unremitting cell division. If you think about what's needed for a cell to divide, probably the principal structural resource-- which, again, this would come from JoAnne's part of the course-- is membranes. You've got to recreate the outside of the cell and all those organelles. And what that means is fatty acid biosynthesis is absolutely going to be paramount. One way that we now know that tumors work, if you understand all the pathways, is a tumor will consume glucose, it will convert that glucose to acetyl-CoA. The acetyl-CoA takes a ride on the molecule citrate until it gets put out into the cytoplasm, and then in the cytoplasm it becomes a factory for producing-- out of acetyl-CoA, it produces the lipids that are necessary for membranogenesis. That's absolutely critical for cancer cell development. Now, the reason that's important is that understanding it, it tells us that, well, there are certain enzymes in the pathway. One of them is called ATP citrate lyase. Another one is called malic enzyme. So, when you look at the charts, you'll see these things. These are enzymes that are necessary for cell division, because they're necessary for fatty acid biosynthesis, and they represent good targets-- next-generation targets-- for cancer chemotherapy. A normal cell, you can tell it not to divide, and it won't divide. But if you can tell a cell that's committed to divide and you tell it not to divide, oftentimes that cell will kill itself. So by blocking these critical points-- test points, we'll call them, in this metabolic chart-- you're able to selectively kill cancer cells-- we hope, anyway. But this study of metabolic biochemistry has identified these new targets. Another thing that's, I think, an important anecdote about cancer cells is that they need other cells in order to survive. If you think about the problems that a tumor faces-- remember, it started from a normal cell that acquired new mutations, converted into a cancer cell, and then started to grow out into a tumor. As it grows, it becomes more remotely placed relative to the blood supply. OK, now, certainly there will be a response, and the blood supply will try to grow toward the tumor cells. But the core of a tumor is hypoxic. It doesn't have enough oxygen to do real respiration. So, what happens is, the cancer cell tries to hard-wire the glycolysis pathway to be on. And rough estimates are that through this-- initially, a hypoxia-inducing factor, which is a transcription factor-- you get an upregulation by 10 to 20-fold of almost all of the enzymes of the glycolytic pathway. So, what happens is, the cancer cell becomes a specialist at glycolysis. It does high-throughput glycolysis-- glucose to pyruvate. But, again, we don't have the metabolic equipment to do a lot of-- we don't have the metabolic equipment to be able to do respiration if you're removed from oxygen. So, the pyruvate gets converted into lactate. Lactate gets pumped out into the blood, and, as I mentioned before, it acidifies the blood. That's what happens with a working muscle. But the tumor sends the lactate into the blood. It's picked up by the liver. The liver is a specialist in gluconeogenesis. The liver then rebuilds the lactate into glucose, sends this back out into the blood. So, the tumor is then able to re-eat the lactate that it sent out. So a partnership emerges between the liver-- the gluconeogenic organ-- and the tumor. So, the tumor finds that it's fed by-- unwittingly-- by the liver. And the liver is contributing to providing the nutrition that's eventually going to kill the organism if something doesn't go in to stop it. But, again, understanding the pathways can give you ideas with regard to how to intervene. So, metabolic biochemistry is pretty critical to understanding this generation's cancer scientific agenda.
How_We_Teach_507SC_Biological_Chemistry_I_Fall_2013	Becoming_a_Toxicologist.txt	JOHN ESSIGMANN: I'm always interested in listening to JoAnne's lectures, and she talks about how she got interested in biochemistry from a background in what I would call more physical organic chemistry by attending a lecture and being completely inspired. And I am a toxicologist by training. And how did that actually happen. I have a similarly inspiring story, so I thought I would tell that. I went to a lecture about 45 years ago, by a fellow by the name of [Richard] Evans Schultes. He was the director of the Herbarium at Harvard-- and I'd been to it; it was very interesting-- and a professor there. And he is arguably the father of the field called ethnobotany. I went to this talk-- there were only about 10 people at the talk. He-- because it was a small talk, he gave it sitting down, he asked permission to do that, he's a very polite man. And it was very informal, only a few slides. And the slides were mainly of him living with indigenous peoples, Native Americans in the Southwest, Amazonian native peoples, very interesting. And he talked about, for example, he had just graduated, his undergraduate degree from Harvard. His parents were eager to have him go to medical school. He was very interested in botany and in native languages. So he went to live with the-- I think it was the Kiowa people in the Midwest-- I think it was probably Oklahoma. And he learned about peyote and a lot of other chemicals that were hallucinogenic. And he realized, of course, that many of these kinds of compounds that were used in a lot of rituals, were also medicines at other concentrations, anesthetics and so on. He then went down to South America, living with various tribes. He'd be gone for up to a year at a time. There are wonderful stories, well actually terrible stories, I guess, about him paddling his canoe for 40 days with malaria-- it was terrible-- to get to a hospital, things like that. But anyway these are stories-- I was a young scientist at the time-- these were very influential to me. And he talked about, I was down in South America and they-- and I found the plants from which the native people got their dart and arrow poisons. And he said, out of that we isolated curare, and initiated the path toward the clinic of curare as a muscle relaxant. He said that it didn't work so well. I remember this lecture like it was yesterday. He said that it was the beginning of World War II, we were cut off from the rubber plantations in the Philippines and other places. And since South America had jungles, his form of, quote unquote "military service," involved trying to find sources in the jungle of latex that could be used to make rubber so that we could have an effective war machine. So anyway, I went up to this fellow after he gave his talk. And I said, look, I just got to do this kind of stuff. This sounds really interesting. And he said, what's your background? I said, well, you know, I worked as a chemist. I was a biology major but I worked as a chemist at an industrial consulting company during my undergraduate years. And he said, oh, you got to go talk with Gerry Wogan at MIT. He said that he isolates toxins from fungi that you find out in the jungles of Southeast Asia. And, so anyway, that's how my career began. As you know, I got to eventually meet Gerry Wogan and work with him. He had already identified this toxin, aflatoxin. But he needed somebody to figure out how it worked, and that's how I got my start. So my interests have been in chemicals from the environment. It could be a pollutant. Or it could be a chemical that could be a precursor to a therapeutically useful molecule, and how do they interact with biological systems. And that's what toxicologists and pharmacologists do.
How_We_Teach_507SC_Biological_Chemistry_I_Fall_2013	Research_Focus_Ribonucleotide_Reductases_RNRs.txt	JOANNE STUBBE: My lab works on the only cool enzyme in the world-- ribonucleotide reductase. It's the only way in all organisms that you make the building blocks de novo that are required for DNA biosynthesis and repair. So if you inhibit this enzyme, you have no building blocks. You can't survive. So from a practical point of view, it's the target of drugs they use therapeutically in the treatment of cancer. And I think in probably not so distant future in the antibacterials because I think there are sufficient differences between humans and bacteria reductases that you could make specific inhibitors. Why am I interested in it? Because the chemistry is sort of unbelievable. So I mean it was the first example where you learn, or you hear about-- you heard from John-- radicals. They're reactive oxygen species and nitrogen species that you can't control. They want to pick up an extra electron and form a stable octet. And if you leave them to their own demise, they react with anything and destroy it. Well nature has figured out how to harness the reactivity of radicals to do really tough chemistry with exquisite specificity. And ribonucleotide reductases have been the paradigm for thinking about that. And from bioinformatics now there are 50,000 reactions in metabolic systems that are going to be radical mediated transformations, yet we never talk about radicals in introductory courses. So I think that's all going to change. So why is it unusual? Well, for the human ribonucleotide reductase, the key to making this work catalytically is the amino acid side chain tyrosine needs to be oxidized to a tyrosyl radical. So automatically nobody believes that. A tyrosyl radical in solution has a half-life of a microsecond. In the active site of these enzymes, the half-life of the enzyme can be on the order four days. And this radical, which is again one electron oxidized amino acid-- if you reduce it with an electron and a proton, the enzyme is completely dead. So this was the first example of-- it would be another example of a post-translational modification that we talked about earlier-- modifying your amino acids. And so nature has figured out a way. How do you do this oxidation? She has a little metal cluster right adjacent to where this tyrosine is. And the function of this little metal cluster is to put this into the oxidized state, which is essential for the way the enzyme works. So the other thing that's amazing about the enzyme is the chemistry. There are two subunits. The chemistry all happens in this subunit, but the tyrosyl radical is there. And this oxidation-- normally when you do an oxidation the two atoms are sitting within a few angstroms of each other-- the oxidation happens over 35 angstroms. So that's unprecedented. It involves hopping radicals which no one has ever seen before. And so that was another thing that was completely fascinating from a chemical perspective about how the system works. The other reason that people in biology are interested in this, besides the fact that makes a building block for DNA, is that if you believe in an RNA world where we have a ribosome where a catalysis of peptide bond formation is all with the RNA, not with the protein. How do you get from an RNA world to a DNA world? The only enzyme that does that transformation making these building blocks are ribonucleotide reductases. And there are many classes of ribonucleotide reductases-- one uses this tyrosyl radical-- but they all have the same active site and do the same chemistry, but they have different metal cofactors depending on where they evolved. And the function of the metal cofactors in all cases, even though one's cobalt, one's iron sulfur cluster, one's manganese, one's iron-- the function in all cases is to generate a radical in the active site and then the chemistry is the same in all these things.
MIT_5310_Laboratory_Chemistry_Fall_2019	1_Introductory_Lecture_to_5310.txt	[SQUEAKING] [RUSTLING] [CLICKING] PROFESSOR: Take a moment to look around you. Look at the person on your right. Now look at the person on your left. Turn around and look behind you and in front of you. If you have a question on mathematics, or you want to know something about the potential new elements in the cosmic dust of space, or perhaps you want to know something about the architecture of the most beautiful bridge in the world, the Millau Bridge in southwestern France, chances are there is a good possibility that someone in this class may be able to answer your question. There are 11 different majors in this small class. This presents a great opportunity for you to actually mingle with these majors and broaden your ideas. Welcome to 5.310. 5.310 is a non-major sequence in the chemistry department. In chemistry, in MIT lingo actually, this is a 2-8-2 course. 12 credits. In MIT policies, one credit unit is 14 hours of work per semester. So if we look at this, we've actually got 28 hours of lecture, 112 hours of lab, and 28 hours of outside work for a total of 168 hours. But you really only have-- you're really only going to be in lecture for 17 of those hours. And there are five labs. Each lab is four days. That's 20 days times 4 hours is 80 hours. One of the labs is five days so that's 84 hours of lab. This outside work is on the low side so I'm going to fix it. I'm going to increase that to 50. Does that make you feel good? We're moving some hours around here. And there's one more thing. 17 hours of lecture but three of the labs on day four you get out right after the quiz. You can finish the experiment in three days. I know. You're all excited about that, right? So we're really only talking 74 hours in lab here. So I'm going to increase this to 60. So we end up with 151 hours. If you subtract those, you have a surplus of 17 hours. So I just want you to see this so that you feel good about it and you know you're not-- if you look at this and do the calculation, you're going to be spending between 10 and 11 hours a week in this course. And on the long side, if you use these surplus hours, you'll be at the 12 credit units. Now take a look at this slide for a moment. If you look at the slide, you can see that 5.310 ties in to 5.35. 5.35, six, seven, and eight are the URIECA modules, Undergraduate Research Inspired Experimental Chemistry Alternatives. I got it all out. OK. Good. So we've got 12 labs here. Each lab is approximately four units. And what happens is 5.310 ties into those labs. Those are the labs that the chem majors take. So what that means is if you're a freshman, if you're a sophomore or a junior, and you suddenly decide that you like chemistry and you want to change your major, or you want to double major, I'll give you full credit for 5.35 after taking 5.310. So you'll eliminate three of those modules from your program. It's a good deal. Now let's talk a little bit about the course. So is this course useful to my future? It is an introductory laboratory chemistry course. But you will learn basic skills that you'll be able to carry away with you for the rest of your tenure at MIT and beyond MIT. What you're going to learn in this course-- you'll learn about small scale synthesis. You'll learn about inert atmosphere techniques, thin layer chromatography and column chromatography. You'll do an atmospheric distillation and a vacuum distillation. You'll also operate a variety of instruments. And these are the most modern instruments that you're going to find in pharma companies, in chemical companies, and industry when you go out. You'll be operating things like polarimeters, refractometers, density meters. You'll operate a tabletop nuclear magnetic resonance spectrometer, 60 megahertz just for you. You'll operate a robotic GC, an IR spectrometer, UV spectrometer, and a mass spectrometer. You'll also get to put your samples in and watch an inductively coupled plasma mass spectrometer running. There's only two at MIT. And you also will go to the X-ray lab here at MIT. And you'll see the most modern X-ray diffraction machine from Germany running some of your samples from the essential oils lab. In one part of the lab, you'll go on a field trip to the Charles River. Can take your lunch. You're going to bring back water samples. You'll be testing those water samples for dissolved oxygen and phosphate levels. Above all these things, you're going to learn organizational skills that you'll have with you for the rest of your career wherever you go. Can you give me any hot tips? Students always ask for a hot tip. And I can tell you one thing that actually works for me. And that is sometimes we all get frustrated and discouraged. And when that happens, I usually find a quiet place and I talk to my brain. And I tell my brain everything is OK. Everything is going to be fine. And time and time again, this works for me. I can get myself out of it. And if you read Oliver Sachs, in one of his books, he says that if you can imagine things, they actually can turn into reality. So are there any brain and cognitive science folks? Oh good. Look at this. I've got four of them. Can any of you offer any comments on how this helps me? Is there something there? Anyone? No takers. Anyone else? So I guess the thinking about, you must become happier and clear your thoughts out. And if you become happier and clear your thoughts, you become smarter too. Right? And I actually brought a brain that I keep in my refrigerator, a beautiful brain. And I'm just going to set it here so that you can admire it. So the brain is very important. Some of you in this course are very, very smart. You're all very smart because you got into MIT or at the top of your class. You're valedictorians. I recall several years ago I had a freshman advisee who came to me. And she actually tested out of every subject. She sat down and I could not find one subject to put this student in. So I was kind of beside myself. I went out of my office and I bumped into the head of the physics department walking down the hall and said, I've got this advisee and I don't know what to do. Did you ever have one like this? He said once every 10 years. So I went back and I put her into all the most advanced classes, some with graduate students. And then I ask her how she managed to do all this because she came from an island in the Pacific. And she said to me OCW, OpenCourseWare. I watched the lectures that MIT puts out and I learned it all myself. But there are geniuses sprinkled throughout MIT. And there are probably geniuses in this class. Should you still take 5.310? Yes, because geniuses need practical skills. And in 5.310 can help you to bind those basic skills and make your genius become reality. Now there are a couple other key things to help you succeed in this course. One, if you feel like you need help and you don't know what to do, you're lost, come to see us. And we'll get you back on track. The second thing, which is important, is you need to be able to accept your mistakes. If you make a mistake, don't start crying and say it's all over. I blew this lab. I just messed everything up. I'm done for here. I don't know what to do. Just accept the mistake and ask yourself, what can I get out of this mistake that I made. And when you do that, you really can help yourself for the long term. I mean it's not anything embarrassing if a student works for three days and then, by accident, they drop their product. It happens. So don't feel bad about it. Just come to us and we'll work something out. But don't get stressed out over it. The last thing that could really help you here is, in this class, it's all about lab reports. So you've got to write these four lab reports and give an oral report at the end. My advice to you is don't wait until the last day of the last weekend when these reports are due to actually try to write this report out. Start early. When you're in the lab, a four hour lab, and a lot of those labs you'll get done at four so you'll have an hour. We have beautiful write up areas in the new undergraduate chemistry lab. You can sit there. And that's the point where you can actually write out a paragraph about what you did that day, what you actually did, what you saw, and what you found. And that's your procedure and observations for your lab report. And while it's fresh in your mind, you do it. And the procedure and observations typically is about a page and a half, no more than two pages, of your lab report. You could also work on the background of the report because you're talking about why you're doing this experiment, what you're going to get out of it, something about the history of the experiment, what was done before. So you can work on these sections along the way rather than wait until the very end and do a marathon session, try to trying to get the lab report done. So with those things, I'd like to talk a little bit about the course. And I'm going to cover seven broad areas. One is academic integrity. The second thing is the lab policies and then, most importantly, grading, how this course will be graded. And then we'll look a little bit at safety, because you do have a safety lecture you're going to. And we'll look a little bit at the lab notebooks that are required for the course. And we'll talk a little bit about waste management. And finally, we'll spend a little bit of time talking about calibration of instruments. So let's start with academic honesty. MIT has one of the best integrity programs of any school that I know. They have a website devoted to it. They also have printed material that you can pick up and you can read through it. And I think probably to summarize it in just one sentence, you don't want to present as your work the efforts and product of another person. And the penalties can be quite severe. You could actually fail the assignment. Could fail the course. You could be suspended from the Institute. You could even forfeit your degree. So it's pretty serious business. In 5.310, I think there are two areas that you need to actually look at. One of them is there are a lot of lab reports out there. They're in the dorms. And they're in the sororities and fraternities. And they call them bibles. So you don't want to actually go out and take pieces out of those and put them in your own reports. The reason for that is it's not right to do that. And the second reason is we could have an electronic copy of one of those reports on file. That would not be good. The other thing is I guess the innocent thing is when students sit down together and they're talking about the lab. You might talk with your lab partner. You can talk and you're writing things down. But what you don't want to end up happening is you don't want to have the same sentences in both lab reports. So you've got to put things in your own words even when you talk with each other and you're writing your reports up. That's pretty much all I have to say about academic integrity. S the undergraduate lab policies-- you're actually picking to work on either Monday/Wednesday or Tuesday/Thursday. And depending on the safety lecture that you elected, some of you went yesterday to the safety lecture and you enrolled in the Monday/Wednesday section. Today the safety lecture is at 1 o'clock right after this class. And Tuesday/Thursday people will go there, attend the safety lecture, and then you'll go up to lab to check in your lockers. If there are any Tuesday/Thursday people who would like to switch to Monday/Wednesday, Monday/Wednesday will have fewer students. So there'll be much better TA interaction with you. So if you can, just let Sarah know. She'll be down front at 1 o'clock registering you for your lockers. And if you'd like to do Monday/Wednesday, you can check in today. We'll just give you a Monday/Wednesday locker. The lab itself opens at 1 o'clock every day. And the TAs will give a pre-lab lecture at 1:05. It's about a 20 minute lecture. It's going to cover exactly what you're doing in that four hour period. And they will also demonstrate some of the glassware, maybe the pipettes, and anything you're going to be using in that lab. And they'll also show you the instruments that you might be running that day. So it's pretty important, the pre-lab lecture. And it will also firm up what you heard in the lecture and possibly didn't understand something, your TAs can really help in that respect. On the fourth lab day of each experiment, there's a quiz. And that will cover-- you've already done the three days of the experiment so you should be in pretty good shape for the quiz. You should understand what you're doing and know. You shouldn't have any problem with that. The laboratory, we try to clean up about quarter to 5:00. I can't recall in 5.310 any time where students have to stay after 5 o'clock. That's a good thing because you want to go home. Some of you have sport practice. And we understand that. And the last thing is we've indicated some select Fridays that are make-up labs. And there will be one Friday at the end of each four day lab period. So if for some reason you've missed something because you're sick and you couldn't do it on day four, then we have that option. And those are scheduled in the lab syllabus in your packets. Safety goggles. You have to buy these at the VWR stockroom, the basement of building 56. And I mean, you put these on and they actually really-- they hug your face. They don't look too glamorous, but you're not going to a beauty contest. You're going to the lab. But you've got to buy a pair of these. And you've got to wear them at all times. The other thing is your lab coat is a fire-resistant lab coat. These are top of the line lab coats. We issue you one of these when you come. We'll also give you a baggy like this. And you can write your name on the bag and hang it in your locker and leave it there. You never take it out of the lab. You leave it there. And first thing you do when you come in, at either entrance, either from building 13 or building 16 when you enter building 12, you'll have lockers. And you can grab your lab coat and goggles, put them on, and you'll be ready for the lab. We've got plenty of gloves. We use nitrile gloves. And generally, those gloves do not give students any problems. But if you have an issue with that, just let us know. The attire. So the lab coats have to be worn at all times. And you can't wear-- you can't come in with open-toed shoes, low cut jeans, t-shirts. You have to be really covered. So my suggestion is that you bring a little bag, a change of clothes, and you keep it in the locker. Students did this last semester. It worked really well. And then you can just change out and change out again when you're leaving. And that way you can wear your sandals, and your shorts, and anything you want, but you can't wear that in the lab. Cell phones, radios, iPods. You have to keep those in your backpacks. And this is what the lockers look like at the entryway. So you just grab one of those. And that'll become your locker. Once you hang your lab coat in there, no one else is going to put anything in there. And we've never had any problems with the lockers in the undergraduate lab. If you want to put a lock on your locker for the semester, that's fine with me. Obviously, no eating and drinking in the lab. You can't bring beverages and food into the lab. There are chemicals on the countertops and around that you just-- chemicals and food just don't mix. This is very important. Report any accidents or injuries promptly. So if you do get cut or you spill a chemical on yourself, you should tell us. If you leave the lab and then a couple of days later come back and you've broken out in a red rash on your legs or arms, it's much harder for us to go back and try to figure out what happened. But if you tell us right away, then we can track it down. We know what chemical it was. We know how to treat it. And MIT Health will help with that. If you need special accommodations or you've got medical conditions that you would like to talk about, you can come and see me on that. And you should do it this week just so we're aware of it. And I mean we don't want-- we had a student about three years ago who just passed out in the lab. I mean literally down on the floor. She was out. And if we know ahead of time if there is a condition or something that we should be aware of, we can know better how to treat that. Grading. This is the grading scale. Pretty traditional. It's not inflated and it's not curved. So it's a traditional grading scale. And this is what we use in 5.310. So the grading is all based on five labs. Each lab is worth 100 points. Total number of points is 500 for the course. And this will make you happy. There's no final exam. There was a final exam when I took over this course 10 years ago. But I got rid of it. It was not nice. So you've got 500 points. And how is that broken down? So of that 100 points, 20 points is your quiz that you'll take. So that incorporates into that. Then you have your pre-lab notebook and your post-lab notebook. That's 10 points. Then there are 5 points which are noted as discretionary points for the TA. And that would be like does this student show up on time. Does the student clean up their area at the end of the lab? Does the student wear their safety glasses or do they walk around with the glasses up in the air? So that's important. And then your lab report, either written or oral, would be 65 points. I'll show you this is the course textbook. This is the book that we recommend that you get. It's Mohrig. and it's Laboratory Techniques in Organic Chemistry. Very good book. It has chapters on all of the instrumentation and a lot of the techniques that you'll be actually using in the course. Well worth to buy this book. The other book that is not required but it's on reserve and we have copies in the lab is this ACS style guide. This will help you in terms of writing up your lab reports, writing up the reference section, knowing how correctly to put things together. Attendance. Attendance is not mandatory for this class. But there is an attendance sheet going around. And each lecture day we will send it around. If you don't attend lecture, your grade isn't going to be penalized. But if you do attend all of the lectures, at the end of the semester, if your grade somehow is within a half a point of a higher grade, 89.5, technically you'd get a B plus, we'll look at the lecture attendance and that grade could be pushed up to an A minus. So that's how the lecture attendance works into this system. And if you have any questions as I'm going along, just ask. So to get a passing grade in 5.310, you need to turn in the four written reports and you need to deliver the oral report. There are some penalties. So for a late lab, we use three times n minus 1 plus 2, where n equals the number of days the lab is late. Also, with each lab, you need to attach a cover sheet to your written lab. No cover sheet is minus 2 points. There are also some late points on the oral report. If you're late for an oral report, it's minus five points. If it has to be rescheduled, it's minus 10 points, just so you're aware of the late points. You don't want to use these if you don't have to. You really want to try to turn your labs in on time. And that two points or five points could make a big difference at the end. So this is the hard copy of the course manual. And you'll be allowed to bring this in with you to lab. You don't have to write up the pre-lab step by step that you're going to do. You can bring this in and follow it. So we're saving you a couple hours a week here. I hope you appreciate that. Students used to have to write the pre-lab out step by step in their own words. So this is a big time saver for you. I want to keep this course under that 12 credit limits. You will need a lab notebook. And the lab notebooks are available either at the MIT Coop or they have them at the VWR stock room. And they're around $15. And the notebook should be like 100 duplicate pages with carbonless paper because what's going to happen is each day you go to lab, the TA will initial your pre-lab. And then at the end of lab, you'll go to the TA with your notebook. And the TA will initial each page of your post-lab notes. Then you'll tear them all out and hand them to your TA. You keep the original. We get the copy. The reason for that is when it comes down to the final lab report, you cannot have anything in the lab report that's not in your post-lab notes in your notebook. So let's just take a quick look and see. For the pre-lab, this is pretty simple. You don't have to write out the whole procedure, but you do need to have your title, date, the name of the experiment, an introduction, a couple of sentences what this experiment is about, what you hope to get out of it, maybe a couple of sentences on safety issues that you spotted in the experiment, and then any pre-lab equations you think you'll need. The first pre-lab is due Monday and Tuesday next week. That's when the lab actually will commence. Tables are very good to put in your lab notebook and in your lab reports as well as drawings that might help you to actually visualize what you're setting up. For the post-lab, this is probably the most detailed part because you've got to write everything down that you're doing in lab, all your observations, everything that's happening. When you're over at the distillation, you're going to record the temperature that the distillate started to come over. You're going to record the drops per minute that's coming over. All of these notes go into your lab book while you're working in the lab. So let me show you a couple examples of lab notebooks, what students have done. This is one example where a student had-- sorry-- where a student had put their pre-lab notes on one side and left the other side for their post-lab. This isn't necessarily the best way to do it because you don't know how much space to leave for your post-lab. So another way to do it would be just to write out your pre-lab on one page, and then stop, and then start your post-lab on the next page. The other thing that comes up is these are four to five day labs. So when you read the whole experiment, one way to do it is write your lab up for the whole experiment all in one time. Then you don't have to write it up each time. That works for a lot of students. But we only require you to write the pre-lab for the day that you're actually doing. So I want to talk just a bit about some questions that come up a lot, like what is the stability of my chemicals. You're going to be working with some very air sensitive chemicals. So you might go over to the balance area and mass out your chemical for the first lab. You have iron chloride tetrahydrate. You mass that out but then you walk away. If you don't put the cover on the chemical, the green chemical will turn brown. And it's not going to be any good for the other students who are doing the lab because the iron gets oxidized. And you need iron-2 to do the experiment. So be aware of that. And then how do I get what I need from a stock solution? So you're going to see chemicals like this labeled stock solutions for the lab. The one thing you don't want to do is open this up and go into a stock solution with a dirty pipette, because if you do that, you'll contaminate the solution for the whole class. And some of the experiments are really quantitative and very sensitive, especially the Charles River where we're looking at the phosphate levels. So what you want to do is you want to make sure that-- and the TA should do this-- have these chemicals poured out in labeled beakers so that they're ready for the students to actually go into and draw out what they need. If you don't see that, always ask your TA. Never go directly into the stock solution. And then the order in which you add chemicals is very important. You always want to-- you always want to go from the concentrated to the less concentrated. You would never want to take water and add it to acid because it would splash right back in your face. You always want to go the reverse. Add the acid to the water. Concentrated to less concentrated. And if you spill chemicals while working, let us know. It's very important. Don't leave them. A couple or few years ago, we had a class during IAP. And one of the freshmen spilled a half a bottle of urea on the floor and left it. And the TA was beside himself. He was saying who did this. Nobody would own up to it. But we just happened to be filming this class. And there is a video online that you can go watch. And you can see-- you'll know who it is when you watch the video. So you always want to let us know. And we always want to clean up if there is a spill. And if it's a spill, you have to let us know right away. We have to determine how bad it is so we don't have to evacuate the lab or something. And then if you get chemicals on yourself, you know you've got to let us know because chemicals on yourself, we can take care of it right on the spot, get you washed off. If we have to, we'll walk you over to MIT Health to have them look at it. And chemical waste. There are a lot of different kinds of waste containers in the lab. We've got boxes here for glass and plastic. And you've got to look at the box before you throw something in. Broken glass would go in the glass box. Plastic pipette tips go in the plastic box. And make sure that you empty them of your chemical first into the waste container before you throw the pipette's tips into the box. There are bottles for liquid waste. And everything is labeled. You can see the red labels here. A couple of things you should know. Don't pour into the top of this. This is a lid so that it actually opens up and then you pour it in. And then you always have to close this container after you've added your waste. If you leave a waste container open during an active lab and we're inspected, MIT can be fined thousands of dollars. So you've got to keep the waste containers closed. The other thing is you've got to be aware of what you're putting in. So read the container. Make sure it's the chemical that you're using that's going in. You never want to put acetone in to anything except a bottle that says acetone, because we're going to be using hydrogen peroxide in this class. And hydrogen peroxide and acetone and you have an explosion. So what you're making is you're actually creating these acetone peroxy compounds. This is the dimer. It's called acetone peroxide explosive apex. And then there's also a trimer. And this is the triacetone peroxide. So what happens with these is they form a white crystalline powder. And it smells like bleach. And when that forms, just any movement could trigger it. This is the same stuff that the shoe bomber had in his shoe if some of you remember 10 years ago on the plane. And so it's very frightening. So you have to be mindful of what you're putting in the containers. The acetone we're going to recycle. So it will have containers just for acetone. And that's where you're going to dump it. The other thing you want to be aware of is nitric acid. We're using nitric acid in the Charles River lab. You don't want to mix this with any kind of organic solvents. If we put this, say, with ethanol, then you're making this C2H5 ethyl nitrate. And this is also a primary explosive. The first thing that happens is you'll see orange smoke billowing out. And then you'll hear this whining noise. And it gets louder and louder. And then the hood goes. The ceiling goes. So if you see smoke or you hear noises, get away from the hood. But don't put nitric acid with anything except in the container that says nitric acid. There are also some containers for solid waste by the scales. So as you're massing your chemicals out, if you have a little bit left over, they go in the can with you with your weigh boats. Don't put gloves into the cans. Gloves can go in the trash. We have a box for needles here, which is great. And don't put needles in the trash, because the cleaners grab those trash bags at night and they could get poked. And that would not be good. So the needles, we're going to try to count them out. And the TA will be judicious in coming around with the needle box and collect them at the end. Calibration of melting point. I just want to show you one thing here. If you go to the melting point and you take a melting point of your sample, an uncalibrated melting temperature might be 64 to 66 degrees. Once it's calibrated, you're up to 79 to 80.9 degrees. So we have four standards. And each standard has a range where it starts to melt and ends melting. So you put your standard in. Then you look through the scope. And you record your observed where it's melting, when it started, when it stopped. And you have two points for each standard. So you can do a linear regression and draw a straight line and get an equation for the line. And then every time that you use that melting temperature, you can calculate-- you put in your experimental and calculate what it should be from the equation. So we've got we've got a couple of minutes left. And this is a chemistry class. So I'd like to do a demonstration just to end this class. And I need a volunteer. Yes. Come on. And what is your name? AUDIENCE: Autumn. PROFESSOR: Autumn. OK, Autumn. So Autumn, I've got a cup here and some water. So I'm going to pour some water into the cup. And you tell me when to stop. OK? AUDIENCE: Stop. PROFESSOR: OK. So what I'm going to do is I'm going to cover this up. OK. And then I'm going to carefully turn this over. So far so good, right? You know where I'm going with this, Autumn? I'm going to put it on your head. Face your fellow students. And we'll go up here very gently. And there we go. Now I'm going to let you hold it, Autumn, because I don't want to be responsible. OK. OK. You OK so far? AUDIENCE: Yep. PROFESSOR: OK. All right. Autumn, what does this say? AUDIENCE: Do not remove this card. PROFESSOR: Whoops. OK. Let me take this off from Autumn. AUDIENCE: What's on my head? PROFESSOR: What happened to the water, Autumn? AUDIENCE: Is there something inside that absorbed it? PROFESSOR: She said is there something inside that absorbed it? OK. Let's see what we got here. We made a polymer. AUDIENCE: Cool. PROFESSOR: So unbeknownst to Autumn, I had a little bit of powder in her cup. And when I put the water in, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1. AUDIENCE: What kind of polymer is it? PROFESSOR: I knew you were going to ask that. What kind of polymer is this? AUDIENCE: I'm Course three. PROFESSOR: OK. So you'll all know this. Hold that for a minute, Autumn. This is the diaper polymer. This is sodium polyacrylate. And I actually took one of these diapers. And I cut it open. And I got 4 grams of sodium polyacrylate out of the diaper. So this is how they work. These polymers, you can see this polyacrylate is a monomer repeating unit. And what happens is if you look inside, it has a lot of sodiums. But when we put the water around it, it starts to send sodium out and pull water in by osmosis to balance the sodium atoms. So all of a sudden it swells up. And you've got this system here. Now we're going to do a little experiment. We're going to take this and put those on now. OK. So I'm going to take this and put it into a little baggy. Hold that bag. AUDIENCE: Add salt [INAUDIBLE]. PROFESSOR: I'm going to add some salt to this. And now we're doing the reverse of what we just did. We had added water to the polymer before but now we're putting salt in. So just zip that bag up. And this is the fun part, Autumn. You get to squish it around. So now there are sodium ions on the outside of the polymer. And it's panicking. It's starting to pull them in and send some of the water back out. So the polymer is actually going back to a liquid. So that's how this works. Great. Give her a hand. She did a great job. Thank you so much, Autumn. Well, thank you all. And the next lecture is Tuesday. Don't forget to go to the safety lecture. And that is downstairs, two flights down.
MIT_5310_Laboratory_Chemistry_Fall_2019	2_The_Ferrocene_Lecture.txt	[SQUEAKING] [RUSTLING] [CLICKING] JOHN DOLHUN: Welcome to the ferrocene lecture. We are going to do a demonstration at the start because I'm going to be talking about additional reactions during this lecture. And I want you to actually see one happen. So I've got Amanda Trainor, who is manning the fire extinguisher. Amanda just had her fire extinguisher testing. So she is ready to go. And Dr. Sarah Hewett will actually assist me with the bromine that we're using. Bromine and me go way back because I made bromine when I was in high school. In the parents of my-- in my parents' home-- in the basement. The whole place filled up with reddish brown gas. And back in those days, the chemistry sets had real chemicals in them. So what we're going to do is we are going to cook some bacon. And we are going to crack the glycerol. And we going to make this unsaturated compound acrolein. Then we're going to throw it into the bromine. And the bromine should add across the double bond-- an addition reaction. This is the acrid smelly stuff that you smell when you cook bacon. This is the burned bacon fat smell that you smell. It's colorless, flammable, and very poisonous. So let's go. We're going to start this. So I'm using a creme brulee torch. It's my wife's. She's probably out of her mind now looking for it. So we're cooking the bacon. And we're going to get that bacon fat-- the glycerol-- broken down. Ready? And here we go. So we've thrown the bacon into the bromine. You can start to see the color disappearing. Color is adding across the double bond of the bacon. And I present to you bacon dibromide. Good stuff. [APPLAUSE] Thank you. I actually don't eat a lot of bacon anymore after doing this demo knowing that stuff is so nasty and a cancer producer too. So all right. Let me get this hot lab coat off. So Emil Fischer and Geoffrey Wilkinson win the Nobel Prize in chemistry back in 1973 for their independent work looking at these organo-metallic sandwich like compounds. It all started here in 1951 with a paper published by Pauson and Keely, "In Nature," where they took a Grignard like reagent cyclopentadienyl magnesium bromide. And they tried to get an oxidative coupling of this ring hoping to make fulvalene. Instead, they got this stable orange complex. Empirical formula C10H10Fe. Right after this paper came out the fellow on the right, Geoffrey Wilkinson, who was at MIT, had just moved to Harvard. And both him and Woodward at Harvard looked at this paper and said, wait a minute. With these sigma metal carbon bonds they're saying that this complex actually is stable at very high temperatures up to 400 degrees. So that these bonds would disintegrate at those temperatures. So they were skeptical of this structure. So they immediately said, well, let's do an addition reaction. Look at all the double bonds here. Should easily be able to do an addition reaction and add across those double bonds. They got no reaction. So then they said, OK. Just for the fun, let's try a substitution reaction. For a substitution reaction you need an aromatic system such as benzene. An electrophilic aromatic substitution reaction involves an electrophile, which simply substitutes itself for a hydrogen on the aromatic ring and gives you your product. So they tried a substitution reaction and they actually got a reaction. Now they were a little bit more puzzled because look at cyclopentadiene. Is it aromatic? How many pi electrons are there? Four. Good. And what is Huckel's rule? Anyone know Huckel's rule? Yeah? Sean? AUDIENCE: Pi electrons are at the aromatic. JOHN DOLHUN: OK. AUDIENCE: So this would be [INAUDIBLE] aromatic. JOHN DOLHUN: That's one way to look at it. So Huckel's rule is 4n plus 2. Right? 4n plus 2 pi electrons where n is a 0 or any positive integer from 1 up. If you put 0 in there you get two electrons. That obviously has four. If you put one in there you get six. So this definitely does not observe Huckel's rule. It's not aromatic. Most of these types of hydrocarbons like this have PKAs that are greater than 50. But it turns out that cyclopentadiene has these hydrogens on there that are slightly acidic because its conjugate base is very stable-- stabilized by resonance. So if we take a-- where did I put my chalk, here. If we take a base here, come in and abstract one of those protons, what we're going to get is this anion. And this is the cyclopentadienide anion. This has six electrons. Now if you look at this system-- all of these SP2 hybridized carbon atoms now have electron density that they can share all around that entire ring. So this is an aromatic system. And what would Geoffrey Wilkinson and Woodward said was, OK, so let's take two of these, make kind of like a sandwich structure-- six electrons on the bottom, six electrons on the top, and six D electrons from iron in the center. So you've got 18 electrons. That's kind of a magic number for an inorganic chemist because it's got that noble gas configuration. So the D electrons from the iron are pi bonding with the P electrons from the hydrocarbons. This is a complete reversal of the classical way of looking at ligand metal bond coordination. Everybody used the sigma bonds. No one ever thought about pi bonds. Can I have two volunteers? Yes. Come on up. Come on. See if you can come over to the front of the table here. And you are? AUDIENCE: Aisha. JOHN DOLHUN: Aisha. And? AUDIENCE: Maya. JOHN DOLHUN: Maya. OK. Aisha and Maya. So let's see what mama packed me for lunch today. Oh good. I got two pieces of bread here. Correct. OK. So Aisha, why don't you hold the bread-- one hand like that and stagger the other one and put a space between it and turn toward this way. Yeah. Turn so it's-- yeah. Put the crust facing the audience on one and away from the audience on the other. Maya, take the orange. And now let's see. Let's fix this a little bit. So there we go. And come down a little bit. Now Maya, come in. Put the orange right there. There it is. [LAUGHTER] A molecular sandwich. That's ferrocene-- the two cyclopentadienide anions and the iron atom in the middle pi bonding with all their electrons. Congratulations. Thank you. [APPLAUSE] Maya, do you like the orange? AUDIENCE: Sure, thank you. JOHN DOLHUN: I know you don't want the bread, but oh, look. There's something else. Here. AUDIENCE: Thank you. JOHN DOLHUN: OK. So we just figured out how ferrocene is put together. Now we have to make it. And to make ferrocene you need cyclopentadiene. But this stuff is not commercially available because it has a half life of 12 hours. What it does is it spontaneously adds to itself in this reverse Diels-Alder type reaction to make the dimer. So let's look at the Diels-Alder reaction for a moment. If you're taking organic now, this is the Mona Lisa of all organic reactions discovered by Otto Diels and Kurt Alder in 1928. And they both won the Nobel Prize in 1950. You need a diene-- an unsaturated hydrocarbon with two double bonds-- and a dienophile-- a substituted alkene-- to make this substituted cyclohexene type derivative. What you've got is four pi electrons here, two pi electrons here, and this is called a 4 plus 2 cyclo addition. And this reaction just goes. You don't have to do it. You put them together and it goes because you're making these sigma bonds, which are much more energetically stable than the pi bonds you're starting with. But look at our system. We have these two cyclopentadiene rings. We don't have a dienophile. We've got two dienes here. And this thing still goes spontaneously-- adds to itself to produce the dimer and other higher polymers. So how are we going to make this? We're going to crack the dicyclopentadiene in the hood. The TAs are going to do this for you. It's highly flammable-- the product. Cyclopentadiene is highly flammable so they're going to cool it in ice. The other thing is, this is very smelly. So don't wear your silk clothes and your wool clothes to lab when you're making this stuff. So you're going to be going over to the hood to get your allocation. The main thing you have to be aware of is when you get your needle and you put it in and you pull your 0.3 mLs-- whatever you need for your reaction vessel-- that you don't grab on to the syringe with your fingers because the warmth of your fingers will dimerize this right in the syringe before you inject it into your reaction vessel. We're going to heat this up to about 180 degrees, collect the fraction that comes over between 38 and 41 degrees. That's our cyclopentadiene. Now we're going to be using no air techniques in some of the experiments that we're doing. Why do you think we need to use no air techniques? Yes? Alex? AUDIENCE: There are things in the air like oxygen that are reactive. JOHN DOLHUN: Very good. There's oxygen in the air that's very reactive so some of the chemicals you're using like iron chloride tetrahydrate could be oxidized. We've also got that cyclopentadienide anion here, which-- this guy-- which actually decomposes in the air. So it's very important to have this atmosphere. So how are you going to do that? Pretty simple. We're going to be working with these little vessels. They're called Assem vials. They have septums on them. So you'll put your reactants in there. And then you'll simply take a vent needle, put a vent needle in into the septum. Don't push the vent needle down too far. If you push it down too far, your liquid might shoot up through the vent needle. Then you're going to go over to the hood. You're going to pull out the nitrogen line. Nitrogen will be flowing. You'll stick the nitrogen line in. Now you're bubbling nitrogen in. And this can go down into the liquid, bubble, get it refreshed. Then you're pushing out the air through the vent needle. After a couple of minutes, take the vent needle out. And then pull out the nitrogen line. Now you effectively have a nitrogen atmosphere for your reaction. So this is the reaction scheme for the synthesis of ferrocene. Notice there are two reactions going on here. You'll actually have two of these little asam vials. In one of them you're going to have KOH and dimethoxyethane. The KOH you'll have to mass out at the balance area. And you've got to work kind of quickly with this because KOH is very hygroscopic. It picks up water very quickly. In the other vessel you're going to put iron chloride tetrahydrate dimethyl sulfoxide. And then you're going to shake those vessels. You're going to work out in the lab. You seriously-- you will be sore after this lab for about an hour of working out. Once you shake them well, your iron chloride tetrahydrate should dissolve. But the KOH will not dissolve. So don't worry about that. Do you see KOH? It's OK. Once you get everything dissolved you take your iron chloride-- or your KOH dimethoxyethane vessel over to the hood and you get your cyclopentadienide and you inject it. You put that back under an inert atmosphere. And then you start shaking it some more. After about five minutes you have this beautiful pink color, which is your cyclopentadienide anion-- sometimes called the Cp ligand that's forming in your flask. Let's just stand back for a moment and take a look at that top reaction. Who can tell me the driving force of that reaction? Why does that reaction go? Alex? AUDIENCE: It's an acid base reaction. JOHN DOLHUN: It's an acid base reaction. Yeah. Yeah. What else up there do you see that just pushes that so fast? Alex? AUDIENCE: Resonance. JOHN DOLHUN: Resonance. OK. Yeah. You're making something that has resonance forms. Yes? AUDIENCE: Creating the aromatic ring. JOHN DOLHUN: Giselle, right? AUDIENCE: Yes. JOHN DOLHUN: Yes. You're creating an aromatic ring. Very good. So you're going from a non aromatic system to an aromatic system. That is a big push. OK. So once you make this, then what you're going to do is you're going to take your other vessel with the iron chloride dimethyl sulfoxide and you're going to start doing injections. You're going to do four injections into this system. After each injection-- when I did this I usually put my system back under an inert atmosphere. And then I'd shake it. Then I'd do another injection. Shake it. Inert atmosphere and so on. And then finally, what you've made is you made ferrocene. So once you get down here you're ready to take a look at that ferrocene. So what you're going to need is you're going to need a small beaker-- about a 30 mL beaker. And then you half fill it with ice. So we're going to have ice in the beaker. And you're going to add to the beaker about 4.5 mols of 6 molar HCl. And then you'll add your ferrocene from your asam vial. You're going to add your ferrocene. And when you do that, you stir it up with your stir bar. And you can use a little bit of dimethoxyethane methane to wash out your asam vial. Get everything out, washed out into that beaker. And your orange crystals should float to the top. Once you get your orange crystals, you're going to set up a little mini Buchner funnel system such as this. And inside of this there's a baby piece of filter paper. You want to be sure that you wet this filter paper and put it in wet. Otherwise if you don't, if it's dry, your product will go under it and end up in the flask. So wet the filter paper, pour your product in. This is hooked up to the vacuum in the lab. And it will just draw your product and you'll have your filtrate will come through. Now the filtrate that's coming through is going to be a bluish green color. What do you think the filtrate could be? Anyone? I know you know Alex. Anyone else? Alex, go for it. AUDIENCE: Iron 3. JOHN DOLHUN: Iron 3. Oxidized ferrocene. Interesting. So you actually started with ferrocene. And in the process of oxidation-- and you've got some HCl in there. So you've got chloride there. So what we've made here is-- you've made what's called ferrocenium chloride. Why do you think we made that? What does that represent? Looks like we lost some ferrocene probably because we didn't keep that right inert atmosphere all along the way. So think about how you would take this and get ferrocene back from it. I'll let you think about that a little bit. If anybody comes up with a great idea and wants to do this on day four when there's no lab going on, let me know what you need. OK? So now, we've made our ferrocene. We've got our crude ferrocene and we're going to purify it. And we're going to purify it by sublimation. Definition of sublimation is the amount of energy and kilojoules per mole that we need to add to one mole of a solid to take it from the solid to the gas directly. Hess's Law defines the enthalpy of sublimation as the enthalpy of melting plus the enthalpy of vaporization. But for this to hold, both of these steps would have to be taking place at the same temperature, otherwise Hess's Law is just an approximation. I brought some carbon dioxide in. Can you see this? It's subliming. It's going from the solid-- and this is very cold stuff. This is about minus 78 degrees. I'm going to burn my hands. So I'm doing this very quickly. OK. You can't see the sublimation when it gets into the air. But I'm going to put it in this cylinder so you can actually see the bubbles of sublimation that are taking place. AUDIENCE: Woah. Cool. JOHN DOLHUN: So there's another definition of sublimation that we can use. We can define it as heating a solid below its triple point to the gas and then collecting that vapor on a cold surface. And that's exactly what you're going to do with your crude ferrocene. You're going to take a biological culture dish, sprinkle some of your ferrocene in there, cover it, put it on a hot plate, and then fill up a beaker with ice. Put the beaker on top of it. Turn the heat on. Keep it under 100 degrees. And after a few minutes, you'll see orange ferrocene start to sublime up inside of the culture dish. And then your crystals will form on the bottom of the cold part of the dish and hang off the dish. It's quite a dramatic reaction. And this sublimation is really great because oftentimes the things that you're trying to purify are more volatile than the impurities that they contain. So it's very clean to actually get a pure substance from sublimation. Couple precautions-- when this reaction is over, if you take your beaker like this and you lift it up, you're going to lose all your product. It'll fall right off. You'll have to start over. So the trick is to slide the beaker off very gently. The other thing you don't want to do is you don't want open this dish when it's hot. Why wouldn't we want to this when it's hot? Alex? AUDIENCE: [INAUDIBLE] JOHN DOLHUN: Yeah. The toxic ferrocene would go up all around us. We'd be breathing again. So keep this closed till it's cool. Then open it up, scrape your crystals off. So now, you've made your ferrocene. So what we'd like to do is we'd like to write a reaction. And then you're going to calculate the limiting reagent, the theoretical yield from your starting materials. You'll take your actual yield and calculate a percent yield. Let's just do a-- just to review-- a general equation for that. We'll do 2A plus B going to C plus D. And we're going to have 0.9 moles of A and 0.5 moles of B. And I want to know how much C can be formed theoretically from my starting materials. First thing to do is look at the equation. The equation is talking to you. What is it saying? It says for every 2A I need one B. All right. How much B do I have? 0.5. So how much A do I need? 1. I don't have enough. That's your limiting reagent. Right? It's going to run out before anything else. So A is going to determine your product. So now again, take a look at the equation. It's talking. For every 2A, you make one C. How much C am I going to make from 0.9 moles of A? 0.45. Very good. So my theoretical yield is going to be 0.45 moles of C. Now what you can do now is you're going to actually do the reaction. You'll mass out how much you actually got so you'll know what your actual yield is. So you can calculate a percent yield, which is your actual over your theoretical times 100. Pretty simple. You're also going to have to determine the melting point of the ferrocene. And I'm going to tell you that if you take your melting point tube and you stick it in the melt temp and you're watching it, you'll never see it melt. Think about that. Think about what you're going to have to do before you put that melting tube into the melting point machine because you know ferrocene sublimes. Right? Just going to disappear on you. Think about that. So now we are going to take our ferrocene and we're going to do a Friedel-Crafts electrophilic aromatic substitution reaction. We're going to take the ferrocene and we're going to a acetylate it. And normally this Friedel-Crafts reaction is usually done with a very strong Lewis acid. Usually they use aluminum chloride. But aluminum chloride is very difficult to work with. You take that stuff and you're walking around with it in the lab. It's producing hydrochloric acid gas. So it reacts with the water vapor in the air. It's nasty. So we have decided to use a much weaker Lewis acid-- phosphoric acid. The good thing is that this cyclopentadienide anion is more reactive than benzene. So we can get away with this weaker Lewis acid. So we've got acetic anhydride phosphoric acid. There are no solvents in this reaction. We're reacting these two things with the ferrocene. What do you think the phosphoric acid is reacting with? Anyone? Yes? AUDIENCE: Is it activating [INAUDIBLE] carbonyl? JOHN DOLHUN: Yes. It's actually activating something to produce an electrophile, which is good. And that's what we need for this reaction. So it's actually reacting with the acetic anhydride. And here it is here. You can see the mechanism of this. Pretty simple. The acetic anhydride phosphoric acid react. And you make acetic acid-- vinegar. That's one of the products. And then you also make this very stable acylium ion. And this acylium ion is actually-- it's resonance stabilized. So we can actually take a pair of electrons from oxygen, come down here, and we can throw the positive charge out onto the oxygen here. This is a very stable system. This is your active electrophile for this electrophilic aromatic substitution. It's your carbonium ion. So here we've got the carbonium ion. And here's our cyclopentadienide-- the carbanion. And this carbanion literally throws its electron density out to that a acylium ion and captures it by the normal steps of electrophilic aromatic substitution. You're just substituting an electrophile for a hydrogen on the ring. And you potentially can make these two products. So what you've got here is you've got-- you either could make the monoacetylated or the diacetylated. Now after you see this mechanism-- let's go back here one more time. Why can't we put more than one of these acyl groups on these rings? Why can we only make the mono and the di as potential products? Yes? AUDIENCE: [INAUDIBLE]. JOHN DOLHUN: Very good. The acyl group is an electron withdrawing. So if you can imagine these groups pulling electrons away from the ring, it's creating all these positive positions here. And the electrophile is positive. So the electrophiles would be repelled away from the other positions. This is a deactivating group here. Great. Now we've got our products, but we'd like to know how many products we've got. Did we make the monoacetylated or the diacetylated? So what we're going to use is we're going to use a technique called thin layer chromatography. How many of you have done thin layer chromatography? Oh wow. Number of you. OK. So what we've got is we've got these little slides. They're almost like microscope slides. They have a nice clear surface on one side. On the other side they have a solid absorbent. And the solid absorbants that we use are alumina-- Al2O3-- and silica gel-- SiO2 times x water. You notice both of these solid absorbants have polar bonds. You've got AlO bonds here. You've got SiO bonds here. What that means is the solid absorbant is going to-- any polar system that you put on this plate is going to stick to that solid absorbent more. We're also going to have a mobile phase. It's going to carry our components by capillary action up the plate. We're going to be spotting this plate with our product. And then we're going to watch the spots move up the plate and separate by partitioning. And what does that mean? In all of these chromatic distributions it's all about the distribution of the solute between the stationary solid absorbent and the mobile phase. And so you can get this distribution constant, which actually should be a constant ideally over a wide range of solute concentrations. Let's say we had a distribution constant that was very high. What would that mean in terms of the spot on the plate? Yes? August? AUDIENCE: It wouldn't move very far because most of the material is the solid [INAUDIBLE] JOHN DOLHUN: Good. It wouldn't move very far on this plate. It would be sitting there attached to that solid absorbent. And if you had a column and you were trying to separate the material, it would move slowly through that column as well. Good. So this is what we're going to do. Going to use a little jar like this to run these TLC plates. Let me just get some board here. So you are going to take a TLC plate. And about 1 centimeter from the bottom you're going to draw a line with a pencil-- a straight line-- so use a ruler because if the line is crooked your spots are going to be going in different directions. We have rulers in the stockroom. And then what you're going to do is you're going to take a spatula tip of your ferrocene and a spatula tip of your diacetyl ferrocene. And you put them into two little scintillation vials. And you go over to the hood. And what you're going to do is you're going to get some dichloromethane. And you're going to put a few drops of dichloromethane into your-- to dissolve your spatula tip. And then you'll use the capillary tube to draw that up. And you'll come back and you'll spot your plate with the smallest spot that you can make and the darkest. One of the spots will be-- at least one will be ferrocene and one will be your acetylated ferrocene mixture. That way you can see if there's any ferrocene still inside of your acetylation product. And then you're going to take tweezers and you'll lower this into the jar. You'll have your solvent in the jar. Put about 2 to 3 mLs of solvent. Don't put more than 2 to 3 mLs. I've seen students put 5, 10, 15 mLs in. It's way too much. And then when this goes down into the jar, the solvent cannot come up and touch your spots or your line. If it does, you've got to start over. So you'll put it in the jar and then you'll kind of just close it. And you'll watch it. You'll watch the solvent move up. And then suddenly it's going to reach up here somewhere. Then you pull it out with your tweezers and you draw another straight line. This is the solvent front. And what we're going to do is we're going to calculate what's known as an Rf value. It's called a retardation factor. And it's a unitless number. You'll measure from the starting line to the spot and then to the center of the spot and the starting line to the solvent front line. You'll divide that. You'll get this number. Ideally, we would like Rf values somewhere between 0.15 and 0.85, which means that we want to get our spots off the starting line but not all the way up to the solvent front line. We have to pick the solvent. Let's start out by picking maybe something non-polar like hexane-- purely non-polar. C6H14. If we pick hexane as our eluent, what do you think is going to happen to the polar component that's sitting on your line there? Who said that? Sean? It's not going to move at all. That's right because it's affixed to that solid absorbent and it's polar. It doesn't like this non-polar solvent. So it's going to sit on the starting line. So this would not be a good choice. How about if we pick something more moderately polar like ethyl acetate. Here's ethyl acetate. So we're going to take this. And now we're going to run the plate with this. What's going to happen to the non-polar component? Think about this. Now you've got ethyl acetate for your eluent. You've got a polar solid absorbent and your non-polar component. What will happen to that? Anyone? Any of the TAs want to chime in on this? Yes, Sean? AUDIENCE: Maybe it's too close to the solvent front? JOHN DOLHUN: Yes. It's going to zoom all the way up to the solvent front. Very good, Sean. That's exactly what's going to happen. So that wouldn't be good, would it? We want something in between. We want to separate them, but don't want them all the way to the solvent front or don't want them off the starting line. So here's what we're going to do. What I want you to do is I want you to try a combination of ethyl acetate and hexane. We'll do like a 1:1 mix. And then do a 4:1 mix. And then try a 1:4 mix. I want you to see which combination gives you the best separation on your plate. And once you do that, then we're going to use that solvent to run the column. TLC is just going to tell us how many components are in our mixture. The column will let us separate them. So we're actually going to fill a column with aluminum oxide and collect our fractions. Here's a typical column. Let's pretend we have ferrocene and acetyl ferrocene in there. One of them is polar. One is non-polar. Which color is the ferrocene? Yes? Jesse? Yes? AUDIENCE: Blue. JOHN DOLHUN: That's you, right? AUDIENCE: The ferrocene would be blue. JOHN DOLHUN: Ferrocene is blue. Good. The non-polar is coming through first because it's not bound to the solid absorbent and it's just flowing right through. And you're a acetyl ferrocene comes after. So what you're going to do is you're going to make a mini column. Here's an example. You're going to fill this with alumina-- about 7 to 8 centimeters of dry alumina. And then you're going to put a little layer of sand on top of it. About 5 millimeters or so of sand. You can see it here-- get an idea what to do. And then you're going to dry load your sample on top of the sand. So how do we dry load our sample? So what you're going to do is you're going to take your acetylated product, take it over to the hood, and you mix in about 50 milligrams of alumina, and then you get our old friend out-- dichloromethane. This is nasty stuff. It causes all kinds of cancers in animals-- laboratory animals-- liver, lungs, everything. So you've got to-- don't breathe this stuff. We're keeping it under the hood. So you add minimal amount of dichloromethane just to get this all wet and a slurry. And then you use a nitrogen line to air dry it to get a nice powdery air dried product. And then you're going to pour your product on top of that top-- the layer of sand there. And then you're going to put another layer of sand on top of your product-- the final layer. And then you're ready to go. What you're going to do is you're going to add your solvent that you picked from TLC that gave you the best separation because we want to separate these components apart so we can collect them. And the thing to remember is when you add your solvent, you're ready to go. Open the stopcock here. Otherwise, nothing is going to flow out. And the other thing I suggest is get a little scintillation vials or use the baby Erlenmeyer flasks and make sure you weigh them and tare them before you do this reaction because you may have so little product it'll be very hard for you to scrape it out to get a weight at the end. But if you weigh the empty vial first, then you can weigh it and get a weight on it and you'll know your mess so you can calculate your yield. Some things that can happen-- if you have bubbles in your column, start over because they're going to distort your bands coming through. If you don't keep the solvent on top of the top layer of sand throughout the whole run-- you have to keep a cushion of solvent flowing-- keep it above that top layer of sand-- your column will dry out. It'll crack and your bands will flow together. It'll make it difficult to separate the different colored bands coming through. The other thing is when you make your column, what I do is tap it a little bit each time you put the sand and alumina in. Make it level so you don't have these kind of irregular surfaces that can cause distortions. So you're going to take your melting point, calculate your percent yields, determine the mass of the components, and that's pretty much all you need to do for that. Now I want to show you what's happening with ferrocene today. This is really something with what's going on. It's been what? How many years? 51-- it's been almost 70 years. Right? OK. Some people have taken the penicilloic acid shell that was synthesized here at MIT by John Sheehan in the 1950s, and they acetylated it with ferrocene making ferrocenyl penicillin. And it actually overcomes some of the resistance that's developed by the penicillin antibiotics that have been around for decades. Another thing-- someone has taken tamoxifen-- breast cancer drug that's been around for decades. It's become resistant to a lot of the breast cancers it's used on. They've taken the phenyl group off here, put ferrocene on, added and OH group, and created hydroxy-ferroccifen, which is also overcoming some of the resistant breast cancer. It's really incredible. This is one of my favorites. What's the most vicious animal on the earth? The mosquito. Exactly. I mean, there are two million deaths by these mosquitoes with malaria every year. Chloroquine has been the source, but it was discovered in the '30s. So a lot of resistance. Right? So what they've done to chloroquine is they've taken the scaffold here and they split it and inserted ferrocene made ferroquine. This is our fairy queen. That's good. Yeah. Ferroquine-- this could be the first organo-metallic antibiotic on the market. Sanofi Aventis has pushed this through stage two clinical trials. I'm not sure where it is now, but I got this most recent paper here. So this looks very promising. Testosterone dihydrotestosterone the nemesis of all men because the prostate gland, it grows and then you get cancer. All men will get cancer if you live long enough. So what they've done is they've made ferrocene derivatives of these hormones that block the receptor site to stop the growth. This is a good one. This is just happening. They took Sedaxane and they removed this group and attached ferrocene and created Sedaxicene. This is an anti-fungal agent. And it's relatively non-toxic. And I mean, you know, these funguses are out of control. They've reached the end of the line on these fungicides that can stop them. So this is a great addition. I'm not sure where this is going to go. And then here is ferrocene attached to a zinc complex. And this rivals the drug cisplatin in terms of these MCF7 breast cancer cells-- knocking them knocking them out. So there's a lot of good stuff happening with ferrocene. And be sure to take a look at the safety on the chemicals here. The TAs will go over this with you. And we'll see you on Thursday for a very important lecture. Probably the most important lecture in the course-- how to write a lab report. It's all about lab reports. And Dr. Sarah Hewett will be giving that. Thank you.
MIT_5310_Laboratory_Chemistry_Fall_2019	11_Catalase_Part_1.txt	[SQUEAKING] [RUSTLING] [CLICKING] SARAH HEWETT: All right. We can probably get started. So good afternoon. And today, we are going to start talking about the final lab that we are going to talk about in the lecture and the final lab that you haven't heard about yet for the course, which is the catalase lab. And some of you guys started that yesterday. And some of you will start it today. And then the rest of you will have to wait a little bit. But the catalase lab is our biochemistry type lab that we were doing in 5.310. And catalase is an enzyme if you couldn't tell by the name. A lot of enzyme names-- you guys are familiar from your biology classes-- end in ase. So catalase is an enzyme. And enzymes are proteins-- just a review of your general bio-- that carry out specific chemical reactions. And they're produced by different living organisms. They work in the cells to do a very wide range of chemistry. And there are many different graphical representations, weird pictures that you can find on the internet that try to depict what an enzyme actually does in cartoon form. And so here are a couple of examples of that. So you have your enzyme and then you have what's called your substrate. And so that is the thing that the enzyme is doing chemistry on. The substrate comes in. It interacts with your enzyme to form an enzyme substrate complex. Then the chemistry happens. And then the enzyme releases the product. So sometimes the products will be rearranging the substrate. Sometimes it will be taking two substrates and joining them together. And sometimes it will be taking one substrate and breaking it apart. So there's a bunch of different reactions that can happen in different enzymes. Similar thing-- if you want to look at your enzyme as a little Pacman kind of guy. You form the enzyme substrate complex. You form your products. And then they break apart. So that's the general idea of how enzymes works in a very quick nutshell. So our specific enzyme is catalase. And here are a couple of pictures of catalase or artist renditions of catalase. So this is a space filling model of what it would look like if all of the atoms were kind of 3D balls. So you can see it has four different subdomains here. And then these darker parts in the middle with the little green dot, those are your heme center, so these are iron molecules and that's where the chemistry happens. So these are the active sites of the catalase. And you can also-- you may have seen in other courses proteins represented like this, which has a little bit more of the features of their secondary and tertiary structure. So you can see the alpha helices and beta sheets. And we're going to talk more about the structure of the active site and how the chemistry happens and what all of those squiggles mean next week when we talk about catalase. AUDIENCE: [INAUDIBLE] SARAH HEWETT: Yes. Or wait. Each sub-domain has one active site. So it has one heme in each of the four parts. And we'll talk more about that next week when we go a little bit deeper into the structure of catalase and how it works. And then the other important thing you need to know about catalase is it's a large molecule. Proteins generally are. There are polypeptides-- lots and lots of amino acids. And so its weight is 240 kilodaltons. And a kilodalton is 1,000 mass units. So it's 240,000 grams per mole. And you'll need that for some calculations that you'll do in the second half of the lab. And we'll go over that again in the next lecture. But to give you an idea of the size of that thing and the molar mass, it is very large. Why do we need catalase? So there are many redox reactions that are happening in your body where you do electron transfer reactions and you oxidize or reduce different things in your metabolism. And so electrons are transferred around cells. You may have heard of the molecule NADPH or NADH. Those transfer electrons between different molecules in your cells and help with metabolism. And while these electrons are being transferred around, you also know that we breathe oxygen and we need oxygen to do-- to perform many of our life processes. So you have a lot of oxygen in your body as well. And during a lot of these metabolic processes you can get electrons that are transferred to oxygen. So if we have our oxygen and it gains an electron, we have what is called superoxide. So now this has a negative charge and an unpaired electron. And so it is a superoxide radical. And what do we know about radicals? AUDIENCE: [INAUDIBLE] SARAH HEWETT: They would like to be stable. So they are not stable because they have this unpaired electrons. So they will either give up this electron or try to take an electron from something else in order to have their electron be-- or not be unpaired anymore. So these are very reactive in the body. And this is actually a problem. And we don't want this in our cells because it is so reactive. So there is another enzyme called superoxide dismutase that breaks this apart into elemental oxygen and oddly enough hydrogen peroxide. But it turns out that hydrogen peroxide in high enough concentrations is also toxic to your cells. And hydrogen peroxide can form hydroxy radicals, which are also very damaging to your cells. There's a couple of reactions that hydrogen peroxide can do in the body. So the first is if you have hydrogen peroxide and then you have some of this superoxide around-- so it's a radical anion there. You can make oxygen, hydroxide ions, which are OK, and then hydroxy radicals. So then you form more radicals and those can go and damage your DNA, your proteins, the different fatty acids in your body, and cause all kinds of problems. Another thing that can happen is if there's just hydrogen peroxide around and it picks up an electron, it can form water and another hydroxyl radical. So these are the reactions that we do not want to happen in our body because it forms these-- it just keeps propagating. And then when radicals react with other things that have all paired electrons, it generates more radicals and you propagate the radical formation throughout your cell it causes a lot of damage. So we need a way to get rid of the hydrogen peroxide in our body and that is what catalase is for. And all organisms have catalase. You can extract it out of humans, all types of mammals, even plants have it. Cells do not want hydrogen peroxide in them. So there are different forms of catalase that you can get from any organism-- bacteria, all the things. The catalase that we're going to be using in the lab was extracted from cows. So just a fun fact. And when we're talking about enzymes, the reason that enzymes are so good and so efficient at their jobs is because they catalyze chemical reactions. And a lot of you are chemical engineers, so you probably know about catalysis. So what does it mean for something to be a catalyst? Anyone? Please give me a quick catalyst definition. AUDIENCE: [INAUDIBLE] reaction. SARAH HEWETT: Yeah. It speeds up a chemical reaction. And it's not used up during the process. So if we look at our energy reaction diagram, if you have energy on this side and then reaction progress on this axis, you can say that you have reactants that are starting at a certain energy level. And then you have some energy that you have to put into the reaction to get it to go. And then in a lot of cases, if your reaction is exothermic, your products maybe at a lower energy level. So it'll release energy overall. But in order to get the reaction to go you have to put energy in. So this part of the curve is our delta H of our reaction. So it would be the energy released if it's exothermic, which in this case this reaction is. But no matter what you need to put in some energy to get the reaction to go and this is called the activation energy. Occasionally abbreviated E sub a. So this is what we care about when we're talking about reaction kinetics and what a catalyst does. So a catalyst functions and it makes the reaction faster by lowering this energy barrier. So if the yellow line is the reaction without a catalyst, then with a catalyst it will be smaller. And the products and the reactants will have the same total energy, but the energy you need to put in to get the reaction to go is going to be less. And so the reaction can go faster and it can go in milder conditions. And we can talk about how enzymes work to lower this activation energy. So does anybody know what methods enzymes use to lower the activation energy of a reaction? Yes? AUDIENCE: Proximity? Just getting the reactants together? SARAH HEWETT: Yeah. Proximity. So it gets the reactants close together. If you have your reactants in a beaker and they're all floating around, they have to find each other before they can react. And so if you have an enzyme that has a specifically designed active site to hold these two molecules close together, then they will react. What else? AUDIENCE: It can stabilize a transition state? SARAH HEWETT: Yeah. It can stabilize a transition state. And how does it do that? AUDIENCE: [INAUDIBLE] SARAH HEWETT: Yeah. So it bonds to the substrate and it can have either electrostatic or even sometimes covalent interactions. And it stabilizes the transition state. And part of the way that it does that is it holds the molecules in the right orientation for them to react. So even if you have two molecules, if they're supposed to interact like this to react and they're in a beaker and they hit on this side or upside down, the reaction will not happen. So we can stabilize transition states. Your transition state and put molecules in the correct orientation. Anything else? There is one more thing that they can do. OK. What's your idea? AUDIENCE: If they raise the temperature, it will increase-- collisions could increase. SARAH HEWETT: So increasing the temperature of a reaction will get it to go faster. Right? But that's just because then you will have more molecules that have the necessary activation energy. So you're not necessarily lowering the activation energy that the reaction needs. But the last thing that they can do is they can provide alternate reaction pathways. So sometimes you may think that this will just be a one-step reaction. If you had an enzyme, occasionally it'll look like this. It might provide an extra intermediate in there that helps to lower the overall energy. And so that's another way that it can lower this overall activation energy is by providing an alternate mechanism other than maybe just two molecules reacting together. There might be a third intermediate that helps actually lower the overall energy. So those are possible ways that the enzymes can work to lower the activation energy. And so our goals for the catalase lab are-- well, there are a few goals that we have. But our goals for days one and two are to determine the activation energy of hydrogen-- the decomposition of hydrogen peroxide as catalyzed by the catalase enzyme. So we're going to try and figure out what the activation energy is after it's already been catalyzed. And in order to do this, we are going to need to first determine the order of the reaction with respect to hydrogen peroxide and be able to write a rate law. That'll help us characterize the kinetics. So in day one of this lab, you're going to do that first part. And you're going to figure out what the order of the reaction is. And in order to have that make any sense we need to talk about kinetics and how we discuss kinetics in a chemical sense. So kinetics deals with the speed of chemical reactions. And if we use everybody's favorite generic reaction a plus b goes to c plus d. You can write the rate of this reaction-- you can express it in a number of ways. So the first way is to think of the rate of the reaction as the change in the reactants over time-- so a and b. And it has a negative sign because you are losing the reactants. Hopefully they're going away as the reaction progresses. And it is equal to the rate of the appearance of c and the appearance of d. So these do not have negative signs because you are making your product. So that is one way to express the rate of the reaction. And when you do it this way, you need to account for the fact that there are different molar ratios. So the reactants and the products will disappear in form at different rates depending on how many of them you need in the reaction. So to account for that, we multiply by the reciprocal of this coefficient. We can also write a generic rate law like this where your rate equals your rate constant, which you can calculate and determine in lab and is dependent on the temperature times the concentration of your reactants raised to a power and your concentration of your other reactants raised to a different power. And you can also write an integrated rate law, which you may have seen before. So integrated rate laws deal with one reactant at a time. And so if we look at a, we can say-- we can write-- if there's only a we can write the rate of a equals the rate constant times a. Or we can say that the rate is equal to the disappearance of a overtime. And you can take the derivative of this. So if we move everything over, rearrange it-- So if we integrate both sides of this-- if we integrate this side from your initial concentration to your concentration at some temperature and this side from t equals 0 to some time t, then if you do that math out you will get the natural log of-- this is your integrated rate law if your exponent here equals 1. So obviously, that will change if you have different exponents here. And then when you do your integration you will get different values. But this is a way to relate the concentration at your initial concentration to a concentration at a final temperature or a final time. So that's one thing that you've probably seen before in some of your other chemistry classes. And we can also talk about-- well, we'll talk about that in a second. You may also have seen in some of your other classes enzyme kinetics or heard of Michaelis-Menten kinetics. And the Michaelis-Menten model of enzyme kinetics says that if you have an enzyme and you have a bunch of substrate, the reaction can only go as fast as there is when there's only one substrate in each enzyme. So if all of the active sites are full of substrate, then that is as fast as the reaction can go. And it will proceed at a steady state. So you can make graphs of the reaction rate versus how much concentration of substrate you have. And you can get this Michaelis-Menten constant here, which is a measure of how much the enzyme-- what its affinity is for the substrate essentially. So does the enzyme need a whole bunch of substrate before it'll start going quickly? Or can it go quickly and efficiently with just a tiny concentration of substrate? So we're not going to worry so much about those parameters for our lab right now. But this is something you may have seen. And one of the assumptions of the Michaelis-Menten kinetics, which is actually kind of important to us is that you have your enzyme and your substrate. They make the enzyme substrate complex. And then they go to enzyme and product. And they don't go in the reverse reaction. So that's kind of important to us that if we are trying to measure the rates of our reactions, that we don't have to contend with the reactions being catalyzed in reverse. All right. So now we can take a little bit of a closer look at the rate law for just a normal chemical reaction. And pretty much the most important thing you want to know about this is that the units of the rate are always moles per liter per second. So whenever you are trying to calculate a rate constant, you want your units to line up. So if your rate-- if we want this in molarity per second-- if your rate equals-- let's say these are both equal to 1 just for now. Then what are our units over here? M and M. So what are the units of k have to be? So that's how you can figure out what the units of your rate constant are because it always needs to multiply with your concentrations and your k to equal moles per liter per second. And that is going to be the units of our rate that we care about in our kinetic equations. The rate constant is different at different temperatures. So if you change the temperature of the reaction, then your rate constant will change and you'll have to remeasure that. And x and y are values that need to be determined. They may be the same as little a and little b but not always. So the kinetics of a reaction are determined if it's a multi-step reaction if their reaction mechanism has more than one part in it. They may not all be reflected in this overall chemical equation. You may not see them, but the rate is going to be dependent on your slowest step. And that slowest step is what is going to determine your rate law. And it may not always match your overall reaction equation. So be careful when you are determining these things. You can't always just assume that it is from the little a and little b. So how are we going to determine the order for our reaction? And this is what are going to do on day one. We will use our rate law expression to determine the order of the reaction. So you're going to-- according to our rate law here. It's the only reactant that we have in this case is hydrogen peroxide, and we need to determine what its order is. So if we change the concentration of the peroxide, we should change the rate, yes? So if we do a bunch of reactions with a bunch of different concentrations of peroxide, we can measure the rates, and then use the relationship between those two things to figure out our concentration of-- or our order of the reaction. So the way that you're going to do this in lab is you will have a series of solutions, and these are your solutions. You'll have a stock hydrogen peroxide solution that you're going to make up. It's going to be about 4% hydrogen peroxide. You'll use a phosphate buffer. Why do we need to use a buffer for this reaction? What's a buffer, I guess is the first question? AUDIENCE: It helps the solution from changing PH2. SARAH HEWETT: Perfect. So a buffer helps the solution, it prevents a solution from changing PH. So you can make a buffer out of certain PH, and then if acid or base gets added to it, it resists the change in PH. It keeps the constant. Why is that important for our reaction? AUDIENCE: Maybe [INAUDIBLE]. SARAH HEWETT: Yeah. So enzymes are most functional at a set PH. So your PH of your body is around 7, so we want to keep the PH of our reaction somewhere around our physiological PH, so our buffer is going to be set to PH 6.8, which is going to help make sure that the enzyme is in its active state. It is not denatured. If you change the PH too much, you'll change the protonation state of the different parts of the protein, and it can fall apart. So we want to make sure that this is happening at the correct PH. We'll add some enzyme, and then we will measure the rate of the reaction. And we're going to do that using this apparatus right here. So you'll have one of these. You'll have a water bath, so that we can keep the temperature constant. So you'll just fill this with room temperature water, and then you can monitor the temperature throughout your reaction to make sure that it does not change. And then this is your reaction vessel here, your pressure tube, because you will be putting all of your solutions in here. You will add your peroxide and your buffer, and then you will put this cap on. And this Teflon cap here, it's important to note, has an O-ring on the bottom. And so you want to make sure when you're doing this reaction that you're O-ring is in there, because that'll make a good seal, so you won't have your products escaping because our product is a gas. So you'll screw this on. And then there's a hole in the top here. You can inject your enzyme really fast. You're going be doing this in partners. Somebody can inject the enzyme really fast. And then you want to connect your pressure tube. And this tube is connected to a pressure sensor. And this pressure sensor will be connected to your computer, which is why you need to bring a laptop for the catalase lab. And we will give you the Logger Pro software. And it will send the data directly to your laptop. And it'll plot it for you. And you'll get a curve that, hopefully, looks something like this. And we will measure the pressure of oxygen formed in kilopascals versus time in seconds. And it'll graph this thing for you. And the slope of the graph is going to be your rate of kilopascals per second. And we want to take the rate at this first part of the graph where it is linear, and why do we want to take the rate at the beginning of our reaction? Yes. AUDIENCE: Reaction rate is dependent on amount of reactants? SARAH HEWETT: Yeah. So the reaction rate is dependent on the amount of reactants, and the-- so the rate of this reaction obviously changes over time, and we set up our reactions so that we know the concentration of peroxide. And the only time in this reaction that we're theoretically going to know the concentration of peroxide is at the beginning, before some of it has reacted and the rate changes. So we want to measure the initial rate so that we know our concentration, and that we get a-- we have a consistent place to take our data from on each measurement. So once we have done all of these different reactions-- you'll do all four of them-- all of the same procedure in the same tube-- you'll make five different graphs. You'll have this. Then how do we analyze this data and get information about the order out of it? So here we are going to have to do a little bit of math. So here are some of the steps of the data analysis. The first thing that you're going to have to do is calculate the concentration of the peroxide that you used. And we are going to give you 30% hydrogen peroxide, which is-- its volume per volume-- so there's 30 milliliters of H2O2, and 70 millimeters of water. So if you remember that your molarity is your moles of your solute over the total volume of the solution, you can turn this milliliters, assuming a density of about 1, into grams, grams to moles, and you can calculate the molarity of this solution. You're then going to take this 30% hydrogen peroxide that we give you, and dilute it 13.3 milliliters to 100 milliliters. So then you can do another dilution equation to figure out your final concentration of your hydrogen peroxide that you're going to be using in the lab. So that's a first step. And then I'm going to kind of rearrange a couple of these other steps, just because it'll make this a little bit easier to go through. But the first thing that we're going to do is the easy part, which is get your rate of oxygen formation in kilopascals per second. And that we're just going to read straight from the slope of the graph. So that's pretty easy. So we'll have our rate of oxygen formation in kilopascals per second. Great. So now we want to take a look at our rate law. And we have our rate of oxygen formation, but what's in our rate law? Hydrogen peroxide. So we need to find a way to go from oxygen and kilopascals per second to moles per liter per second of hydrogen peroxide. So the first way that we're going to do that is to go from kilopascals per second here to molarity of oxygen. And we can do that using our gas constant here. So if you divide by the gas constant, multiply by 1 over 8.314 moles, liters times kilopascals, we can cancel out our kilopascals. And we'll have moles per liter, which is good, but then we still have this K, which is our temperature in Kelvin, so we also have to divide by our temperature in Kelvin. And this will get us our rate of oxygen in moles per liter per second, which is pretty good. We're close. But we still need to get from oxygen to hydrogen peroxide. So how can we get from oxygen to hydrogen peroxide using this information? AUDIENCE: [INAUDIBLE] SARAH HEWETT: It would be-- so the ratio is 2:1, right. So there's two hydrogen peroxides in this reaction for every one oxygen. But these coefficients are in moles. And this is in moles per liter. So we need to figure out how many moles of oxygen we have before we can use our stoichiometry ratio here. So how are we going to figure out how many moles of oxygen we have? We need to know what our volume of oxygen was. And for that we can go to our pressure tube. So you'll have some of this is going to be your solution down here, so that'll be liquid. And then we need to calculate the volume of the gas above our reaction, which is where oxygen is going to be formed. So we'll need to know the volume of this, and the volume of the pressure tube. And the volume of the pressure tube has already been measured, and we'll give that to you. And you guys are going to measure in the lab what the volume of your reaction vessel is. You're going to fill this thing with water, weigh it, then weigh it empty, and then you can calculate by difference in the density of water what your volume of your whole tube is. And then you know your reaction volume is 25 milliliters, so you can subtract those and get the volume of the gas. So if we know these two together, you'll get the volume of the gas above your reaction. So if we have our rate of oxygen formation in moles per liter per second, we can multiply that by our volume that we calculate, so liters of oxygen. And then we have our rate in moles of oxygen per second. And now we can use our stoichiometry, because we have it in moles, so we can take our rate in moles per second, and then we know that it is 1 mole of oxygen for 2 moles H2O2. Then we get our rate H2O2 in moles per second. And what are the units of rate that we want? Moles per liter per second. So we have it in miles per second. We're so close. Then we just need to divide by the liters of our reaction, which if you go back a couple of slides, is 25 milliliters, so all of our reaction volumes are 25 milliliters. So if you convert that to liters, divide by 0.25 liters, and then we will have our rate in moles per liter per second, which is what we want. Now this still doesn't get us to a, but we can rearrange this equation by taking the natural log of both sides. So if you have the natural log of the rate equals the natural log of K plus, then the A comes down, a times the natural log of your hydrogen peroxide concentration, then-- we've just figured this out from all of that math. We know this concentration. And this is going to be our y-intercept. So if we have y equals b plus mx, if we make a graph of the hydrogen-- or the natural log of the peroxide concentration and the natural log of the rate, then our slope is going to be our order. Hopefully, we haven't lost you. So the way that you're going to treat all this data is you can, instead of having to do this calculation out for every single trial, you can make a giant spreadsheet. And in the lab manual, it tells you what data we want you to collect. And this is all of it here. And then you can make a spreadsheet that does all of the calculations for you, that gets you down to the natural log of rate, and the natural log of hydrogen peroxide. So this is an example of a pretty good way to present your data. And I know it's kind of hard to see on the printed out slides, but these will be on Stellar if you want to look at them. And then your graph will look something like this. And you'll have a straight line. And so from that straight line, you can figure out what your order of your reaction is based on your slope. So that was a lot. So once we have that done on day one, then, if you remember our second goal for the lab, it was to figure out the activation energy of the reaction. And so the way that we're going to do that is to use the Arrhenius equation, and that says that the rate constant is equal to A, which is this collision frequency factor, times e to the negative activation energy over RT. And if we remember the things that can change the rate, we can change the concentration and that'll affect the rate, and also the temperature. So if we do our reaction at different temperatures, then we can determine our activation energy. So what you're going to do is you're going to pick one of the trials from day one. Usually people pick the middle one because this is easy. It's just 1 milliliter, no decimals. Just easy to measure and it's right in the middle. You'll pick one and you'll hold the concentration of peroxide constant, and then we will vary the temperature. So you'll do seven runs at varying temperatures. So you'll pick a temperature in each of these ranges and you will measure the rate. Again, you'll get the same graph, the measure the rate of oxygen per second. And then you can do all of this same math to get your information in concentration of peroxide to go from oxygen to peroxide, because that's what we care about. The keys to success for this reaction are to wait for the peroxide and the buffer to reach the correct temperature before you add the enzyme. So when you have your reaction here in this tube, you'll put it in your water bath and then you want to give it a few minutes to stir and come to equilibrium at the right temperature, because it'll all be at room temperature. And then if you're trying to do your reaction at 0 degrees or 5 degrees, your reaction part won't actually be at 5 degrees even if your water bath is. So give it a few minutes to equilibrate before you take your measurements and before you inject your enzyme. Another key to success is to start at the hottest temperature and then add ice to cool it. It's easier to control the cooling than it is to control the heating with these hot plates. The hot plates tend to get really excited and then they'll heat your solution up way above what it needs to, and then it won't be able to cool. So if you start at your hottest temperature and then add ice, you'll be able to slowly lower the temperature and do it in a more controlled fashion. The other important thing about this reaction for day one and two, and I'm sure your TAs will emphasize this when they tell you in lab and you guys have a chance to have this in front of you, is to do everything really quickly. So the reaction starts as soon as you add the enzyme. So you'll have your micropipette, you'll stick it right in that hole, add the enzyme really fast, and then you want to attach your pressure tube and then hit go on your computer to start collecting the data. And that all has to happen in like, a second so that you don't miss that beginning of your data collection. So those are some important things. If we talk about the data analysis for this reaction, it's kind of similar to the other one. So you'll calculate the concentration of peroxide, you'll calculate the volume of air above your reaction. You'll have the initial rate of oxygen formation in kilopascals per second. Then you can get the initial rate of oxygen formation in molarity per second and moles per second. Then you can change your rate of oxygen formation to the rate of peroxide decomposition, same math. And then using the rate law that you determined on day one, you're going to calculate the rate constant. So if we have our rate, our general rate law, we'll measure this in the lab or we'll calculate this, I guess. We will know this from day one. So you'll plug in the value that you get from your first set of calculations right there. And then we measure this in the lab or we can calculate/measure this. So we can calculate our rate constant, which is, if you just rearrange this, it'll be k-- so that's not so bad. And then in order to get our activation energy out of this, we are again going to take the natural log of both sides. I think that I did that out correctly. No plus sign here. All right, so this is your linear form of this equation. So we have, again, y equals b m and x. So if we do our reaction at different temperatures, then we will know the temperature of our reaction. And then we will get k from our rate constant from our rate law, and you'll calculate that for each of your trials, as well, based on the rate. And then our slope is going to be the activation energy over the ideal gas constant. So we can get the activation energy from the slope of a graph of 1 over t times the natural log of k versus the natural log of k. And then you can also get your collision frequency factor, this A term, from your y-intercept, so you'll also be able to determine that. Then you'll use your Linus program to get the errors in all of these things, and that is essentially day one and day two of the lab. Do you guys have any questions about that? There's a lot of math. So again, there's another data chart that you can make for day two of the lab that has all of the information that you're going to need for these calculations. And then this is hopefully what your graph will look like. It should be linear with a negative slope, and then the negative will get taken care of with that negative sign in the equation. AUDIENCE: This will be posted on Stellar? SARAH HEWETT: Yes. Yeah, all of the slides will be posted on Stellar so you can see it in a larger form, because I know they didn't print out super well. OK. So now we can take a look at the reaction that you're going to do in a slightly different form. And you may have seen this before, but we're going to do it anyway. So hydrogen peroxide, you may have some at your house. They sell it in a drugstore. It's like, 3% so it's not as concentrated as the stuff that we're going to be using in the lab. But nonetheless, hydrogen peroxide is a thing that you can buy. And it naturally decomposes over time, so this reaction is always happening. If you have a bottle of hydrogen peroxide, usually the caps are vented because if you seal it for too long, you'll build up pressure of oxygen and that's a problem. The stuff that we have in the lab is 30%, so that's definitely vented, and we store it in the refrigerator so that we slow down the reaction and keep our product for longer. So it is always happening and you can speed it up in a number of ways. So one of the ways is obviously using enzymes, catalase. That'll speed up the reaction. But there are other catalysts that you can use, as well. So have you guys seen the elephant toothpaste reaction before? Yes. Do you guys know what the catalyst is that we use for this? There's a few you can use, but does anyone remember? So we're going to react hydrogen peroxide with potassium iodide in this case. And you can use a couple different ones, like manganese dioxide, I believe, works. You can use different iodide salts, but potassium iodide is the one that I have today. And we're going to do a little bit of an experiment. So we said that concentration effects rate, right? So we will try our first reaction with some hydrogen peroxide. And I'm going to pour out about 10 milliliters of this and then dilute it so that our new concentration is about 7%. Yeah, that's right. So pour that in there. And then we want to use a potassium iodide solution. So we can pour some of this in here. And then we have the oxygen bubbles, and who did the catalase reaction yesterday in lab? Anybody who's here? So what did you guys see when you added the enzyme to your peroxide in the tube? Bubbles, good. But it didn't foam up, right? Because they just popped and formed oxygen. So the way that we can get this to foam is by adding some soap. This is just powdered soap. And we can add a couple of scoops of that. And now hopefully, if all goes well, when I add these together, we will see the decomposition of hydrogen peroxide. I can probably hold it up so you can see what's happening. So what's happening in there? It's bubbling, good. Excellent. So what are the bubbles? Oxygen. All right, so it's taking its time. So while that is going, we can set up another one. And this time, we won't dilute the hydrogen peroxide, so we'll just use 40 milliliters of hydrogen peroxide. Need our soap. Yeah. Yeah, so it looks like toothpaste maybe. Toothpaste that an elephant would use, yeah. What? Elephant toothpaste. Yeah. I also, in the course of doing some research for this, found that some people call it old foamy, like a guyser. So you may have heard it by that name. All right, and then we add the same amount of potassium iodide. Hopefully I measured this out properly. So if that was 7% hydrogen peroxide, what do we think is going to happen if we use 30%? Faster. Let's find out. So can you see the steam coming off of it? Yeah, so what does that mean about the reaction? It's exothermic. Yeah, it's very hot. If you were to come up here and touch this, it is quite warm. But yeah, so that went faster, right? So we can do a little bit of math about how much faster the potassium iodide makes the reaction go than just what would happen in your bottle at home. And so our activation energy of hydrogen peroxide decomposition that is uncatalyzed, just happens in nature, is 75 kilojoules per mole. So if we use our Arrhenius equation, then we can plug in 75 kilojoules or 75,000 joules to match our or gas constant units. And then the activation energy of the decomposition as catalyzed by potassium iodide is about 56 kilojoules per mole, so it lowers it, makes the reaction go faster. If you do this math out-- I don't want to get my numbers wrong here-- it is about 2,500 times faster or 2,400 times faster than what would happen in nature. Now, if we talk about catalase, and you guys will calculate the actual activation energy of the catalase-catalyzed reaction, I will start and tell you that it is less than 10 kilojoules per mole. So that is a pretty significant change, right? Going from 75 kilojoules per mole down to 10 or less. That's a lot. So if you do this math out, where you go from 75,000 joules to 10,000 joules, does anyone have any guesses as to how much faster the catalase is than just normal decomposition? A lot. So that's a lot faster. So you can be thinking about that when you are thinking about what happens in the cells of your body because you are forming these superoxide radicals and hydrogen peroxide all the time in your cells. And this reaction is happening on this scale, or the reaction that you just saw is happening this many times faster in your body, and you will see it happen also in your flask. So any questions, thoughts? No? All right, well, thank you guys. You can head to lab.
MIT_5310_Laboratory_Chemistry_Fall_2019	Elephant_Toothpaste_Reaction.txt	PROFESSOR: So have you guys seen the elephant toothpaste reaction before? So we're going to react hydrogen peroxide with potassium iodide, in this case, and I'm going to pour out about 10 milliliters of this and then dilute it so that our new concentration is about 7%. So what's happening in there? It's bubbling. All right, so it's taking its time. So while that is going, we can set up another one. We said that concentration effects rate, right? So if that was 7% hydrogen peroxide, what do we think is going to happen if we use 30%? Let's find out. [AUDIENCE EXCLAIMING] AUDIENCE: Whoa. PROFESSOR: So hydrogen peroxide naturally decomposes over time, so this reaction is always happening. So you can be thinking about that when you are thinking about what happens in the cells of your body, because you are forming these superoxide radicals and hydrogen peroxide all the time in your cells. And the reaction that you just saw is happening this many times faster in the cells of your body.
MIT_5310_Laboratory_Chemistry_Fall_2019	6_Ellen_Swallow_Richards_Part_2.txt	[SQUEAKING] [RUSTLING] [CLICKING] JOHN DOLHUN: Good afternoon, everyone. Welcome to The Ellen Swallow Richards lab part two. There is-- the room will be a little bit more sparsely populated today. I wonder why. Lab reports are due, right? So we're going to get started. And I'm going to start off by talking about probably the most important parameter in measuring the health of the river, and that's the dissolved oxygen. So when we look at the dissolved oxygen concentrations out there, for a river to really be healthy, we're looking for something greater than probably about 8 PPM. If the concentrations fall down to 5 or less, then you'll start to see the fish move around erratically, because they're trying to get their oxygen. So less than or equal to 5, and we have some stress placed on the aquatic life. If the dissolved oxygen concentration goes below 2, even for an hour or two, you're going to have fish kills. So let's take a moment to actually see how this oxygen gets into the water, and this is the big picture. So if you look at this, you've got two processes going on. You've got the oxygen coming in from the atmosphere, and it's diffusing into the water system. You also have down below, you've got aerobic biodegradation taking place. So we've got oxygen diffusing into the water, and then we've got aerobic biodegradation. These are the two main processes that are taking place, and both of these processes are going-- they have different kinetics, yet they're coupled together, coupled in the sense that if aerobic biodegradation uses up the oxygen, more oxygen will start to dissolve in. There's a transfer driving force that actually lets more oxygen dissolve into the water. The rate at which oxygen is dissolving is actually proportional to the deficit of oxygen that's in the river. And that deficit is equal to the equilibrium level that we would expect minus the actual level that we actually find. So the amounts of oxygen that we're talking about are very tiny. And there was a brilliant chemist by the name of William Henry, who actually, back in 1803, came out with Henry's Law. And what Henry's Law says is very simple. The solubility of a dissolved gas in a body of water is proportional to the partial pressure of that gas over the water. There's even a Henry's Law constant here, and there are tables of these. There are thousands of them. For every solvent, for every gas, for every temperature combination that you can think of, there is a Henry Law constant that you can plug in. Let's think about, what is the partial pressure of oxygen on any given day? How do we calculate that? Yes, yeah. Alec. AUDIENCE: So if you have total pressure, and then you know the makeup of the atmosphere. You can just break it down. So say your pressure is 1 atmosphere and you have 20% oxygen in the at-- that's not right. But 20% oxygen in the atmosphere, your oxygen would be contributing 0.20 atmospheres to the pressure [INAUDIBLE]. JOHN DOLHUN: Very good. Very good, Alec. So Alec said that you've got 20.9% oxygen in the atmosphere. So we can convert that to a decimal. Partial pressure of oxygen on any given day would be the percent of oxygen that's in the atmosphere times the atmospheric pressure on that particular day minus the pressure of the water vapor that we're talking about. So that gives us a handle on this. I want to show you probably the simplest example of Henry's Law. I brought a bottle of Coke here, and these are hard, right, because they pack them-- there's a head of carbon dioxide gas over the liquid. Now when I open this, I'm going to release the gas, so the partial pressure of CO2 over this liquid is gone. We should start to see bubbles coming out of the solution, right? [HISSING] Oh good, it's not an explosive one, so that's good. So there are the bubbles of the dissolved carbon dioxide gas starting to come out. And that's a simple example of Henry's Law. Can anybody think of a more complex example? Anybody a diver here? Kelly, you're a diver? AUDIENCE: Oh, no, I'm just [INAUDIBLE].. JOHN DOLHUN: OK. When you-- AUDIENCE: Yeah. It's like the bends, right? Because as you go down further, the pressure increases so that more nitrogen can dissolve in your blood, you said? JOHN DOLHUN: Yeah, very good. Yeah, so you've got gases in your blood. And when you go down, when you're diving down under a great pressure, when you start your ascent, all of those gas bubbles are going to come out. And they have to go somewhere. They could migrate anywhere in your body, and it could cause a rash. It could cause some type of joint pain. You could end up with paralysis, even death. So divers have to really, really time their ascent. That there's a name for that. Kelly said the bends. That's one of the names. It's also called DCS, Decompression Sickness. That's a great example of Henry's Law. What about if we think about temperature and dissolved oxygen? Let's actually take a look at that. Here is a graph of oxygen concentration and temperature. What stands out to you here? Sean? AUDIENCE: It decreases exponentially with temperature. JOHN DOLHUN: Yeah, as the water is warming up, look what's happening to the dissolved oxygen. Why do you think that's happening? And why, when the water is cold, can we hold so much oxygen in that cold water? Kelly. AUDIENCE: Is it because, as the temperature increases, the average kinetic energy of the molecules increases, and the distribution broadens, so more oxygen has the ability to escape? JOHN DOLHUN: Good, good. As the temperature increases, the kinetic energy of the water molecules is increasing, and they're starting-- think about when you boil water. Bam, they're bubbling out. That hydrogen bonding network is gone. All those intermolecular forces of attraction are gone. Now think about this side when the water gets really cold and you form this hydrogen bonding network. I mean, it expands, right? Pipes break. That's why our pipes break. It's because of the hydrogen bonding in the ice crystals when they expand out. But look at the crevices here in these things. So the oxygen molecules can swim in and out of those, and they can become weakly trapped and pinned in. And there you've got a dramatic increase in the amount of oxygen that can dissolve in the colder waters. The other thing to keep in mind about the water is the heat capacity of water is much greater than the heat capacity of air. It takes a lot more energy to change the temperature of water. I mean, you can-- I've gone out when it's 85 degrees, and I want to go for a swim across from my house. And I jump in, and it's only 67 in there. So the water hasn't caught up to the temperature of the air. Now there are a lot of different equations out there that actually would let us calculate the potential of a body of water to hold oxygen, theoretically, how much could be out there on a given day. And the more complex the equation, the better the results. I found a couple empirical, simple equations that give really good results, so I'm going to go with these. And they're all based on altitude and temperature. If you look at the equation, it's all about the atmospheric pressure, the water vapor pressure, and the temperature of the water, which is in Celsius. So if we look at that equation, if the pressure, the atmospheric pressure goes up, right, what happens to the dissolved oxygen concentration? If you're trying to calculate the saturated level of dissolved oxygen, and the pressure goes up, the atmospheric pressure, what happens to the DO concentration? I promise this is not a trick question. This is-- Alec. AUDIENCE: It increases. JOHN DOLHUN: It absolutely increases. Yeah. Now what happens if we have a high water vapor pressure that day? You might be on a mountaintop stream. Water vapor pressure is very high. What happens to the DO? Someone? AUDIENCE: Decreases. JOHN DOLHUN: Sam, decreases. Good. And the other situation, which if the river temperature is high, then it's intuitive, right? Your DO is going to be smaller. So that's how you use those equations. And then what you can do with the equation is you can calculate a thing called the percent saturation level, which is the actual DO that you get in the lab divided by the potential of water to hold oxygen based on the temperature and pressure above. And that saturated level is going to tell us a lot about the condition of the water. Usually-- I mean, you could have from 90% to 110%, something like that. That's normal. If you get to 120% or greater, that's a problem, because there are different diseases that the fish can-- they have an oxygen bubble disease fish can get if it becomes too saturated. So this is something that you'll do these calculations, and the TAs will carry a pH meter. They'll record the air temperature, the atmospheric pressure, the river water temperature each day you go down, and they'll put that on the whiteboard. Here is some simple data that will allow you to interpolate the water vapor pressures based on temperatures. And you can go in between these, and you'll get very good results. If you can't find it on here, you could use this equation. But the T here is the temperature of air, and it's in Kelvin. And back here, this is the temperature of the river in Celsius. So don't get confused with that. And now I'd like to spend a few minutes talking about the actual method that we're going to use in this lab. This method was actually discovered by a graduate student by the name of Winkler back in 1888. And the method has withstood time. What he did is he developed this series of oxidation reduction equations to actually measure the dissolved oxygen concentration in saltwater. And he came up with this series of equations. And it's been 130 years, and this is still here. Today they have the fancy dissolved oxygen meters, which we're not using, but you can just drop it in and get your DO. They used this method to calibrate those meters today. So you're using-- you're going to be doing the real chemistry here. The whole method is based on that if you've got oxygen in the water, iodide is going to get oxidized to iodine, and you're going to be able to titrate the iodine with sodium thiosulfate. So let's just go through the method just a little bit here. So we start with manganese sulfate, and we form a white precipitate. But if oxygen is present in the water, oxygen is an oxidizing agent here. It's going to oxidize this manganese hydroxide to this tetravalent manganic species. So you've got manganese over here, which is a plus 2, and over here, you've got a plus 4. There are a couple-- in the literature, there's some argument about this. Some people feel the species is a trivalent, and they're saying it's MnOH3. So on this side, you'd have a trivalent manganese species. Other people are saying no, it's MnO2. It's a hydrated form of mnO2. It's tetravalent. What I've done is I've combined both these to give you this manganic species here, which works. This is tetravalent. So notice that when you've formed this, this is like a brown flock. You've captured the oxygen at this point. Now you've got to dissolve that, so we add sulfuric acid to dissolve that brown precipitate. And then there's iodide in there. So this oxidized manganese will oxidize iodide to iodine. We can then detect it with sodium thiosulfate, and the iodine gets reduced back down to iodide. If you look at this, for every oxygen, every one oxygen, you make to manganic species. Each manganic species gives you one I2, and each I2 requires two thiosulfate. So that's a 4 to 1 ratio, thiosulfate to oxygen. So let's take a look at your first day, which is the standardization of the thiosulfate. We have to know exactly what the concentration of that is when we titrate the river water to actually get-- to home in on the exact concentration. So we're going to be using a primary standard, potassium biiodate. Does anybody know what the qualities of a primary standard are? When you pick a primary standard, it's pretty important. You want something that has certain properties. Anybody ever worked with a primary standard? No? OK, well, first thing, notice how big this is. It has a very high formula weight. So that's actually a good thing. Not all primary standards have that. When you mass it out, you're going to have less error on the balance because of the mass of this thing. Also, it has to be something that's pure. And this is like 99.9% pure. The other thing is you need something that does not have any water vapor attached, no attached water. The TAs put this in the oven. So no hydrated water. And then the final thing is, you want-- it should be stable at room temperature and when heated. And oftentimes we'll look at the cost, too. That's another factor that comes into play. But what you're going to do is you're going to weigh out 0.0818 grams of this. And if you divide by the molecular weight of that, you'll get moles. And you're going to make a 100-mil solution. So divide that by 0.1 liters, and you'll get your concentration. You're actually making up something like a 0.0021 molar solution of that standard. And then you're going to use that to standardize your thiosulfate. We're also going to be using starch in this reaction. So why do you think we need to use starch when we're titrating something? Alec. AUDIENCE: Starch reacts with iodide, and it creates the blue color so that when we react-- when we were titrating, it could turn really pale. JOHN DOLHUN: OK. AUDIENCE: So it was really hard to tell if it was clear or not. So I think the starch helps indicate whether or not you've gotten rid of all of the iodide. Iodide, yeah. JOHN DOLHUN: Good. Good. That's very good. So starch actually reacts with iodide and iodine, gives you that blue-black color. So if you're titrating something yellow to clear, sometimes it might be harder to see. So what Alec said was your solution actually reacts with starch. So I actually brought some of the solution in here, and I brought a piece of bread in. I don't know if this is going to work, but bread has starch in it, doesn't it? So I'm going to put someone on this bread. Wow. Look at that blue black. So something's going on here. It's reacting with the starch, right? Can I have a volunteer? Some brave person? I know you're all tired, but one of you. One of you, come up. Come on up, Maida. Maida, right? It's Maida, right? AUDIENCE: Yes. JOHN DOLHUN: OK. Maida, stand up front here. So what we're going to do is we're going to open this up. And put a pair of these on, Maida. And I'm going to let you hold this beaker and face your fellow students. And just hold it nice and-- and what we're going to do is we're going to add something to it. It's clear, right? OK, keep your eye on the beaker. Maida, don't drop but whatever you do. AUDIENCE: I won't drop it. JOHN DOLHUN: OK. [CHUCKLES] OK. So keep your eye on that beaker. Don't take your eyes off the beaker. Now what-- don't worry. Keep watching it, Maida. Don't get nervous. Oh! Now that's what I'm talking about. You see that? This is what we're talking about. And I mean, you're titrating. You can't see the end point. You put this in, now that last drop of titrant, it's going to turn it clear. You're going to be able to see your titration. And thank you very much, Maida. So what's going on with the starch? Let's take a look at this. Starch is made up of about 25% amylose, which is the linear helical form. And it also is made up about 75% of the branched amylopectin. What happens is we have iodine and iodide present in our solution, and when those two come together, they actually form this pentaiodide anion. So you've got some I2, some I minus. Remember, I2 is amber. I minus is clear. When you get these two together and they insert into this helix, the amylose helix of starch, and what amylose does is it forces the pentaiodide anion to go in linearly into that helix. Then the energy spacings change. So you've got-- the way the wavelength of light hits that, you're going to see blue black. It's all happening inside of the starch with the amylose. That's the key thing. There are different people-- some people still believe it's I3 minus. There's somebody else out there saying no, no, it's a polyiodide. There's always going to be some controversy in the-- but they're working on it. I like I5. And someone actually made an inorganic complex to make it look like starch, and they proved it was I5. But even after this paper came out, there's still a lot of controversy, so. So for your standardization, pretty simple. You're going to go through, and you're going to just follow these steps. The TAs will go through this with you, very simple. And you're going to start off with probably something like this, kind of like a reddish solution. And then you're going to start adding your thiosulfate. And gradually, your titrating the iodine in this solution to iodide. So here you've got a more yellow solution. What you want to do is you want to find a spot when it turns yellow to add your starch. And the starch has to be bubbly hot on the hot plate. And if you add it too early, there's so much iodine in there, it's going to destroy the starch complex. You won't get a reaction. But if you wait until it's so pale yellow, what happens, Thomas? AUDIENCE: It turns blue. It makes the complex successfully, it turns it dark blue. JOHN DOLHUN: It turns it dark blue. Yeah. But if you wait too long, right-- AUDIENCE: [? I ?] [? mean, ?] if you add too much, [INAUDIBLE] JOHN DOLHUN: Did you-- you had a reaction yesterday where your starch was an globules, right? Is that-- AUDIENCE: Oh yeah. It formed a film because we didn't keep it hot. JOHN DOLHUN: Oh, the starch was not hot enough. OK, that explains that. AUDIENCE: [INAUDIBLE] JOHN DOLHUN: Yeah. AUDIENCE: We put it in and stirred, and it made a bunch of little blue specks that [INAUDIBLE].. JOHN DOLHUN: Yes, yes. Yeah, I've seen that before. So you want to keep your starch hot, and just be patient. And then you just take a plastic pasture pipette, take a swig of it, shoot it in, and you should get your blue black. And then look. You've got your blue black. You put that last drop of thiosulfate in, and you've got your clear solution. So you turn around, and you're writing this down in your notebooks, right, and then you look back, but it's starting to turn blue black again. What should you do? What would you do? AUDIENCE: Add another drop of titrant. JOHN DOLHUN: Add another drop of titrant. That's what I would do, Thomas. But it's not correct. AUDIENCE: [LAUGHS] JOHN DOLHUN: But I would do the same thing. I would add another drop of titrant. AUDIENCE: Oh, what if it just turned blue by itself, [INAUDIBLE] and you're just [INAUDIBLE] JOHN DOLHUN: There's a side reaction going on in the air. When you get this clear, you've got all iodide present in there. But what happens is-- so you've got iodide there, but you also have oxygen in the air. And the oxygen is oxidizing the iodide to iodine, and we don't want this iodine coming from the air. We want it only from the river water, right, from the oxygen in the river. So this is a side reaction that can go on if you let it set. So just ignore it. Just take your end point, your final neutralization, and you're good. Take a look at the stoichiometry here. One biiodate make six I2. Each I2 reacts with two thiosulfate. So it's 12 to 1 thiosulfate to biiodate. What you're going to do is you're going to do three trials, and they all should agree to within 2% or 3%. If they don't, do an extra trial or two. And what you're going to do is you're going to find your mean, your standard deviation, and your confidence intervals and then give all that information to your TA. Yesterday the TAs did a beautiful job. They put everybody's on an Excel spreadsheet, had it all averaged out. They really did a good job yesterday. The students really homed in on the exact concentration of the thiosulfate. So it's pretty simple. You do your calculations right there in the lab. And then you have a choice of using the class average or using your own results for the dissolved oxygen that will take place on the next day. So collection of water samples. So you're going to be going to the river for day two. And we have these poles. If you have long arms, you'll take a short poll. If you're short and have short arms, then we have real long poles. They're like hockey sticks. So you get your stick, and what you do is you insert your-- your BOD bottle snaps into the clip that I've got inside. You take the stopper out, and then you go to the edge of the dock. Don't fall in, and don't push anybody, OK. Remember the cyanobacteria and all that out there. And take gloves with you, because when you put this under water, it's got to be completely submerged. You have to reach over the dock. You've got to stopper it underwater. So you've got to have gloves with you, all right. So I stoppered mine underwater. I bring it up, take it out, and then I look at the-- I take the bottle, and I do this test. I don't see any bubbles. That's a good sign. That means it's perfect. If you see bubbles, you've introduced more oxygen in there. Your DO concentrations are going to be too high. Pour it out, and restart again. OK, so that's the collection. Then you bring the stuff back to the lab, and you're going to treat the bottles in the lab. This here is wrong. You don't want to use these digital pipetters to treat the water, because you'll be introducing oxygen into those water bottles. What you're going to use is your 10-mL glass pipette. And what we're going to do here is each pair of students will have four bottles. So you're going to-- first, you're going to treat it with the manganese sulfate, 2 mLs of manganese sulfate. That's the first reaction on that oxidation reduction Winkler series. And the way you do it is-- what I would do is I would take up 10 mils of manganese sulfate to prevent any airflow, any air. And then what you're going to do is you're going to take the stopper out. You're going to go just below the surface of the liquid and put in 2 mils. And then your partner can stopper it. You go to the next one. You do all four of them. The last 2 mils in here, shoot it into waste. And then do the same thing with the alkaline-iodide-azide reagent, 2 mils in each bottle. And you should look at the bottle at this point. After you add those reagents, there should not be any bubbles. If there's a bubble, it means you've introduced air, and your DO values will be higher by doing that. So once you've treated with these two steps here, you've essentially trapped the oxygen. You're going to have this brown flock like this. Now you just shake that a bit, and then you're going to dissolve it now by adding sulfuric acid, 28 drops of sulfuric. Acid for the sulfuric, you don't go below the surface. You just open the lid, and you drip, drip it in. The acid is heavy. It's going to fall right to the bottom of the bottle. And now you should have a bubble in there. You will have a bubble after you add the sulfuric, and that's OK. So when you're done with this, you're ready to titrate. And we've got to-- we're supposed to titrate 200 mils. That's what you titrated when you did your standardization as well. But we've got to make up for the 4 mils that we added there in the beginning. We've displaced something there. So you want to titrate 200 mLs times-- you've got a 300 mL BOD bottle, and you've taken and added 4 mLs of stuff to it. So if you do the math to make up for that, you really have to titrate 203 mLs. So there's a couple ways you could do this. You can use a 100-mL graduated cylinder, and the error on that is about plus or minus 0.5. You fill that up twice, put that in your container. The last 3 mils, you could use this for accuracy to get your last 3 mLs in, and then you're good. But you can also just titrate 200 mLs and then multiply your answer by a correction factor, which would be 203 over 200. And that will give you the same answer as titrating the 203. So the math is pretty simple here. You're converting the moles of your titrant to moles of oxygen, grams of oxygen. You divide by the liters. If you're doing 200 mLs, that's 0.2 liters. And then you get your milligrams per liter in PPM. I kept mentioning we're using the-- we've got to add this alkaline-azide solution. We're actually using the azide modification of the Winkler method. And what is that? Well, there are NOx gases in the atmosphere. What's the nastiest NOx gas that you can think of? I'll give you a hint. It's a big greenhouse gas, and it's not CO2. AUDIENCE: Ozone? JOHN DOLHUN: Ozone is a gas up there, yeah. But that protects us. Our ozone layer is a layer of protection. But what's-- yes. AUDIENCE: Is it NO2 or-- JOHN DOLHUN: The other way. AUDIENCE: Or N O? I know that [INAUDIBLE] JOHN DOLHUN: All right, please don't laugh at this. It's laughing gas, N2O. You're all-- I mean, the atmosphere is loaded with laughing gas. I know. Everybody's laughing now. It's great. Where does it come from, N2O? All the fertilizer. 1% of all the fertilizer in the world goes up in the atmosphere as laughing gas. It's not from a dentist's office. It's from fertilizer. I know. I don't want to think about dentists. I was just at one yesterday. I don't like dentists. But every ton of laughing gas that's in the atmosphere. is like 300 tons of CO2. And it stays up there for over 100 years. And what does it do? Well, who said ozone back there? There you are. OK. Laughing gas reacts with ozone, and it forms dinitrogen dioxide. And this dinitrogen dioxide only lasts for about an hour. And immediately, the N2O2 reacts with air and water to form nitrites. And here we are talking about greenhouse gas in the world, and this is affecting our little tiny reaction in the Charles River experiment, because these nitrites, look what they do. They get in and oxidize iodide to iodine. And we don't want our iodine coming from some reaction from laughing gas, right, from nitrite. We want it coming from the oxygen in the river. So we add sodium azide. And that zaps the nitrites, convert them to harmless nitrogen and water. So that's the theory behind why we're using the azide modification. All that for these nitrites. So let's talk for a moment about pH, pH in natural waters. Let's see here. Pulling down some board, here. Who knows the definition of pH? Remember your chemical principles from a long time a-- Alec. AUDIENCE: I think it was log of concentration of hydrogen ions, [INAUDIBLE] ions. JOHN DOLHUN: Very good. The negative log of the concentration of the hydrogen ions. So pH. And I mean, you all know the pH scale is 0 to 14, and acid is less than 7. And I hope you know what color litmus paper changes, right, with pH. That was a question on a TV show with Regis Philbin, You Want to Be a Millionaire. A guy actually got up to the million dollar question. And I happened to turn it on just at that point, and they ask him, what color does litmus paper change in base? And the guy said, oh, I don't know, but can I call my lifeline? And they said yes. So he called this prestigious biologist at one of the California universities. And they said red. [LAUGHTER] And the guy answers red, and he loses the million dollars. Oh, I was beside myself. So if you remember anything, remember what color litmus paper is in acid. But in the river, the pH can go from 6.5 to 8.5. And the pH effects everything, from the solubility of metals-- if it gets too acidic out there in the river, the metals become more soluble, mercury, cadmium, arsenic, all those metals. So the fish uptake the metals, and we eat the fish. And with global warming, the acidity of the rivers is gradually drifting very slightly lower. It also affects the forms of phosphorous. So remember, you've got PO4 to the 3 minus. But if it's slightly acidic, you might have the hydrogen phosphate or the dihydrogen phosphate. Or you could end up with phosphoric acid, depending on how acidic it gets. What about photosynthesis and pH? Where are my biologists at, my resident bi-- there must be somebody in bio in here. Come on. Don't be afraid. Yes. There you are. What's the equation for photosynthesis? AUDIENCE: Water and carbon dioxide. JOHN DOLHUN: Good, good. Water and carbon dioxide. Let's just write that down for a moment. So CO2 plus water, little bit of sun. AUDIENCE: Oxygen and glucose. JOHN DOLHUN: Oxygen and sugars, good. So CH2O, n. So does the pH go up or down during photosynthesis? I mean, it's like a 50/50 chance. Sean, you want to answer, don't you? AUDIENCE: I would say the pH goes up. JOHN DOLHUN: It goes up? OK. Anyone else? Alec? AUDIENCE: It goes down? JOHN DOLHUN: It goes down? OK. [LAUGHTER] There you go. I told you it's like a 50/50, right? All right, let's do a little experiment with this. I'm going to pour myself a drink here. This is good stuff. It's not Gatorade, I can tell you that. This is a classic test in the medical profession, if you're going to medical school, for breath. And when I'm doing this, you cannot make me laugh. If you make me laugh, I'm dead, OK. Please. I'm going to play some music to relax myself here. Let me just-- let me see if we can get this on here. OK. There we go. So I'm breathing into this. We don't hear any music coming out. Going to-- [MUSIC PLAYING] There we go. You're making me laugh, Sean. I may have to have you come up and help me with this. [MUSIC PLAYING] I may not be OK. The color's supposed to change. [MUSIC PLAYING] There we are. Good? I'm OK. So what just happened? AUDIENCE: You blew carbon dioxide into the water. JOHN DOLHUN: I blew carbon dioxide in the water. So we've got CO2 plus water going to what? Yeah. AUDIENCE: Carbonic acid. JOHN DOLHUN: Carbonic acid. Good. H2CO3, which breaks down into H plus plus bicarbonate. Now photosynthesis needs carbon dioxide, right? So we take that out of the equation, which means we're also taking out the H plus. So does the pH go up or down? AUDIENCE: Up. JOHN DOLHUN: Alec? Up, up, up. OK? Good. And pollution and pH, same thing. If you've got pollution, you've got all this vegetation. So you've got photosynthesis, so the pH is going to be up. This is Lassen Lake, Volcanic National Park, pH 2, 2.0. You do not want to stick your foot into this lake. And then you've got some safety of the chemicals, which the most serious is the azide reagent, which it's a neurological toxin. And if you ingest it, it can cause death. So please be careful with that. Sulfuric acid, you know how bad that is. You don't want to get it in your respiratory system. And the manganese sulfate seems innocuous, but it attacks the central nervous system, targets blood and kidneys. So be careful with that. Sodium thiosulfate is a respiratory irritant, can cause breathing problems. So if you feel like you're having breathing issues, it could be that. Biiodate can burn your eyes. Very, very dangerous stuff around your eyes. So all of these things, you have to be careful with. OK. So we'll see you Thursday for the last lecture in this series.
MIT_5310_Laboratory_Chemistry_Fall_2019	7_Ellen_Swallow_Richards_Part_3.txt	[SQUEAKING] [RUSTLING] [CLICKING] JOHN DOLHUN: Good afternoon, everyone. So I'm going to start off today with a small demonstration. And I wonder if somebody could tell me what are the states of matter? Yeah? Aisha? AUDIENCE: Solid, liquid, gas, and then [INAUDIBLE].. JOHN DOLHUN: Solid, liquid, gas, and plasma. Good. Good. OK. So the plasma is one that we don't oftentimes talk about. And that's what we're going to be talking about in this lecture. So what we're going to do-- a plasma basically is a group of ionized gas molecules. The sun and the stars are plasma. This is a plasma globe, which on a small scale you're not actually going to be able to see the plasma inside because it's not hot enough. But we'll be able to see the colors from the emissions. So ionization is when an electron hits a gas particle, kicks an electron off, and produces a gas ion. That's ionization. That's what's happening on the Sun and the stars. I mean, you've got this sea of ions that's molting hot. And then emission happens when the gas ion grabs its electron back. And what it does is then it gives off light. And that's what we're going to see here. So I've got two plasmas actually. I've got the plasma globe. And I've also got a fluorescent light bulb, which is also a plasma. And I need a volunteer-- someone who wants to be a conductor between the two plasmas. Someone who's not-- Alex, come on down. All right. So Alex, you can stand right in the front actually, kind of over here. So we're going to start by just shining 120 volts through this globe. That's 120 volts going through. And what I'm going to be doing is putting 70,000 volts through this. And then we're going to-- Alex is going to be the conductor. So we're going to put the 70,000 volts through Alex. They'll crawl along his skin-- the surface of his skin. And he's going to hold the fluorescent light bulb in his other hand. And I don't know. Hopefully he'll be able to light it. I mean in that fluorescent light bulb, it's plasma. There's mercury. You have to ionize the mercury first. It gives off UV radiation, grabs its electron back, and then it shines that invisible UV on the phosphorescent coating of the bulb. And we see the white light given off. So we'll try this out. Can someone shut the lights off there? Just turn those lights off? Yeah. I think so. Yeah. Just hold that in. That's perfect. So before we start Alex, I think we're going to have you-- let's see if we get this thing going here. You want to just bring your hand up toward that? Yeah. OK. All right. Put this pair of goggles on just in case. OK. Mainly for the fluorescent bulb. OK. Now what's going to happen now is I'm going to have you hold your hand there. And don't take it off. You're not going to get shocked. AUDIENCE: OK. JOHN DOLHUN: And I'm going to have you hold this in your other hand. Now put your hand there. Good. Now here we go. Ready? Wow. AUDIENCE: Really cool. JOHN DOLHUN: All right. You feel a little warmth on your hand? AUDIENCE: Yeah. JOHN DOLHUN: Not too hot? AUDIENCE: Not too hot. No. JOHN DOLHUN: 70,000 volts going through him along the surface of his skin coming out the hand and ionizing the mercury in a fluorescent light bulb. So that's pretty good. Thank you very much, Alex. You're very brave. Yeah give him a hand. [APPLAUSE] All right. So you saw two plasmas there. And the plasma we're going to talk about today-- and here we'll bring the lights back up there. Oh, there we go. He's got it. We've got our own technician here. So excellent. So we've reached the final lecture in this series. We're going to be talking about inductively coupled plasma mass spectrometry. And this is a lecture where you'll be able to impress yourself and your friends because there's only two of these machines at MIT. And it's a very rare opportunity. We're actually introducing this machine in 5.310. You're going to be the first ones that have an opportunity to use this machine. So we're going to answer a series of questions here. What is ICP-MS? What can be detected with it? What are the main components? How it works. And some of the challenges we're going to face in using it. And then we'll talk a little bit about the MIT Experiment. And we'll spend the last 10 minutes or so talking about mercury analysis. So inductively coupled plasma mass spectrometry. There are two things that separate this from all other forms of mass spec. And they are high temperature and high energy. And it's a combination of those two things that allows the sample to decompose. It undergoes atomization and then ionization. So what you can actually detect with this is pretty much most of the elements in the periodic table at the part per trillion level. That's mind boggling-- at the part per trillion level. And what this machine does is it scans from 5 lithium-- this is the mass scale up to 260, which is uranium. Now that's another big difference between this and the other forms of mass spectrometry. Because the other forms-- we have molecular weights that are in the hundreds of thousands for these nucleic acids, these carbohydrates, the proteins that we're trying to study. And from regular mass spec, which is a much lower energy, much lower ionization, we're looking for molecular weight information about these biomolecules and some fragmentation information. So we're primarily concerned about carbon, hydrogen, oxygen, nitrogen, phosphorus, and sulfur. Those are pretty much the six elements regular mass spec would be concerned with. With this machine we're rapidly scanning the whole range of all these elements and the mass range-- the top mass range is 260 for this machine. So that's the big difference. Now, what are the main components? So what we've got is we've got our sample introduction. And the sample is going to be a liquid. So it's a liquid that enters the sample intro. And that liquid is converted to an aerosol. And the aerosol gets shot into a plasma ion source. And in that ion source, that's where your ionization takes place. Sample is going to be dried out, decomposed, atomized, and the elements are going to be ionized. And then we've got an ion lens, which focuses that ion beam. So this focuses the ion beam. We also have a collision reaction cell, where we actually introduce helium. And the helium bombards our ions and gets rid of the interferences, like the polyatomic ions we're going to talk about. So this removes interferences. And then the monatomic ions that are left to enter this quadrupole mass analyzer, which is four rods-- the ions travel down the center of those rods and they're sorted by their mass to charge ratios. The ions are then counted at the detector. And we've got-- the detector actually records the counts per second of every ion hitting it. And these counts can be like hundreds of thousands of counts for each ion every second. So counts per second recorded. And interestingly, the detector takes those counts per second and then it goes and looks at our calibration standards. And it associates those counts per second with our concentrations in our calibration standards. And then you've got concentration for your samples. So the counts per second then head into our data system and the software analyzes all this and produces us some data. Let's take a look and see how it works. So here's our sample-- a liquid sample. And we've got a little peristaltic pump that pumps the liquid up to this thing called the nebulizer. The nebulizer is going to convert it into an aerosol. But coming in here, notice there's a dilution gas. The dilution gas is argon. And argon actually dilutes our sample right at that point before it enters this spray chamber. Once the aerosol gets in here, there's a make up gas-- also argon-- that pushes the droplets down to the bottom of the tube. Once they're down here, they have to make two right turns to end up outside the ion source. And those two right hand turns cause the larger droplets to be pumped out and fall by the wayside. So the most sample that is actually going to enter this ion source is only about 2% of our original sample. We've gotten rid of the rest. Now once it goes into this ion source, there are three concentric glass tubes. So the ions will go into the center tube here. And look at these gases coming in here. Plasma gas and auxiliary gas-- they're coming in at right angles. And both of those gases are argon. So the gas comes in at right angles and it forms like a mini tornado inside of this tube. It's like a hurricane going on in there. And that cyclonic motion picks up the sample into a vortex. And what goes into a vortex stays in a vortex. Right? So you've got your sample trapped up in this vortex moving through this tube. And then there's an electrode sending electrons out. And look at this. We've got this Rf coil wrapped around the glass tube. That's producing about 1,500 watts of power. It's like 27.1 megahertz. And look at my hand. The old right hand rule goes into play. Remember this. What are my fingers doing? What are we making in that tub? Roberto? AUDIENCE: [INAUDIBLE] JOHN DOLHUN: Yeah, an electromagnetic field. And that electromagnetic field is thrashing around in there. And it's so powerful that it can rip an electron off argon. So we've got our argon hitting that energy. There's your high energy. And you've got argon ions plus electrons. And those argon ions and electrons are just smashing around, twirling around in there. And the collisions from that, the kinetic energy that's given off-- that's your plasma. So that's all happening inside of that tube. Let's take a bigger view of it. This is a blown up view of what's happening here. So here is your aerosol sample going down the center tube. What happens to the sample is it's actually-- the liquid is dried out to a solid in that tube. And then that solid is vaporized. It's atomized, decomposed, and then ionized. The temperatures in here-- they can get up to 8,000 kelvin. I mean, you're talking like the temperature of the sun is what? 6,000-- a little under 6,000 Kelvin? So the temperatures are very hot. And you can see this plasma when the machine is on. You'll see the glow of this white hot plasma that's actually formed in there. So what you've got is your ions coming out. Your plus charged ions will come out here. And what's going to happen is they will then enter the ion lens, which I'll show you. So what I've done here is I've actually opened up our machine. And this is the ion source. That's where the plasma is generated. It's a glass tube. And you can see the Rf coil there. And right behind it, you can't see, is this sample cone. So what I did is push a button here and moved this back to reveal the sample cone. Now think about this. Inside of this box you've got like 6,000 Kelvin going on in there. Outside is room temperature. It's like putting the Earth a couple of miles away from the sun. That's what you're doing here. And what this cone is, it's made of copper. And it's got a nickel center with the little hole in it. And what happens is there's a grounding system here. So the electrons coming out of this torch box, coming out at the speed of light, go to ground. The positive charges-- the ions-- cannot go to ground. So they build up on this cone. And here you've got a cone with all these positive ions building up with a tiny hole in it. It's a no brainer. They get pushed through. And so on the other side of this box is the high vacuum low pressure area of the mass spectrometer. So we've got here-- we've got this high temperature, high pressure. We've got room temperature and then we've got low pressure. Three areas of this mass spectrometer. So the ions going through this, that's the best definition of an ion lens you can have. And I unscrewed this so you could see inside. There's a skimmer cone-- another cone-- before you get into the high vacuum area. So now let's talk a moment about the challenges with this system. There are some challenges. Nothing is easy. Right? In this world everything can be challenging. So it turns out that there are a lot of isotopes of different elements that have the same mass. They overlap. These are isobaric overlap-- calcium 40 and argon 40, iron 58, nickel 58, indium 115, and tin 115. Isobaric overlaps are pretty easy to take care of because we can choose an interference free isotope of the element. That means that every one of these elements has at least one isotope that doesn't overlap. So with the ICP-MS we can key in on that isotope and measure just that isotope and we're good. The only problem is indium 115 doesn't have any isotopes. They all overlap with something. So what we have to do is type an equation into the mass spectrometer to take care of that. And the main interference is tin 115. So the equation is pretty simple. We take the counts per second of indium that we want to find. And we take the counts per second of everything, which is the indium 115 plus the tin 115. That's the total counts we're seeing. And then we subtract the counts per second of the interferent. And the way we get that is we multiply this by an isotope ratio. We multiply it by the abundance of the interferent divided by the abundance of an isotope of tin that does not interfere, which would be tin 118. So we can take those two abundances, get a ratio there. Multiply that times the total counts and end up getting our counts for indium 115. And all this is done by the software. There's one other equation I have to put in this mass spectrometer. It's for lead because lead 206, 207, and 208-- any time you dig up lead anywhere on the Earth basically, the isotope ratios will always be different because of all the radioactive decay that's going on from when the Earth was formed. And so we put this in. And we add all the isotopes of lead up to the 208 and we get a total and that that's good. That's how we do it. Then we have these polyatomic ions. In the plasma you've got argon and oxygen. So they can combine with each other to form these polyatomics, which interfere with other elements. They overlap directly. Argon, argon, which would be argon 40 and argon 38 overlaps with selenium. And then if we add our matrix like our acids-- hydrochloric acid you're putting chlorine in. Sulfuric you're putting sulfur. Nitric you're putting nitrogen. So you can have a whole slew of these. The two most challenging ones are selenium 78 and arsenic 75 because those two elements give the weakest signal of all the elements for ICP-MS. The only ionize about 30%. So we've got to get rid of these polyatomics. Another thing that can happen is you can have doubly charged ions form. Cerium is an element in our tuning solution. Cerium has a molecular weight of 140. If it's doubly charged, you divide that by 2 and you get 70. So a doubly charged cerium would interfere with gallium. So somehow, we've got to take these into account. And there's a whole table of them. Look at this. I'm giving you this so you don't have to search for these in the dark. This is everything right here. Everything that I wrote up there is included here. And typically, most of these interferences come below mass 82. So how are we going to deal with these? We've got to figure out a way to deal with them. And in comes the collision reaction cell. So just to put this back in perspective-- here's our nebulizer and our tube-- our torch. And then this is the high vacuum low pressure area of the mass spectrometer. So we've got a collision reaction cell here that we put helium in. And we fill it with helium and the helium starts colliding with the ions-- both the polyatomics and the monatomics. And those collisions give off the same kinetic energy, whether it's a plus 1 ion or polyatomic. However, think about this. Polyatomics are bigger so they start colliding more frequently with the helium so they give off more kinetic energy. So there's a positive discrimination voltage-- a kinetic energy of discrimination that prevents the polyatomics from going out of that octupole, that collision reaction cell. This is amazing. I mean, 15 years ago or something they didn't have this. They had to put equations in for everything. Now at least there's a way to get rid of the polyatomics. So what goes through are the monatomic ions down this quadrupole mass filter toward the detector. This is the detector. It's a pretty fancy detector. It's got these dynodes, which are electrodes in vacuum that produce electrons. They multiply electrons. This thing has 26 dynodes connected together. So when the ion hits, it produces a couple electrons. Those electrons hit the next dynode. They get multiplied exponentially and then it continues. And then finally, you get down here to the last dynode and that's called your pulse signal. And that's where you could have a million counts or something. And once that signal becomes saturated then the machine says to itself well, wait a minute. I have to pull back. So it goes back a few dynodes, picks up the analog signal, and then the software multiplies that by some pulse analog ratio to make it look like a pulse. It's quite complex. But you can actually-- when it's graphing your elements, if a point goes on the graph, you can tell whether it's a pulse or analog point and if it's been corrected. So this is pretty much the detector. Let's see what else we have here. So what are we going to detect in this lab? So we're actually going to be looking at these 29 elements. We picked 29 elements that we're going to be scanning and monitoring during our river lab. What we did is we actually got standards that contained these 29 elements so we could make up calibration standards for you for this lab. We also have a set of internal standards, which are four elements that are not part of the 29 elements that we're looking at. And the internal standards are there to actually-- they're pumping through the machine constantly with every sample, with every calibration standard, with your blanks, and they're telling us about the drift of the machine. We can look at this and see, oh, things look pretty good. They're hugging together very nicely. This run here is about a five hour run. And so if those internal standards are staying together, we know the machine is doing well. But if something happens to the internal standards, then we see we might have a problem. So we can actually go in and try to figure out what's going on. Along with this, we also have quality control standards. Here's your 29 elements again. But we bought these from a different company than our calibration standards. And each one of the elements in this mix has a defined concentration. So this mix comes from the National Institute of Standards in Gaithersburg, Maryland. And we'll be running one of these with your samples. So you'll be able to look at this and say, oh, these look pretty good. We're very close to the ranges we want. That means things are working well. Your results are really going to mean something when we have all these controls and all our calibration standards and quality control standards. So a little bit of EPA terminology-- when you get your report, which will be a PDF file, you'll see various things like calibration blank. What this is just reagent water that's acidified the same way as our calibration standards. And we run that blank before we run the calibration standards. And then we'll run a series of maybe 10 calibration standards, do another blank, then we'll run our quality control standard. And we'll also be running something called a laboratory reagent blank where one of the TAs will actually take water to the river Milli-Q water. And open it up and just let it breathe the air there. And then bring it back to the lab. And then they're going to filter that water the same way you're filtering your real river samples. And then they're going to acidify it exactly like you're acidifying your river samples. And so we're going to have a blank called the laboratory reagent blank that will tell us, hey, there may have been something in the funnel we're using or something in one of those new filtering membrane disks that got into this sample and it's also going to be in your sample. So that's another quality control. And then we've got-- we're going to run 10 samples. And then we run a CCB, which is a continuing calibration blank. It's another blank just to make sure everything's OK. And then we run a CCV, which is a continuing calibration verification, which ends up being one of our-- we pick one of our calibration standards. Usually the midpoint standard. And we stick it in there just to make sure things are still OK. Then we'll run another 10 samples, another CCB, and a CCV. So that's what those terms mean. When you see these you're not overwhelmed. You'll kind of understand what these terms are. This is from the EPA method that we're actually using. The protocol is very detailed. And the TAs are going to go over this with you in the lab. They'll pull out the tubes, they'll pull out the filtration system. They'll show you how to connect it to the vacuum, show you what kind of bottles to take to the river and collect this from. So they'll be going through all of this. Now we have to talk about mercury. There's a lot of mercury up there in the atmosphere. Who knows where all this mercury's coming from? Where does all the elemental mercury in the atmosphere come-- Brian? AUDIENCE: Coal. JOHN DOLHUN: Coal is a big one. Yeah. That's a man made source of some of the mercury. Yeah. What else? I mean, look at the mercury. Look at the elemental mercury floating around up there. Where else could it come from besides our energy source? Yes, Autumn? AUDIENCE: Maybe if there's like a forest fire. JOHN DOLHUN: Forest fires. That would definitely be a big source of mercury. Yeah. Anything else? Yeah, Ryan? AUDIENCE: I mean, it's definitely in the water, but like for [INAUDIBLE] JOHN DOLHUN: Yeah. Yeah. Oh, yeah. It's in the dirt and rocks and evaporating out. Yeah. I mean, another big source would be volcanoes-- natural source. Yeah. So probably about 2/3 of it comes from our fossil fuels and a third of it comes from natural sources. But once it gets up there, once it's in the atmosphere, this elemental mercury-- there are plenty of things up there that can oxidize it. There's ozone up there. There's hydroxide radicals. There's chlorine and bromine in the troposphere. So this elemental mercury gets oxidized to mercury 2. And then it rains outside. Right? Where do you think that mercury 2 goes when it rains? It's coming down on us. Right? It's going into the water. And once it gets in the water there are a couple of things that can happen. It can have it can be photoreduced here. And you can form the elemental mercury back. And some of that can vaporize back up into the atmosphere. Or the mercury too can get down here into the depths of the water. And this is where the bad things happen. This is where the nasty methyl mercury is formed. So once it gets down here we know that mercury loves sulfur. So it can attach itself to this-- there's plenty of hydrogen sulfide in the water. It can attach itself to the sulfur and form mercury sulfide. And this is a neutral molecule. Being a neutral molecule it can go right through a bacterial cell wall. And once it's inside of a bacteria-- there are some bacteria down there that produce methyl mercury. Nobody knows how it's done. They know that the mercury sulfide goes in, but they don't know the exact mechanism. The other thing that's not known is that there are some fish out there that have millions of parts of mercury in their systems, much more than the surrounding water. So there's got to be some other sources of this methyl mercury down there somewhere that they haven't really pinpointed. So once we get this methyl mercury-- I just told you it loves sulfur. Right? So you get this stuff in the body-- this organic form of mercury. It's going to go for your cysteine amino acids. And it forms a covalent bond to the sulfur. So you've got this carboxy ethyl sulfonyl methyl mercury here. Now you think about the cysteine amino acids-- we've got them in our proteins. So this methyl mercury, once it's inside of ourself it can go for all the proteins and infiltrate covalently bond and hook up to all these cysteines. Once we get methyl mercury inside of us from eating the fish, it's like bioaccumulation. It's down the biofood chain. It starts with the plankton, then the small fish, and the bigger fish. Then we get it. This stuff-- 90% of the methyl mercury can actually come out of our gut, get into our bloodstream, and it can pass through the blood brain barrier. So it gets into our central nervous system and can wreak havoc. It can also go through the placenta. And the fetus is just in there. I mean, it's just developing. And once methyl mercury gets in there you can have total decontrol of the whole thing. Everything can fall apart for that. So this is really bad stuff. Now what we're going to be doing in this lab is actually we're going to be detecting this and we're going to be using our new DMA 80 atomic absorption spectrometer. And this spectrometer operates under three things. There are three things happening here. So we've got thermal degradation. You've got amalgamation. And we've got atomic absorption. This spectrometer has two detectors and three cells. It's called a tri cell. So on the nanogram scale and the PPB scale-- one of the cells will detect from about 0.01 to 10 nanograms, which is like 0.1 to 100 PPB. The next cell will detect between 10 and 20 nanograms, which is 100 to 200 PPB. And the third cell will pick up the last range from 20 to 1,500 nanograms, which is 200 to 15,000 PPB. The detection limit of this machine is to the thousandths of a nanogram. So detects text down to 0.001 nanogram. Can actually-- you're talking almost a part per trillion there with this machine. So it's really a fantastic machine. So let's actually see how this machine works. So this is a little schematic of this machine. And I did this on ChemDraw. So ChemDraw is amazing. It is just-- you can do just about anything with ChemDraw. So we've got a tank of oxygen that you'll see it sitting in the lab. And then we have this autosampler, which is a 40 position autosampler. And so we'll be massing out our fish, putting it into the autosampler. And then this little pneumatic arm comes out, grabs your sample out of the autosampler, and inserts it into this drying decomposition oven. And the drying decomposition oven will heat the sample up to about 650 degrees or so. And it combusts everything. And all of the combustion products of your sample are carried by the stream of oxygen gas into this catalyst tube furnace. Everything goes in the catalyst tube. And that catalyst tube gets heated up to about 500 degrees. And it pulls everything out-- literally all the NOxes, SOxes, everything you can think of. Not only that, it converts every mercury species, including methyl mercury down to the elemental mercury. The only thing that comes out of that catalyst tube is the elemental mercury. I know it's hard to believe that, but everything else stays in the catalyst tube. So the elemental mercury comes out and goes into a gold amalgamator. And all it is a glass tube filled with tiny gold beads. And the mercury comes out, goes in there, and sticks to those beads. Then this gold amalgamator is flash heated up to 900 degrees. And bam! You release the mercury vapor. And the vapor goes into the atomic absorption part of the instrument that has our tri cells-- our three cells. So we've got two mercury lamps. They're shining light on the samples-- like 254 nanometers. And the light goes in, shines on the sample, and then we record the height of the peak in the absorbance that's going on. And we figure out our concentrations of the mercury in our samples. So this is a great machine. Do you guys have any questions about this machine or the ICP-MS? There's no sample prep for this machine, which is amazing. We can do solids, liquids, or gases. And you can actually follow your sample through. There's a system status that you can turn on and you can see your sample traveling through the various positions while it's going through. It's pretty easy. Just three simple steps. You cut up your fishy. Right? And we'll have several native fish to the Charles River. So you'll be able to-- I know. It's not that bad. Maida. Don't pass out on me. No, it really won't be that bad. But you'll take your fish, put a piece on the boat, and weigh it-- mass it-- and then you type your mass into the machine, put it in the autosampler, and that's pretty much goes. You're going to do this on Monday and Tuesday. You'll do this at the beginning and then after that, you'll make up your standards for the phosphate lab. And you'll do the phosphate testing. You'll go to the river and get your bottle of water for the phosphate. Any questions? Yes, Autumn? AUDIENCE: Is there any research on how to remove mercury from other animals or from us? JOHN DOLHUN: They have-- there are certain chemicals that you could get prescribed that would actually chelate some of the mercury. Yeah. And chelate means to latch on to it and try to pull it out of your bloodstream. Yeah. I don't know anyone that's actually been mercury poisoned to that extent. But I know there are chemicals that you can take that will help mitigate some of that. Yeah. Other questions? So when we're doing the ICP-MS next Wednesday and Thursday, we'll have you-- you can come in and take a peek at it. You can look at the plasma. You'll see it lit up. And you can see the signal on the screen-- how we're looking at the signal and we're getting it all ready for your samples. I'll also have an associate here from Agilent-- a PhD chemist who is actually going to-- he wanted to come just for this lab. So I told him to come on. So he'll be a great source to talk to when you're coming in. Yeah. Yeah. So I'm kind of excited that you're the first group to use this machine. And I think it'll be exciting for you. I mean, the Charles River is probably the cleanest river in America. Yes. Believe it or not. But you know, there's still-- it has to be monitored. We still find problems from time to time. So we will see you up in the lab. And next week, Dr. Sarah Hewett will start a new series of lectures.
MIT_5310_Laboratory_Chemistry_Fall_2019	3_Writing_Up_the_Lab_Report.txt	[SQUEAKING] [RUSTLING] [CLICKING] SARAH HEWETT: All right, let's get started. And if anybody else shows up, then that'll be fine. So today, we are going to talk about how to write a lab report, which is a pretty important part of this course, since it's going to determine a good portion of your grade. And in general, it's good to know how to communicate the science that you do, whether it's in this class or in your research, or in any other context, really. So I wanted to start just by thinking about these two questions, which is why is it important to write up your results, and then how should you write a lab report? And to help get us thinking about these questions, I printed out on this handout that has a good chunk of text on it. The top part is Ira Remsen's account of his experiment with copper and nitric acid. If you have not read it before, it's a pretty good read. So if you could skim that. And then at the bottom, there is a shorter description of the same experiment in a way that you may find it written either in a lab report or in a scientific paper if you were going to publish these results. So if you guys want to give those a quick skim through, and then we'll use those to sort of talk about these topics of how do you communicate your science. And if you've never seen this experiment done before, I have a little bit of video to show what happens when you put nitric acid on a penny. So you can have an even more vivid visual of what Ira Remsen was going through when he decided to pick this up and throw it out a window. NARRATOR: A few drops of nitric acid are placed on an older copper penny. SARAH HEWETT: And it goes for a while. So that should give you a little bit of an idea of the situation that he was in. And so having had a chance to skim these two things, does anyone have any answers to these questions about why is it important to write up your results, or how should you communicate your results to other people? Yeah. AUDIENCE: So it's, like, not ambiguous, so people know what to expect or they know how to handle the situation. [INAUDIBLE] oh, let's see what happens [INAUDIBLE] SARAH HEWETT: Yeah, using really clear language, so that people know what is going to happen. Like he said, the language acts upon is very vague. And it led to this experiment happening where Ira Remsen burned his hands on some nitric acid. So instead of acts upon, saying things like-- what else could you say instead? What are better words you could use to warn people of what's going to happen? Yeah. AUDIENCE: Corrosive. SARAH HEWETT: Yeah, corrosive. Those things that Scott talked about in his safety lecture. So say some of the general terms that we use to describe chemicals. It's corrosive, it will burn, creates toxic gases, is carcinogenic, things like that. What other guidelines should there be for how you want your results written up? Yeah. AUDIENCE: Indicate amounts, because of the [INAUDIBLE] SARAH HEWETT: Yeah, yeah, definitely. You want to communicate how much you used. So in that first experiment, he said I put some nitric acid on a penny. So you don't know what scale that was on or what scale it can be safely done at. So using exact quantities, so that if somebody is going to redo the experiment, they would know exactly how much you used and what they should expect. In terms of the length of these two pieces of writing, which one is easier to read? AUDIENCE: [INAUDIBLE] SARAH HEWETT: The bottom one so being clear and concise, using objective, short sentences, so that people can follow what you're writing. And they don't have to read this whole, huge chunk of text in order to get the gist of what's going on. So those are some things to keep in mind while writing up your lab report. There's a picture of Ira Remsen. He was a chemist in the 1800s. He was born in 1846. And he became the president of Johns Hopkins University, and also is well-known for discovering the sweetener saccharin, which he also discovered by tasting it on his hands as a result of some more poor lab technique. I mean, he became pretty famous. But don't follow his lead necessarily in that way. So a good lab report starts before the lab even begins. And so here are some things that you should be keeping in mind before you even come into the lab to help set you up to be able to do the experiment successfully, and to be able to have the data that you need to write a lab report. So you want to plan your procedures ahead of time, things that can influence your results, what quantities you need to measure, and what data and results you'll need to collect, so that you can have all of this in your notebook, so that when you go to write up your report you have all of the information that you need. It's very hard to go back into the lab and write something down that you forgot after you're in your dorm room at 10:00 PM the night before the lab's due, going, oh no. How much did this weigh? So you want to plan out ahead of time what you're going to need to collect. There are a bunch of parts to the lab report. And this looks slightly overwhelming, but it's actually there to help you organize your thoughts and present things in a format that other people can recognize. So if you've ever written a report for another course, or if you've read scientific articles in the literature, these titles may seem pretty familiar to you. You guys have written reports for other classes before, yes? Read articles, most of you, maybe? OK, so we're going to go through these parts of the lab report, and talk about in detail what belongs in each section. And we're going to try to do that in the context of the ferrocene experiment to help you guys plan out your report for the one you're going to have to write starting next week. Hopefully, you've already started the little pieces of it. So the first thing is the title. That's usually pretty boring. Keep it straight to the point. Have something to do with what the experiment that you did is. And then the first thing that you're going to write after the title is the abstract. And the abstract that you guys are probably pretty familiar with is very short. It's three to four sentences. Keep it in complete sentences, though. And then you discuss the point of the experiment. You briefly tell what you did and what you found. You can talk about your results-- if you have any yields, melting points, easily digestible results that you can put at the end. So for your ferrocene, you would say, I synthesized ferrocene this many grams, this was its melting point-- something like that. And the abstract is best written at the end of your report. So after you've done everything else, then you can go back and write the abstract, because the abstract is essentially just a short summary of everything else you've written. So if all the other stuff is there, then you can look at each section, take a sentence out of it, smush it all together, and then you have your abstract. So then after your abstract, on the start in the guidelines for how to format this and how to write everything are in your lab manuals. So you should definitely look at those while you were preparing your lab report. And it'll tell you that, after the abstract that goes on your first page, the start of the second page of the lab report is going to be your introduction. And the introduction should probably be about a page or two long give or take, depending on the experiment and how much you need to introduce ahead of time. And you're going to tell the reader what you plan to do and why they should care about it. Give any background that is necessary-- so any historic background, any scientific background, experiments that have come before this one that influenced your work. Include balanced chemical equations of important reactions. This is very important. So if you're going to be doing some sort of chemical reaction, which in this lab we did-- we did two, then you should include the balanced chemical equation for the work that you're planning to do. And then also, any fundamental mathematical equations that you plan to use to analyze your data. In this case, we don't have so many in this lab. But in future labs, like the catalase lab when you're doing kinetics, you'll have a lot more mathematical equations that you're going to need to use and explain to your reader at the beginning, so that they know what's coming. And then you want to discuss any important techniques and why you need to use them in the lab-- their relevance to the experiment that you are planning to do. So with this in mind, let's brainstorm what might go in the introduction of your ferrocene reports. So you can think about the ferrocene lecture from Tuesday, stuff you've done in the lab so far. Yeah. AUDIENCE: Like, how it was discovered, and how it launched the transition metal chemistry. SARAH HEWETT: Yeah. The discovery and history of ferrocene and other organometallic chemistry. Yeah. AUDIENCE: Relevant uses of ferrocene. SARAH HEWETT: Yeah, uses of ferrocene. You guys performed the acetylation of ferrocene. So why do we care that you can add different groups to the ferrocene rings? It's a good thing to mention. So we've got some historic and scientific background. What else can we put in there? AUDIENCE: Like, synthesis of ferrocene. So like, the equation's of the organic molecules. SARAH HEWETT: Yeah. AUDIENCE: And also the acetylation of ferrocene. SARAH HEWETT: Yeah, chemical equations for ferrocene and acetylferrocene. We got our balanced chemical equations. Do we have any mathematical equations that we need? No? Now, what techniques might you talk about? Yeah. AUDIENCE: [INAUDIBLE] sublimation. SARAH HEWETT: Yeah, sublimation. AUDIENCE: Inert atmosphere [INAUDIBLE] SARAH HEWETT: Yeah, inert air-free technique. Yes. You want to talk about that and why we care about that in relation to what could happen to the different components of our ferrocene synthesis. What other techniques? AUDIENCE: Thin layer chromatography. SARAH HEWETT: Yeah, TLC. And? AUDIENCE: Column. SARAH HEWETT: And the column. Running out of room. Yeah, TLC and column chromatography. So how are you going to purify your products when you're done. Yes, anything else? AUDIENCE: Filtration? SARAH HEWETT: Yeah, we can talk about filtration, how you're going to isolate your products during the synthesis. AUDIENCE: Measuring a melting point calibration [INAUDIBLE] SARAH HEWETT: Yeah, melting point. Melting point and how you can use the melting point analysis. So what does the melting point tell you? What information are we getting from that? Why are we taking melting points? Yeah. AUDIENCE: Purity. SARAH HEWETT: It'll tell you the purity, yeah. So you can compare it to the literature values, and you can look at the width of the melting range to see how pure your compound is. So all of these things are good things that you can discuss in your introduction. And you don't need to go into crazy amounts of detail, but you want to give enough detail that the reader will know why those are important for your particular experiment. Good. So a note on including equations in a lab report. We said that you need to include any mathematical or chemical equations that are going to be used in the introduction. And the way that you do this is you give each equation a number. And when you write it in your report, you'll write either the chemical equation or a mathematical equation. And then over to the right in parentheses, you'll number them. And you'll number them in order. And you can either number them both, the chemical and the mathematical equations, sequentially. So any equation, no matter what kind it is, just go one, two, three all the way down. Or if you want, you can separate and have one of the types of equations be in just regular numbers, and then the other one in Roman numerals. Both formats are acceptable. And if you have any questions about how to do any of the formatting things I'm going to talk to you about, it's all from the ACS Style Guide. So we have these books in the lab if you want to borrow one. There's some information online as well, or you can talk to me or John or the TAs if you have questions and can't find anything. But that's where all of the information for how to format things from this presentation are coming from. So we're going to use ACS formatting for everything. And then the important thing is that equations and anything else that you add, like tables and figures-- and we'll talk about those in a little bit, they can't stand on their own. You must reference them in the text. So you can't just throw an equation up here and not talk about it. You'll have to throw in a sentence that says, the reaction of copper nitric acid as shown in equation 1. So the next part is procedures and observations. So this includes what you actually did in the lab. And the really important thing about this is that it has to match what is in your lab notebook. So we already gave you an idealized version of the procedure-- an idea of how you're supposed to be doing it. But we want to know what actually happened when you did the experiment. So if you accidentally added twice as much cyclopentodiene as you were supposed to, write that in your procedure. Don't just re-copy what is in the lab notebook. Draw a diagram of any specialty glassware that you used. So you don't need to tell us piece by piece how you assembled your glassware. You can just draw a picture and say, I set up a distillation as shown in figure 1. And that's all you need to do. Then you need to give enough information for one of your classmates to recreate the procedure. So again, you don't need to go into excruciating detail about how you injected things out of a syringe. Assume that one of your classmates is reading this, and they have the same knowledge that you do. So if you say, I used a syringe to measure this, or a syringe was used, because you're not supposed to use pronouns, then that would be enough information for one of us to recreate the experiment. Include all the information about a chemical with the correct precision. So when you're measuring-- and we'll talk about this next week in our lecture, about the different precision of glassware, you want to include all relevant significant figures. So if you're measuring something that has more than one decimal place, include all of the decimal places. So 5.2 milliliters of 8 molar nitric acid was added, not just 5 milliliters of added in-- if there's any specific way that you added things-- like when you guys added your aliquots, you did 0.25 milliliters at a time, you want to include that so that people don't add it all at once-- something like that. Or if you add something drop-wise, make sure that's included. And then you want to give brief observations about the color, texture, and state of matter of your product. So you can say, I formed 5 grams of a white powder-- something like that, just so that, again, when the reader's are doing the lab, if they get a white powder, they want to know is this correct? Yes. And then if there are any safety concerns that are relevant or unusual, those can also go in your procedure and observation section. So again, thinking about ferrocene, what are you going to write out the procedures of? What was the first thing that we did? I guess not even that you guys did. Cracking the cyclopentodiene. So even though you guys didn't do that necessarily yourselves, that was an important part of the procedure. So you should include cracking the cyclopentodiene monomer. AUDIENCE: I have a question. SARAH HEWETT: Yeah. AUDIENCE: Like with the examples where we draw the figures. So if we're drawing the chemical equation for the [INAUDIBLE] or drawing sublimation, do we just scan those into the lab report? SARAH HEWETT: Yeah, so if you're going to be drawing any pictures of glassware or chemical equations, you can handwrite them and scan them in, and insert them as pictures into your lab report if that's easier. You can also use, for chemical equations especially, ChemDraw if you have access to that on a lab computer. Or there's some free versions, like MarvinSketch or ChemDoodle that you can find online that will give you the actual chemical structures that you can draw. And then you can just copy and paste those into your lab report. And also, if you have ChemDraw, it has a glassware feature, where you can actually build different glassware setups. So you can build the distillation in there if you wanted do. But yeah, if you handwrite anything, like equations or pictures, you can scan those in and insert them as a picture. So once you crack the Cp, what was the next big part of the procedure. First thing you made. We'll just call it synthesis of ferrocene-- of ferrocene. So that would be, yeah, preparing the KOH. Preparing the iron chloride. Mixing them together. Shaking for who knows how long. And then your filtration and your isolation of the ferrocene. Then the next thing was the synthesis of acetylferrocene, which some of you have done, and some of you will do today. And then what are we doing next week, in the last day? TLC. The important parts of that are running the TLC, and also choosing your solvent. So you want to make sure that you include both of those things in there. And then what's the last thing we're going to do to purify the product? Column chromatography. So you'll have a bunch of different parts to the procedure for this lab, and for most of the labs that we do, especially since they're all multiple day labs. So you will have a lot of things to write about in the procedure. And so you want to keep those straight between your days. And this is where your lab notebook and the notes that you take in the lab are going to be super-important and helpful in writing up what is happening in this section of the lab. The way that you write the whole lab report, but especially the procedure and observation section, is in the third-person passive voice. And this feels awkward for a lot of people at first. But instead of writing something like, I added 5 milliliters of nitric acid to the copper, it took this long, and I used 6.2 molar nitric acid and copper shavings, you would write it in the passive voice. So, to a round bottom flask containing copper metal shavings was added 5 milliliters of nitric acid. The acid was added drop-wise over the course of 15 minutes. So there are no real actors in your lab report, except for the chemicals themselves. So the chemical was added. By who, we don't care. You want to write in the passive voice. And as an example, here is an article that was recently published in JACS, the Journal of the American Chemical Society. And you can see that this is how a procedural section is written for something that's going to be published. And one of the ways that you can do it-- you can either say in the sentences, like, 10 millimoles of 2,4-Dibromobutyryl chloride was added, or you can put the quantities in parentheses. And in this case, they've chosen to do it in millimolar. In your lab report, you can use whatever quantity you measured. So if you measured it out in grams or milliliters, then that's what you should write in your report here. So that's an example of thing-- and something to note. This didn't copy over well when I copied and pasted it. But you should definitely always make sure to superscript and subscript things as appropriate. Take the time and do it. Yeah, that should go without saying. And one of the handouts that I gave you is also another example of a procedural section that has been written for a lab that you guys are not going to do. But it's another example of how the language can go and what it looks like when it's all written. The next section is the results. So the results that you collected are going to be summarized in your results section, obviously. This is best done using tables or graphs if you can. And this is not the place to analyze your data. So you don't want to be making any comments about it, saying, oh, I got this terrible yield of 22% or whatever. You really want to write that anywhere. But here, you're just presenting your results. And then you will talk about them and what they mean in your discussion section. So what sort of results are you going to have for your ferrocene lab? And if you're going to put them in a table, what would our table look like? What are some good headings for the data that we will have from ferrocene? AUDIENCE: Yield? SARAH HEWETT: Yield. What units? AUDIENCE: Grams? SARAH HEWETT: Grams, sure. You can do grams, you can do milligrams, depending on how successful your synthesis was. AUDIENCE: The first column should be, like, name? SARAH HEWETT: Yeah, compound name. What other data can we talk about? All the way on the left. AUDIENCE: Melting point. SARAH HEWETT: Melting point, yeah. We'll throw that over here because it's small. AUDIENCE: Molecular weight? SARAH HEWETT: Molecular weight is not necessarily a result. So that would be something that you could include in your calculations when you're doing your theoretical yield calculation, something like that. AUDIENCE: RFs. SARAH HEWETT: RF. So you could include that in the table, but it may be smart to do a separate table for your RF values. But that definitely should be in there. Yeah. AUDIENCE: I mean, you could include qualitative-- like, appearance, color. SARAH HEWETT: Yeah. Color or appearance. So you can say it was light orange, dark orange, red. It was a powder, it was clumpy. You got big, giant crystals of it-- whatever you got. What other information are we going to get? Related to yield, but what's another way to report yield? AUDIENCE: Percent. SARAH HEWETT: Percent yield, yeah. Excellent. So this would be a really great table to include in your ferrocene report with all of this data in it. Then what compounds are we going to have all of this information for? AUDIENCE: Ferrocene. SARAH HEWETT: Ferrocene. What kind of ferrocene? AUDIENCE: [INAUDIBLE] crude ferrocene. SARAH HEWETT: Crude ferrocene. What? AUDIENCE: Purified. SARAH HEWETT: Purified ferrocene. And? AUDIENCE: Acetylferrocene. SARAH HEWETT: Acetylferrocene, both crude and pure of that as well, pre and post column? You may not have all of this data for all these compounds, but you should be pretty close. And if you made any diacetylferrocene, you can put that in here, too, if you have enough to collect off of your column. And you'll find out next week if you enough of that. So yeah, those are your results. Anything else that we're missing in terms of results for this lab? No, it looks pretty good. So if you wanted to insert a graph, which in this case, we don't really have any graphs necessarily that would go into your report. Yes? AUDIENCE: I was wondering, where does the calibration come from? SARAH HEWETT: What a great question. So you guys are making the calibration curve for your melting points. Where would you put that? We have one vote for calculations, one vote for appendix. Any thoughts? So the things that get inserted into your results section, or your calculation section, are things that are very directly related to the goals of the lab. So if you need something to get whatever data that you care about-- so like in the catylase that you guys are going to be doing, you'll need to make graphs in order to get some rate constant data. So those graphs are super-important to the goal of the lab. Is a melting point calibration curve very important to our stated goal of this lab? Not necessarily, but we need it in order to get the data that we care about. So that's something that can go in an appendix. And that would be an excellent spot for your melting point calibration curve, because just like anything else, if you put something in an appendix, you need to reference it in your lab. Because why would you include it anywhere if it doesn't matter for your lab? Maida? AUDIENCE: So would the procedure for that go under procedures, or would we not include that? SARAH HEWETT: The procedure for making the melting point calibration curve? That's a good question. Any thoughts? Put it in the appendix? Yeah, so again, that's something that can probably go in the appendix, because it's not super-important to your actual lab, but-- AUDIENCE: What about in the procedure section a list of every instrumentation we use, it is typically written in the synthesis section and then a list of different techniques. Can we put melting point determination in there? The machine's calibrated x, y, z. SARAH HEWETT: Yes, that's also a good way to do it. So there's a couple of ways. So one would be to put the procedure in the appendix with the melting point calibration curve, and have a note in your procedure saying, see appendix for calibration curve and the procedure for generating it. Or when you are making your procedure section, you can have different sections for all of the different things that we did. So you would have sections of the procedure for the synthesis pieces, and then sections of the procedure for the techniques that you use. And if you wanted to put a technique section for the melting point, then you could say melting point was determined this way, and then talk about how you made the calibration curve there. So there's a couple of ways to do it. As long as the information is there and referenced well, then that is acceptable So if you are planning to insert a graph into your lab report, if you want to put the calibration curve or any other graph that you make throughout the semester into your lab report, you will insert it as a figure. And the way that you reference your figures is that you insert the figure or the graph or whatever it may be. And then you need to put a caption, which goes underneath the figure or the graph. And even though this is a graphic, it's labeled as figure 1. And then you number your figures 1, 2, 3, 4, or 5, as many as you have throughout your lab report. And then you need some sort of description of what the figure is or what the graph is showing. And if it's a graph, then you need to make sure that the graph itself has a title and axes that are labeled with units. That goes without saying, and a legend if you need one. And then all of that information also gets reiterated in the caption. The caption goes below the graph, which is important, because if you're going to insert a table, then the tables also get inserted. However, they are called tables, and the caption goes above the table. So you want to make sure when you have your table that you have all of your columns with headings and with appropriate units, and if you choose a unit that gives you a reasonable number of digits in your data. And if something is getting out of hand, or if you have one measurement that's on a different scale than the others, use scientific notation. Or you can change the units for one column, but try to avoid that. So yeah, that's how you insert a table into your lab report. Calculations-- so any time that you present data that was not directly measured, you need to show how it was calculated with appropriate units. So when the data is presented you should show an equation-- so the general form of the equation that you're using, a sample calculation with one set of your data, and then the final answer. So if you're going to be doing a calculation repeatedly, like percent yield you're going to calculate percent yields for a whole bunch of different compounds. You just need to show the calculation once, and then just show the yield for the other three compounds that you're calculating it for. If there are lengthy calculations that you can do in an Excel spreadsheet, then you can include the Excel spreadsheet in an appendix, as long as in your report you have shown a sample calculation, and the equations that you're using to get all of the data in that Excel spreadsheet. If you have a lot of calculations, you can include them in an appendix, as long as the data is well-labeled, and the sample calculations and equations have been shown. And again, all of this should be in your report somewhere. And then if you need to add more in an appendix, you can if your report's getting really long. So the discussion-- this is where you finally get to talk about your data and what it means. So you will summarize your key results. Explain any difficulties or errors that led to erroneous results. So if you accidentally spilled some of your ferrocene solution, then you might talk about how that impacted your yield. Offer suggestions to improve the experiment. So one of them could be maybe change the glassware that you're using if you're spilling a lot of chemicals. Or if you have an idea for different chemicals that we could use that would be better for the similar procedure, that would be a good time to talk about it, or adjustments to the length of time that you do something. Anything that you can think of that may improve the lab, this would be a nice spot to put it. And then answer any questions that are posed in the lab manual. There are no questions in the lab manual for the ferrocene experiment. But you'll notice, if you look at the other labs throughout later in the semester, at the end of the lab, there are a set of discussion questions that relate to the procedures in the data that you will collect in the lab. Do not just answer those questions in a list. A lot of them are numbered. Don't go through and make your discussion a bulleted or numbered list of answers to these questions, and don't just write one sentence after the other. That's very obviously just answers to the questions. Your discussion section should flow nicely. This will be the longest section of your lab report, and it should be the one with the most thought put into it. So make it flow like a nice piece of writing. Your TAs have to read these. They will appreciate them much more if you write with good grammar, and in a way that is intelligent and easy to follow. The answer should tell a coherent story throughout all of your discussion. You can talk about sources of error that either came from you or random errors. And we'll talk about different types of error again next week. And then analyze your data in your errors. So your calculations should have already been done. So do not include more calculations in your discussion. If you need to calculate something, go back and do it in the results section. But now you want to analyze the data and talk about what it means. So you've reported your melting point. You've reported all of your yields. You've reported your RF values. What does it mean? What does it say about the success of the experiment? Go back to your intro and say, hey, this is what I said I was going to do. Did I do it? And here is my data to explain why. So what can we talk about in the ferrocene discussion? AUDIENCE: You get a sense how our percent yield isn't 100% because of errors, potentially because you didn't scrape all the ferrocene off of the culture dish, something like that? SARAH HEWETT: Yeah. Yeah, so you can talk about your percent yield. It's not going to be 100%. And why might that be? So different parts of the procedure, where did you lose product? Scraping it out of the round bottom, that was really hard. A lot of people were struggling to get all their acetylferrocene out of the round bottom yesterday, or scraping stuff off of the ferrocene when you sublimed, different pieces. So you can go back again-- and this is a good spot when your notebook is going to help you a lot. If you take good notes in the lab, then you'll know, oh, yeah. That's where my product went. What else can we talk about? AUDIENCE: After we do chromatography experiments we'll have a percentage of [INAUDIBLE] compounds and products. SARAH HEWETT: Yeah, so after you do your TLC, you'll have one way to tell how pure your final mixture was. Did you still have ferrocene left when you thought you only had made acetylferrocene? So amounts of compounds left over. So you'll have that information from TLC. And from your column, when you run your column, and you separate out your ferrocene and your acetylferrocene, you'll see how pure your product was. And you can talk about that and why you may not have had a completely pure product. What else? So what else is in our results chart that we have not discussed over here? AUDIENCE: Melting ranges. SARAH HEWETT: Melting point. And what does that tell us? AUDIENCE: Same thing-- purity. SARAH HEWETT: Same thing. You can get purity. So was your melting point too low or a wide range? What else can your melting point help you tell, to some extent? In our case, we're using it to determine the identity of our products, because we don't have a lot of really spectroscopic ways of characterizing this product. So we are going to use it to identify your products. So you can tell us how pure your product was, and then compare it to the literature to see what the identity is. And hopefully, your melting points of ferrocene and acetylferrocene are not the same. So you did, in fact have some evidence that you made a different compound. Anything else? AUDIENCE: Maybe explain the color and appearance [INAUDIBLE] SARAH HEWETT: Yeah. So you can, again, bring in some more of your results. Talk about the color and the appearance of things. So your ferrocene and your acetylferrocene are different colors. You can talk about why that might be, and how you can use that to identify your different compounds, especially on your TLC plate. So when you run your TLC, in your column, you'll be able to tell your compounds apart by color-- hopefully. So yeah, and then again, if you had any suggestions for how to improve the procedure, those can also go in your discussion. If you were doing something and said, oh, this would be much better if we did it this way, or the sublimation, I found this cool trick for it, please tell us. And perhaps your genius idea will help us improve the lab for future semesters of students. Then at the end, there's a conclusion. So you briefly summarize your results. This again is pretty similar to the abstract. It'll just be about a paragraph, maybe a little bit longer. A statement about whether you achieve the goals for the lab, then wrap up your discussion section and tie everything together. Based on the abstract and the conclusion, if people read those two parts, they should have a generally pretty good idea about what happened in the lab. And if they want details, then they can read the rest of it. So conclusion-- again, wrap it all up. And then once you're done with all of this, go back and write your abstract, because now we have all of the information that needs to be neatly summarized in our abstract. The very last thing that we need to talk about is references. So at the end of your report, you need to list all the sources that you use, but you also need to cite them in the text. And this should not be anything new. Do not use Wikipedia as a reference. You can cite the lab manual and the lectures that's a good idea. And then there's also a handout that I gave you as to the format of how to cite different commonly-referenced sources, like books, articles, things like that. The ACS Style Guide also has information about how to cite any type of reference that you could ever need to cite. The in-text citations, there are three ways that you can do them. So if you're planning to cite this article in your lab report for some reason, then you would have a sentence. And then the first way to do it is to include the author's name and then the year. You can also have a numbered list, and you superscript at the end of the sentence. Or the last way is to put the number of the reference in parentheses in italics at the end of the sentence. So up to you. All three ways are ACS-approved, whichever one you find the easiest or most familiar. Appendices, we talked about this a little bit. It's a really good way to include relevant information that doesn't fit well into the body of the lab report, or maybe isn't the most important thing to the goal that you're trying to achieve. They don't count towards your page limit. So if your lab report is getting long, and you can find things that would go in the appendix, that's not a bad thing. Don't put stuff that should be in the lab report in the appendix just for the sake of giving yourself extra space in the lab report. We will take points off for that. Appendices have a number and a title. So appendix 1, and then you would say what's in appendix 1. Refer to that in the text of the report like anything else. The format-- this is probably the most important thing that you guys care about. There's a 10 page limit, plus or minus 2 pages. So if yours is significantly shorter than 10 pages or significantly longer, then you will start to lose points. 10 pages should be the right amount of space to talk about all of the results in all of these labs. 1 and 1/2 line spacing in Word, one inch margins, 12 point Times New Roman font-- pretty standard stuff. And then print it out. If we want an electronic version, we will request it. But most of the grading is done by hand. So we print it out, and we will give you back the hard copy the following week. Ethics-- we've talked about this before already, but do your own work. Don't use a lab reports from prior students. Do not copy and paste anything that you did not write yourself. Cite your sources, and do not go looking for similar reports on the internet. Some of the labs that we do here are similar to labs they do other places. Some of them are wildly different, so you won't find anything, anyway. The TAs and instructors are here to help you succeed. So we're the ones who are grading your lab reports. So instead of going, looking up some random report from some other person at a different institution on the internet, come talk to us. We are the ones who know how we will be grading it, what we are looking for, and what you did specifically, so we can help you write your lab report the best way possible. Here is the point breakdown for how most of the lab reports are graded. You can see that the discussion and the results portion are weighted more heavily than the rest of it. In the ester lab, you will be identifying an unknown. And so that's only for one lab, which is why the range is on here. It varies from lab to lab based on how much time and effort you're going to be putting into each of the sections. Submission and grading-- so labs are due at the start of on the dates listed in the lab manual. There is a locked box outside of the stockroom in the lab, and that's where you will turn your lab in. Do not turn your lab into your mailbox or to my mailbox or to John's mailbox. It goes into the lock box, then the TAs will collect them. They will grade them, and they will be returned one week from when you turned it in. So if have a Monday, Wednesday lab, if you turn your lab in on Monday, you will be graded the following Monday. When you get it back on that following Monday, you have one week to dispute any points with your TA. So they'll give you back the lab report with their comments on it. And if you disagree with something, talk to you TA. Try to figure out why they graded it the way they did. If you guys can resolve whatever point conflict you think that you're having, if the TA made a mistake, if you made a mistake and didn't realize it, figure it out. If you can't figure it out, then you can submit your report to me, and I will regrade the entire thing for either more or less points, depending on how well you wrote your lab report. So the last resort is giving it to me. And then grades will be posted on Stellar one week after the reports are returned, once any point disputes have been resolved, so that you'll be able to keep track of your scores. Looking ahead, the final report is an oral report. It'll be a chalk talk, so no PowerPoints. You'll get a chalkboard and any handouts that you want to bring. It'll be you and your TAs, and you have to convince them that you understand the experiment and your data analysis. So this will be for the final report of the semester. So it's a long ways off, but I wanted to give you a heads up. Just something to be thinking about. It's the same information that's in a written report. It's just a different way of presenting it, and it should not be scary. You guys know what you're doing. And by that point, you'll definitely know what you're doing. And the TAs are, obviously, here to help you guys with anything that you need. And there will be a couple of class lectures later in the semester, where the TAs will give you beautiful examples of good oral reports and bad oral reports. So if you want to come see your TA's acting skills, put that on your calendar. Does anyone have any questions about anything that we have talked about today? Yeah. AUDIENCE: For the equations and figures that we draw [INAUDIBLE] lab report, or should we draw or scan them, and then hand in the scanned drawing? SARAH HEWETT: You should scan them in and put them in your lab report, and print it out all together. Try not to write extra notes on the end afterwards, yeah. We want to have everything printed so that it doesn't get confused with the TAs notes and people adding things after they've been graded. Yeah. AUDIENCE: So you talked about having office hours before having the labs turned in? SARAH HEWETT: Yes. AUDIENCE: Are those on Stellar? SARAH HEWETT: They will be. So yeah, there will be office hours before every lab report is turned in. And the TAs are going to-- they'll be posted on Stellar next week once we schedule it with all the TAs. Great.
MIT_5310_Laboratory_Chemistry_Fall_2019	8_Essential_Oils_Lecture_Part_1.txt	[SQUEAKING] [RUSTLING] [CLICKING] SARAH HEWETT: All right. Good afternoon. Today, we are going to start talking about a new lab, the Essential Oil lab. And if we look ahead a little bit in the semester, so we're still working on finishing up the Charles River lab. We have today, then we have day four on Wednesday and Thursday. And then next Monday and Tuesday will be day five of the Charles River lab, and that'll be your quiz day. And then after that, we're going to start a whole new set of labs. And the last three labs of the semester-- so there are five total labs-- we're going to rotate so not everybody is going to be doing the same lab at the same time. So each bay in each group with your TA, you'll be doing a different lab. So everybody will get a chance to do all three, but you'll just do them in a different order. So after the Charles River lab, the A prime 2 group, the closest to the middle of the lab, you'll be doing the essential oil lab. The center group will be doing the catalase lab, and then the group closest to the doors, A prime 4, will be doing the ester lab. And your TAs will help make sure that which lab you're supposed to do so you know which pre-lab to write up. And if you any questions, it corresponds to groups A, B, and C in the printed version of the lab manual, and I think the version on Steller has been corrected with the A prime notation for telling you which lab you're going to be doing when so you can keep track of what you need to write and what pre-labs you need to do. And then if we take a moment and look back a little bit at what we did for the Charles River, I went on to the EPA website, and they have a buoy outside the Museum of Science just down the river a little ways where they keep track of a whole bunch of different metrics in the water. And you can go check out what the buoy has recorded. And so if you're interested, you can go to this website. And they have, also, the Massachusetts standards that you can compare these numbers to for some of them anyway. And so the most recent reading that they had was from Monday, September 23, which was last week. And you can see that the pH was around eight and a half which is similar to what you guys measured. The dissolved oxygen that they had was around 10 and 1/2, which is a little bit higher than what you guys had, but again, it changes we know based on the temperature and the day. And then this pink line that I added down here at the bottom is the phycocyanin which is indicative of the cyanobacteria that you heard about in lecture before. And so you can see it was it peaked here in July and the beginning of August when we had the cyanobacteria bloom. So something that you can check out if you want to when you're writing up your lab report if you want some more information about what metrics they look at and keep track of in the Charles River. And now, talking about our next lab, essential oils. So the word essential has a few different definitions depending on how you're using it. And some people will say it's essential, like, it's the most important thing. The definition of essential that we mean when we are talking about an essential oil is that it is a fundamental or central to the nature of something or someone, like the essence of a thing. And so the essential oils come from plants, typically. And so we are talking about the essence of the plant or something that comes from that plant specifically. A little bit of history of essential oils. Their recorded use is far back in history as ancient Egypt. The Egyptians were big into perfumes and cosmetics and all of that. And they have records of pressing plants to get the oils out to use in different perfumes for the different scents. And also, in the days of the plague in the medieval era, the doctors would wear these masks full of different plants. And they thought that breathing through the plants and the oils would help protect them from disease. And if you look around now at essential oils, you can find them almost anywhere. But you may come across something called thieves' oil, which is a blend of the oils from those different plants. And the story behind that, which may or may not be a legend, is that there during the plague, everybody would throw all their corpses out into the street and then there would be people who would go and loot the corpses to steal what they could. And there was a group of thieves who was running around stealing stuff off of all these dead bodies but they never got sick. And rumor has it that they concocted this oil, and they would wear that and put that on themselves and it prevented the plague. And so that's what the story of the thieves' oil may or may not be true. So today, if you look online and you do a search for essential oils, you can find a million different places to buy them. You can find all sorts of information, some true some not, about what essential oils do. So you may see something like this that has different types of essential oils, different plants that they come from, and all of the things that they are rumored to treat. You can buy the essential oil of almost any plant that you like, depending on where you look. And not all of this is just hearsay. There are people that are actually doing different studies, especially in the veterinary medicine world, of using different essential oils to treat different fungal infections or bacterial infections. A lot of these have antibiotic properties, and they can disrupt some biofilms depending on the different properties which isn't super surprising since a lot of these are just hydrocarbons that you could also synthesize and are similar in structure to some of the drugs and synthetic products that we make to do these same things. So essential oils, where do they come from? So you ... how do you go from something that looks like a plant from the garden to a little vial of oil? And the ratio of how much plant you need to get a few milliliters of oil is very, very large. So it's not the most efficient process. But the way that it is most commonly done commercially now is through steam distillation. So you can grind up your plant material, chop it up a little bit to increase the surface area. You heat up water, put steam through the material. It helps volatilize the oils. And then the steam and the oils co-distill. You can condense it back down. And then you'll get a mixture of this water with all of the water soluble parts of the plant and then your essential oils, and you can separate them out. And the reason that you can separate them out is due to their structure. So most essential oils are made up of isoprene units. And so that's the structure of an isoprene. It has five carbons and eight hydrogens. And then when you stick them together, you get a class of molecules called terpenes. And so a terpene is more than one isoprene unit. So the way that you name these things is that if you have two isoprene units, that's the smallest terpene you can have, so it's called the monoterpene. Then sesquiterpene, diterpene is four because it has two of the monoterpenes. Triterpene and tetraterpene is when you have eight. So if we look at some of the molecules that you may know from everyday life, does anyone know what this is? So that's vitamin A. If you look at the structure of it, we can try and find all of the isoprene units, so these five carbon units. So if you start at the top there is one there. And we have another one, two, three, four, five there. And then you can keep going down the chain. So how many isoprene units do we have here? We have one, two, three, four. So this would be a diterpene. And then does anyone know what this molecule is? So that's menthol use in minty flavorings. And this has two isoprene units and then this hydroxy group. So you can have these terpene structures that have the isoprene units and then they also can have different functional groups attached. A lot of times it'll be a hydroxyl group or a carbonyl group. And then this molecule, which you also may have heard of, is camphor. So that's used in lotions a lot of times to treat irritation. And this one's a little bit tricky, but you can find the isoprene unit. So there's one there and then one there. Oh, other way. So those are some common terpenes that are found in essential oils that you may or may not have seen in other contexts. The structure that we care about, in this particular lab-- yes, Jesse. STUDENT: I'm a little bit confused. So on the slide said five carbon and eight hydrogens? SARAH HEWETT: Yes. STUDENT: So for menthol, for instance, there's five carbons and more than eight hydrogens. Right? SARAH HEWETT: Yes, in this case they would. STUDENT: So does it require a double bond in order for it to be called-- classified as an isoprene? SARAH HEWETT: No. I was also kind of curious about that, and I personally didn't find a good answer on the internet. But when I was looking through the literature and stuff, menthol was referred to as a terpene. So I don't know, if maybe once they get combined together with the double bonds that it's not as strict, or once you start adding extra groups. I'm not sure. That's a good question, and I can get back to you on that and how they actually name and classify these things. Because, yeah, in some of the cases, the double bonds go away, and it doesn't have quite the right ratio. So in our lab, the essential oil component that we are going to be looking at is carvone. And there are two types of carvone. So carvone is a major component of spearmint oil and is also a major component of carraway oil. And those are two very different things, and if you've smelled either of them, then that they smell different, they taste different. And the reason for that is because we have a chiral center down at the bottom. So there are two different possible isomers of this molecule and they have different properties, some properties are different. So we'll need to take a moment and look at chiral centers. So a chiral center occurs when four different substituents are attached to one carbon center. And you have probably talked about this in your organic chemistry class or in your other chemistry courses. So as a quick refresher to determine, they are labeled the R versus S. And to determine whether it's an R or an S stereocenter, you go through and you look at each group that's attached to the carbon, and then you assign priority to each group. And this is typically done most straightforward is through atomic mass. So you look at the atoms that are attached to the carbon center. And then the highest atomic mass has the highest priority. The lowest has the lowest priority. And if you have a double bond, it counts as two bonds the atom counts twice. So if you have longer chains and they look similar at the first point, then you keep going down the chain until the first point of difference and then you can help assign priority. So if we look at our carvone molecule, usually, if your stereocenter has a hydrogen, that's pretty much always going to be your lowest priority group. So I've drawn this particular isomer with the hydrogen pointing away from us so that we can more easily determine R versus S. So can anyone help assign the priority of these three groups? Does anyone know what the highest priority would be? Alec. STUDENT: It would be the substituent towards the end. SARAH HEWETT: Yep. Why? STUDENT: Because it's attached to a carbon that is secondary. It's attached to two more carbons. SARAH HEWETT: Yes. STUDENT: And a double bond. SARAH HEWETT: Yeah, no, you're saying it right. So this one's attached to two carbons and one of them being a double bonds so that counts kind of twice. And these carbons are just attached to two hydrogens each, so this has an overall higher atomic mass, so this is going to be our highest priority. Then what? Pointing out this way. So then you go to this carbon, and this one's double bonded to a carbon. But this one's double bonded to an oxygen so that has higher priority and that just leaves our final group. So does this go counterclockwise or clockwise? Counterclockwise? So R or S? S. So the way that chiral molecules work is if you take the mirror image, then you get the opposite configuration. So if this is our S, if we flip these two substituents on our chiral center, then we get the R. Or if you prefer to look at it as the actual mirror image, if you kind of ignore this, then this molecule and this molecule are the mirror image of each other. So even though this group is pointing forward in both, the oxygen and the double bond have flip sides, so these two are mirror images. So this is also R. And a big part of organic chemistry and figuring these things out is being able to manipulate the molecules spatially in your head. A lot of times it's easier with models. But does that makes sense how we get those? Excellent. So we can talk about different cultural centers, and we can also talk about chiral molecules as a quick review. So if you have chiral centers in your molecule, then you'll have, potentially, a chiral molecule. So a molecule's chiral if it is not superimposable on its mirror image. And then within that, we have two other ways to name these stereoisomers. One is in enantiomer which is a pair of molecules that are mirror images that are not superimposable on each other. So that would be like this pair of molecules. So these are enantiomers. They are mirror images. And if you try to flip this around and stick it on this one, you'll see that if you flip this over so that the chlorine and the hydroxyl group are on the same side, they'll be pointing back and these are not superimposable. Same thing with these two. These are enantiomers. They are mirror images, and they are not superimposable on each other. But you can see that all four of these molecules are related and that they are isomers and that they have the same atoms in a very similar configuration. The only thing that differs is the stereochemistry at each of these chiral centers. And so these molecules, say, are related to each other and that they are not mirror images, but they are also not superimposable on each other. And so these are called diastole diastereomers. These two have the same relationship. These are diastereomers. So are these two and these two. So that's the terminology that we are going to be using when we talk about different molecules that have different numbers of chiral centers. So if you have more than one chiral center, you can get all of these different relationships. This becomes important in biological systems. So if you have a protein, your amino acids in your protein are chiral. So you end up with protein the protein structure is determined by the chirality of these amino acids. So you can end up with a chiral surface that has a bunch of chiral and individual molecules in it. And then if you have a substrate for your enzyme that is also chiral and you have different enantiomers, one will fit and one will not. And you can also look at it if you have a cultural center that has three different things to it and a receptor that has three different locations, then there is only one orientation that will match up properly. So if you start rearranging those substituents around that carbon center, then you won't be able to line up with your target properly. And this comes into play in your eyes and in your smell and in your taste. So these carvone isomers, these enantiomers, one of them taste like mint and the other one tastes like carraway . And most people can tell the difference. There is about 10% of the population that cannot tell the difference between these two isomers. So when you get your oil in lab, if you smell yours and then if you smell your neighbor's, hopefully you should be able to smell a difference. But it'll be interesting to see if anybody can or cannot tell the difference between these two chemicals. One of the ways that this chiral recognition and this chirality in biology has played out is in the case of thalidomide, which again, is something that you may have heard of in your other chemistry courses. So this is the structure of thalidomide. And there is a chiral center. Where's the chiral center in thalidomide? Right there. You be a little more specific. To the right of the N, yes. So here's a chiral center, so you can have an R and S versions of thalidomide. And as it turns out, let's see, I don't want to say this wrong. The r version is used to treat nausea and is used uses a sleeping aid. And the S version causes birth defects. And so this drug was given in the '70s and the '80s to a lot of women who had morning sickness. And they took it while they were pregnant and their children ended up with a lot of birth defects because they were given both enantiomers of this drug. And even if they had been given enantiomerically pure thalidomide, your body has enzymes and you can do reactions that will convert in between the stereoisomers. So there is no safe way to give thalidomide to a pregnant woman. In a less traumatic case, ibuprofen, this is the structure of ibuprofen. Where's our chiral center? STUDENT: That one. SARAH HEWETT: That one? Excellent. So you can have R and S versions of ibuprofen as well, and only the S version of this drug works in your body as a pain reliever. And it inhibits certain chemical reactions in that pathway in your body. And biology majors, I'm sure you know way more about this than I do. So the S version works in the R version has no biological activity, at least in terms of the target of this drug, which is to treat pain and inflammation. But it's given as a racemic mixture because the second enantiomer does not have any negative effects that we know about. And your body can actually convert between the two. So if you're given all of the S form, which they have done to people and that actually has more of a benefit to them, but it'll convert some of it into the R form which is useless anyway. So if we go back to our molecule carvone, we can look at the two types of carvone. And these are the two isomers, so they have the same molecular weight, same boiling point but different physical property in how they smell and how they taste. So carvone is what we care about, but essential oils are not pure substances. So if we give you the spearmint oil and we give you the carraway oil, then they'll have more in it than just the carvone that we care about. So the major impurity that you guys are going to see in both of these essential oils is called limonene. And that is the structure of limonene. It is also chiral. So it has a chiral center down here at the bottom. And-- oh, my notes didn't show up. Bummer. And so one of the isomers of this, I believe it's the R smells like oranges and the S smells like lemons. So it's found in high quantities in citrus plants. It's a monoterpene. It has two of these isoprene units. And in our case, it's going to be an impurity. So we are going to try and separate the carvone in our essential oil from the limonene in our essential oil. So if we look at these two compounds side by side, how are we going to separate them? Alec. STUDENT: Carvone has an oxygen so we're going to pull it in limonene? SARAH HEWETT: Yeah. So one way you could think about separating these is by they are very similar in structure, but the only major difference here is this oxygen, which makes the carvone slightly more polar. So you could think about using some sort of chromatographic technique, maybe, like we did before to separate them based on polarity. So that's one way we could do it. What else is different about them? STUDENT: Boiling point. SARAH HEWETT: The boiling point. And so using the polarity is a little bit more complicated. But if we want to use straightforward basic gen chem principles, then we can separate them by our boiling point using distillation which is a technique that you all probably heard of. And I have the distillation apparatus set up here. So this distillation apparatus is a short path simple distillation. So the way distillation works is if you have either a mixture of two liquids that have different boiling points or if you have a liquid that has some nonvolatile impurities in it, you can put your mixture in here, heat it up, and then re condense the vapor and then you can collect, hopefully, your purified substance at the end of it. So if we have this mixture of two liquids, then we need to talk about different laws that govern how two liquids and how to vapors interact with each other. So the first thing that we want to talk about is Raoult's law. And what Raoult's law says is that the partial pressure of a substance is equal to the mole fraction of that substance, which is the x, times the vapor pressure of the pure substance. So if we have a mixture of two things, and we want to figure out what the vapor pressure of one of them is above the mixture, and we look at the mole fraction within the mixture. And the mole fraction is just the moles of the component that we care about over the total moles in your mixture. So if you have two things, you add to the total number of moles, divide that by the number of moles of the thing that you care about. And then you can look up the vapor pressure of what the pure substance would be, and then you can get the vapor pressure of that substance above a mixture. And then Dalton's law of partial pressure says that the total pressure of a gas is going to be equal to the sum of the partial pressures. So if you can figure out your partial pressures using Raoult's law, then if you have a mixture of pentane and hexane-- and this was taken from your textbook if you want to look this up. If you read this, it's in figure 12.3. Chapter 12 is all about distillation. So that's a good resource for this lab in particular. But if you have pure pentane, then your total pressure is going to be just the pressure of pentane. And this is your pressure of pentane. And then you can see that if you add up these two lines, then you'll get the total equaling your blue line, which is your total pressure at various different mole fractions of each of these substances. So the way that it plays out for us, if we're going to be heating up a mixture and at-- hello-- and a different mole fractions, then we'll have different amounts of each vapor in our total vapor pressure, then we need to think about that when we are doing our distillation. And so you can make a temperature composition diagram. And this is a little bit confusing to look at it first, or at least it was for me. So we can go through how this plays out in real life. So if you have a mixture of hexane and pentane-- this is just a theoretical situation. And the boiling points of hexane are 68 degrees and pentane boils at 36 degrees. And we wanted to get pure pentane which is our lower boiling point thing. So if we start out with a mixture that's about 75% hexane and we vaporize it, then the boiling point of that liquid will be closer to the boiling point of hexane because there's more hexane in it. If we cool that vapor down so it's at the same temperature, so heat it up to 65, cool it to a vapor at 65, and then re-condense it to a liquid phase, now our mole fraction of hexane is about half. So we've purified our vapor. If we take a starting mixture that has about half and half hexane and pentane and we heat that up to its boiling point, which is now going to be lower because it has a higher fraction of pentane in it, if we cool it down at the same temperature and then re-condense it to the liquid phase, now our mixture has about a little less than 0.4 of our more fraction of hexane. And then if we heat that back up and vaporize it, cool it back down, now we have even less hexane. Heat it up, cool it down, now we are getting very close to pure pentane with no hexane in it. So we get very close to a mole fraction of zero for a hexane, and we get closer to the actual boiling point of pure pentane. So if you look at this diagram, then how many of those heating and cooling and re-vaporization cycles did we have to go through to get down to a vapor that is pure in pentane? So in this case, it's about five cycles of that. And depending on the difference in boiling point of your two liquids that you're trying to separate, it may take even more cycles to get to your pure compound that you care about. And if the boiling points are greater in difference, then it'll take fewer cycles to get to your pure liquid phase. So if we have these two liquids that we were trying to separate and we want to get down to a pure fractions of limonene in carvone and we want to separate them and make them pure, how are we going to do that? A lot of distillations. Or we can do what's called a fractional distillation. So I told you this before. This one is a simple distillation, and you can see that there is not a lot of room in here for the vapor to vaporize and then re-condense before you collect it in your collection vessels over here. If you provide more surface area, then the vapor has more chances to come into contact with the cooler glass. It'll re-condense into the liquid phase. And then if you're heating this, it'll drip down, it'll be reheated by the hot vapor coming up, and so then you can have multiple of these heating and cooling cycles before you start collecting your final product. And so this is a fractionating column or a Vigreux column. And you can see, hopefully maybe, that it is not just straight glass, that it has all of these little divots in it and it has a lot of kind of spikes going into the middle that provide a lot of surface area for this vapor to hit to cool and to reheat. So this provides a much more efficient separation than just the simple distillation when you can only go through a couple of heating and cooling cycles before you collect it. So this will help us to get a more pure product. And it is very helpful for when the two things that you're trying to separate have boiling points that are relatively close to each other, being like less than 50 or 60 degrees apart. So there are some things to consider if you're going to use distillation as a technique anyway. And so one of them is the boiling point of liquids that you're trying to separate. So how hot does this thing need to get? Is it a feasible temperature for you to reach in the lab? One of them is how pure your fractions need to be. So if you don't really care about the purity of your fractions, then you can do a quick simple distillation, collect your product, call it a day. And then do your compounds decompose if you heat them too high? And in our case, yes, they do. So if we heat our compounds too high, so they have a pretty high boiling point if you remember back or if you look back in your slides. So we try to hit them aggressively to that boiling point, then our products may decompose before we can collect them. So we have to figure out a way to make things boil at a lower temperature. So if we think about our definition of boiling, it is the temperature at which the vapor pressure of a liquid equals the pressure above the liquid. So there are two ways that if we need to lower our boiling points that we don't have to heat it up to over 200 degrees, then how do we lower the boiling point? We can either increase the vapor pressure of the liquid. So usually, we increase the pressure of the liquid by just heating it. You heat the molecules up, they become into the gas phase, and you increase the pressure within the liquid itself. Or you can reduce the pressure above the solution. So if we reduce the pressure above the solution, then we don't have to heat it as much in order for those pressures to be equal. So that is what we're going to do in class. We're going to use both of these. We're going to have to heat it, and we're going to reduce the vapor pressure in order to make the vapor pressure a reasonable temperature for us to get to in the lab. And the way that we're going to be doing this is with a vacuum distillation. So this distillation setup is identical to the one that you will be setting up in the lab. And this is kind of nice because the glassware is all sealed together. So your column, your condenser, and your distilling head over here have all been made as one piece you have fewer joints where you could lose your vacuum. So when you get this, you're going to get it as a kit from the stockroom, and it will have this one big piece of glassware in it, so be very careful when you are opening and taking things out of this kit because this is a large piece of glass where it should be wrapped in bubble wrap in most cases, but we don't want to break it because it is expensive and a specialty piece of equipment. So if we go through this and talk about different pieces, they're all very important. So this is where your mixture will go. And if you look at the picture of an actual set up in lab, you'll have your stirring plate. So whenever you heat something you want to stir it so that it helps the bubbles to form because you don't want your solution to get superheated and then all start boiling all at one time because it'll shoot up into your column. And then if you flood your column with your mixture, then there aren't any surfaces for the vaporization cycles to happen, and so you will get very inefficient separation of your two liquids. So you want to make sure that you have stirring and you don't heat it too quickly so that you don't flood your column with the bubbles and that you give it a chance to just have the vapor go up your fractionating column. So you'll have your heating mantle, your stirring plate, and then you'll have your mixture in here. This is your fractionating column. And then you'll have your thermometer. And our thermometers are all set up to have a ground glass joint, so they'll just sit right in the top here. And you want to make sure that the thermometer bulb is right in the path of where your vapor is traveling so that you can monitor the temperature of the vapor that you're collecting so you know what the temperature is. And you can use it to help identify which fraction is which. So if you know the temperature of the vapor that you're collecting, then you can compare that to the boiling point you know what you're collecting. Then you'll have your condenser, and this is going to be filled with cold water. So we have cold water supplies from the hood. You will attach the water in at the bottom and out at the top. Your TAs will go over this, too, but this is very important because you want this whole thing to be full of water. So if you put the water in the top, then gravity will kind of do this thing, you can see it's on an angle. So the gravity will come, it'll just go straight out the bottom, and then this whole top part will be full of air. That's not helpful. So we can use gravity to help us here. If you put the water in the bottom, it'll fill up the whole condenser and then go out the top. And this could be, possibly, the most important thing I will tell you today. This little metal piece is very important to the success of your lab. Does anyone know what this does? So this piece goes when you attach your tubing from your waterlines, you want to have one of these little metal guys. And it'll wrap around your tubing and your glassware, and then it'll clip together to secure your glassware to your tubing. And this is important because once you turn the water on, the water is at a pretty decently high pressure. And if you are not paying attention, the tubing does not stay on these little adapters very well. Your tubing will pop off, and then you have a faucet of water coming through a rubber hose. I don't know if you've ever seen those like wild inflatable tube bend, yeah, like that's what's going to happen in your hood. And so your lab partner will be upset with you. You'll be upset put yourself and everything will get very wet. And there are no drains in the hoods, so it's a big mess to clean up. So before you turn your water on, make sure that all of your tubing is clamped. It's my public service announcement for the lab. And your TAs, I'm sure, will also be checking this very carefully. They know what happens. So then, we have our condenser, and then we will have this piece here. And you can see that there's another spout out here. And this connects to your vacuum line. So you know those manifolds that you used with the nitrogen lines in the ferrozine lab? Yeah, so one end is connected to the nitrogen lines and the other end is connected to a vacuum pump. So you're going to use the vacuum side of those this time. And so there's a pressure gauge on there that will tell you what the pressure is once you turn the vacuum on in the system. It's a digital one, so you can just read it. It gives you the output value in torr. And we're going to get this down to close to one torr or below for this particular experiment. So you will make sure that your vacuum line is connected here. You'll turn your vacuum on. And then if we're going to make sure this whole system is under vacuum and you want to be able to collect different fractions so your things will boil at different temperatures, so you can't be swapping your collection vessel in and out if your whole system is under vacuum. So we use what's called a cow adapter. So this is a cow thing because it looks like some cow udders. And you can attach four different flasks to the bottom of it. And the ones that you'll see in lab will have a little spout here. And so you can see which flask your spout is pointing towards when you are using it. So if you want, you can rotate this so that you collect your different fractions in different files or in different flasks. And you want to make sure that when you do all of this that all of your joints are nice and tightly clamped. So you want to put Keck clips, these little yellow guys, on all of the joints that you attach to each other. And then you're going to use vacuum grease, and your TAs will show you how to do that. You just need a little bit of grease, but you want to make sure that the grease is there to provide a good seal and so that you can undo your glassware after you've put it under vacuum. So that is the case. And then the last thing that you need to know is the ice bath. So once you have heated up your mixture, you've re-condensed your vapor, and you're collecting hopefully another liquid over here, we have this under a reduced pressure, which means that the boiling point has now been lowered. So you don't want what you've already collected as pure product to re-vaporize and go back into your system. And you don't want these to kind of evaporate and then re-condense into each other and contaminate the fractions that you've worked so hard to collect. So you're going to have to kind of engineer your ice bath to only cool one flask at a time, especially the limonene fraction. That one tends to be very volatile. So your TAs, again, will tell you about this when you get to lab, but you want to make sure that you are cooling your fractions but not cooling too many of them so that you don't get spillage into different vessels. And so that will be how you collect your limonene and your carvone. And hopefully, you should be able to separate both of those components from your essential oil mixture that you're given. So some of you guys will start with the carraway oil, some of you will start with the spearmint oil, and then you will both end up with limonene and carvone. It will just depend on which isomer of the carvone that you have. So when we were doing this, if we know the boiling point of the limonene and the carvone at room temperature, then we need to be able to figure out what the boiling point is going to be under a vacuum. So you can use what's called a nomograph. And there's one of these in your lab manual, and I've reprinted it here just to give an example of how you use one of these. And so the way that you can use this to calculate your corrected boiling point at lower pressure is to figure out what the pressure is that you are doing your experiment at. So you can read, like I said, the pressure off of the pressure gauges in your vacuum lines. And let's say, for example, that you have gotten your experiment down to about one torr. So you put it out there. And then that this is your boiling point at 760 torr, which is atmospheric pressure. You know that the boiling point of whatever you're starting with is a little bit over 300. Then you put a point there. And then you draw a straight line through those points that intersects the observed boiling point line. Ta-da! And then you can find out that your boiling point at reduced pressure would be somewhere around 120 degrees. So you can see that by reducing the pressure down by significantly, that we can also significantly reduce the boiling point so we don't have to heat it up as much. And we can reasonably get to these temperatures in the lab. Any questions about how to use that? It's pretty straightforward. So you can use that to predict the temperatures that you will collect your limonene and your carvone fractions so you know when to be looking on your thermometer to switch your fractions and when you should be collecting which ones. And it'll help you identify what you've collected. So that is all of day one of the lab. If we made it through day one of the four day lab. And so then how will we know if it worked? Smell it. So yeah, so part of the way that you can tell is you can smell it. Waft it gently, don't ever stick your nose-- so whenever you're trying to smell these, even though that these are chemicals that people eat, be gentle. You guys know and your TAs can show you if you're unsure, but don't ever stick your nose straight into a vial of any chemical. So yeah, we can check by smell. And there are a whole host of other ways that we are going to tell whether you successfully separated your two components of your mixture. And I will leave you with that, and we will talk about it on Thursday all of the different ways you can determine your success. Are there any questions about anything from essential oils today? Anything else? Yeah. STUDENT: Do we make the essential oil in the labs? No. We have already gotten it from the plant, so you don't have to do the steam distillation part. We will hand you the oil, and then you will just separate it into its components. All right. See you on Thursday.
MIT_5310_Laboratory_Chemistry_Fall_2019	12_Catalase_Acid_Part_2.txt	[SQUEAKING] [RUSTLING] [CLICKING] SARAH HEWETT: Today, we are going to talk about the second part of the catalase lab. So, in the first part of the catalase, we had catalase and hydrogen peroxide. And we were measuring the rate of the decomposition of hydrogen peroxide as catalyzed by the catalase enzyme. And we were doing that by measuring the pressure of oxygen. And, for the people who are currently doing the catalase lab, you've already done part one. And, for everybody else, you'll get to experience that coming up in the next lab or two. And then, in part two of the catalase lab, we are going to look at quantifying the amount of catalase that we have in a sample and then looking at the iron centers in the catalase and trying to quantify those as well. So we are going to go back to the beginning and talk a little bit more about proteins and protein structure. So, if you have taken a biology course at any point in your life, then this will probably be review. But, just so that we're all on the same page, we want to go back and say that the building blocks of proteins are amino acids. And this is the general structure of an amino acid. And, if you change this R group here to any one of these R groups over in this table, then you can get all of the different amino acids that are naturally produced in nature. And there are 20 amino acids that occur in nature. And they vary by these R groups. And, depending on the R group, there are different classes of amino acids that you can have. So there are the nonpolar ones where you have an alkyl or an aromatic side chain. You can have polar side groups where you have a hydroxyl group or a thiol or some amine groups. And then you can have acidic or basic groups that are electrically charged. So, depending on the pH of the solution, they'll either be protonated or not. And then you can have positive and negative charges. And all of those contribute to the protein structure and the properties of the protein, what it can do. And just a review of terminology, so proteins are made of chains of amino acids. A peptide is two or more amino acids stuck together. A polypeptide is when you get 10 or more amino acids stuck together. And then, if you have beyond that, once it gets to longer and longer chains of amino acids and they start folding up and having specific functions, that's when it becomes a protein. So, if you hear those terms, that's what we're talking about. So the first-- the most basic structure that you can have in a protein is the primary structure. And that is just the sequence of amino acids. So you have this long chain of amino acids. You stick them together. And that is the primary structure. So, if this is our little peptide chain here, we have alanine, threonine, tyrosine, and valine. And those are from these side groups is how you know what amino acid it is. And then the bond in between the amino acids here where your carbonyl group of one amino acid bonds to the amine group of another amino acid, that is your peptide bond. And so you can get chains of these, and the primary structure again is just the list of amino acids in a line. That's about as simple as it gets. The secondary structure is how the amino acids interact with one another to form 3D structures within the polypeptide chain. So, if you have two chains of amino acids or if you have one that's folded onto itself, it can form hydrogen bonds between these oxygens of the carbonyls and the hydrogens that are attached to the nitrogens in the protein backbone. And you can get these beta sheets that are kind of pleated if you look at them in actual 3D space. And you can have one long chain that bonds to itself in the similar fashion with the hydrogen bonding. And you can get alpha helices. And it creates a helical shape within the protein backbone. And these are the main types of secondary structures that you can get. There are other ways that the protein can interact with itself and form different structures, but these are the major two. Structures are held together using hydrogen bonds. And then you can get tertiary structure. So there are many different ways that proteins are represented in graphical form. So you can have-- you've seen in our past lecture with the catalase, you can have a space-filling model where all of it's kind of like the ball and stick where it just looks like one giant blob. And that can give you a sense of the overall shape of the protein. You can also have line structures where it's kind of like the line structure that you would draw in organic chemistry where it shows all of the different side chains in the backbone. And then you have these ribbon structures where you can see sort of the alpha helices and maybe some beta sheets over here. And it shows some different features of the structure of a protein. But the tertiary structure is how all of the elements of the secondary structure interact to form the overall shape of the protein. And it can be formed by various interactions. And so, while the secondary structure is mostly formed by interactions between the backbone functional groups, the, tertiary structure comes from the interactions between the side chains. So you can have these hydrophobic interactions if you have alkyl or aromatic side chains. So, if your protein is in a cell, then it is in a mostly aqueous environment. And aqueous environments are polar. And so these nonpolar groups will tend to coagulate together. You can have disulfide bonds. So, if you have the protein side chains that have sulfur groups, then they can make covalent bonds between the sulfurs. You can have hydrogen bonding. Again, those different side chains have again hydrogens that are attached to nitrogens and oxygens and carbonyl groups that can form hydrogen bonds. And then those electrically charged side chains can form salt bridges. So, if you have a positively charged and a negatively charged amino acid near each other, then they can have an ionic interaction like that. Interactions with the solvent also play a role. And this is what holds the protein together in its functional shape. And then, lastly, we have our quaternary structure. And this is formed by the interaction of multiple subunits coming together to make a larger protein. So this is a picture of catalase. And you can see each of the subunits of the catalase is a different color. So catalase has four different subunits. So these four subunits all have their own secondary and tertiary structure. They're identical. And then they come together to make the overall catalase protein. Not all proteins have quaternary structure. Some just have normal folding and secondary and tertiary structure. And the quaternary structures are typically held together by dispersion forces and hydrogen bonding between the subunits. So it's not usually a covalent interaction, but it is strong enough to hold these subunits together into the correct shape for the protein to function. Another key piece of protein structure are prosthetic groups. And these are groups that are not made out of amino acids. So they are not peptides, but they are very important for protein function. And some examples are iron-sulfur clusters. So these are some 3D representations of what an iron-sulfur cluster would look like where your iron centers are red, and the sulfur are these yellow balls. So you can have different numbers of irons and sulfurs bonded together. And these play key roles in photosynthesis and in metabolism. So they're really good at electron transport. So, in the electron transport chain in your cellular metabolism or in photosynthesis when you have to transport electrons in order to make energy, those iron-sulfur clusters, that is where they are typically found in nature. And another really common prosthetic group is the heme group, which you may recognize from hemoglobin. It is used in oxygen binding and transport. So it binds to the oxygen and carries it through your blood. And it can also be used in oxygen reactions or oxygen activation, which is what we're going to talk about today. Other types of prosthetic groups, you can have lipids or sugars that are bound to proteins that help with protein recognition and things like that, but metals and metals centers are the most common that are used. So, if we want to talk a little bit more about the heme group is what we're going to focus on, the heme group is based off of this porphyrin structure. And so this is a porphyrin. It is made up of different pyrrole rings that are bridged together. And, if you look at this shape, there's a nice hole in the center, which is perfect for inserting a metal center. And pyrroles are found-- or porphyrins are found in many different contexts. So you can find them in hemes. Obviously, we've said that already. So, if you put an iron center in the middle of that and you can add different functional groups to the outside of the pyrrole, then you can make a heme. In chlorophyll, it has a magnesium ion in the center of it. Enzymes have these to hold a whole bunch of different metal centers or even to not hold any metal centers, just the very common organic group. The organic chemists said, wow, these enzymes use all of these porphyrin groups, and it does some really interesting redox chemistry. So we can make these in the lab. So they have made synthetic versions of porphyrins with manganese, iron, and cobalt that catalyze a bunch of reactions in the lab, not necessarily in nature. And they're also found in petroleum complexed with vanadium and nickel. And one of the ways that they're used in the petroleum industry is to fingerprint petroleum. So, by analyzing the composition of the porphyrin complexes in the petroleum, they can detect the source of oil spills. They use it in geochemistry and forensics and things like that. So now, if we look back at our heme molecule, you can see that all of the hemes contain this porphyrin structure. And then you can add different groups around the outside, and that will change the structure. And that will change the function and change the way that it is able to bind to different proteins. So some of the hemes are just kind of stuck and held together with non-covalent interactions. And some hemes can actually be covalently bound to proteins, depending on how they are functionalized. And, like we said, they're good for oxygen binding, oxygen transport, and oxygen activation. And one of the interesting things that I found was the role of hemes in Impossible meat. So have you guys heard of the Impossible meat or the Impossible Burgers, the Impossible Whopper? Has anybody tried it? Yeah? What are-- is it actually like meat? What do we think? Is it good? I haven't had it personally. AUDIENCE: It's pretty good. SARAH HEWETT: Pretty good. Mixed reviews? Not so great? I haven't actually gotten the chance to try it, but an interesting thing, chemically speaking, about the Impossible meat is that, if you're going to have normal hamburger from a cow, then one of the proteins that is highly abundant in red meat is myoglobin. And this is the structure of myoglobin. And you can see that this group here that is not part of the peptide arrangement is a heme. And that happens to be what gives red meat a lot of its flavor. So, when you cook it, it releases the heme, and the iron center provides a lot of flavor. So what they did was they found that, in soybean roots, they have a protein called leghemoglobin, which is very similar in structure to myoglobin and also contains a heme center. And so, if they extract this protein out of the soybean plant roots, then they can add it to the Impossible meat. And then you will have a plant-based source of heme that will give you the meaty, irony flavor that we have associated with red meat. So they take proteins from soybeans and potatoes, like they make most vegetarian protein options out of, and then add this leghemoglobin from the soybean roots. And it is a red color. So it's also a colorant. The heme center is what gives your blood its red color. So having those conjugated pi systems in the porphyrin molecule and combined with an iron-- or a metal center will give you colors. And so it gives it the color and the flavor of actual meat. So that's an interesting role of hemes outside of your blood or catalase. Going back to catalase, again, this is the overall structure. And it is very hard to see with these colors, but there are heme centers-- you can see them-- in each of the four subunits of catalase. And it contains also a binding site for NADPH. And this is the structure of NADPH. And the NADPH's role is to maintain the oxidation state of the iron center. So it is pretty important that the iron center maintains its iron 3 oxidation state. It goes between iron 3 and iron 4 while it is active, but, in order for it to start the chemistry, it needs to be iron 3. And so the NADPH can donate electrons to make sure that the iron is in its active form. Now, if we want to take a moment and look at the actual mechanism for the reaction of hydrogen peroxide with catalase, this is a very pared down version of the catalase activation site. So there is a histidine residue here. You have your iron center and your heme. And then, when hydrogen peroxide comes in, the first step is that those electrons can remove one of the hydrogens from the hydrogen peroxide. And then this oxygen will bind to your metal center. So then you have your histidine now that is protonated. You have your oxygen bound to your metal center. And then this oxygen can take the hydrogen. And the iron center can donate some electrons here to form water and an iron-oxygen double bond. And now this is iron 4. So iron has donated some electrons to this oxygen center, and it's actually a radical and a cation. So that's the first step. And so that's where our first hydrogen peroxide molecule comes in because, if you remember, the overall reaction that we're working with is two hydrogen peroxides goes to two waters and one oxygen. And then the second step is, once you have this iron radical cation, there are two proposed mechanisms for how this reaction can go. And it can either be also mediated by this histidine residue where one of the hydrogens ends up on the histidine. The other one adds to the oxygen bound to the metal center. You release the oxygen, and this hydrogen comes back in. And you form your water. Or you can kind of ignore this histidine and do two hydrogen transfers onto this oxygen bound to the iron. And then you make your water and your oxygen. And they have done isotopic labeling studies where you can make this first complex and then add in hydrogen peroxide that's been labeled with oxygen-18 isotopes. And they have found that all of the oxygen that is produced is oxygen-18. So they know that the oxygen here comes from this peroxide. And then the oxygen that is bound to the iron ends up in the water. So that's kind of how they were able to narrow down some of the mechanisms for this. And, if you remember, our reaction, our decomposition of hydrogen peroxide can happen on its own. So here is a mechanism for how it may happen without catalase. So you can compare. One of the proposed mechanisms is that the hydrogen peroxide breaks into two hydroxy radicals. Then the second molecule of hydrogen peroxide reacts with one of those hydroxy radicals to form one molecule of water and this peroxy radical. And then you have one of these and one of these that are formed. So those can react and form your water and then your molecular oxygen. So it takes a few more steps. It's a little bit slower, but that is a comparison of how the enzyme can catalyze this reaction to happen much faster than what may happen in nature. So that is what is happening in the decomposition of hydrogen peroxide, either just hanging out on the bench top or with your catalase catalyzation. And now we're going to talk about our goals for day three and four of catalase. So, after day one and day two, you have seen this reaction happen. And now, for days three and four, we are going to try to quantify the amount of catalase in an unknown protein sample. And then we were going to quantify the amount of iron that is present in our sample of catalase and try to figure out how many iron centers there are per one molecule of catalase. And, based on the work of a lot of other scientists, we know that, theoretically, it should be how many? We can go back. So there are how many subunits in catalase? Four. How many hemes per subunit? One. So how many total iron centers in a catalase protein? AUDIENCE: Four. SARAH HEWETT: Four, excellent. So we know that there should be four. And hopefully-- that is our theoretical value. Hopefully, you guys are going to be able to get that as your answer in the lab. So how are we going to do that? First, we're going to talk about how to quantify proteins. So it's important to be able to determine the amount of protein in a given sample. In terms of for nutritional studies, biochemical studies, you need to know how much protein that you have. And there are a couple of ways that you can determine the amount of protein in a sample. You can do a nonspecific assay, which will just tell you how much overall protein that you have. It's not specific to certain proteins. And some examples of those are the biuret assay. You can use UV spectroscopy. So we did visible spectroscopy with our phosphate samples in the Charles River lab. If you use ultraviolet light, you can detect the amount of protein that you have. So some of the amino acids have the aromatic residues or the pi bonds. And those will absorb UV light. So you can quantify proteins that way. Or you can do a Bradford assay, which is more similar to the assay that we did with our phosphate samples in that it is a visible color change that you can see and same with the biuret assay. And the Bradford assay is actually the one that we're going to do in lab. So we'll talk about that more in a second. And, if you want to know specifically what-- if you want to identify the amount of one specific protein, you can do protein-specific assays such as a Western blood or an ELISA. And those use antibodies to select for specific proteins. And then you can either attach a fluorescent tag to the protein or a color-changing tag. So, when the antibody matches up with your protein, you get a color change or some light that you can quantify. And you can also do protein mass spectrometry and look at-- you can use that to quantify the specific proteins also. So the Bradford assay is the assay that we're going to be doing in the lab. And the Bradford assay uses Coomassie dye. And this is the structure of Coomassie dye. And, if you just pour the Coomassie dye out of the bottle, it is this brownish sort of reddish color. And, when it reacts to proteins, it turns blue. So you can quantify the amount of blue. And that will tell you how much protein you have in your sample. And the protein reacts with these sulfonyl groups over here and causes the color change. So, when you have all of these aromatic systems and electron-rich groups when you change the electronic structure by bonding to a protein, then you can change the color. So this is what we are going to do. And, in order to quantify the amount of blue or amount of protein that we have, similar to our phosphate analysis before, we need to make a series of standards. So you need to know what your absorbance is at different concentrations of the thing that you're trying to measure. So we made our phosphate standards, and those also happened to turn blue. And we are going to make a series of protein standards so that we know what color our Coomassie dye will turn a different protein concentrations. To do this, we are going to use bovine serum albumin. And it's a serum albumin protein, which is found in blood. And bovine means that the one that we're going to be using is coming from cows. And that's helpful because there is a lot of cow blood left over from the meat industry. And it is found in the blood plasma, and it maintains-- its role in a living animal is to maintain the osmotic pressure in the blood and carry biologically important molecules through your blood plasma, but we are going to use it as a primary standard for our protein quantification. And we can do this because it is abundant, inexpensive, stable, and reacts well with Coomassie dye. So we can get a nice calibration curve. And it's also similar enough to our protein, catalase, that we can use it to make our standard curve. So typically you would try to use the same molecule that you are quantifying to make your standard, but that's not always possible. So, in that case, it's helpful to have a protein that can kind of stand in, is abundant, and easily quantifiable. So you can buy different concentrations of this Bovine Serum Albumin, or BSA, from a bunch of different chemical suppliers. So you know what the concentration is, and you can use that as your standard. The way that we are going to do this in the lab is to prepare standards very similarly to how you did for your phosphate. You will have your BSA stock solution. And the BSA that we're going to be using is in solution form. And the stock solution is 2,000 micrograms per milliliter. And you will be diluting it with buffer. So again it's really important to use buffer any time that you're working with proteins because of the different structures that we showed you before. The side chains could be charged. And that will impact their interactions with each other. So you want to make sure that the pH is correct so that your protonation states of all of your amino acids are what they should be in terms of like a physiological pH. So you'll add-- dilute your BSA with buffer. And then you will have a bunch of different standards at varying concentrations. And then you'll have one where you don't add any BSA, and it's just the buffer. And that will serve as your blank. The way this is going to work in lab is that you will pipette-- you'll be using little microcentrifuge tubes and the micropipetters. And so this is a very quantitative experiment. So you need to get really good with your micropipetting technique and make sure that you don't contaminate your samples because you're going to be working with very small quantities, microliters of things. So you want to make sure that you are changing your pipette tips at an appropriate time and using the pipettes accurately. So you will pipette the standards into your microcentrifuge tubes. And then we will give you a standard sample-- or an unknown sample of catalase. And then you will put catalase in each of the microcentrifuge tubes. And we're going to do five samples of the catalase so that we have five unknowns that you can do an analysis of your error on that, similar to the phosphate where we ran five standards from-- or five samples from the river. You guys saw how much those can fluctuate depending on how you prepared the samples or how well you pipetted. So it'll be the same thing. We will have multiples, multiple trials. Then you will add the Coomassie reagent to each of the standards and your samples. And this is where it is going to be very important that you pay attention to the timing of this experiment. So you will add your Coomassie dye. And then you will shake it up a little bit. And then, as soon as you add the dye, you will start a timer. And you will close the tubes, shake them, allow the color to develop for two minutes. And then, at two minutes, you will pour all of your samples into cuvettes. And, in this case, we will be using the smaller cuvettes than what you guys used for the last samples, but they go in the same instrument. You will transfer your samples to the cuvettes. And then you will measure the absorbance at 595 nanometers. And the program on the UV/Vis instruments are set up to go to that wavelength when you click on it. You need to start running your samples at 10 minutes. So this is why it's really important. So, once you start adding the Coomassie dye, you need to start a timer because the dye is-- it's important that all of your samples incubate for the same amount of time so that it's consistent. So you don't want to take your time like adding it to the beginning samples so that, by the time you add it to your unknowns, it's been like five minutes. So you want to work quickly and carefully. The dye is most sensitive around 10 minutes after addition. So that's when you will get really good spectra. If you wait too long, then you will see that the protein-dye complex will start to precipitate out of your solution. And you'll get these black chunks in your cuvettes. And that's when you know that you can no longer measure the absorbance of your sample. So that'll be careful, and we will try to stagger people so that not everybody is using the UV/Vis at the same time so that you have your-- you can do everything in the allotted amount of time. You will make a calibration curve, and it will look something like this. And, as you can see, it's not the most linear thing. BSA has three linear regions when you are doing a Bradford assay. And the first one is from 0 to 125 micrograms per milliliter. We don't really have any data points there, and your protein concentration in your catalase sample should be higher than that. So we're not really going to look at that region. And then the other region is in the middle here, either from 125 to 1,000 or 125 to 750 micrograms per milliliter. And, when you get your data, you can look at this and graph both of these regions to see which one gives you a more linear and more steeper slope. And that's the one that you can use to calculate your unknown samples with. And the third region is above 1,000 micrograms per milliliter, but, as you can see, you're getting above one absorbance unit there. And so then it's not as accurate beyond there. So we're not going to worry about that. So, when you get your data, you'll need to figure out where it is most linear, where the slope is the steepest. And that is what you will use to calculate your unknown concentrations. And then it is just like you did for phosphate, and you'll be able to calculate your unknown concentrations. Any questions about the quantification of the amount of catalase protein? So our calibration curve, also one thing to note, is in units of micrograms per milliliter. And you'll know how many milliliters of solution that you added. And we know that the molecular weight of catalase is 240 kilodaltons or 240,000 grams per mole. So you can figure out how many moles of catalase protein you have from the concentration and that conversion factor. So that's something to note. And then, once we have our amount of catalase protein, we can determine the amount of iron in the protein. So this is-- and we'll be doing that using the ferrozine assay. This is the structure of ferrozine. And the ferrozine molecule by itself is colorless. And then, when you complex it with iron, it turns into a magenta color. And there are three molecules of ferrozine for every one iron ion. And so it forms in an octahedral sort of geometry. So, if there are six binding sites on iron, then you'll have one ferrozine here, one there, and one there. And it bonds to these two nitrogen centers here. And again, like the Coomassie dye, there are a lot of pi electrons and aromatic systems, which help to give it its color. So the way that we're going to do this is we will be using again UV/Vis spectroscopy because we have something that goes from colorless to colored when it interacts with our molecule of interest or our ion of interest. So the first step in this procedure is going to be adding methanesulfonic acid. And then you will heat it at 104 degrees for 40 minutes. And it's very important that you keep the temperature range around 104 degrees. And you don't want to go too high because we'll be heating them in the microcentrifuge tubes. And, if you heat it too hot, then your centrifuge tube can boil over, or it can build up pressure, and the cap will pop off. And you'll lose all of your solution. So you need to be careful with that. And the purpose of this step is to release the iron from the heme group. So, when you add a bunch of acid, the iron gets released. And then we can quantify it because it won't be bound to our heme. Then we will add sodium hydroxide to neutralize the acid. And then you're going to get a ferrozine complex mixture that will be prepared by your TAs. And you will add it to all of your samples. And the mixture is ascorbic acid, which reduces the iron 3 to iron 2+ because that is what will complex with our ferrozine molecule. Ammonium acetate helps to buffer the pH. Neocuproine binds to any copper ions that are in the solution. So the ferrozine ligand is not necessarily specific to iron. So, if there are any copper contaminants, then it will also bind to copper, but the neocuproine is more specific for copper. So it will bind to the copper ions and make sure that it does not contaminate your assay. And then, of course, the ferrozine, that binds to the iron to make the colored complex that we are going to measure. And then the-- so the measurement of the ferrozine is going to be pretty much the same as the BSA and the phosphate. Similar to UV/Vis, you'll make a bunch of standards of iron sulfate. And then you will have your catalase samples that have iron in them. And then you will make your standard curve. The ferrozine is linear. So you'll be able to make your standard curve, just graph it, and use the line. And then you will be able to use the equation of your line to determine your concentration of your unknown samples from your catalase. The data analysis for this lab is going to be using the protein assay results and the iron assay results. You will determine the number of iron centers per catalase. And so you have the micrograms per milliliter of your catalase protein. So you can convert that using your molecular weight to moles of catalase. And then you will also get your iron in micrograms per milliliter. And, using the molecular weight of iron, you can convert that to moles and then do a mole-to-mole ratio of iron to catalase. And hopefully your answer is somewhere around four if all goes well. So, in your discussion, you can talk about sources of error, how close you were to the theoretical value of four, any discrepancies between your calculated ratio, the expected ratio. And then you'll do an error analysis of the protein and iron concentrations. So you will run five unknown samples of catalase and five samples with the ferrozine assay of iron. So you'll have five measurements that should be the same. So those you can do your average, your standard deviation, confidence interval. And then, if you have any outliers, that's when you can use the Q test for the outliers. And there was a couple of questions that came up during the Charles River lab report. When we were making the standard curves for the phosphate determination, people had some outliers in their standard curves. And they were trying to figure out how they could get rid of those or if they should. And the Q test only works if you're measuring the same thing multiple times. So that does not work for getting outliers out of a standard linear curve. But if you have-- in your standard curve, if you have one sample that is supposed to be a higher concentration than the one before it and it has a lower absorbance or something wildly higher, then you can look at it and say I know for a fact that, if something has a higher concentration, it should have a higher absorbance. I can get rid of this point. You can also just kind of by looking at it-- that's not as scientific, but you can make an argument for why you would remove a data point based on how it looks compared to the line of best fit. And you can also compare the R squared values of the line with the point and without the data point. And, if it gets closer to 1 when you remove it, then it is more linear. You obviously don't want to be taking out data points left and right until you only have like your three best points that give you a super straight line. But, if there are any that are very obviously not on the line, then that is one way that you can remove them. So yeah, are there any questions about catalase or any of the other labs? Anything? This is all I have for today. This was kind of a short one. No. All right, then those of you who are going to lab, you can head up there. And don't forget to turn your reports in. And yeah, the clipboard is around.
MIT_5310_Laboratory_Chemistry_Fall_2019	14_Mass_Spectroscopy_Esterification_Lecture_Part_2.txt	[SQUEAKING] [RUSTLING] [CLICKING] JOHN DOLHUN: Hello. Good afternoon, everyone. And welcome to the second to the last lecture. Next week, the X-ray diffraction, Peter Mueller will deliver that, I believe, on Tuesday. And this is the mass spec lecture, and then we'll keep you posted as what happens in between. There are a couple of workshops for the oral reports, and we'll also have a couple of town hall meetings, one of them being, I believe, next week, next Thursday, which will cover all three of the labs that you're working on. You can come here with your questions and computers and calculations, and all the TAs and both instructors will be here to help you navigate through the third lab. So today, I'm going to talk about mass spectrometry. And J.J. Thompson, discoverer of the electron, won the Nobel Prize in 1906 in physics, but not for the discovery of the electron, for the conduction of electricity through various gases and discharge tubes. And then, after he won that Nobel Prize, seven members of his research group won Nobel Prizes. And then, in 1937, his son won a Nobel Prize for figuring out the wavelike properties of the electron that his father discovered. Nine Nobel prizes in one research group. It's just amazing. So J.J. went on to build the first mass spectrometer in 1912. And in honor of him, we're going to do a little electrical demo, just to start off with you today. So what we're going to be doing is I'm going to be showing you an incandescent light bulb. And you all know them. This is a big version. This is the small version. Inside of the incandescent light bulb, there's the filament. And they've used tungsten since the turn of the century, the turn of the last century, 1906, because tungsten has the highest melting point of all the metals. Melts at around 3,400 degrees Celsius. So inside of there, you can see it in this bulb, but I'm just going to turn this on, just for a moment. So you all know the incandescent bulbs. They get so hot. When the electrons flow, they flow through the circuit, and then the tungsten atoms start to vibrate inside and it heats up to about 2,200 degrees. Have any of you ever touched one of these? You do it only one time because they are so hot, and that's why they're so wasteful of electricity. That's why we're going to the LED lights today. But what I've done here is inside of that light bulb and this bulb, there is an inert atmosphere. There's argon and nitrogen gases to protect that filament. If they weren't in there, I scratch my head and I'd wonder what would happen to that filament. So what I did is I took a bulb here and I'm going to break one. Hold your ears. And out-- oh, beautiful. The filament's completely intact. See, I didn't break it. But I've already got one here to show you this demo with. So what we're going to do is I am going to take one of these filaments outside of the light bulb and I'm going to turn on the electricity and see what happens. Let's turn the lights down now. Yeah. And he just shut this light off here. You ready? AUDIENCE: Whoa. JOHN DOLHUN: Wow, didn't take long, right? In the oxygen atmosphere, the electrons are flowing through there and the tungsten atoms are boiling off with the electrons and the thing just disintegrates pretty instantly. So I said to myself, I want to do one more experiment. And Amanda's going to assist me with this. We're going to fill this beaker with liquid nitrogen and we're going to take one of these filaments and we're going to stick it down into the liquid nitrogen and then we're going to turn it on. So think about that for a minute. What do you think is going to happen? AUDIENCE: [INAUDIBLE] JOHN DOLHUN: Go ahead, Amanda. I just blew one. OK. OK. All right. I ruined one, sorry. I forgot this was on. OK. All right, let me turn this off for a minute. And I think I can put in the one that I took out here on the desk. I'm going to put that one in because the filament is intact. OK, Amanda. Just tighten it a bit. Go ahead. You OK? AUDIENCE: Yeah. JOHN DOLHUN: Liquid nitrogen, minus 196 degrees Celsius. Beautiful stuff. Put your finger in there and you know what's going to happen. It's the skin effect. Won't get you for the first few seconds. OK, good. So here we go with our experiment. That's good, Amanda. So we're going to lower this down in. Amanda, do you want to hold this? AUDIENCE: Sure. JOHN DOLHUN: Just try to get it in the center and just lower it all the way down in. AUDIENCE: All the way? JOHN DOLHUN: All the way. Just go ahead. Take it down. Leave more slack. Yeah. Let it go down in. OK, good. Ready? There it is in the liquid nitrogen. Is it burning out? AUDIENCE: No. AUDIENCE: No. JOHN DOLHUN: No. Take it out, Amanda. Doesn't take long in the air, does it? So even the liquid nitrogen is surrounding that filament and protecting it. And you've got the situation where you don't have the oxidation that's going on. OK, so we take the lights back up. So in case you're interested, tungsten it had-- anyone read Oliver Sacks book, Uncle Tungsten? It's a great book. You've got to get that. Tungsten plus oxygen goes to tungsten oxide. And you can actually-- if you take one of these filaments that burned out, you can actually see the yellow-white powder that from the tungsten oxide that was left over. So J.J. Thompson, because of his discovery of the electron, I wanted to show you this electrical demo. And now, we're going to get into the mass spec, which is pretty important because you're going to be using the mass spec to characterize your ester products in this lab. So the inside of the mass spec has several basic components. You've got an area outside here that is at atmospheric pressure, and the area inside that is under a high vacuum. Anyone have an idea why that area is under a high vacuum inside? No? So you're generating ions. The ion are going to get generated in this source. The filament is going to shoot electrons onto your molecule and it's going to ionize your molecule, and then the molecule's going to break apart. And positive ions are very short-lived species, so we manipulate them under vacuum. And the vacuum-- the vacuum actually is great because it allows us to let the ion have a mean-free pathway from the ion source to the detector without any biomolecular collisions. So the ions are generated here and then they go into the mass analyzer and they're sorted by their mass to charge ratios, and then they're counted at the detector, and out comes a spectrum. You kind of get something like this with abundance here and the mass to charge ratio. And depending on the iron, so you might-- the detector may see a lot of this, less of that and less of that. So you're going to get vertical lines representing the abundance of the ions that were detected in that spectrum. Each vertical line represents an ion. And we're talking about mass to charge ratios, the charges are usually plus 1. So what we're looking at in a mass spectrum are the masses of the individual ions. Mass spec is-- the basic principle of mass spec is you have to have an ion that enters the magnetic field and it gets deflected. It gets deflected dependent on the actual mass to charge ratio, how big that system is. Bigger, heavier atoms are going to be deflected less than small, lighter atoms. But that's the whole underlying principle of mass spectrometry. And now, I'm going to talk about a couple of the types of ionization. Electron impact is the basic form. So what we have is we've got our molecule and we send it into the ion source. It gets bombarded by electrons, and you create an ionized molecule, an M plus dot. And this ionized molecule can do one of two things. This could break apart. So the positive charge could be retained on one part of it. The radical would be retained on the other. So you could get something like A plus plus some radical given off. Or it could break apart. So one part retains both the plus and radical. So you could get this type of ion and a neutral molecule given off. What we detect with mass spectrometry is we're detecting these daughter ions here. These are the peaks we see. We don't see the radicals or the neutron molecules, but we could figure them out by subtracting the fragments from the molecular weight. And then we can-- we'll know what's been lobbed off. So if you have a molecule like this, it could ionize anywhere in this chain. And if it ionizes, say, here, and then you have a homolytic cleavage of the bond, you're going to get an R prime CH 2 plus fragment, and you'll get an R2 CH2 radical. So that's the idea. Now, sometimes, some of these bigger molecules, these proteins and peptides, you don't see molecular ion peaks in the mass spectrum. Even for some small molecules you may not see them. So we have another technique, a softer ionization technique called chemical ionization that we can use. So in chemical lionization, what we do is we take a guess and we flood the ion source with a gas. I'm going to choose methane for this. Methane is often use. And we ionize that methane. And then the ionized methane reacts with more methane to produce a super acid, CH5 plus, and a methyl radical. Now, your molecule goes in and it encounters the CH5 plus. What do you think happens to it? AUDIENCE: It's acidified? JOHN DOLHUN: Yeah, it's going to get acidified. It's going to get protonated. So this CH5 plus protonates your molecule, and you get this huge M plus 1 peak. So this is great. If we have these big proteins and peptides and we want to know what the molecular weight is, we can use chemical lionization, put them in there, and we'll see the big M plus 1. We won't see a lot of fragmentation, but at least we can get some molecular weight information out of the system. CH5 plus is an interesting molecule. You all know from your chemical principles that CH4 is SP3 hybridized. So when those two methane molecules collide and it throws the hydrogen in, that hydrogen pushes another hydrogen out of the way and it forms a three-centered, two-electron bond. This is a pentavalent carbon atom with a positive charge. That's a carbocation. That's the definition of a carbocation in chemistry. This is also called the methanium ion. And this is one of the last unsolved problems in physics, because no one can isolate this stuff. It's very difficult to isolate. And about three years ago, at the University of Cologne, they actually trap some of this stuff in an ion chamber at very low temperatures, near absolute zero, and they studied the vibrational spectra. What they saw was all these hydrogens are coming off, moving around the carbon atom. They're breaking off and moving around. So now, scientists are wondering whether this thing actually has any structure at all. So that's chemical ionization. Sometimes, electron impact and chemical lionization, both of them won't work for us. We may have a molecule that's too big or that's too nonvolatile. So we go to fast atom bombardment, electrospray, or matrix-assisted laser desorption spectroscopy. Fast atom bombardment is pretty simple. You take your sample, mix it with a little bit of glycerol, put it on a metal target, and then we shoot xenon and argon atoms at it, very high speed, high energy. And the glycerol in your sample absorbs the shock of the impact with those atoms. And we have some trifluoroacetic acid in there, TFA, so that we can produce these M plus 1 peaks. The advantages of fast atom bombardment are for high molecular weight samples, nonvolatile compounds, EICI don't work. Molecular weights here, I've seen 20,000 or so. So you can go out-- they're constantly making innovations with these. The next technique, electrospray ionization, is quite interesting. The ions are produced, the molecule is ionized, and it's done at a very low pH. And there's a nebulizer that actually shoots out like an aerosol through a high voltage and you get these charged droplets coming out, very large droplets with a lot of positive charges on them. And then we can take a stream of warm nitrogen gas and evaporate those down and you get a smaller droplet and then that disintegrates. And what you end up with are these multi-protonated molecular ion peaks. You could have an M plus 20. You could have 20 hydrogens on there, or 10 hydrogens, or you get a variety of numbers. And what that does is it expands the mass range. Let's say, for example, you have a molecule that maybe weighs 70,000, and you produce a-- you produce an M plus 20. So what you have to do is-- you're going to have a molecule like that. You're going to have to divide, now, by the charge to get where this molecule is going to show up. Because it's mass to charge ratio, and if the charge is 20, if you divide this out, you're going to get something around 3,501. That's where the peak is going to show up in your spectrum. So the advantage of this technique is you can take molecules that are 70,000, 80,000, and your peaks could come out at 3,500 or much less. So it expands the whole mass range of using a mass spectrometer. The last technique is MALDI, Matrix-Assisted Laser Desorption Ionization, and we would use that principally for solids. And these would be like the big carbohydrates, the big peptides and proteins. And you take your crystal and you dissolve it in a matrix, a solvent, and you put a chromophore in to absorb the laser light, and then this sample begins to evaporate and you get beautiful crystals on this metal target. And then you shoot a nitrogen laser at it, 337 nanometers, and you end up getting M plus H speaks out. So you can take these large solids. And molecular weights here can go out quite a bit. So the advantages of all these techniques are they can help us with nonvolatile, high molecular weight samples and getting spectra. We've already talked about the inductively coupled plasma in one of the lectures, so I'm not going to talk about that. But I would like to cover a couple types of instruments that you will experience. The first is the magnetic sector. The last is the one we have in the undergraduate lab, the radio frequency quadrupole filter trap. So let's start with the magnetic sector. You'll see some similarities to these. So here is your ion source. You can see the filament here. And the filament is shooting out an electron beam at your sample. It's about 70 electron volts. That's like about 1,600 kcals of energy. And 100 kcals, you can break a bond. So with all that energy slamming into your molecule, it not only ionizers the molecule, it starts to break apart into fragments. And the fragments in this magnetic sector instrument get ushered through a pair of focal plates and then they get sent into the mass analyzer. There's an electric field perpendicular to a magnetic field. The electric field controls the velocity of the ions, and the magnetic field will cause the deflection with the heavier ions deflected less than the lighter ions. So you kind of get a spectrum here on the detecting screen based on how they're deflected by the magnet. Time of flight, this is actually one of my favorites. There are a couple advantages to this. One is it has almost an unlimited mass range. The second advantage is you can do very small amounts of sample with this. So what happens in time of flight is your samples get ionized in the ion source here. They get ionized similar to all the other mass spectrometers. But then they get shot out into a flight tube and they get shot out at the same kinetic energy, all the ions that are going in there. And kinetic energy is equal to 1/2MV squared, which is also proportional to the charge times the voltage when they're being shot out. So if you look at the kinetic energy, you can see that the velocity is square root of 2 of the kinetic energy divided by the mass. So that means that the heavy ions are kind of lagging here. They're traveling slower because they're heavier. So when they're in this tube, they actually measure the time of flight through the tube. That's what this-- it's called time of flight, right? So the time of flight is the distance divided by the velocity. Now, if you put that back into this equation and you solve it out, you'll see that the mass to charge ratio is equal to the square of the time of flight divided by the distance. This is a great salute to the engineers. They designed this system. This machine is so simple. There's no electric field. There's no magnetic field. All there is is a tube. Doesn't this remind you of TLC with the spots? Except there's no mobile phase and no stationary phase here, right? So this is a great instrument. And that's how your mass spectrum is determined. Now, the next one, which is also kind of like the Cadillac of all mass spectrometers, is the Fourier-transform ion cyclotron resonance instrument. This instrument, ions are generated the same way as in the other mass spectrometers, but when they're generated, they start to get pumped to different pumping stations, and every pumping station has a higher and higher vacuum. So the pressures continue to drop until the ions reach this box, and then everything breaks loose here. Because in this box, you've got a temperature of about 2 Kelvin. You've got a magnetic field of about 21 tesla, and there's an electric field in there. And if you think about this, you have a charged particle traveling at a certain velocity and it enters-- it enters the magnetic field. What happens to it? What's going to happen to that charged particle when it gets into that magnetic field? Autumn? AUDIENCE: It'll go around. JOHN DOLHUN: It's going to start to spin, yeah, like a cyclotron. It's going to be-- it's going to be spinning like this. In fact, when the particle goes in there-- let me give you an example, like 100 molecular weight fragment, 100 Dalton could travel 30 meters in about one second inside of that box just crazy. So it has a centripetal force on it. And force is mass times acceleration, right? So mass times acceleration. So this is our system. And the angular velocity of that particle is given by velocity over r. So if you plug that in here, the cyclotron frequency of that particle, that velocity is nothing to do with its velocity. It's only to do with mass and charge. That's the bottom line. That's incredible. And if we hold the magnetic field constant, then the cyclotron frequency is the mass to charge ratio of that particle. So what comes out of this is convoluted signals like this FID, these sine waves, and we do a Fourier-transform on that signal and pull out the mass spectrum that we want. So it's quite interesting. It's the most sensitive method of ion detection in the world. The resolution is greater than 10 to the 7 on this instrument. And if you think about it, that spinning particle, it's spinning so many times, the detector is on the outside here. The difference between this and all other forms of mass spec is the detector is on the outside, so it doesn't-- the ions never reach the detector. They only record the image current from the ions as they're going by. And it's recording it over and over and over again. That's why you've got such beautiful resolution here. And then you've got the system we're going to use, the quadrupole filter radio frequency system. So what we have for our mass analyzer is four rods in parallel, and the opposite rods are electrically connected. There's a DC voltage put on those rods. And then an RF voltage is superimposed on one pair of rods over the other. And it's the voltage of that pulsed radio frequency field and the frequency that determines which ions get through these rods. Only one ion can actually make it through the rods at a time, depending on the frequency of that radio frequency pulse and the ratio of voltages on those rods. And the other ions basically just crash into the sides here. So a couple of things, before you actually come in the lab and do the lab, we have to actually tune the mass spectrometer up. Because mass spectrometers have an internal mass scale. Can actually go off kilter. And so we've got to make sure that every mass is where it's supposed to be. The detector gain has to be cranked up so that we can see peaks far enough out. To do that, we use this compound, perfluorotributylamine. This is the stuff that we actually have in the mass spectrometer in a little vessel, and when we do the tune, the vessel opens up, and a whiff of this comes out. And the beauty of this is it can fragment down here. ScF3 can fall off. You get a 69 peak. Can do that from three directions. You can lose one of these polyfluorinated butyl groups from either of three directions and you get a 219 peak, or you can clip it right here and you get a 502 peak. And that's pretty much all you see. You see the 69, the 219, and the 502. The spectrum is very simple. And the molecular weight is 502. So We key in on these and adjust the internal mass scale of the instrument and make sure it can separate peaks 1 AMU apart. And for your samples, your samples will be under molecular weight of 200. So if we can go out to 500 and have it tuned up, we'll be fine. This is water. Very simple molecule. This is your chance to talk. I want you to-- we're going to actually look at this. What I'd like to do is I'd like to see what the mass spectrum of water looks like. So we're going to ionize some water. And we've got our abundance here and our mass-to-charge ratio. So what would you see in the mass spectrum of water? Which peaks would you see? Royce? Oh, you were scratching yourself. Yeah. [CHUCKLES] What would you see? Yes, Alec? AUDIENCE: M-to-C equals 18. JOHN DOLHUN: 18, yes. You'd definitely see an 18 peak. That's your ionized water molecule. What else? Alec? There's not much to fragment, is there? Well, what would you get if you tore this apart? AUDIENCE: You'd get a 1. JOHN DOLHUN: A 1, yes, you'd definitely see a 1 here. That's your hydrogen. What else? Yeah. AUDIENCE: You might see a 16. JOHN DOLHUN: Yep, you'd see a 16. What else? AUDIENCE: Will you see a 17? JOHN DOLHUN: Yes, you would. Very good. And that is-- that's the whole spectrum of water, four peaks. Yes, Autumn. AUDIENCE: Could you get 32 or 2 in the oxygen and hydrogen diagrams? JOHN DOLHUN: You could get-- if you're looking at air, air has diatomic gases in it. So if you put air in, you would see some of those peaks, yeah. Yeah, let's look at air, since you mentioned that. Let me just put this down here. I mean, air has diatomic gases. So what would you see in air? Yeah, Noah. AUDIENCE: A 28. JOHN DOLHUN: A 28, good. So you'd see a 28 here. Yep, what else? AUDIENCE: 32. JOHN DOLHUN: Yep, you'd see a 32. AUDIENCE: 44. JOHN DOLHUN: Very good. Good old carbon dioxide. Yep. What else? AUDIENCE: 18. JOHN DOLHUN: Yeah, you'd see water. We hate water, but it's in the air, right? So you definitely, definitely would see an 18 peak. What else? How about some of the noble gases? They're in the air. Which one? AUDIENCE: Ne. JOHN DOLHUN: Neon, yeah. Neon is 20. Any others? AUDIENCE: Would you see argon? JOHN DOLHUN: Yes, argon. Argon is 40. What other gas? Yes. AUDIENCE: Would you see helium or not? JOHN DOLHUN: Very little. Very little. What else? What's a couple of the other big inert gases? AUDIENCE: Xenon? JOHN DOLHUN: Xenon, yes, 131. What about the Superman gas? AUDIENCE: Oh, krypton. JOHN DOLHUN: Krypton, yes. 84, krypton. And you may see a 29 peak, because you might see nitrogen-15, nitrogen-14. Because the mass spec will detect isotopes. You also, for oxygen, you could see a 34 peak, because you've got-- you might have some oxygen-18, oxygen-16. But you've hit them. And these just came out-- this was I think in not Time magazine, but one of the-- one of the magazines came out with the periodic table. The whole issue was on the periodic table. And they listed all the gases that are in the air. So it's kind of neat. So let's move on here. I want to show you what a mass spectrum looks like. This is hexane, your good old friend, right? C6H14. So what you've got here is you've got your molecular ion peak at 86, right? And then everything to the left of that is fragments breaking-- the molecule breaking apart. And notice the intensity of the peaks. One of the peaks is a base peak. That means the detector counted that more than any other peak. So what the detector does is gives that 100 and all the other peaks are relative to that base peak. And when we give you your mass spectrum, we'll give you a sheet with the abundances on it. Notice, if you take this base peak, 57, and you subtract it from 86, that's a loss of 29, isn't it? So it's pretty much just an ethyl radical falling off, and you've got this butyl cation. The butyl group has the plus charge. That's your 57 peak. It's that simple. So you take your peak, subtract from the molecular ion, see what's been thrown off. What about the m plus 1 peak here? What is that? There's no chemical ionization going on here. [CHUCKLES] What's the m plus 1 peak? Yes, Deb. AUDIENCE: [INAUDIBLE] JOHN DOLHUN: Did you say something with carbon? AUDIENCE: Yeah, 13. JOHN DOLHUN: Carbon-13, very good. Yeah, carbon-13. So carbon-13 has an abundance of 1.1%. 1.1% of all carbon is carbon-13. Look up here. You got six carbons, right? So 6 times that-- 6.6% of the carbons are carbon-13. So if I take this molecular ion peak, which is-- my eye is saying it's about 15% abundance, if I multiply that by 0.066, I get 1%, that m plus 1 peak. That's approximately what we're talking about. What if we didn't know the number of carbons? We didn't know the structure? We could work backwards and figure it out from the molecular ion abundance and the m plus 1 abundance. The number of carbons would be equal to the abundance of the m plus 1 divided by the abundance of the m plus dot times 100 divided by 1.1. That would give you the number of carbons in your molecule. So mass spec can not only determine the molecular weight, you can determine the molecular formula of your system. You can also determine the number of isotopes and elements that are present in your system. So there are other isotopes. Look at chlorine-35 and chlorine-37 here. If you see this in the molecular ion region of your spectrum, and your molecular ion is separated by 2 mass units, it's a dead giveaway. That's chlorine's signature. That means you have a chlorine in your molecule. Bromine is even simpler. Bromine has two peaks, both equal abundance-- the 79 and the 81 separated by 2 mass units. Here's an example. So here's a mass spectrum. Look at our molecular ion region here, separated by 2 mass units, ratio of 3 to 1. What do we have? AUDIENCE: Chlorine. JOHN DOLHUN: A chlorine, yes. OK? So if you take this-- take this peak here, this is 77, subtract 112, you have a loss of 35. So if you take the-- if you simply take the two things and put them together, the 77 is the phenyl ion. So if you just stick a chlorine on there, you got chlorobenzene. That's the spectrum. Here's another spectrum. This is very interesting, because all these peaks are separated by methylene units, 14 mass units, CH2 units, all through the whole spectrum. When you see that, you know you've got a long chain of carbon atoms as part of your spectrum. So this particular spectrum is decane. And it ionizes at all these different bonds, producing this spectrum with this logical lost ion series. There's another one, dodecanoic acid, which has all these methylene units, which is a dead giveaway for a long chain of carbons connected to something. Here is a simple spectrum. This is 2-propanol. Now, the molecular weight of this is 60. But look down here. Do you see 60? There's no molecular ion there. So this molecule is doing something that's energetically very favorable to itself to produce a 59 peak. What do you think it's doing? It's one less than the molecular ion, right? Yeah. AUDIENCE: It's losing the H on the OH. JOHN DOLHUN: Yes? AUDIENCE: It's losing the H on the OH. JOHN DOLHUN: Yes, Hannah. Loses the H, right. So if you take-- this guy ionizes here. And it has resonance, because you can throw that positive charge out onto the oxygen. So it's really, really a very stable system. It loves to do that. And look at the base peak in this spectrum, 45. You can lose a methyl group from either side here, and you've got a 45. It's left over. And it's resonance-stabilized, because the positive charge can resonate with this oxygen here. So that's the idea. When you see a base peak, you know the molecule is loving to do something that's very favorable. And in this case, it could cleave from two sides. So this is an ester. This is ethyl-isobutyrate. I don't know if this is one that's been given out. I'm not talking. But this is a simple spectrum. And the idea here is, what you do is you're going to take this, and you're going to break it apart to try to figure out where those peaks are coming from. So if you cleave the ester here, right, right by this carbonyl, you lose this-- do this alpha cleavage, you'll get this 71 fragment, which can then lose carbon monoxide to give you a 43 fragment. So if we actually go back here, there's our 71, and there's our 43. And then, look at this right here. You can actually lose a neutral molecule of ethylene. Transfer the hydrogen back to this point. And you're losing CH2-CH2. That's an example where one piece of the molecule retains both the plus charge and radical that I talked about. And here's your fragment, your 88. There it is there. So the idea is to go through here and try to take your ester and try to break it up and substantiate some of the fragments from-- in a table or something, to show that what you've got. And that way-- that way you'll convincingly convince someone that you-- indeed that is your product. Do you have some questions about this? So if you're on day four, you'll be doing the mass spectra today. And I guess you turn in your guesses for your unknowns today, right? Good. It was easy, right? Yes. It was too easy, wasn't it? AUDIENCE: Nah. [CHUCKLING]
MIT_5310_Laboratory_Chemistry_Fall_2019	15_NMR_Spectroscopy_Esterification_Lecture_Part_3.txt	[SQUEAKING] [RUSTLING] [CLICKING] JOHN GRIMES: OK, well, I guess I'll get started, and let people trickle in, if anybody else is coming in. So my name is John Grimes. And I work in the chemistry department's Instrumentation Facility. And down there, we've got a number of different instruments. We have five mass spec instruments. That is not my specialty. So other than being able to point them out, I can't really tell you that much about them. I help run NMRs. And so what I do is I teach students how to use the NMRs. I will help them select what experiments they possibly need to use in order to give them the answer that they're looking for. And I'll also help them interpret the data, or at least get them started off on interpreting the data so that they can do that on their own when they're doing their own research. So what I hope to talk to you about today is what an NMR instrument is and what it actually consists of as far as the parts, what the analytical technique of NMR is, and how we measure the signal, and then go into some examples of how to interpret the data. So here's a picture of one of our instruments there. And here's an example spectrum of adenosine. So nuclear magnetic resonance is what NMR stands for. And it's the study of molecular structure by measuring the interaction of radio frequency energy with a collection of nuclei that you've taken and you've put into a strong magnetic field. So it's an analytical technique that is based on a nucleus's-- or nuclei-- intrinsic angular momentum. It is a nondestructive analytical technique. And that's important if you're a graduate student in the chemistry department, wherever, even an undergraduate, and you have worked long and hard to synthesize some natural product that's 15 steps into a synthesis, you've only got a half milligram of that, and it's a year's worth of your life's work, you don't want to destroy that sample analyzing it. So you can take that sample, and you can put it in a small, little, cylindrical glass tube. You can analyze it. And then you can take that sample back out and use it for something else. So the technique allows you to determine connectivity within a molecule. So I've drawn-- this is something I'll bring up a spectrum of later. It's just three heptanone. But it will allow you to see that protons on this terminal carbon are connected to that and next to a carbon here that has two protons on it. So it looks through bond connectivity. And it won't necessarily give you connectivity all the way through the molecule, but you can build up, say, this chunk of the molecule and this chunk. And then you can link it together-- picture linking together a chain that allows you to put together the whole molecule. It will also show you interactions through space. I'm not going to embarrass myself and try and draw a protein. But there can be two parts of a molecule that are hundreds of atoms away from each other if you were to try and go through the chemical bonds. Yet they're held near each other in space. And you can monitor how close they are. And that helps determine the three-dimensional structure of molecules. And so all the time protein structures are solved by NMR. And you can use it to monitor other processes too, such as whether a protein has bound a small molecule, whether there's hindered rotation about a bond, so something like-- where did my chalk go? If you take something like dimethylformamide, this bond here has partial double bond character. And you can see separate peaks for those methyl groups. And you can rationalize it by the hindered rotation around that bond. And there even other techniques. And so everybody is going to be familiar with what NMR is. And hopefully none of you have had to have one, but it's the same physical technique as an MRI. So here's an MRI of, unfortunately, my daughter's head after she swam into the pool end in a swim match. Nothing happened to her, but you can take pictures with NMR. In the past, I've used it to take pictures of insects. You can also do analytical techniques of in vitro diagnostics. So there's a test out there called the NMR LipoProfile. And it will analyze your cholesterol, i.e. the density-- or the concentration of lipoproteins that's circulating around in your blood. So what is an NMR instrument? NMR instruments come in two flavors. Or at least-- maybe they come in more flavors, but, here at MIT, we have two types of NMR instruments. There are ones that are referred to as high-resolution instruments, which usually have a stronger magnet, and they're bigger. There are also desk-- they're not desktop, but benchtop instruments, which is what you're going to use in your lab. So each of these has the exact same constituent parts. I didn't go over and try and take your benchtop instrument apart to get a picture of those parts because I wouldn't have gotten it back together. And it would have never worked. So I'm going to go through one of our instruments and show you the individual parts, but keep in mind it's the exact same thing that's in the instrument that you'll be using. So you've got to have a strong magnetic field to immerse your sample in. And obviously that's supplied by a strong magnet. So magnets will come in two flavors. In the benchtop instruments, they are a permanent magnet. Has anybody ever taken apart old computers, and you can get the hard drives, and there are strong magnets in there that are sort of silver colored? Those are made from a neodymium-iron-boron alloy. And that is what they use for the permanent magnets that are in the benchtop systems. There's been a great improvement in those in the past, I guess, 15 years or so. There used not to be any benchtop instruments. It was difficult to engineer and machine permanent magnets that would give a uniform magnetic field. But they've been able to do that. And so there are a lot of benchtop instruments that are out there now. The standard NMR-- well, they're termed high-resolution NMRs because they have stronger magnetic fields that then can be generated from permanent magnets-- use what are called superconducting magnets. So the magnetic field is generated by the circulation of electric charge in a superconductor. And, if you're familiar with superconductors, usually, they have to be below some specific temperature in order to maintain their conductivity. While the temperature, the critical temperature, has come up in recent years for superconductors, as far as producing something that's easily machinable into wire that you can wrap into a coil, the higher temperature-- higher critical temperature superconductors aren't easily malleable. So you still have to use something that you've got to get really cold, i.e. down to liquid helium temperature. So, in a superconducting magnet, you've got-- think of it as a giant thermos, which is what this can is. You've got a hole through the center, which is called the room temperature bore. It's room temperature because it is not cold. Your sample, which is in this little tube that I showed you generally, will be held in what's called a spinner, so this little blue thing. You will put it in the top of the magnet. And it will just ride down on a cushion of air somewhere to about there in the center of magnet-- in the center of the magnet. On the benchtop instrument, what's nice-- let's see if I can back up a slide. All you do-- you can see it, and it'll be obvious when you run it in the lab for yourself. You just put the tube right down in there. You don't have to put it in any specific holder. So your sample tube goes down that bore. From underneath the instrument comes the NMR probe, which I'll talk about in a second. So that superconducting wire is wound in a coil around that room temperature bore. This chamber here, which, if I could see, is number 6, that is a chamber that is full of liquid helium. So, when you set up one of these magnets, you cool it off. You fill that with liquid helium. And then you put a charge on this superconducting wire. And the charge is about 100 to 200 amps. And 200 amps is the amount of charge that goes through a medium-sized house. So it's got a good amount of electricity on there that's circulating around. As long as you keep it cold, meaning as long as you top it off with liquid helium every few months, it's going to remain a magnet and generate a powerful field. So, if you just had liquid helium touching metal, the outside of that metal would be a big chunk of ice. So this has an evacuated-- not layer, but I guess a portion of it that's evacuated with a high vacuum to provide insulation. Outside of that is a layer of liquid nitrogen. And we fill that weekly. And that just cuts down on any thermal transmission, even though you've got a high vacuum there. And then outside of that is another high vacuum layer and then the room. And so you can walk up to the can, and you can touch it. And it won't feel cold at all. So that's what the magnet consists of. The NMR measurement is based on the strength of the magnet-- so B0 is what I'm calling that-- and the gyromagnetic ratio of the nuclei that you're looking at. And we're going to talk about hydrogen today. And so you've got to be able to synthesize precise frequencies with precise durations and power levels in order to send those to your sample. So you've got this console. It's got amplifiers in there. 100-watt amplifiers is pretty much the standard. Actually, I shouldn't even say that's the standard. I think ours have 500-watt amplifiers in there. You've got different boards. It used to be that these all were plugged in to these long things with connections. And it talked through what was called a backplane, but, now that these are modern digital consoles, it all talks via ethernet. So everything has an address, and it talks to each other. It routes the signal to where it needs to go. You've also got some preamplifiers here. So all this material or everything that's in the console will generate the signal that is sent to your sample in order to excite it the way that you need to in order to get the information out that you want to. This also will take the signal that your sample gives off. And it will amplify it and digitize it and send it to the computer so that it can be processed into something you can use. To send the sample-- well, so the console generates all that signal, but it's got to be broadcast to your sample somehow. And so we think of the probe as the NMR antenna. So probes can come in a number of different formats. There can be probes for looking at solids. So you wouldn't even dissolve your sample in a liquid. There can be what are called flow probes where you've got just-- we call it a cell, but it's just a container that's a certain volume. And you pump your sample up through a tube into that cell, analyze it, and then you pump it out. There's what we call a micro coil probe, which just has a small cell. So I've used ones or had them in the past in other labs where it had a 5 microliter cell. So you could look at just a very small amount of things. There are also probes that are known as cryogenic probes. Those, the electronics that are in the probe are held at liquid helium or liquid nitrogen temperature. And, by doing that, it cuts down on the inherent electric noise that's present in the circuits. And it makes them more sensitive. So I've brought a probe here, and you're not going to be able to see this from where you're sitting back there, but you can come up and look at it later if you want. Your benchtop instrument will have the same stuff in it. It's just not going to look like this exactly. So this is what gets inserted up from the bottom of the magnet. And it's just-- it's screwed in, and it stays in the bottom of the magnet. There's only a couple of connections where the wires from the console are hooked up to this. And so this one, I can take the cover off of. And you can look at this when you come up. Up in the very top of the probe, there's a little glass insert. And there's some flat ribbons of wire that are wound around here. And so I've got that pointed out. In fact, I think that's the same probe that I took a picture of. And so your sample will go down, and it will go right into where those coils of wire are. And so the coils of wire will send the signal to your sample that's being generated in the console. And then, when that signal gets turned off, your sample will relax back to its equilibrium state. And it will induce a small voltage in these coils, which gets picked up, sent back through that console and off to the computer to generate your spectrum. So I will leave this right here. If you come up later to look at it, feel free to pick it up. Just be very careful. This is glass. And you don't want to bang on it or bend it because it will-- you can break it, not that it's working anyways anymore, but we like to have it for demonstrations. OK, so the NMR signal itself, it's generated when a collection of nuclei, meaning your sample, is placed in a strong magnetic field and irradiated with radio frequency energy of the appropriate frequency. And we'll see what that is in a second. The signal is a very small amount of energy that's given off, as the nuclei in your sample transition back to their equilibrium state. And it's really-- it's a time-dependent current that's induced in the coil in the probe on the order of microvolts. So it possesses four different-- four properties and only four properties that we make use of. So pictured right here is an actual NMR signal. It's what we call a free induction decay. It's just a damped sinusoid. And, out of that, you can get these four properties that you can make use of. The one that we usually make the most use of is the frequency. And so I'll tell you how you can convert this to this in a few slides, but where lines will appear on this graph tells us something about the molecular environment that whatever gave rise to that signal is in. So that's when-- most of the time, that's what you use. The next most common piece of information you use out of it is the intensity. So the intensity of a resonance in the NMR spectrum is going to be directly proportional to the number of nuclei that give rise to that signal. And that doesn't mean just-- well, it also means just every nuclei that's in there, but specifically, for instance, if you've got one signal from this group of protons and one signal from this group of protons, their intensity is going to be equal because three protons gave rise to this signal, and three protons gave rise to that signal. So you can use that as an internal check in molecules to make sure that you're identifying peaks correctly. You can also use it to quantify molecules, different molecules that are present in a sample. And you can even make a sample where you've spiked a known amount of something in there to serve as a standard and then quantify the amount of an unknown that you've put in there. Another property is the phase of this signal. So what I'm showing here is not something you're going to acquire. It's called a two-dimensional spectrum, but what I'm trying to highlight is that each of these colors, be it-- I called it red-- I think it might be some blend of that or blue-- are a different phase. Specifically, think of this. Does anybody know what a two-dimensional map is? Ever look at a topographic map where you've got mountains that are outlined by contours? So you can think-- what did I call it? So I said blue is negative. So think of the negative-- think of the blue cross peaks as being holes or going down into the plane. And think of the red ones coming out of the plane. So the way that this experiment is acquired, it makes methylene groups have a negative phase. And it makes methyl and methine groups have a positive phase. So that's really useful when you're looking at an unknown because, right off the bat, you can just say, OK, I know that this, this, this, and this are from a methyl or methine. And I know that these blue peaks are from methylenes. And then, specifically, I can look at it and say, OK, since this one and this one are in a line next to each other, I know that these are protons on the same carbon. The last piece of information that comes out of an NMR signal is the duration of the decay. So it can be longer. It can be shorter. You can use that like for things like I hinted at before where you have-- small molecules usually have a long decay. Large molecules usually have a very short decay. So, if you have a protein that's binding a small molecule substrate, its decay is going to transition from something long to something short. And you can use that to tell that your molecule has been bound. Any questions? All right, so unfortunately not all nuclei can be measured by NMR. Any nucleus that possesses angular momentum will exhibit a magnetic moment that will interact with a magnetic field. Just like electrons, if you've learned about in general chemistry where you learned the quantum numbers and you learned about spin, it's the same for nuclei. So we say a nucleus possesses spin in reference to its spin quantum number, which is labeled I. It's easy to think of nuclei as cute little balls that are rotating around, but remember they're not spinning. It's just an inherent physical property that seems like they're little spinning balls when they're not. So there are rules for determining if a nucleus has spin or not. It's present in either half integer or integer values. You don't really have to worry about that for this class. We're going to be looking at spin 1/2 nuclei protons, which are the easiest to interpret. And luckily protons have a 99.9885% natural abundance. So it's the most sensitive and strongest NMR signal that you can get out of any nucleus. There are, like I said, the rules for determining whether something has spin. Nuclei with even protons-- an even number of protons and an even number of neutrons do not have nuclear spin. And so they're NMR inactive. Unfortunately, the next most common thing that we would love to look at as organic chemists is carbon. And carbon has six protons and six neutrons for carbon-12. And so we can't. It's NMR inactive. Luckily for us, though, carbon has an isotope that's 1.1% naturally abundant, which is C-13. And we can look at that. We take a hit on sensitivity, but we can still get an NMR spectrum of that. So that's good. Some nuclei have multiple NMR-active isotopes. That doesn't mean they always appear in the same spectrum. They will have different gyromagnetic ratios. So they will appear at different overall frequencies, but you can look at-- sometimes, you can use that to your advantage. You could take a spectrum of 10 boron and a separate spectrum of 11 boron. Or a proton, we use the signal from deuterium as a lock signal for the magnet to focus on and counteract its inherent drift. So what's the physical basis of the NMR signal? In a magnetic field, all those little magnetic moments are going to adopt an orientation relative to that field. The allowed orientation of these moments is going to be explained by quantum mechanics. Luckily, we don't have to really get into that. And the process that nuclei undergo during an experiment can be rationalized in two ways. You can think of it in terms of vectors, so which way those little magnetic fields are pointing, or you can think of it in terms of the energy levels that the nuclei adopt when they're put in that magnetic field. So I tried to make a little cartoon here. With no magnetic field, these are supposed to just be all randomly oriented, but, when I immerse my collection of molecules that's in my sample in a magnetic field, they will line up and be either with the field or against the field. And so, if we look at one nucleus when we place it in a magnetic field, quantum mechanics tells us that it's not just going to point straight up. There's got to be some uncertainty in where that nucleus is pointing. And so it is going to precess, meaning it's going to rotate around, the direction of the magnetic field with a characteristic frequency, which we call the Larmor frequency. It's named for-- what's his name? Joseph Larmor who was a physicist back in the late 1800s, early 1900s. That frequency is going to be directly proportional to the strength of the magnet that you put your sample in. I've unfortunately-- so gyromagnetic ratio can be specified in either radians per second per tesla or in hertz per tesla. I apologize for not being too careful in that I will jump back and forth between the two. And so, for a proton, if we take a magnet, that's 11.75 tesla and we put our sample in there, it's going to precess around the field at 500 megahertz. And so, when we talk about NMR instruments, just as far as what size they are, they are not specified by the strength of their magnet. They're specified by the frequency that a proton precesses in a field with a magnet of that strength. So, if you come down to the DCIF, I'll say I have a 500, or I have a 600, or I have a 400. In the undergraduate teaching labs, you have a 300. And I think the benchtop is a 60 megahertz. And I'd have to go look up in a table or do the calculation how strong in tesla a 60 megahertz NMR magnet is, but that's the way it's specified. So that's for one nuclei when you put it in the magnetic field, but our sample is actually a bunch of different nuclei. Or not-- well, yes, it's a bunch of different nuclei. It's a collection of nuclei. We don't have to keep track of every individual nucleus and deal with the quantum mechanics when we look at an NMR experiment. We can treat the whole sample as a collection of the nuclei, so summing up all the individual magnetic moments, and just look at the bulk magnetization. And so we can use statistical mechanics in order to figure out what's going on. So we put our nucleus-- here's our sample. We've got, say, 10 milligrams of material. We've got it dissolved in about 600 microliters of a deuterated solvent. We drop it down so it goes in our probe in the magnet. And our collection of nuclei will start precessing either aligned with the field or aligned opposite the field. So there will be a slight energetic preference for those nuclei to have their magnetic moment aligned with the field. And that population difference will result in this net magnetization that we call the bulk magnetization. Let me put that down. We can jump from thinking of vectors to thinking of energy levels. So everything that is aligned with the field is going to be at a lower energy level. And we call that just the plus 1/2 nuclei. And everything that is aligned against the field is going to be at a higher energy level at negative 1/2. And so the difference between these two levels is going to increase as the strength of the magnetic field increases. And so maybe over here, on the 60 megahertz, the difference is only that much, but, when you get to our 600, it's a lot more. Here's where the measurement-- or the principle behind the NMR measurement comes in. You're making nuclei transition from one energy level to the other energy level. So you're perturbing their equilibrium distribution, and then you're letting them relax back. And that's what gives off the signal that we make use of in NMR. So I guess I jumped too far ahead in my verbiage. So we have our sample in there. It's lined up. And we perturb it with an RF pulse. So now I've jump back to vectors. If you think of it in terms of vectors, when you generate that radio frequency pulse that has the frequency equal to the difference in those energy levels, you are, in essence, generating a small magnetic field that is aligned. In this case, it's arbitrary, but we'll say it's aligned along the x-axis. That acts to topple-- or not topple, tip this bulk magnetization vector off of being pointed with the main field over into the xy-plane. It's still precessing around at that characteristic frequency. And, when it has a component in the xy-plane, that will generate a current in these little coils in the probe, which is then received back at the console and sent to the computer. So we pulse our sample. And depending on how long we turn on that pulse for-- and it's usually the order of microseconds. I think our pulses are set up to be about 10 microseconds. We can tip this over to some varying degree. And so usually we try and tip it over by a specific amount, which is a 90-degree pulse, because that will generate the maximum amount of signal that we can get out. So we tip it over into the xy-plane. We turn off that pulse. And then we let it relax, and we collect our signal. Our signal-- I think I said this before-- is called the free induction decay. And so here's another diagram of it. We've turned off that pulse. The signal is precessing here, but it relaxes back so that the component here gets shorter and shorter while we grow back the component in the z-direction. That gives us this voltage-- and my laser died-- that gets picked up in the coil. We can do that multiple times. So, if you've got a strong sample, you can just take one scan, but usually we'll take multiple scans because you can do what's called signal averaging, which is add them together. And that can help you remove artifacts, increase your signal to noise, and other things. So that's what the free induction decay is in the NMR signal. I put this back in my slide pack after I gave the slides to Professor Dolhun to print. So you don't have this in your handouts unfortunately. This is just-- I was thinking this is still a good way to show about the NMR signal, but in terms of the number of spins and the energy levels. So here's your equilibrium. You've got more spins pointing. I'm saying they're pointing down in this lower energy level. You pulse it, and that equalizes the energy level. So I forget how many are in each, but these are supposed to be an equal number of arrows. Then, after you turn off that pulse, the spins that got transitioned to the upper energy level will relax back down. So there's a predominantly-- they're more predominantly in the lower energy than the upper energy. As they do that, they give off the free induction decay, which is your NMR signal. Are these any questions? OK, so what do we do with that FID? Now, I've been doing this-- I don't know-- since 1999. I can look at an FID. I can say, well, that's a long one. I can look at an FID and say, yeah, that's got several different frequencies in there. But, as far as looking at an FID and saying, oh, that comes from DMF or, oh, that comes from ethyl acetate, no, I can't do that. And I doubt that anybody else could. So we have to transform that and somehow make sense of it. And so that is done using a Fourier transform. And so a Fourier transform takes something that is in the time domain. And it transforms it to the frequency domain. And, a long time ago, before the advent of computers, NMR wasn't done using Fourier transforms because it was computationally too difficult. And so someone back in the '60s-- actually, someone famous at IBM developed a way to do this to make it a little bit easier, but they still had to print out little cards. And you'd punch holes in them. And it would take days and days to feed it into a machine. And nowadays your phone can do it. It's got more computational power than something that had a whole room. So everything is done by Fourier transform now. That gives us our spectrum, which consists of lines, which we can look at, and we can interpret and figure out. And, no, I couldn't do a Fourier transform or solve one in my head or even on paper. So it's just something the computer does. So let's back up. I've given away a lot of this because I've already showed you several spectra, and you see that there are multiple lines. But here's the free curve for the equation for the frequency being proportional to the magnetic field strength. And you might think, OK, I have protons. Why don't I just get one peak because I have protons? And I would have one peak for protons and one peak for other nuclei. If it did that, I wouldn't be up here talking to you about this because, while it might be a fine and dandy measurement for a physicist to use, it'd be useless for us in chemistry because we'd only get one peak for all the different protons that are in our sample. Luckily, when you put your sample in a magnet, whatever the local magnetic environment is that the nuclei reside in, that is going to modify the [INAUDIBLE] or the external field that those nuclei feel. And so that's what spreads out our single signal from a proton into the different regions of the spectrum. So this is supposed to be ethyl acetate. I've got a doubly bound oxygen here. I've got a single bound oxygen here, a methylene, methyl, and methyl. So oxygen, I think everybody might know is electronegative. It's really greedy. It doesn't like to share its electrons. So it pulls electron density away from things that are nearby it. And that's why I've got these little deltas up here, indicating the partial negative charge. The things that are bound closest to it and even further out, they're going to be more positively charged or partial positively charged than they would have been because the electron density is being pulled away from it. So that's what helps spread out those signals. We call this chemical shift. It's denoted on a spectrum as ppm. And, oftentimes, it's denoted with delta, not to be confused with the delta I've used for the small charges, but you might see that on the axis of it. So anything that can perturb electron density will affect we call it the shielding of the nucleus, not only electronegative things, where nuclei are oriented in relation to double bonds. In a benzene ring, you've got the clouds of electron density in those pi orbitals. And things that get oriented directed into that will be more shielded. Things that are sticking off the ring equatorially-- or not equatorially, but in the plane will be deshielded. So that has an effect. So all these things will combine together to spread out what's in your spectrum. So here is just a spectrum of my ethyl acetate. And so notice I've spread it out. Well, I haven't spread it out. It is spread out into three separate signals. You can use NMR solely as a fingerprint and tabulate. I know that only such and such resonances come at 2 point-- I don't know. We'll call that 2.01. And so you can go look in a table and say, oh, well, this must be from one of these small subset of molecules because they only have something at 2.01. It's more important to be able to rationalize where things appear by-- or yeah, where things appear on this spectrum by where they are in the molecule because that will help you analyze the spectrum better. So, if we look at this, we've got three peaks. Now, I talked about intensity being one of the properties of the signal earlier. I don't know if you can see this, but there's a 3.10 under there, a 3.10 under here, and a 2 under here. So that's the relative intensity of those signals. Now, one thing that is common when you're first learning NMR is to think that the integrals are dead on exact so that it should be 3.00. No, it's going to be close, but it's not going to be exact. You've got to take great care when you're acquiring the spectrum to get your integrals to be as close to perfect. So we'd call 3.1 3. So we know-- we can look at our molecule. We've got two methyl groups. So we can guess that these are both from the methyl groups because they integrate the 3 and that this is from the methylene because it integrates to 2. So why is this methylene all the way down at 4 and these are up here? Well, what's the methylene next to? It's bound straight to the oxygen. So the oxygen is withdrawing the electron density away from that methylene. And it is shifting the peak what we call downfield, which means to the left on an NMR spectrum. That's a leftover term from in the old days when they would sweep. You would actually adjust the frequency-- or not frequency. You'd adjust the strength of the magnet. So anything that was down in this direction used a weaker magnetic field strength. Anything that was up in this direction used a stronger magnetic field strength. Nowadays, we don't do that. The magnet is always just what the magnet is, but those terms are still around. So anything to the left is downfield. Anything to the right is upfield. So this one is deshielded the most. It is at 4.1. The next peak is this one. Now, we've got to choose. Is it from this methyl, or is it from this methyl? And so you would look, and you'd say, OK, both of these are bound to carbon, but the carbon that this one is bound to is a carbon that is doubly bound to an oxygen. So electron density is being drawn away from that carbon by the oxygen. So that's still going to also have electron density being pulled away from this methyl. And so that's going to shift it down here. This carbon is just bound to a plain carbon without a double bound oxygen on it. And so it's not deshielded as much. Although, if I took a spectrum that had-- so, if I just had an alkane like pentane and I looked at the terminal methyl on pentane, it would be over here because it would not be deshielded at all compared to this. Another thing you might be questioning is, why are these ones split into multiple peaks, but this one is only a single peak? Let me make sure I kept my slides in order. OK, I did. That is due to what is called coupling. So protons that are bound to a carbon will, in essence, talk to protons on neighboring carbons through the bonds. And it's called spin-spin coupling or scalar coupling. And so you will have protons split apart into characteristic patterns. What else? So the splitting on those peaks is not dependent on the main field so that, if I took that ethyl acetate spectrum-- and I forget what strength. I maybe will say I acquired that at 500 megahertz. And I measured the difference between those peaks. And we'll say it's 8 hertz. If I take that molecule, I put it in a gigahertz machine, which is twice as strong, and I measure the splitting, it'll still be that same value. So, for simple spectra, the splitting follows what's called the n+1 rule. And so you look at the number of protons on neighboring carbons, and you add that up. So I guess I should have drawn another molecule. Where did my chalk go? So, for instance, we'll take this one here. So CH3, I've got two protons over here. So it's going to give me a simple spectrum. So it's going to be split by 2 plus 1 equals 3. And let's see. I'm going to close this and bring up my real spectrum. So this spectrum is of 3-heptanone. And the methyl here and the methyl here are these two resonances over there. And so you can, in fact, see that those are split into three peaks because each of them has two protons next to it. Now, not everything behaves that way. When you get into more complicated molecules, splitting can be completely non-rationalizable. So there are several ways that can happen. The most common way is, when the difference in chemical shifts between two nuclei is not much bigger than their coupling constant, you'll just get a whole bunch of different peaks. I can drag up an example of that in a second. So let's see. Oops, OK, so that crashed. Oh well, so I won't do that. OK, so I've given you a table in there that gives some of the common splitting patterns that you will observe. Yes? AUDIENCE: So what do you mean when you say simple spectrum? JOHN GRIMES: A simple spectrum is where the splitting obeys this n+1 rule. And so all the multiplets will be analyzable that way. And you'll know it. If you look at something and you don't see these common patterns, you can automatically say, OK, there's more complex splitting that's going on in or non-first-order. The intensities of those peaks in a first-order multiplet will obey or agree with the coefficients of a binomial expansion, i.e. Pascal's triangle. So, for n equals 2, you will get 1 to 2 to 1 and, for 3, 1 to 3 to 3 to 1. So they will obey that. If it was non-first-order, you might see four peaks, but you wouldn't have that same intensity pattern. So here's some other examples of NMR spectra. Here's a simple one, ethanol. We can look at this, and we can rationalize where the peaks appear in the same fashion. We've got a methyl group and a methine. So, if we look at the methyl group, we see that there's one, two protons next to each other. So we would expect the resonance for that to be split into three separate peaks. And there, in fact, we see a triplet. And then, for the methylene, not that it's default now because there's nothing-- or that's the only other one, you would expect one, two, three, four peaks. And you see that. And now this is tricky. Why do you not get three peaks for the OH, even though it's got two protons next to it? OH and NH have exchangeable protons. And so the proton is coming on and off that molecule in a faster time period than the NMR measurement. So you just see an average of the chemical shifts, meaning it gives you a single peak, rather than splitting into a triplet. These didn't come out very big, but it's just showing you, with bigger molecules, you get more peaks. If you zoom in on these, you'll see that a lot of these do not give simple triplets or quartets or doublets, that you've got a lot of more complex splitting going on in the molecule. And so here's an example of an ester. I think that you all are going to be synthesizing esters. So, if we look at these two compounds-- and something I didn't point out, well, I'll show you this in another slide-- anything that appears in an aromatic ring is going to be deshielded. So it's going to be far downfield. And I think I said that before. You've got the electron density of the pi orbitals above and below the ring, which would shield something. But those protons are held not there, but straight out from the ring. So they're in a deshielded region. So, right off the bat, we can look, and we can say, OK, we know that this must be-- or these peaks must be from the protons on the phenyl rings. Unfortunately, there's no integration on here, but you also, if I had the integration values, you would see that those both integrate to 5. And that would tell you something about it too. So now the question becomes, which splitting patterns in this region down here agree with what we see up here? So, if we look at our ester, we see that, on this ester over here, we've got-- and we saw this ethyl acetate. We have the methyl and the methylene bound to the oxygen. So we know that the methyl and the methylene are going to split into a triplet and a quartet. And we know that that quartet is going to be shifted downfield because it's bound to that oxygen. Now, that's not to say that also, in this one, they're not going to be split into a triplet and a quartet. But this carbonyl carbon is not going to drag the peak as far downfield as it does over here. So we can say that this compound here is from this one. And this peak right here is my single methylene that doesn't have any protons next to it, whereas this compound over here is this one here. Did I just do that? No, I just said that backwards. This compound here is this one. This compound here is this one. So here's the single methylene, and here it is. Here's the methylene that's split into a quartet. And it's right there, whereas, on this one, this methylene is shifted a little farther downfield because now it's bound to the oxygen. Does that make sense to everybody? OK. I'm not going to go over this completely. You can look at this. You can also look up-- you can find stuff like this online everywhere. This is a fellow over in England who puts out these graphics called Compound Chem. I don't know if anybody follows him on Twitter, but he's got all sorts of great chemistry education graphics. This is one that just gives you an idea of the different chemical shift values and where things appear. And so you can see an OH on a carboxylic acid is going to be very deshielded. Amide protons are going to be in this region and et cetera. So that I can give you some idea of where to look for resonances. I said that we can take spectra of carbon. Carbon is a lot less sensitive than proton. In fact, sensitivity-wise, if you just compare the gyromagnetic ratio of carbon to proton, it's a fourth of proton. So, like I said, we specify our magnets by the precession frequency of protons. So, on a 500-megahertz instrument, it would be a 125-megahertz carbon instrument. So you take that one fourth of a hit because of the gyromagnetic ratio, but then you also take a big hit because only 1.1% of the carbon present in your sample is made of carbon-13, which is the NMR-active carbon. The rest of it is carbon-12, which is NMR inactive. But you can still acquire carbon spectrum. A carbon spectra has a much bigger frequency spread. So you don't have overlap as much. That can be very useful. And this combined with a proton can tell you a lot about your molecule. You're not going to acquire these on the benchtop instrument. Although, I guess it probably will if you have a very, very concentrated sample. This is just to show an example. You can do very complex samples or experiments. So this is a three-dimensional spectrum of a protein. So this is something you would use in determining a protein structure. I've never acquired one of these. So all I can tell you is that you're looking both at carbon resonance-- what do we have up here? Oh OK, sorry. So it's the protein was expressed by bacteria that were growing in food that was labeled with N-15 and C-13 so that there's incorporation of those nuclei in there. And it will give you a signal, and you can use that. Let's see. I'm almost finished, but I think we're about out of time. Sample preparation, when you're preparing your samples, it is important to prepare clean samples. There should not be particulate matter in your samples. You should filter them if you do have particulate matter from your reaction because that will-- having particles in there will lead to poorer spectra that will be difficult to interpret. NMR are the very thin, glass-walled tubes. So be careful with them. If you snap this, you can easily stick it in your hand. So be very careful with that. Use a deuterated solvent when you're preparing your samples. I think you will be given that by your TAs anyways. And never put a dirty tube in the instrument. You should always clean the tube off on the outside. And then I think the last slide that I have is about shimming. Shimming is adjusting the homogeneity of the magnetic field. So, if you remember from that equation-- and you don't even have to know how to solve this-- so your frequency is directly proportional to the magnetic field strength. Shimming means making your magnetic field homogeneous so that the top of your sample feels the same strength field as the bottom of your sample. The machine will do it automatically, but, if the top of your sample feels a different magnetic field strength than the bottom, then it's going to have two separate frequencies for where those protons precess, which means the line broadens out. And, if that line broadens out, it makes it harder to interpret. And then I'll skip over this one. The last thing, I guess, questions, I put in some references in here. This is a great thing to do with old magnets. If you're artistic with cutting tools, I would love to have my own pizza oven with an old magnet. So, if anybody has any questions, please let me know. AUDIENCE: Pretty cool lesson. JOHN GRIMES: And no, that's not a friend of mine's either. I just snagged that off the web. AUDIENCE: That's hilarious. JOHN GRIMES: Anything else? Thank you. [APPLAUSE] And, if you want to look at this if you have time, you can come up.
MIT_5310_Laboratory_Chemistry_Fall_2019	4_Whats_Significant_in_Laboratory_Measurement_Error_Analysis_Lecture.txt	[SQUEAKING] [RUSTLING] [CLICKING] SARAH HEWETT: All right. I guess we can get started. So today, we're going to talk about what's significant in laboratory measurement and how to take measurements in the lab, how to do calculations with the lab, and how to do some of the data analysis when you have a lot of quantitative data, which you will have in the lab coming up when we do the Ellen Swallow Richards or the Charles River Lab. One thing I wanted to point out-- so there's hand-outs in the back. We're going to be going through how to do the calculations and how to do all the statistics. And there's an example problem that we're going to work through as we go in the back. So if you want to make sure you have a copy of that, that might be helpful. And one of the things that was pointed out this week in the lab is that in the lab, there is a typo left over from when we were in the old labs in Building 4. And so this Wednesday and Thursday, the TA session that it says, the help session about how to write the ferrocene lab report is going to be in the lab, not in 4:00, 4:30 as it says in the lab manual. So just come to lab as normal. The beginning of the lab period will be a quiz on the ferrocene lab, so anything procedure wise, calculations, reactions, all that good stuff, things that you should know, having done the ferrocene lab and hopefully having started to write up your report a little bit. And then after the first 20 minutes or so, it's going to be the quiz. And then your TAs will give a little bit of a lecture about what they're looking for in the ferrocene reports. So that's a good time to ask any questions about-- if you're unsure about where to write anything, how to write anything up if you have anything that you've already written and you want them to look at. They will be in the lab to help you out with that. And we have some more office hours, too, that got posted to Stellar. And I will have a slide about them at the end of this lecture, too, for more help. But, yeah, day four of ferrocene-- come take the quiz, then get some help on your reports. It is in the lab. You don't have to go anywhere else. Just come to lab as normal. OK, so if we're going to be talking about measurement today, then we need to talk about what things you should be thinking about if you're going to measure something. So if you're going to measure the length of this piece of wood with this ruler, how long would you be able to say this piece of wood is? AUDIENCE: There's no units. SARAH HEWETT: There's no units. Yeah, that's a problem. What else is wrong? AUDIENCE: It's not long enough. SARAH HEWETT: It's not long enough. So what's the minimum we could say about this piece of wood? AUDIENCE: [INAUDIBLE] SARAH HEWETT: It's longer than 1 something. So this is not a great measuring tool. What about this? Any better? Slightly better. So now, what could we say about the length of the piece of wood? AUDIENCE: Between 1. AUDIENCE: Between 1 and 2. SARAH HEWETT: It's between 1 and 2, probably a little closer to 2. But we can't really say too much more about it than that. And we still don't have any units. So this is just to get you thinking about what we need to be considering when we are choosing how we're going to measure something and when we were recording measurements, what information we can reasonably get from the measuring tools that we're using. So to talk about measurements a little bit more, we're going to need to talk about some terminology and get this out of the way, so that we're all using the same language. And you've probably seen these terms before in your other science classes in high school and middle school, going way back. But just as a quick refresher, so we're all on the same page, precision is how close repeated measurements are to one another. So if you measure the same thing a bunch of times, you would like the results to be the same. And you've probably seen these bulls-eye diagrams where if the results are all really close together, that is very precise. And you can measure that with the standard deviation. So the standard deviation gives you an idea of relatively how close your points are to each other. Accuracy is how close a measurement is to the true value or the value that you actually are trying to measure. So if you are throwing darts and you are trying to get the bulls-eye, then if you have high accuracy, then you have them all in the bulls-eye. If you have a high accuracy and high precision, then all of your darts always go to the center. You can have high accuracy where you're always around the target, but your points are scattered. And then you can have low accuracy and low precision where you're just all over the place. We measure accuracy by the percent error. So it's the error relative to the result that you're trying to get. And the answers don't need to be close to each other to be accurate. Like I said, they can be spread out, but still all close to the target value. So these are some terms that you probably heard there a little bit, used differently in chemistry sometimes than you may use them colloquially. So we just want to go over that. More terminology-- absolute error is how far away a measurement is from the true or accepted value. So if you are trying to measure, let's see, with this here, pipette, this pipette is designed to measure 10 milliliters. And you can look at it. And it has a tolerance of 0.04 milliliters. So that's an absolute error. It is how far away your measurement will be from the true value if you're trying to measure 10 and you measured 10.04. Then your absolute error is 0.04 milliliters. So you just subtract what you got from what you intended to get. The relative error is how far a measurement is from the true value, but it's relative to the quantity that you're trying to measure. So if you've measured 0.04 or 10.04 and you intended to measure 10, then your absolute error is the 0.04. To get your relative error, you'll make it a percent and divide it by the 10 that you intended to measure. So now, you have a 0.4% error. One way to think about this is if you have an absolute error of 1 milliliter when you're measuring out 2.5 liters of material, that's pretty small. But if you have an absolute error of 1 milliliter when you're measuring out 2.5 milliliters of material, then that becomes a much bigger problem. So depending on the quantity that you're measuring, sometimes it's a little bit more useful to report the relative error than the absolute error and vice versa, depending on the application. If you say, yeah, it had an error of 1 milliliter, and your friends are all saying, oh, you did such a great job, and then you say, I was only trying to measure 2 milliliters, then not so great. Other types of error are random error and systematic error. So random error is things that we can't really control for or identify. And it causes data to fluctuate relatively uniformly around a mean value. And that's one of the things that's given on the uncertainty in the measuring apparatus that you're using. So this pipette measures 10 milliliters, plus or minus 0.04 milliliters. That is a random or indeterminate error. The data will fluctuate around 10 milliliters within 0.04. You know that. And you can control for that using statistical analyses, which we'll talk about in a little bit. Systematic or determined error is error that has a known cause. And that could be from faulty or poorly calibrated instruments, human error, or chemical behavior inside reactions. So if you intended to get 5 grams of product and you got less than 5 grams, then you know that there is some error associated with your experiment. And it could be because maybe some of your iron oxidized. Or maybe you spilled some of your ferrocene. Or maybe you were not tearing the balance every time you used it. So that'll introduce error into your measurement if you were using the equipment improperly. Or if you're reading from a burette and you're always reading in the wrong direction or you didn't read to enough significant figures, that's systematic error. And so that's not necessarily from the glassware itself. That's from how you were using it. And these are types of error that you can talk about in your discussion section of your lab report. So you could talk about the error that is associated with the measurements that you can control and that you cannot control. So the last term that we need to talk about in terms of when we're making measurements or doing things in the lab is, what does it mean for something to be significant? So you may have heard of the term "significant" figures or this is a significant result. What does it mean for a number or measurement to be significant? And what makes a measurement that we take significant in the lab? Yeah? AUDIENCE: Ideally, significant means all the numbers that you're certain about plus one estimate or one final. SARAH HEWETT: Exactly. Yeah. So a number is significant. And you report the significant figures-- are in a measurement, all of the numbers that you're certain of, plus the first uncertain digit. So a lot of times, you'll have some sort of-- you won't have measurements every-- maybe tenth of a milliliter or 1 milliliter, depending on the size of the glassware that you're using. So you can be certain of some of the measurements. And then you're uncertain of others. So in our piece of wood, we were certain that it was bigger than 1, but we were uncertain of the next digit. So we could estimate that second digit. And that counts as significant. A quick review of significant figures and how to use them. All non-zero digits in a number are significant. Zeros in between non-zero digits are also significant. Zeros to the left of a non-zero digit are not significant. Zeros to the right are only significant if there's a decimal place. And you can avoid ambiguity in that with scientific notation. So if we just go through these really quickly, how many significant figures does this have? Four. AUDIENCE: Three SARAH HEWETT: Three. AUDIENCE: Six. SARAH HEWETT: Six. AUDIENCE: Two. SARAH HEWETT: Two, maybe. AUDIENCE: Maybe? SARAH HEWETT: As written, yeah, you would probably call it two, because the zero is to the right. But if you wanted the zero to be significant, then you could write it like this. And now, how many significant figures do we have? AUDIENCE: Three. SARAH HEWETT: Three. And if the zero is not significant, then to avoid people being confused about it, you could write it like this. And we have two. So that's one way you can use scientific notation to get around ambiguity. Yes? AUDIENCE: Yeah, I have a question. So for 590, if someone put a decimal point after the zero-- would it be three significant figures, or would it be two? SARAH HEWETT: So that's a question that I've always gotten. I think, just conventionally speaking, if you wrote something as like this, maybe. More conventionally correct would be to write it as 5.90 times 10 to the 2. Because you don't usually have a decimal place if there's nothing after it. And then if you wrote it like this, though, then you have four significant figures. And that's more than you want. So just go with the scientific notation, instead of having a hanging decimal place. Because that's not the typical way to write numbers. When you're doing math with significant figures, if you're adding and subtracting, then your final answer should have the same number of decimal places as the number you started with that has the smallest number of decimal places. When you are multiplying and dividing, the answer should be rounded to the same number of significant figures as the number you started with that has the least number of significant figures. So when you are multiplying and dividing, you want to count up your sig figs. And when you are adding and subtracting, then you pay attention to your decimal places. So if we go back to our piece of wood, then using that ruler that we had earlier, we can estimate. Maybe this is 1.8. So we have gradations every one unit. We still don't have units. Whatever this is. And then you can estimate this, one digit pass that. And then our uncertainty is our gradations divided by 2. So we know that we are within 0.5 of the correct answer. Because we can estimate that it's within this half of our interval. If we add more gradations to our ruler-- so if we have markings every 0.1, still no units, then we can say with certainty that our piece of wood is 1.567 bigger than 1.7 and smaller than 1.8. So it's 1.7 something. You can estimate that last decimal place. And then your error gets smaller to your uncertainty in that measurement. This is important in the lab. Because you need to make sure that you're choosing the correct apparatus for the amount of uncertainty that you want in your measurement. So if you see something in your lab manual that says measure 1.2 grams, then this balance is totally fine. Because the balances-- if you've never noticed at the top, they have the uncertainty written on there. So the uncertainty is in this last decimal place here. So if you want 1.2 grams, then you can't get 1.2. And then your last digit is the uncertain one. Should always write down all of the digits that are on the balance screen. But when you're going to calculate uncertainty or do an error propagation, then you know that the last digit is where your uncertainty is. This is plus or minus 0.01 grams. So we have three different types of balances in the lab. So you want to make sure that you're choosing the one that has the correct number of decimal places for the quantity that you are trying to measure. And the same thing goes for glassware. So the uncertainty in the glassware is frequently reported on the glassware itself. And there are standard tolerances for various sizes and grades of glassware. So if you've ever seen glassware that's volumetric, it may say either an A or a B on it. So the A is the highest standard. And then B is a slightly higher tolerance. And there are standard things of those that you can look up. But it's usually written on the glassware. And so this is an example of the 10-milliliter pipette that I was showing you earlier. So you can look at the pipette. And then on the top part here, it'll say 10 milliliters. And this one says plus or minus 0.04. This pipette says plus or minus 0.02. So that one is calibrated a little bit more precisely. These are also 10-milliliter pipettes. And you can look on the top part here to figure out what their tolerances. These are both 0.06. And one of the other things that you need to make sure when you are using different types of glassware is to figure out where the markings end. So these are both 10-milliliter pipettes. And they are designed to measure 10 milliliters within 0.06 milliliters. This one-- I don't know if you can see it from here. Probably not, but maybe if I hold it up here. The markings-- and they go from 0 to 10. And it ends here. And there are no more markings at the tip. So that means the only time you're measuring something is when your liquid is within where the markings are. So if you're going to measure 10 milliliters, you need to start your liquid here, end it at 10. And don't go below that, because that quantity is not calibrated. There are some pipettes like this one that are also designed to measure 10 milliliters, but these have gradations all the way to the end of the pipette. So to get 10 milliliters out of this one, you would fill it up to here and then drain it all the way out to the bottom. So you want to make sure that you check your glassware ahead of time to figure out how much of it you can use to measure liquids and what you get if you empty it all the way out, versus measuring by difference. If you look at your graduated cylinders, your graduated cylinders are different sizes. And the markings come in different levels of precision. So this has markings every half of a milliliter. And its tolerance is listed at the top as plus or minus 0.3. The 50-milliliter graduated cylinder has markings every 1 milliliter. And at the top, it'll tell you that its tolerance is plus or minus 0.5 milliliter. So again, that's the 1 milliliter divided by 2 rule. So sometimes that holds. And sometimes it's a little bit different. Volumetric glassware always has a smaller tolerance, so this is to 250-milliliter volumetric flask. And on here, it will tell you that its tolerance is plus or minus 0.12. So you should always look at these. And when you are making measurements in the lab, when you're writing things down in your lab manual, you should always write down what the uncertainty in the measurement that you're making is. So whether it's on one of the balances or a volume, always make sure that you write down what the uncertainty of the glassware that you're using is. If you look at something like a beaker, this also has a tolerance on it. And it's plus or minus 5%. So that's a lot when you are looking at a 300-milliliter beaker. That's going to be a lot more uncertain than any of these other measuring implements. So it's good to know before you choose, what piece of glassware you going to use to measure something, how precise you want your answer to be, and how much uncertainty is acceptable in the measurement that you are making. With burettes-- so this is a 50-milliliter burette. And it doesn't have a tolerance listed on it, but it has markings every tenth of a milliliter. So what would be uncertainty in the burette? Point? So if the markings are every-- a 50-milliliter burette. The markings are every 0.1 milliliters. So the uncertainty is-- AUDIENCE: 0.05. SARAH HEWETT: 0.05, so plus or minus 0.05 milliliters. In a 10-milliliter burette, the markings are every-- let's see. I think they're every 0.2. No. What are these? 0.05. Yeah, these are every 0.01 in a 10-milliliter burette. So what would the uncertainty be here? AUDIENCE: 0.005. SARAH HEWETT: Yeah. So make sure that you are looking at what glassware you're using, and you record the correct number of significant figures. Because it changes based on the type of burette and even within different types of glassware where they are, made different with varying levels of quality. So we can make one measurement. And then we can figure out what the uncertainty is in that one measurement. But what happens if we take multiple measurements and have to do math with them? So if you look at your worksheet here, this is an example of something that you might do in the lab where you have done a series of titrations to calculate the concentration of some sort of HCl solution. So the first question is, what is the uncertainty associated with a 50-milliliter burette? We already figured that out. And then if we were going to calculate the volume dispensed in each titration trial with the correct error, how would we do that? So one of the ways that you could think about adding up the error in these measurements is just straight up, adding the error. So for this first example, we have 12.52 milliliters. This chalk is no good. And then do volume by difference. We have 0.24 milliliters. And each of these has an uncertainty of plus or minus 0.05 milliliters. So if we added up the error in these measurements, then we would get 0.1 milliliters. But it is probably pretty unlikely that both of these measurements were off by the full 0.05 milliliters. So this would tend to overestimate the amount of error in your final answer. So what we do is we propagate the error. And when you're adding and subtracting, you use the absolute errors. Because you should be adding quantities that have the same units. So units will be consistent throughout your calculation. And when you do this-- did anybody subtract this out? I don't know if anyone has a calculator. Got one? AUDIENCE: Yeah. SARAH HEWETT: Great. So if we subtract these two numbers and we get 12.2 milliliters. And then how do we propagate the error for this calculation? So our error is going to be the square root of the squares of the errors of each individual measurement. So each one is-- so if anyone has done that-- or you do it in your head. Why not? The answer that you get is 0.070710678. So that's a lot of extra decimal places. And what we really care about in uncertainty is, where is the first decimal point that is uncertain? What is that first digit that we don't know for sure? And so we always round an error to the first significant figure. So the error associated with these measurements is just 0.07 mL. So to right this perfectly, you would write it as 12.28 minus 0.07 milliliters. And you can calculate the volumes for each of those trials. And then the error for all of them is going to be the same. Because the error for each of your direct measurements is going to be 0.05. So then we can talk about what happens to the error in a calculation when you are multiplying or dividing something, which is this next part. So if you're going to use this value to calculate the concentration of the HCl in this fake experiment, then you will have to do some multiplication and division. And you'll be using different quantities that have different units. So you can't just use the absolute error, because they have different units. So if you have your error with your burette reading, that'll be in milliliters. If you have your error with your concentration, that's in molarity. So we can't use the absolute error. So we'll have to use the relative error, which, if you remember, is the absolute error divided by the measurement that you've made. So you want to take a second and do out that calculation for how to calculate the concentration of the HCl. Then we can do it all together in a second. And we'll just do it for the first trial. And then if you guys want to have more practice, you can do it for the others afterwards. So if we're going to set up this calculation for the concentration of the HCl solution, where would we start? It's the first thing that we have to do or to calculate in this. Yeah? AUDIENCE: Figure out how much sodium hydroxide we have. SARAH HEWETT: Yeah. In what units? AUDIENCE: Moles. SARAH HEWETT: Moles. So we can figure out how many moles of sodium hydroxide we have by taking our volume. And then we have our units, our concentration return, moles per liter. So we need to turn this into liters. And then we can use our molarity to get moles. I guess we could do that as moles of NaOH in 1 liter. And then we can go from moles of NaOH to moles of HCl. What's our mole ratio? AUDIENCE: One to one. SARAH HEWETT: Too easy. One to one. Yeah. 1 mole. And then we have moles of HCl. And then the last step is to divide by our volume of HCl. Yes, which in this case is 0.0100. Yeah, liters. And that should give you, if anybody did it out, 0.60172 molar, hopefully. So that's our concentration. And now, we have to figure out what the error associated with that concentration is. So we will look at the error involved in each of these terms. So we have our error associated with our burette measurement. So our first one is going to be the 0.07 over 12.28 squared plus-- what's the next error that we have? AUDIENCE: [INAUDIBLE] SARAH HEWETT: Which one? No, say it. AUDIENCE: The last one. SARAH HEWETT: Last one. Yeah, we have error associated with this measurement, right? And the error associated with that is 0.02 milliliters. So you have 0.02 milliliters over your 10 milliliters. And then what's the last error that we have? Yeah? AUDIENCE: Concentration of NaOH. SARAH HEWETT: The concentration of NaOH. The 0.04. So you have 0.04 over 0.49. That's how you will calculate your error for the concentration of the HCl. And if you do this out, you get 0.08. So then, how would we report these two together? That's the thing from before. So what is this? What type of error is this? Is it an absolute or a relative error? Relative. So we calculated it from all of the relative errors. So this is a relative error. And it's also-- you could think of this as 8%. So in order to get it back into a standard error that we can report with our 6.60172, then we have to multiply these two together. And if we go back to our sig figs from before-- in this calculation, how many significant figures should our final concentration answer have? AUDIENCE: Two. SARAH HEWETT: Two. So this has two sig figs. So we'll round this to 0.60. Then you can multiply that by your 0.08 relative error. And your final answer should look something like this, way down here-- 0.60 plus or minus 0.05 molar. Any questions about calculating errors and doing error propagation? So this is why it's important to make sure that you have the correct tolerances and the correct errors associated with all of your measurements. Because when you go to do all of your calculations and write your lab report up, it will be very hard to figure out your error if you are missing some. OK. So now that we know how to deal with the various independent measurements, what happens when we make the same measurement more than once? And this goes back way-- probably to middle school when we talk about the mean or the average of a sample. So in statistics land, they call all of the possible values that you could measure of something the population. And it's really hard to know the true mean of the population, unless you have access to the entire population and you've taken all possible measurements, which is pretty much impossible, especially in the case of 5.310. We're not going to be making all of the possible measurements there are for each quantity that we measure. So in the lab, we can take the mean of a subset of the population. We call that the sample and then calculate our sample mean. So population mean, if you ever see in statistical literature, is denoted as mu. And then our sample population is denoted as the x bar, where you just add up all of your measurements, divide by the number of measurements you took. And that's your mean. So we calculate an average or a mean for the HCl solution on the back. If you didn't do the calculations from before, the concentrations that you should get are 0.60, 0.61, 0.61, and 0.64. So if you add all those up and divide by 5, then your mean concentration is 0.615 or rounded to the correct number of significant figures-- 0.62 molar. The other thing that you can calculate is the standard deviation of your measurements. And so remember, that's a measure of precision or how close all of your measurements are to one another. So small standard deviation means that all of your measurements are very close together, very precise. And to calculate the standard deviation, again you could calculate the standard deviation of an entire population. It's the sigma up there. And then you need to know your population mean. But in the lab, we are taking a smaller subset of the population. So we have to calculate a sample standard deviation, which is denoted as S. And the major difference here is that instead of dividing by N, which is the number of samples, you divide by N minus 1, so the number of measurements you took, minus 1. So to calculate a standard deviation, you calculate each of your measurements, subtract it from the sample mean, square it, add those all up, divide by N minus 1, and then take the square root. And you can do this on a scientific calculator, a graphing calculator. Excel does it for you, any statistical program that you want. You don't have to calculate this by hand in your lab manual or in your lab report. You could just show the formula for it. And then you can calculate it using any sort of statistical program. So if we calculate the standard deviation for our concentration of the HCl solution, then you should get-- not going to do this all out by hand right now, because we don't have a lot of time. But if you wanted to try it out later or check your answer for somewhere else, it should be 0.1732. It keeps going. So the standard deviation is typically rounded to the same number of significant figures as the measurements that you are using to get the standard deviation. You'll see it reported pretty frequently like that. So we can report our standard deviation as 0.017. Since we are taking a mean that is not the population mean, we know that we may not have exactly-- the mean of your sample will probably not be exactly the same as the population mean. But you can figure out how good of an estimate your mean is, of the overall population mean, by calculating the standard error of the mean. And that is done by taking the standard deviation of your sample and dividing by the square root of the number of data points that you have. So if you want to get a better and better estimate of the true mean of your population, then you can keep increasing the N value. And eventually, it'll make your standard error smaller to a point, since it's the square root. Once you get a big enough number of N, then incrementally, you get less and less benefit from adding more and more data points. But you can also make your standard error smaller by decreasing your standard deviation. And so if you can make more precise measurements, then that will also help improve the quality of your mean and how accurate it is toward the actual population mean. All of this is leading up to doing statistics. And all of statistics is essentially based on the Gaussian distribution or the normal distribution. And you've probably seen this before. And this graph is an axis of where the x-axis is the number of standard deviations away from the mean. And then the y is the probability of finding a measurement in that space. So you can see that the highest probability of all of your measurements is going to be very close to the mean. So if you're taking measurements accurately, they should be very close to the mean. And then as you get further and further away, there is less probability that some measurement you take will be three standard deviations away from the mean and so on. So this number Z is calculated by subtracting your number from the mean and dividing by the number of standard deviations. So it's just essentially the number of standard deviations away from the mean-- your measurement is. Oh, back up. We cannot go back. There we go. One way that we can use this is to figure out confidence levels of the measurements that we take or the means that we calculate. And so you can come to an error under the curve analysis here-- or an area under the curve analysis. And so for all measurements that are within one standard deviation, plus or minus from the mean, that accounts for 68% of the area there. If you go within two standard deviations, you can stay within 95% confidence that your mean is within that area. And then within three standard deviations, plus or minus, so 99% chance that your mean is within that area. So we can use this when we are calculating the accuracy or how confident we are that have measured the population mean with the samples that we have taken in the lab. We can do this because of the central limit theorem, which states that the distribution of sample means in a population will constitute a normal distribution, even if the population itself is not normally distributed. So if you take a bunch of samples or take a bunch of measurements in the lab, then you can use the normal distribution to statistically analyze them, even if you don't know the distribution of the population itself. So we can use that information to calculate confidence levels of a mean that we calculate. So what that means is we can calculate how confident we are that our mean falls within a certain range of the actual population mean. And you can say it with different levels of confidence. You could say I'm 99% confident. And you'll get a wider range or 95% confident. And you'll get a little bit of a smaller range. And the range of the values is what we call the confidence interval. And you can calculate a confidence interval for the actual population mean. And that is your standard mean, that Z square root we were talking about, times the standard deviation of the population, divided by the square root of N. To use Z as in the previous slide, you need to have a big enough sample size that your estimates of the mean and the standard deviation are a good enough substitute for the actual sigma, the population standard deviation. That's really challenging in lab situations. And in 5 through 10, we will not ever have a big enough sample size for that to be the case. So as an alternative, we can use the t statistic. So to calculate a confidence interval for a mean that you calculate in lab, you can take your mean, plus or minus the t statistic, times your sample standard deviation, over the square root of N. And you can calculate t statistics using this formula if you have all of this information. Or you can get a table of t values for varying confidence levels and varying degrees of freedom, which is N minus 1, which is the number of measurements that you took, minus 1. So if we're going to calculate a confidence interval for the mean of our HCl concentration, then we will have something like-- we need our average, plus or minus ts, square root of N. And you'll notice that this standard deviation over the square root of N is the standard error of the mean. So if you calculate that, then it'll make it slightly easier to calculate your confidence interval. Yeah. And so to do that, we're going to need some t table, which gives you the t statistics. Our average of the mean was 0.62, plus or minus. So the t value-- if we have four measurements, then our degrees of freedom is going to be 3, so N minus 1. And then we want to use a two-tailed t-test. Because we don't know which way our measurement is going to vary. So the two-tail means that it could be higher or lower than the actual mean. So you want to calculate one that has a value of 0.05. So that corresponds to the 95% confidence interval. And 3-- so 3.182 is our t value and then times 0.017. And what you get, if you do that out, is-- so when you're going to report your 95% confidence interval, you would add this number and subtract this number from your mean and then report it as a range in parentheses, so 0.593,0.647. And so that's your 95% confidence interval. And so what that's saying is that there is a 95% chance that the actual population mean lies between these two numbers. You are 95% sure that the actual mean is in there. So in your lab reports, when it says to calculate a 95% confidence interval, that is what we are looking for. Other issues you may run across in your data is if you take repeated measurements of the same quantity. You may have outliers. And sometimes you can look at your data and say, wow, there's definitely an outlier here and other times-- but even if you can do that, it's nice to be able to mathematically demonstrate that it is, in fact, an outlier. And so to avoid subjectivity in whether you're tossing out data points left or right, just to make yourself look better, you can use the Q-test to help decide whether a value can be kept in a data set or should be rejected as an outlier. And the way that the Q-test works is you take the absolute value of the result that you're worried about, the questionable value. Subtract it from its nearest neighbor, so whatever the next closest value that you measured was. And then divide it by the spread of the data, which is just your highest value that you measured, minus your lowest value that you measured. And then you have to look at another table of standardized Q values. And if the Q that you calculate is greater than the Q in the table for the number of data points in the confidence level that you want, then you can reject that point as an outlier at that confidence level. So the last question on here is not really related to the first whole set of problems. But if you took the following measurements for a concentration of an NaOH solution, are there any outliers in that data set? So what's our Q calculation for this data set? Which result might be questionable? 2.86. Yeah, that seems to be a little bit higher than everybody else. So our questionable result is 2.86 minus-- AUDIENCE: 2.52. SARAH HEWETT: 2.52 is its next closest neighbor divided by-- how do we calculate the spread of our data? AUDIENCE: [INAUDIBLE] SARAH HEWETT: So 2.86, which is our max. And our minimum is 2.38. So if you do that out, you get 0.34 divided by 0.48. So our Q value is 0.708. Now, if we look at a table of values for our Q-test-- so we can either calculate it at 90% confident that it's an outlier, 95% confident that it's an outlier, and all the way down. So if we wanted to calculate at 95% confidence level that this point is an outlier, then we had how many data points in this data set? 6. So we'd look at 6. 95%. Our Q value is 0.625. So 0.708 is greater than 0.625. So is it an outlier or not? The Q that you calculate is bigger than the Q in the table. Then it is, indeed, an outlier. And we can confidently say that that does not belong in our data set. Ooh, we're working on it. Come on. So you can see that if anything had changed, like if we had had fewer data points, then it would not be an outlier. Or if you wanted a higher confidence level, then it also would not have been an outlier. So it's a little more strict, how far away from the rest of the points it has to be before you can call it an outlier. Last thing we're going to talk about is doing the least squares regression. You'll make a bunch of calibration curves when you are doing different measurements with UV-Vis spectroscopy. So in UV-Vis, which you'll talk about in the next couple of labs, the absorbance of a sample at a certain wavelength, how much light it absorbs is related to its concentration. And this is a calibration curve with the concentration of bovine serum albumin protein versus absorbance, which you guys will be making a similar one in the catalase lab coming up. So it assumes that one variable is known. So that's our concentration, that we have known concentrations, and that all of the variation in the y-axis is linearly related to our x values. So that's one assumption that you have to have before you are going to make a least squares linear regression. The way that you can calculate all of the values in a least squares regression-- which the whole idea of is to get an equation for a line in the form of y equals mx plus b. So that's the point of all this. And you'll have different points. And you want to calculate a straight line through all of your points. So some of the terminology that is associated with this is the residual value. And so that's your vertical distance between a point and the line of best fit. So this is your residual value. Each point has a residual value. And the way that the line of best fit is generated in the "least squares method" is they take the square of all of these residual values and try to minimize it. And so you can calculate various quantities if you take all of the x values, subtract them from the average x and square them. Then you'll get the Sxx. You could do the same thing with the y values and then the x and the y values. The slope of the line is this value over this one. To get the y-intercept, you take the average y, subtract it from the slope and the average x. And then the r squared. This was a misprint in your slide hand-outs. It should be 1 minus this quantity in the hand-outs. The 1 is not on there. And so the R squared value, which you've probably seen before, is the coefficient of determination. And that is a measure of how well this best fit line can explain the variation in y in a linear fashion. So essentially, how well do your points fit a linear relationship? Is that a good way to explain your data? So the best way to generate this is in Excel. You could calculate all those quantities by hand if you want to. But Excel will do it for you or your other favorite mathematical software program. You graph your points as an x-y scatterplot. Then you can right click the data points. And it'll say add trend line. And then you can have options to display the equation and the R squared on the graph. So you'll get your y equals mx plus b equation there and your R squared value there. So you can see that this line is-- this is not a very linear set of data. So your R squared, ideally, is close to 1. And this is close-ish to 1, but that is definitely not a linear relationship. You can get it higher than that. And we'll talk about that more when you guys make your calibration curves for the bovine serum albumin. The Coomassie blue dye is only linear in certain regions of the calibration curve. So you'll have to calculate different lines for different pieces of the curve, depending on what your concentration is. The last thing that we can do to get more information out of a set of linear data is to use the LINEST program in Excel. And if you've never done this before, you type in your data as a series of x and y points. And then instead of graphing it-- well, you can graph it, too. But in addition to graphing it, you highlight a 2 by 5 area of empty cells. And while that's highlighted in the first cell, you type in equals LINEST. And then it'll prompt you to highlight your y values, then highlight your x values. And then you can type true and true. And what that'll do is if you type false, it'll set the y-intercept to zero. And we don't want to force our lines through zero. So you will have your slope. And then if you press Control-Shift-Enter, even on a Mac-- so on a Mac, press Control, not Command. Press Control-Shift-Enter. And it'll give you this array of data. Once you get this array of data, don't try to change any of these values or Excel will get mad at you, so just leave it. And this is the key to what each of the cells is telling you, because it won't give you this information. You can look it up online, or it'll be on these slides. So your first thing-- it'll just give you your slope and your intercept. And then it'll give you-- these are the two that we care about the most, are the standard deviation of the slope and the standard deviation of the y-intercept. So sometimes in this course, you'll make graphs where the slope is representative of a certain quantity. Or the y-intercept is representative of a certain quantity if you're graphing any equation in linear form. So then you'll have the standard deviations of each of those measurements. Then it'll also give you your R squared and a bunch of other information that you want if you're doing different statistical tests.
MIT_5310_Laboratory_Chemistry_Fall_2019	9_Essential_Oils_Lecture_Part_2.txt	[SQUEAKING] [RUSTLING] [CLICKING] SARAH HEWETT: All right, good afternoon. We should get started, because we have a lot to talk about today. So today is the second in a series of three lectures about the essential oil lab. You'll get a third lecture and a little bit about X-ray crystallography. But today, we're going to finish talking about the main synthetic parts that you'll be doing in the essential oil lab. So today, we're going to talk about how if your separation worked. And before I get too far into that, there was a question in the Tuesday lecture about the naming of terpenes. And so if you remember, the terpenes come from the isoprene structure, which was five carbons and eight hydrogens. But then there are some terpene derivatives, like menthol, that don't necessarily have that five carbon, eight hydrogen structure. So this obviously has an O-H group and more hydrogens. And so what I found in the literature is that there are terpenes, which follow the strict pattern. And then there are terpenoids, which are derivatives of terpenes. They are synthesized from the same backbone. But then they get extra hydrogenation or oxidation done to them. So, like, your carvone has the oxygen double bond in it. So that's technically a terpenoid. They seem to be referred to pretty interchangeably in the literature, which I thought was interesting. But that is probably the more accurate way to name these types of compounds. So hopefully, that clears up a little bit of that confusion. So jumping in to the rest of the essential oil lab, on Tuesday, we talked about what you're going to do on day one of the lab, which is you'll get your essential oil, which will either be spearmint oil or caraway oil, and you will separate it into its two major components, which are your carvone, there on the left, and your limonene. So essentially, you'll take an oil that looks like that, and you'll separate it into two other oils that will also look really similar to that first one, except hopefully, they're pure compounds. So if you do your vacuum distillation really well, and you separate those, and you get two pure compounds, we need to figure out how to characterize your separation, and figure out how well you were able to separate your carvone from your limonene. And we're going to do that in a whole number of ways. You'll get a lot of experience with different analytical techniques. And these are the major methods that we're going to be using to characterize the success of your separation. So we'll be doing refractometry, gas chromatography, infrared spectroscopy, polarimetry, and X-ray crystallography. And so today, we're going to talk about the first four of those. And then, like I said, in a week or two, Peter Muller from the X-ray crystallography lab will come and do a much more detailed explanation of X-ray crystallography and what information you can get from that. So to start with, refractometry-- refractometry is a way to measure the refractive index of a compound. And that is a characteristic property of different compounds. And it is-- it comes from the ratio of the velocity of light and air to the velocity of light in a liquid. So you have your light traveling through the air. Then it hits the liquid and it slows down, and it changes the angle. So you'll notice, if you ever look through some water, you'll know that the image is slightly distorted. And that is because of water having a different refractive index, or water having-- the light slows down as it travels through the water. So all of our organic liquids-- so like I said, you're going to be separating your oil into two other oils. So we'll have liquids, which means that they will have refractive indices as well. And most organic liquids will have a refractive index somewhere from 1.3 to 1.7. And the way that you calculate that is it's represented as n. And you can either do the ratio of the velocity of the light in the air to the velocity of the light in the liquid. But that is hard to measure. So in the lab, we can measure the angles at which the light travels. So if you have light that is coming through the air-- so if this part is the air, and you have your light, it'll hit your liquid interface at a certain angle, which is theta from straight up and down. And then, it'll get refracted at a different angle. We call that theta prime. So you can measure that in the lab and calculate your refractive index. The refractive index is dependent on the wavelength of light. So you might imagine that if the refractive index and how much this angle-- and how much the speed of the light changes is dependent on how the light interacts with your liquid, then it'll depend on the properties of your light-- so the wavelength-- and the properties of your liquid. And one that we care about is the density. So the way that we account for this is that we have the refractive index. And we call it refractive index D20. And so D represents that you use light from the sodium D line. So if you remember from, maybe, gen chem or physics, if you heat up an element very hot so it emits light, you can-- each element has a characteristic set of wavelengths of light that it emits. And sodium's happens to be around-- its brightest emission happens to be around 586 nanometers. So if you use a sodium lamp, and you can select for these 586 nanometers, then you get a characteristic one wavelength of light that you can pass through your sample. So you know what the wavelength is, and you can know that you're just getting that one wavelength of light. And then, you want to make sure that all of your samples-- or your measurements are taken at 20 degrees Celsius so that the density of your liquid. So if you change the temperature, you change the density. So we'd make all of our measurements at 20 degrees Celsius. And here are the approximate refractive indices of limonene and carvone. And you can find different values for them in the literature, because the compounds that they used to measure these in the literature are of different purities. So you can by limonene and carvone at 95%, or 96%, 98% purity. And depending on what purity you use, you'll get a slightly different value. But they should be within that range. And when we measure them in the lab, we go out to four decimal places. The way that we'll do this in the lab is with the refractometer. And this is a picture of the refractometer in the lab. And this part over here is the prism or the crystal. And so you'll put your liquid sample-- you just put a few drops right on the crystal. And then, you close the lid and the refractometer instrument shines light through your sample. It can measure-- it knows what angle the light is hitting the sample at. And then it can measure how much light it gets back out. So it'll change the angle of the incident light until it gets total internal reflectance until it reaches the critical angle. You remember from physics? And so once it figures out what the critical angle is, then it can figure out the refractive index of your sample. And so it'll tell you what the refractive index is right here. You don't even really have to do any math. And it'll also tell you what the temperature is. So you want to make sure that it's stabilized at 20 degrees before you actually take your measurement. And that's about it. So it's a pretty easy measurement to take, but it will help you to identify the purity of your compounds, because the refractive index is-- we can think of it as a linear quantity made up of the refractive indices of the two substances that we have in our mixture, multiplied by their molar fraction. So your refractive index of a mixture is the sum of the refractive index of pure limonene times your mole fraction of your limonene, plus your refractive index of your carvone times your molar fraction of your carvone. And so that you don't have to sell for a million variables, if you remember the mole fraction, mole fractions have to add up to 1. So your mole fraction of limonene is 1 minus your mole fraction of carvone. So you can plug that in up there and, using the measurements that you take in the lab, you can solve for the mole fractions of each of these components in both of your fractions that you collect from your distillation. And you can determine their purity that way. So another way to determine the purity of your-- or fractions that you've collected is through gas chromatography. And this is a picture of the GC instrument in the lab. And it's right next to the ICPMS, so you may have seen it if you were in lab yesterday. And if not, you can take a peek and see it today. So this is the instrument itself. This is the autosampler. So you guys will make your sample vials, put them in up here, and then it'll pick them up, put them into the instrument, and then it'll automatically inject the sample for you, which is kind of nice. And then this thing over here, it generates hydrogen and air, which are used in the detector of the instrument. So the way that gas chromatography works, if you wanted to take a peek inside the instrument in a very, very simplified fashion, you have a carrier gas, which in our case is helium. And the carrier gas, if you think about-- so this is a type of chromatography. And you guys did chromatography in the ferrocene lab with your thin layer chromatography and your column chromatography. So in your TLC and in your column chromatography, what was your stationary phase? AUDIENCE: Alumina? SARAH HEWETT: Alumina, yes. So you had your alumina, and it was coated on the TLC plate. Or you packed your column with the alumina, and that's your stationery phase. And then, what was your mobile phase? AUDIENCE: Hexanes and ethyl acetate? SARAH HEWETT: Hexanes and ethyl acetate. And you guys made different mixtures of those to determine the best separation of your compound. So in thin layer chromatography and in column chromatography, which of those phases had a bigger determination on the separation of your two components? AUDIENCE: The mobile phase? SARAH HEWETT: The mobile phase, yeah. So you could change the polarity and it would change the separation. In gas chromatography, it's kind of the opposite. So you have your carry your gas. And that's going to be your mobile phase. So that'll help push your compounds through the column. And then the column is your stationary phase. And you can change the properties of your stationary phase in order to separate-- get different types of separation. So there are two major types of compounds that they use in column chromatography. And the first one, this is-- anyone know what this is? Polyethylene glycol, which is something you may have heard of before. So these are your ethyl groups, and then the glycol, because it's got alcohol groups. And so this notation is the notation for a polymer. So the way that this is written is you could have any number of this repeating unit until the end. And this is a polar stationary phase. So if you're trying to separate compounds that have differences-- large differences in polarity, a lot of times you'll use the polar compound. Because it has these oxygens that have their lone pairs. So it can interact with polar compounds, it can form hydrogen bonds, all kinds of neat stuff. But the one that we're going to use in the lab is this compound here. And it is called a polysiloxane. So polysiloxane-- and it has these silicon groups that have to methyl groups attached. And another name for this particular-- so polysiloxane is the overarching name for this class of compounds. This one has two methyl groups attached. So one of the other names for it is dimethicone. I don't know if you've heard of that before. It's in a lot of things. They use it extensively in lotions, shampoos, and sometimes in food. It prevents foaming and it makes things feel nice and slippery. So that's why they use it in a lot of cosmetics, and lotions, and everything. So the next time you're in the bathroom, you can take a look at some of your products. And you may see dimethicone. And now you know what it looks like. And we're going to use it in the lab to help separate your limonene and your carvone to see how pure your separation was. And the GC column looks like this. So it's represented in this diagram as a curled up circle. And so this is actually what it looks like. So this is an old column taken out of the GC in the lab. And you can see that it's very, very thin. So this is a capillary column. So this is actually a hollow tube. And your sample will travel through this tube around, around, around. Does anyone have a guess about how long this is? AUDIENCE: Long. SARAH HEWETT: Long. [LAUGHS] Yeah, so this is 30 meters of capillary tubing all wrapped up here. And on the inside of the capillary tubing, it is coated with this polysiloxane mixture which will interact with your sample. And it'll help cause the separation. So your sample gets inserted into the injector port. This is an oven, so it gets heated up. And you can change the difference in the temperature. And so the difference in the temperature will change the amount of separation that you get. So if you do it hotter, then your compounds will travel through faster, and you don't maybe get as good of a separation. If you cool it down a little bit, then you tend to get better separation, but sometimes it can broaden your peaks. So there's a trade-off there. We have already made a program for you that optimizes the separation of the two compounds that you guys are looking for. So you don't have to worry about that. You'll just make up your sample, inject it, it'll go through the column, and then it reaches the detector. And we use a flame ionization detector. So that hydrogen in the air, they get lit on fire. The stuff that comes out of the column goes into the fire. It gets lit on fire, it produces ions, and then the ions are detected by the detector, changes the electrical current. And that is what gives you your signal. This is a very sensitive technique. So you do not need to prepare very concentrated amounts of samples. So we're not going to inject your oil straight into the instrument. You are going to do what's called a double dilution. So you will take 50 microliters of your sample in one of those micropipettes that you guys have been using. You'll dissolve it in 1 milliliter of pentane, so you're already making a very dilute solution. And then you'll take 50 microliters of that solution, and you will dissolve it in another milliliter of pentane. And that's what you will inject into the GC instrument. Your TAs will help you with that. But that's just to show you that it is a very, very sensitive technique. So you do not need a lot of volume. This is what the output of the GC looks like. And you will get your GC chromatograph. And the units on this are in abundance and time in minutes. And so you can see that this is a GC chromatograph of the oil before it's been separated. So it has two major components and a couple of smaller impurities. And hopefully, if you guys do your distillation correctly, then you'll get-- your fractions will look like there's not very much of one and a lot of the other, and then vice versa for your limonene and your carvone. And the way that you can tell which peak is which is that-- so this column is pretty non non-polar, like I said. And the interactions with the column are what separates your mixture. But the way that it is separated is mostly through boiling point. So when you heat this compound up-- and we'll talk about it a little bit more in the next slide-- but it'll travel through the column. So things that are more volatile will travel through the column faster, so things with lower boiling point. And then, things with a higher boiling point stay on the column for longer. So you can use boiling point to sort of identify your compounds. And you also get this information at the bottom, which tells you the retention times of your peaks in the minutes. And then, it'll also tell you the area of your peak. And you can use the percent area to calculate your percent purity. So in this case, we have 41% of one and 57% of the other. So it is not a very pure sample. And hopefully, yours will get on the order of-- you can get well above 90% separation. So that'll give you an idea of how well your distillation went. So some things about gas chromatography that are important to note is that you can't really identify an unknown without a standard. So if you just-- if you don't know what your compound is already and you inject it into the GC, all you're going to know is that retention time. It doesn't give you any information about its structure or anything else. So you can compare retention times. Those are consistent as long as you use the same method, and the same column, and the same carrier gas. But you need to have a standard that you can compare it to. Or if you know that there's two components in your mixture, if you know what's in them, then you can tell which is which, again, by their boiling point. So it is very useful for determining the purity or the percent composition of a sample, which is what we're going to use it for. And like I said, separation is determined by your stationary phase. And the stationary phase is a liquid coating on there. So when you're using GC chromatography, you want to make sure that you pick a stationary phase that matches the type of compound that you're separating. So we're going to use this non-polar one because our compounds are relatively non-polar. But you'll see it used in extensively in other applications. So if you're doing a lot of polar compounds with a lot of oxygen groups or nitrogen groups, then you may want to use a more polar compound. You can also get chiral stationary phases that will help separate enantiomers. There's all kinds. If you go on any of the Agilent website or anything, you can get a whole list of different types of stationary phases with different types of polarity. You can substitute these methyl groups out for other things depending on what application you're trying to use it for. And so the way that we can characterize the efficiency of the separation is by theoretical plates. And we mentioned this really, really briefly when we were talking about the distillation. So if you remember, there was the grow column versus the simple distillation. So you get better separation when you have more and more of those cycles where the vapor can vaporize and recondense. Does that sound vaguely familiar? Good. So essentially, that's what's happening in this GC column. So you have a liquid coating on the inside of this tube. And your compounds are traveling through it. And they can be heated up so they'll repeatedly dissolve and then revaporize in the liquid. And the more times they can do that as they travel through this 30 meters of column, the more efficient your separation is going to be. And we can calculate that using a measure called theoretical plates. And it is based on the idea that one plate is one equilibrium between the liquid in the vapor phase, or one of those vaporization recondensation cycles. So you can refer to the temperature composition diagrams from the last lecture if you want to get a refresher on what I mean by the vaporization and recondensation. And then, you can calculate this from your chromatogram data. So when you have that chromatograph data that has the peaks on it, you can use this equation. So n is the number of theoretical plates. This is just a standard constant. And then your tr is the retention time. So you'll use the retention time of your peak in some unit. And then you want to take the width of the peak at 1/2 of the height of the peak. So I can't go backwards. Oh, there it is. So for this peak, you would say your retention time is 1.434. And then, you would want to go halfway up the peak, and then take the width of that peak, which is going to be a very small number. And the best way to do this is to probably use a ruler, and actually measure, physically, the height of the peak, and then measure the width at the halfway point. So if you do that, you need to make sure that when you are using these measurements, that they are in the same units. So you can either do it in the units of time, which is what it's given to you on the GC. But it's probably a little easier if you do it in millimeters or centimeters, however you want to measure it. Just make sure that you also-- if you're going to measure your width in centimeters or millimeters that you also measure your retention time in centimeters or millimeters. And the retention time is just the time from the beginning to where your peak is. So that's GC spectroscopy. And now, we can talk a little bit about IR spectroscopy. And if we take a moment and think about our electromagnetic spectrum, we can think about the different types of energy that you have available in the electromagnetic spectrum. So if this is our wavelength in meters, what is our thing with the smallest wavelength, highest energy? Anyone? Gamma rays. Then? AUDIENCE: X-rays? SARAH HEWETT: Then? UV. The little tiny one? AUDIENCE: Visible. SARAH HEWETT: Visible. AUDIENCE: And then infrared. SARAH HEWETT: Infrared. AUDIENCE: Microwave. SARAH HEWETT: And then, yeah, microwave and radio. All right, so from highest energy to lowest energy, this is our electromagnetic spectrum. And so IR spectroscopy uses IR radiation to give us information about a molecule. And the way that this happens is that it's very useful for identifying functional groups in a molecule. And you pass this IR radiation through the molecule. And all of the bonds in your molecule have some sort of vibrational energy associated with them. They're vibrating at a certain frequency which corresponds to energy in the IR region of the spectrum. So if you pass IR radiation through your sample, then some of the wavelengths will match up with the frequencies of the vibrations of your bonds. And it will get absorbed. And then, you can measure how much light comes back out and how much light gets absorbed. And you can get an IR spectrum of your molecule, which is representative of all the different bonds and the energy that they absorb. The frequency of light or energy that a bond absorbs is dependent on the mass of the two atoms that are attached in the bond, the bond strength, and the chemical environment. And this is related by Hooke's law, if you're familiar with physics, that talks about-- you can think about it as two masses on opposite ends of the string-- or a spring. And so how much force you need, or what the frequency is that that spring will oscillate on depends on all of these factors. And so if you have something that has a high bond order, like a double bond or a triple bond, then those-- that's a really tight spring. So it's going to vibrate at a very high frequency, and it's going to take a lot more energy to get that vibration to happen. Whereas if there are two light atoms that are attached by a single bond, then they will vibrate at a much lower frequency-- less energy. Make sense, sort of? So vibrations are only IR active if they change the dipole moment of a bond. So you can't see all the bonds in your molecule using IR spectroscopy. You'll be able to see the ones-- we can see most of them, since most molecules are not perfectly symmetric. But like carbon-carbon bonds, that stretch does not really change the dipole much. So you don't see those very strongly, if at all, in most of your IR spectra. So there are a bunch of different ways that a bond or a molecule can vibrate. And the number of possible vibrational modes in a molecule is determined from the degrees of freedom. So if you think about a molecule, it can move in the three dimensions of space translationally. And so all of the atoms can also move in the three dimensions of space. So you get-- you start with 3N degrees of freedom, so N being the number of atoms in your molecule. And then in a linear molecule, you have-- you can also have rotationally modes. But one of the rotationally modes does not quite work as well, because it's along the axis of the bond. So you're not changing anything if you rotate it that way. So we end up with 3N minus 5 vibrational stretching or bending modes. And then, in a nonlinear molecule, you get all three translational and all three rotational modes. So you do 3N minus 6. And so that gets rid of the translational and rotational motion. So what's left is the vibrational stretching or bending modes in your molecule. And so the possible vibrations that we can have are as follows-- the symmetric stretch, the asymmetric stretch, the bend, the wag, the twist, and rocking. So I need everybody to stand up. If you've done this before, we're doing it again. This is a rite of passage in a chemistry lab. We are going to-- I will wait. We are going to pretend that we are molecules, and we are going to act out all of these different vibrations that can happen in your molecule so that you have an idea of what you are looking for when you see your IR spectrum. So if your body is like a carbon, and then the rest of, like, your legs are another carbon chain, then say you have two hydrogen atoms in your hands. Great. We are excellent methylene groups. So a symmetric stretch-- any ideas? Yeah, when they go at the same time. Excellent. The asymmetric stretch? Yeah, opposite, excellent. The bend or scissor? Excellent. So you're all getting a workout today. This is great. The wag? The wag is back and forth, like-- yeah, there you go. Excellent. Twisting? One goes back, one goes forward. There we go. And then last one, rocking? That's what you had before. They're going back and forth at the same time. Excellent! Well done. Give yourselves a hand. It's a good way to get everybody up and moving. So those are our IR vibrational modes, and those are all the ways that you can make your molecules vibrate. And so now, how do we measure this? And this is the ATR spectrometer. It's an infrared spectrometer. This is the one that we have in the lab. And it's in the very back corner by the door in A prime 4. So some of you guys may have seen it. You may have seen some of the other lab groups coming in to use it. And the way that this works is, it's a pretty simple instrument in terms of what you need to do to use it. There is a crystal right here. And the crystals are usually made of zinc selenide, or I believe, in our case, it's a diamond. And it's a pretty tiny crystal. It's just that very, very small little dot in the center. And you can take your compound and put it straight on the crystal. And if it's a solid, then you can use-- this is a little pressure thing. So you can lower that, and it'll press your solid right up against the crystal so you get good contact. Or you can just put a couple of drops of your liquid right on the crystal, and then it has good contact anyway because it's a liquid. And-- oh, so the ATR stands for attenuated total reflectance. And how it works is you have a source of your IR energy. And these are some mirrors. And so you have your energy. It comes in here. It hits the mirror, and then it gets directed up through this crystal. And like I said, you're going to put your sample on top of the crystal. And you want to get really good contact, because the IR energy will travel through the crystal, and it'll interact with the very bottom layer of your sample there. And then, it'll get reflected back down. And in some cases, there's only one reflection, and then it goes to the detector. And in other cases, depending on the size of your crystal, you can get multiple reflections. And when the light interacts with your sample, like I said, it'll absorb some of the wavelengths of the IR light. So some of this will get absorbed. And then, that's the attenuation part is that some wavelengths will be decreased in intensity because they'll be absorbed by your compound. And then, the reflectance part is the light gets reflected down through this crystal into the detector. And then the detector can determine which wavelengths of light were absorbed and how much. And that is IR in a very simplified fashion. There's more descriptions of it in your Mohrig book. So if you guys have this book or if you want to borrow it, there's an excellent description of how different IR spectrometers work. There are a couple of different ways to get IR samples. So like ATR is great for liquids and solids. You can also have IR spectrometers that just-- you set your sample up on some sort of support that's, like, vertical. And then you pass the beam straight through it, and you measure what comes out on the other side, kind of like the UV-Vis that you did. So there's a couple different ways to do IR. But this is the way that we're going to be using in the lab. And what you get out of it is an IR spectrum that looks something like this. So I took these straight from the lab manual. And these are IR spectra of carvone. And that's the carvone from the caraway seed oil, and that's the carvone from your peppermint oil. And do we see any differences? Not really. So what do we know is different about the carvone from the caraway seed and the peppermint oil? The stereochemistry. So we know that one is the R form of the molecule, and the other is the S. So this is the S and this is the R. So is IR spectroscopy good at differentiating between isomers? Nope, not at all. It just tells you what functional groups are there. It doesn't really tell you in what order they are in. So you'll need to do a different spectroscopic technique if you want to figure that out. But we can get a lot of information about different bonds that are in our molecule, which is helpful for identifying different things. What do we have next? So, yeah, we can talk about interpreting an IR spectrum. So in your book or on the internet there are many, many charts that have lists and lists of the IR-- oh, my bookmark fell out. Oh here it is. So there is a chart in the Mohrig book that has a list of all of the different stretching frequencies for different functional groups. And it has the stretching, the bending, and anything that you are typically able to see in an IR spectrum. And it tells you where you should look for it in the spectrum in terms of wave numbers. So if you look at the axes of these things, the left axis here is percent transmittance, so how much of the light gets through. And then, the-- so the top is 100. So if nothing is absorbed, it'll be a baseline at the top. And then if things are absorbed strongly, then the transmittance goes down and you get a big peak. And then the wave, the other axis along the bottom here, is-- well, on the bottom of this one, it's in micrometers. But in most cases in IR now, we use wave numbers because it's a linear measurement instead of non-linear. So wave numbers corresponds to the amount of energy in the molecule-- or in the photon. So we can get these charts of where different functional groups absorb in terms of wave numbers. So these are all in wave numbers, which is inverse centimeters. So when you get your IR spectrum back and you take it in the lab, you're going to print it out. And then, you can use one of these charts to help you. And the best place to start looking at an IR spectrum is between 4,000 and 1,400 wave numbers, so, like, this half. Because you can see, on this side, there's a lot going on down here. And you might say, oh, that's got a ton of information in it. Not so much. So this is called the fingerprint region. And it does have a lot of information in it. And before there were other spectroscopic techniques, people spent a lot of time trying to identify peaks down here. But they're less representative of actual specific bonds. A lot of it's, like, overtones and other resonance happening. And these are unique to every chemical. So if you have a reference spectrum and then you have your spectrum, you can match them up and the fingerprint region should match really well. But it's kind of hard to interpret, and it's usually very messy. So we kind of ignore this at the beginning. And then, if you look over here, then there's a lot fewer peaks to deal with and they provide a lot of information. So you'll see that the C-H stretches are typically around, like, 2,800 to 3,100 wave numbers. And it depends on whether it's a single bond like an alkane C-H, or alkene, or an aromatic where they come out. So these guys, you'll have different peaks, because we have some alkene C-H's and some alkane C-H's. So you'll have a whole variety of C-H stretching there. And then, what other functional groups do we have in the molecule? What's the other main one? AUDIENCE: CO. SARAH HEWETT: The CO. And the CO double bond is one of the most characteristic peaks that you can find in an IR spectrum. And it always comes out somewhere between 1600, 1700. So you can see, at 1700, there is this huge peak. It is the biggest peak in the spectrum. And that corresponds to that CO double bond there. So that's always a good place to start if you are looking to identify something that you think may have a carbonyl in it. Yes? AUDIENCE: So can you tell how many C-c bonds there are based on the height of the peak? SARAH HEWETT: No. So the height of the peak doesn't give you any specific information like how many there are. In amines, if you have a primary versus a secondary amine-- so if you have an amine with 1 H on it, and some other R group versus two H's, you'll see either two peaks and the amine or one peak. So that's when you can quantify atoms through this. But no, the intensity does not always correspond to how many of the bond there are, since the intensity is mostly a function of how much the dipole moment changes. So you could have a lot of C-H bonds, but you won't see a whole-- like, a very intense peak. Yeah. Whoops! Go back. So things that you should do is to look for what is there and look for what is not there. So if you know what's supposed to be there in your functional groups because you know the structure of your molecule, then you can try to identify the peaks that correspond to those functional groups. So if you are anticipating having an O-H stretch, like you've made an alcohol or a carboxylic acid, then you should see a giant, broad peak around 3,500 wave numbers. And you should also, if you are making a carboxylic acid, you should see this O-H stretch, and you should see your carbonyl peak. So you need to be able to identify all the peaks that are associated with a certain functional group. So don't say that you have a carboxylic acid if you cannot find either-- if you cannot find both of these peaks. They will be there. And then, less helpful for us maybe now, but in the ester lab, which we'll talk about later, you can also look for what is not there. So if you're trying to figure out if your synthesis was successful, and you start with an alcohol, and you're supposed to end with something that does not have an O-H peak, then you can look for the absence of an O-H stretch. Or if you're trying to get rid of a carbonyl, then you can say what's not there if you're trying to hydrogenate some sort of double bond. You can figure out what is there and what is not there. So those are things you can talk about in your discussion. And your IR spectrum in your report should be attached as an appendix with key peaks labeled. So you can actually, on your spectrum, write what each peak represents. So if you see a giant peak at 1700, you can draw an arrow to it and say, C double bond O stretch. And the way that this is typically reported in the literature-- and there's a bunch of different ways to do it. You can check out the ACS style guide for more information. But you'll say, IR spectroscopy. You use the type of IR spectroscopy, which in our case is going to be ATR. So there is, like, thin film, there's potassium bromide pellets, there's all kinds of different ways that you can take an IR spectrum. And the method that you use will also affect the peak intensity. So that's why it's not as helpful of a thing to look at. And then, your units, wave numbers, and then your key peaks-- so if you have a peak that is really broad, you only have to report. And you'll see that most of the peaks in an IR spectrum are not super sharp. So this carbonyl peak, if you look at the base, it ranges through a good number of wave numbers. But when you report it, you only report the wave numbers of the highest intensity. And the instrument will print that out for you on your spectrum, so you'll know what the highest intensity is for your peak. So you can report the highest intensity wave numbers for each of your peaks. And if you know what the peak is, in some cases, people will put what bond it represents. You don't have to. It was acceptable to do it both ways according to the ACS style guide. So that's kind of up to you. A little more helpful for the person reading it, but-- So if we want to take a look really quickly at a couple of IR spectra of molecules that-- well, this one you may know. So this is the IR spectrum of ethanol. And what is the major feature that we care about here? So there's the C-- C-O, but the-- yeah, there's the O-H. So the biggest, strongest feature here is our O-H peak. And O-H peaks are typically quite broad. So they're not as sharp and defined as the other peaks in the spectrum. So that's one of the characteristic ways you can know if you have an alcohol. And then, you can look. And we have some methyl C-H's and ethyl C-H's here. So you have alkane C-H's. And so those show up a little bit below 3,000 wave numbers. Great. And then, you may be able to find the C-O bond that typically shows up around 1,000, give or take. So maybe one of those peaks is your C-O stretch as well. So sometimes you can go into that fingerprint region if you know that there is something there that you are looking for. So the C-O stretch is one that you typically can see, and it's typically pretty strong. So in this case, it is there. But, yeah, and then another example is this compound, which is 3, 7 dimethyl octonal. And what do we have here that's really strong and sticking out? D double bond O, again, right here around 1700 wave numbers, that's always a dead giveaway that there is some sort of carbonyl peak. And if you have an aldehyde peak, then-- I didn't write it up here-- but you'll have a characteristic stretch for this aldehyde hydrogen that is also up here. And then you have a couple of alkene C-H stretches, and a bunch of alkane C-H stretches. So in this case, there is a lot going on in our stretching region. And those are the major features of that spectrum. So we'll go over this a little bit more also, again, when we talk about the ester lab. Because you're going to be using IR for that lab as well. We can talk about some of the different functional groups that you can see in that case, because we're going to be dealing with, obviously, esters, and some alcohols, and some ketones, and some carboxylic acids. So that is a brief overview of IR. So we have one more technique left to talk about, and it is the polarimetry. And to talk about that, first, we're going to do another round of synthesis with your products that you've separated in your initial distillation. So you have your limonene fraction, your carvone fraction, and we're going to take the carvone fraction and synthesize a semi-carbazone, which will look something like this. And you will make this molecule. It'll still have your stereocenter. We're not touching that. So it'll keep your RS configuration. And it'll be a solid, though. So you're going to start with an oil. You will go through this synthesis. And then you'll end up with white needle-like crystals. So you're going to recrystallize your product very, very slowly. And your TAs will show you how to do that. There's a good procedure in your lab manual, but you're going to do the reaction, and then you're going to let it sit in your lab bench until the next lab period, so for a couple of days. And you want the crystals to grow really, really slowly. So you will not see them when you first make them, but you'll see them, hopefully, when you come to lab the next time. And the slower the crystals grow, the more pure they are. And then, we are going to need very pure crystals, because these are what you're going to analyze by X-ray crystallography. And like I said, Peter Muller will come and give you more information on that. So stay tuned. But what we can do with these crystals is use them to do some polarimetry. So one of the things that you'll know about your-- so I said you're going to make some white crystals. So one of the ways that we've been analyzing our solids is by melting point. And you can get two possible diastereomers out of this synthesis. So you can either have-- since there's not a lot of rotation around the C-N double bond, you either have that extra nitrogen group pointing up towards this methyl group or away from it. And these two compounds have different melting points. So you will characterize your crystals by melting point to figure out which of these isomers you have, the alpha or the beta. Most people will make the beta, because it has less steric hindrance, so it's a little bit easier for that to happen, just synthetically. And so that's one of the first ways that you will characterize these compounds. And the second way is by polarimetry. And so if we talk about polarized light really fast, so what does it mean for light to be polarized? It's all going in the same direction. And so all-- so you have a light source, and it emits light. And all of the waves are traveling in all different directions. But you can put it through a polarizing filter, and then you only filter out the light that is-- that has, like, the molecules are all arranged in slits so that it only selects for light traveling in one plane. So you can put that there. And if you-- if I have two pieces of polarizing paper, and I put them on top of each other in the same orientation, then the light pretty much gets through. These are a little bit colored, so not all of it. But then, if I rotate so that the bottom one is selecting for light going this way, and the top one is selecting for light going the other direction, then no light gets through, because it can't pass through the filter. So that's what we're going to-- this is the essential principle behind polarimetry. So if you remember from either your organic chemistry lectures or experience before, different molecules that are chiral will rotate plane polarized light. And so what that means is if you put a polarizing filter on your light, select for light all going in one direction, and then you shine that light through a chiral sample, it'll get rotated to a certain degree based on a number of features, but essentially, how the light interacts with your chiral sample. And so if you have two polarizing filters, and you have your sample in between them, you can rotate one of them, and eventually, it'll match up again, and you'll see all the light come through. And so that's how you can tell how much your compound rotates the light. So you put a polarizing filter on each side, and then kind of rotate them until you get all of your light back. And then, you can measure the polarimetry. So that's kind of the way that they did it in the old days, but we have an instrument that'll do it for you. So you don't have to worry about that too much. I'll turn this back on really quick. But the rotation, like I said, we can measure it. And it's characteristic of the molecules. So the R and the S forms will rotate in opposite directions. So in our case, the R form rotates light in the negative direction, or counterclockwise, and then the S form will rotate light in the positive direction. And the R and the S are not really related to the plus and the minus. So for different compounds, the R might be the plus isomer and the S might be the minus. It's something that you have to measure. You can't just know off the top of your head. And from this, we can calculate the specific rotation of our light, which is how much the light has rotated. And it depends on the length of the sample, the concentration, and the wavelengths of light that is used, and then, again, the temperature, because that impacts the density of your solution or of your compound. So the way that you're going to do this in the lab is you're going to take a sample of your crystals, and then you're going to weigh them out, and you're going to dissolve them in ethanol. So you're going to make a solution that you know the concentration of so that we can plug that in for our concentration. And you will put it in these tubes. And then you will insert the tube into the polar emitter, and it will shine the light through. And then it will calculate what the angle is that the light gets rotated by. And the polarimeter actually will calculate the specific rotation for you, which is kind of nice. But you can also calculate it. It gives you all the information to calculate it yourself as well. So this is notated very similarly to our refractive index, in that it is taken at 20 degrees for the density. And we use the same wavelength of light from that sodium D-line, the 586 nanometers, in order to have a consistent representation. So you may see these constants in the literature. And if the temperature is different, it'll say something like 23 or 25, or whatever the temperature they took it at. And you can also change this to whatever nanometer wavelength of light that you used. But we're going to be using these conditions. And then this is the rotation of the light in degrees, the length the travels in decimeters-- so you're going to measure the tube that you use in decimeters-- and then your concentration in grams per milliliter. And you can calculate the specific rotation of the molecules. So hopefully, the people who had different isomers will rotate-- the light will get rotated exactly in the same number of degrees, but in opposite directions if we've done everything correctly. So you'll see what you can get from there. And I think that is all for today. Do you guys have any questions about anything that we are about to do in the essential oil lab? Autumn? AUDIENCE: Why is-- in this case, why is gas [INAUDIBLE]?? SARAH HEWETT: In this case, to be perfectly honest, I am not super familiar with HPLC. I'm sure you could also use it to separate these compounds. GC is-- I mean, part of it is the techniques that we have available to us. So there's that. But this also gets separated really nicely based on boiling point. So it's kind of fast and easy for us to do. But I can also-- yeah, we can talk about it more. Yeah, no, it's a good question.
MIT_5310_Laboratory_Chemistry_Fall_2019	5_Ellen_Swallow_Richards_Part_1.txt	[SQUEAKING] [RUSTLING] [CLICKING] JOHN DOLHUN: Good morning, everyone. And welcome, or good afternoon. Welcome to The Ellen Swallow Richards Lecture Series. This is our beloved Charles River. This is the river you're going to be testing. Once you've tested this river, you can actually take this testing and apply it to any body of water. Why should we be concerned about this Charles River? Yes? Because we live next to it. Because we live-- that's a good reason. Because we live next to it. Anyone else? Aisha? AUDIENCE: To care about your environment. JOHN DOLHUN: You care about your environment. And speaking of caring about your environment, we've got some problems with phosphate out there. We've got high phosphorus concentrations. And those high phosphorus concentrations lead to algal blooms. And those algal blooms produce toxic chemicals and odors. And when all this algae dies, it heads down to the bottom and breaks off and it's acted on by decomposers. These microbes start to chew it apart and they use up the dissolved oxygen so that we get lower-- lower dissolved oxygen in the water. And what that does is it leads to fish kills. And our recreational ability is impaired. So here are some examples of what I'm talking about. This is Florida, 2016. This is Lake Okeechobee, one of the largest fresh water lakes in Florida. This is a 30 mile long fish kill. It involves some 50 species of fish. The cause, most probably, an algal bloom, the result of leaking septic systems, fertilizers from lawns going into the water. This is an economic disaster. It's going to take decades to recover from this. Is Bradenton, Florida, 2018. This is their harbor filled with dead fish. This started from an algal bloom that turned into a red tide. And the red tide stretched about 150 miles off the coast of Florida, and gradually, the wind and the currents brought it into shore. And when that red tide came in to shore, it started releasing toxins into the air and water, and then the nutrients broke off and microbes started digesting them and used up the oxygen, and all these fish died. This is Australia, 2019. This is the Darling River, but it also happened in the [INAUDIBLE] River. And they had a successive run of these fish kills, one right after the other. Again, it's global hot temperatures and agricultural runoff. This is the Charles River, August, 2019. This is the largest algal bloom, I think, that we've had out there. It actually stretched from the BU bridge to the Museum of Science. And cyanobacteria was detected. This is a health problem. So we're going to be measuring phosphorus in the waters out here. That's one of the things we're going to do. And there are two types of phosphorus, there's the inorganic, which is simply salts of phosphoric acid, and then if you create esters of the inorganic form, you have the organic form of phosphate. So let's take a look for a moment at the inorganic phosphate. I mean, phosphorus is like, the 11th most abundant element on the planet. And it's not found in elemental form. You won't find any pure phosphorous anywhere on the Earth. It's found in these types of phosphates, in rocks and soils, and that's how it exists. So the main inorganic player here is the orthophosphate. And that's the PO4 to the 3 minus. This is the most stable form of phosphorus. And this is the form that's readily available to plants for uptake by the plants. I mean, all plants and animals need phosphorus for growth. It's the backbone of our DNA and the Krebs cycle. Plants need it in photosynthesis. They have to extract it from their environment because they're not going to make sugar unless they first make ATP to actually connect those bonds in the sugars that they're making. So we've got this orthophosphate, the main player here, but in the inorganic category, you can actually connect several of these together and form a polyphosphate, such as our detergents. A lot of detergents are polyphosphates. P3O10 to the 5 minus would be a polyphosphate. The interesting thing about the polyphosphates is as soon as they hit the water, they hydrolyze into the orthophosphate. And then we've got the organic phosphates, which are esters of the inorganic form. And organic phosphates are found in all living tissues. So all living tissues, both plants and animals, have organic phosphates. And waste is also another form of the organic phosphates. So when something living dies, it starts to decay. What happens is the phosphates actually convert to the orthophosphate. That's what happens to them. So this is what we're going to be measuring. And now, I'd like to talk for a few minutes about how it gets into the water, where all this stuff is coming from. So we're going to look at some of the primary sources of the phosphorus. The first one is storm water runoff. Can anyone give me an example of some phosphoruses, phosphates that can get into the water from storm water runoff? Yes, Aisha. AUDIENCE: I'm not sure if there's a phosphate in dirt. JOHN DOLHUN: Absolutely. There's phosphate in the dirt. And that would get washed in. What else? Yes, Jimmy? AUDIENCE: Probably less here, but in agriculture, I'm pretty sure they're used in fertilizer. JOHN DOLHUN: Oh, gosh, yes. Fertilizers are a big thing because of lawns. So we've got soil here and fertilizers. Anything else? Jimmy? AUDIENCE: I guess animal droppings? JOHN DOLHUN: Absolutely. Animal waste. I mean, think about where do they put pig farms? They put them all by a river, right? And all those geese, the guano, droppings, everything, they're all out there by the river. And all that stuff is being washed in. So animal waste is a big, big source here. Anything else? You ever got your car washed in a car wash? Do you ever sit in it while you're going through, see all that soap coming down? Tons of soap. And all that soap's going into the sewer systems, and when it starts to rain, heavy rains, it bubbles over. So car washes would be a big source, and there's your polyphosphates. Another one that you might not be as familiar with is car exhausts. Car exhausts have a catalyst tube in there. When that tube gets hot, like 500, 600, 700 degrees, it can form cerium phosphate, which is released in the exhaust effluent. So cerium phosphate would be a culprit here. And then probably the biggest source is discharge from wastewater treatment plants. Did any of you ever go to tour a wastewater treatment plant? Anyone? Oh, you did? Kelly, right? Could you tell us-- tell us about it, what your experience was? AUDIENCE: It was a school fieldtrip a long time ago, I think. It was interesting. So they purified or treat the water with several different methods. On of them was just like, bacterial, and then they introduce it [INAUDIBLE].. JOHN DOLHUN: Yeah, they aerate it with bacteria, I think, in the secondary treatment. And they do that to get rid of organic matter or to digest it down to sludge. AUDIENCE: Yeah. And then there's a UV method. JOHN DOLHUN: Very good. I mean, the most modern plants have this ultraviolet rays at the very end. You can walk along and you can see a glass floor. You can see the water going through with the ultraviolet rays hitting it. And then, at the end, they have a faucet and they offer you a drink. I mean, there was no one in my group that availed themself to take a sip of that water after going through that. But let's put this in perspective. So wastewater treatment plants, they're all built along rivers or oceans. And when a heavy rain, they start to discharge. They have to discharge. They can't take the flow. First thing, they may discharge some of the secondary treated water. Sometimes, they have to discharge the raw sewage. But to put it in perspective, all of us produce about 2.2 grams of pee per day. I'm talking about phosphorus here. That's about 1.8 pounds per year. Now, when that phosphorus hits the sewage treatment plant, it's in the effluent, it gets diluted down. You're talking somewhere between 2 and probably 20 milligrams per liter PPM of phosphorous in the water. After the secondary treatment, they only take out between 1 and 2 milligrams per liter. So you end up with a large excess of phosphorus in the treated water. So when they release, it's a ton of phosphorus hitting the water. But the good news is-- I'm going to draw a smiley face here, because the EPA just filed a regulation forcing-- they're going to force all these wastewater treatment plants to cut back, get rid of the phosphorus in the water, and they're going to have to-- they're going to have to take it down to less than 1.0 milligrams per liter. So all these plants are running around now trying to figure out how they're going to do that. This, I believe, just went into effect this year, and may go-- may be starting in January of 2020, but there are EPA regulations that are just coming out. The other major source is sewer overflows. And in New England, everyone-- it's notorious that you have a sump pump in your basement. So when your basement floods, the pump starts up and it pumps everything. They're connected to the sewer systems. So everything in the kitchen sink is going into the sewer system and it's bubbling over. So those are the primary sources. Now, let's look at the ecological effect of all this phosphorus. This is the Charles River, the famous Charles River. This is up by Newton, Mass. There's a guy in a canoe trying to pull out the vegetation out of the water. What this vegetation does is two things. First, it's blocking the sunlight to organisms and other plants down below the surface that need that sun. And the second thing is it's going to die and produce these swamp-like odors, and then it's going to get decomposed by microorganisms that are going to use up the oxygen. This is the result. This is blue-green algae. This is really-- another name for this is cyanobacteria. It's the cyanobacteria that give it that green color on the surface of the water. Here are some other forms of it. You can get this pea soup kind of look, or you can get this mossy look, or you might get a painted look. The bottom line is it's all bacteria. It's unicellular bacteria. These are prokaryotic bacteria. They have no nucleus, but they make their own food and they secrete chemicals. These are the same bacteria, believe it or not, that gave us life 3.5 billion years ago. And now, they're out to get us. Isn't that amazing? Every time I look at this, I can't believe it. I mean, when we had no oxygen, these were the guys that were giving our oxygen atmosphere, and now, look what they're doing. Now, if these are out there in the water, you don't want to go in the water. If you do, you are dead meat, and I'll tell you why. You can have all kinds of symptoms, you can get covered with a rash, you can have diarrhea, flu-like symptoms, eye and ear problems, respiratory problems. I gave you an article in the news. This is The New York Times. Central Park in New York, all of their ponds, infected with blue-green algae. Here's a good example. This is today, "Ohio strikes a Blow in Algae Fight." This is The Wall Street Journal this morning. This article just came out. Interestingly, Ohio had this algae problem 10 years ago, and they took around one of their lakes and they built up these wetland areas to prevent the runoff from reaching-- the agricultural runoff from reaching the lake, and it's actually working. So there are ideas out there that you can come up with an idea and solve a problem. So some of these cyanobacteria, some of the fresh water bacteria produce very toxic chemicals. One form of these are the microcystins. There are something like 50 different micocystins that have been identified to date. It's a cyclic peptide here. And this is a hepatotoxin. So once this gets through your skin into your body, your liver is going to get attacked, and you're pretty much gone. There's not much you can do about it. The article mentions the dogs-- one woman had three dogs in North Carolina. She let them go for a swim in a pond. All three dogs died within a few hours. So this is really nasty stuff. And I challenge you to think about coming up with an antidote for this. There's your startup company right here. I'm giving it to you. When this stuff is active, you go out to the Charles River, you'll see these signs posted warning people and pets to stay out of the water. Here's another example. This is the summer of 2014. This is a satellite picture of Lake Erie, one of the five Great Lakes in this country. And the lake actually borders Canada on one side, separates Canada from the US near Ontario, and then there are several states that border the lake. Out here to the west is Toledo, Ohio, and Toledo, fourth largest city in Ohio, has a population of about a half million. This was their tap water in 2014. And I had a 5.310 student in class four years ago who remembers this. I mean, this is serious business. And it's happening all over, all over the world. Here's another picture. This is the largest landlocked body of water on the Earth. Anybody from Europe here recognize this? What? Who said that? Yes, Sean, exactly correct, that's the Caspian Sea. It's bordered by five countries. But look at the massive, massive algal growth from this satellite picture. Here's the Volga River, Europe's longest river, pouring into it. It's a 2,000 mile long river. Here's a new word for you, eutrophication. It's from the Greek meaning well nourished. So how much phosphorus is acceptable? The EPA came out in 2000-- that was almost 20 years ago-- and said 0.0238 milligrams per liter. Well, we know today that if you have anything greater than or equal to 0.016 milligrams per liter, you're going to have really a large algal growth proliferating in your water. Now, these concentrations of phosphorus, they're low. And it's going to be challenging to measure those. This is what we're going to do. The other thing that makes it challenging is phosphates are colorless. So how are we going to use UV vis to measure these concentrations? Anybody have an idea? Yes? Maybe we can react them with something that will make them colorful? Maybe we can react them with something that can make them colorful. Very good. Very good. Yeah, I like that. Keisha, right? AUDIENCE: Gizelle. JOHN DOLHUN: Gizelle. I'm sorry, Gizelle. Where's Keisha? There she is. OK. All right, so react them with something that makes it colorful. So here comes chemistry to the rescue, right? So phosphates are very reactive. So we can actually take river water and this method here, this is the ammonium metavanadate method. When I tried to develop this Charles River water testing, I started with this method because it was written up as the method to detect phosphorus in river water. So you would take the river water, mix it with molybdate, ammonium metavanadate, and you create this color heteropoly molybdic acid that has a yellow color and it absorbs light at 400 nanometers. What I found is that this method was not sensitive enough to actually measure the phosphorus levels in the Charles River. It's a great method for measuring phosphorus in sewage, but not the rivers. So I looked around and I found what's called the ascorbic acid method, an EPA-approved method where you actually took river water, mixed it with molybdate, sulfuric acid, and you create this heteropoly molybdic acid, which is colorless. But the good thing is this heteropoly molybdate anion can accept electrons and be reduced down and ascorbic acid can cause that reduction. And you end up getting this molybdenum blue complex, a mixed valence complex that absorbs light at 880 nanometers. So this is great because the concentration of the phosphorus in the complexes is proportional to the absorbance of the light in these things. So this is what you're actually making. It's beautiful. This is a Keggin structure. It captures the phosphorus in the center, surrounded by 12 molybdenums and 40 oxygens. I want you to take a moment and look at this. And I'd like you all to close your eyes for a moment and think about this image. Close your eyes. OK, open your eyes, please. I want you to carry this image with you into the lab when you do this experiment. You're actually going to be making this in your beakers when you add the color developer to your water samples. You're creating this in about 15 minutes in your beaker. This is inorganic chemistry at its best. Now, I want to spend the next several slides showing you how we're going to actually measure the concentrations of this. So we're going to be shining electromagnetic energy on a sample. And if you look at the visible light here that I broke out of this electromagnetic spectrum, on the red end of this, we're going to be looking at our samples on that far red end in the near IR. So that's where you're going to be-- where you're going to be taking your readings. Now, what can happen when you shine radiation on your sample? Anyone? Yes, Kim. AUDIENCE: Photobleaching JOHN DOLHUN: Sorry? AUDIENCE: Some of your sample could get photobleached. JOHN DOLHUN: Some of your sample could get photobleached, yeah. That's a possibility. What else? Yes? AUDIENCE: [INAUDIBLE] JOHN DOLHUN: Exactly. I mean, electrons could get chewed up to a higher energy levels. Little nuclei could see that happen and get nervous and start to rearrange themselves. And the molecule, as Kelly said, could burst into vibration. And your UV is actually monitoring all of those electronic transmissions that we can't see with our eye. And what the UV does is it draws you a smooth curve through all of those electronic transitions and you end up somewhere with your lambda max. What UV vis is, a good definition is it's just the interaction of light with matter as a function of wavelength. So here's your UV cuvette. Here's the radiation hitting that cuvette. What happens? What do you see up there happening? Yes, Ryan? Yeah, the lights focused. And what's happening to the sample? I'm sure it's heating up, yeah. Yes, Autumn? AUDIENCE: It absorbs sunlight and transmits sunlight and also re-emits. JOHN DOLHUN: Yeah, good. So some of the light's going through and some's getting absorbed. So let's look at that for a minute. So we've got absorbance minus the log of the transmitted light, which is i over i0. Now, absorbance is-- we're actually monitoring the absorbance. We're not monitoring the transmittance because absorbance is actually directly proportional to concentration by Beer's law. So we have this relationship. And E, the extinction coefficient, is the molar absorptivity constant, is simply the amount of light absorbed per unit concentration of your sample. Let me just rewrite this. Let me get rid of the logarithm. I want to show you something here. So I'm going to rewrite this. Let's actually graph the intensity of the incoming radiation here. We're going to graph that as a function of concentration. If you do that, you're going to see from that equation that the transmitted light decreases exponentially as the concentration increases. I want you to keep that in the back of your mind. This equation fascinated me. I like Beer's law. What this tells you, this extinction coefficient tells you, that it has to be a constant. So if you cut your concentration in half, absorption should be cut in half. So I wanted to prove this. So I went out and I made this compound, hexacyanoferrate(III). And I made up five solutions of this, and then I measured the absorbance of each solution. It absorbed light at 420 nanometers. And if you look here, 10 times e to the minus 4, if I cut that in half to 5 times e to the minus 4, indeed, the absorption gets cut in half as it should. So I graph this, got a nice, straight line. The change in absorption over the change in concentration is my slope. And it's 1,056.7 so that's my extinction coefficient. And this worked really well. But I want to caution you-- if you try this, and you're graphing absorption versus concentration, and you're doing Beer's law, you've got this nice, straight line, you might end up with something like this, where Beer's law falls apart. And it all comes back to this here-- the intensity of the transmitted light decreases exponentially with concentration. So eventually, if the concentration is too high your sample becomes saturated, and you're not going to be-- this Beer's law falls apart. I just want you to be aware of that. What I did is I made up all of my concentrations are very low. Beer's law worked fine. So now we're going to get to some serious business. This is what you have to do for this lab, for it to work. Otherwise, you will be a goner-- gonzo. You've got to clean this glassware. This is a list of the glassware that you'll need to clean. And you've got to do it with 10% hydrochloric acid, triple rinsed with Milli-Q Water. Why do you think you need to do that? Yes. AUDIENCE: Any contamination might change the products concentration. JOHN DOLHUN: Any contamination is going to just destroy the experiment. It's kind of like the Nano Building. You've seen them in there with their bunny suits on. One speck of dust, even a dander from your hair, is like a wrecking ball to the experiment. Well, one speck of phosphate from any detergent is going to wreck this experiment. So you've got to judiciously sit down. There'll be two of you-- you'll be partnered up for this. So you clean this up. And you'll do this on day two after the dissolved oxygen testing. This is what you're going to need for day three for the phosphate testing. So you can leave this glassware in the top drawer above your locker. It's not locked. And it'll be nice and ready for when you come in to do the testing. So this is what you have to do in this lab. First of all, we need to make up a set of standards that we can interpolate our river samples against to find the concentrations of the phosphate and phosphorus. So you're going to make seven standards up. And you're going to be using a stock solution. And the formula to use in all these tables is you're going to use this M1V1 equals M2V2. So if you have a 10 to the minus 1/3 molar stock solution, and you're taking 1 milliliter of it out, out of the bottle, how much molarity do you want to make to make up 100 mil solution? You'll be diluting this 1 mil to 100, and you'll see that your x is 10 to the minus 5. That's your stock solution of phosphate that you're going to create. So you just use that formula for all these. You're taking this much out of your 10 to the minus 5 molar stock solution, and you're diluting it up to 10 mils. What's my concentration? Perfect. What you'll do is you'll come into the lab, and the TAs will go through this with you. You'll make up your stock solutions. And then you'll go to the river to get your water. And when you bring the water back to the lab, there'll be two of you. So one of you will go over to the hoods and get the color developer. And these are the four chemicals that we talked about in the color developer-- the ammonium molybdate, sulfuric acid, ascorbic acid, potassium antimonyl-tartrate. Potassium antimonyl-tartrate is there to actually speed up the reduction that's going on with ascorbic acid. That's important. If I didn't mention that before, that's the purpose of that. The ammonium molybdate, sulfuric acid, you're creating that Keggin structure, that heteropoly, colorless, molybdic acid. You also have to take this color developer in the order that it's written here. It'll be set up in burettes in the hood. If you, for example, take it in a wrong order, you could have a side reaction, and not get the color developer that you want to put in your sample. So it's important. So one of you will go to the hood, get the color developer. The other one will go to the river water you brought back, use a clean pipette, 10 mL pipette, and pipette five beakers with river water, five 10-mL beakers. So you'll end up with 12-- seven standards and five samples. And then you add the color developer, and you wait 20 minutes, and you're ready to go. Just a couple other precautions that you should take-- we're going to be using 4-mL cuvettes. These are big inside. Don't use the 1 and 1/2 mL cuvettes. The other thing is all these cuvettes have a fill line. It becomes frosted at one point. And you want to stop pouring when you get to that line. You're going to take your beakers, and you're going to swirl them gently. And you're going to pour them by hand until you reach the fill line. Don't go beyond that. Also, all of these UV cuvettes have an arrow on one side. You want to be sure that the arrow is in the light beam when you put these cuvettes in the UV spectrometer. A lot of people have made mistakes, put them in the wrong way, and then you're not going to get very good readings. So the arrow's clear to see. What I usually do is arrange all my cuvettes in a box ahead of time. And then I pour my samples and put them in the box, and I know the arrow's in the right place. And when I go to the UV, I just lift them up and put them in. Also, keep in mind what Dr. Sarah Hewett told you the other day that there's two kinds of pipettes in the lab. This one is a blowout pipette. You've got to blow it all out to get your 10 mLs. This one is a to deliver pipette. You only go up to that last line. You don't blow the tip in, otherwise you put too much-- going to wreck your experiment. So make sure you look at the pipettes carefully. So you're going to get your graph here, a nice graph. And what you're going to do is you're going to interpolate now your river absorbances against the curve so you can read off the concentrations. So the concentrations in that graph are in micromolar. So you're going to want to take those and convert them to milligrams per liter. So you want to convert this first to a molarity, moles per liter. Then you take that, and you want to go down to grams per liter, and then finally milligrams per liter. So you're going to be calculating two things. You want to calculate the phosphate concentration in ppm, which is milligrams per liter, and the phosphorus concentration. So you'll take your mass from the curve in milligrams per liter, and take it times the ratio for phosphate of PO4 over KH2PO4. And that ratio is 0.70. And then for phosphorus, do the same thing. The ratio there is 0.23. And this is the most important part of this lab-- this is the whole thing, calculating these concentrations in the end. So it's important to know how to do that. So once you get your concentrations, you've got a series of things to go through here for your data analysis. There's no error propagation on this part of the lab, which is good for you. You will have to use the LINEST equation that Sarah talked about, which is pretty easy to use. And that'll help you calculate the errors of your slope intercept and y values. And then you find your average and standard deviation of the five measurements, calculate the 95% confidence interval. Most importantly, report the final concentration of P and PO4. Make sure all these results show up in your abstract. First thing I do when I get lab reports is I look at the abstract. I want to see a line that shows my results. And they also should appear in your conclusion, and then you can discuss them in your discussion of your lab report. So any questions about this? I know you're going to have a busy weekend because you're going to be working on your ferrocene lab, your first lab report. And I want to tell you that please, feel free to reach out to me or Sarah if you have any questions. I'm going to be here tomorrow. I probably will be here Saturday and Sunday. So if there's a last minute question, just send me an email, and I'm happy to invite you in, and we can answer your question. I should be here in the afternoon, probably, on Saturday and Sunday. Now, I'd like to end the lecture today by doing a demonstration. Actually, did I turn that off? I can show you this here. I'm going to do this Briggs-Rauscher reaction. Actually, we're going to make this iodomalonic acid. We're going to actually attach an iodine to malonic acid. We're going to create this in a beaker. The reason I'm showing you this reaction is because it has everything in it, including starch. And it has a lot of colors. And these colors are things that we're going to talk about in the next lecture, what starch does and how it works. And this is kind of a preview to that. This reaction that you're going to see was actually discovered by two high school chemistry teachers. They're Briggs and Rauscher from Galileo High School, my favorite city, San Francisco. So these guys came up with this back in, I think, 1973. They published a paper in the Journal of Chemical Education. And they had every scientist in the country puzzled. And it took about 10 years to work out all the and sundry reactions that are going on in this reaction. So I'm going to put on some safety glasses. And what I'm going to be doing is going to be mixing three colorless solutions in here. This is my first one. And I'm going to use kitchen chemistry, which means I'm kind of looking at that scale over there and I'm going to pour these in. So let's put a little more. That's colorless, right? OK, next colorless solution. That's about right. And the final colorless solution-- keep your eye on it. Oh my goodness, wow. It wasn't supposed to do that. What? Are you kidding me? What's going on here? Get your clock out. This is a clock reaction. You can keep time with this. So I'll give you a little hint. There iodide in there, I minus. And I minus is colorless. There is iodine in there, and iodine is amber. When they're both present, it's blue-black. And we're going to see why that is in the next lecture. So there's a lot of reactions going on in there. When these reactants react, they form hypoiodous acid. And sometimes, the hypoiodous acid actually oxidizes iodide to iodine. So you've got collarless going to amber. But sometimes, there's so much hypoiodous acid formed, you can't handle everything. And what happens is you have a little bit of I minus and I2 present at the same time. And you get blue-black. This is kind of the color you're going to get when you do your titrations and you add the starch, because there is starch present in this. So I'm going to leave you with that. And I'll see some of you up in the lab. Yes, you have a question. AUDIENCE: [INAUDIBLE] JOHN DOLHUN: She just asked me if this will ever stop. Can someone-- Hannah wants to know if this is going to ever stop. Who can tell me, anyone? Aisha? AUDIENCE: I feel like it won't, because it's not releasing gas. JOHN DOLHUN: Aisha says it probably won't because it's not releasing gas. But in a minute, it's going to. Iodine vapor is going to start pouring out of it, and Tristan is going to carry it up to the lab in a bucket quickly. But in answer to Hannah's question is, will this stop? AUDIENCE: [INAUDIBLE] JOHN DOLHUN: Limiting reagent, right? There's always a limiting reagent. OK, see you.
MIT_5310_Laboratory_Chemistry_Fall_2019	10_Fischer_Esterification_Part_1.txt	[SQUEAKING] [RUSTLING] [CLICKING] SARAH HEWETT: All right, good afternoon. We're going to get started because we have a lot to talk about for this one lab before a lot of you guys get to do it starting next week. So we are done for now talking about the essential oil lab, and you'll get one more lecture about that in the X-ray crystallography stuff coming up next week. And for now, we're going to switch gears and talk about the ester lab. So before we get too far into it, the Ellen Swallow Richards reports are due next Wednesday and Thursday, the 16th and 17th. The TAs will be holding office hours and I will post those onto Stellar this afternoon. And then starting this Wednesday and Thursday, we're going be starting our next round of labs, so wherever you are standing, whichever bay you're in in the lab, that will determine which lab you are going to do next. So A prime 2, center of the lab, you'll be doing essential oils, middle group, catalase, and then the people closest to the wall, you'll be doing the ester lab, which we're talking about today. If you're doing the catalase lab, and hopefully your TAs will remind you of this as well, but you need to bring a laptop. You'll be working in pairs, so if you don't have a laptop, then we can pair you up with somebody who has one. But we need a good number of laptops to do that. That's how you'll be collecting your data, and we'll talk more about that starting on Thursday. But moving on to esters, so the structure of an ester, which hopefully you guys have seen before in your organic chemistry or maybe your gen chem classes, is something like this. You have an R group where this first R group can be a hydrogen, any alkyl group or an aromatic group. Then you have your carbonyl, another oxygen and then a different R group. And this one can only be an alkyl or an aryl group. It has to have carbons. It can't be a hydrogen, or else you have a carboxylic acid. So that's the general structure of esters. And talking a little bit about background information about esters, they are found naturally in many plants, and you can synthesize them in the lab from carboxylic acids and alcohols, which we are going to be doing. They are highly fragrant, as you guys will experience when you do this lab, and so as such, they are used extensively in flavorings, scent and polymer industries. And so some esters that you may have seen before in the world, this is a triglyceride. This is how your body stores fats, and it makes it from glycerol, which is an alcohol.. It has three OH groups and a bunch of fatty acids. So that's one biological example of an ester that is very common in all of our bodies. And then this is ethyl cinnamate, which is an ester that is found in the essential oil of cinnamon, and it is what gives cinnamon its cinnamony flavor or scent. The most ubiquitous of esters is probably polyester. And so many of you are probably wearing polyester right now. It's in your fabrics. It's what plastic bottles are made out of. You have water bottles or food containers, all of these things. If you see this symbol that is the symbol for this plastic, which is the most common one used in our fabrics and in the food packaging that we have, and it is polyethylene terephthalate, and this is the structure. And so you can see that there is the ethylene group. There's the terephthalate group, and then there is our ester bond in the middle. And if so if you stack a lot of these together, you make a giant polymer, then you have all type of plastics that we use for many, many applications in our daily life. So a little bit of background about esters. And here's a chart of all of the different types of esters-- or not all of the esters. There's many, many, many types of esters that you can make, but here are some very common ones, especially ones that are found naturally in different food and natural products. So you can see there's the part from the carboxylic acid and the part from the alcohol. So if you make any of these combinations of esters, then they'll have all these different scents. And so in the lab, you guys are going to be synthesizing a whole bunch of different esters, and one of the ways that you may be able to identify it is by what it smells like. So if you look in the lab manual, there's a whole chart of the esters. It gives you their name. It gives you a bunch of physical information about it, and it also gives you the scent. So when you synthesize your ester, you will carefully smell it and see if it matches up to what it is supposed to smell like. AUDIENCE: What are the boxes that say ethereal? SARAH HEWETT: Ethereal? That is kind of-- I've never smelled something that smells ethereal. Does anyone have a good description of what that may smell like? I think it doesn't have like a concrete scent. That's how I kind of interpret that. But you can see there are some that smell like vanilla, pineapples, different fruits. Those are ones that smell like balsamicy, like vinegar, coconut, all kinds of different things. So we're going to talk about the reaction that we're going to be doing. This is Emil Fischer. He is half of the team that is responsible for creating or inventing this reaction. I could not find a picture of the other guy. He won the Nobel Prize for chemistry in the early 1900s, and now it is typically just called a Fischer esterification reaction. So you take your carboxyl acid, your alcohol, some acid, and then you can synthesize an ester. And so we'll walk through the mechanism really quickly so that we know what is happening. And you guys have probably-- have you guys seen this in your organic chemistry classes? Yes, so this hopefully isn't too new. So you start off with your carboxylic acid. We're going to add a strong acid in our case, sulfuric acid, which is very corrosive. Be careful when you're handling it in the lab. That is our proton source. So the first thing that we're going to do is activate this carbonyl. We get our carbonyl. Now it has a proton and a positive charge on it, and we can draw a resonance structure where that positive charge gets put down on this carbon here. And when we do that, we have our alcohol. We can add our alcohol in, and these electrons can come up here and attack that positively charged carbon. We can add our alcohol group to our original molecule. So now we have this guy here, and now the positive charge is on this oxygen. And so we can lose a proton to get rid of that positive charge. So then we end up with a proton over here. That's an unfortunate proton. And now we have this structure here with our extra proton. We can protonate this oxygen up here and form this charged species. And now we have made positively charged water, and we know that water is a good leaving group. So we can leave and make water, and that is where the water comes from in our synthesis. And to kind of balance this whole thing out, you're also going to have these electrons come down and form a double bond to help drive that water out. So now we have a double bond here. It has a positive charge and a proton still on it, so we can have this proton leave as a proton. And we have made an ester. Tada. And then we've regenerated our acids, so that's why the sulfuric acid is our catalyst. So I guess we can leave this here for now. So that is the mechanism of the reaction, and like I said, you guys have probably seen that before. It's pretty straightforward, and so this is the reaction that we will be doing in the lab. Now we need to talk about naming esters, and there are a couple of conventions that are used when naming esters. There's a few ways to do it. So the first one is the IUPAC straightforward way to name esters, and you start with the part of the molecule that comes from the alcohol. So if you notice over here, the blue stuff came from the alcohol, and it ends up as this group that's attached to the oxygen, not on the carbonyl side of the molecule. So you're going to start there. You'll name it as though it's an alkyl group, so something that is attached. So it'll have that -yl ending, like methyl, ethyl, that kind of thing. So this is a propyl group. It has three carbons. The second step is to look at the other half of the molecule, and you want to name it as though it isn't just an alkane and count up all the carbons including this one attached to the carbonyl. So you have one, two, three carbons over here as well, so that would be propane. And then you want to drop the e off the end of the name and add -oate, So proponoate. So the IUPAC way to name this thing is then to combine the names. So you'll get propyl, proponoate. So clear enough? It gets a little bit tricky because chemists don't always use the IUPAC or traditional names for everything. There are some common names that get used and thrown around when people are talking about different chemicals. So does anybody know what this carboxylic acid is? Acetate or acetic acid. So acetic acid is what we typically call it. You'll hear it as an acetate group if you take off that proton. If you're going to name this according to the IUPAC convention that I just told you about, there's two carbons, so that's ethane, and you would call it ethanoic acid, but that's not commonly used. This alcohol is ethanol. So if you combine these two, what would we call that ester? Ethyl ethanoate, or you can use the common name and call it ethyl acetate, which you guys may have heard of or remember from the ferrocene lab. Yes. So there are a couple of different ways to name the esters, and there's a whole list of esters. If you guys have looked in the manual, there's a whole list of possible unknowns that you can have and that you can make in this lab, and they come from all different combinations of carboxylic acids and alcohols. And so in order for you guys to have some idea of what you may be making and the structures that you will be looking for when you are characterizing your esters that you make by different types of spectroscopy, we need to be able to name and draw the esters. So if you got this handout in the back, on one side, it has a sheet that has all of the common names for the structures that you may find in that list of esters that we'll be making in the lab. And then on the back, there is a blank chart. Mine's already filled in, but there's a blank chart that has a bunch of different ester names. So if we want to take a moment and practice naming these esters using the information in the past two slides you should have on your PowerPoint handout and the structures on the back of here, you should be able to draw the structures of all of these different esters. So take a moment do that and talk with your neighbors. Work it out. Ask your TAs if you're back there. And then I'm going to have people, when you are confident that you know the structure of one of these guys, come down here and draw it please. So I'll give you a couple of minutes to do that. All right, can I get a few people to come help draw some of these on the board if you have drawn some of these on your paper? Go for it. Going to need a few other people, or else this is going to take forever. Excellent. Wonderful. Anyone from the back want to come down? Go for it. Thank you. AUDIENCE: [INAUDIBLE]. SARAH HEWETT: Don't worry if it's wrong. If you want to draw more than one, go for it. If anyone else wants to come down here and be really brave and share their knowledge, that would be excellent. All right, we'll see how many of them these guys can do. Yeah, if more than one, go for it because it'll be faster. AUDIENCE: [INAUDIBLE]. SARAH HEWETT: Yeah, sorry about that. One more. All right, how are we looking? Good, except this one, I think, these are the same molecule. AUDIENCE: [INAUDIBLE]. SARAH HEWETT: So butyl acetate, it's just no double bond. Thank you. Well done. So there are the structures of some of the esters that you may or may not be making during this lab. It's good practice. So these aren't all of them, so you'll still have to draw out some of the possible structures when you are trying to figure out what your unknown might be, but this is a good start and good practice. So it looks like you guys are good at drawing the esters. Well done. All right, so now that we have the idea of what the reaction looks like on paper and what our products could possibly be, we're going to talk about how we can actually do this in the lab. And so I brought some of the glassware that you're going to be using. And I'm going to put gloves on because I don't know how well whoever used this last semester cleaned it. So the first technique that you're going to use is reflux, and so that's to do the first part of, or pretty much do the whole reaction here, where you're going to combine your carboxylic acid and your alcohol. You're going to heat it up, and to reflux means to boil without losing solvents. So it'll be boiling. You'll have a stir bar in there. So you can see you have your stir plate. You're going to use a heating mantle again to heat your reaction. It'll be boiling in there, and then instead of using our Vigreux column like we did in the distillation, you're just going to put a condenser on there. So you'll have water going through your condenser. You'll want your water going in the bottom and out the top so that the whole thing fills up with cold water, and so that's when you're boiling. Your solvent will be evaporating, and then it'll condense and it'll go back down so that you don't boil to dryness and you don't lose all of your product as you're boiling it. And then on the top, you're going to put a drying tube, and your drying tube will look like this. And when you get it, it will be empty just like this one is, and then you will fill it. You'll put a little bit of cotton in here as a plug, and then you will take this stopper off and fill the rest of it with calcium chloride. Does anyone know why we're going to do that? And it goes right on top here. So calcium chloride is CaCl2. It is among other things used as a road salt. So there are three ions in the structure, and if you remember your colligative properties, then it'll lower the freezing point of water when it has three ions in it. It's a very good electrolyte. It'll also lower the vapor pressure of a solution or increase the boiling point. And the dissolution of calcium chloride is exothermic. It's very thermodynamically favorable and it's also entropically favorable, so it is a very spontaneous reaction, and it is a hygroscopic material, which means that it absorbs water. So it's a desiccant. You may see those like silica gel packets in things that you may buy to keep the water out. Calcium chloride is another material that's commonly used as a desiccant because it's hygroscopic, but it has a property even beyond being hygroscopic. It is deliquescent, which means it'll absorb water until it becomes a solution. So this is what dry calcium chloride pellets look like. So it's just little white chunks of solid. And if you leave it out on the benchtop for long enough, it'll actually pull in the water from the air and turn itself into a calcium chloride brine solution. So if you spill some of this on the bench, you want to clean it up really quickly, or else it will start to look like that. And so what we're going to use it for in our reaction is-- what are the products of our reaction? We're going to make an ester and? Water. So if we go back to our mechanism, we lose water here. And if you notice, most of these steps here are reversible steps. So if you remember Le Chatelier's principle, if this is our overall reaction and one of our products over here is water, and this is a reversible reaction, then how can we force the reaction to go towards the product side? AUDIENCE: Take out the water. SARAH HEWETT: Take out the water. You can either add more reactants or take out the products, and so we are going to be taking out the water with our drying tube. And so that will help ensure that our reaction goes to completion while we are refluxing. So once you've done all of your reflux and you have your product, you've heated it for a while-- it's kind of boring to watch, but reactions take time-- so then you will have your product in your round-bottom flask here. And we will have our ester, hopefully, and what else? Potentially all of these things, right, and some sulfuric acid. So we don't know that our reaction went to completion. We hope that it got close, but we need to purify it from any impurities or remaining starting material that we may have. So we do that in a separatory funnel, and this is a separatory funnel. And we do a liquid-liquid extraction, which means that we're going to have one liquid, and then we're going to add a different liquid to it. So we have two liquid phases, and we're going to partition the different compounds between those two liquid phases. And the only way this works is that we have to have two immiscible liquids that have different densities. So what does it mean for something to be immiscible? AUDIENCE: They won't mix together. SARAH HEWETT: They don't mix together. Good. So when you pour your two solvents in here, they need to not mix so that have two distinct layers and that you can separate your product between them. And it will separate them based on density. So when you have your separatory funnel, you will pour your two things into it, and you should get two layers. And so your more dense layer will be on the bottom and your less dense layer will be on the top. So in our case, water has a density of about 1 and most organic liquids have a density of less than 1. So if you take your product, which is an ester, and you add water to it, what will be on the top and what will be on the bottom? AUDIENCE: The water will be on the bottom. SARAH HEWETT: Yep. So this will be our aqueous layer and this will be our product or our organic layer. And it's really important that you keep track of what is where when you're using the separatory funnel and that you know what you've drained out and what you have kept in there. And you want to save everything. Save all of the stuff that comes out of here. Save all the things that are in there until you know that you have your product. So there are a couple of ways that we can use a separatory funnel or as a sep funnel, the abbreviated version. And the frequently used solutions for this type of extraction, the first type is an acid-base extraction or a chemically active extraction, and that's the first thing that you're going to be doing. So in our reaction mixture, we have hopefully a lot of product. We probably still have some carboxylic acid left over, and we know that we have some sulfuric acid in there. Yes? Great. So the way to get all of that acidic byproduct away from our product is to use sodium bicarbonate, which is a base. And when we do that-- so if we have our carboxylic acid, if you add a base to it, then you can deprotonate it, and if we have sodium bicarbonate, it will form a sodium salt. And that is more polar than this, so it will be more soluble in our aqueous layer, and we will pull it away from our product. So that's the idea behind the base extraction. And so hopefully, that first round of extraction will get rid of our acidic impurities, and then we're going to do another extraction using a sodium chloride solution. And that is sometimes referred to as salting out. So we will keep our product in there, and then we will add sodium chloride solution. And the sodium chloride makes our aqueous layer really polar, and so it makes our product less soluble in the aqueous layer, and it makes any water that's left over in our product layer more likely to come into the aqueous layer. So when this is polar, than all of the polar things, all of the water, get pulled into the aqueous layer, and any organic-y things, the product that we care about, gets forced out into the product layer. There's some terminology that you may hear when you are using a separatory funnel. So there's extraction, which is if your product is in a mixture and you to add another solvent to extract your product out of what's already there. And then there's washing, which is we're going to be doing, which is where you're just going to pour your product in there and you are going to add other solvents to extract the impurities. You leave your product where it is and you pull out the impurities. A note on how to use a sep funnel, and I'm going to put goggles on just for safety here. This is just water, but the way that you're going to do this is you'll have a ring stand. It'll hold itself up right here, and then you will first make sure that the stopcock is closed. So if you pour your product through here and this is open, then that's going to be a really sad time in the lab. So then you'll pour your product and whatever you are washing it with into the sep funnel. You will get two layers because you'll have two different liquids in there. This is just water. Then you will cap it. And then you're going to shake it like so. Then you will point it away from any humans and into your hood and you will open the vent. When you are shaking things that have are really volatile like organic solvents, they'll build up pressure in here, and so you don't want anything to explode. You don't want this top to come flying off. You don't want the glassware to break. So you want to vent this. You're going to shake it a little bit, vent it. When you first start, you want to vent it very frequently so that the pressure doesn't have a chance to build up. When you do this, you want to point it away because sometimes, liquid will come flying out. You'll hear it. It'll go pssh. So you want to be very careful when you are using this. Safety note. What happens when you add sodium bicarbonate to an acid? You get a gas. You get carbon dioxide. Think baking soda and vinegar volcano. So when you are first adding your sodium bicarbonate to your product, you want to not do it right away in the separatory funnel, or else you're going to build up a whole lot of pressure, and it's going to create an unsafe situation. So you will add those to a beaker first. Wait for the bubbling to stop, and then you can pour it into your separatory funnel and you can do the extraction. And what you're going to do is you will open the stopcock, and then you'll be able to watch the layers go down. And here's something. So if you open the stopcock and you say, oh my gosh, nothing's coming out, what's our problem? The top is on. So you want to close it first. Take the top off and then it will drain smoothly. And then you'll just pay attention, and you can stop it right when the interface between those two layers gets right to the bottom, and that's how you're going to use this to separate your solutions. But yeah, inevitably, somebody always forgets to take the top off, and they're like, my sep funnel's broken. It's not. Just physics. So I guess we can still leave these on. So that's going to be all in day one. You will reflux your product. Then you will use your sep funnel. You will start to purify it, and then on day two, you're going to-- Oh, wait. Before, sorry. So after you have isolated your product, we have just added a whole bunch of water to it, right. We've shaken it up with sodium bicarbonate and sodium chloride solution. We don't want water in our product. That's not the point of this. We want to just have our ester, so we need to remove the water that gets left over from our separatory funnel situation using a drying agent, and a drying agent is similar to calcium chloride. We typically use sodium sulfate or magnesium sulfate in the lab because they're easy to work with and they suck the water into their crystal lattice, and they necessarily dissolve very well, which is nice. And so these are fairly interchangeable. They're the most commonly ones used in lab situations. Magnesium sulfate sometimes can harm acid-sensitive compounds, so if you're doing something very sensitive in the lab, you may want to stick with sodium sulfate, but for our purposes, it will be fine. So what you're going to do is it comes in powder form, and you will add some of it to your product and you will swirl it around. And you will look at it, and then you will run to your TA and say something like this, like, ah, is it dry yet. How much do I add? And your TA will look at you and say, I don't know. You should know this. So this is how you could tell if it is dry yet. The first time that you add your drying agent, it will clump up and it'll all be in one big chunk, especially if you have a lot of water in there. Sometimes you can even see the water. If you hold up your flask, you'll be able to see a little bubble of water at the bottom. That's fine. You'll add your drying agent. It'll all clump up. You'll add a little bit more. It'll have some smaller clumps, and then you'll add a tiny scoop more. And the rest of it that you add won't clump up. It'll look kind of like a snow globe. It'll swirl around and be free-flowing crystals, and that is how you know when you are done, when it doesn't clump up anymore. So you don't need to go over and weigh it. I think there's an approximate weight in your lab manual. Like usually, it's maybe around a gram. But don't bother weighing this out. You can just kind of eyeball it, scooping a little bit at a time. Don't go too crazy with the first scoop, because the more of this that you have in your product, the harder it will be to isolate your product later. So let's say, if you think of it like at the beach, if you have a bunch of sand and then you put a bunch of water in it, your water kind of disappears. And in this case, our product is the liquid, so in order to get our product back, we will gravity-filter this away from the drying agent. And so you want to have minimal amount of drying agent so that your product doesn't get stuck in it and it's easy to filter later. OK, so that's all day one. Then you'll have your semi-purified and dried product, and then on day two, we will purify it from anything that did not get taken out in your extraction process using distillation. And what I didn't mention is that for this lab, you'll be checking out a kit from the stockroom, or your TAs will check this out, and you will get a kit that has all of the glassware that you need to do the entire lab in it. And there's a nice list on here of what goes in this kit. So on the first day, you will set up your reflux just like this, and then the second day, we're going to set up an atmospheric distillation, which is going to be very similar to the vacuum distillation that we talked about before. But this time, instead of having all the glassware in one piece, you get to assemble it yourself. So you'll have your Vigreux column. Then you'll have a distilling head up here, and then you will put your thermometer in the top. And most of our thermometers have ground glass joints. And then you will use the same condenser that you used for your reflux on day one, and that will go across like this. And you will clamp all of this glassware very well, and then you will add your spout to the end of it right here. And that is your distillation setup. You'll have keck clips in your lab, those yellow things that hold all of your joints together. So you want to make sure that everything is clamped and secure before you start distilling, because if you have gaps in your glassware and then you start heating and your product becomes a gas, you will lose it all. So the distillation will purify your product from any remaining insoluble impurities or higher boiling impurities that we do not want in our final product. And when you do this, you're going to collect a few different fractions. And so the way that you're going collect your fractions in this case, we don't need to use a cow adapter because we're not going to be attaching anything to the vacuum line. You can see that the spot over here, instead of attaching it, this is where you put your vacuum. It's just open to the air. And so you can collect your fractions in test tubes on ice, and then you will collect a few different fractions. So you usually collect the first few drops and then a few different fractions. If the temperature changes, you will switch your fractions, and your TAs will tell you how to do that. And then you will monitor your purity by IR. So if we go back and think about the IR that we talked about last time, and if we think about our products and our reactants, what IR bands are we going to see in our carboxylic acid reactant? We have a C-O stretch, an O-H C double-bond O. And? You might see the CC, you may not. Those ones are kind of hard to do because they don't change dipole very much when that bond happens. So sometimes, maybe a C-C bond. And what else? What's in this R group? Yeah, C-H stretches. What about our alcohol group? We'll have another OH stretch. Of we have a C single-bond O. Yep. Do we have one of these? No. None of those. We have some of this? AUDIENCE: Yeah. SARAH HEWETT: Yeah. And then again, maybe the C-C bonds, sometimes those are in the [INAUDIBLE] region. You probably won't. Don't spend too much time looking for these. These are kind of there but not easy to see. So now if we look at our product, what do we expect to be in our product, assuming we don't have any water because we've done our distillation and our extractions very well? We have a C double-bond O. A C single-bond O. A C-H. Do we have an O-H? So what are we going to look for in our IR to tell if we still have starting material in there or not? AUDIENCE: The O-H [INAUDIBLE]. SARAH HEWETT: The O-H. And so this will still have a C double-bond O, so that one might not be as easy to tell. But we definitely should not have an O-H peak. So if you take your Ir fractions and you take your fractions, you take the IR of them and then you start to see the O-H, the characteristic O-H peak up way by like 3,000 wave numbers, then you may want to test a different fraction because that one either has some water in it or it still has some of your starting material. And then once you've determined which of your fractions is the most pure, then you will continue on with that to do the rest of our characterization techniques. And the first one of those is going to be boiling point determination. So we can determine the boiling point of the ester, and that is a characteristic of each ester. So you have a chart. That chart at the beginning of the lab, it has a list of all the boiling points. So we will measure the boiling point of your ester, but before we do that, we're going to calibrate the thermometer just like we calibrated the melting point apparatus. So at this time, there are only two calibration points. So you'll measure the freezing point of water. So you'll get a beaker. You'll fill it up with ice, some water, let the temperature reach equilibrium. And you want make sure there's still ice in it when you measure so that it's not water and it's not heating back up to room temperature. And then you will measure the temperature of the very cold water after it's sat for about 10 to 15 minutes. While you're doing that, you can also heat up a beaker of water on a hot plate, measure it and heat it up to boiling, and then you will measure the temperature of the boiling water. And there's a correction factor in the lab manual that you will use to calculate the theoretical boiling point of water at whatever the atmospheric pressure is on that day. So you'll go get the barometer from the lab like we brought down to the river. You can measure the pressure in lab because we know that boiling point is related to the pressure in the atmosphere and the vapor pressure, so there is a correction factor for that. And then you will plot your theoretical boiling points and your theoretical freezing point versus the ones you actually measure, and that'll give you a two-point calibration curve for your thermometer that you're going to use to determine the boiling point of your ester. The apparatus that we will use to determine the boiling point of the ester is like so. You will have your hot plate. Then you'll have a sand bath, and then you're going to use a very small test tube. And you will put a very tiny amount of your ester in, maybe a milliliter. And then you will suspend the thermometer. We're going to use digital thermometers. You'll suspend the thermometer a few centimeters above the surface of your liquid, and when you heat this up, your liquid will vaporize. It'll hit the thermometer tip and it'll condense, so you'll see drips coming off of the tip of your thermometer. And the temperature will start to go up, and you want to wait. So the second thing that you'll need is a lot of patience. So the temperature will go up very, very slowly as the vapor reaches the boiling point. So if you've ever boiled water and you cooked something, you know that you'll start to see steam and water vapor before the liquid itself is boiling. Same thing happens here. You'll start to see the drips, but then the temperature may still be going up. So this is one of those things that you don't want to sit there and watch because you will become very impatient and you'll say, oh, good, the temperature hasn't changed in 30 seconds. This must be it. But then if you come back in five minutes, the temperature has indeed gone up, and then you have the incorrect boiling point. So this is one of those things you can set up and then check on it after a while. And once the temperature stops increasing, that will be your boiling point. The next thing that you will do is you will determine the density of your unknown, and this is our density instrument that is in the lab. So instead of having to measure the mass and the volume yourself to get grams over milliliters, which is our unit of density, you can inject your sample into the side of this instrument. So there's the little lower-lock valve here, and there's a syringe, so you will inject your sample in and it'll fill up this tube. The instrument stays at 20 degrees Celsius so that we know for sure that it is the density at 20 degrees Celsius. And then you will press Go and it will measure the density for you, and it'll pop out the density number right there. So very simple, and then you can use that as an identifying characteristic of your ester, and you can compare that again to the chart in the beginning of the lab manual to use as information to help you identify your unknown. Then we're going to measure refractive index. We talked about refractometry a little bit in the essential oil lab. In the essential oil lab, we used it to-- oh, that's a typo. In the essential oil lab, we used the refractometer to determine the purity of our samples, but in this lab, we're going to use it as an identification technique for our esters. So every liquid has a characteristic refractive index, so we can measure the refractive index, compare it to the literature value, and that will also help you identify your unknown ester. The second to last technique we're going to use is NMR spectroscopy. And how many of you guys have seen NMR before in your classes? A few people. All right, so in, I think about two weeks, Walt Massefski, who is the Director of the NMR Facility here in the chemistry department, is going to come and do a very, very thorough lecture on NMR and how it works and how to interpret it. Unfortunately, that lecture will happen after some of you guys take these spectra in the actual lab, so I will do a quick briefing on NMR because we have some time. And then again, stay tuned. You will get a much, much better idea of this technique from Walt in a couple of weeks. So NMR spectroscopy, the idea behind it is that it uses a very strong magnetic field to align nuclear spin states. And you don't have to know too much about that, at least for right now. I'm sure Walt will talk more about it. But the hydrogen nucleus has a spin associated with it, and if you apply a magnetic field in a certain direction, the spin can either align with the magnetic field, which is the lower energy state, or it can go against the magnetic field, which is a little bit higher in energy. And so this is a difference in energy here. So once you have your protons in your field-- and you can do other nuclei too, but we're going to focus on protons for the moment-- there's a radio frequency pulse that is applied that causes some of these spins to flip. And then you remove the radio frequency pulse, reapply the magnetic field, and then you wait for the spin states to go back down to the ground state. And because there's an energy difference associated with getting the spin to flip, there's also an energy difference associated with when it goes back to its ground state. So it will emit energy at a certain frequency depending on the environment of the proton. We can measure the energy that gets emitted and plotted, Fourier-transform it, and then you get an NMR spectrum. This is the really quick, five-minute version. This will make a lot more sense when Walt talks about it later. So the important thing to note here is that the frequency of the energy that a proton emits as it changes spin state is related to the environment of the proton. So we can use this to get information about the different protons in our molecule, and we can determine connectivity, the number of protons that we have, and some information about how they're bonded together depending on the different NMR experiments that you do. And the three major pieces of information that we will be using in our lab are the chemical shift of the proton-- so that's again related to the frequency of the energy-- the integration-- this tells you how many protons there are-- and then sometimes the coupling. So if there are protons next to each other, they will split each other's signals and you'll get multiple lines in your NMR spectrum. So as a really, really quick example, we can look at our favorite ester here, ethyl acetate, and we can look at the different types of protons that it has. So how many types of protons are in this molecule? Three. So we have these methyl protons here, the ethyl protons here, and then these methyl protons over there. So these three are all in the same chemical environment. These are in the same chemical environment and these are in the same chemical environment. So we should expect to see three signals in the NMR spectrum of ethyl acetate. So the way that an NMR spectrum is laid out, it's on a scale of 0 to 12, give or take. It can go beyond that, but for the purposes of most organic molecules, all of the peaks will be found in this region. And the location that a peak appears or a proton peak appears is again related to its chemical environment. And the things that are very alkyl or have a lot of stages around them are going to be further upfield. We call this upfield with a lower PPM number. And things that are closer to oxygens or electron-withdrawing groups are going to be-- they call it deshielded. So the electrons are withdrawn away from those protons. It doesn't shield= them from the magnetic field as much. So they come up more downfield, and the way that you can remember that is downfield or deshielded both start with D. And so if we look at these protons, which of these do we think is going to be the most upfield or the furthest away from all of our oxygens? This stuff all the way on the right? Yeah. I just want to make sure that I am doing this right. So yes, these methyl protons will be the furthest to the right, and you'll get a signal here. And so this signal, the chemical shift value will be somewhere probably around 1 or 2. And then the integration tells you how many protons it's for, and that shows up down here at the bottom. So how many protons will the signal equal? Three from our methyl group. All right, so if we look at the remaining two groups, which one do we think would be kind of the middle? All the way on the left. So these protons here are right next to an oxygen, so they're going to be more deshielded, and these have a carbon in between, so these will be our next signal. So then we'll have another signal here. How many protons? From this group, three. And so that leaves our methylene group over here. That will have another signal that's further downfield, and this one will be two protons. So already, you can see that there are different ways that you can use this to identify your molecules. So if you count up the number of different unique protons there are, then you can look at the number of signals you see, and that is one way to identify your product. You can also use the coupling, which is what is going to break these signals into not just one peak, but it'll be a few. So coupling happens when there are protons that are next to each other. So this methyl group is next to two other protons, right. And so each of these protons, each of its neighbors, will split this signal one time. So if you have your signal and it gets split once, then you have two signals, and then if it gets split again in an equal magnitude, you end up with three signals. So this splitting kind of combines and this peak gets a little bit bigger. So this is what is called a triplet. So if you have two neighbors, you get a triplet. So this peak, that methyl group will actually look something like this. It'll have three peaks to it with the middle one being the biggest, and that's the characteristic pattern of a triplet. What about our ethyl group here, or ethylene group, methylene group? We have our two protons. How many neighbors does this group have, proton neighbors? So this has three neighbors. So that signal is going to get split three times. So you'll split it once. Split it again, so that would be our triplet. And then if we split it a third time, we get four lines. So this proton signal will actually look something like that. How many proton neighbors does this have? None, so will this get split? No. So this will stay as a singlet, one single peak, because it does not have any proton neighbors. So anyone have any questions about where all of this came from? So again, that was the super quick version of NMR and the type of information that you can get from it. So when you are looking at the structures of the potential esters that you think you may have, you can probably narrow it down based on your boiling point in your refractive index, your density. And you can narrow it down to a few, and then you will draw out the structures. And then you can, based on the structure, predict how many NMR signals you expect to see. And you can figure out what you expect the splitting to be, so if you expect them to all be single peaks or if you expect to see different types of multiplets. And then when you get your NMR spectrum, you can compare the number of peaks, the integration of the peaks. So if you know that you have a methyl group, you should be looking for some signals that integrate to 3. And that is how you can use this as a technique to identify the structure of your unknown. And again, Walt will do a much better job explaining all of this in a bit. But just so you've seen it, before you get a chance to take your spectrum in lab, that is a quick introduction. So once you have all of this information, you have your boiling point, your refractive index, your density, your NMR spectrum, your IR spectrum, you're going to attempt to identify your unknown, and this should all happen at the end of day three. You'll have all of this information, and then you'll be overwhelmed. You'll sit down, put it all together and try to figure out which of those unknowns in that table is the one that you made. You'll fill out an identification form that your TAs will give you, and then you will bring it to your TA at the beginning of day four on the lab and you will say, this is my ester. And they will tell you if you are right or wrong, and you'll find out that day if you were correct or not. And then you will do one more technique for your final confirmation. So if you already know, then your mass spectrum should be super confirmation for you. And if you were a little bit off, then hopefully your mass spectrum will be that last piece that helps you to get your final identification. Mass spectrometry, you have already seen a little bit. We did the ICPMS in our last lab. But there are different, many different types of mass spectrometry, and a bunch of different ways that you can use that technique. So ICP uses plasma to break the compounds apart into their atoms and ionizes the compounds that way, if you remember, hopefully. What we're going to be doing this lab is electronic impact mass spectrometry, which instead of using plasma just shoots a high-energy beam of electrons at your molecule. And it doesn't have enough energy to break your molecule apart into its atoms or anything, but what's going to happen is the electrons will hit the compound and it will eject an electron from the compound. So you'll make what is called a radical cation. So it'll have one less electron, so it'll be a positive charge, but it only lost one electron, and since it's organic-y, it will be a radical. This also frequently causes the molecule to break apart, not always. Sometimes you will get the radical cation of your whole molecule that will make it through the mass detector, and you will get the mass of your actual compound. And other times, it'll break apart and you will see a bunch of pieces of your compounds. You'll see the mass of different fragments of your molecule. So you can use either the mass of your molecular ion-- so I'll show you what this looks like in a second. So this is what the instrument looks like. It's right near the ICPMS. You may or may not have seen it, and it is slightly older and looks a lot like the GC that we talked about before in the essential oil lab. And that is because this is actually a GC mass spectrometer. So you inject your compound. It actually goes through gas chromatography, so if you have more than one compound, it'll split it into the different compounds. And then it'll take a mass spectrum of each of those compounds. We hopefully are only going to be injecting one compound in, so you hopefully purified it sufficiently well at this point. But then it'll still give us a mass spectrum, and the mass spectrum looks like this. So this is our mass-to-charge ratio or our mass units. So usually, the furthest thing, the heaviest thing, that is where you will look to see if that matches with the expected molecular weight of your compound. That's your molecular ion. So if it gets hit with the electron, forms a radical cation and doesn't break apart anymore, you will see a peak at your molecular weight. And so that is a giveaway of yes, this is my molecule. Sometimes, that doesn't happen. If it's really unstable, it'll break into pieces, and you will see-- so each of these represents a piece of the molecule that has broken off. So frequently, you'll see losses of 15. So that's when a methyl group breaks off. And Dr. Dolan will be talking a lot more about mass spectrometry and what you will do with this information and how it all works in another lecture coming up. Just to give you, again, an idea before you see it and have to do it in the lab. This is just a quick overview and you'll get a lot more detail about what all of this means coming up in a couple of lectures. Last but not least, safety for this lab is very important. The carboxylic acids are corrosive and toxic. They smell terrible. You can ask Tristan. He was the one who made all of the unknowns. And Brydon did the alcohols, so he got it slightly better, but Tristan will tell you that the carboxylic acids are very nasty to work with. Sulfuric acid is also highly corrosive, so you don't want to get that on your hands. And then you want to vent the sep funnel, like we said, away from people. So if you're working in a hood with someone, make sure that they're not around. Don't turn around to talk to somebody and point it in their face. The starting materials smell very bad. Your product will smell really nice, but it'll still smell a lot, so keep everything in the hood. This is a very, very smelly lab. Even if you keep everything in the hood, if you're walking by, which everybody is doing this, you will know. So we want to limit the amount of fumes that get out in the lab. Keep everything in the hood. Do not put vials in the glass waste. If anything breaks, or if you like break a pipette or if you break a beaker or something that has contacted your solutions from the ester lab, there will be a separate waste container for those. Your TAs will come around with a capped, plastic solid-waste container to collect all your vials so that they are not in the glass waste stinking up the entire lab. And this is key for everybody. Regardless of what lab you're doing-- so starting on Wednesday and Thursday, we're going to be doing three different labs at the same time, and we're going to try to keep the waste containers in the bays with the proper labs they're associated with. But pay attention to the waste labels. Read the red tag. If you're holding something and you're going to put it in the waste container, take the extra second to make sure it is the right one for the lab that you are doing. There will be three different sets of waste containers out there, and we do not want to mix in between, especially not acetone with the catalase waste. If you remember from before-- we may have talked about this. You will hear about it again. If you mix the acetone from any of these organic-y labs with the hydrogen peroxide from the catalse waste, you will generate explosives. So we are not going to do that because everybody is going to read the labels and dispose of their waste properly in this lab, and keep everything in the hood that should be. Good? Excellent.
Khan_Academy_AP_Microeconomics	Changes_in_Market_Equilibrium.txt	What I want to do in this video is think about how supply and/or demand might change based on changes in some factors in the market. And then think about what that might do to the equilibrium price and equilibrium quantity. So let's say at some period, this is what the supply curve looks like and this is what the demand curve looks like. And then all of a sudden, this thing happens. A new disease-resistant apple is invented. What's likely to happen for the next period? Well, a new disease-resistant apple being invented, this is something that clearly impacts the growers, clearly impacts the suppliers. All of a sudden, they'll have fewer apples succumbing to disease. And so they will be able to produce more apples. So at any given price point, this will shift the quantity supplied up. So at any given price point, it will shift the quantity of apples supplied up. Or you could say that the entire supply curve is shifted to the right, or supply goes up. And let me draw the entire curve. And obviously, if now we have disease-resistant apples, even our minimum price to start producing apples is lower. Now, when we had the supply curve shift in this way, when it shifted to the right, what happens to the equilibrium price? Well our old equilibrium price was right over here. Our new equilibrium price-- so this is the old one. And this is our new equilibrium price. We're assuming that demand has not changed at all. So this is our new equilibrium price. So our new equilibrium price is lower. So the price went down. And you don't have to-- you could have probably reasoned through that before, taking an econ class. But this way, at least you have some way to think about it and think about how the curves are changing. Now, let's think about this scenario. So this is before. So in all of these examples, the graph is what happened before the news came out, or the event came out. So this is before. And then a study is released on how apples prevent cancer. So what is that likely to do? Well, no one wants cancer. And so more people are going to be eager to have apples. This will change customer preferences. They will prefer apples even more when they're at the supermarket. So this is clearly affecting demand customer preferences. And so at a given price, people will want-- they will demand a higher quantity of apples. The quantity of apples demanded at a given price will go up. So the demand curve will shift to the right. Or you could say, the demand would go up. So that's the new demand curve. So here, demand goes up. And let me write it over here. In this situation, supply went up. Here, demand goes up. And what happens to the price? Well, this is our old equilibrium price. This is our new equilibrium price. The price clearly went up. So the price went up. And actually over here, let's think about the quantity too in this first situation. This is our old equilibrium quantity. This is our new equilibrium quantity. Quantity went up, which makes sense. You have fewer apples dying, price went down, more people want to buy them. Here, price went up, and what happened to quantity? Quantity-- this was our old equilibrium quantity. This is our new equilibrium quantity. Quantity also went up. More people just want to buy apples. They don't want to get cancer. Now let's think about these scenarios right over here. The pear cider industry launches an ad campaign. And for the sake of this, let's assume that the same growers who grow apples can also grow pears. That makes it interesting. So you have a couple of interesting things. By launching this advertising campaign-- we're going to assume it's a good advertising campaign-- this clearly will make demand go up for-- sorry, it'll make demand go up for cider, for pear cider, relative to apple cider. Most people, when they think of cider, they think of apple cider. Now all of a sudden, pear cider comes out. It'll make demand for apple cider go down. So this is apple cider demand will go down. Now, if apple cider demand goes down, the apple cider producers are going to demand fewer apples. So this is going to mean that apple demand will go down. At any given price point, apple demand will go down. So apple demand, the demand curve, will shift to the left. Or I should say at any given price point, the quantity demanded will go down. And so the entire demand curve, the entire relationship, will shift to the left. Now, that's not all that might happen. Because if you think about it from the suppliers point of view, and I don't know if this really is the case, but let's assume that the farmers who grow apples can also grow pears. Well, they might say, well, now that there's more demand for pears, they're doing this advertising campaign, I want to-- and probably the price of pears has gone up-- they might say, well, I'm going to devote more of my land to pears and less of my land to apples. And so the supply of apples-- so apple supply-- want to be clear here that we're talking about apple-- the apple supply might go down. So it'll also shift to the left. So they're both shifting to the left. Now what is likely to happen here? So the demand went down and the supply went down. They both shifted to the left. Well, here the way I drew it, this was our old equilibrium price, this is our new equilibrium price. It actually looks the way that I drew it right over here, that it did not change. The equilibrium quantity definitely did change. So let's see, this is our old equilibrium quantity. This is our new equilibrium quantity. This clearly, the quantity, went down. It was a bad day for apples. But the price didn't change, because, at least in the example, we assume that the farmers actually also produced fewer apples. It turns out, I could have drawn this in multiple ways. And actually, let me draw it in different ways here. So the quantity definitely-- so let's think about other scenarios. Let me draw it slightly different. Let's say that the supply goes down even more dramatically. So let's say the supply shifts all the way-- the supply shifts really far back. Now, what happened? Well now, our equilibrium price-- because the reduction in supply was kind of more extreme than the reduction in demand. And it really depends on how the curve shapes and all of that. The main thing is to reason through it or to actually see what the actual results are. But in this situation, all of a sudden that the price went up, but the quantity definitely still went down. So in this case, the one thing that you're always going to be sure of is that the quantity will go down but the price went up. Because this effect-- the supply went down much more than the demand did. And so the price went up. Now I could have done another scenario. I could have done another scenario where maybe the supply barely budged or maybe the demand went down dramatically. Let me draw it where the supply barely budges. So maybe the supply, it only gets shifted a little bit to the left. So maybe the supply curve looks like this. Now all of a sudden, once again, quantity definitely goes down. So in all of the scenarios, the quantity will go down. But I've just done three scenarios where the price could be neutral, the price could go up, or the price could go down. So you actually don't know what is going to happen to the price based on this. You would actually have to look at the actual curve and see what the new equilibrium prices are. Now let's look at this one. The apple pickers unionize and they demand wage increases. So this is an issue for the suppliers. So all of a sudden, one of their inputs, one of their costs of production, which is labor, has gone up. So if their cost of production has gone up, now at a given price point, they are less profitable, less willing to produce apples. So at a given price point-- so we're talking about the suppliers-- at a given price point, they will supply a lower quantity. So this is going to lower supply. And when you lower supply, what's going to happen? Well, your equilibrium quantity-- this was our old one, this was our new one-- equilibrium quantity definitely goes down, the quantity went down. And what happened to the price? We're assuming nothing changes to the demand. So this was our old equilibrium price. This is our new equilibrium price. It went up. Quantity went down, and price went up. And I encourage you to-- well one, I should have told you this at the beginning, too. You should have tried to do these yourself and then see what I had to say about them-- but I encourage you to try this out with different situations. Think of situations yourself and even think about different markets other than the apple market.
Khan_Academy_AP_Microeconomics	Change_in_expected_future_prices_and_demand_Microeconomics_Khan_Academy.txt	- [Instructor] We've been talking about the law of demand and how if we hold all else equal, a change in price, if price goes up, the quantity demanded goes down, and if price goes down, the quantity demanded goes up. So if you hold all else equal, ceteris paribus, we are just moving along this curve depending on what price. But what we started talking about is what happens when you change some of those things that we have been holding equal, how does that change demand? In the last video, we talked about the price of related goods, price of related goods. And if the price of related goods change, both complements and substitutes, how that might change the, how that might increase or decrease demand, the entire curve, not just one particular scenario. Now let's talk about another one of those factors that we've been holding constant, and think about how that would change demand, the entire curve, if we were to change that, and that's expectations of future prices. I'll do that in this green. So expectations, expectations of future prices, of future, future prices. So let's say that, let's talk about a first scenario right over here, where, let's say that this curve, people didn't expect prices to change for my ebook. And now, all of a sudden, people expect, there's a change in expectation, now all of a sudden, they expect the prices to go up going forward. So now, now, now expect, expect the future price, the future price to go up. What's going to happen? If you expect the future price to go up, and the good or the product in question is something that you can store, well, and depending on how much you expect it to go up, you're probably more likely to buy it now, buy it before the price goes up. So regardless of what point on this curve we're at, regardless of the price point, at any one of those price points, people now, because they want to, instead of buying it later they want to buy it now, they are more, the current demand will go up at any of these price points. So at $2, more people will want to buy it 'cause they think it's gonna go up. At $4, more people will want to buy it 'cause they think it's gonna go up. At any of these price points, because now there's an, the expectations have gone from being neutral to now expecting prices to go up, it will shift the entire curve to the right. So this will shift the entire curve to the right. So this right over here is scenario one. And it depends how much this changes to say how much this shifts to the right. This is just a general idea, this is scenario one. And the shifting of the entire curve, you could say they increased demand. So this is literally demand increasing, demand, demand increased. And when we talk about demand, remember, and you're probably tired of me saying this, I'm not talking about a particular quantity. I'm talking about the entire curve shifting to the right because people expect future prices to go up, so the current demand went up, the current demand curve shifted to the right. And now we can just take the other side of that. Imagine what happens in scenario two. Before people were neutral, that was our curve right there. They didn't have any opinion about whether future prices were gonna go up or down, or maybe they just assumed they were gonna stay the same. And now they expect future prices to go down. Now expect future prices, future prices, to go down. And this is something that happens in consumer electronics all the time, you see, whenever you buy a laptop or any type of electronic device, we now assume that the prices will go down. Now what we're talking about is a change in expectations. So you're going from neutrality, or let's say you're going from, you expect them to go down, but now you expect them to go down even faster. And if all of a sudden you expect them to go down even faster, you're even less likely to buy them now. So if you expect, if before you thought prices were going to be roughly constant, and now you expect them to go down, now you're gonna say, well, hey, at any given price point, why don't I just hold off a little bit and wait a little bit? So it's going to lower demand. So in this scenario, the whole curve will shift to the left. At any given price point, the quantity demanded will go down at any point in that curve. And so, the entire demand curve will be shifted to the left. So because of scenario two, demand, demand was decreased, demand was decreased.
Khan_Academy_AP_Microeconomics	Introduction_to_utility_AP_Microeconomics_Khan_Academy.txt	- [Instructor] We are now going to introduce ourselves to the idea of Utility in Economics. Now in everyday language, if someone says what's the Utility of that? They're usually saying what's the usefulness of doing that. And Utility in Economics takes that view of Utility and extends that a little bit. You could view Utility in Economics as a measure of usefulness, usefulness, worth, value. Some economists will even say it's a measure of happiness 'cause things that might not have a practical use can still have Utility to them in Economics because they're giving you some satisfaction or some happiness, or I'll even write that over here. And as we'll see, it is something that economists try to measure or try to quantify, and they do it with just Utility units. So let's see a tangible example of that. So let's say you wanted to think about your Utility from scoops of ice cream. So if we say, let's make a col, let's make a table here. So number of scoops, that'll be in my left column, and then on my right column, let's think about Total Utility, and I will do it in utils. You could view that as your unit of Utility. And let me put my columns in here. So, there we go. And so let's say if I have zero scoops of ice cream, well you might guess what my Utility is going to be, it is going to be zero. Now what if I have one scoop of ice cream? Well let's just say that that is 80 Utility units. And I know what you're thinking, Sal, where did you come with 80 Utility units? And this is really just an arbitrary number that I'm throwing down here. What's more important is what this is relative to my Utility for other things. So, for example, using this scale, if I said two scoops of ice cream, my Total Utility is 140. 80 and 140 aren't what matter. What matters is the ratio between the two. So if I said my Utility for one scoop of ice cream was 800, then, if this ratio is true, then for two scoops of ice cream, my Total Utility would be 1,400. It could be eight million and 14 million. What matters is the relative Utility. I just happened to anchor on one scoop gives me eight units, Total Utility units. But let's keep going. If we go with this scale, then three scoops of ice cream, let's say that this gives me 180 units of Utility. And I know what you're saying. Even if you get the ratio right, how do you even know that this is the right ratio? Well, economists will debate how to measure this, but there might be ways that you could measure it maybe with dollars, with what people are willing to pay, and then you can get the ratios. You could survey people. You could say on a scale of 10, one to 10, how happy will it make you if you got one scoop of ice cream? What if you got two scoops of ice cream? What if you got three? And then you would wanna get these ratios right. But, of course, it isn't an exact science, but people are trying to quantity this. Now let's just go to four. Four scoops of ice cream would give you a Total Utility, let's say we knew it would give you a Total Utility of 170. Now something interesting is happening. As you got more scoops of ice cream, from zero to one, from one to two, from two to three, it looks like you're getting more Utility, but then all of a sudden, when you have four scoops of ice cream, your Total Utility goes down a little bit. Maybe it's because people can't eat four scoops of ice cream and they say what do I do with that? And they just have all, they're left with a bowl of melted ice cream. And so it doesn't give them as much Utility, it makes them feel bad somehow as having three bowls of ice cream or three scoops of ice cream. Another thing to think about is how much does the Total Utility increase every time you get an incremental unit of that thing? And we'll talk about it in more depth in future videos, but that general idea of how much more Utility you get for that incremental unit. In Economics when we're talking about what happens on the increment, we use the word marginal a lot. Marginal Utility, sometimes abbreviated mu. And this would still be in Utility units. And so we could start with that first going from zero to one. I'll start with that first scoop of ice cream. What's the marginal utility? Well it gave you an incremental 80 units of Utility, so the marginal utility is 80. Now what about that second scoop of ice cream? Well we know when you had one, you had 80 Total Utility units, and now when you have two, you have 140, so that incremental second scoop gave you to go from 80 to 140, it gave you 60 extra units of Utility. So notice, you are really, it really increased your happiness or, you got a lot of value out of that first scoop and you still got value outta that second scoop, but it's a little bit less because you're not maybe just as not as hungry, you're getting a little bit tired of the ice cream. And then that continues to happen on that third scoop, to go from 140 to 180, that third scoop gave you 40 units of Utility. And then as we talked about, when you add on that fourth scoop, it didn't even add to your Total Utility, it took away from your Total Utility. So it actually had a negative marginal utility. It is negative 10. That fourth scoop actually took away from your happiness. So I will leave you there. You have this idea of Utility, Total Utility, and we also looked at Marginal Utility. And you see in this example, and this is typical, that Marginal Utility typically decreases as you get more and more units of that thing. And in future videos, we're going to use this framework of Utility, Total Utility, Marginal Utility, to think about how folks might make rational decisions to optimize their Total Utility.
Khan_Academy_AP_Microeconomics	Long_run_average_total_cost_curve_AP_Microeconomics_Khan_Academy.txt	- [Narrator] We've talked about the idea of average total cost in several videos so far, where it was the sum of your average variable cost and your average fixed cost. But when we're talking about fixed costs, by definition, that means we're talking about things in the short run. Remember, the short run is defined as the amount of time over which at least one of your inputs is fixed. But if we talk about longer term, so let's say you're running a factory, and, in the short run, the short run would be how long it takes to build another factory or how long it takes to close down or sell another factory. But in the long run, you can always add more factories or shut down factories. So in the long run, everything is variable. So what we're gonna do in this video is think about how the average total cost that we've studied in previous videos, which were actually short-run average total costs, how those relate to the long-run average total cost. So let's imagine that we are trying to open up a food truck business. And let's say that each food truck, so each food truck, and let's say we're going to sell tacos, so these are taco food trucks. And so each food truck can optimally, optimally, I'll just write it like that, serve 100 tacos per day. And we haven't started our business yet, but we have to decide how many food trucks to buy. And we do some market research, and we feel pretty confident that we are going to be able to sell 200 tacos per day. So we're going to target, target 200 tacos, tacos per day. Now, in this world, what you would want to do is optimize your fixed cost to minimize your average total cost for 200 tacos per day. Remember, your fixed cost is essentially going to be, let's say it's just your food truck, and then you're going to have a variable cost. It might be the staff that's making the tacos. It might be the supplies for the tacos, things like that. And so you might have an average total cost curve that looks like this. So let me make some axes here. So this is going to be quantity of tacos per day, quantity of tacos. This is going to be per day. And then in the vertical axis, this is going to be cost per taco, cost per taco. And let's say since you're optimizing for 200 tacos today, you want to minimize your cost per taco, 200 tacos per day, that happens with two food trucks. So if we're at 200 tacos per day, let me put it right over there, 200 tacos per day, we get to a cost per taco, average total cost per taco. Let's say that is 50 cents. So that is 50 cents right over there. But the actual number of sales, the actual number of tacos that you might have to produce in a given day, might vary from that, and that will actually help construct your average total cost curve. And so your average total cost curve might look something like this. It might look, might look something like this. We've seen curves like this in the past, and we would have call this our average total cost. But now because we're differentiating between our short run and long run, let's make this very clear. This is our short-run average total cost, and this is a situation where we have two of our food trucks per day, two food trucks. Now, what if instead of 200 tacos per day, it ends up that we only have to produce 100 tacos per day because that's how many people are demanding? So let's say this is 100 right over here. Well, if we keep the number of trucks we have constant, so we don't change our fixed cost, well, then our cost per taco is going to be higher. Let's say that this right over here is, let's say this is 70 cents, 70 cents per taco. And then there's the other scenario. Let's say that our tacos sell better than expected. Let's say that we need to somehow produce 300 tacos per day. Well, if we can't change our fixed cost, which is, by definition, what the short run is, well, then we might be at, say, this point. It looks like it would be about, let's just call that 80 cents, 80 cents per taco as our short-run average total cost. Now, in either of these situations, let's say that we have the more pessimistic scenario actually happens, that there's only demand for 100 tacos per day. Well, in that world, the rational thing would be, hey, let's sell one of those trucks. We're only at 50% utilization at 100 tacos per day. Let's sell one of those trucks to lower our average total cost. And so in the long run, you can adjust your fixed cost, so with one truck, with a curve that looks like this. So at 100, at 100 tacos per day, our costs are 60 cents per taco. And the curve might look something like, something like this. So if things were to get even worse than that, our cost would go up. And if for some reason the market were to actually go back to what we expected or even beyond, then our cost would go even higher. So this cost curve, which is based on one truck, so let me call this our short-run average total cost, and this is for one truck, this would be suboptimal if we actually do have 200 sold, 200 units being produced a day or 300 units produced per day. But it is optimal for 100 units per day. Now, things could go the other way. Well, you might start with those two trucks that are optimal for 200 units per day, 200 tacos per day. But you're in the world where people want to buy 300 tacos per day, and 300 tacos with two trucks is not optimal. So in the long run, you order another truck, and maybe it takes a couple of months for it to show up and be outfitted and whatever. But once you get that third truck, now you can optimally serve 300 tacos per day. And so you might be in this situation. So at, if you get another truck, you could have another short-run average total cost curve that looks something like this right over here. So this is our short-run average total cost curve, and so this is when we have three trucks. And remember, the short run is when at least one of your inputs is fixed. And in this one, for the simplified model, we're assuming that input is the truck, that everything else is a variable expense. Now, when you look at this, it helps us think about a long-run average total cost. What would that be? Well, in the long run, we can change the number of trucks we have. And if we can, in the long run, we can change the number of trucks we have, we would always be picking the optimal number of trucks for the quantity we're producing. So in the long run, we would want to be at that point. So if there's only 100 that we need to produce a day, we would only use one truck. If there's 200 produced a day, we would use two trucks and be at that point. If we need to produce 300, we would have three trucks and be on that point. And so your long-run average total cost curve would be connecting these dots, and so it would look something, it would look something like this. And some of you might be thinking, well, but this situation right over here is where you have 1 1/2 trucks. What's the deal with that? But in the long run, you might be able to get a custom truck size that is 1 1/2 times as big as your typical truck or 2 1/2 times as big as your typical truck. But the big takeaway here is that your long-run average total cost curve you can view as the envelope of all of the minimum points of all of your various short-run average total cost curve. Because at any given, for any given quantity, you want to optimize your fixed cost, which puts you at the minimum point of one of these short-run average total cost curves.
Khan_Academy_AP_Microeconomics	Market_equilibrium_Supply_demand_and_market_equilibrium_Microeconomics_Khan_Academy.txt	So, let's say we are in the apple market. What I want to do in this video is think about both demand and supply for the apples at different prices. Let's draw ourselves a little graph here. We already know this right over here, the vertical axis is the price axis, and this we're going to say is price per pound. The horizontal axis this is the quantity. The quantity of apples. Let's put some tick marks here. Let's say that's $1 a pound, $2 a pound, $3 a pound, $4 a pound, and $5, and let's say this is thousands of pounds produce and we have to set a period. Let's say this is for the next week, and so this is 1000 pounds, 2000, 3000, 4000, and 5000. Now, let's think about both the supply and the demand curves for this market, or potential supply and demand curves. First I will do the demand. If the price of apples were really high, and I encourage you to always think about this when you are about to draw your demand and supply curves. If the price of apples were really high, what would happen to consumers? Well, they wouldn't demand much. The quantity demanded would be low. If the price were high, maybe the quantity demanded is like 500 apples. And once again I am being very careful to say the quantity demanded is 500 apples. I'm not saying the demand is 500 apples. The demand is the entire relationship. The actual specific quantity, we call that the quantity demanded. The price of $5 of quantity demanded would be about 500. Maybe at a price of $1, the quantity demanded would be maybe 4000 pounds. Our demand curve might look something like this. Might look something like that. Let me draw it a little bit less bumpy. So, our demand curve might look something like that. I can label it. That is our demand curve. I'll think about our supply curve. Well, there some price below which we aren't even willing to produce apples. Let's say that's like 50 cents. So at 50 cents that's where were even just willing to start producing apples. Let's say if apples ... if the price of apple got to a dollar where the quantity we've be willing to supply is about a 1000 pounds, and it just keeps increasing as the price increases. So this is the supply curve, and when I talk about we, I'm talking about all the suppliers in this market. We could be doing this for a specific supplier. We could be doing this for a specific market. We could be doing for the global apple market. However, you want to view it, but for the sake of this video let's just assume its like our little town that is fairly isolated and all of that. Let's think about what happens in different scenarios. What happens if the suppliers of the apples going into that week for their own planning purposes ... They just think for whatever reason, that they're only going to be able to sell the apples at $1 per pound. Given the supply curve, they only supply 1000 pounds. This is what the suppliers plan for, and this is where they set the price point at $1. One dollar per pound. Now, what's going to happen in that scenario? Well in that scenario they supplied 1000. The quantity supplied is 1000 pounds. Let me write this down. So, I'll do it in pink for this scenario. So, this scenario the quantity supplied is 1000 pounds. What is the quantity demanded? Quantity demanded. This is all the scenario where the price ... the price or the initial price that the growers or producers set was $1 per pound. One dollar per pound. Well the quantity demanded at $1 per pound is 4000 pounds of apples. 4000 pound of apples. What do we have here? Well, here we have a shortage. We have a shortage of 3000 apples at that price point. At a dollar, a lot more people are going to want to buy apples, and the producers just didn't ... I guess they didn't figure that out right. They didn't produce enough apples. Now what will naturally start happening? If you have the shortage ... you have all these people who want to buy apples, and you only have so many apples there, what might happen in the next period in the next week? Well, first of all, those apples that are out there they might get bid up, so, the prices start going to start going up. The prices are going to start going up. People are going to start bidding up the apples. They want them so badly. Their going to start bidding them up, and as they start getting bid up, the producers are going to say, "Wow! There's so many people are running out of apples. We also need to increase the quantity produce." The quantity will also go up. The price will go up. If you look at from the suppliers point of view. The price will go up, and the quantity will go up. They will move along this line there. So maybe in the next period there's less of a shortage, or they move away from that shortage situation. If the price and quantity increase a little bit, so maybe the price goes to $2, and the quantity goes to ... I don't know, this looks like about 1900 ... 1900 pounds, now all of a sudden you have less of a shortage. I think you see that I'm getting to an interesting point over here. I won't go there just yet. I won't go there just yet. Let's think about another situation. Let's think about after this happens. Price and quantity increases so much that essentially overshoots this interesting point right over here. So in the next week the suppliers they'll say, "Wow! People want our apples so badly, let's set the price really high at $3, and at $3 we're really excited about producing apples." So, we the suppliers are going to produce ... let me do this in a color I haven't used yet. We the suppliers are going to produce at $3 a pound. We are hoping to sell 3000 pounds of apples. This is where, maybe, they adjust to the next week. What's going to happen there at a price of $3. That's the scenario right over here. The price of $3. So, the price is now $3 per pound. Well, now the quantity supplied is going to be 3000 pounds. I could write 3000 pounds. What is the quantity demanded? The quantity demanded is now much lower. The price is high now, because the consumers might want to go buy other things, or they can't afford an apple, or whatever it might be. Now the quantity demanded, now that's looks like about 1300. 1300 pounds. What situation do we have now? Well, now we have a much bigger supply then ... or the quantity supply is much bigger than the quantity demanded. Now we face a surplus. So, now we have a surplus. Let me draw that line there. I want to make it clear this is all the same scenario. We now have a surplus of ... what is this? 700 will get us to 2000. We have a surplus of 1700 pounds of apples. Now what happens in a surplus situation? Well, apples won't stay good forever, so maybe the producers get a little desperate. They start selling. They start reducing the price, maybe to start attracting some consumers. They start reducing the price. When they start seeing that the prices are going down, and you have this glut of apples, there're all going bad and not getting sold, the quantity is also going to start going down. They'll produce fewer and fewer apples, so we'll move here along the supply curve. As you decrease the price, what's going to happen to the demand curve? Well the demand is going to go up. Over here the prices was too high, so it's natural for the sellers to lower the price. When you lower the price it also reduces the quantity. We go this way. When you lower the price it increases demand. You go that way. If the price from the get-go were too low, then you have this huge shortage, things get bid up. The prices go up. As the price goes up, the suppliers want to produce more. They move up the curve. As the price goes up then the people will demand less. You see that's it's all converging on a point right over here where the two lines intersect. Let me do that in a ... its all converging right over there. That's the price at which the quantity supplied will equal the quantity demanded. We call this, which looks like for this scenario, maybe about $2.15. Let me just write it there $2.15. We call that the equilibrium price. Equilibrium price is $2.15 a pound. It's the price at which the quantity supplied is equal to the quantity demanded. This quantity supplied is equal to the quantity demanded. That's the equilibrium quantity. That right over here looks like it's right about ... I don't know ... 2200 pounds. 2200 pounds. Assuming that nothing else changes, this is a good scenario for both the consumers and the producers. They keep producing 2200. They charge this price, and everything's happy. All the apples get sold and none of them go bad.
Khan_Academy_AP_Microeconomics	Marginal_utllity_free_response_example_AP_Microeconomics_Khan_Academy.txt	- [Instructor] We are told that Theresa consumes both bagels and toy cars and they tell us that the table above shows Theresa's marginal utility from bagels and toy cars. And the first question is, what is her total utility from purchasing three toy cars? So pause this video and see if you can answer that. All right now lets work through this together. So let's just make sure we understand this table here. So this says that the first bagel that Theresa consumes, she gets eight units of marginal utility from that. Then the second bagel, she gets a little bit less marginal utility. Some or her bagel craving has already been satisfied by that first one. And then the third bagel, the marginal utility goes down a little bit and then that keeps happening for each incremental bagel. And on the toy side, we see that that first toy, she gets a lotta marginal utility, 10, and then the next toy gets a little bit less, and then you see that the marginal utility for each incremental toy gets a little bit lower and lower. So now let's answer the first question. What is her total utility from purchasing three toy cars? Well that first toy car, she gets utility of 10. Then that second toy car, she gets a utility of eight. And then that third toy car, her marginal utility for that incremental car is six. So the total utility is going to be 10 plus eight plus six, which is what, 10 plus 14, this is going to be equal to 24 units of marginal utility. All right now let's do part two. Theresa's weekly income is $11, the price of a bagel is $2, and the price of a toy car is $1. What quantity of bagels and toy cars will maximize Theresa's utility if she spends her entire weekly income on bagels and toy cars? Explain your answer using marginal analysis. So once again, pause this video and see if you can figure that out. All right now let's do this together. I'll scroll down a little bit so I have some space. So the key thing is, is when once we know the price of a bagel and the price of a toy and we know the marginal utility for every incremental bagel or toy, we can figure out our bang for our buck. We can figure out, what is going to be the marginal utility per dollar from that incremental bagel and that incremental toy car? And so we can, let's just explain first. So Theresa, Theresa will maximize, maximize her marginal utility per incremental dollar, per dollar, or let me put it this way, per dollar, when making purchases on the margin, making maybe, making purchases on the margin. So her next incremental purchase, her next incremental, incremental purchase. So we can write over here bagel marginal utility per dollar. That'll be one row here. And then we could write car or toy marginal utility per dollar. And then we set up these rows right over here. And then we could think about it if she for the first one, for the second one, for the third one, for the fourth one, let's see we go up to six, fifth one, and then we go to our sixth one. So let's start with bagels. Bagels cost $2. So that first bagel, if she gets eight marginal utility units, well that's going to be four marginal utility units per dollar, eight divided by two. So that's four units per dollar, and then that second bagel, she gets seven units but it costs $2, so it's seven divided by two units per dollar. So that's going to be 3.5. And then six divided by two is three, five divided by two is 2.5, four divided by two is two. So that fifth bagel, two marginal utility units per dollar, and then that sixth bagel, three divided by two is 1.5 marginal utility units per dollar. And now we can think about toys. Each toy is $1. So if she gets 10 marginal utility units from that first toy, it only cost her $1, so it's 10 utility units per dollar. So it's 10 there. It would be eight here. We're just dividing each of these by one. So six here, so this is gonna be the same number again. Four, three, and two. So now that we set this up, and let me scroll down a little bit so I have a little bit more space. I have all the data I need. We can think about what would be rational for her if we're thinking about how she's gonna spend that $11 per week. Her first purchase, she's like wow, from the get go, that if I'm picking between bagels and toys that first toy has a much higher marginal utility per dollar than that first bagel. So she's going to start here, and then she says, okay next do I wanna buy a bagel or a toy? But even that second toy, the marginal utility per dollar is still higher than that first bagel. So then she'll buy a second toy. Then she'll think about it and so far she's only spent $2, so we have a lot of money still left. Then she'll think about okay, do I wanna spend that next incremental amount on a toy or bagel? Well still, she gets more marginal utility per dollar from the toy, so she'll spend that. She's spent $3 so far, $1, $2, $3. And now, when she thinks about how to spend her next few dollars, she says, well know I'm indifferent between bagels and toys. The marginal utility per dollar is the same. So she might maybe spend the next one on a toy and then right after that, she'll go to bagels finally and buy a bagel. Well let's think about how much she has spent so far. She's spent $4 on toys and $2 on bagels. So the order might look something like this, and then she goes and maybe buys her bagel. And now the marginal utility per dollar for that incremental bagel is higher than for her next toy, and so then she'll probably buy, she would buy another bagel right here, and let's see how much money she has spent. Two bagels are $4 plus she's spent $4 on toys because they're $1 each, so it's $8. So she still has $3 to spend. Now, her marginal utility per dollar is neutral between bagels and toys, between the incremental, the third bagel and that fifth toy, so she's indifferent between the two. So she could probably get both of them. So she might do something like that, buy that, and then she could buy that or she could do that in the other order. And let's see how much money she's spent. She has spent $5 on toys and she has spent $6 on bagels, and so she has spent her $11. And so to answer the first question, so she would buy, she would buy five toys, five toys, and three bagels, and three bagels based on this strategy of maximizing marginal utility per dollar for each incremental, incremental purchase. Did I answer all of the questions? We said the quantity of bagels and toys that will maximize her marginal utility if she spends her weekly income, and then we have explained using marginal analysis. Yep, we're looking good.
Khan_Academy_AP_Microeconomics	Opportunity_Cost.txt	Let's say we've been hanging out in scenario E for a bunch of days. On average, we've been catching one rabbit, but gathering 280 berries. We were in, I guess, a berry mood. So this is scenario E right over here. But now all of a sudden, we're in the mood for more protein. So let me write down, we are in scenario E. And we're in the mood for more protein. And so we want to think about what are the trade-offs if we try to catch more rabbits? So what I want to do-- I want to say, if I want to catch 1 more rabbit, what am I going to have to give up? So if I catch one more rabbit-- so I go from 1 rabbit on average to 2 rabbits a day. So I'm really going from scenario E to scenario D. What am I going to give up? So this is plus 1 over here. Well, I'm going to give up 40 berries. And you can see it visually right here. If I try to get 1 more rabbit, I can't go into this impossible, this unattainable part right over here. I have to stay on the production possibilities frontier, sometimes abbreviated as PPF. Or I guess the acronym for it, I should say, is PPF. But if I want 1 more rabbit, the production possibilities frontier drops off, and I will have to give up 40 fruit. So 1 more rabbit means that I have a cost. So I have to give up, on average, 40 berries. And the technical term for what I've just described is the opportunity cost of going after 1 more rabbit is giving up 40 berries. So let me write this down. The opportunity cost of 1 more rabbit-- and this is particular to scenario E. As we'll see, it's going to change depending on what scenario we are in, at least for this example. So the opportunity cost of 1 more rabbit is 40 berries, assuming we are in scenario E. 1 more rabbit, I have to give up 40 berries. And another term when we talk about the opportunity cost of going after-- after producing I guess you could say-- the operating cost of producing 1 more rabbit here, when we talk about the opportunity cost of producing 1 more unit, that's sometimes called the marginal cost. So this right over here, you can also view it as the marginal cost. In the context of this video, our costs are in terms of the thing that I'm giving up, the opportunity that I'm giving up. In other scenarios, you'll see sometimes a marginal cost be given in actual monetary units, like dollars or whatever else. What was the cost of producing that extra unit, that extra widget, right over there. But let's make sure we understand opportunity cost. So that's when we were sitting in scenario E, the opportunity cost of 1 more rabbit. But what's the opportunity cost-- let's say, we're tired of eating meat. We're sitting in scenario E, and we want to become vegetarians altogether. So we want to go to scenario F-- essentially not eat any rabbits and eat as much fruit as possible. So another thing you could ask in scenario E is the opportunity cost of-- and just to make the numbers easier-- I'm going to say opportunity cost of 20 more berries is, well, I'm going to give up a rabbit. So over here, what we're doing is we're saying, OK, I want to increase my berries by 20, but to do that, I have to decrease my rabbits by 1. So the opportunity cost-- assuming we are in scenario E-- the opportunity cost of 20 more berries is 1 rabbit. Now this right over here is not a marginal cost, because I'm talking about the cost of 20 more units, not just 1. If I want to write this as a marginal cost of 1 more berry, then I could just say, well if 20 berries is 1 rabbit, you could essentially divide both sides by 20. So 1 more berry-- and I'll assume, for those of you who want to get technical, that it's somewhat linear right over here-- 1 more berry if we divide both sides by 20 is 1/20 of a rabbit. So if I go for one extra berry sitting in scenario E, on average I'm going to get 1/20 less of a berry. And when I phrase it this way, it is being phrased as a marginal cost. Now for those of you who want to get a little technical, this is a curve right over here. So it might not be exactly this. Well, I don't want to get too technical for the sake of this one right over here, this is a safe way to think about it. The opportunity cost of 20 more berries is 1 rabbit, but if you assume that this is somewhat linear right over here-- it's not so curved, it's somewhat of a line between those 2 points-- then the opportunity cost of 1 berry is 1/20 of a rabbit. Or the marginal cost of an extra berry is 1/20 of a rabbit. And we can do it at different points of this curve, and I actually encourage you to do. Based on the data that we have in this table that we constructed in the last video and maybe this curve, think about what the opportunity cost is in the different scenarios. If you're in scenario B and if you want an extra rabbit, how much is that going to cost you in terms of berries? Or if you want more berries, what's that going to cost you in terms of rabbits?
Khan_Academy_AP_Microeconomics	Monopolist_optimizing_price_Dead_weight_loss_Microeconomics_Khan_Academy.txt	Based on what we've done in the last 2 videos we've been able to figure out what the marginal revenue curve looks like for the monopolist year, for the monopolist in the orange market and this is what we got. Right over here, it was a line with a slope twice as steep as the slope of the demand curve, we'll see that's actually generalizable. There's an optional video that I'll do very shortly where I prove it with a little bit of calculus. It's very important to realize that this marginal revenue curve looks very different than the marginal revenue curve if we were dealing with perfect competition. If we were dealing with perfect competition there would be some equilibrium price in the market and all of the competitors would essentially just have to take that price. Let's say that that equilibrium price was $3 per pound then our marginal revenue curve would look like this if we were not a monopolist, if we were one of the many perfect competitors. I guess you could view it that way. Because we would just have to take that price. If we wanted to sell 1000 pounds, each of those pounds we would get $3 per pound and then if we want to sell 1001, we'll just get $3 per pound for the next one. It doesn't change. We're just taking that price. With the monopolist things do change because we are the only producer in the market. The price at which we can get changes depending on what we produce because we are the entire supply for the market and we have this downward sloping marginal revenue curve. Now, with that out of the way, let's think about what will be the optimal quantity for us to produce if we wanted to maximize profit? If we think in pure economic terms, that's what firms try to do. They exist to maximise profit. To do that, we're going to have to think about, and remember, it's not to maximize revenue. To maximize revenue we would have said, "Oh, they should just produce 3000 pounds." It's not about maximizing revenue, it's about maximizing profit. We have to take the cost into consideration. To do that, we'll have to draw a marginal cost curve. Let's say I did the research. Let's say we're the owners of this firm and we have a marginal cost curve that looks something like this. Let's say our marginal cost curve looks like this. It's important to realize, we are the market. We are the only producers here. This isn't just our marginal cost curve. This is a marginal cost curve for the market. Another way to think about it, this is the supply curve for the market. It tells you at any given price how much the market is willing to supply. You could view it as a marginal cost or you could view it as a supply curve and we've talked about it before. You could view a supply curve as a marginal cost curve. If you want the market to produce 1 extra pound, what's the minimum price you would have to give? that is the marginal cost. Now, with this out of the way, let's think about what you would produce. Well, you would definitely want to produce something you definitely start to produce a few pounds right over here because the marginal revenue you're getting is way above your marginal cost. Each incremental pound you're producing right over here, you're getting much more revenue, you're getting $5 or $6 of revenue and it's only costing you a little over a dollar. It's like, "Okay, I'm going to keep producing. "I'm going to keep producing." Over here, you're still, each incremental unit you're getting, you're still getting more revenue than the cost of that incremental unit. That keeps being true all the way until you get to 2000 pounds right over here. At this point right over here you don't want to produce an incremental unit because if you produce one more unit, if you produce that 2001st pound right over here then for that 2001st pound, your cost is going to be slightly higher than the revenue you get in. You will actually take a slight loss on that. Your total profit will start to go down and you don't want to produce less than this because you'll be leaving a little money on the table. You'll be leaving that little incremental pound where the total revenue was just slightly higher, or the marginal revenue on that incremental pound was just slightly higher than your marginal cost on that incremental pound. You will produce right over there. Now, this is interesting because this is a different equilibrium, or I guess we say this is a different price or this is a different price and quantity than we would get if we were dealing with perfect competition. If we were dealing with perfect competition, our equilibrium price and quantity would be where our supply and demand curves intersect. It would be right over here. It would be a price of $3 per pound and a quantity of 3000 pounds. Now, in order to maximize profit, we are intersecting between the marginal revenue curve or our quantity that we want to produce as the monopolist is the intersection between our marginal revenue curve and our marginal cost curve which is right over here. So we can see that there is a dead weight loss. There is a dead weight loss by being a monopoly although it's good for us. It's good for the monopolist, it's not good for a society at least in this example and there's very few where I can imagine it being good but I guess there are a few if you're trying to protect the national industry or something like that. Over here, this is the quantity that we are deciding to produce. The consumer surplus is the area above the price and below the demand curve. This right over here is the consumer surplus. The producer surplus is looking pretty good and this is essentially what we're trying to optimize. Our producer surplus is this whole area. Our producer surplus is this whole area right over here. Producer surplus right over there. But we have a dead weight cost. There's a total surplus that we would have gotten, that society would have gotten if we were dealing with perfect competition, right over here that's now being lost. But as we lose that, we were able to increase the producer surplus and decrease the consumer surplus. Beyond just having this dead weight loss over here, it's also obviously given much more value to the producer, to the monopolist and given much less value to the consumer.
Khan_Academy_AP_Microeconomics	Graphs_of_MC_AVC_and_ATC.txt	- [Instructor] In the previous video, we began our study of ABC Watch Factory and we tried to understand the economics of the business based on some data that we had already collected on our costs and how much output we could produce based on how many labor units we had. And then from that, we calculated things, like the marginal product of labor, the marginal cost, the average variable cost, the average fixed cost, and the average total cost. What we're going to do in this video is take this information, especially total output and all of these things that we just calculated, so that we can better appreciate how these various calculations and the curves that we can get from the calculations are interrelated, so let me scroll over a little bit so we have some space and then let me set up a little coordinate plane here. And so what we have on our vertical axis, this is our cost, and then down here, in our horizontal axis this is our output. So, first let's just hand graph it, and I encourage you to go through the exercise yourself. It's one thing to watch me do it, but when you actually graph something you digest the numbers that much better. And so, let's start with marginal cost. And I'm going to do it in this blue-green color. So let's see, when our total output is 25, our marginal cost is 267. So, when our out put is 25, 267 would be right about there. And we're just trying to get, be able to visualize what's going on. And then, when our total output is 45, our marginal cost is $150. So 45 is here and then 150 is right about there. And then when our total output is 58, our marginal cost is 231. So 58 is right about there, and then it's gonna be 231, so it's about, right about there. And then, when our total output is 65, our marginal cost is 429, so the 65 is right over there and then 429 will get us right about, right about there, so you see our marginal cost is going up a lot now, it might be a little bit lower than that, so it's gonna be right over there. And then last but not least, when our total output is 70, our marginal cost is $600. So at 70 we get to 600 and I'm eyeballing it, that's not exact graph paper, but this gives you a sense of what the marginal cost curve looks like. And here we've kinda graphed it based on where we are in terms of output. So, that's our marginal, marginal cost curve. So I'll just label that marginal cost. And now let's see how that relates to the curves for average variable cost and average total cost. So average variable cost I'll do in this orange color. So, at an output of 25, our average variable cost is $240. So 25, we are going to be at $240, which is right about, right about there. And then when we are at 45 units, our average variable cost is 200. So at 45, units our average variable cost is right over there. And then at, we did that one. And then at 58 units, it's $207. 58 units, it is 207, so it's going to be right about there. And then at, we did this one. And at 65 units, it's 231. 65 is, and then we get to 231 which is right maybe about there. And then, this we did this one, and then at 70 units, we're at 257. So 70 units, 257 looks something like this. Now, before I actually draw into this scurve, connect the dots, so let's just think about how the average variable cost relates to the marginal cost. When the marginal cost is less than the average variable cost, well that means that as we produce more and more, our average variable cost should go down, and we see that happening in this early stage. I won't go into all the details on what's happening exactly right over there, but that early stage, as we see that while our marginal cost is less than our average variable cost, our average variable cost is trending down. And that makes sense. Every incremental unit is a little big cheaper to produce, so it brings down the average. But as soon as the marginal curve crosses the average variable cost and the marginal cost, every incremental unit is now more than the average, well that should bring up the average. And so then the average variable cost should start sloping up. So, it's good to realize, one is a rule of thumb but even more important to realize why, that where the marginal cost curve and the average variable cost curve intersect, that that's going to be the point at which the average variable cost goes from trending down to trending up. If you viewed as this very wide U shape, that would be the bottom of the U. And we can do the same thing thing with average total costs. Now, they're going to cross a little bit later because the average total costs are higher because they're factoring in the fixed costs as well, but you can imagine that while your marginal costs are lower than your average total costs, every incremental unit is going to bring down the average total cost, but as soon as the marginal cost crosses the average total cost, it's gonna start bringing up the average. And we can see that by trying to graph average total cost, and I'll do that in this yellow color. So, at 25 units, we're at 440. 25 units, we're at 440 that makes sense 'cause we have all that fixed cost that we're spreading along amongst not that many units. And then at 45 units, we're at 311. 45 and we get to 311, might be right around there. Then at 58 units, we're at 293. 58 units, we are at 293, which is right about there. And then at 65 units, we're at 308. 65 units, we are at 308. And then at 70 units, we're at 329. 70 units, we are at 329, so it maybe something like this. And so this is our average total cost. And just as you can imagine, while your marginal costs, every incremental unit, the cost of that, is less than your average total cost, it'll bring down, when you do that incremental output, it will bring down your average total costs until the point that they cross and then, now, after you, after these two curves cross, now every incremental unit is bringing up the average cost, 'cause it's costing more than the average. And so, once again, where these two curves intersect, if you view the average total cost curve where there's this big wide U, it would represent the bottom of the U. Now, the last thing that we didn't graph, and this is maybe the most intuitive, is the average fixed cost. And this is just going to asymptote down. At 25 units, we're at 200. 25 units, we are at 200. At 45 units, we are at 111. 45, 111, it's maybe right over there. At 58 units we're at 86. 58 units, 86. At 65 units, we're at 77. 65 units, 77. And then at 70 units, we're at 71. And so you can see that that just gets lower and lower and lower over, as you produce more and more output because you're able to spread those fixed costs amongst more and more output, so that makes sense that the average fixed costs just trends downward like this the entire time. But the big take-aways here is not just to understand the rule of thumb that where the marginal cost curve intersects the average variable cost or the average total cost, that that's the, you could view it as the minimum point of the average total cost or the average variable cost curves, but to understand why that is happening.
Khan_Academy_AP_Microeconomics	Identifying_tax_incidence_in_a_graph_AP_Microeconomics_Khan_Academy.txt	- [Instructor] We are asked, which of the following correctly identifies the areas of consumer surplus, producer surplus, tax revenue, and deadweight loss in this market after the tax? So pause this video, have a go at it. Even if you struggle with it it will make your brain more attuned to when we work through it together. All right, now let's work through this together. And I just want to sort of understand what's going on here before I even try to answer their questions. So let's first take a look at what's going on before the tax. So before the tax, I have this supply curve right over here in blue. And I have this demand curve. Where they intersect gives us our equilibrium price. Right over here. And our equilibrium quantity right over there. And if we wanted to look at the consumer surplus it would be the area above this horizontal line. And, below the demand curve. So that is our original consumer surplus. And our original producer surplus is above the supply curve and below this price horizontal line. And so, the total surplus would be this entire triangle right over here. All before the tax. But they're not asking us before the tax they want us to figure out everything after the tax. So what happens to the tax? Well, if we assume it's a tax on each unit that is being supplied. The effect it has, and we see it here, they've drew it for us. Is it shifts the effective supply curve up. And I say the effective one because that's the one that's going to affect the equilibrium price, or the new equilibrium price. But as we'll see there's some nuances in terms of considering the surplus. So first, let's think about the consumer. Well, actually let me label the now price with the taxes. So, this is now the R equilibrium price where we have the taxes. It's where our demand curve hasn't shifted. That's where the existing demand curve intersects with this new shifted supply with tax curve. And similarly, that point of intersection also tells us our quantity with the taxes. Now, now that we've understood everything, or hopefully we have, let's think about the various surpluses and the deadly weight losses and the tax revenues. So first, let's think about the consumer surplus. Well, the consumer surplus is going to be the region above our new horizontal price. And below the demand curve. So that is this region R right over here. That still, you have this consumer right over here who was willing to pay a lot but still has to pay less than that even with the taxes. So they're getting this benefit more than they would have needed in order, it would have been willing to pay more than the tax, and so they're getting this surplus. And so if you look at the entire market right now the total consumer surplus after the tax is R. R is equal to consumer surplus. And this is all after the taxes. Consumer surplus. Now, what about the producer surplus? Well, if we weren't dealing with the tax we would just look above the supply curve and below this equilibrium price line and say hey, maybe it's that area. But remember what's happening from the producers point of view. The producer does not see this new increased price at this quantity. The producer, remember, they don't get to keep the tax revenue. That, they have to give to the government. So the producer actually this is the price that the producer sees. So you can see this is this is what what producers what producers get after taxes. After taxes, or I say net of taxes. May be a better way to think about it. Net of taxes. And so the producer surplus is going to be the area below what they're getting from the market, net of taxes. And above what they the price is at which they were willing to produce various quantities. And so the producer surplus is this area of V over here. So, V is equal to the producer. Producer surplus. And now, what about the tax revenue? Well, the tax revenue is, is essentially going to be all of this other part of the total surplus. This is what goes to the government. The difference between these two. If the producers did not have to give that tax to the government then they wouldn't have been able to keep all of this. But this, right over here. Let me do this in a different color. So this region, right over here, is what the government is able to keep. Notice, it's this quantity and they get this much tax per unit quantity. And so this area is the government, is the revenue to the government. So, S plus U is equal to tax revenue. Tax revenue. And then last but not least, what about the deadweight loss? Well remember, the deadweight loss is the difference between the original the total surplus. When we just let things naturally go to equilibrium. The difference between that and now our new total surplus, which is now lower because we have not allowed the market to function in a very natural way because of this tax on it. Well, as we said before, the original total surplus was this entire triangle. Now the total surplus is this trapezoid that's the sum of all of these areas. And so what we lost is this area right over here. So that is the deadweight loss. So T plus W is equal to the deadweight loss. And we're done.
Khan_Academy_AP_Microeconomics	Determinants_of_elasticity_example_AP_Microeconomics_Khan_Academy.txt	- [Instructor] We are asked, "which of the following describes a good "that is likely to have the most elastic demand?" Choose one answer. So pause this video and see if you can answer that. All right, so the first choice right over here, they talk about "a luxury with many substitutes." So we already talked about, when you're dealing with substitutes, if there's a lot of substitutes, that makes the quantity demanded very sensitive to price. So this would make it more elastic to have many substitutes. More elastic. And then the fact that it's a luxury. It's not something that people need, this would also make quantity more sensitive to price, generally. So we would also say more elastic. So this is looking like a good candidate, but let's check the other options here. "A necessity with few substitutes." Well, this is the opposite. If it's a necessity, this would be more inelastic, or less elastic. Less elastic. And few substitutes, if you have a change in price for that thing, people say, well, I still have to buy that thing, I can't substitute it with other things. This would also be less elastic. And remember, we're looking for the most elastic demand, so we can rule this one out. "A broadly defined good such as food." Well, we just talked about that. If we're talking about food, and there's a price change in food, well, we need food, so our quantity demanded might, would not likely change, or our percent change in quantity would not likely be that much. This would be fairly inelastic. Rule that one out. "Goods that make up a small share of the budget." Well, this goes back to that example with bubblegum. If bubblegum goes from 25 cents to 30 cents, we might not care so much. Versus if a car goes from $25,000 to $30,000. So the small things that we might not care about price changes so much, if we don't care so much about price changes, that would imply less elasticity, so that definitely would not be the most elastic demand. "Goods that have to be bought "under a short time constraint." Well, a good example is that it's raining and people need umbrellas right now, in, you know, the next five, 10 minutes, and there, they wouldn't necessarily be so sensitive to price, so this is going to be less elastic, and so once again, we would rule this out. If we had a long time frame, well, then people might be able to shop around for substitutes and then things might get a little bit more elastic. They would be more sensitive to price. So we definitely like, in this scenario, choice A.
Khan_Academy_AP_Microeconomics	Economic_profit_for_a_monopoly_Microeconomics_Khan_Academy.txt	- [Instructor] In this video, we're going to think about the economic profit of a monopoly, of a monopoly firm. And to do that, we're gonna draw our standard price and quantity axes, so that's quantity, and this is price. And this is going to of course be in dollars, and we can first think about the demand for this monopoly firm's product. And the demand curve would look similar to other demand curves that we've seen multiple times, that at a high price, people wouldn't be demanding a lot, and then at a lower price, or as price goes lower, people are going to demand a higher and higher quantity, or the market will demand a higher, and higher quantity. So that might be the demand curve. Now what's interesting about any imperfectly competitive firm, and the extreme case is a monopoly, is what the marginal revenue curve looks like given this demand curve. In a perfectly competitive firm, the marginal revenue curve is equal to the demand curve, and in that situation, it's actually a horizontal line. But here, because when the monopoly firm reduces price, it doesn't just reduce it on that incremental unit, it would be typical that it would have to reduce its price on all of the units, and we've studied this in other videos. You have a marginal revenue curve that would go down faster than the demand curve, it would look something like this, and if this is unfamiliar to you, I encourage you to watch some of those videos that go into depth why this is happening. So it's a monopoly, or actually any imperfectly competitive firm, its marginal revenue curve will go down faster than the demand curve. So what would be a rational quantity for this firm to produce? Well to think about that, we have to think about its marginal cost curve. So its marginal cost curve, the typical way we often think about it is, at first you get some economies of scale, but then you start having coordination costs, and maybe some diseconomies of scale, your inputs start getting more expensive, and so your marginal cost curve might look something like that. And the rational quantity produced is, as long as your incremental revenue for every unit is higher than your incremental cost for every unit, you would wanna produce more, and more, and more, and more until the point that your marginal cost is equal to your marginal revenue. And so the rational quantity to produce right over here would be right over there. I'll do that Q, I could call that Q for the firm, I could also call that Q sub M, because we're dealing with a situation where the firm is, at least from the producer side, it is the market, it is the only producer, it's a monopoly. But what's the price here? Well to know that, we just have to look at the demand curve. At this quantity, the price is right over here. So the price is right over here, and once again, we could call that the market price, and so something interesting has happened here for the monopoly firm. In a perfectly competitive firm, where the marginal cost and demand curves intersect, that's what dictated the demand, because the demand curve and the marginal revenue curve were the same. But here, we are now producing a quantity less than that, we're producing a quantity where price is greater than marginal cost, you could see it right over there. At this quantity price is greater than marginal cost, and so you can view this difference right over here as kind of a markup that is possible for a monopoly firm to do that would not be possible with a perfectly competitive firm. And this also introduces an idea of dead weight loss. Because at least in theory, at a higher quantity, people were willing to pay more than the marginal cost, so you would think that there is some type of a benefit that the market as a whole could gain from that incremental unit, or those incremental units, and then even some more incremental units. It feels like there's to gain, but because of what is rational for this monopoly firm, and there's insurmountable barriers for entry for other people to enter, this is not going to be captured until you have this dead weight loss. Now an interesting question, and this is where I started off is, well what would be the economic profit for this monopoly firm? And to think about that, we have to think about the average total cost curve. And so the average total cost, I'll draw a typical average total cost curve, it might look something like this. While marginal cost is below the average total cost, the average total cost will trend downwards, and as soon as marginal cost is higher than average total cost, well now of course, average total cost is going to start trending upwards. So marginal costs intersects the average total cost curve at the minimum point right over there. And so based on this average total cost curve, it looks like this monopoly firm is earning an economic profit, because at that quantity, this is the price per unit it's getting. This is the average cost per unit, so on average per unit, it's getting this height, it's getting this difference right over here, and then if you were to multiply it times the number of units, well that's going to give you its economic profit. So you could view the economic profit in this situation as being this shaded area of this rectangle. So I'll leave ya there. The big thing to appreciate is, when we're dealing with imperfect competition, and the extreme form of a monopoly, your marginal revenue curve is no longer your demand curve, and your marginal revenue curve is downward sloping like this, it's not the flat curve that we saw with the perfect competition. And because of that, your marginal cost is going to intersect marginal revenue at a quantity where price is greater than marginal cost, which introduces dead weight loss in the market, and the way to think about the economic profit is to compare what that price in the market is at that quantity, to the average total cost at that quantity. And what's also interesting about this monopoly firm is because of the barriers to entry, we talked about in the long run with perfect competition, if there's economic profit going on, more entrants would enter into the market, but that's not going to happen in a monopoly because the barriers to entry are so high. So this monopoly is sitting pretty, it's going to be able to keep earning this type of economic profit, unless something dramatically changes in the market somehow.
Khan_Academy_AP_Microeconomics	Equilibrium_allocative_efficiency_and_total_surplus.txt	- [Instructor] What we're going to do in this video is think about the market for chocolate and we're going to think about supply and demand curves, but we're going to get an intuition for them in a slightly different way. In particular for the demand curve we will think about the idea of marginal benefit. Now marginal benefit, when we're talking about margin it's really thinking about, well, what happens on the increment? What happens for each little extra that you do? So this is saying, what is the benefit that I get if I get a little bit more of, in this case, chocolate? Well, from the market's point of view, imagine if there was no chocolate, but there's people in the market who crave chocolate, who dream of chocolate. If all of a sudden they were able to get their hands on some chocolate, they would get a huge benefit for that incremental amount of chocolate. Maybe for these folks, their benefit, which we could quantify as, in terms of dollars, maybe their benefit is 50 dollars per pound. One way to think about it, they'd be willing to pay 50 dollars because they get that much benefit, or if they paid less than 50 dollars, let's say they paid 10 dollars for it, well then they're getting 40 dollars of extra benefit a kind of surplus of benefit from being able to get it at a price lower than their marginal benefit. But then let's say more chocolate becomes available. People still like it but some of that really deep need, that deep addiction for chocolate has been satiated, and so the marginal benefit tends for, in most markets, the marginal benefit tends to go down as quantity increases. One way to think about it, that first initial amount of quantity if you, so we have some small amount of quantity right over here, I'll say delta quantity. That first quantity, if you multiply it times the marginal benefit, well that gives you an area roughly of a rectangle like this, it's not quite rectangular at the top, it's more of a trapezoid if this is downward sloping, but you could approximate it as a rectangle. But either way, the area right over here, the area under the marginal benefit curve, you could think about this as, well, that's just the benefit that the market is getting from consuming this chocolate in this case. And so let's just continue on this trend. If there's more and more chocolate the market will get benefit from it, but people aren't as excited about it anymore. They're saying, oh, well, the chocolate's around, yeah, it'd be nice to have a little bit more, but I don't need so much more. And at some point people might be all chocolated out, and they have maybe even zero marginal benefit from that incremental amount of chocolate, chocolate has filled up the town, there's nowhere to actually put it. Now that won't always be the case, you might go someplace like that, but either way you think about it we would view this as our marginal benefit curve. And notice, this is exactly the same as a demand curve in the market for chocolate. We have plotted price versus quantity in the market for chocolate, but we've thought about it in terms of marginal benefit. Now on the supply side there's a related idea, we're going to think about marginal cost, marginal cost. So let's say at first there's no chocolate being produced in this market. And a savvy entrepreneur says, hey, I know some folks who are addicted to chocolate, they would get a lot of benefit from it, so I'm going to try to produce some chocolate. And they look around and they find out, hey, there's actually a derelict chocolate factory in town that no one is using and it's surrounded by these wild cocoa bushes that are perfect for chocolate. And there are some people in town who are actually unemployed, but they are amazing at producing chocolate. And so the first units of chocolate, the marginal cost to produce it is actually quite low. But once you utilize those folks, you utilize that derelict factory, you utilize those free cocoa bushes or whatever, cocoa trees, well then you've got to plant new ones, you've got to train new employees, you've got to build a new factory. And so to produce that next increment, well that's going to cost a little bit more and then a little bit more and then a little bit more, which is the general trend in most markets. Initially that first amount you produce in as cheap a way, using the low hanging fruit, as possible, but then you've got to go up the tree, find higher and higher fruit, maybe I'm mixing metaphors. But your cost, your marginal cost per unit goes higher and higher and higher. Now, what have we constructed here? Well you might say, hey, Sal, that's a marginal cost curve. But once again, this also could be viewed as the supply curve for this particular market. Now what is happening at these low quantities right over here? Well, the cost of production is, let's say they produce this delta Q amount, the cost of production would be the area right over here under the marginal cost curve, that would be the cost of production. But they're able to sell it, the benefit to the market I should say, would be the total area under this red curve, would be the benefit to the market, the total area under this curve. So if you have the total benefit to the market, you take out the cost, then what you have in between these curves, you could view this as a surplus, you could view this as a surplus of benefit right over here. So let me write this down, this is surplus, and you won't hear this term but I like to use it, because it makes it intuitive on what we're talking about, this is surplus benefit. So as long as there's surplus benefit the suppliers are going to say, hey, wow, I can produce this cheaply, people have a, people get a lot of benefit for it, they'd be definitely willing to pay 10 dollars a pound wherever I am. If people are getting this much benefit, they're definitely going to be willing to pay 10 dollars for it. So I'm going to produce some, or actually I'm going to produce some and I could even charge, I could charge anywhere in between these areas. Maybe I could charge right over here and I get some of the benefit and then the consumers get some of the benefit. But then another maybe entrepreneur realizes, hey, well, there's more benefit to be had in this market, so they keep producing, they keep producing as long as there is benefit here, as long as the marginal benefit is higher than the marginal cost, all the way until we get to that point right over here. Now what happens, what happens right over here? Well we talked about just supply and demand, we talk about that's an efficient price and efficient quantity, but let's just think about, we said up until this point it makes sense to produce more and more and more. Even this increment, if we're already at this quantity, it makes sense to produce even a little bit more because you're going to have this cost, you're going to have this cost to incur, but then the market could have all of this, the market could have all of this benefit, which is larger than the cost. And so you say, well, as long as I sell it for something in between we can split that surplus benefit, so to speak. But once these two lines intersect and we have the situation where our marginal benefit, marginal benefit, is equal to our marginal cost, well at that point there is no surplus benefit now to be had, there's no really incentive to produce more than this. Beyond this point, your incremental cost of production, your marginal cost is higher than your marginal benefit. So, if you actually wanted to give it to someone for their benefit, you would be taking a loss. Or even if you just think about the market itself, the society would be incurring more incremental cost per unit than they would be getting of benefit, so why even do it? And so this point right over here where these two lines, these two curves intersect and we've talked about this with just supply and demand, but when we think about it in terms of marginal benefit and marginal cost, we think about this quantity right over here, let's just call it Q subzero, this quantity is considered allocatively efficient, allocatively efficient. Which is a very fancy word, allocatively efficient. Why is that the case? Well, any other quantity would not be efficient. For example, let's say for some reason we were at this quantity right over here, let's say Q, Q one. Well what happens at this quantity right over here? Well, at this quantity, at this quantity right over here, the marginal benefit is higher than the marginal cost. Marginal benefit is greater than the marginal cost. And so we're leaving a bunch of stuff on the table, the market is leaving a bunch of surplus benefit, you could say total surplus, on the table. And so this benefit that the market could have had, but it does not get, this is called a deadweight loss, deadweight loss, and we talk about it in other videos. Remember, in the allocatively efficient quantity we have this huge total surplus, which is the area under the marginal benefit curve and above the marginal cost curve up until the point of intersection. But if you do a quantity less than that allocatively efficient quantity, your marginal benefit is higher than your marginal cost, and you are leaving, you are leaving all of this total surplus on the table, regardless of how you would have actually allocated it or distributed it between the consumers or the producers. And what if you produced a quantity larger than the allocatively efficient quantity? Once again, very fancy word, so let's say that's Q two, what happens over here? Well, here you're able to take advantage of all of this surplus right over here, this total surplus right over here, but now you're creating negative surplus. So, in this part, now all of this area shows a net negative benefit, or a net I guess I should say a net cost that our market is incurring. And so this here it was a deadweight loss because we were leaving stuff on the table that we could have had. Here we're producing at a cost that our market, not just our suppliers are producing at a cost, the benefit our market is getting is less for each incremental unit, is less than, or is far less than the cost and so we are incurring a net negative total surplus. And so this, too, would be considered, this, too, would be considered a dead, let me write that in a color you can see, a deadweight loss. Deadweight loss we often assume it was, hey, we're leaving some total surplus on the table, but we also have deadweight loss in the case where we are producing unnecessarily because the benefit is less than the actual cost. And so whether our marginal benefit is greater than our marginal cost, or in this case our marginal cost is greater than our marginal benefit, we are going to produce deadweight loss in either situation. And a properly functioning market should be producing the quantity that is allocatively efficient. In an ideal world and of course all of our models assume a lot of assumptions to make things a little bit cleaner, so we can do lines to describe market behavior.
Khan_Academy_AP_Microeconomics	Trade_and_tariffs_AP_Microeconomics_Khan_Academy.txt	- [Instructor] In this video, we're gonna think about how trade affects the total economic surplus in a market, and we're also gonna think about tariffs, which are a per unit charge that a government will often put on some type of good that is being imported, usually to protect a domestic industry, but sometimes it's also to raise revenue. So, right over here, we have a simple model for the sugar market in some country. And we're originally initially going to assume that this country is operating in isolation. So, this is the supply curve for the suppliers of sugar in that country, and then this is the demand curve for the people who would want to use sugar in that country. And you can see the equilibrium price and quantity in that country. Now, in this world, we've reviewed this in many videos, what's the total economic surplus? Well, the total economic surplus would be defined by this triangle right over here. It's the area above the supply curve and below the demand curve. And we know that the part above this horizontal line at the price of three, this would be the consumer surplus; and then down here, this would be the producer surplus. Now, let's say that this market opens up to the world, to the world price. And let's say when it does so, it does not affect the world price itself, the world market is so large, and let's say this country's market is relatively small. And so, the world market, let's say that sugar is trading at $1.50 per pound. So, this right over here is the world price, $1.50 per pound, let me write it right over there. So, this is our world, our world price. Now, if we assume that it's opened up to this world price, what will happen? Well, at the world price, the consumers in this market, the people who are using the sugar, well, they're going to use a lot more. At $1.50, the place where that intersects the demand curve is out here. So, now, what is the consumer surplus in this country, in this market? Well, the consumer surplus in this country is now much larger. It contains the triangle that it contained before, and then all of this area that I am now shading in. And that has come at the cost of the producer surplus. The producers in this country, or in this market, they are now only getting that producer of surplus right over there. But if you look at the total economic surplus, it has definitely grown. The total economic surplus, instead of just being that original triangle, it has now extended to include this entire area that goes all the way out there. And you could see that that completely contains the previous total economic surplus, which we had right over here. So, theoretically, when a market opens up to the world price like this, it's going to increase your total economic surplus. And if that world price is below the equilibrium price in your isolated economy, then it's probably going to be to the benefit of the consumers, but the producers are going to lose out on some of their surplus. Now, let's say that a government comes into power in this market, and says, hey, I've been elected by the sugar producers of this country. I don't like this thing going on. Our sugar producers in our country are getting hurt a lot, and they're a big voting block, so I am going to enact a tariff. And once again, a tariff is a per unit charge, or it's oftentimes a per unit charge. And let's say the tariff is 50 cents per pound, per pound on imported sugar. Well, then what is the world price going to look like to the market that we're talking about? Well then, for the consumers in this market, instead of being able to get the world price at $1.50, they would have to pay 50 cents per pound higher than that. So, the tariff would make the price go over here. So, in that situation, what has just happened? Well, now, where we intersect the demand curve is a lower quantity than when we used the world price. At the world price, we were consuming a lot of sugar in this market, and now we're going to consume a little bit less sugar. But since, even with the tariff, our price is still lower than our previous equilibrium price, when we were operating in isolation, we're still consuming more sugar, using more sugar, demanding more sugar in this market than we were when we did not have it opened up to trade. Now, what did this tariff do to the surpluses? Well, the consumer surplus has now gone down relative to the free trade scenario. We've lost this area down here. So, now, the consumer surplus, I will shade it in this blue color. And we have increased the domestic producer surplus. It has increased to this, right over here. But what about this region that we seem, that seems to no longer be there, either in the consumer or the producer surplus? Well, some of it is the government revenue. What's the government revenue going to be? Well, it's going to be the amount of the tariff times the quantity. So, the amount of the tariff is going to be that 50 cents, so that's that height right over there. And then what's the quantity that they're getting that tariff on? Well, this whole section right over here is the imported quantity. This section right over here is the domestic production, and this is the imported quantity, so the imported quantity times the tariff, so this area right over here, that is going to be government revenue. But you do have some of that total economic surplus that is just, becomes deadweight loss now. You have this region right over here that is now deadweight loss, and this region right over here that is deadweight loss. So, I'll leave you there. As you can see here, that when you open up to trade, theoretically, it increases the total economic surplus. But that could have consequences on the producers. And actually, there's cases where it can have consequences on the users of whatever, or the people who are the buyers in this market. And many times, a government will enact a tariff. Now, you can see that that tariff will reduce the total economic surplus. Some of that will go towards revenue, while other parts of it will just be deadweight loss. Another idea that a government might sometimes do is an idea of a quota, where they're saying, hey, we just don't like the total amount of imports that are happening, so they might just put a cap on it. I'll let you think about how you might deal with a quota and how that might also affect the economic surplus.
Khan_Academy_AP_Microeconomics	Change_in_supply_versus_change_in_quantity_supplied_AP_Macroeconomics_Khan_Academy.txt	- [Instructor] We're going to continue our discussion on the law of supply and in particular in this video we're gonna get a little bit deeper to make sure we understand the difference between a change in supply and I'm just using the Greek letter delta here for shorthand for change in supply versus a change in quantity supplied and just as a bit of review, we've talked about it in other videos, supply is referring to the entire supply curve and this curve right over here has the typical shape of a supply curve following the law of supply. At low prices, suppliers would provide low quantities and at higher prices, suppliers would provide higher quantities, so a change in supply would be a shift in this entire curve, so for example, if you were to go from this curve, let's call this S1 and we were to have a shift to the right, this right over here would be a change in supply, so we'd call this S2 and we would have this shift, you could view it as to the right or to the right and down, so this would be our change in supply. Likewise, you could have a change in supply the other way where you go to the left and up depending on how you want to view it and so, this would be, we could call that supply curve three. These would all represent shifts in supply or changes in supply. When we talk about quantity supplied, we're talking about shifts along one of these curves, so for example, at some price, so let's say we have this price P1 right over here, associated with that price we would have some quantity supplied, we have some quantity supplied. Let's call it quantity supplied one and then let's say for some reason, we have a shift in price with the market forces not changing from a supplier's point of view and so, let's say we go to price two, let's say we go to price two, we would shift along that same curve, the curve itself wouldn't have shifted and so, then you have quantity supplied two, so change in supply is a shift of the curve to the left and up or to the right and down versus a change in quantity supplied is moving along the curve and the associated quantities. Now, with that out of the way, let's do some tangible examples and think about would it result in a change in supply or a change in quantity supplied? So, let's say that the government decides that gas prices are too high and so, they institute a price cap and we're gonna talk much more about price caps in future videos but a price cap might just say, and let's say that price cap is below the current price. So, let's say the current price is at P2 and that the price cap is at P3, so the government says, no one is allowed to charge more than P3 for gasoline. What would that result in? Would that result in a change in supply or a change in the quantity supplied? Well, this is a classic case of a shift along a supply curve, the price was there before, now it shifts here and so, now we're going to have a different quantity supplied, so this would be quantity supplied three, so this is a change in quantity supplied and in this case, the change in quantity supplied would go down assuming that the price cap is below what the price was before the price cap. Now, let's give another scenario. Let's say that the price of refining gas goes up. Price of refining goes up. What would that do? Would that be a change in supply or a change in quantity supplied? And pause this video to think about it. Well, this is something that would increase the cost of producing gasoline which is refined from oil across the board regardless of what price we're at, so this would be a general shift, this would be a change in supply and the entire supply curve, think about which way it would shift, think about it from a supplier's point of view. At a given quantity, so let's say we're at this quantity right over here, at a given quantity, they would now want to charge a higher price and it doesn't apply to just that quantity, it could be this point in the curve, this point in the curve, this point of the curve, they'd want to charge a higher price to make up for the fact that refining is now more expensive and so, this would be a shift, you could view it up or shift upward and to the left. You could also view it the other way. At a given price, suppliers would want to provide less quantity because they need to make up the fact that they're paying more for refining that gasoline and so, you could view that as a shift to the left or a shift of up and to the left and so, that would be in that direction, we're kind of shifting like that and then of course we could talk about a scenario that goes the other way. Well, let's say that the property tax in the entire market, property tax on gas stations goes down, so in theory, if the property tax goes down, the cost of running a gas station goes down and this is for everyone in the market, not just one player in the market and so, they might for a given price be able to supply more of a quantity or for a given quantity be able to lower the price. Either way you could imagine shifting from S1 to something that looks like S2, going down and to the right and so, once again, this would be a change in supply because you would have a shift regardless of what price and quantity supplied you are actually at.
Khan_Academy_AP_Microeconomics	Minimum_wage_and_price_floors_Microeconomics_Khan_Academy.txt	Voiceover: Let's think a little bit about the labor market. In all of these videos, whether we're talking about renting units or hiring people, these are huge oversimplifications, but we're doing it in this way so we can apply some of these basic ideas that we're being exposed to in this survey of microeconomics, so that we can apply those basic ideas to real world things. It's important to realize we're making huge oversimplifications and often times the real context can be more complicated or a little bit nuanced, but it gives us a way of thinking about things. This is the unskilled labor market, so people who don't have any specific training or experience for a given job. The vertical axis is their wage rate per hour. It's essentially the price of labor. This little gap here shows I started at zero, but then I jumped up to five, six, seven. This right here is a quantity of labor. We're measuring that in terms of millions of hours per month. Once again, we have this little gap here, so we can jump to 20 million hours, 21 million hours. It's important to realize, when we think about demand in the labor market, we're not talking about individual consumers, we're talking about employers. In most cases, demand comes from individual consumers, but now the demand is coming from employers. These are the people who are essentially buying labor. The supply is not coming from corporations. The supply is coming from the people who provide labor, so now it's coming from individual workers. Now it is coming from workers. Let's just say that this market starts off completely unregulated, so it has a natural equilibrium price or equilibrium wage at $6 an hour and an equilibrium quantity of labor supplied, which is 22 millions of hours per month. Let's say the government in this hypothetical city or country says, "You know what? "$6 is a really low wage. "We have trouble imagining how people live well "off of a $6 an hour wage." They say this right over here is too low. The government does not like it and maybe many of their voters are people making that wage, so they say, "Hey, you know what? "We are going pass some well-intentioned legislation. "We are going to pass a minimum wage. "We are going to pass a law, minimum wage, "that says any employer has to pay at least $7 an hour." $7 an hour. It has to be at least $7 an hour, so this right over here is a price floor. This is a minimum price in the market. When we talked about rent control, that was a price ceiling. That was a maximum price for rent, now this is a minimum price for labor. Since the price floor, this minimum price, is higher than the actual clearing price, it's going to distort the market. Our price floor is right over here, $7. This right over here is our minimum wage. What's going to happen here? If you look at the demand side of things, the employers are going to say, "Wow! "If I have to pay $7 an hour now, I can only afford "21 million hours of labor." They're going to say, "I can only afford now "21 million hours of labor," but if you look at the workers they're going to say, "Gee, if I can make $7 an hour, "more people are going to be willing to work." Either an individual might say, "If I was working 40 hours a week making $6 an hour. "If I'm making $7 an hour, I'm willing to work "45 hours a week." Or there might be a student who's on the fence, who says, "Wow! "Now wages have gone up enough that it makes sense "for me to work." There might be someone who's retired and now, at $6 wasn't enough for them to come out of retirement, but $7 is. Maybe a stay at home parent now says $7 is enough for them to come out of retirement or not stay at home anymore. The labor, the quantity supplied of labor, in terms of hours, will increase. At $7 an hour, people will be willing to supply that much labor, but what's going to happen in this situation right over here? In this situation you have all of these people who want to work, but there's only demand for this much work. Right here, this is going to be an oversupply of labor. Another way to think about it, there's only jobs for 21 million people now and now 23 million people want to work. You're going to have 2 million people who are, by the classical definition of unemployed, people who are looking for work who can't find work now. Once again, this is completely oversimplified, because at this point right over here, based on the way I just viewed that, you would have no unemployment and we all know even when the economy is humming maximumly and there's no regulation, there is some unemployment, just due to frictions in the market, people just randomly quitting jobs or looking for a new job, so you could almost view this as excess unemployment. Or you could view this as just a very oversimplified model and in the ideal world you'd get close to zero unemployment. Now you have more people looking for jobs, because the wages have gone, but fewer jobs, because the employers are forced to pay more. If we make all of these assumptions in the model and you just want to say how many fewer jobs are there, because this, obviously, we're talking about more people even looking for jobs because the perceived wages have gone up. In the absolute level, based on these linear supply and demand curves, before there was demand for 22 million jobs and that was what the quantity demanded was and that's also where the quantity supplied was, but now its only 21 million. Based on this model, you're going to have 1 million fewer jobs. When you think about it in terms of surplus. Before the minimum wage, the entire surplus was this entire area over here. This entire area that's below the demand curve and above the supply curve. This entire area was the total surplus and it was being divided between the consumer surplus and the producer surplus. This right over here, between the price and the supply curve was the producer surplus. The producer surplus, remember the producers of labor are the individual workers. This was the benefit above and beyond the opportunity cost that the workers were getting was this area right over here that I'm doing in dark white or filled in white and the consumer surplus or the employer surplus here was the value that the employers were getting above and beyond the price that they had to pay. Now, in this situation of a minimum wage, now this is the set price, this is the quantity of labor that is demanded. What you lose now, the surplus that we lose is this quantity right over here. We could figure out that area quite easily. Let's see, this height right over here is 1 million hours per month, so it's going to be 1 million. I'll just write 1, we'll just remember it's on millions. Times this height right over here, which is $2 per hour. Times one half. If we just multiply these, we get this whole rectangle for the area of the triangle, we multiply it times one half. That gives us exactly 1 and the units are dollars per hour times millions of hours per month, gives us millions of dollars per month. It becomes $1 million per month of surplus, of benefit above and beyond, of total benefit that is lost to this market because of this regulation, if you assume all of the things in this model. Just like we talked about in the last video, we have a $1 million per month dead weight loss. Now, not everyone loses here. Because the price is set up over here, for the people who are working those first 21 million hours per month, their producer surplus has now increased, because the space between what they're getting and their opportunity cost has now increased. For those lucky enough to actually have a job, those workers now do have a higher surplus, but for those employers, which is on the demand side right now, who are employing those first 21 million hours of labor, they now have a smaller consumer surplus or demand surplus or employer surplus right there. For the first 21 million units of labor, it's redistributing the pie between the employers and the workers, but then because you are making the wage higher, it's reducing the overall demand, so there is, if you believe this model, some job destruction taking place.
Khan_Academy_AP_Microeconomics	Graphical_impact_of_cost_changes_on_marginal_and_average_costs.txt	- [Instructor] In the last video, we numerically studied how changes in productivity or cost might affect your marginal cost, your average variable cost, your average fixed cost, or your average total cost. In this video, we're gonna think about it visually. So, we constructed these curves several videos ago to visualize how average fixed cost trends over time. As you take that fixed cost and you spread it over more, and more, and more units, you see that that just asymptotes toward zero as you get more and more units. You see your marginal cost curve, and this is something that you'll typically see in a lot of textbooks. It's kind of u-shaped. And we talked about where it intersects the average variable cost. That's where the average variable cost goes from trending down to trending up. So it hits that minimum point, and the same thing happens at average total cost. It hits the bottom of that u of average total cost. It goes from trending down to trending up. And then over time, this difference that you see between your average total cost and your average variable cost, that difference right over there, that is your average fixed cost. And so, since your average fixed cost are asymptoting downwards, you see that this difference between average total cost and average variable cost gets less and less over time, that they are going to, over time, converge to each other as your average fixed costs gets closer, and closer, and closer to zero. But now let's think about how these curves might be impacted if you have changes in productivity or cost. So let's start with a change in your fixed costs. Let's say your rent goes up. What would happen then? Pause this video and think about what would happen visually. Well then your average fixed cost would shift up, and it might look something like this. Your average fixed cost might look something like this. And then, which of these other curves also have fixed costs embedded in it? Well, your average total cost is a combination of your average variable cost and your average fixed cost. So the amount that your average fixed cost went up for any quantity, your average total cost would also go up that amount for that quantity. So it would look something like this. It would look something like this. And once again, just as before, it will trend downwards until you intersect with your marginal cost curve. And then it'll start trending upwards. So a change in your fixed costs, either upwards or downwards, would affect your average fixed cost and would affect your average total cost. The reason why it doesn't affect your average variable cost is because your average variable cost are taking out out your fixed costs. They're just thinking about the variable costs. And your marginal costs are thinking about a difference in costs between two different states of output. And the fixed costs are in either of those, so they will cancel out. What would be a change in your variable costs? Let's say you have to give everyone a pay increase. Well then your variable costs will go up. And your variable costs might look like something like this. They will just shift up. And once again, they will trend downwards until you intersect with your marginal cost curve, and then you will trend upwards. Now, a change in your variable costs will also affect your marginal costs. Because as you produce more output, well then you are likely to incur more incremental costs. So then your marginal costs, and I know this is getting very messy, might start looking something like, might look something like that. So, big picture, changes in productivity would likely affect your average variable cost, likely affect your marginal cost, and of course, average variable cost feeds into average total cost, so that would be impacted as well. But changes in just your fixed cost would affect your average fixed cost curve and your average total cost.
Khan_Academy_AP_Microeconomics	Increasing_opportunity_cost_Microeconomics_Khan_Academy.txt	What I want to do in this video is think about how the opportunity cost can change as we move from scenario to scenario. And this is going to be particular to this example, but it's a phenomenon that you will see in many economic scenarios. So let's say we're starting off in Scenario F. We are vegetarians. We are only getting berries. We are not spending any time going after rabbits. But now we're starting to, I guess, crave protein. And we say, well, what is going to be the opportunity cost if I go for that extra rabbit? If I go for that extra rabbit, then what's going to happen? Well, I'm going to have to stay on my production possibilities frontier. And so I'm going to move to Scenario E. So if I go after that one extra rabbit, I'm going to give up 20 berries. So my opportunity cost in Scenario F, sitting in Scenario F, of going after that 1 rabbit is 20 berries. Now let's keep going. What happens if I'm in Scenario E? I'm already, on average, eating 1 rabbit or finding 1 rabbit a day. And I want to go to 2 rabbits a day. What am I going to give up? Let me do that in that same color. What will I give up? Well, now I am going to give up 40 berries. This is interesting. Now let's say we're in Scenario D and we want even more rabbits. We're really starting to become carnivores now. What am I going to give up? Well, I'm going to give up 60 berries. If I'm able to get 3 rabbits, every day, on average then I'm only going to get 180 berries now instead of 240. And let's just keep going. So if I want yet another rabbit every day, then I'm going to have to give up 80 berries. And then finally, just to feel some sense of completion, if I become a complete carnivore and if I want to get on average, 5 rabbits a day, I'm going to have to give up another 100 berries and go to not having any berries at all. And so you might see something interesting. The more squirrels-- sorry, not squirrels although I guess they're similar-- the more rabbits that I'm going after, every time I try to go after another incremental rabbit I'm giving up more and more berries. My opportunity cost is increasing. And so this phenomenon, it's not always the case but it's the case in this example, increasing opportunity cost. Increasing opportunity cost as we increase the number of rabbits we're going after. And you could do it the other way. You could say, OK, as we increase-- especially if you did it on a unit basis, if you said every incremental berry or every incremental 100 berries we're going after, but the numbers aren't as easy right over here-- you'll actually see something going the other way. But the question, an interesting question is, OK, Sal. You set up the numbers like this earlier two videos ago. But why would this make sense? Why is this idea of increasing opportunity cost showing up in a lot of different economic, and you can call this an economic model. We have simplified our economic reality, the choices that we have to make, down to two variables the number of rabbits we have to go after or the number of berries. But why does this show up in economic models? And just to be clear, it does not show up in all of them. But to think about our example, as a hunter gatherer, we started here in Scenario F. In Scenario F, we've decided to not pursue any rabbits. Even the slower, not so quick witted rabbit who maybe likes to hang out with you, next to you, and it likes to play with your spears or your bow and arrow-- you are not even going after that rabbit. Instead you are choosing to spend all of your time on the berries. And not only are you getting, literally, the low hanging fruit, the easy berries, you're getting the berries that are further up the bush, the berries that you have to get cut by thorns to get, the berries that you have to climb trees to get. So you're getting even hard to get berries and you're not going after even easy to get rabbits. But now all of a sudden if you say, well, you know, that rabbit who's been hanging out with me, he's been kind of asking for it. And so that was very easy to get. It didn't take much time on a given day to get those really easy rabbits who like to hang out with you. You're not give a lot in terms of berries. One, it didn't take you much time to get those, literally, those slow and maybe less quick witted rabbits. And you're giving up, in that same amount of time, the very hard to get berries. So you're only going to give up about 20 of them. Now if you want to 2 rabbits a day, not only are you going to get the slowest of the rabbits, the ones that aren't afraid of humans, now you're going to have go get the slightly faster rabbit-- the slightly faster rabbit, who wants to die a little bit less and is maybe a little bit sharper. And you're now not giving up the berries that are way up in the tree and that are protected by thorns. You're giving up berries that are closer down the trees. So this is going to take you a little bit more time to do than this right over here. And in that little bit more time, you're also giving up berries that were easier to get. And so this phenomenon is going to happen all the way until in this scenario we're trying to get 5 rabbits a day. You are literally going after the quickest and the smartest rabbits. But you insist on going for them and in your pursuit of these quick, fast rabbits you're even ignoring berries. You're literally, like, stepping on berries. You're not eating the berries that are right next to you because you're so obsessed with eating rabbits. So hopefully that gives you a sense of why increasing opportunity cost does show up. And when you graphically show it in terms of a production possibilities frontier, it shows up in this bow-shaped curve. And you can see it, because as we go from this point to this point, you see that as we increase one the slope, the negative slope, is increasing. Or another way to think about, in Scenario F, the slope is roughly like this. And I encourage you to review the algebra playlist if the idea of slope is confusing to you. But at F, the slope is like that. I'm drawing the slope of the tangent line right over here. At E it gets even steeper. You're giving up even more of the berries per unit rabbit. And now in D you're giving up even more. And then you're giving up even more. And so whenever you see a bow-shaped curve like this, so a curve that literally looks like this, this shows that you have increasing opportunity costs. As you increase more and more units, you're going to have to give up more and more of the alternative.
Khan_Academy_AP_Microeconomics	Marginal_benefit_AP_free_response_question_AP_Microeconomics_Khan_Academy.txt	- [Instructor] We're told Martha has a fixed budget of $20, and she spends it all on two goods, good X and good Y. The price of X is $4 per unit, and the price of Y is $2 per unit. The table below shows the total benefit, measured in dollars, Martha receives from the consumption of each good. All right, we see that here, this is total benefit, not marginal benefit. What is Martha's marginal benefit of the fifth unit of good X? So just to answer this question, let's see, she has a total benefit of $40 when she has four of X. And then when she goes to the fifth, her total benefit is an incremental $1. So she goes from $40 to $41. The marginal benefit of that fifth one is that extra dollar. So we added a dollar of total benefit, so that's the marginal benefit. So it is $1. Calculate the total consumer surplus if Martha consumes five units of X. Show your work. Well, the consumer surplus is going to be the benefit, benefit minus the cost, which is going to be equal to, well, when she has five units of X, her total benefit is $41. So I'll write that here, $41. And then what's her cost of five units of X? Well, X costs $4 per unit. So five times four is $20, so her cost is going to be $20. So her consumer surplus is going to be equal to $21. Martha is currently consuming four units of X and two units of Y. Use marginal analysis to explain why this combination is not optimal for Martha. So pause this video, and see if you can answer that. All right, well, let's just think about what the marginal benefit is from every incremental unit of X or Y, and then let's think about the marginal benefit per dollar. So I'm gonna make an extra column here. Let's call this marginal benefit of X, and then let's call this marginal benefit of Y. I'm doing it over this table just for the sake of space. And so the marginal benefit of this first one is going to be 16. We went from zero to 16. The second one, we go from 16 to 28, so it's $12. And then to go from 28 to 36 is eight. To go from 36 to 40 is four extra dollars of benefit. And to go from 40 to 41, we already talked about that, that's $1 of marginal benefit. If we talk about Y, well, the first unit, you get $10 of benefit. The next one is the total benefit increase eight, by $8, so that's the marginal benefit of the next unit. The next one, to go from 18 to 24, six, to go from 24 to 28 is four more, and then 28 to 30 is two more. And then we could use this information to think about marginal benefit of X per price of X, and we could also think about marginal benefit of Y per price of Y. And so, let's see, and we're gonna start with the first units. And so for this first unit, if you take the marginal benefit of X divided by the cost of a unit of X, $16 divided by $4 is going to get four. 12 divided by four is three. Eight divided four is two. Four divided by four is one. And one divided by four is 0.25. And then for Y, the cost of Y is $2 per unit. So the marginal benefit per dollar of this first unit right over here is $10 divided by $2, which is five. Eight divided by two is four. Six divided by two is three. Four divided two is two. And then two divided by two is one. And so let's just think about what would be an optimal combination for Martha. When she's thinking about spending her first few dollars, she'll get a higher marginal benefit per dollar by going with Y, so she's going to start here. And then after that, her second unit of Y has the same marginal benefit per dollar as her first unit of X. So she's indifferent. She would do these in some order. So maybe she could do this one and then move on to that one, or, though, it could go in the other order. And so far, she's only spent, let's see, $2, $2 is $4 plus another $4, she's only spent $8, and she has a budget of 20. And then after that, her next incremental unit of either X or Y, the marginal benefit per dollar is the same. So just thinking about whether this could be an optimal combination, she's already bought two units of Y. Let's just give the benefit of the doubt here. Let's say that she goes for the X, so she buys this one here. But once she has two units of both, and she hasn't spent all of her money, she spent $8 here plus another $4. She has $8 to spend. The next rational thing for her to do, her marginal benefit per dollar for that third incremental Y is higher than the third incremental X. So it would be optimal for her to buy a third Y. But here, we see that she only has two units of Y, so that's why we know it's not an optimal combination. So we could say once she has two of each, the marginal benefit of Y per price of Y is greater than the marginal benefit of X per price of X for the third unit, so she will buy more than two Ys, let me write, let me scroll down a little bit, buy more than two Ys. All right, the next they say is what is Martha's optimal combination of goods of X and Y? Well, we've already started that conversation up here. She would buy this Y, and so far she spent $8 plus $6, so she has another $6 to spend. And then now her next incremental unit, she's indifferent, so maybe she buys another Y. $8 plus $8, this is $16, so she has $4 left. And so then she would buy this, and she has spent all of her money, $12 here, $8 here. So she would buy three Xs and four Ys. So I would say three Xs and four Ys. All right part e, indicate whether each of the following will cause the optimal quantity of good Y to increase, decrease, or stay the same. So look at these and pause this video, and see if you can answer those. So the price of good Y doubles. Well, if the price of good Y doubles, then the marginal benefit per price of Y will go down. So she will buy less of Y, so it would decrease. She would get less bang for her buck on Y, so she would buy less of Y. Martha's income falls to $10 with no price changes. Well, if we go through the exercise we just did, her budget would run out much faster, and so she would definitely decrease the number of Ys she would buy. So the Ys would decrease. Martha's income doubles, and the price of both goods double. Well, in that case, things would stay the same, stay the same. Because once again, she could buy that exact same combination. It would just cost twice as much, but then her budget is now twice as much. So things would stay the same. She would buy the same quantities of both Xs and Ys, and they're just asking about Ys. And we're done.
Khan_Academy_AP_Microeconomics	Scarcity_Basic_economics_concepts_Economics_Khan_Academy.txt	- [Instructor] The entire field of economics is based on the idea of scarcity. And, arguably, we wouldn't even need a field of economics, if there wasn't the notion of scarcity in the world. So what does scarcity mean? Well, think about what does it mean in everyday life? It means that there's not enough of something to go around. If we're talking about scarce goods, scarce services, scarce resources, we're talking about things where if there was no cost associated with them, people would use far more of that than there actually is around. And in this video we're gonna think about different types of goods and services or just resources and think about whether they are scarce or not. So a related idea to scarce resources is it's opposite, which is the notion of a free resource. So this is something that, you could argue, is infinitely abundant or at least in a certain context is so abundant that it feels like people can have as much of it as they want. The more that one person has of it, it doesn't take away from someone else. And the reason why scarcity is essential to economics is because economics is the study of how do you allocate these scarce resources. If there's more demand for it than the amount of thing that there is, well, who gets it, how much of it do they get, and what do they have to give up in exchange to get those scarce resources? But for the sake of this video, let's just first make sure we understand and have a good idea of what resources are scarce and which ones aren't, and why. So this is a picture of caviar, which is essentially fish eggs, and it's not easy to get. The fish eggs are deep in the water, someone has to get to them, and then they have to package it in some way, and they have to get it to your plate. And so, do you think that caviar is a scarce resource or a free resource? Well, if it was a free resource, that means that we're just swimming in caviar, that it's so abundant that I could just have as much caviar as I want and there's still as much as you want and that everyone gets as much caviar as they like. Well, that's clearly not the case. Caviar is a scarce resource. In fact it is a quite scarce resource, and because of that, if you want it, you have to give up a good bit to get it. This is a picture of some people working in a factory, and the resource that jumps out here is that of labor. And labor's interesting because it's not as tangible as something like caviar but it is a resource. And one could even argue that caviar on your plate, some of its scarcity comes from the labor involved of getting it to your plate. But here these are clearly, it looks like these are gentlemen who are putting together some type of fabric. And so, would you consider labor, would you consider that a scarce resource or a free resource? Well, it would be a free resource if people were willing to just do as much work for other people, actually willing to do an infinite amount of work for other people, which isn't even humanly possible. And even is it was humanly possible, people aren't willing to do that. They want something in return. And so, once again, it is a scarce resource. There's many resources that are pictured right here. You have this beautiful town next to this alpine lake. And so, some clear scarce resources are here. Many people would love to have a view like you would get from this house or hotel right over here, but not everyone, and many people would love to live there because of the view, but not everyone can live there. So that is a scarce resource. The water here is an interesting one. I can imagine in earlier times, if before there was a town here, if there was just a primitive village living next to this fresh water, they would probably view it as a free resource. If someone was thirsty, they would just go up to the lake and they would just drink from the lake. They would not have to give up anything to drink from that. But now the town, it might be a little bit more of a scarce resource. They might want to preserve it for various reasons. In order to get the water to your sink in your house, there might be some services or goods or labor involved. Someone has to set up the pipes, maybe it has to be cleaned in some way. Well, then it might become a little bit more of a scarce resource. Air for most of human history has been considered a free resource. And even today I'd argue that something like oxygen, at least on our planet, is considered a free resource. When I take a deep breath (breathes deeply) it does not affect your ability to take a deep breath. It does not take oxygen away from you. Now is there an infinite amount of oxygen in our atmosphere? No. But for our purposes it feels like there's an infinite amount. Now if the photosynthetic plants were to disappear and all of a sudden oxygen started to get diminished, or if we were in a space station where there isn't a seemingly infinite amount of oxygen, well then you could imagine a world where it could become a scarce resource. You can imagine a colony on the Moon or on Mars or in the space station where it had some type of economic system to decide who gets how much oxygen. So I will leave you there. As already mentioned, scarcity is the central idea in all of economics. It's the reason why we even need a field called economics. And as you go forward in your study of both micro and macroeconomics, we'll be looking at ways to allocate these scarce resources. We'll try to study what people have to give up in order to have access to these resources, and we will have models that will help us understand what are the implications for these different methods of allocating resources.
Khan_Academy_AP_Microeconomics	Producer_surplus_Consumer_and_producer_surplus_Microeconomics_Khan_Academy.txt	We have now talked a lot about the demand curve and the consumer surplus; now let's look at the other side. Let's think about the supply curve and you could imagine that there might be something called the producer surplus. So let's say that this is price axis, this is the quantity axis and let's say that we are running some type of a berry farm and this is our supply curve. That is the supply curve and this is our demand curve. So that is the demand and just like what we did to the supply curve, for the demand curve, now instead of thinking of a price and think about how much quantity would be supplied, let's think about a given quantity and think about what price would it have to be in order for the producers to produce that quantity. And let's say that this quantity right over here, this is in thousands of pounds of berries, thousands of pounds. So this is 1 thousand pounds, 2 thousand pounds, 3 thousand pounds, 4 thousand pounds, and 5 thousand pounds. And let's say this price right over here is 1 dollar per pound, $2, $3, $4, maybe I could make it more even, so this is $3, this is $4, this is $5 per pound. Let me write this all in per pound. So let's say that we want the suppliers to produce 1 thousand pounds of berries, so this is we want them to produce 1 thousand pounds of berries, What does the price have to be for them to produce 1 thousand pounds of berries. Well think of it from the suppliers from the berry farmers' point of view. If they are going to produce 1 thousand pounds of berries. in order for them to produce it, in order to convince them produce it, they have to get at minimum as much as they would get using the same resources to produce something else. So if they could get a dollar per pound or equivalent in dollars of a dollar per pound for those first thousand pounds, so about a thousand dollars. If they could get that by using their land for an apple orchard or using it to graze or maybe renting out the land to someone else, that's the minimum you would have to pay them. Because if you pay them less than that they would go do the other thing. They would go and rent their land out or they will allow their land for grazing. So you would have to pay them the opportunity cost for them to produce a thousand pounds. So the opportunity cost for them to producing a thousand pounds would be right over there. And this is on average first thousand pounds you could also think that the very first pound, the opportunity cost would be right over there, and the next pound would be right after that. The five hundred pound would be there, the thousand pound would right be there. or you could say the first thousand pound on average would be right over there. Now let's say that we wanted them to produce another thousand pounds. So we want the market or this entire farm to produce or maybe it's multiple farms to produce a total of two thousand pounds. What would we have to do? Well, same exact thing. We kind of assuming the market is already producing that first thousand pounds. So now we would have to think about what are they giving up to produce that next thousand pounds. And now we would assume that for that first thousand pounds, they would have used the land and the inputs that are most suitable so this is the most suitable resources. So we are talking about the labour that really knows how to grow berries. The land where the berries are the best grown and maybe they are really close to transportation networks so it's much cheaper to produce and ship from there. But now if we want another two thousand pounds of berries at this time period and maybe this per year if we want another thousand pounds. They are now going to less suitable resources, maybe the land is slightly further away from the transportation resources, they are now going to have labours that are slightly less efficient, they are going have to take land away from that. might have been slightly more suitable for other things. So now the opportunity cost for these growers for the next thousand pounds is going to be slightly higher. So their opportunity cost is going to be like that on average for the next thousand pounds. You could that the opportunity cost for the one thousand pounds will be right over there for the two thousand pounds would be right over there. But on average for the two thousand pounds, this is their opportunity cost now, same thing, the next thousand pounds after that If we want to get the market, if we want the whole supply be three thousand pounds they would have to produce, they would have to get that their opportunity across that incremental thousand pounds that opportunity cost of that incremental thousand pounds. So view it as this way, the supply curve no longer and it is the same exact curve, before we used to say, oh if we want how much would people produce if the price were 3 dollars. Oh they produce 3 thousand pounds, now we are looking at the other way, we are saying if we want the suppliers to produce 3 thousand pounds, what would the price actually have to be. Now with that out of the way, now we can think about the supply curve is really a opportunity cost curve for the suppliers. And let's say that this is supply and the demand, and then this would be the actual price which supply equals demand right over there so let's just say that is the market price. So what's going on over here, all of the suppliers, so this is the price here let's just for making the math simple, let's just say that price here is 4 dollars and the quantity demanded and the quantity supplied here is 4 thousand pounds. What's going on here, the very first 4 thousandth pound produced by the suppliers, the opportunity cost for them to produce it would be 4 dollars. We are gonna get exactly 4 dollars for it so they are right on the fence. but for the first three thousand 999 pounds, the opportunity cost of producing it was lower than the price to get it, so in this situation the producers are getting more, for the first 3999 pounds. They are getting more for their berries than their opportunity cost and just like we talked about, the consumer surplus, this is the producer surplus. So, for example, for the first thousand pounds right here, the producers, their opportunity cost was a little over a dollar a pound but they are getting 4 dollars a pound for it. For the next thousand pounds, the opportunity cost is approaching 2 dollars per pound, like a $1.75, just eyeballing it. Once again, they are getting 4 dollars a pound for it so they are getting this surplus, so if you think about the entire market, the producers as a whole, they are getting this entire area, this entire area represents the excess value that they are getting above and beyond their opportunity cost, and we call this right over here the producer surplus, the producer surplus. And we are assuming or we will assume a linear supply curve right over here. This is just a triangle, the area of a triangle. This length right on this side is just 4-1, it's just 3, 3 dollars per pound and then this length right over here is 4 thousand pounds, 4 thousand pounds. So to find the producer surplus, we are just finding the area of this region. So, let me write this, the producer surplus here is going to be, I will use the same color, 3 times, I want to do it with pink, 3 times the 4 thousand, and that would give us the area of this entire rectangle, so we have to divide it by 2. That's just finding the area of the triangle, so times one half, dividing by 2. And so this gives us one half times 4 thousand is 2 thousand times 3 is 6 thousand. And you could look at the unit, it's 6 thousand or 3 dollars per pound times thousand of pounds per week so we end up with, so the, we end up with 6 thousand dollars of producers' surplus per week.
Khan_Academy_AP_Microeconomics	Property_rights_in_a_market_system_Basic_Economic_Concepts_APR_Microeconomics_Khan_Academy.txt	- [Instructor] In this video we're going to talk about an idea that's crucial to the proper functioning of an economy under a market-based system. And that's the idea of property rights, and it's just the idea that everyone agrees on who owns what and what can they do with that property? And for many of us who live in a part of the world with strong property rights, we take all of that for granted. We know who owns that house and what they have the right to do with that house and if they were to sell that house, how that would occur, but in some parts of the world or in some parts of history, that wasn't so clear. Someone might say they own the house, but then another person might live in that house and they say well I've been living here for 10 years, it's my house now, deal with it. Or they might go hire some thugs to say hey owner sell me the house for less than the market value otherwise we're going to hurt you in some way and so in some ways they're infringing on those property rights or the government might just come in and say we're gonna take that property from you because we want it and in those situations property rights would be weakened, and what we're going to do is a little bit of a thought experiment to see why it's so crucial for the proper functioning of a market economy. And so let's stick with the house analogy. So let's say that we have some blue houses in our economy that look like that. Let's say it's owned by this person right over here. Let's say we have some pink houses that look like that. Let's say it's owned by that person right over there and let's say that we have some orange houses that look something like that. They have some kind of arch on the top and let's say it's owned by something like this, and let's say these people are all interested in selling their house. Maybe they're downsizing or they're retiring or they're moving someplace else. And so there's a market of potential buyers. So let me draw the buyers right over here and so there might be some people and if we have properly functioning property rights, there might be some people who are really interested in the blue house and so whoever is willing to pay the most for that blue house will get it and so let's say that this person is willing to pay I would say one dollar sign for the house and so the ownership of the house will go to that person. Same thing for the pink houses. Maybe this person right over here is the person who really likes the pink houses. They pay a different price, maybe a little bit more. I'll do two dollar signs to represent that, and then they will get title to the house and maybe a ton of people are really interested in these arched houses and maybe they bid for it and the bidding keeps going higher and higher and higher and this person wins at the end and they have to pay up a lot for that orange house that they get title for, and let's just assume that for whatever reason, that they're all about the same cost to build. Well what would happen in this market then? Well home builders or even people in other types of houses will say wow, I can get a lot more for the orange house. The market is giving us a price signal. So this right over here, this is a price signal. In fact, they're all price signals, and when you take 'em together, you're saying, hey, I get more for an orange house than a blue house and so maybe if they all cost the same to build we'll start producing more of these orange houses. So builders will produce more of these orange houses and maybe some people might remodel their blue houses to have these orange arches on 'em, and so you could imagine that might happen from the price signal because it's clear that that's where users preferences are. That's where the demand is, but now let's imagine a slightly more dystopian world and this actually is what much of human history was and even some significant parts of the world today where there aren't clear property rights. When this person says that they have this house for sale, these people are like is it really your house? And then this person comes along and says no it's my house and I have this proof that my grandfather owned it and he never sold it to your grandfather and then this person says I have a lot of guns and I don't care what y'all say and what paperwork you have, but I'm taking the house. Well how much would this person be willing to pay this person right over here in that circumstance? And so this person is much less likely to get these three dollar signs This person said hey, this is kind of a risky investment. I don't really know if I take title from this person whether it's still my house. So they're not willing to give three dollar signs, they're only willing to give one dollar sign or maybe no dollar signs. Maybe this house doesn't even sell. Well then the price signals have broken down, and so then in this market people will tell me maybe we'll build more of the arched orange houses because that's what the market demands and so you can quickly see that when property rights break down, the market system breaks down 'cause the market system is all about people using price to figure out how much they're willing to pay for things but that assumes that when you get something that it's really yours, that it's not going to be disputed and the person you're buying from really has ownership and this break down would often be characterized as a market failure. Now you could say okay there's other types of systems that we've talked about in other videos. We talk about command economies and in the extreme in a command economy, you have no private ownership of things and so you might say maybe that is a solution to this property rights problem, but command economies have significant problems of their own. In fact, very few of them or really none of them in history have proven to really work because they have a major incentive problem because if you're just being told what to build by the government, you're told how to build it by the government, you're told who that gets it by the government. There's very little incentive to try to innovate, to try to build more, to invest, or whatever else, and we talk about that in other videos. So I will let you go there. This is just an introduction to think about this idea of property rights and ask your parents or talk around or if you are a parent, look at the world of how much infrastructure we have in a society like the United States or in much of the world today to enforce property rights.
Khan_Academy_AP_Microeconomics	Markets_and_property_rights_AP_Microeconomics_Khan_Academy.txt	- [Instructor] In other videos, we have touched on the idea of property rights, but in this video, we're going to go a little bit deeper, and think about how property rights connect to the notion of a market. So, first of all, think about what a market means to you. You have probably heard of things like the stock market or you have probably gone to a supermarket to do your groceries. What's common about these things? Well, if we wanna say as broad of a definition of a market, you could view it as a market forms, let me write this down. Well, this is an informal definition. Forms, when multiple parties, multiple parties, exchange things of value. Exchange things of value. And let's see whether our notions of a market hold up or whether this definition holds up when we think about our notions of a market. Well in a stock market, you have a bunch of people together, and they are trading stocks, and usually what happens is, let's see if this is a stock right over here, these are all different shares of the same stock or different stocks, what typically happens is if there might be parties who want to sell this stock and then there's other parties who want to buy this stock and then whoever of the buyers is willing to offer the most for that share, well then that money will go to the seller of the stock and then that stock will go to the party that just paid that amount. And so you see that there's an exchange of things of value. At a supermarket, you will see aisles and aisles of goods. This is my drawing of a aisle of goods, and there's all sorts of merchandise on 'em and you put 'em in your shopping cart and then when you're done, you go to the checkout, this is my little shopping cart here. You go to the checkout and you pay for them. So once again, you are picking which items you want. There's a price on them, so the seller which in this case is the supermarket, tells you what they're willing to take for those items and then when you put them in your cart and then take it to the checkout, that's you agreeing to pay those prices and so you exchange, once again, money for those things of value. So the money has value and those groceries, whatever you're buying, might have value. Now, we tend to believe that markets are the best way of allocating resources and different markets work different ways. As you could just see, the stock market could be very different than a supermarket and then you could have an auction where things are auctioned off. That would also be a form of a market but the actual mechanics of how things happen would be a little bit different. But a key factor that you need in order for markets to function properly is that you need to have a notion of property rights, and as we've talked about in previous videos, property rights are the idea that things can be owned. Now what does it mean to own something? We almost just take this for granted but it's not some law of the universe, it's something that we just assume culturally and it's become so embedded in us that we just say of course you can own something but at the end of the day, there's three real properties to owning something. One is the idea of a party being able to exclusively own something. So let's say that you own a piece of land that you want to farm on. Well that means that you can exclude others from using that land and whatever that land produces. It might just be a fun place for you to run around or sunbathe or it might be a place where you grow some food that you have the rights to the benefits of that thing. Now another key dimension of property rights is that those rights have to be enforceable. Enforceable. What does that mean? Well, if someone obnoxious wants to come and sunbathe on your property that you have enjoyed running around and sunbathing on, you say hey, you're infringing on my property rights and you should be able to call the police or some type of enforcers to take that person off your land if you really do have property rights and if they are truly exclusive. Or let's say you have property rights on your shoes and if someone were to steal your shoes, you should be able to call the police and say a crime has been committed and the police should enforce those property rights. They should go and get those shoes back and punish that shoe stealer in some way and then last but not least, in order for markets to work well, those property rights have to be transferrable. Remember, a market is all about transferring property rights. In the stock market, one party is giving, is transferring their property rights to that money to the seller of the stock in exchange for getting the seller of the stocks property rights to the actual stocks. If this was not transferrable, then it would actually make no sense to have a market as we know it. So I'll leave you there. These are things in our daily life that most of us take for granted because we live in a market economy and we are used to things like ownership but there are definitely ways of organizing society where it's not as based on markets in terms of who gets what and even today, markets in many sectors or in many parts of the world don't operate as well as they could because some of these dimensions of property rights aren't working as properly as they should. It might be hard to transfer property rights in certain markets. In certain markets, if someone, let's say, just takes over a property, the government might not be so good at enforcing those property rights. Or it might be hard to keep one party from using something of value that is, at least according to the property rights, owned by someone else.
Khan_Academy_AP_Microeconomics	Perfect_inelasticity_and_perfect_elasticity_of_demand_Microeconomics_Khan_Academy.txt	To get a better intuition for the price elasticity of demand, I thought I would take a look at some of the more extreme cases and think about what types of elasticities of demand we would see. So this right over here is a vial of insulin. Many diabetics, not all diabetics, but many diabetics need to take insulin daily. They need to inject it in order to maintain their blood sugar level. If they don't do it, bad things will happen to their body. And they might even prematurely die if they don't take their insulin on time. So let's think about what the elasticity of demand might look like for something like insulin. So in one column, I'll put price. And in the other column, I will put quantity. So let's say that insulation right now is going for $5 a vial. And we have a group of diabetics who need insulin. And they're all going to buy the insulin they need. And let's say, in this group, that turns out to be 100 vials per week. So this is in vials per week. Fair enough, that's exactly what they need to do to maintain their insulin. Now, what happens if the price changes? What happens if the price were to go down? Let's say the price were to go down to $1. Well, what would the quantity be? Well, they're not going to buy any more insulin. They're going to buy just what they need in order to maintain their diabetes. And remember, we're holding all else equal. We're not assuming any change in expectations of price. They expect price go up or down or anything like that So in this case, they'll still just by 100 vials. Now, what happens if the price went up a ton? And what happens if the price went to-- what happens if we went to $100 a vial. Well, it would be hard for them. But they need it to survive. So it's going to squeeze out any other expenses that they need to spend money on. And so they still will buy 100 vials a week. And so you could keep raising price, within reason. And they would still buy the same quantity. Obviously, if you raise it to $1 billion, then they would just wouldn't be able to afford it. But within reason, they're going to buy 100 vials per week, no matter what the price is. So this is an example of perfect inelasticity. Another way, so if you think of the physical analogy that we talked about with elasticity. It's like a brick. It doesn't matter how much, within reason once again, any amount of force pulling or pushing that a human could put on a brick, it's not going to change. It's not going to deform the brick in any way. And likewise, any change in price within reason, within reason here, isn't going to change the demand in any way. It's perfectly inelastic. And if you want to do the computation, you could look at inelas-- you could figure out the demand elasticity for, let's say, when you're going from a price of $5 to $1. So the price went down by 4. And the quantity changed by 0. So your percent change in quantity, so delta percent-- I'll write it-- percent change in quantity is equal to 0. And then, your percent is going to be over your percent change in price if you use the averaging method. It was-- it would be going down by 4 over an average of 250. It'll be a fairly large number. But at 0 over anything is still going to be 0. So it doesn't matter what that thing is over here. Your elasticity of demand in this situation is 0. And if you wanted to see what this demand curve would look like, let's plot it. So this right over here is my price axis. And that is my quantity axis. And so no matter what, let's say this is a quantity of 100 of vials per week. That's true when the price is $5. So that's true in the prices $5. They're going to demand 100 vials a week. That's true when the price is $1. They're going to demand 100 vials a week. And that's true, if the price is $20 or $100 or whatever. They're going to demand 100 vials a week. And so a perfectly inelastic demand curve would look like this. It is a vertical line. It doesn't matter what price you pick. The quantity demanded is always going to be the exact same thing. Now, let's go to another extreme. So this is perfectly inelastic. You can imagine. Well, what is perfectly elastic. Something that changes a lot if you have a small percentage change in price. And to think about that, let's look at these two vending machines. And you see that they both do sell cans of Coke. That's a can of Coke there. That is can of Coke there. And let's say, starting off, the can of Coke, let's say that they cost $1 in each vending machine. And we're going to assume that this one, remember all else equal. So we're going to assume that this vending machine right over here doesn't change. Does not change. So it's just going to be consistently charging $1 for a can of Coke. And they're sitting next to each other. And it looks like they have a little coffee machine in between right over here. So let's think about the demand curve for this, for Coca Cola in this vending machine right over here. So let's think about the price and the quantity. So I'll do-- let me do price column and quantity demanded. So let's say if the price is $1. So if the price is $1, then just odds are, it's going to get about half of the sales per week. And let's say that ends up being, I don't know, let's say that ends up being 100 cans. This is in cans per week. Now what happens? And let me put some decimals here. So this is $1.00. The price is $1.00. It sells 100 cans per week. And probably this one also would also sell about 100 cans per week. Now, what happens if we have a very, very small change in price. So if we change, if we go from $1.00, instead of $1.00, we are at $0.99. What's going to happen? So this, remember, this machine right over here is not changing. This is-- we're talking-- our demand curve is for the quantity of Cokes sold from this machine. And the price was for this machine. So if this machine is even a penny cheaper. And assuming that people, there aren't lines forming and things like that, people are just always going to go to this machine. If it's easy enough, if there's no difference, they're always going to go to this machine. So this machine will be able to get, will sell all the Cokes. So it's going to sell 200 Cokes. Now, what happens if, instead of lowering the price by a penny, you raise the price by a penny. So instead of $1.00, your at $1.01. Well, now everyone's going to go to the other vending machine. They're going to say, oh, we don't-- even a penny, might as well walk to this one. Assuming everything else is equal. So then, they're going to sell 0. And so what would the demand curve look like here. Let's plot it out. So this is the price. This right over, this axis right over here is quantity. And this is in cans per week. And so this is 0. This is 100. And then, this is 200. And then this is a price of $1. That's $1. So at $1, the quantity demanded is 100 cans. Fair enough. Now, at $0.99, the quantity demanded is 200 cans. So at $0.99, the quantity demanded is 200. So $0.99 is right below that, it's 200. So it's right over there. It's like right, right, there's a little bit lower. And $1.01 a little bit over here, the quantity demanded is 0. So the demand curve here is looks something like that. So it's going to be almost horizontal. So it's going to be approaching perfect elasticity, very small changes in price end up with these huge changes, huge changes in percent quantity demanded. And I courage to work out the math to see here, that you will get a very large number for elasticity. And so something that is, this is approaching perfect elasticity. A truly perfect elasticity would be something that is a horizontal line. So in this case, so over here, our elasticity of demand-- and I'll talk about the absolute value of it, is 0. And over here, the absolute value of our elasticity of demand is infinity. '50 Because, remember, it's percent change in quantity over percent change in price. When you go from either, from one scenario to another over here, you're percent change in price is very small. It's roughly about 1% in this scenario right over here. Changing the price up or down about 1%. But then, you see your quantity is changing, depending on which one you're looking. Your quantity is changing on the order of 50% to 100%, from that 1% change in price. So you have a huge elasticity of demand here. It would be a real-- it would actually be a number. But as you can imagine, as it becomes more and more sensitive, as quantity demanded becomes more and more sensitive to a percent change in price, this curve is going to flatten out completely. And you will have an infinite, absolute value of your elasticity of demand.
Khan_Academy_AP_Microeconomics	Taxation_and_dead_weight_loss_Microeconomics_Khan_Academy.txt	Voiceover: Let's look a little bit at the market for hamburgers. This is the supply and the demand curve for the price and the quantity of hamburgers sold per day. If we have a completely unfettered market, no intervention, no taxes, nothing like that, then we see we have an equilibrium price and an equilibrium quantity. The equilibrium price looks like it's about $3.75 per hamburger. The equilibrium quantity looks like it's about a little bit more ... Maybe if I draw that line a little bit differently, the equilibrium quantity looks like it's about $3 - Sorry, it's about 3.5 million hamburgers per day. Just to review what we've talked about before, up here, below the demand curve and above the price. The price equals $3.75 line, right over here. This is how much value, this is how much benefit the consumers are getting above and beyond what they have to pay. That is the consumer surplus. Then, between this price equals $3.75 line and the supply curve, you have your producer surplus. This is how much more the producers are getting for each hamburger, relative to what their opportunity cost of producing that incremental hamburger was. This right over here is the producer surplus. Now, let's say ... Actually these numbers are quasi-realistic. I have a 3.5 million hamburgers per day. I actually looked it up before this video. It looks like McDonalds, at least based on the information I got, sells a little bit over 4 million hamburgers per day in the United States. I didn't clarify whether this is just hamburgers from one vendor or multiple vendors, but it's not a crazy number of hamburgers to sell in a fairly large country. For the sake of this, it's not necessarily McDonalds hamburgers, we're just talking about this is the total market for hamburgers in a country. We're making the simplifying assumption that all hamburgers are created equal, which we know is not true. Now, the government in this hypothetical civilization says, "Wow, a lot of hamburgers are being sold. "We need more revenue for the government "to do other things," or maybe to pay off their debt or whatever they need to do. So they decide to tax hamburgers. They want to tax hamburgers. They're going to make it very simple. They're not even going to do a percentage. Most sales taxes tend to be a percentage of the price, but instead they're just going to do a tax of $1 per hamburger. Let's think about what this does to the surplus, to the price at which transactions will go on and what people will have to pay versus what they will have to get. At any given point, if we look at the supply curve right over here, in order to get someone to produce that very first hamburger, they have to get at least $2 for it, because that's their opportunity cost. They could use those exact same resources, that land, the labor, whatever else, to produce something else that has $2 of value, so you have pay them at least $2 in order for them to produce hamburgers. The more hamburgers you want the suppliers to produce you have to pay them more and more for those incremental hamburgers, because they're going to start using resources that might have better used for other things and that are not as efficiently used for hamburgers. You have to pay them more and more and more. This is what the supply curve that I originally drew in magenta is what the suppliers need to see in order to produce a certain quantity. If you want them to produce 3 million hamburgers, you have to be willing to pay $3 per hamburger, because that's their opportunity cost of those incremental hamburgers up here. Now, let's think about what happens when you add the tax. This is what the suppliers are going to get or the producers are going to get, but when you put a tax, the consumers are going to have to pay a dollar more. Over here, in order to produce this much, the suppliers are going to have to get $3 per hamburger, but then the consumers are going to have to pay a dollar more, so they're going to have to pay $1 more. In order to get the suppliers to produce 2 million hamburgers, you're going to have to pay them this much, you're going to have to pay them about $2.50, but then the consumers are going to have to pay a dollar more than that. They're going to have to pay that much. In order to get them to produce it all, you're going to have to pay at least $2, but then if the suppliers or producers are getting $2, the consumers are going to have to pay a dollar more for the tax. One way to think about it is the supply curve, from the consumer's point of view, is going to be shifted a dollar more than the supply curve from the producer's point of view. It's going to be shifted up $1, so it's going to look something ... I can do a better job than that. It's going to look something like that. At every point, because this is a fixed dollar, it's not a percentage, at every point, this distance right over here is going to be $1. What happens there? From the consumer's point of view, what we have is now a new price that they're willing to consume at, because now this reality is not possible anymore. There's no way for the consumers to pay $3.50 and for the producers to see $3.50, as well. So we get to a new equilibrium price and equilibrium quantity now, because now, since this is from the consumer's point of view, the point at which they intersect is right over there, which is about a little bit over $4 per burger and it's a slightly lower quantity. It's about, let's just say just for round numbers, that's about 3 million burgers per day. What happened there? Before this whole area was a total surplus. Below this green line was the producer surplus, above the green line and below this curve right here was the consumer surplus. Now we've lost part of it. We've lost this part right over here, so this is our dead weight loss. This is no longer part of the total consumer and producer surplus. That is dead weight loss. The taxation got us from an efficient situation, where we had that maximum consumer and producer surplus. This is our dead weight loss over here. How much revenue is the government going to get now? Well, if we assume that this is 3 million, they're going to have 3 million burgers. This is 3 million right over here. They're going to have 3 million burgers times a dollar per burger. Let me do it this way. This length right over here is going to be the area of this rectangle that I'm doing in orange. This length right over here is 3. That length right over there is 3 million and then height is that dollar. Let me shade it in. The height is that dollar right over there. This is going to be $1 height. The tax revenue that the government is going to get is 3 million times $1. 3 million burgers times $1, which is going to be $3 million per day, which is interesting, because maybe the government officials thought they were going to get more, because they look at the projections and they say, "Wait. "There's going to be 3.5 million burgers sold per day, "so I'm going to get $3.5 million." What they didn't realize is that they're making the burgers more expensive, so there's going to be a lower quantity demanded. The actual clearing quantity or the actual equilibrium quantity now is only going to be 3 million. The way we see it, it removed this surplus here, from both the consumer surplus and the producer surplus and no one's getting that, not even the government's getting that. No one's getting that white part right over there and this orange part right over here is eating into the consumer surplus, so now they're paying more than ... Another way to think about it is the difference between the benefit they're getting and what they're paying at any given point, for any given incremental consumer, is now less and the producer surplus is less. The excess of what they're getting for each hamburger versus their opportunity cost is now less. The producer surplus has now been shrunken back to this area right over here and these are curves here, so we can't just do simple geometry to figure out the area of triangles. We would actually have to do a little calculus to figure out the area of these curves. Then the consumer surplus has been pushed back to this area above the orange right over here. You see, governments, for the most part, have to do some type of taxation in order to get revenue and it could be income tax or it could be a sales tax, like this right over here, but when they do it, it gets us into a non-efficient state and it does cause some, depending on how these curves are shaped, it does cause some dead weight loss. Some benefit in excess of what had to be paid, some of that disappears, but it allows, at least, the government to get revenue, depending on whether you think that's a good thing or not.
Khan_Academy_AP_Microeconomics	Market_demand_as_the_sum_of_individual_demand_AP_Microeconomics_Khan_Academy.txt	- [Instructor] In this video, were going to think about the market for apples, but the more important thing isn't the apples, it's to appreciate that the demand curves for a market are really the sum of the individual demand curves for every member of that market, and most markets will have many tens or hundreds of thousands of actors in it, maybe millions or tens of millions of actors in it, but for the sake of simplifying things, we're going to assume that the apple market has only two buyers, and we have their demand curves right over here. This is the demand curve for buyer one, and this is the demand curve for buyer two, and so if the vertical axis is price, and maybe this is price per pound of apples, and quantity, let's just say that's pounds per time period, maybe pounds per week, we can see that from buyer one's demand curve that at a price of one, two, three, four, five dollars per pound, they don't wanna buy any pounds. At a price of three dollars per pound, they're willing to buy one pound per week. At a price of one dollar per pound, they're willing to buy two pounds per week. We can similarly look at the demand curve for buyer two, and sometimes you'll see this in table form where it's called a demand schedule, but you can see at one, two, three, four, five, six, seven, at seven dollars, buyer two is not interested in apples at seven dollars a pound. At five dollars a pound, they are interested in buying two pounds of apples per week. At three dollars per pound, they're interested in buying, so let's see this is one, two, three, four, five pounds per week, and at one dollar per pound, they're interested in buying six, seven, eight pounds per week. So based on this data here, buyer one and buyer two are the only individuals in this market. Once again, a huge oversimplification. What would the market demand curve look like? Pause this video and try to think that through. Well, if we go to the various prices, so let's see, at a price of seven dollars, there is not going to be any interest in any apples. So, I could maybe put that right over there at a price of seven dollars, but what happens is the prices goes down and we could just sample what happens when we get to a price of five dollars? Buyer one is still not interested, but buyer two is now willing to buy two pounds per week. And so, at a price of five dollars, the market as a whole is willing to buy two pounds from buyer two and zero pounds from buyer one, so we'll have a total of two pounds. So we're right over there. So that is at five dollars per pound. The market is willing to, is demanding a quantity of two pounds per week. And then let's go to three dollars. At three dollars, now, buyer one would buy one pound per week and buyer two would buy five pounds per week. So in total, there would be six pounds demanded or the quantity demanded would be six pounds. So three dollars, the quantity demanded is three, four, five, six. So that would put us right about there. And then last but not least, and once again, I'm just sampling these points to make the point to you that we really would just add, we would take the sum of these curves but we're kind of stacking them, we are stacking them horizontally as opposed to vertical because for any given price, we're adding up the quantities. So let's go to one dollar a pound. At one dollar a pound, buyer one is willing to buy two pounds, and at one dollar a pound, buyer two is willing to buy eight pounds. You put those together, two plus eight, you get to 10 pounds. So this was two, three, four, five, six, seven, eight and then nine and ten, we're going a little bit off the screen here, I could have planned better for it, but let me go all the way over here so I'll extend my axis so that's nine and then this is ten so that at one dollar, the market would be willing to buy ten pounds per week. And you could sum at any other point or any other points in between and what you would do is you would get a market demand curve that looks a little something like this. And you can see, visually, what has happened here. For any price value, we are summing the quantities for all of the buyers in the market. Now here, there's only two buyers. Now if you were doing this in the real world, you might be dealing with millions of buyers, but this is just to understand how a market or where a market demand curve is actually coming from.
Khan_Academy_AP_Microeconomics	Total_product_marginal_product_and_average_product_AP_Microeconomics_Khan_Academy.txt	- [Instructor] In previous videos, we introduced the idea of a production function that takes in a bunch of inputs. Let's call this input one, input two, input three. And that based on how much of these various inputs you have, your production function can give you your output. In this video, we're going to constrain all of the inputs but one, to really take it down to how does our output vary as a function of one input. And as we do that, we're going be able to understand these ideas of total product, marginal product, and average product. So, to give you a tangible example, let's say that we are running an ice cream factory and we care about how much our ice cream production per day varies as a function of the number of people working in the factory. So, let me write this down. So, per day ice cream, ice cream production, production. And so, let me make a table here. So, in our first column, I am going to put our labor, which you could view as the input that we're going to see how does that drive output. So, I will put Labor. So, you could view this as workers per day. Workers. And we're going to see how our output varies whether we have zero workers, one worker per day, two workers per day, or three workers per day. Now, our next column would just be our output, and we'll say that's our total product as a function of labor. TP standing for total product. And let's say that we know, if we have zero people working in our ice cream factory, well then, we're going to produce zero gallons of ice cream, and let's just assume that our output is in gallons, and it's gallons per day. If we have one worker at our factory, well then, we're going to be able to produce 10 gallons a day. If we have two workers in our factory, we're going to produce 18 gallons a day. And if we have three workers in our factory, let's say we can produce 24 gallons a day. Fair enough. Now, I'm going to introduce an idea, and you've seen this word marginal, perhaps, in other times in your life. I'm going to introduce marginal product of labor. And the way to think about marginal, that's how much for every increment of one thing, how much more of the other thing do you get? So here, our marginal product of labor says, for each incremental unit of labor, for each incremental person working there per day, how many more gallons of ice cream am I producing? So, my marginal product of labor, when I go from zero to one worker, I'm able to produce 10 more gallons from that first worker. Now, what about when I go from one worker to two workers? Well then, I go from 10 to 18 gallons. So, that second person gets me an incremental eight gallons per day. And then as I go from two people working there to three people working there, well, my total product goes up by six. So, my marginal product of labor for that third worker is going to be six. Now, there's something interesting that you're immediately seeing here, and this is actually pretty typical, is that your marginal product of labor will oftentimes go down the more and more people that you add. And you might say, why is that the case? Well, they're just not gonna be quite as productive. That second person might be waiting while the first person is using the mixer and that third person is gonna be waiting while the first person and the second person, maybe they're using the restroom or something and the third person has to go. And you can imagine, you add four, five, six, at some point, you're not even be able to fit people into the factory, and so you're going to have what's known as a diminishing marginal return, and you see that right over here. As you're adding more and more labor, your marginal return is getting smaller and smaller, so this is a diminishing marginal return. Now, the last concept I'm going to introduce you to in this video is that of average product, and this is average product as a function of labor. So, AP for average product. And all that is, is our total product divided by our labor. So over here, when we have one worker, our total product is 10 gallons, and we're going to divide that by one worker. So, our average product per worker is going to be 10 gallons. Now, when we have two people working per day and we're producing 18 gallons per day, our average product as a function of labor is gonna be 18 divided by two, which is gonna be nine gallons per worker per day on average. And then in this last situation, it's going to be 24 divided by three, which is eight gallons per worker per day on average. And you can see this visually as well. I can draw this on a curve. Let me do that. So, if on our horizontal axis, I have our labor units, which is workers per day, so one, two, and three. So, this is labor right over here. In our vertical axis, I'll have our total output. So, total product, I could say. So let's say that's 10, 20. Let's say that is 30 right over there. Well, this first one right over here, when we have one person working in the factory, we produce 10 gallons per day. And this is total product right over here. When we have two people working in our factory, we produce 18 gallons a day. So, it's gonna be just like that. And notice, the slope has gone down a little bit. We have a certain slope here, but it's a little less steep there. And that steepness of that line or of that curve, that tells you about the marginal product. So, it's a little bit less steep, so our marginal product of labor has gone down a little bit. We're having diminishing marginal returns. And then last but not least, when we have three people working, we're able to produce 24, so three and 24 might be right over there. And once again, we can see our diminishing returns gets even a little bit flatter. We go from zero to one, we added plus 10, and you can see that there in the marginal product of labor. And then as we add one more person, it goes plus eight. And then we add another person, it guess plus six. So in general, if you see total product as a function of labor, or total output as a function of labor, and the curve is getting less and less and less steep, well, that tells you that your marginal product is going lower and lower and you're getting diminishing marginal returns.
Khan_Academy_AP_Microeconomics	Comparative_advantage_specialization_and_gains_from_trade_Microeconomics_Khan_Academy.txt	Let's now move away from the world of the hunter-gatherer and into the dinnerware market. So let's say we're going to talk about two products -- two types of dinnerware. We'll have cups on this axis, and we will have plates on this axis. And let's say we have a producer, Charlie, and if he were to focus all of his time on cups, he could produce - let me put these [labels]10, 20, 30. So if he were to focus all of his time on cups, he could produce 30 cups, and if he were to focus all of his time on plates, he could produce 10 plates. And we're going to assume he has a linear Production Possibilities Frontier. So, this is what his PPF is going to look like. We draw a little bit, actually connect the 2 dots, so that's.. I want to make it more looking like a line, so that's about as good as I can do. So that right over there is the PPF for Charlie. Now let's think about his opportunity cost. And because this is a linear PPF his opportunity cost does not change. The slope of this line is not changing. It's not that bow-shaped curve that we saw for the hunter gatherer. So it's going to be a fixed opportunity cost for one product relative to the other, at any point along this production possibilities frontier. So let's say we're sitting over here, this will just make things simple to just think about the end points, and he's producing 30 cups, what is his opportunity cost of producing 10 plates? Well to produce 10 plates, he's going to have to give up those 30 cups. So his opportunity cost of producing 10 plates, is equal to 30 cups. Or if you want the opportunity cost for one plate, you just divide both sides by 10, and so you get the opportunity cost of 1 plate, is equal to 3 cups. That's fair enough. Now let's think about the same scenario or let's think about another producer, in this market for dinner ware. Let's call her Patty. If Patty focused all of her time on cups she could produce 10 cups in a day and if she focused all of her time on plates, she could produce 30 plates in a day. So that is.. and she also has a linear production possibilities frontier, so that right over there is the PPF for Patty. And let's think about her opportunity cost for producing a plate. So the opportunity cost, if she's sitting right over here, and she was focused all on cups, and if she wanted to produce 30 plates, and I'm intentionally using the end points to make the math more obvious. If she wanted to produce 30 plates then she would have to give up 10 cups. So her opportunity costs to produce 30 plates is equal to 10 cups. Or if you divide both sides by 30, the opportunity cost of her producing 1 plate, in terms of cups, is 10 divided by 30, is 1/3, 1/3 of a cup. Now this is interesting, we can now compare their relative opportunity costs. The opportunity cost for Charlie to produce a plate is 3 cups, the opportunity cost for Patty to produce a plate is 1/3 of a cup. So for Patty, especially when you measure it in terms of cups, it is cheaper for her to produce a plate. She has a lower opportunity cost than Charlie does in producing plates. So relative to Charlie, we say, because her opportunity cost is lower in producing plates, 1/3 relative to 3, we say that Patty has the comparative advantage in plates, relative to Charlie. And it's not just because she can produce - We'll see situations in maybe the next video where we'll actually show this. It doesn't even have to be the case that she can produce more plates in a given day. This is not why she has a comparative advantage. This is called an absolute advantage, and we'll talk about that more. She has a comparative advantage because her opportunity cost is lower. Her opportunity cost for producing a plate is lower than it is for Charlie. Now let's think about it the other way around. Who has a comparative advantage in cups? Well, if we divide both sides of this right over here by 3, well let's swap both sides, so the opportunity costs for Charlie of producing 3 cups, is equal to 1 plate. Or if you divide both sides by 3, opportunity cost of 1 cup is 1/3 of a plate. If we go to the situation for Patty, let's swap these 2 around, the opportunity cost for 10 cups is 30 plates. If you divide both sides by 10, the opportunity cost of 1 cup is equal to 3 plates. And obviously, and we've talked about this before, the opportunity cost of 1 incremental unit is the same thing as the marginal cost of a cup. But anyway, who has the lower opportunity cost for producing cups? Well, let's see, Charlie can produce a cup, or Charlie's opportunity cost for producing an extra cup is 1/3 of a plate, and Patty's is 3 plates. So Charlie has the lower opportunity cost for producing a cup. So, it's only 1/3 plate relative to 3 plates. So this is where Charlie has the comparative advantage. What we're going to see is if both of these parties specialize in their comparative advantage and then trade, they can get outcomes that are beyond each of their individual production possibility frontiers. So what we can see is, for example, they can get an outcome where they are each able to get 15 cups and 15 plates, which would have been impossible left to their own devices. So let's see how they can actually do it. So we've said that Charlie has a comparative advantage in cups. His opportunity cost of producing a cup is lower than it is for Patty. It's only 1/3 of a plate relative to 3 plates. So let's make him specialize in cups. So cup specialties. So he's going to specialize in cups, and Patty, for the same reason, is going to specialize in plates. So Charlie specializing in cups means he's going to focus only on cups. So he's going to produce 30 cups every day. And Patty specializing in plates means that she's going to produce 30 plates every day. (Let me do this in a different color: magenta). She's going to produce 30 plates every day. Now imagine, I'm going to make an assumption here, but imagine that they both do that but they don't each only want to have what they're producing they want to have some combination of them, so they decide to trade. And I'm going to fix the price here. We're going to talk more about markets in the future. But I assume that they agree to trade at 1 cup for 1 plate. And this makes sense for either of them because this trading price, or this market price, is lower than their opportunity cost. So here's Charlie, he's got all of these cups, left to his own devices, if he wanted an extra plate he would have to spend 3 cups but now in the market, with this price over here, he only has to spend 1 cup for an extra plate. So, this makes sense for him because the market price is lower than his opportunity cost. So he would definitely rather get a plate in the market than have to do it by producing it himself. It‘s cheaper this way. And the same thing for Patty. She has all of these plates, but if she wants a cup, left by herself, she would have to spend 3 plates to do it. She would have to give up 3 plates. But now in the market, she would only have to give up 1 plate. So this is a good deal, this is lower than her opportunity cost. So she'll want to transact. And so they can do, each of them, so for example, Charlie could keep trading cups for plates and he could end up anywhere on this line over there. And Patty could actually do the same thing: she could trade the cups for plates and end up someplace over there. But obviously where they end up is dependent on how much the other one is willing to trade. But let's say that they both want to get to that 15-15 scenario so they can both trade 15 cups to the other person. So Charlie could trade 15 cups for 15 plates and obviously Patty would be trading 15 plates for 15 cups. And they would both be able to get right over there. Which is a situation that was unattainable left to their own production possibilities. So hopefully you found that interesting. By specializing they could get these gains of trade. They specialize in their comparative advantage.
Khan_Academy_AP_Microeconomics	Monopolist_optimizing_price_Marginal_revenue_Microeconomics_Khan_Academy.txt	>>Now that we figured out the total revenue given any quantity, and we've also been able to express it algebraically, I want to think about what the marginal revenue is at any one of these points. To think about marginal revenue, marginal revenue is just how much does our total revenue change, given some change in our quantity. Then later, we can use that so that we can optimize the profit for our monopoly over here. I'm going to try to do it without calculus. It actually would be very straightforward to do it with calculus because we're essentially just trying to find the slope at any point along this curve, but I'll try to do it algebraically and maybe it will even give you a little intuition for what we end up doing eventually in calculus. The first thing I want to do is essentially find the slope, the slope right over here. The best way to find the slope right over here is say how much does my total revenue change if I have a very small change in quantity? If I have a very small change in quantity, how much does my total revenue change? Let me think about it this way. The other ones I will be able to approximate a little bit easier. Let's think of it this way. If my quantity is 0, my total revenue is 0. That one's easy. If I increase my quantity very, very, very, very little, so let's just make it 0.001, what is going to be my total revenue? We could think about it in terms of this curve right over here, or we could just use this expression, which we derived from price times quantity, and we will get, I'll get my calculator out, if our quantity is .001, our total revenue is going to be negative ... Let me turn the calculator on. Total revenue is going to be -.001², squared, so that's that part, plus 6 times .001, 6 times .001. That's going to be our total revenue. It's going to be 0.005999. It's 0.00599. Now we can figure out or get a pretty good approximation for that marginal revenue right at that point. Our change in quantity is .001, so our ΔQ, this right over here is 0.001. That's our change in quantity, and our change in revenue is 0.00599, and so we just have to divide. We just have to divide .005999, that top one, our change in total revenue divided by our change in quantity, divided by .001. We get 5.99999. If you try it with even smaller numbers, if you tried this with .00000001, you'll get 5-point, and you'll get even more 9s going on. The closer that you get, the smaller your change in, and this is what you essentially do in calculus. You try to find a super small change right over here. This is essentially going to be 6. Our marginal revenue at this point is essentially going to be 6. What I want to do is I'm going to plot marginal revenue here on our demand curve as well or on this axis where we've already plotted our demand curve. When our quantity is 0, our marginal revenue, if we just barely increase quantity, the incremental total revenue we get is going to be 6. I'll just plot it. I'll just plot it right over there. That makes sense. The marginal benefit in the market is 6, right at that point. If we were to just sell a drop of orange juice or I guess we're selling oranges in this case, not juice, but if we were to sell a millionth of a pound of oranges, we would get the equivalent of roughly $6 per pound for that millionth of a pound because that's the marginal benefit for that very first incremental chunk of orange out there in the market, so it makes complete sense. Now let's think about the slope at these other points. These, I'm going to approximate. I could do it this way, but I'll just approximate it. I'll just approximate it by using other points. If I want to find the slope right over here, when our quantity is equal to 1, the slope would look like, the slope would look like that. I'm going to approximate it by finding the slope between these two points. I am going to approximate it, and actually, it's going to be a very good approximation. I'll do it later with calculus to show that it is a very good approximation. But I'm going to approximate it by the slope between these two points. Between those two points, our change in quantity is 2, and our change in total revenue is 8. Our change in total revenue is 8. When we produced 2, or 2,000 pounds, our total revenue was $8,000. So we have a change in total revenue of 8, or 8,000, I guess we could say, divided by a change in quantity of 2,000, so our marginal revenue at this point is 8 divided by 2, or 8,000 divided by 2,000, which is $4 per pound. When our quantity is 1, our marginal revenue is $4 per pound. It is $4 per pound, just like that. Now, let's think about the marginal revenue when our quantity is 2. To do that, I'm going to find the slope between these two points. We really want to find the slope of that line, but it looks like the slope between these two points is a pretty good approximation. It's actually almost an exact number because of the way that this is just a parabola, so we can actually do this. But anyway, this is fairly straightforward. Once again, our change in quantity is 2, and our change in total revenue, our change in total revenue is, we're going from 5 to 9, which is 4. This was 9 right over here from the last video. Or you could say it's $4,000 divided by 2,000 pounds gives you $2 per pound. Our marginal revenue right over here, if we have quantity of 2, is $2 per pound. Right at that point, for that incremental millionth of an ounce that we're going to sell them oranges, we're getting the equivalent of $2 a pound of increased total revenue from doing that. Let's just do one more point here, and I think you'll see why I'm only going to do one more point. If we try to go up here, and we try to figure out what is the marginal revenue or if we essentially say what is the slope there, how much do we get an increase in revenue if we just barely increase our quantity, and this is actually easier to look at. This is a maximum point right over here, in the calculus terms. The slope up there is 0. We can even see that by approximating the slope between the slope between these two points. We have some change in quantity, but we have no change in total revenue, so right at that point. Right over here, the slope is barely positive. Right at that point, the slope is 0, and then right past it, it becomes barely negative. But right at that point, our marginal revenue is 0. When our quantity is 3,000 pounds, our marginal revenue is 0. Then after that, our marginal revenue gets negative. Over here, our marginal revenue gets more and more negative. But something very interesting happens. When we plot our marginal revenue curve, or our line, in this case, we are getting a line, we are getting a line, we are getting a line that is twice as steep, twice as steep as our demand curve. This is actually generalizable. If we have a linear demand curve like this, it can be defined as a line, then your marginal revenue curve for the monopolist will also be a linear downward-sloping curve or downward-sloping line, and it will have twice the slope. This slope over here was -1. This slope over here is -2. For every increase in quantity, the price goes down by 2; increase in quantity, price goes down by 2; increase in quantity, price goes down by 2. This is marginal revenue. Let's remind our self, we've been doing all of this algebra and all of this math here, what is marginal revenue telling us? This was the demand curve. It tells us for any given price what quantity is demanded or for any given quantity, what is the incremental marginal benefit, or I guess what's the price at which they could sell that quantity. From that, we were able to figure out the total revenue as a function of quantity, and from that total revenue, we were able to say, well, look, if at any of these quantities, if we were to increase a little bit more, if we were to increase quantity a little bit more, how much is our revenue increasing? Obviously, we want to keep increasing quantity while our revenue is ... while the marginal revenue we get is larger than our marginal cost. I'll take that up in the next video.
Khan_Academy_AP_Microeconomics	Perfect_competition_Microeconomics_Khan_Academy.txt	- [Instructor] In our study of the different types of markets, we are now going to dive a little bit deeper and understand perfect competition. Now this notion of something being perfectly competitive, you might have a general idea of what it means. You might feel like it's very competitive, that there's a lot of people there maybe competing for your business, or maybe there's a lotta buyers, and there are a lotta sellers. And that is generally true, but we're trying to be economists here, so we wanna be very precise with our language. So when economists talk about perfect competition, they're talking about this somewhat very abstract state where you have many buyers and sellers, many sellers and buyers. Now that doesn't seem too abstract so far. We can imagine a lot of markets that have many sellers and buyers. Now another thing that defines perfect competition from an economics point of view is that they're selling identical, identical products or services, products, products or services. Now this one seems a little bit harder because even when you can imagine a fairly competitive market, does everyone sell exactly the same thing? Well you imagine certain markets, maybe the market for water or maybe the market for some type of energy or maybe the market for produce, gets pretty close to identical products or services. So so far it doesn't seem like that abstract of a thing. Now another aspect of perfect competition is that every agent, so that would be the buyers, the sellers, the producers, the consumers, they have perfect information, perfect information. Now what does perfect information mean? It means that every participant in the market, the buyers and the sellers, they all know exactly what is happening in the market. So what goods or services are selling for what price and who is selling to whom. So once again, this gets a little bit more abstract because to get truly perfect information, you can't, not everyone in a market will always know everything that's going on. So once again, this is a little bit of an abstract idea that economists have introduced to be a little bit more precise. And the last aspect we're going to talk about, and this is also something that is a bit idealized that doesn't truly exist in the real world, things close to this exist in the real world, is that there is no barriers, barriers to entry or exit. Now we already mentioned some markets, say the market for agriculture. That doesn't quite have no barriers to entry or exit. You would somehow have to get land, you would have to get seeds, you would have to get fertilizer, you would have to hire people to put the seeds in and to harvest the crops. And so almost any industry, any market you imagine, will have some barriers, but this is an idealized notion that economists like to think about, and of course in the real world things might approach this or be closer to perfect competition than say other markets. But when you're in this situation, let's analyze what will be happening. So we can look at the market as a whole for whatever this product and service is. So let me draw price versus quantity here for the market as a whole. So this is price, and this is quantity. And this is the market right over here. And so, we've seen this multiple times in our economics journey. That you have an upward-sloping supply curve, and once again this is for the entire market. Let me do this is in a different color. So you have an upward-sloping supply curve like that. And you would have a downward-sloping demand curve like that. And we know what the equilibrium price and quantity would be for the market. So this right over here would be the equilibrium, equilibrium quantity for the market, and this right over here would be the equilibrium price for the market. Now how would this affect the decisions for the firm in perfect competition? Well let's draw, let's draw a similar analysis, but now at the firm level. So on this axis, you could view this for the firm, and so this is going to be the firm right over here, one of the participants in the perfect competition, one of the producers, one of the sellers. So on this axis, you could view this as price. You could also view this as marginal revenue. And you could also view this as marginal cost because we're going to plot the different curves here. And then on the horizontal axis, we're going to have quantity again, but this is once again the quantity that the firm produces. Now, first of all, we could think about the marginal cost for the firm, and we've seen this multiple times. That the marginal cost for the firm, it might look something like this. It over time might trend upwards something like this where at some point every incremental unit is costing more and more to produce. Maybe it's harder to get the resources, harder to get the labor, whatever you wanna say. So that's the marginal cost curve, fairly typical for a firm. And then we could think about their average total cost. And so the average total cost curve might look something like this. So draw something like this. So our average total cost, we've seen this multiple times. Now what is going to be the marginal revenue for this firm that is operating in perfect competition? Well when it's operating in perfect competition, it just has to be a price taker. So every unit it sells is just going to get the market price for that unit. So in perfect competition, the firm, every participant that is really identical in a lotta ways, they're just gonna take that price. Think about it, they won't be able to charge any more for their product or service than the market price because their product or service is identical to everyone else's, and everyone knows it because of perfect information, and they would have no motivation to charge less either. They're just passive. You could view it that way when it comes to price. So if we just take this market price across just like that. This right over here, this price, is going to define the marginal revenue curve for that firm. So let me make this a bold curve right over here. This is going to be the marginal revenue for the firm. For every unit it sells on the margin, that's how much more revenue it's going to get. Now you could also view this as the demand curve for the firm's product. You could also view this as the average revenue for the firm's product. And let me make this clear, this is for the firm, demand for the firm, which is equal to the price that the firm actually gets. So the big takeaway here is in perfect competition, which is this somewhat idealized state that doesn't quite exist in the real world, certain markets can approach it, the firms are passive price takers. They have no say on what the price is going to be, and so it would be rational for them to just produce where their marginal cost intersects with their marginal revenue. Because anything more than that, then for every incremental unit, they're going to be spending more money than they get in terms of revenue. And this passivity goes a little bit against some of our everyday notions of fierce competition. When we think about fierce competition, we often think about many players trying to constantly undercut each other, and in future videos, we'll talk about scenarios where that might happen. And you might think about whether or not you would want certain markets to have perfect competition. Because no barriers to entry means that frankly anybody could get into that industry. So for example, you might not want perfect competition when it comes to someone being say your doctor because you want barriers to entry. You want some level of training. You want some level of experience before someone gets into that service.
Khan_Academy_AP_Microeconomics	Constant_unit_elasticity_Elasticity_Microeconomics_Khan_Academy.txt	We've already talked about linear demand functions that actually have changing price elasticity as we go down the curve. And we've shown the extremes. We've shown things that are perfectly inelastic and things that are perfectly elastic. What I want to do in this video-- and it'll be a quick little video-- is think about can we construct a demand curve, or at least understand what it looks like, that has a constant elasticity across the curve? And just for fun, let's make it a constant elasticity of 1. So it has constant unit elasticity of demand. So let's think about how we can create that. And hopefully, it will give us a bit more intuition on how this elasticity business even works. So let's draw our axes. So there you go, that is price. And that right there is quantity. And let me put quantity. Now let's put some numbers there that'll just help us draw this demand curve that has unit elasticity at every point, at every price, in every quantity. So I'm just going to put some numbers here. So let's say that that right over there is 10. So that's $10 or whatever we're doing. And then this is 10 units per time period, 10 units per week, or 10 units per month, or whatever else. Now, we want the absolute value of the elasticity of demand to be equal to 1 at all points. And we're going to assume that this curve meets the law of demand, which means as price goes down, quantity demanded goes up. So let's think. This is going to be a downward sloping, so really we're going to say that the elasticity of demand is going to be equal to negative 1. If we have a 1% decrease in price, we're going to have a 1% increase in quantity, and vice versa. So let's think about it. If we're up here, where the price is near $10, and maybe where the quantity is closer to $1, let's think about what a 10% movement in price would look like, a 10% movement down. It would be roughly about this size. A 10% movement would be roughly there. And I'm just trying to get the general shape of this curve. I'm not going to go into the deep mathematics or the calculus of it. So that is a 10% price movement down. And we also want to 10% quantity movement up. But remember, our quantity is only at 1. So a 10% quantity movement up would only be 10% of 1. So if we're moving 10% in price downwards, this is a 10% upwards in quantity. So our curve up here would look something like this. It would actually have to be quite steep. Now let's think about what the curve would look over here. Once again, we want 10% for both of them, because we want the price elasticity of demand to be 1 throughout the curve. So if we go over here, a 10% movement in price-- so let's say we're down here, where price is close to 1-- a 10% movement in price is going to be very small. So a 10% movement in price is going to be like that. It's going to be roughly a tenth of a movement. So that's a 10% movement in price. But a 10% movement in quantity demanded over here, it's going to be much larger. It's going to look something like that, because the quantity is approaching 10, so 10% of that is about 1 unit just like that. So at this point in the graph, it would look something like this. It would flatten out a good bit, just like that. And then when the price and the quantity is about the same, so let's say this point right over here, where the price and the quantity is about the same-- so let's say that that is 2, this is 3, this is 2, this is 3 right over here-- your percent movements are going to be the same. But since the price and quantity are the same, the absolute movements are also going to be the same. So at that point, our curve should look something like that. It should have a slope of 1. And so if you connect the dots, you get the general shape of a demand curve that has a price elasticity of demand at negative 1 throughout the curve, or whose absolute value of the price elasticity of demand is 1. So let's just do that. So the curve would look something like-- I'll just draw a dotted line; it's easier to do-- so it'll look something like that. It'll keep getting steeper as we get the quantity closer to 0, and it'll keep flattening out as the quantity grows and grows and grows. Anyway, hopefully you found that interesting.
Khan_Academy_AP_Microeconomics	Marginal_Utility.txt	What I want to do in this video is think about a concept that we've already thought about multiple times in the context of many, many videos. And this is the idea of utility-- utility, which is really just a way of saying how much benefit or satisfaction or value do you get out of getting a good or service. But the angle that we're going to take in this video is going to be slightly different. In the past, when we were measuring benefit or value, we either measured in terms of dollars, where we said, hey, the benefit of getting an incremental Honda Civic was $5,000. And we talk about the incremental-- we're talking about, and we've heard the word many times-- we were talking about the marginal benefit. Or early on, when we talked about the production possibilities frontier and we talked about the marginal benefit of another squirrel, we were talking about it in terms of berries. We were talking about it in terms of another good or service. What we're going to do in this video is just think about it in absolute terms. We're just going to think of some arbitrary way of measuring utility and then just assign values to. What's the value of getting one chocolate bar? And then what's the value that we give to the next chocolate bar and then the chocolate bar after that? And we're going to do the same things about fruit. And from that, we're going to see if we can build up some of the things that we already know about demand curves and how things relate to price and the price of other goods and things like that. And in particular, we're going to focus on marginal utility. So obviously, you could have total utility. If I have four chocolate bars, you could say the total utility I'm getting from all four of them. Or, you could think about marginal utility, the utility I'm getting from the next incremental chocolate bar or the next incremental pound of fruit. And before I move on, there's one thing-- and this was a point of confusion for me when I first learned this-- is OK, I'm using the word marginal utility now. In the past, I've used the word marginal benefit. They sound very similar. In fact, I even used the word benefit when I defined the word utility. How are these two things different? And the simple answer is, conceptually, they aren't. Conceptually, they are the exact same thing. The difference is how the words tend to be used in the context of a traditional microeconomics class. So when people talk about utility, they tend to measure it in terms of some type of absolute measure that they just came up with. You can view them as utility unit, some type of satisfaction units. While when they talk about marginal benefit, they tend to measure it either in dollars or in terms of some other goods. But I've seen either term used either way. So they really do mean the exact same thing. But in this video, we're going to use the term utility, and we're going to come up with a measuring scale, and it's a somewhat arbitrary one. And we're going to use that to come up with some conclusions about the basket of goods someone might purchase depending on different prices. So as you could imagine, I pre-wrote these two things. We're going to talk about chocolate bars, and we are going to talk about fruit. So right here in these little tables here, I've shown the marginal utility of each incremental. In the case of chocolate bars, each incremental bar, and in the case of fruit, each incremental pound of fruit. So this is saying that first chocolate bar-- obviously, if I have no chocolate bars I'm getting no utility from chocolate bars-- and this is saying that that first chocolate bar has a marginal utility. So the utility of that next incremental one is 100. I'm not saying $100. I'm not saying it's equivalent to 100 pounds of fruit. I'm not saying it's equivalent to 100 berries. I'm just arbitrarily saying it is 100. And what matters is not that this is 100 or 1,000 or a million. What matters is how this compares to other things. So for example, if I-- let's say this is 100, and if I know that I like fruit-- a pound of fruit-- 20% more than that first-- Or if I like an incremental-- my first pound of fruit-- 20% more, then I would have to say that the marginal utility of my first pound of fruit is 120. And this is what we said right over here. And if, another way to think about it is, if the marginal utility of the second chocolate bar I get-- because I've already enjoyed a little bit of chocolate bar, and I'm a little chocolated out-- is 20% less than that, then if this is 100, then this would have to be 80. I could have set this to be 1,000 and this to be 800 and this to be 1,200. I could have set this to be 10 and this to be 8 and this to be 12. What matters is, is that they really just have the same ratios between them that really do reflect my actual preferences. So let's just think about this a little bit. My first chocolate bar, I'm pretty excited. I just call it 100. The next chocolate bar, I'm a little bit less excited about it. I've already had some chocolate. My craving has been satiated to some degree, but I still like chocolate. So I'll call that an 80. We could call it 80 satisfaction units, whatever you want to call it. Then the next chocolate bar after this-- now I'm starting to get pretty stuffed, and I'm really chocolated out. And so I'm not getting as much benefit from it. And then finally if you give me another chocolate bar, it's even less. And if we were to list a fifth chocolate bar, I might not want it at all. My marginal utility might go to 0 maybe for that fifth chocolate bar. Maybe that sixth chocolate bar, I have to somehow get rid of it somehow, because I'm so tired of chocolate bars. Maybe it'll have a negative marginal utility. And we could think about the same thing with fruit. The first pound of fruit, I'm pretty excited about fruit. I have a fruit craving. I like that first pound of fruit even more than that first chocolate bar. I like it 20% more. So I get to 120, you could call it utility points or whatever arbitrary unit you want to call it. Then my next pound of fruit, once again I'm having diminishing utility, diminishing benefit as I get more and more incremental pounds of fruit. Now, it's very important to realize this is marginal utility, not total utility. This is a utility I'm getting from each incremental pound. It's positive, so I'm still enjoying that next incremental pound. I'm just enjoying it a little bit less than the pound before. And to realize what total utility is, if I were to have two pounds of fruit, I would have 120 of utility from that first pound. And then I would have 100 from the second pound. And so you would say I had a total utility of 220, you could call them utility units, from both pounds. Now with just the information that I've given here, there's a few things you could say. You could say, well look, my first pound of fruit I enjoy more, 20% more than my first chocolate bar. You could also say that my second pound of fruit, I enjoy it or I could derive about the same amount of value as my first chocolate bar. You could say that my second chocolate bar I enjoy less than my first chocolate bar. You could even say 20% less if these numbers are good. But this still doesn't give you a lot of information about how you would actually spend your money. You might say, well, obviously wouldn't you want to just buy fruit over chocolate bars, or at least that first pound of fruit over that first chocolate bar? Well, you might, but it depends on how much that fruit actually costs. Just looking at this alone, we can just make relative judgments about how much we prefer each incremental bar or each incremental pound or them relative to each other. But it really doesn't tell us how we would spend our actual money. So let's think about things. Let's put some prices on some of these goods and think about how we would actually allocate our dollar given these marginal utility numbers right over here. So let's say that the chocolate bars are $1 per bar. And let's say that the fruit is $2 per pound. So this is going to be per pound. This is going to be per bar. And what we're going to think about is we're going to think about marginal utility for that incremental chocolate bar per price of that incremental chocolate bar. And here the price is going to be at $1 per pound. So here, for that first bar, I'm going to be spending $1, and I'm getting 100 marginal utility points, whatever you want to call it. So I'm getting 100 marginal utility points for that dollar. So I'm getting 100 marginal utility points per dollar. Here, same logic. I'm getting 80 marginal utility points per dollar. This is pretty simple math. Here I'm getting 60 marginal utility points for the dollar. Here I'm getting 40. So that doesn't seem too interesting. It might be a little bit more interesting here. What is the marginal utility per incremental fruit that I'm getting per dollar, per price, or actually per price of the incremental fruit here? Well here, that first pound of fruit I'm getting 120 marginal utility points we could call them. But I paid $2 for it. So 120-- let me write it over here. So for that first incremental fruit, the marginal utility for that first fruit is 120. And the price of that first pound of fruit is equal to 2. So I'm getting 60 marginal utility points per dollar. I'm getting 60. Here, 100 marginal utility points, but I'm spending $2. So that's 50 points per dollar. This is 25 points per dollar. This is 10 points per dollar. Now this makes things a little bit more interesting. If I had $5 to spend, how would I want to spend my $5? What you really just want to think about, where are you getting the most satisfaction for each dollar? Where are you getting the most bang for your buck? So where am I going to spend my first dollar? So dollar one. So let's think about it a little bit. My first dollar, where am I going to get the most satisfaction per dollar? Well, I get the most satisfaction per dollar right over here. I get 100 satisfaction units for a dollar. Even though I like a pound of fruit, I'm getting less satisfaction per dollar. So I'm getting less bang for my buck. So my first dollar is going to go right over there. I'm going to buy one candy bar. Then where am I going to spend my second dollar? So once again, I just want to look at all of my options, and we're going to assume that I'm going to spend my $5 on either of these two just to limit our universe. Once again, I'm going to maximize my bang for buck. I get 80 satisfaction points or marginal utility points over here per dollar. I only get 60 over here. So I'm going to buy even a second chocolate bar. Let's keep going. Where am I going to spend my third dollar? Now, it gets a little bit interesting. I could spend my third dollar right over here and get 60 points per dollar, or I could spend it over here and get 60 points per dollar. I'd actually get the same amount. There are both 60 points per dollar. So I'm kind of neutral. I'm going to get the same bang for my buck whether I get another chocolate bar or whether I get another fruit. So just for simplicity, let's say I get another chocolate bar. I could have got the fruit too. It's really a toss up. I could flip a coin, and I choose to get another chocolate bar. So I first spent my first $3 on three chocolate bars. Now where am I going to spend my fourth dollar? Well, my fourth dollar, now my best bang for my buck isn't to get another chocolate bar. I'm only going to get 40 units per buck there. Now it is to spend it on fruit. So now the next dollar I could spend on half a pound of fruit, and I would get this. So my fourth dollar I could spend on this for half a pound of fruit because it's $2 per pound. And then I could spend my fifth dollar there too. So this is my fourth and my fifth dollar because it's $2. You could think of it that we're spending $2 for one pound of fruit. And we're getting 60 utility points per dollar. So we're getting the best bang for our buck right over there. But what was useful about this is it allowed us without thinking about money to say how much do we like these things irrespective of their actual price and then give it a certain price. It allowed us to think rationally about, well, how would we actually spend our money. In this case, when chocolate bars are $1 and fruit is $2 per pound, we decided to buy three chocolate bars and only one pound of fruit.
Khan_Academy_AP_Microeconomics	Production_possibilities_frontier_Microeconomics_Khan_Academy.txt	Let's say you're some type of a hunter gatherer and you're trying to figure out how much of your time to spend hunting and how much of your time to spend gathering. So let's think about the different scenarios here and the tradeoffs that they involve. And just for simplicity we're going to assume that when you're talking about hunting, the only animal around you to hunt for are these little rabbits. And when we're talking about gathering, the only thing you can gather are some type of berries. That'll keep our conversation a little bit simpler. So let's think about all of the scenarios. So first, let's call this first scenario Scenario A. And let's say-- so let's call this the number of rabbits you can get and then let's call this the number of berries. Let's do this column as the number of berries that you can get. So if you were to spend your entire day going after rabbits, all your free time out-- making sure you have time to sleep, and get dressed, and all those type of things. Let's say that you can actually get five rabbits, on average, in a given day. But if you spend all your time getting rabbits you're not going to have any time to get berries. So you're going to be able to get 0 berries. Now let's say that you were to allocate a little bit more time to get berries and a little bit less time to get rabbits. So we'll call that Scenario B. We'll call scenario B the reality where you have enough time to get 4 rabbits on average. And when you do that, all of a sudden you're able to get 100 berries. And when we do these different scenarios, we're assuming that everything else is equal. You're not changing the amount of time you have either hunting or gathering. You're not changing the amount of sleep. You're not changing your techniques for hunting rabbits, or hunting berries, or you're not somehow looking to do other things with your time. So all other things are equal. And the general term for this, and it sounds very fancy if you were to say it in a conversation, is ceteris paribus. Which literally means-- so any time someone says, oh ceteris parabus, we assume this variable changes or whatever else-- they're saying we're assuming everything else is being held equal. So ceteris means all other things. You're probably familiar with et cetera. It's the same word, essentially. Other things in paribus, other things equal. So when you're going from Scenario A to Scenario B you're not changing the amount of time you're sleeping. You're not changing somehow the geography where you are in a dramatic way. You're not changing the tools you use or the technology. Everything else is equal. The only variable you're changing is how much time you allocate to finding rabbits versus finding berries. So let's do some more scenarios assuming ceteris paribus. So let me do Scenario C. You could, on average, have enough time to get 3 rabbits. But if you get 3 rabbits then all of a sudden you will to get-- or if you're only getting 3 rabbits, you're now able to get 180 berries. And let's do a couple more. I'm going to do two more scenarios. So let's say Scenario D, if you reduce the amount of time you spend getting rabbits so you get 2 rabbits, now all of a sudden you have enough time on average to get 240 berries. And then, let's say you spend even less time hunting for rabbits, on average. Then you have even more time for berries. And so you're able to get to 280 berries and I'll do one more scenario here. So let's say Scenario F-- and let's call these the scenarios. Scenarios A through F. So Scenario F is you spend all your time looking for berries. In which case, on average, you're going to be able to get 300 berries a day. But since you have no time for rabbits you aren't going to get any rabbits. So what I want to do is plot these. And on one axis I'll have the number of rabbits. And on the other axis I'll have the number of berries. So let me do it right over here. So this axis, I will call this my rabbit axis, rabbits. And we'll start. That will be 0. And then this will be 1, 2, 3, 4, and then that will be 5 rabbits. And then in this axis I will do the berries. So this right over here, let's make this 100 berries. This is 200 berries. And then this is 300 berries. And so this is my berries axis. Now let's plot these points, these different scenarios. So first we have Scenario A. Maybe I should've done all these colors in that Scenario A color. Scenario A, 5 rabbits, 0 berries. We are right over there. That is Scenario A. Scenario B, 4 rabbits, 100 berries. That's right over there. That's 100 berries. So that is Scenario B. Scenario C, 3 rabbits, 180 berries. 3 rabbits, 180. Let's see this would be 150. 180 will be like right over there. So 3, if you have time for 3 rabbits you have time for about 180 berries on average. So this is Scenario C. And then Scenario D we have in white. If you have time for 2 rabbits, you have time for 240 berries. So that is right around there. So this is Scenario D. Actually, a little bit lower. So this would be 250, so 240 is a little bit lower than that. So it'll be right over there. That is Scenario D. Scenario E, if you have time for 1 rabbit, you have time for 280 berries. So that gets us right about there. That is Scenario E. And then finally Scenario F. You are spending all of your time looking for berries. You have no time for rabbits. So all of your time for berries, no time for rabbits. 0 rabbits, 300 berries. That's right over there. So this is Scenario F. So what all of these points represent, these are all points-- now this is going to be a fancy word, but it's a very simple idea. These are all points on you, as a hunter gatherer, on your production possibilities frontier. Because if we draw a line-- I just arbitrarily picked these scenarios. Although I guess you could on average get 4 and 1/2 rabbits on average, on average get 3 and 1/2 rabbits, and then you'd have a different number of berries. So these are all points on the different combinations between the trade offs of rabbits and berries. So let me connect all of these. Let me connect them in a color that I haven't used it. So let me connect them. And do you see-- this should just be one curve. So I'll do it as a dotted line. It's easier for me to draw a dotted curve than a straight curve. So this right over here, this curve right over here, represents all the possible possibilities of combinations of rabbits and berries. I've only picked certain of them, but you could have a scenario right over here. Maybe we could call that Scenario G, where on average the amount of time you've allocated, on average you would get 4 and 1/2 rabbits. So some days you would get 4 rabbits and every other day you would get 5 rabbits, so maybe it averages out to 4 and 1/2 rabbits. And then maybe it looks like you would get about 50 berries in that situation. So all of these are possibilities. You don't have to just jump from 4 rabbits to 5 rabbits. Or maybe in this scenario you're spending 7 hours and in this scenario you spend 8 hours. But you could spend 7 hours and a minute, or 7 hours and a second. So anything in between is possible and all of those possibilities are on this curve. So these five scenarios, actually these six scenarios that we've talked about so far these are just scenarios on this curve. And that curve we call, once again-- fancy term, simple idea-- our production possibilities frontier. Because it shows all of the different possibilities we can do, we can get. 3 rabbits, and 180 berries. 2 rabbits and 240 berries. What we cannot do is something that's beyond this. So for example, we can't get a scenario like this. So this right over here would be impossible Let me scroll over to the right a little bit. Let me scroll, see my scrolling thing. OK, so this right over here is impossible, this point right over here where I'm getting 5 rabbits and 200 berries. If I'm getting five rabbits, I'm spending all my time on rabbits. I have no time for berries. Or another way to think about it, if I'm getting 200 berries I don't have enough time to get 5 rabbits. So this point is impossible. This point would be impossible. Any point that's on this side of the curve is impossible. Now any point that's on this side of the curve, you can kind of view it as inside the curve, or below the curve, or to the left of the curve-- all of these points right over here are possible. All of these points right over here are-- these points, for example, it is very easy for me to get 1 rabbit and 200 berries. So that right over there is possible. Now, is that optimal? No, because if I were to really work properly, I could get many more berries. Or I could get more rabbits. If I have 200 berries, I could get more rabbits. Or if I'm concerned, if I only want one rabbit, I can get more berries. So this is possible. All of the points down here are possible. But they aren't optimal. They are not efficient. So the points in here, we'll say that they are not efficient. Maybe somehow I'm not using my resources optimally to do this type of thing, when I'm over here. Or maybe I'm just not being optimally focused, or whatever it might be. If you're talking about a factory setting, when you're talking about maybe deciding to make one thing or another, then maybe you just aren't using the resources in an optimal way. Now all the points on the frontier-- these are efficient. You're doing the most you can do. Right now we're not making any judgment between whether any of these possibilities are better than any other possibility. All we are saying is that you are doing the most that you can do. Any of these things, you are making the most use of your time.
Khan_Academy_AP_Microeconomics	Opportunity_cost_and_comparative_advantage_using_an_output_table_AP_Macroeconomics_Khan_Academy.txt	- [Tutor] What we're going to do in this video is draw a connection between the idea of opportunity cost of producing a good in a certain country and comparative advantage between countries in a certain good and below, right over here we have a chart, that shows production possibility curves for two different countries and as we see in many economic models, this is a, I would argue oversimplified model, but it helps us get some insights, where in each country workers can only produce some combination of sneakers and basketballs and to help us understand this and to appreciate that you can see this information in multiple ways, let's present this also as an output table, output table, which you will sometimes see and from either the production possibility curves or from the output table, we can calculate the opportunity costs of shoes and the opportunity costs of basketballs and then try to deduce some things about comparative advantage. So in an output table, we would look at country A and we would look at country B and we would think about, well, what is the max, and I'll just draw it, what is the max basketballs and this is all per worker per day and we would also think what is the max shoes, shoes, those look like socks, but you get the idea, once again, per worker per day and so let me draw a little chart here, so we can do that and so what I'd like you to do is pause this video and see if you can fill in this chart, what is the maximum basketballs per worker per day in country A and then in country B and then do the same thing for shoes. Alright, now let's work this together, so first in country A, what is the maximum number of basketballs? Well, if in country A, they put all of their energy into basketballs, we are right over here on the production possibilities curve, they can produce eight basketballs and if on the other end of the curve, they put all of their energy into shoes, they would produce no basketballs and six pairs of shoes, we're assuming that these are pairs of shoes, that we're talking about, six pairs of shoes and similarly if we go to company, (laughs) if we go to country B, I keep saying company, instead of country, if we go to country B, if we say what's the maximum number of basketballs, well, if they put all their energy into basketballs, we get four basketballs and no pairs of shoes, so that's four basketballs, but then if they put all of their energy into pairs of shoes, they produce no basketballs, they could produce four pairs of shoes and so it's as simple as that, this output table is just showing the extremes from the production possibility curves for these countries. Now with the information about the output table and these production possibility curves, let's calculate the opportunity cost, so let me set up another table and let me just say this is going to be our opportunity cost table, OC, not Orange County, opportunity costs and once again, it's going to be for country A and country B and we're gonna think about the opportunity costs of producing basketballs and that's gonna be in terms of pairs of shoes and then the opportunity costs for producing pairs of shoes and that's going to be in terms of basketballs and so let me set up another table and so I encourage you once again, pause this video and see if you can fill in this table, what is the opportunity costs? We'll start with what's the opportunity costs for producing basketballs in terms of shoes in country A? Alright, well there's a couple of ways to think about it, imagine a world in country A, where you're producing no basketballs and you're producing six pairs of shoes, but then if you were to increase the number of basketballs you produce by eight, so if you add eight basketballs, well, you're gonna give up six pairs of shoes, you see that right over here, you give up six pairs of shoes and so in country A eight basketballs cost six shoes, let me write that down, so in country A, eight basketballs and I'll just say B for short, cost six, six S, S is shoes for short, or another way to think about it, if you divide both of these by eight, one basketball costs six over eight shoes, all I did was eight basketballs cost six shoes and one basketball's gonna cost six divided by eight pairs of shoes and so what is that gonna be? Well, six over eight is the same thing as three fourths or three fourths of a pair of shoes, so one basketball costs three fourths of a pair of shoes or we could say that as 0.75 S, where S is a pair of shoes for this is my simplified notation and what about in country B? Well, in country B, if I go from no basketballs to four basketballs, then I would have given up four pairs of shoes, I would have given up four pairs of shoes, so in country B, so in B, four, four basketballs cost four pairs of shoes or divide both by four, you could have a basketball, one basketball costs one pair of shoes, so a basketball here in country B costs one pair of shoes, so one pair of shoes, S once again is a pair of shoes and you could have also gotten it from this information here, you could set up an equation, you could say look, if I put all of, in country A, if I put, so let's look at this part right over here, you could say in country A, if I put all of my energy into basketballs, I could produce eight basketballs, but if I put that same energy into shoes, I could produce six pairs of shoes, so with the same energy, I could produce either one of these and then if I want the opportunity costs for basketballs, I divide both by eight and that's essentially what I did over here and I get a basketball, it costs six eighths of a pair of shoes or three fourths of a pair of shoes, which is exactly what I have over here. Now let's do the opportunity cost for a pair of shoes in either country, well, there's a couple of ways to think about it, you could just view it as the reciprocal or you could even go back to this equation right over here, if we are in country A, we would say six shoes, if we put all our energy in shoes, we could produce six of them or six pairs of shoes, I should say and if we put all of our energy into basketballs, we could produce eight basketballs, but if you divide by six, you get per pair of shoes and so per each pair of shoes, the energy to produce one pair of shoes is equivalent to the energy to produce eight sixths of a basketball and eight sixths is the same thing as four thirds of a basketball and if we wanted to write it as a decimal just for simplicity or maybe to make it easier to compare, we would say that this is approximately 1.33, obviously the 3s just keep going on, it repeats forever, but approximately 1.33 basketballs is the cost of producing a shoe and the opportunity cost of producing a shoe in country A, 1.33 basketballs and what about in country B? Well, in country B we could set up a similar type of equation, where the same energy for four shoes, I could produce four basketballs and that's essentially what we set up right over here on the left, you divide both sides by four, the energy of a shoe is equal to the energy of a basketball, or I should say the energy of a pair of shoes is equal to the energy of making a basketball, so the opportunity cost of making a pair of shoes is equal to one basketball. So now we're ready to draw the connection, given the opportunity costs that we calculated, what country has the comparative advantage in basketballs? Pause this video and try to figure it out. So now let's look at the opportunity cost of producing a basketball in either country. In country A, each basketball costs a worker three fourths of a pair of shoes, while in country B, it costs them a whole pair of shoes, so country A actually has a lower opportunity cost of producing basketballs and so it has the comparative advantage here, comparative, comparative advantage and then if we look at shoes, it goes the other way around, country A has an opportunity cost of one and one third basketballs for every pair of shoes, while country B has an opportunity cost of only one basketball per pair of shoes, so it has a lower opportunity cost and this one actually might be a little bit counterintuitive, because if you look on the shoe axis right over here, country A has the absolute advantage in producing shoes, a worker per day in country A can produce six pairs of shoes, while a worker in country B can only produce four pairs of shoes, but even though country A has the absolute advantage, it would actually make sense for country A to focus on basketballs, while country B focuses on shoes and in the next video, we'll see how they can trade with each other to get to a scenario, that is beyond their production possibility curves and why focusing on your comparative advantage, at least in this theoretical, very simplified world, makes sense.
Khan_Academy_AP_Microeconomics	Changes_in_income_population_or_preferences_Microeconomics_Khan_Academy.txt	So we've been going through all of the other things that we were assuming are held constant in order to be moving along one demand curve. And now let's list a few other. And before I do any more of them, let's talk about the ones we already talked about. So one, we said that one of the things we held constant-- let me write this down. So held constant. One of the things that we held constant to move along one demand curve for the demand itself to not shift, for the curve to not shift, is price of related goods. The other thing we assumed that's being held constant is price expectations for our good. And now we'll list a couple of them that are fairly intuitive, but you'll see in the next few videos that there are often special cases even to this. So the other thing that we've been holding constant to stay on one demand curve is income. And this one is fairly intuitive. What happens if everyone's income were to increase? And in real terms, it were to actually increase. Well then, all of a sudden, they have more disposable income, maybe to spend on something like e-books. And so for any given price point, the demand would increase. And so it would increase the demand. And once again, when we talk about increasing demand, we're talking about shifting the entire curve. We're not talking about a particular quantity of demand. So income goes up, then it increases demand. Demand goes up. And remember, when we're talking about when demand goes up, we're talking about the whole curve shifting to the right. At any given price point, we are going to have a larger quantity demanded. So the whole curve, this whole demand schedule would change. And likewise if income went down, demand would go down. And we're going to see in a future video-- it's actually quite interesting-- that's not always the case. This is only true for normal goods. And in a future video we'll see goods called inferior goods where this is not necessarily the case. Or by definition for an inferior good, it would not be the case. Now the other ones that are somewhat intuitive are population-- once again, if population goes up, obviously, at any given price point, more people will want it. So it would shift the demand curve to the right, or it would increase demand. If population were to go down, it would decrease demand, which means shifting the whole curve to the left. And then the last one we'll talk about-- and remember, we're holding all of these things constant in order for demand not to change. The last thing is just preferences. We're assuming that people's tastes and preferences don't change while we move along a specific demand curve. If preferences actually change, then it will change the curve. So for example, if all of a sudden, the author of the book is on some very popular talk show that tells everyone that this is the best book that was ever written, then preferences would go up, and that would increase the total demand. At any given price point, more people will be willing to buy the book. If, on the other hand, on that same talk show, it turns out that they do an expose on the author having this sordid past, and the author plagiarized the whole book, then the demand will go down. The entire curve, regardless of the price point-- at any given price point, the quantity demanded will actually go down.
Khan_Academy_AP_Microeconomics	Determinants_of_price_elasticity_of_demand_AP_Microeconomics_Khan_Academy.txt	- [Instructor] In other videos we have already started talking about the price elasticity of demand, and what we're gonna do in this video is think about the factors that might drive the price elasticity of demand in a given market to be more or less elastic. So one could say that we're gonna think about the determinants of the price elasticity of demand. Now before we even talk about those determinants or those factors, let's just give ourselves a little bit of a review of what an elastic or an inelastic market might look like. So let me draw my price and quantity axes that we are pretty familiar with at this point. So quantity on the horizontal axis, price on the vertical axis, and remember, price elasticity of demand is percent change in quantity for given percent change in price. So a high elasticity would say that you have a large percent change in quantity for a given percent change in price, so high elasticity would look something like this, it would be a flatter demand curve. So this might look something like that, so I'll write that as high, high elasticity elasticity. And low elasticity would be that your percentage in quantity does not change much depending on your percent change in price. So low elasticity, the closer and closer we get to a vertical curve, the lower our elasticity, so low elasticity would look something like that. A low elasticity demand curve. Low elasticity. Elasticity. In other videos we even think about a perfectly inelastic market in which case you would have a vertical demand curve. But let's now think about the factors that might lead us to be closer to the high elasticity case or closer to the low elasticity case. So the factors that economists will generally point to are substitutes, timeframe, income share, whether the market we're talking about is about a luxury or necessity, and the narrowness of a market. So let's start with substitutes. So let's imagine first a world where there are many substitutes for the good or service that we're talking about. Many substitutes. And we can think of examples in our heads for markets of goods or services where there are many substitutes, let's say it's the market for Fuji apples. Well, the other substitutes are the other types of apples out there, McIntosh apples and Red Delicious apples, and all of those, and so for a given percent change in price, would you expect the percent change in quantity demanded of Fuji apples to change dramatically? Well if there are many substitutes, and only the Fuji apples, say, get a lot more expensive, then people will go to the substitutes, they're more likely to go the the Red Delicious, or the McIntosh apples, so when you have many substitutes, that tends to lead to more elasticity. More elasticity. People quantity, I guess you could say, would be very sensitive to price. And you could go the other way around if you have few substitutes. Few substitutes. Well, then, even if the price changes a little bit, or even if it changes a lot, people say well I don't know what I could substitute that with, so they might still buy a reasonably similar quantity, so this would be less, less elastic. Less elastic. Now what about timeframe, how does that affect elasticity? Well, imagine that you are selling umbrellas and it is raining right now. So for thinking about a short timeframe, while it is raining, then you could probably raise the prices on umbrellas a good bit, and assuming you have good foot traffic, a lot of people are probably going to be willing to pay that price, and so in a short timeframe, in a short, short timeframe, things tend to be less elastic. Less elastic. But over a longer timeframe, so longer timeframe, people might say, hey you're trying to really rip me off with those umbrellas and take advantage of me, I can go someplace else and find umbrellas, I could go online or whatever else, and so there, people tend to be more sensitive to price on the longer timeframe, they can find their substitutes, going back to the previous determinant, and so things tend to be more elastic. So once again, you could view elasticity as how sensitive quantity is to price. So next, income share. So let's first think about something that makes up a very small percentage of your income, say bubble gum, and let's say bubble gum right now is 25 cents, and if it were to go to 50 cents, that would likely reduce the quantity demanded, but it might not be so significant because going from 25 cents to 50 cents isn't gonna make a big difference for most people's pocket books. So in general, the lower the income share, lower share of income, the less elastic, the less elastic that market is going to be. But imagine something that is a high share of income. So let's say we're talking about, let me just write here, so high share, high share of income, so let's say we're talking about an automobile, and if people are already spending 20% or 30% of their income on that automobile and that automobile were to double, the cost of that versus the gum ball drop, the bubble gum, well then people just wouldn't even be able to demand the same quantities that they were able to before because their income just can't support it, they have other things to spend that money on, that extra money because their incomes just can't support it, so they will be highly sensitive to changes in price. So high sensitivity to changes in price, more elastic. Now what about luxuries versus necessities? Let's start with necessities. If this is something that you absolutely need, then even if the price were to go up a good bit, as long as you can still afford it, you might still go for that thing. So for example, let's say there's some medicine, let's say you're a diabetic and you need insulin, if you don't get insulin, really bad things are going to happen. If they were to raise the price of insulin by 20, 30, 40%, assuming that you could still afford it, you would still buy the same quantity because you need that insulin, and so if something is a necessity, necessity, you're gonna be less price sensitive, the quantity is going to be less sensitive to price, and so you're going to be less elastic, but if something's a luxury, if we're talking about you know, gold tiaras, and the price of gold were to go up dramatically, well then a lot of people will say, I might not need that gold tiara anymore, it's really not gonna make a big difference in my life. So, in general, luxuries, luxury will be associated with more elasticity. Now there could be exceptions, if something isn't kind of the ultra luxury category, and if maybe the price were to go up, maybe the people buying it, it's a very low share of their income, and maybe it's a brand that, at least the people buying it feel that there's no substitute for it, well then maybe it might not be as sensitive, but we're talking about in broad generalities. Now the last factor that is sometimes talked about is the narrowness of the market. Now what are we talking about here? So, for example, we could be talking about the market, market for apples, or you could talk about the market, market for food. Which of these markets, they're kind of both describing food, but which one is more narrow? Yes, apples are a subset of all food. And so, if we're talking about the market for apples, the narrower situation, so if we're talking about the narrower, narrower market, you tend to have more substitutes. So if the price of apples go up, people say well maybe I'm gonna go buy some pears, or bananas, or something else instead of the apples, and so you're gonna be more, quantity will be more sensitive to changes in price, and so you're gonna have more elasticity, but if you have a broader definition of your market, the market for food, well now the food looks a lot more like it's a necessity, there are very few substitutes for food, if I stop eating food, well I, it's not like I can eat, you know, change or just live off of air, or whatever else, there's really no substitutes for food, it is an absolute necessity. So the broader the market definition, so the broader the market, we tend to be dealing with a less elastic, less price elasticity of demand.
Khan_Academy_AP_Microeconomics	Consumer_surplus_introduction_Consumer_and_producer_surplus_Microeconomics_Khan_Academy.txt	In the last video, we saw how you can actually view a demand curve as actually a marginal benefit curve. That for any given the quantity of the good you're selling, that that point on the curve is actually showing the marginal benefit for that incremental unit. So this is a marginal benefit for that first unit. This is the marginal benefit for that second unit. And there's multiple ways that you could view this, assuming that we're talking about this new car here. Maybe if you're going to only sell one unit, someone really wants it really bad, the benefit for them, the marginal benefit for that first unit for them, is going to be $60,000. Now, let's say if you want to sell two units, that second unit might be bought by that same person. And they might say, well, I already have one car. The benefit of getting that second one's only $50,000. That's the point at which I am neutral. That's the point at which I'm right on the fence of willing to buy that car. Or it might be another person, another person who's just not as enamored as the first person, who says, OK, for $50,000 I do like that car. And then for the third, the third person there, once again, they're not as enamored as the first two, they would be willing to buy it for $40,000. And what we saw is at some point you could say, look, let's say that we decide that the price ends up being-- for whatever reason-- $30,000. And so when the price is $30,000-- and this is kind of viewing it in the traditional notion of, at a price, what quantity were you selling it. But when you think about that reality, what's actually happening is that this fourth person is right on the fence. Their marginal benefit is exactly $30,000. So in their mind, they're saying, I am giving away $30,000. And in exchange for that I'm getting something that is worth $30,000. So it's kind of like, hey, will you be willing to trade this dollar for a dollar? Well, you probably would be kind of on the fence about that. You're very close to going either way. You feel like it's a good deal if you could get it for maybe a penny less. It's a bad deal if you're getting it for a penny more. So right on the fence, but you're going to just barely get this fourth person to transact at this price. But what we hinted at is if you do have one price for everybody-- in the future we'll talk about not having one price for everybody-- but if you did have one price for everyone, these first units were kind of sold below where they could have been sold. They were sold below their marginal benefit. So remember, we're viewing this same demand curve we're now viewing as a marginal benefit curve. So this first unit right over here, it could have been sold at $60,000. But now, we're selling it for $30,000. So this right over here, this was $30,000. I'll just write 30 for $30,000. The marginal benefit is $30,000 higher than the actual price. The marginal benefit of that unit, the benefit that the market got out of it is $30,000 higher than the price. The marginal benefit for the second unit is $20,000 higher than the price at which the product is being sold. The marginal benefit for this third unit, assuming this is $40,000, is $10,000. Or another way to think about it is, the consumer surplus for this first unit was $30,000. The consumer's got $30,000 more in benefit, marginal benefit for them and value for themselves, than they had to pay for it. Here, the consumer surplus was $20,000. The consumer got $20,000 more in value than that second consumer was willing to pay for it. And here is $10,000. And then this fourth consumer is neutral. The marginal benefit is what they paid for it. And so when you think about this, you can say, well, what's the total consumer surplus here? Let me write this down. What is the total consumer surplus? And another way of thinking about it is, what is the total excess of marginal benefit above and beyond the price paid? So how much surplus marginal benefit did they get, if you take out the price paid? And over here, the total consumer surplus is going to be the $30,000 for that first unit, plus the $20,000 for that second unit, plus the $10,000 for that third unit. And so the total consumer surplus in this scenario when we sold four units at $30,000 is-- And we're assuming we're selling cars here. So we can't sell parts of cars here. We can't sell 1.1 cars. I guess if we're talking about averages, maybe we could. But let's just say we're selling just whole numbers of cars here. The total consumer surplus in this situation was 30 plus 20 plus 10, which is $60,000. Everything's in thousands. So this is $60,000. So in this scenario, in that week, the consumers would get $60,000 more in benefit for them, in perceived benefit for them, than what they actually had to pay for it. And if you think about it, it's a little unideal for the seller, because they were selling something at a lower price than maybe what they could have gotten from at least these first few consumers here. And that was because they, just really based on the model that we have here, they just had to set one price.
Khan_Academy_AP_Microeconomics	Introduction_to_price_elasticity_of_demand_AP_Microeconomics_Khan_Academy.txt	- [Instructor] We are now going to discuss price elasticity of demand, which sounds like a very fancy concept, but really, it's a way for economists to sense how sensitive is quantity to change in prices. And in this video, we're gonna denote it as a capital E, so E, price elasticity of demand. And the easy way to think about it is it is your percent change in, I'll use the Greek letter delta as shorthand for change in here, percent change in quantity over your percent change in price. And so, you might say, wait, how does this relate to the everyday idea of elasticity? Well, imagine two bands. So, let's imagine an inelastic band, inelastic, right over here, and let's imagine an elastic band right over here. So, in an inelastic band, if we apply some amount of force, you're not going to be able to stretch it much, it might stretch a little bit, while an elastic band, if you apply that same amount of force, you might be able to stretch it a lot more. And so, the analogy here is we're not using force, but we're saying how much does quantity stretch for a given amount of price change? And so, something where the quantity changes a lot for a given price change would be very elastic. So, this, the magnitude of this will be larger. And if the percent change in quantity doesn't change a lot for a our given percent change in price, well, then we're dealing with an inelastic price elasticity of demand. And we'll be able to internalize these more as we work through the numbers. And actually, let's do that for this demand schedule that we have right over here, and it's visualized as our demand curve. In the vertical axis, we have price of burgers; and then in our horizontal axis, we have quantity, in terms of burgers per hour. And so, let's just use this definition of price elasticity of demand to calculate it across different points on our demand curve. So, I'm gonna make a new column here, so price elasticity of demand. And the way I'm gonna do it is really the simplest method for calculating this. In other videos, we can go into more in-depth methods, like the midpoint method. And I'll show you the weakness in what we're doing right here. But for the sake of, say, an AP economics, microeconomics course, this would be sufficient. So, let's think about our price elasticity of demand as we go from point A to point B. Well, remember, that's just going to be our percent change in quantity over our percent change in price. So, what is our percent change in quantity? Well, we're starting at a quantity of two, so I'll put that in our denominator. And we're going from two to four, so we are adding two. So, we have two over two, we could multiply that times 100% if we like. So, this would give us, we have 100% change in quantity over, now what was the corresponding change in price, percent change in price? So, our corresponding percent change in price, our initial price is nine, and we go from nine to eight, so we're going down by one. And then we multiply that times 100%. So, this is going to be about a negative 11% change in price. And this math is reasonably straightforward because the 100%s cancel out, this is just a one. One over negative 1/9 is just going to be equal to negative nine. So, you have a negative nine price elasticity of demand. So, before I interpret that more, let's look at the price elasticity of demand at other points, or starting from other points to other points on this curve. So, let's think about it going from, actually let's think about it going from E to F. So, as we go from E to F, we're going to do the same exact exercise. What is our percent change in quantity? Well, our initial quantity is 16. And we're going from 16 to 18, so we have a change of two. So, two over 16 times 100%, that is our percent change in quantity. And what is our percent change in price? Well, our initial price is two. And we're going from two to one, so we have a price change of negative one times 100%. And so, what you see here is this is 1/8 times 100%, this would be 12.5% up here. So, this is 12.5% up there, and then this, over here, is going to be negative 50%. So, when price went down by 50%, you had a 12.5% increase in quantity. 12.5% is 1/4 of 50%, so this is going to give us a price elasticity of demand of negative 0.25. So, there's a couple of interesting things that you might already be realizing. One is even though our demand curve right over here is a line, it actually has a constant slope, you see that the price elasticity of demand changes, depending on different parts of the curve. Now, the reason why this is, is really just boils down to math. When we're going from A to B, our initial prices were relatively high. So, even though you had a price decrease of one, it was from an initial price of nine. So, your percentage change in price looked fairly low, while your percentage change in quantity was high 'cause you're going from a low quantity of two, and you're adding two to it, so you had 100% change in quantity. When you go to the other end our curve, and you go from E to F, it's the other way around. Your price starting point is low, so your percent change in price, when you decrease price by one, it looks like a fairly large magnitude; while your percent change in quantity when you go from E to F because you are already at a quantity of 16, adding two to that is not that large of a percentage. Now, another thing you might be appreciating is if we tried to calculate the price elasticity of demand up here on the curve, and instead of going from A to B, if we went from B to A, we would've gotten a different value because our initial prices and quantities would have been different. Our initial price, we would've put an eight right over here, and our initial quantity, we would've put a four over here, and we would've gotten a different value. And that's one of the negatives of the technique, which is arguably the simplest technique, that I just used. There's other techniques, like the midpoint technique, that can give you a more consistent result, whether you're going from A to B or B to A, but I won't cover it just yet. But let's think, now, about how to interpret this. And the best way to interpret it is to think about the absolute value of the price elasticity of demand. So, over here, the absolute value of our price elasticity of demand is equal to nine, and then, over here, the absolute value of our price elasticity of demand is equal to 0.25. And a general rule of thumb is if your absolute value of your price elasticity of demand is less than one, you are dealing with an inelastic, inelastic, elastic situation; and if your price elasticity of demand, the absolute value of it, is greater than one, you're dealing with an elastic situation. Why does that make sense? Well, in this first scenario, it's saying for a given percentage change in price, you have a smaller percent change in quantity; while here, for a given percent in price, you're going to have a larger than that percentage change in your quantity. So, once again, it goes back to these rubber band analogies. So, when we're going from A to B, the absolute value of our price elasticity of demand is definitely larger than one. So, economists would consider this to be an elastic situation; while when we go from point E to point F, our price elasticity of demand, or the absolute value of it, is definitely less than one, so this going to be an inelastic situation.
Khan_Academy_AP_Microeconomics	Scarcity_and_rivalry_Basic_Economic_Concepts_Microeconomics_Khan_Academy.txt	- [Instructor] What we're going to do in this video is talk about two related ideas that are really the foundations of economics, the idea of scarcity and the idea of rivalry. Now, in other videos, we do a deep dive into what scarcity is. But just as a review, in everyday language, you could think of something is scarce, a good or a service is scarce if there's not enough for everyone. Another way to think about it is a scarce resource is one that is limited. It is a limited resource, and there's not enough to go around because there are potentially unlimited wants from people, so potentially, potentially unlimited, unlimited wants. And we could think of a lot of scarce resources. Oil would be a scarce resource. There's a limited supply of oil. And potentially, if oil were free, there's an unlimited amount of people who would want to use that oil. And so a lot of economics is, well, when you have a scarce resource, like oil or land or housing, how do you allocate those resources amongst people, people who are demanding those resources? Now, rivalry is a related idea. When we think about the everyday word rival or rivalry, you imagine multiple parties competing for something, and that's essentially getting pretty close to the economics definition of it. Something is a rival good or a rival resource, I'll just call it a rival good right now, if, when one person uses it, it limits the ability for other people to use it. So one, one person consuming it or using it, consuming it limits ability, ability for others, for others to use. And there's a lot of examples of rival goods and things that are both scarce and rival goods. For example, if I were to put a nice, delicious cake that could only serve four people in our office here at Khan Academy, where we have 80 or 90 folks work, well, you can imagine, that cake's going to be a rival good. It's also a scarce good because many people, many more people are gonna want that cake than the amount of cake we have. But when you look at what the definition of a rival good is, every time I, if I eat the whole cake, that's going to limit other people's ability to use it. And economists will sometimes create a spectrum of how rivalrous a good is. So, for example, let me draw a spectrum right over here. So on this line, so on the left-hand side, I will call this highly rivalrous, which is, they'll actually use that word, but I'll just call this rival goods. And then at the other extreme here, I'll say non, non-rival, non-rival good. And at the left end, it's pretty easy to come up with a bunch of rival goods. If you're living in a place where housing is tight, where all of the housing is taken up, housing is often a rival good. I live in the San Francisco Bay Area. And when a house goes on rent, you'll have multiple people who are competing for that house, or if it's going for sale. And so when one person gets it and gets to live there, well, that's going to make it hard for other people to use it. You could imagine, you know, land in a lot of urban areas is a rival good. You could imagine something like, you know, a cake, especially if there's not a lot of cake to go around at a birthday party. Now, what would be the other extreme? What would be a non-rival good? Well, there are very few perfectly non-rival goods, but there are things that are close to it. Because at least relative to where people's, where people are trying to use it today, it seems like there's almost an unlimited supply of it. One example might be something that's close. I'm not gonna put it all the way at the end. I'm gonna put air, air to breathe on Earth. Now, right now it's a non-rival good. When I take a deep breath, it doesn't make it hard for you to take another simultaneous deep breath. And actually, let me put a little qualifier here, simultaneously, simultaneously. That's actually a key qualifier for a rival good. So, for example, a hammer is also a rival good. Because if I'm using it right now, it becomes very hard for you to use it simultaneously. Now, as I mentioned, air to breathe, if I take a deep breath right now, it doesn't make it any harder for you to take a deep breath. But if you were to take a extreme circumstance that, let's say that if we were in a closed room with a limited supply of oxygen, well, then the air might become something closer to a rival good. So let me put it this way, air to breathe outside, while here I'll put air in airtight, or let me put oxygen in an airtight container or airtight room, oxygen in airtight room or maybe a room that is running out of oxygen. Well, then every time I take a breath, it's gonna make it harder for you to take a breath and vice versa. There's other things like, well, roads are rival goods, especially if we're talking about rush hour. So let me put this right over here. So let's call this the roads during rush hour, roads during rush hour. The more people that are on the roads, that it's gonna make it harder for other people to use it simultaneously. It will get all this traffic. People won't even be able to get on the highway 'cause there's so much gridlock. But then you could imagine roads in the middle of the night are non-rival goods. If I decide to take a drive at three in the morning on most highways, it doesn't make it any harder for another person to take a drive on that highway simultaneously. So let me put it over here, roads, roads at 3:00 a.m. in most places is closer to being a non-rival good. So I will leave you there. These are ideas that we're going to keep revisiting in economics. But it's good to have a sense of what they mean, and then it'll inform how we think about allocating these scarce goods amongst folks and thinking about how we allocate these rival goods amongst various parties.
Khan_Academy_AP_Microeconomics	Substitution_and_income_effects_and_the_Law_of_Demand_AP_Microeconomics_Khan_Academy.txt	- [Narrator] In other videos, we have already talked about the Law of Demand, which tells us, and this is probably already somewhat intuitive for you, that if a certain good is currently at a higher price, that the quantity demanded will be quite low, and then as the price were to decrease, the quantity demanded would increase. So if we were to graph demand, and so this right over here is our demand curve, where price is on our vertical axis and quantity is on our horizontal axis, which is the standard convention for most economists, you would have a downward-sloping demand curve. Well, what we're gonna do in this video is dig a little bit deeper into why we have that downward-sloping demand curve, and I know what some of y'all are saying. "Well, it kind of makes common sense. "As the price goes down, I would want more of that, "and so would everyone else." But let's dig into why you would want more of something as the price goes down. So one category of reasons why you might want more of it as the price goes down, economists will call the substitution effect. Substitution, substitution effect. And this is the idea that if we're looking at the price versus quantity, say, of candy, and let's say at first, the price is right over here at $4, and at $4, the quantity demanded in the market would be, let's say that is 100 units of the candy, maybe it's 100 pounds of the candy, that if the price were to then go to $2 for some reason, so let's say the price is at $2, well, then, a lot of folks could say, "Gee, that candy is looking a lot better "relative to other things that I might buy "with my money." So, for example, people might be picking between candy and fruit, and maybe, at first, they were both $4 a pound, but now all of a sudden, if the candy is $2 a pound, or $2 per unit, well, then, it's looking a lot better relative to the fruit. So some of that quantity of fruit people would have bought, they'll say, "Hey, now candy is a better deal. "I'm going to substitute the fruit with candy." And so that's why you have a higher quantity of candy demanded. This might maybe be now 250 units. Another major category why you would expect this downward-sloping demand curve for normal goods, and we'll talk about things like inferior goods in future videos, is the income effect, income effect. And in some ways, this might be the most intuitive. Well, if the price went from $4 to $2, well, the cost of those 100 units would now be half as much. It would go from $400 to $200. And so the market would have an extra $200 to use to buy things with, and some of that extra $200, they'll buy more candy with. But then they might also buy other things with that. Now the last dimension that economists will often talk about for why the Law of Demand is downward-sloping like this, and we talk about this in other videos, is this idea of decreasing, decreasing marginal utility, and that's that idea that that first, if you're just that first amount of candy, there's gonna be people the market who take a lot of value from it. They are just addicted to candy. Their bodies are dependent on that candy. But as soon as folks are satiated, that next incremental amount, that next marginal amount, the utility might be a little bit lower. And so as you have more and more candy, the marginal utility goes down. And so that's another way of thinking about why we have a downward-sloping demand curve.
Khan_Academy_AP_Microeconomics	Taxes_and_perfectly_inelastic_demand_Microeconomics_Khan_Academy.txt	Let's think about who bears the burden of a tax in different situations. In this video, we're going to focus on insulin. Insulin is interesting. It's what's needed by Diabetes in order to maintain their blood sugar level so for them, you can almost imagine they need this just to survive. It almost has an infinite marginal benefit for them. So they're willing, no matter what the price, they're essentially willing to take the insulin that they need to take. So, for example, even if the price of insulin were a dollar, if the doctors in this town say collectively all the diabetics need 3,000 vials a year, they will take 3,000 vials a year. If the price is $80 a vial, they'll still take 3,000 vials a year. So within reason, within a reasonable price range, you have no change in quantity demanded. So, in this case, at least in a reasonable price range, the demand curve for insulin is vertical. Obviously, if we went up to prices like $9 million per vial, then all of a sudden, some of the diabetics just won't be able to afford it, and all of a sudden, the curve wouldn't be able to be vertical anymore. But at least in a reasonable price range, you have a vertical curve. So this right over here is our demand curve. That is our demand curve. You might remember when we talked about elasticity, this is perfectly inelastic demand. It's perfectly inelastic ... perfectly inelastic. The way you can think about it, I kind of think of a brick as perfectly inelastic. No matter how much you push or pull on the brick within reason, at least with my level of strength, you're not going to be able to deform the brick. That's the opposite of a rubber band, which is very elastic, or you can think about the definition of elasticity, the one that we've been using, elasticity is equal to percent, change in quantity over percent, change in price. Over here, no matter how much we change price within reason, at least in this range of price along this curve, people are still going to demand a quantity of 3,000 vials per year. Let's just draw a supply curve here, so let's do a supply curve, looks something like that, So if you have ... this is supply, so if you have no taxes, no regulation of this market, based on the way I've drawn it right over here, the equilibrium price lands us right around $75. I did a little research before this video, it actually turns out that is about the market price for a vial of insulin. The equilibrium quantity, because that is the exact quantity that people need is 3,000 vials. A slightly interesting thing to think about in this situation where you have perfectly inelastic demand, is what is the producer's surplus and the consumer's surplus? The producer's surplus is how much more money they're getting relative to their, you can view them as their opportunity cost or their incremental marginal cost, and here we will [unintelligible] multiple times, this is the producer's surplus right over here. It's the area between the prices equal to the clearing price and our supply curve. So, that's our producer surplus. Producer surplus. Our consumer surplus is where things get a little bit interesting. Consumer surplus is how much more marginal benefit people are getting than what they are paying. We've traditionally said that's the area between the demand curve and the price. But now, all of a sudden, this area is infinite. This area is infinite. One way to think about it is that these diabetics get, you could almost say close to infinite marginal benefit from that insulin. It allows them to have a healthy life. It allows them to stay alive. For them, it's essentially priceless. It's kind of an interesting idea that you have infinite consumer surplus. It's not necessarily saying that this is like a great deal for the diabetics, it's really just saying that their benefit is something that they need to survive. If this was just slightly more elastic, so if we were to get, maybe to a slghtly more real world scenario. In a real world, if things got a little bit more expensive, there might be a few diabetics who would all of a sudden try to lower their dose or something like that. The curve, in a real world, actually might have some very slight elasticity. It would still be a very steep slope, but it would actually have some slight elasticity. You could imagine if I kept taking this up and up and up, and at some point, it actually would bound the area, but it would, so maybe it goes up here. Maybe if this was like $2 million up here, then the demand would go down dramatically, but it would be bounded. But it is a very, very, very large consumer surplus. Now with that out of the way, let's think about what happens if some misguided politician decides to tax insulin. Obviously a very bad idea, and nothing that I would ever advocate, but let's think about who would bear the burden? I think you could probably guess who would bear the burden if you had to put a tax, but we'll actually see it. We'll think it through with our supply and our perfectly inelastic demand curve. What ends up getting passed is a tax of $10 per vial. I'm just making it, instead of a percentage, I'm just doing it as a fixed amount so that we get kind of a fixed shift in terms of the perceived supply price. For the producers, this is what they need to get. If you want them to produce 3,000 vials, they need to get $75. If you [unintelligible] that first vial, they need to get $60. What the producers need to get, plus the tax, we can draw a new curve. We've done this multiple times. For the very first vial, the producer needs $60, but then you add the tax there, it's going to be $70. For 1,000 vials, it looks like it's going to be I don't know, 60 something ... you add the tax, it's going to move up to here. For 3,000 vials, the producers need around $75, $76, you add $10 to it, it gets to $85, $86 like that. What you get is this new curve, you could use the price from the consumer's point of view, or you could view it as the supply plus tax curve. I'll call this supply plus tax curve and that's hard to read, but that says tax over there. This is the supply plus tax curve. Where does that intersect our perfectly inelastic demand curve? Well, you can imagine people, even though the prices are higher, people still have to get exactly 3,000 vials per year. They intersect right at that quantity, but now we have a new equilibrium price. Our new equilibrium price is exactly $10 higher. If this was $75 or $76, this is $85 or $86. This distance right over here is $10. Let's think about a few things. Let's think about the total revenue that the government is going to get in this situation. The total revenue is going to be that $10 times the 3,000 vials per year ... times 3,000. So they're going to get $30,000 per year. Let's think about whose surplus that came out of. The tax revenue, this right over here is the tax revenue. That right over there is the tax revenue. The producers are still going to have the exact same producer surplus, so all of that tax revenue came directly out of the consumer surplus. Another interesting thing to note here is, because we had this perfectly inelastic demand, that even when you raise the price, it didn't lower the quantity demanded that we actually don't have a dead weight loss here because this was perfectly inelastic. We're actually having the same quantity produced so you have a transfer of surplus from essentially the diabetics to the government in this situation, but you don't have any lost surplus here because there's no lost area, I guess you could say, between where the supply curve and the demand curves intersect. Another way to think about it is the quantity demand did not go down because the price went up.
Khan_Academy_AP_Microeconomics	Types_of_competition_and_marginal_revenue_AP_Microeconomics_Khan_Academy.txt	- [Instructor] We've already had several videos where we talk about the types of markets that we might look at in economics. At one end, you might have perfect competition, let's write perfect comp, and this is where you have many firms, what they produce is not differentiated, there is no barriers to entry, and in that situation, we have looked at that the market price, the firms just have to take that market price, and that market price is going to describe what their marginal revenue is going to be. No matter how much each of those individual firms produce, they're just going to get that market price, so that marginal revenue will be that market price, but then we looked at a whole sort of what we could call imperfectly competitive firms, imperfectly, imperfect competition. At the extreme, you have the monopoly, where you only have one firm in the market, huge barriers to entry and so that company or that firm essentially is the market and so their demand curve for their product essentially is the market demand curve. But in between, you have things like monopolistic competition right over there, and in monopolistic competition, you have many firms that are competing but they are all differentiated in some way, and there are some barriers to entry. A good example of monopolistic competition or imperfect competition might be the athletic shoe market. In the athletic shoe market, you have many competitors, you have your Nike, Adidas, Reebok, and I could keep listing names, and they are all differentiated in their own way, they all have their own brands, which they have built up over time, they have associations with certain sports figures, some their shoes might be perceived as better in certain categories, but they are also competing with each other. So the competition is that they are competing with each other but you could consider monopolistic competition because only Nike can sell, well, Nike shoes, and so you could imagine a demand curve for say only Nike shoes, so in imperfect competition, every firm would have their own unique demand curve, and how much they produce actually will affect the price that they get for the product or the service, and what we're going to see in this video is when we are dealing with imperfect competition, the demand curve, the price, isn't exactly what marginal revenue is going to be, and to understand that, let's look at a simple model here. So right over here, I have a very simple model of a demand curve for a firm in an imperfectly competitive market, and you can see here that the more that that firm produces of its goods, the lower price it can get for that good, and we can see very clearly this is a classic downward sloping demand curve, but what's going to be really interesting is to think about, what is going to be the marginal revenue, especially the marginal revenue in a world where if they sell one unit, they get 32.50, but when they sell two units, it's not like they'll get 32.50 for one of those units and then they'll get 25 for the second unit. If you have a market price out there for $25, you're going to get $25 on all two units, so even though someone was willing to pay 32.50 for one, they are still only going to pay $25, so let's think about what that does to the marginal revenue. I encourage you to pause this video and try to fill out this table yourself before I do it with you. All right, now let's do it together, so our total revenue, obviously when we sell nothing, we have, let me do this in another color, we have zero total revenue. Now, when we sell one unit at 32.50, well, then our total revenue is going to be 32.50, no surprise there. Now it's going to get interesting. When we sell two units, what's going to be our total revenue? Well, both of those units are gonna be sold at $25, it's not like, as I just said, it's not like that first person is still willing to pay 32.50, like hey, your market price is $25, that's what everyone is going to pay, so now your total revenue is $50, two times $25. Now when you go to three, the market price that you can get is 17.50, let's see, that is going to be, 52.50. 52.50 of total revenue, and then if you, if your market price was $10, you could have a quantity of four. If you wanted to sell four, you could do so at a price of $10, you can do it in either way, but then your total revenue is going to be $40. Now, from this, we can think about, well, what's our marginal revenue? Well, our marginal revenue for that first unit is the same as what the price of that first unit is, we went from zero to 32.50 with that first unit, so that's 32.50 right over here, but what about as we go from that first unit to that second unit? Well, our units go up by one, but our revenue from 32.50 to 50 goes up by 17.50, and so we are already seeing that there is a discrepancy between our marginal revenue and our price, and we can going. When we go from two to three units, our revenue only goes up by 2.50, and so that's going to be our marginal revenue, and then something very interesting happens. As we go from three units to four units, our total revenue actually goes down, it goes down by 12.50, negative 12.50 right over here, and that's because when the price gets that low, you are taking a hit on all of the units that you are selling, so you'll actually get a lower total revenue right over here, and if we plotted, we'll see very clearly that the marginal revenue curve, the parts from the demand curve for that firm that's competing in an imperfectly competitive market, and so we can see here at one unit, our marginal revenue is the same, but at two units, our marginal revenue is 17.50, at three units, our marginal revenue is 2.50, and so we have a marginal revenue curve that looks more like this. So the big takeaway is here that a firm that's operating in an imperfectly market. It isn't just a price taker, it's not that no matter how much it produces it's going to get the same price, it's going to have its own unique demand curve, because there is some differentiation in the market, and so it's going to have a downward sloping demand curve, and because of that downward sloping demand curve, you are also going to have a downward sloping marginal revenue curve and that marginal revenue curve is actually going to be downward sloping at a steeper rate, so when we start doing the firm analysis of marginal cost and where does it intersect the marginal revenue, if you're dealing with a firm that's operating in a perfectly competitive market, that marginal revenue curve when we've seen it before was horizontal, but when we think about that marginal revenue curve for a firm in an imperfectly competitive market, that's going to be downward sloping, it's going to be sloping downward faster than its demand curve.
Khan_Academy_AP_Microeconomics	PPCs_for_increasing_decreasing_and_constant_opportunity_cost_AP_Macroeconomics_Khan_Academy.txt	- [Instructor] So we have three different possible production possibility curves for rabbits and berries here, which we've already talked about in other videos, but the reason why I'm showing you three different curves is because these three different curves clearly have different shapes, and we wanna think about why you would have and under what scenarios would you have these different shapes? Here, our production possibility curve, or our PPC, it looks like a straight line. Here, it looks like it's bowed out from the origin, it looks like it's popping out in that direction. And here, it looks like it's bowed in to the origin, it's popping in in this direction. So the first thing I'm going to do is ask you a question. Which one describes the scenario where for every extra rabbit I catch, every incremental rabbit, I'm giving up more and more in terms of berries? Or another way of thinking about it is, as I catch more and more rabbits, the opportunity cost in terms of berries is increasing. Which one of these curves describes that? Well some of you might have already seen the video on KhanAcademy, on increasing opportunity cost, and you might recognize that this curve here. But let's just review it, so there's a world where I'm eating all berries, and I can get, I can pick 300 berries a day, but maybe I decide to go after that first rabbit that just likes to hang out and play with my knives, and so when I catch that, it's very easy to catch, so I don't give up a lot in terms of berries, especially because I'm probably not, the berries I'm giving up are probably the ones that are hardest to pick. And so let's say that first rabbit, the opportunity cost, I pick 20 less berries, so notice, when I increase the rabbits by one, my berries go down by 20, so my opportunity cost is 20 berries for that first rabbit. But let's say that second rabbit is a little bit harder to catch, and I'm not giving up the quite so hard to pick berries, and so when I pick that next, or when I hunt that next rabbit, I should say, then I've given up 40 berries. So notice, my opportunity cost has increased. For that first rabbit, my opportunity cost was 20 berries. For that second rabbit, my opportunity cost is 40 berries. And it keeps going, then third rabbit, I'm going to give up 60 berries. That fourth rabbit, I'm gonna give up 80 berries, 80 berries, and then last but not least, that fifth rabbit, which is the most that I can hunt in a day, I'm gonna give up 100 berries 'cuz here, I'm going after the really nimble rabbit, the really sly rabbit, and I'm giving up literally the low-hanging fruit in terms of berries, the one, they might be on the ground, just ready for me to pick up, and so, the important realization from this video is this bowed out shape right over here, this is describing an increasing opportunity cost. Let me write that down, increasing, increasing, O.C. for opportunity cost. So with that out of the way, which of these would describe a decreasing opportunity cost? Maybe you could imagine a scenario where every incremental rabbit I catch, I get better and better at catching rabbits. Well you might guess that, well look, if this one is increasing and I'm bowed out, then being bowed in would be a decreasing opportunity cost. Decreasing opportunity cost, and let's make sure that it makes sense, so we could go back to the scenario where we're doing nothing but picking berries, and let's say that first rabbit, so we're gonna talk about a different scenario now, that first rabbit, I had to train myself to be able to get rabbits, I have to buy the tools, I have to stretch, it takes me a lot of effort to get that first rabbit. And so, there, I give up 100 berries, so my opportunity cost for that first rabbit was 100 berries. But then for that second rabbit, my opportunity cost is 80 berries. Maybe now, I've kind of gotten the hang of it. I've already bought my rabbit catching shoes. I've already invested in that. I'm all stretched and limber, maybe those rabbits like to hang out together, and so that keeps on going. So that third rabbit, my opportunity cost is 60 berries. I'm getting really good at catching rabbits, so clearly, you see here, that for each incremental rabbit I get, my opportunity cost is decreasing, all the way to that fifth rabbit, maybe my opportunity cost is 20 berries. To catch that next extra rabbit, I'm giving up those 20 berries. So very clearly, you see a decreasing opportunity cost. And so, by deductive reasoning, you might be able to say, "Well, okay, this straight line must represent "a constant opportunity cost." And that is, indeed, what it shows. For every rabbit, every rabbit you catch, you're giving up exactly, you're giving up exactly 60 berries, every time I catch a rabbit, I give up 60 berries, so my opportunity cost for rabbits, in terms of berries, is just a constant 60. And so this is a scenario, if you were imagining in this fictional world we created, where every rabbit is about as easy to catch as any other one, and every berry is about as easy to pick or find as any other one, and so, the trade off, the amount of time I spent for each incremental rabbit, I'm giving up a fixed amount of berries. No matter how many rabbits I go for, and no matter how many berries I am currently at, so that's a constant opportunity cost, when you have a straight line.
Khan_Academy_AP_Microeconomics	Perfect_and_imperfect_competition.txt	- [Instructor] In this video, we're going to give an overview of the types of markets that you might encounter in an economics class. And we're going to get a little bit precise with our language 'cause you'll hear words like perfect competition or monopoly or oligopoly a lot in economics and frankly, even in your broader life. Now before we even go into those terms, I will differentiate between what's sometimes referred to as a product market. And other markets that are referred to as resource. Resource markets. Now product market is a market where the output of that market, what the market is producing or what it's buying and selling it is something that people will consume and it doesn't just have to be physical product it could also be some type of a service. So examples of product markets, it could be the market for shirts, it could be cars or it could even be a service. It could be tax preparation, tax preparation. These would all be product markets because it's something that people would consume. I would call this consumer tax preparation, not business tax preparations. So this is consumer tax preparation. Now based on my clarification, you might guess what a resource market is all about. These are markets for the inputs into other products. Or into the production of other even resources. So, these would be your famous inputs of or factors of production. It could be, for example, the market of labor. It could be something like farm land. Where farm land is used to produce something else. It could be the market for capital goods. Maybe robots for factories. But either way, whether we're talking about product markets or resource markets, we can think about them in broad terms based on how many players there are in the market and how differentiated the players are in the market and how much control they have over the price and how are the barriers to entry. Let's set up a spectrum here to explore that a little bit. So I will set up a spectrum. Now the extreme end of the spectrum right over here, when you only have one player, one player in the market. In the market, or actually let me just say one firm. Because player's not really clear on what I'm talking about whether I'm talking about a buyer or seller. One firm in market. And let's say, many buyers. Many buyers. You are probably familiar with what we call this market or what we would call this firm. It has a monopoly! It has a monopoly name for a famous game because the whole point of that game is to try to be that last firm standing. The firm that owns all of the real estate. Now what are the situations that would describe a monopoly? Well, a monopoly is a situation where you have very high, one could argue insurmountable barriers to entry, so very high. High barriers, barriers to entry. And monopolies can sometimes be controversial but they're not necessarily illegal. In fact, in many countries, a monopoly can be granted to a firm through things like the intellectual property or through patents, for example a drug company if it discovers a cure for a drug or something to maintain a drug, well they might be granted a monopoly for that pill for some period of time and the government does that so that they can recoup their investment in all of the R&D that they actually produced. What often is illegal in a lot of countries, is if firm misuses its monopoly power. But anyway, now let's go to the other extreme. Let's imagine a situation where instead of high barriers to entry, there is no barriers. No barriers to entry. Now let's say that there is no differentiation. And you have many players. So many, or let me write many firms. I keep wanting to say players, but that doesn't make it that clear. And actually let me say many firms and many buyers. And many buyers. Now this is a state that we'll often study in our economics class, we'll call it perfect competition. Perfect competition. In a perfect competition world, the firms are essentially have to be price takers. They take whatever the market price is and we have used that assumption in a lot of situations. In a monopoly, on the other side, they could be the price setters. They're the only player in that market. Now, in general when anything is described as perfect it's usually theoretical and so is perfect competition. There's no markets that I can think of that are perfectly perfect, but I can think of ones that are close. For say, some agricultural commodities. So say the sugar market. So the market for sugar might be pretty close to perfect competition. There could be many firms, those would be the farmers, the suppliers. It would be many buyers obviously who want sugar. There would be some barriers to entry. You'd need to know how to grow sugar, you would need suitable land for growing sugar. But there's a lot of farmers who might be able to swap out either sugar cane or beet, which is where most sugar comes from. With soy bean or vice versa. So they can change which crops they plant and generally speaking, there's not much differentiation whether you get sugar from one farm or another. So sugar would be pretty close to perfect competition and it is the case for a lot of agricultural commodities that they do have to be price takers. There is just a market price that the individual farmer is gonna say, oh actually I wanna charge a little bit more for that sugar because they won't be able to. They're just going to have to take whatever the price is in the market. Now as you can imagine, there is a lot of other types of markets that are in between these extremes. Closer to a monopoly and similar to a monopoly in a lot of ways is a situation where you have only a handful of firms and that's referred to oligopoly. And this is a situation where you still have high barriers. So high barriers to entry. You might have a handful of firms, so a few firms and you still have many buyers. Examples of oligopolies, this could be things like the aircraft industry. Air craft. Where there's huge barriers of entry. You need to deploy a lot of capital billions of dollars. You might have to get government approval and so that's why, especially for large aircraft you only have a few firms that can produce, like Boeing or Airbus, those really large aircraft. Even in certain cases, automobiles, sometimes computer manufacturers, things that have very high barriers to entry. If we go a little bit further to the left, you get a situation that's known as monopolistic competition. Monopolistic, that's fun to say, competition. And this you could view as right in between, depending on what you're thinking about. This is a situation where there's low barriers to entry, low low barriers to entry. There's many firms. Many firms. But you do have differentiation. You do have differentiation so you can tell the product of one firm for another. And I can think of many, in fact most industries I can think of fall roughly in the monopolistic area. Although we've just mention some oligopolies and monopolies. But examples of monopolistic competition, I can imagine to be things like, cereal, breakfast cereals and the breakfast cereal industry, there is many firms. There's generally low barriers. There's some barriers but they're pretty low if you want to start a cereal company a lot of folks might be able to do it. But there is some differentiation. Some people say hey our cereal is more delicious and it's sweeter while others say our cereal is more nutritious and they build a brand and they do marketing, etc, etc. And because there is some differentiation, there's a little bit more ability for the individual players unlike in perfect competition there's a little bit more ability for them to dictate their price. They might say, hey we're a premium product, people think we're healthier so we might be able to charge a little bit more. You can almost imagine that they have their own unique demand curve because of that differentiation. You can imagine the market in something like, well shirts. That's another example. Where a lot of folks can produce shirts, but some people might be able to differentiate themselves. They're more stylish, there's better quality, they advertise, they build a brand. And so once again, that would be monopolistic competition. So anyway, the big picture here is really just for you to get familiar with these words. What do they mean? And then what context or what will they imply about the differentiation or the number of firms? And actually before I leave, I'll throw out one other word that you'll hear a little bit less than what I just talked about and it sounds like monopoly but it is monopsony. And I'm gonna do this in a unique color here. Let me see, I haven't done anything in this salmon yet. Monopsony. Which you won't hear it as much as monopoly. And it's really the opposite situation. Instead of one supplier and many buyers, a monopsony is one big buyer and many suppliers. So for example, if you have one big box store in a small town, and so they're the only employer in that town they might have monopsony in the labor market, where they're the only people who can hire and there's a lot of people who are looking for jobs. But we can talk more about that in other videos.
Khan_Academy_AP_Microeconomics	Price_of_related_products_and_demand_Microeconomics_Khan_Academy.txt	We've talked a little bit about the law of demand which tells us all else equal, if we raise the price of a product, then the quantity demanded for that product will go down. Common sense. If we lower the price, than the quantity demanded will go up, and we'll see a few special cases for this. But what I want to do in this video is focus on these other things that we've been holding equal, the things that allow us to make this statement, that allow us to move along this curve, and think about if we were to change one of those things, that we were otherwise considering equal, how does that change the actual curve? How does that actually change the whole quantity demanded price relationship? And so the first of these that I will focus on, the first is the price of competing products. So if you assume that the price of-- actually I shouldn't say competing products, I'll say the price of related products, because we'll see that they're not competing. The price of related products is one of the things that we're assuming is constant when we, it's beheld equal when we show this relationship. We're assuming that these other things aren't changing. Now, what would happen if these things changed? Well, imagine we have, say, other ebooks-- books is price-- price goes up. The price of other ebooks go up. So what will that do to our price quantity demanded relationship? If other ebooks prices go up, now all of a sudden, my ebook, regardless of what price point we're at, at any of the price points, my ebook is going to look more desirable. At $2, it's more likely that people will want it, because the other stuff's more expensive. At $4 more people will want it, at $6 more people will want it, $8 more people will want it, at $10 more people will want it. So if this were to happen, that would actually shift the entire demand curve to the right. So it would start to look something like this. That is scenario one. And these other ebooks, we can call them substitutes for my product. So this right over here, these other ebooks, these are substitutes. People might say, oh, you know, that other book looks kind of comparable, if one is more expensive or one is cheaper, maybe I'll read one or the other. So in order to make this statement, in order to stay along this curve, we have to assume that this thing is constant. If this thing changes, this is going to move the curve. If other ebooks prices go up, it'll probably shift our curve to the right. If other ebooks prices go down, that will shift our entire curve to the left. So this is actually changing our demand. It's changing our whole relationship. So it's shifting demand to the right. So let me write that. So this is going to shift demand. So the entire relationship, demand, to the right. I really want to make sure that you have this point clear. When we hold everything else equal, we're moving along a given demand curve. We're essentially saying the demand, the price quantity demanded relationship, is held constant, and we can pick a price and we'll get a certain quantity demanded. We're moving along the curve. If we change one of those things, we might actually shift the curve. We'll actually change this demand schedule, which will change this curve. Now, there other related products, they don't just have to be substitutes. So, for example, let's think about scenario two. Or maybe the price of a Kindle goes up. Let me write this this way. Kindle's price goes up. Now, the Kindle is not a substitute. People don't either buy an ebook or they won't either buy my ebook or a Kindle. Kindle is a compliment. You actually need a Kindle or an iPad or something like it in order to consume my ebook. So this right over here is a complement. So if a complement's price becomes more expensive, and this is one of the things people might use to buy my book, then it would actually, for any given price, lower the quantity demanded. So in this situation, if my book is $2, since fewer people are going to have Kindles, or since maybe they used some of their money already to buy the Kindle, they're going to have less to buy my book or just fewer people will have the Kindle, for any given price is going to lower the quantity demanded. And so it'll essentially will shift, it'll change the entire demand curve will shift the demand curve to the left. So this right over here is scenario two. And you could imagine the other way, if the Kindle's price went down, then that would shift my demand curve to the right. If the price of substitutes went down, then that would shift my entire curve to the left. So you can think about all the scenarios, and actually I encourage you to. Think about drawing yourself, think about for products, that could be an ebook or could be some other type of product, and think about what would happen. Well, one, think about what the related products are, the substitutes and potentially complements, and then think about what happen as those prices change. And always keep in mind the difference between demand, which is this entire relationship, the entire curve that we can move along if we hold everything else equal and only change price, and quantity demanded, which is a particular quantity for our particular price holding everything else equal.
Khan_Academy_AP_Microeconomics	Equalizing_Marginal_Utility_per_Dollar_Spent.txt	In the last video, we thought about how we would allocate our $5 between chocolate bars and fruit. And the way we did it, and it was very rational, we thought about how much bang would we get for each buck. And we saw, look, starting off, our first dollar we got a lot of bang for our buck-- and this is really just another way of saying bang for the buck, marginal utility per price. So we got a lot of utility for price starting off for that first chocolate bar. A little less for the next chocolate bar, but still more than we would get for a pound of fruit. Then more for the next chocolate bar, and only then did we start buying some fruit, buying some pounds of fruit. What do I do in this video is generalize it. I want to think about maybe a more continuous case where we can buy very, very small increments of each of the products. It doesn't have to be in chunks, like chocolate bars. And what I'm going to do is I'm going to plot the marginal utility per price, which is really bang for your buck, on the vertical axis. So This right over here on this axis. Let's say this is the marginal utility per price. And let's say it also goes from 0 to 100. So that would be 50. And the numbers actually don't matter so much here. And then this will be dollar spent. So dollars spent, so your buck. So this is bang for your buck and then this is your buck. So this is 1, 2, 3, 4, 5 and 6. Now we're going to do arbitrary products. So let's say one product looks something like this. And once again, you have diminishing utility as you get more and more of that product. In the case of fruit, the more pounds of fruit you get the more tired you get of fruit. The less fruit you need for that, or the less you want fruit for that next incremental pound. So let's-- but it could be anything. This is true of most things. So this is product A, could be a service as well. So product A, let me write it this way. So this is the marginal utility for A per price of A. And let me get another product right over here. So let's say my other product looks something like this. So this is my marginal utility for product B per price of B. So it's really saying bang for the buck. So just to start off-- and I won't even constrain how much money we have. I just want to think about how we would spend that money. So if I were to spend, if I had a penny, where would I spend a penny. And I'm assuming I can buy these in super small chunks, as small as maybe the penny or even maybe fractions of penny. So if I just had a penny, and I had to think about where am I getting the best bang for my buck for that penny, I'm clearly getting it with product A. So I would spend that penny on product A and I would get this much bang for my buck, which would be this entire part right over here. Let me color it in. So my first-- I'll spend it right on A. Let me do it in a color that's more likely to be seen, so I'll do it in this blue color. So I'll spend it on A. My first, in fact, where would I spend my first dollar? Well, the whole first dollar I'm getting a better bang for my buck on A. So my first dollar I will spend on A. And the total utility I will get is actually going to be the area under this curve. It's going to be this whole area. It's going to be dollars times marginal utility with price. That would give you, obviously, the area of this rectangle right over here. The reason why it wouldn't be the area of this larger rectangle, it would just be the area under the curve, is you're not getting 100 marginal utility per price for the entire dollar. It's going down the entire time. And so your actual total marginal utility is actually just the area under this. And when you take calculus you'll get a better appreciation for that. But let's just think about, once again, where our dollar is going to be spent. So actually even if we've spent already $1, our next penny we would still want to spend on product A, because we're still getting more bang for the buck. We're still getting more bang for the buck all the way until right around there. Now something interesting is happening. So we've spent about $2. We've spend our first $2 all on product A because we're getting more bang for buck, even though that bang was diminishing every penny or even every fraction of a penny that we spent. But now where will we spend our next penny? Well, we could spend it on product A again. But look, we can get about the same marginal utility spending it on product B. So we could jump right over there, spend it on product B. Now where could we spend our next dollar? Well, we get about the same marginal utility whether we spend it on a little bit more of product B, or a little bit more of product A. So we could do either. If we spent a little bit too much on product A, then we could have gotten more marginal utility spending on product B. So what we would do is, once we've gotten to this threshold right about here, we actually are going to spend every incremental fraction of a penny-- we're actually going to want to split between product A and product B. If we spend too much on one and we go down this curve, we could have gotten higher utility spending on this one. If we spend too much on this one we could get higher utility spending on this one right over here. So there's a very interesting phenomenon here. Assuming that we eventually spent enough that we buy some of both, obviously we started just buying product A because it had higher utility, at least, for those first few dollars-- but assuming that we end up buying some mix of the two, which we do end up spending if we spend more than $2-- there's an interesting thing. The marginal utility for B, or the marginal utility for price for B that I spent on that last little increment is going to be the same as the marginal utility per price for that last increment of A. So if this was, if B was, I don't know, if it was fruit and let's say A was chocolate but we could buy them in very, very small increments-- we're saying for that last fraction of a pound of fruit you're getting the same marginal utility per price as you're getting for that last fraction of a bar or fraction of a pound of chocolate. So there's a general principle over here. And it really just comes from this very straightforward thing that as soon as you can get better marginal utility on the other one, you start spending there. But then they start to look equal. And you would keep dividing your money between the two. And so the general principle, if you're allocating money between two goods, for that last increment-- not across the board, just that last increment-- that's why the word marginal is so important. For that last ounce of chocolate versus that very last ounce of fruit, the marginal utility for price for that last increment of one good will be the same as the marginal utility per price of the second good. Now I really want to emphasize what this is saying. This is not saying that the marginal utility for price of the two goods are the same. And not even that one is better than the other. This is just saying as you spend money, and let's say you spend enough money to buy both, at some point you're going to get to a threshold where you're neutral between the two, where the marginal utility for price is the same for an incremental of B versus an incremental of A. And at that point you're juts going to keep switching between the two products. Because obviously, if you focus too much on this right over here-- let's say you focus, let's say at that point you switch and you just start buying a bunch of product B right over here. Well, that didn't make sense. Because you were buying product B when you could have actually gotten higher marginal utility buying some of product A. And that's the same reason why you didn't just keep going down A, because you could have gotten higher marginal utility over here. This is closer to, I don't know, 75 while you're only getting 70 right over here.
Khan_Academy_AP_Microeconomics	Introduction_to_economics_Supply_demand_and_market_equilibrium_Economics_Khan_Academy.txt	As we begin our journey into the world of economics, I thought I would begin with a quote from one of the most famous economists of all time, the Scottish philosopher Adam Smith. And he really is kind of the first real economist in the way that we view it now. And this is from his The Wealth of Nations, published in 1776, coincidentally, the same year as the American Declaration of Independence, and it's one of his most-famous excerpts. He generally indeed, he being an economic actor, neither intends to promote the public interest, nor knows how much he is promoting it. By directing that industry, so that the industry in control of that individual actor in such a manner, as its produce may be of the greatest value, he intends only his own gain. 'He intends only his own gain'. And he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention. And this term "the invisible hand" is famous. Led by an invisible hand to promote an end which was no part of his intention. He is saying, look, when individual actors just act in their own self-interest, that often in aggregate leads to things that each of those individual actors did not intend. Then he says: nor is it always the worst for society that it was no part of it. So, it was not necessarily a bad thing. By pursuing his own interest, he frequently promotes that of the society more effectually than when he really intends to promote it. So, this is really a pretty strong statement. It's really at the core of capitalism. And that's why I point out that it was published in the same year as the American Declaration of Independence, because obviously America, the Founding Fathers, they wrote the Declaration of Independence, the Constitution, that really talks about what it means to be a democratic country, what are the rights of its citizens. But the United States, with its overall experience of an American, is at least as influenced by the work of Adam Smith, by this kind of foundational ideas of capitalism. And they just both happened to happen around the same time. But this idea is not always that intuitive. Individual actors, by essentially pursuing their own self-interested ends might be doing more for society than than if any of them actually tried to promote the overall well-being of society. And I don't think that Adam Smith would say that it's always good for someone to act self-interested, or that it's never good for people to actually think about the implications of what they are doing in an aggregate sense, but he is saying that frequently .. frequently, this self-interested action could lead to the greater good. Could lead to more innovation. Could lead to better investment. Could lead to more productivity. Could lead to more wealth, more, a larger pie for everyone. And now Economics is frequently .. and when he makes a statement, he is actually making a mix of micro-economic and macro-economic statements. Micro is that people, individual actors are acting out of their own self-interest. And the macro is that it might be good for the economy, or the nation as a whole. And so, now, modern economists tend to divide themselves into these two schools, or into these two subjects: microeconomics, which is the study of individual actors. Microeconomics .. and those actors could be firms, could be people, it could be households. And you have macro-economics, which is the study of the economy in aggregate. Macro-economics. And you get it from the words. Micro -- the prefix refers to very small things. Macro refers to the larger, to the bigger picture. And so, micro-economics is essentially how actors .. actors make decisions or, you could actually say 'allocations', allocations .. decisions or allocations. Allocation .. of scarce resources. And you hear the words scarce resources a lot when people talk about economics. And a scarce resource is one you don't have an infinite amount of. For example, love might not be a scarce resource. You might have an infinite amount of love. But a resource that would be scarce is something like food, or water, or money, or time, or labor. These are all scarce resources. And so microeconomics is how do people decide where to put those scarce resource, how do they decide where to deploy them. And how does that .. does that affect prices and markets, and whatever else. Macro-economics is the study of what happens at the aggregate to an economy. So, 'aggregate', what happens in aggregate to an economy, from the millions of individual actors. Aggregate economy. We now have millions of actors. And often focuses on policy-related questions. SO, do you raise or lower taxes. Or, what's going to happen when you raise or lower taxes. Do you regulate or de-regulate? How does that affect the overall productivity when you do this. So, it's policy, top-down .. 'top-down' questions. And in both macro- and micro-economics, there is especially in the modern sense of it, there is an attempt to make them rigorous, to make them mathematical. So, in either case you could start with some of the ideas, some of the philosophical ideas, so of the logical ideas, to say someone like Adam Smith might have. So, you have these basic ideas about how people think, how people make decisions. So, philosophy, 'philosophy' of people, of decision-making, in the case of micro-economics -- 'decision-making' And then you make some assumptions about it. Or you simplify it .. let me write this .. you simplify it. And you really are simplifying. You say "oh, all people are rational", "all people are gonna act in their own self-interest, or all people are going to maximize their gain", which isn't true -- human beings are motivated by a whole bunch of things. We simplify things, so we can start to deal with it kind of a mathematical way. SO you simplify it, so you can start dealing with it in a mathematical sense. So, this is valuable to clarify your thinking. It can allow you to prove things based on your assumptions. And so, you can start to visualize things mathematically, with charts and graphs and think about what would actually happen with markets. So it's very valuable to have this mathematical, rigorous, thinking. But at the same time, it could be a little bit dangerous, because you are making these huge simplifications, and sometimes the math might lead you to some very strong conclusions. Conclusions, which you might feel very strongly about, because it looks like you've proven them in the same way that you might prove relativity, but they were based on some assumptions that either might be wrong, or might be over-simplifications, or might not be relevant to the context that you're trying to make conclusions about. So it's very very very important to take it all with a grain of salt, to remember that it's all based on some simplifying assumption. And macro-economics is probably more guilty of it. In micro-economics you are taking these deeply complicated things that are the human brain, how people act and respond to each other, and then you are aggregating it over millions of people, so it's ultra-complicated. You've millions of these infinitely complicated people, all interacting with each other. SO, it's very complicated. Many millions of interactions, and fundamentally unpredictable interactions, and then trying to make assumptions on those, trying to make assumptions and then doing math with that -- that could lead you to some conclusions or might be leading you to some predictions. And, once again, this is very important. This is valuable, it is valuable to make these mathematical models, with these mathematical assumptions for these mathematical conclusions, but it always need to be taken with a grain of salt. So, then you have a proper grain of salt, so that you are always focused on the true intuition. And that's really the most important thing to get from a course on economics. So you can truly reason through what's likely to happen, maybe even without the mathematics. I'll leave you with two quotes. And thse quotes are a little bit .. a little bit funny, but they're really I think helpful things to keep in mind, especially when you go deep into the mathematical side of economics. So, this right over here is a quote by Aflred Knopf, who was publisher in the 1900s. "An economist is a man who states the obvious in terms of the incomprehensible." And I'm assuming what he is talking about as the incomprehensible, he is referring to some of the 'mathy' stuff that you see in economics, and hopefully we're going to make this as comprehensible as possible. You'll see there is value in this. But it's a very important statement he is making. Oftentimes, it's taking a common-sense thing. It's taking something that's obvious .. that's obvious. And it's very important to always keep that in mind, to always make sure that you have the intuition for what's happening in the math, or to know when the math is going into a direction that might be strange based on over-simplifications or wrong assumptions. And then you have this quote here by Lawrence J. Peter, most famous for Peter's Principals, a professor at USC. "An economist is an expert know will know tomorrow why the things he predicted yesterday didn't happen today." And once again -- important to keep in the back of one's mind, because especially relevant to macro-economics, because in macro-economics there is always all sorts of prediction about the state of the economy: about what need to be done, about how long the recession will last, what will be the economic growth next year, what will inflation do ... and they often prove to be wrong. In fact, few economists even tend to agree on many of these things. And it's very important to realize that, because oftentimes when you are deep in the mathematics, economics might seem to be a science, like physics, but it's not a science like physics. It is open .. it is open to subjectivity, and a lot of that subjectivity is all around the assumptions that you choose to make.
Khan_Academy_AP_Microeconomics	Production_Possibilities_Curve_as_a_model_of_a_countrys_economy_AP_Macroeconomics_Khan_Academy.txt	- [Instructor] Let's say that we have some country, let's call it Utenslandia, that can only produce one of two goods or some combination of them. So it can produces forks, or it could produce spoons. And so this axis is the quantity forks, this axis is the quantity of spoons and let's say that if it puts all of its energy into forks, well it would produce that many forks and no spoons, and but then if tried to focus some of its energy, some of its resources on spoons, well then it would produce fewer forks and then the more spoons it produces, it will produce fewer and fewer forks all the way to the point that if it only focused on spoons, well it could produce that many but then it would produce no forks. What this curve is, and we touched on it on other videos, this is the production possibilities curve for our country of Utenslandia that makes utensils and obviously, most countries are much more complex, they don't only produce some combination of two things but this helps us, this is a nice model for understanding what countries might be capable of. Now one way to understand this production possibilities curve is it shows what can be efficiently produced by this country. If it efficiently utilized all of its resources, then it will produce some combination of forks and spoons that sit on the production possibilities curve. So this point right over here, this combination of spoons which would be that many spoons and that many forks, this combination over here, this would be efficient. That point x would be an efficient production for Utenslandia. So at this point right over here, let's call that point y. Now what happens if Utenslandia goes into some type of recession. For whatever reason, it's not able to use its resources as efficiently, and we're talking about resources, we're talking about land, we're talking about maybe its factories, we're talking about the materials it has, maybe its labor, well on that situation, let's say it was operating efficiently here but then the recession happens and so it then it operates right over here, let's call this point right over here z, this would be an inefficient use of its resources, sitting behind the production possibilities curve. So this is inefficient, just like that. And so one question you might have is well what about points that are beyond the production possibilities curve like point, let's just call that point a right over there. What about that point? Well, unless you have more inputs, unless you have more land, more capital, more labor, if you don't change the resources here, this is actually going to be an unattainable point for Utenslandia. But let's say you really wanna reach it, how can that happen? Well, you can actually have investment or you could have more land or more labor. So let's think about that scenario. So let me draw the two axes. So that's my fork axis, that's the quantity of forks that Utenslandia will produce in the year. This will be the spoon axis, right over there. And let's draw our original production possibilities curve. So I'll try to make it look pretty similar to what we had before. So that's our original production possibilities curve. Another way of thinking about it is it's showing the trade off between producing forks and spoons. You can actually think about what is the opportunity cost of producing an incremental spoon in terms of forks. How many forks do you have to trade off because remember, there's scarcity at play. You don't have an infinite amount of metal to produce things with, an infinite amount of labor, an infinite amount of factories. But let's say Utenslandia, they are able to get some more land on which to build factories, maybe they build some more factories so capital goes up, maybe some people migrate to Utenslandia. So in that situation, you would have growth and your production possibilities curve would actually shift outward. So here, we are showing, let me make it a little bit, we are showing a situation right over here, this is still a production possibilities curve but we're showing what happens when you have growth. And once again, what are the drivers of growth? Well this could be the amount of land that you have goes up. The amount of capital that you have goes up. Capital could be things like factories, it could be machinery, you could have people, more people are able to help produce the spoons or forks. You could just have better technology for producing spoons and forks. Sometimes people will even talk about entrepreneurial spirit, that people are able to figure out better ways of combining these resources so that you could produce more spoons or forks. But let's imagine now the other scenario. Let's imagine a scenario where Utenslandia gets into a war with Platelandia. And Platelandia sends their bombers in and starts destroying some of the factories of Utenslandia and so what will happen in that situation? So before the war, this is that production possibilities curve for Utenslandia. But now, because of the war, maybe Platelandia is able to take some land from Utenslandia, maybe it's able to destroy some of the factories and other forms of capital, maybe people flee Utenslandia so there's less labor. And maybe for whatever reason, they can support less technology or they forget how to use some of their technology 'cause the war is so long and protracted. Well in that situation, your PPC, you would see contraction. And contraction, I could depict it, let me shift my PPC, my production possibilities curve inward just like this. So this is a situation where we are seeing contraction. So big picture here, your production possibilities curve is exactly what it says it is. It shows what can a, what is the potential combination of, in this case, goods that this nation can produce and if you're sitting on the curve, it shows that that nation, that country is efficiently using its resources. If you're sitting within the curve, it's inefficiently using its resources. And if you're on the right of the curve or beyond the curve, well that's a situation where if you don't change the inputs, all else equal, this would actually be unattainable. The way that you actually do attain, get to points beyond the curve, is by shifting the curve itself. By having more land, more capital, more labor or more technology which we see in this middle scenario.
Khan_Academy_AP_Microeconomics	Shutting_down_or_exiting_industry_based_on_price_AP_Microeconomics_Khan_Academy.txt	- [Instructor] We've spent several videos already talking about graphs like you see here. This is the graph for a particular firm, maybe it's making donuts so in the donut industry, and we can see how the marginal cost relates to the average variable cost and average total cost. We go into some depth several videos ago, but we see that trend, that marginal cost, can trend down initially because as quantity increases each incremental unit could benefit from things like specialization. And then the marginal cost, the cost of each incremental unit as a function of quantity could go up because of things like coordination costs. And then we've also seen how that relates to average variable costs, that while marginal cost is below average variable cost, every incremental unit is going to bring down the average variable cost, but then when marginal cost crosses average variable cost, well now every incremental unit is going to bring up the average variable cost. And the same thing happens once it crosses the average total cost. And of course the difference between, for any given quantity, between the average total cost and the average variable cost, that is the average fixed cost. Now with that out of the way, we're going to think about how this firm would react under different market conditions. We're going to assume that it's in a very competitive or we could say a perfectly competitive market and so it is a price-taker. And so let's first imagine what would be a positive scenario for this firm. Let's imagine the price up here, so let's call this P sub-one and in a previous video, we already said it would be rational for a profit-maximizing firm to produce at a quantity where the marginal cost and the marginal revenue is meet. And if we're talking about a competitive market, then this price right over here is not going to be a function of the firm's quantity, so that's why it's horizontal, and it would be the same thing as the marginal revenue. So in this situation at P sub-one, the firm would produce Q sub-one, and this is a good situation for the firm because the price that it's getting is higher than its average total cost and so there is going to be a nice amount of profit for this firm. The profit is going to be the price minus the average total cost at that quantity times the actual quantity so because P one is greater than the average total cost, we have a situation where the firm is profitable, firm is profitable, it would want to stay in the market but because you have a profitable firm in this market and you're likely to have many profitable firms in that market, it will probably attract entrants. Other people might say, hey, I wanna make just as much money as this donut company right over here, than this firm, and so you'll probably have more and more entrants into the market, which will probably reduce the prices. Now they could reduce the prices until you get to a price that looks something like this. So I will call that P sub-two. Now, a profit-maximizing firm in this world would keep producing until the marginal cost is equal to the marginal revenue, which in this case is the price, and this would be, my lines aren't completely straight there but you get the idea, so that's Q sub-two. Now in this situation, P sub-two is equal to the average total cost, so the firm is break-even. It's not running at a loss or a profit. So it is break-even and so here the firm is neutral about whether in the long-run, it stays in the market or it exits the market, but you're no longer likely attracting entrants, so no longer attracting, attracting entrants. But it does make sense for the firm to keep operating at this situation even in the long run because it is at least break-even. Now let's imagine another scenario, let's imagine this price level. So for whatever reason, the market price gets to that as we've talked about, a rational firm would be producing at Q sub-three, and at P sub-three right over here, there's some interesting things. Because P sub-three is less than your average total cost, your firm is running at a loss, it's running at a loss here. So running, so firm, firm not profitable. Not profitable. Now you might say, well what is this firm likely to do, would it just shut down? Well in the short-run, it would not make sense for this firm to shut down because the price that it's getting is still higher than its average variable cost, in the short-run, the fixed cost, they've already been spent, so you might as well get as much incremental profit on the margin as you can and so as long as the price is higher than the average variable cost, well outside of their fixed cost, they're still making some money to make up those fixed costs so you have two things going on. So they would stay operating in the short run, stay operating, operating in the short-run, short-run, but what would this firm do in the long-run? Well in the long-run, it makes no sense to have a, to be in a market where you can't make a profit so in the long-run it will exit, so it will exit in the long-run. And in general, the terminology when people are talking about, well, do you start or stop in the short-run, they usually talk about, do you either shut down or operate in the short-run, and then in the long-run, where it's like, hey, are you going to sell your factories or somehow dismantle them or are you going to build new factories, that's all about exiting or entering the industry. And of course, you have another even worse scenario for this firm, which might be down here, where you have price sub-four. Here, in theory, this is where we intersect the marginal cost curve, Q sub-four. Now here it makes no sense for the company to operate at all, so because P sub-four is less than the average total cost, you would want to exit in the long-run, exit in long-run, exit the market but you wouldn't even wait for that long, wait to sell your factories, because P sub-four is less than your average variable cost, you would also just shut down, shut down in the short-run. So big picture from a firm's point of view, you obviously want to be at P one where you make a profit but you might attract entrants. At P sub-two, you as a firm in the long-run are neutral versus exiting the market or entering the market or other people entering the market, you're at breakeven. At P sub-three, in the long-run, you'd wanna exit because you're not profitable if the prices stay at P sub-three, your price is below your average total cost at the rational quantity to produce, so in the long-run, you would exit. But because P sub-three is greater than your average variable cost at the rational quantity, you would stay operating in the short-run and then the last scenario of course is P sub-four where the price gets so low that it just doesn't make sense to even operate another moment.
Khan_Academy_AP_Microeconomics	When_there_arent_gains_from_trade_Basic_economics_concepts_AP_Macroeconomics_Khan_Academy.txt	- [Instructor] So let's say we're in a very simplified world where we have two countries, Country A and Country B and they're each capable of producing apples or bananas or some combination of them and what this chart tells us if Country A put all their energy behind apples in a day they could produce three apples, and if they put all of their energy behind bananas in a day they could produce six bananas. Similarly, Country B, if they put all of their energy behind apples in a day they could produce two apples, and Country B if they put all of their energy behind bananas in a day they could produce four bananas. So given this, who has the comparative advantage in apples and who has the comparative advantage in bananas and how should they trade? Pause this video and try to figure it out on your own. All right so when we're thinking about comparative advantage we really want to think about, well, what is the opportunity cost of producing an apple in each country and what is the opportunity cost of producing a banana in each country? And so let me make another little subcolumn right over here. Opportunity cost, and so what is the opportunity cost of an apple in Country A? And pause this video at any point if you get inspired. Well, to produce three apples they would have to trade off six bananas. And so that means that per apple, they are not producing two bananas. So this is two bananas, two bananas. I'll just write bana, bananas per apple. And their opportunity cost for bananas is just going to be the reciprocal of that. So one over two apples, apples per banana and then for Country B we can do a similar calculation and you might be noticing something interesting is about to happen. What's Country B's opportunity cost of apples? Well, one way to think about it, if they produce two apples, that means they're giving up four bananas. Or they're giving up two bananas per apple. So two bananas, bananas per apple. And once again, if we want to think in terms of the opportunity cost of a banana, well, to produce four bananas they're giving up two apples. So this is one half of an apple per banana. Per, I'll just write, banana right over there. So this one is a little bit interesting. They have the same opportunity cost for apples in terms of bananas, and they have the some opportunity cost for bananas in terms of apples. And so because they have the same opportunity costs. So let me write this down, same opportunity costs. There is no comparative advantage. So no comparative advantage in either. Advantage in either. And so based on our very simple model here there are no gains from trade. Another way we could visualize this that maybe makes it maybe hopefully a little bit more clear. So let me make one axis here. I'm trying to draw a straight line, all right. And then this is my other axis right over here. And let's make this one right over here, this horizontal one let's make this the apples axis and let's make the vertical one the bananas axis. And we're saying per day and this of course is apples per day and so if we look at Country A. Let me do Country A in a new color. So Country A, let's say orange. If they put all their energy behind apples they could produce one, two. Let me spread this out a little bit. They could produce one, two, three apples in a day. If they put all their energy behind bananas they could produce, let's just say this is two, four, six. So that's six, this is four, this is two. This is three right over here. Let me put markers in-between to make this clear. So if they put all of their energy into bananas they could produce six in a day and so their production possibilities if we assume it is a linear trade-off would look something like this and the slope right over here, this would be the opportunity cost. So the slope right over here, every time we increase apples by one we decrease bananas by two. So in this situation, we would have, so the slope here is equal to, well, it's actually a negative slope. It's equal to negative two bananas, bananas per apple. So this right over here, this slope based on how I picked the axes, this is giving me the opportunity cost for apples in terms of bananas. Every time I increase an apple how many bananas am I actually giving up? So that is my opportunity cost there. And now if we think about Country B. Let me do this in a new color. I'm running out of colors. Country B right over here they could either produce four bananas or two apples or things in-between. But notice, it has the exact same slope The slope is the opportunity cost. And if we switch these axes right over here then the slope would be the opportunity cost for bananas in terms of apples, but the big takeaway here, if you see the production possibilities of two countries and we're talking about two goods and they have the same slope, then that means their opportunity costs are going to be the same, and there's not going to be a gain from trade. Remember, the whole point of comparative advantage and trading is that both countries will benefit. That's really the big takeaway here. But there are situations where both countries wouldn't benefit because they have the same opportunity cost and this was an example of one of them. Now the other case, sometimes one will have a comparative advantage over the other. They do have different opportunity costs and then you might have no gains from trade. Maybe there's some way that they can't know each other's opportunity costs. There's some way that they don't trade. Maybe irrespective of what the models tell us about comparative advantage some country says, hey, I don't want to produce bananas. Apples are the future, that's a higher skilled industry, whatever else, so there's definitely scenarios, especially even in our model, in our very simplified model where there might not be gains from trade. And the classic one of course is when there's no comparative advantage and both countries have the same opportunity costs in the goods.
Khan_Academy_AP_Microeconomics	Taxes_and_perfectly_elastic_demand_Microeconomics_Khan_Academy.txt	Let's think about how a tax on a product might affect it, if the demand for it is very, very, very elastic. So what I've done here -- We're going to think about flags -- the market for a certain type of flag that's made in China. And to think about this flag -- think about it this way. If the price -- the price right now -- the equilibrium price between where the supply and the demand intersect -- the supply curve and the demand curve intersect -- is right about seventy dollars per flag. So this is a pretty nice flag. It's right at seventy dollars per flag. And the quantity demanded, in thousands per year, it looks like it's about twenty five thousand flags are demanded per year. Now if at the price were to go slightly above that equilibrium price,what's going to happen? Well, if the price goes slightly above that equilibrium price, people are going to say, "Well, I can go by the American flags made in Taiwan, or even the ones made in America, or made in Mexico, or made some place else. [Because...] "People won't be able to tell the difference from a distance." So I'm going to buy one of the substitutes -- [because] especially the ones from Taiwan or Mexico or wherever else. are identical to the ones made in China. So if the price for slightly -- even slightly higher, the quantity demanded would be much, much, much lower. And if the price were even a little bit lower, then people say, "I'm not going to buy the Mexican flag-- or the Taiwanese [or] American flags. I'm going to buy the ones that were made in China." And then the quantity demanded would be much larger. And so what you have here is a very large, a high elasticity of demand. So this right over here, this is almost perfectly elastic. If it was perfectly elastic, it would be completely horizontal. So this is almost almost almost perfectly -- perfectly elastic -- elastic demand. A very small change in price leads to a huge change in quantity. In particular a very small percentage change in price leads to a huge percent change in quantity. So let's say that -- that some government official decides, "You know what? [I] don't like the idea of American flags being made in China." So they decide to tax American flags made in China. So what they do is that they place a tax, they place a tax -- And once again I'll do a fixed dollar tax. It could be a percentage and if a percentage then it'll change the sup -- the supply plus tax curve It'll be -- the shift will will be a percentage change instead of a fixed change. But the fixed change is a little bit easier to draw, so I'll do that. So let's say that there is a tax -- Let me do that in a different color Let's say that there's a tax placed of ten dollars -- ten dollars per flag. Ten dollars, actually -- Let's do an even a smaller amount. Let's say that there is a tax placed of of one dollar per flag -- one dollar per flag. I'll make it a little bit larger. Let's say it's five dollars per flag -- five dollars per flag. So now what is the supply plus tax curve? So the supplier / just to make the flags in China and ship them to United States and get the story here even to get that first flag done even if is that in the most efficient way possible looks do you need at least looks like around fifty to fifty three dollars now Now they're going now they're still going to need that plus there's going to be a five dollar tax on it So supply plus tax is going to be that plus five dollars is going to be right around there Over here, you add five dollars. So at any given point, we're gonna add fivedollars to essentially what the consumer would have to see. \\So you would have a curve that looks something like this you would have a curve that looks something like this you would have a curve that looks something like this. That dotted line right over there is our supply is our supply plus tax. This right over here was just our supply --was just our supply. So you're essentially -- So let's think about what happens here. Your equilibrium price was at seventy before. Now our equilibrium price is still -- Our equilibrium price is still pretty much at seventy. But our equilibrium quantity has gone down dramatically. Our equilibrium quantity has gone down to -- our equilibrium quantity has gone down to -- I don't know. It looks like about eighteen thousand. Eighteen thousand flags per year. So who bore -- who bore the bulk of this right over here? So let's think about the tax revenue So the tax revenue in this situation is going to be eighteen thousand times the five dollars. So this is the five dollars right over here. That is five dollars -- and then times eighteen thousand -- times eighteen thousand. So this right over here is the tax revenue. That right over there is a tax revenue. Actually, let me draw a little bit more carefully so the tax revenue is This is going to be between this line right over here and five dollars. So just like that. So that's all the tax revenue. And notice. It all came out of the producer surplus. The original producer surplus -- the original producer surplus was -- Especially if we assume perfect elasticity -- The original producer surplus was this green rectangle plus this and plus this. Now this is going to be -- This little area right over here is going to be dead weight loss -- dead-weight loss. And all of that came from the producer's surplus. And then the all the tax revenue, also -- If you especially if you assume this top-line was horizontal -- also came out of the producer surplus. So in this situation where you had almost where you We could say, if if you do have perfect elasticity if you have perfect elasticity of demand for the product, The person who's going to bear the the brunt of the tax -- so -- is going to be the producer. The producer surplus is going to be eaten into from the tax. Bears -- bears the Actually that's not -- that's not (I'm not talking about the animal, "bears.") The producer, -- You know -- I'm not -- well -- The producer gets the burden the producer The producer gets the burden in that situation. And this is an interesting thing to think about. Because when you have almost perfectly elastic demand -- so a -- almost -- or if you said perfectly elastic demand -- a flat -- a flat demand curve right over here -- there's -- there's actually no consumer surplus, because the marginal benefit, even the incremental marginal or -- (I'm -- I'm being redundant with the words incremental and marginal.) But the marginal benefit at any point for the consumer for -- that -- for that next unit is equal to the price they're paying, when you have -- There's no -- There's -- Especially if the the especially if the demand curve is perfectly elastic -- and it's perfectly horizontal -- There is no area between the demand curve and the price paid. So there's actually -- There's isn't any -- even any consumer surplus to take any -- to take any of the -- to take -- to eat into. It all gets eaten out of the out of the producer surplus.
Khan_Academy_AP_Microeconomics	How_costs_change_when_fixed_and_variable_costs_change_AP_Microeconomics_Khan_Academy.txt	- [Instructor] In the last few videos, we were studying our watch factory, ABC Watch Factory. And based on some data, knowing what our fixed costs are, our labor units, our variable costs, our total costs, and then our total output, and that would be for for different amounts of labor, we were able to calculate marginal product of labor, marginal costs, average variable cost, average fixed cost, and average total cost. What we're gonna do in this video is start to explore how these various calculations will change, and eventually, how these curves will change based on changes in cost and productivity. So let's say our rent has gone up by $2000 a month, and we have to pay that extra rent regardless of what our output is. So what is that going to do to marginal product of labor, marginal costs, average variable cost, average fixed cost, and average total cost? Pause this video and think about what's going to happen before we actually model it in this spreadsheet by raising our fixed costs, our monthly fixed costs. So we are going to go from $5000 a month of fixed costs to $7000 a month of fixed costs. So it's gonna be $7000, but we're not done yet. We want to scroll all the way down. And so, what changed from what I had before? Well if you were paying close attention, your marginal product of labor hasn't changed, your marginal cost hasn't changed, your average variable cost hasn't changed, your average fixed and average total cost did change. And that should, hopefully, make intuitive sense. If you look at the formulas for these things, for example, the marginal product of labor, you would see that it involves total output and the labor units. It doesn't involve the fixed costs at all. So if the fixed costs change, you wouldn't expect our marginal product of labor to change. When you look at marginal costs, you are involving total costs. And you say hey, isn't fixed costs part of total costs? But remember, fixed cost is, the $7000 is part of the $13000, and it's part of this $9000 right over here. So when you take the $13000 minus the $9000, which we do in the numerator right over here, we're doing our change in total costs over our change in output, those two $7000 cancel out. The fixed costs cancel out, and so your marginal costs is not dependent on your fixed costs. Similarly, your variable costs is separate, you can view in a lot of ways, from your fixed costs. So your average variable costs aren't going to be affected by fixed costs. And, of course, you would expect your average fixed costs to change, because that is directly derived from your fixed costs and your output. And then, average total costs are also derived from total costs. It's not a change between total cost, and that total cost has the fixed cost in it. So you might be asking yourself, well what would change your marginal product of labor, your marginal costs, your average variable cost, or your average total cost? Well, think about a change in labor productivity. Let's say that each person, there's some magical new device, or new process, that allows them to be a little bit more productive? Well then one person, instead of producing 10, let's say they now produce 11. And let's say two people now, instead of 25, can now producer 27. Let's say three people, instead of 45, can now produce 47. And now four people, and I'm making these numbers up, they can no produce 59. Lemme say this is 66. And then let's say that this is 72. And so notice, that did change our marginal product of labor. And once again, marginal product of labor is based on the difference in total output, as we have a difference in our labor units. And that change in productivity, it might be more pronounced. In the way I just happened to pick the numbers, it was more pronounced when you have fewer people, and then it got more diminished as you had more and more people. But when you had that change in productivity, you might have noticed that that changed our marginal cost, and that changed our average variable cost. Because, once again, your marginal cost, if we look at it right over here, it is calculated by looking at your change in total cost, divided by your change in total output. And when we had this productivity improvement, our change in total output improved. Now there could be a situation where you have a productivity improvement, but the change in total output from one person to the next, might not change. So it's not always going to change either the marginal product of labor or the marginal cost. But changes in productivity will often change those two things. And similarly, if you look at your average variable cost, it is based on your variable costs and your output. When you have this productivity improvement, that's going to improve your output for any given amount of variable cost. And so, that's going to have an affect on your average variable cost. And then your average total cost is, of course, based in part on your total variable cost, which is driven by that productivity improvement. Similarly, you could have changes in variable cost. Let's say all of the people who work at your factory have gotten together and say we want a raise. And you give in, and you give a raise, well now, instead of $2000 per worker, it's going to cost $2200 per worker. You gave a 10% raise per month. And so let me get that all the way down. And notice, the things that you would have expected to change did change. Your marginal product of labor didn't change, because marginal product of labor is not driven by cost. It only looks at the labor units and the total output. But your marginal cost did change, even though our output for every incremental person did not change, because the underlying cost of the people changed. Similarly, the average variable cost, you would of course expect it to change, 'cause our variable costs all went up by 10%. Your average fixed cost isn't going to be affected, 'cause we changed the variable cost, not the fixed. And the total costs were, of course, affected, because the average variable cost were affected.
Khan_Academy_AP_Microeconomics	Rent_control_and_deadweight_loss_Microeconomics_Khan_Academy.txt	Voiceover: Let's think about the market for real estate in a given city. Here on the vertical axis I have plotted rent in terms of dollars per square foot per month. Here on the horizontal axis, is essentially the quantity of square foot square foot per month available in millions. This is 1 million, 2 million, 3 million, 4 million, 5 million. Here in blue we have the demand curve. You see as the price is high, one way to view it is that the demand for square footage is low and as the price is low the demand for square footage is higher. But what I really want to focus on in this video, is viewing the demand curve as the marginal benefit curve. Marginal benefit curve. When that first incremental square foot that is added to the market, that has a huge marginal benefit where people are desperate to get an apartment. To get someplace where they could rent and they could live. So it has a huge marginal benefit. Then the marginal benefit for every incremental square foot starts to go down. Likewise, we can look at the supply curve. We're going to look at this as the marginal cost curve. The marginal cost curve. The marginal cost of that very first incremental square foot for the suppliers for the landlords in the city is $1 per square foot. One way to think about it, that very first square foot, we don't know what its price would have been, but let's say its price was at $3 if it was. I'm just making that up. In that reality, if that very first square foot's price was at $3, there is definitely an incentive for someone to make that first square foot because their marginal cost is only a dollar and they could rent it out at $3 per month. There is definitely an incentive for someone to rent it. The marginal benefit is $4 and they just have to pay $3 for it. It could be rented out for anywhere or it would exist, or this kind of transaction would happen as long as its price was between $1 and $4. You could imagine, based on how this is drawn, where the actual equilibrium price is. The suppliers will keep adding more and more square foot as long as they can actually rent it out, all the way until the point that the marginal benefit is equal to the marginal cost. Right over here marginal benefit is equal to marginal cost. It wouldn't make sense for suppliers to produce an incremental square foot right over here. If they produce an incremental square foot, their marginal cost has gone beyond $3, while the marginal benefit is below $3, no one is going to rent that thing out. We reach an equilibrium point at 2 million square feet per month on the market. Let me make that line a little bit straighter. 2 million square foot per month on the market and at a price of $3 per square foot per month. You can look at the total surplus here. In this equilibrium scenario, we can calculate the consumer surplus. So all of these folks, for this first incremental foot, someone was willing to pay $4 per square foot. They only have to pay $3. The next one a little less than $4. Benefit they only have to pay $3. All the way to this point right over here. So the area of this triangle right over here, this right over here is the consumer surplus. So that right over here is consumer surplus. Consumer surplus. We can calculate it. This is a triangle. I'm assuming actually both the supply and demand curves are lines. So let's see this has a height of 1 and it has a base of 2 so its area is going to be 1 times 2 times one-half. That is going to be equal to 1 million dollars. We are multiplying $1 times 2 million times one-half. That's going to be 1 million dollars of consumer surplus per month. Let's think about the producer surplus. The producer surplus is going to be this area. It's going to be this area right over here. That first incremental foot it only cost those producers $1 but they are able to rent it out for $3. Then they will keep producing, keep producing all the way until they do 2 million square foot. For all of their square feet, they are able to rent it out for more than it was their cost to produce it. So the area of this triangle is the producer surplus. This is the producer surplus. Producer surplus. We can calculate that as well. The height right over here is $2. $2 times this width is 2 million square feet per month. 2 times 2 times one-half is 2. This is equal to 2 million dollars. If we were to talk about what the total surplus is, it is 3 million dollars. Now, this equilibrium rent, $3 per square foot per month is actually quite a lot for 1,000 square foot apartment. My last apartment was a two bedroom, two bath apartment. It was about 1,000 square foot. So that means you're going to be paying $3,000 per month for that. That's pretty high rent. That's the type of rent you might pay in a city like San Francisco. Let's say people start complaining about it. So the government says, "Okay that rent is not fair. "It's too high. "We want to introduce some type of price control. "We want to introduce rent control." I'm oversimplifying how this works, but just so that we can deal with this model right over here, Let's say that the city just sets a ceiling on the price per square foot per month. Let's just say they set a price ceiling, a price ceiling of $2 per square foot per month. $2 per square foot. Let me write it this way. $2 per square foot per month. So they set a price ceiling right over here. Given that, what is going to happen? What is going to happen? What I really want to think about is what is going to be the new consumer surplus or the new producer surplus? I encourage you to pause the video and try to think about that on your own. Well let's think about what's going to happen. From the producers point of view, it doesn't make sense for them to produce more than 1 million units. 1 million square feet per month. I have to rent out more than a million square feet per month because that extra square foot above that, its marginal cost is going to be more than what they're going to get. The producers are just going to stop there. The producer surplus is going to be the area of this triangle right over here. Let's see, this is $1 times 1 million times one-half. This is now a producer surplus. Producer surplus. A new producer surplus under the rent control of $500,000, half a million, of $500,000. So we see that the rent control immediately hit the producers pretty hard. The producer surplus has gone down dramatically. Now what about the consumer surplus? We're talking about a million units, or a million square foot per month I should say. So now the new consumer surplus is the area, is this entire area. So you see that at least for this first incremental million square feet, the consumers have started to win out a little bit. To figure this out, what the total area is, we just need to figure out what we could break this up into two sections. We could break this up into two sections. This is the point, 1 million square feet at $3.50 dollars per square foot per month. This is right over here, the point, the 3.5. We could use that to figure out this new area. Actually let me do it in a different color, in this green area right over here. What is it going to be? Well the area of this thing right over here is one-half high. One-half times 1 times one-half. This right over here is 250K. We add that to this area right over here, which is one and a half times 1. $1.5 dollars per square foot per month times 1 million. Did I do that right? Yep. So that's going to be plus ... plus this, which is 1.5 million. You add these two together. The total consumer surplus ... So the total consumer surplus is now 1.75 million. So the consumer surplus definitely did go up in total because it gained all of this from the producer, but let's think about what has now happened in our society or in our city. The producers definitely don't want to put out as many square foot per rent anymore. It does look like we have lost some total surplus for our little city here. We have lost out on this entire area. We can calculate it by looking at what the total surplus was before the rent control and what the total surplus was after the rent control. The total surplus before, so before the total surplus was the 2 million producer surplus plus the 1 million consumer surplus, so it was 3 million. After, it is the 1.75 million consumer surplus plus the $500,000 producer surplus, which is 2.25 million. What we've lost is the difference here, which is $750,000. So this area right over here. This is per month. This right over here represents the lost total surplus. This lost total surplus of $750,000 per month is referred to as the dead weight loss. You can debate about rent control. Is it good? Is it bad? Is it good for this kind of dynamic? Who gets what share of the surplus? This of course is an oversimplification of a market and even the way rent control would be instituted. This is a model for beginning to think about what happens to the total surplus when these types of price controls are instituted.
Khan_Academy_AP_Microeconomics	Demand_Curve_as_Marginal_Benefit_Curve.txt	Voiceover: In all of our conversations about demand curves so far, I've been generally talking about price driving quantities. So for example, we've been saying, using say this demand curve right here for a new car in terms of how many would be sold per day, we would say things like, "Well look, if we price it at $60,000 per car," this is in thousands of dollars. "If we price it at $60,000 per car, "we are going to sell one car. "If we price it at $50,000 a car, "we are going to sell two cars." The way that I've been talking about it is given a price, how many are we actually going to sell? What I want to do in this video is think about it the other way around. We're going to look at the exact same demand curve, the exact same relationship between price and quantity, but we're going to conceptualize it in our heads in a slightly different way. We're going to think about it in terms of quantity driving price. To think of it that way, imagine that we are the producers of this given model of a new car. We go the other way. We don't say, "How many will we sell "at a price of $60,000?" Or, "How much will we sell at a price of $50,000?" We'll go from the point of view of what if we only produce one car a week? If we only produced one car a week, how much could we get for that car? Let's say somehow you're able to figure that out. You're able to read people's minds or you have some type of a market study. When you ask that question you're like, "Look if you only allowed one car to be sold each week, "you determine that in that week there "is going to be somebody, "somebody's going to think that it's worth "$60,000 to buy that car." That person, they're willingness to pay, that person is going to be willing to trade $60,000. They're going to be willing to forego what else they could have bought for that $60,000 and instead they want that car. Then you would plot that point right over there. If you only had one unit, you could sell it for $60,000. Now let's go, let's keeping asking ourselves for more units. Let's say, what if we wanted to sell two units? Well, if you wanted to sell two units, you could definitely sell one unit for $60,000, assuming that you could get that first person, but that second person, this might have been the person that just wants a car so badly it just resonated with them in some way. For that second unit, the second person who is going to need to buy your car, might not be as excited about it. That second person will only be willing to forego $50,000. That second person would be willing to forego 50. So if you wanted to sell two units, if you insist on selling two units, and if you're assuming you're going to give the same price for everyone. We'll talk about in the future how you might give different prices to different people. Assuming you want to give the same price to everyone, you're going to have to sell your car for $50,000. Now clearly that first person is definitely going to jump at it. They're going to be able to get the car for more than they were willing to pay. More than what it was worth to them. More than the benefit for them, but if you want two people, now you're going to have to set this up for $50,000. Now the same logic. Now what if we want to sell three cars? What if we want to sell three cars a week? Well, if we price it at $50,000, we'll definitely get those first two, but the third person might not jump. The third person isn't going to be as excited about it or need it as much as these first two. So you do a market study or you're able to read people's minds. You're like, "Look the third person, "for the market, the marginal benefit." Let me write this word down. The marginal benefit. The marginal benefit for the next unit, the next unit is going to be $40,000. To get that next buyer, and it could be multiple buyers buying each unit or it could be one buyer buying all of the units. Maybe it's some type of a car rental company saying, "Oh, we don't need to get ... For three "of these cars I'm not as excited about it anymore. "My marginal benefit is lower." This is really the same marginal benefit that we talked about when we talked about the PPF, the Production Possibilities Frontier. In that, we talked about it very explicitly in terms of trade off, in terms of opportunity cost. Here we're measuring the marginal benefit in terms of price, but price really can be viewed as a foregone opportunity. If you spend $40,000 on this car, you're making the decision not to spend $40,000 on something else. A down payment on a house or a nice boat, or whatever else it might be. So really what we're doing, is at any point in this curve, this really is the marginal benefit for that next buyer. That marginal benefit to the market of that next unit of whatever you are producing. This is a very different way of viewing the exact same demand curve. Before we said, "Okay, if we want to price "it at $50,000, how many are we going to sell?" Now we're saying, "If we want to sell only two units, "where can we price it?" We can price it at $50,000. If we want to go from two to three units, we're going to have to price it at the marginal benefit of that third unit to the market and it could be the marginal benefit to that next consumer. Convincing that next consumer to say, "Hey it is worth it to buy this car. "Let's price it at $40,000." I'm going to leave you there in this video, but what I'm going to think about is depending on where you price it, let's say that we decide that we want to sell four units every week. So we say, "Well look, to get that fourth "person to buy this car, we have to price the car "at $30,000." What we're going to talk about in the next video is if you did that, if this is where you decide to price it so that you can sell four units, these other people got really good deals. The first unit could have gone for much more. The second unit could have still also gone for a good bit, not as much as the first unit. The third unit could have gone for a little bit less than the second unit, but still more than what you ended up selling things for. We're going to talk about this idea right over here that some of these consumers are getting more for their money than what they have to pay, or at least in their own minds they are.
Khan_Academy_AP_Microeconomics	Total_revenue_and_elasticity_Elasticity_Microeconomics_Khan_Academy.txt	So we're going back to our little burger stand where we had our demand curve in terms of burgers per hour. And now, I want to think about something from the perspective of our burger stand. And think about, at any given point on this demand curve, how much revenue would we get per hour. And when I talk about revenue, for simplicity, let's just think that's really just how much total sales will I get in a given hour. So let me just write over here total revenue. Well, the total revenue is going to be how much I get per burger times the number of burgers I get. So the amount that I get per burger is price. So it's going to be equal to price. And then the total number of burgers in that hour is going to be the quantity. Pretty straightforward. If I sell 10 things at $5, I am going to get $50 of revenue, $50 of sales in that hour. Now, let's think about what the total revenue will look like at different points along this curve right over here. And actually, let me just make a table right over here. So I'll make one column price, one column quantity. And then let's make one column total revenue. So let's look at a couple scenarios here. Well, we could actually look at some of these points that we already have defined. At point A over here, price is 9. So I'll do it in point A's color. Prices is 9. Quantity is 2. $9 times 2 burgers, $9 per burger times 2 burgers per hour. Your total revenue is going to be $18. And you can see it visually right over here. This height right over here is 9. And this width right over here is 2. And your total revenue is going to be the area of this rectangle. Because the height is the price. And the width is the quantity. So that total revenue is the area right over there. Now, let's go to point-- let me do a couple of them just to really make it clear for us. Let's try to point B. So at point B when our price is 8 and our quantity is 4, 4 per hour. Our total revenue is going to be 8 times 4 which is $32 per hour. And once again, you can see that visually. The height here is 8. And the width here-- so the height of this rectangle is 8. And the width is 4. The total revenue is going to be the area. It's going to be the height times the width just like that. Now, let's go to a point that I haven't actually graphed here. Actually, let me just-- actually, I'll go through all the points just for fun. So now at point C, we have 5.50. 5.50 is a price. The quantity is 9. 9 times 5.50. 9 times 5 is $45. And you have another 4.50. So that is 49.50. So once again, it's going to be the area of this rectangle. Area of that rectangle right over there. So you might already be noticing something interesting. As we lower the price, at least in this part of our demand curve, as we lower the price, we are actually increasing not just the quantity were increasing the total revenue. Let's see if this keeps happening. So if we go to point D, I'll do it in that same color. We have 4.50. And we are selling 11 units. So 11 times 4.50. Let's see, this is going to be 44 plus 5.50. Once again, that is 49.50. So that this rectangle is going to have the same area as that pink one that we just did for scenario C. And I'll actually just do one more down here, just to see what happens. Because this is interesting. Now we lower the price. And it looks like things didn't change much. And now, let's go-- let's just do one more point actually for the sake of time. Point E. And I encourage you to try other ones. Try F on your own. Point E, my price is $2 per burger. My quantity is 16 burgers per hour. I sell a total of 32 burgers. Now actually, let's just do the last one, F, just to feel a sense of completion. So $1 per burger. I sell 18 burgers per hour. My total revenue, when you multiply them, is $18 per hour. And once again, that's the area of this rectangle, this short and fat rectangle right over here. And E was the area-- the total revenue in E was the area of that right over there. And you could graph these just to get a sense of how total revenue actually changes with respect to price or quantity. Lets plot the total revenue with respect to quantity. So let's try it out. So if you-- let me plot it out. So this is going to be total revenue. And this axis right over here is going to be quantity. And we're going to, once again, go from-- let's see. This is 0. This is 5. This is 10. This is 15. And this is 20 right over here. And then total revenue. Let's see, it gets as high-- it gets pretty close to 50. So let's go. This is 10 20, 30, 40, and 50. So that's 50, 40, 30, 20, and 10. So when our quantity is 2, and our price is 9. Well, we don't have price on this axis right over here. But when our quantity is 2, our total revenues 18. So it's going to be something like there. Then, when our quantity is 4, our total revenue is 32. Right about there. Then, when our quantity is 9, our total revenue is almost 50. So right over there. And then, when it's 11, it's also at that same point right over there. And then, when we are quantity is 16, our total revenues 32. 16. So 32. Right there. And then finally, when our quantity is 18, our total revenue is 18. And what you see is that it's plotting out a curve that looks like this. And if you remember some of your algebra 2, this is a concave downwards parabola right over here. And you can see there was actually some point at which you could maximize your total revenue. And if you really tried all the points here, you would see that maximum point is if you tried this point right over here, right at price 5 and quantity 10. At price 5 and quantity 10, in that hour, you would sell $50. So this is the maximum point right over there $50. Now, the whole reason why I'm talk think about this. I could have talked about this independently of any discussion of elasticity just to see how total revenue relates to price and quantity at different points on the demand curve. But there is an interesting relationship. In that very first video, and we actually used this exact demand curve for it. When we explored elasticity, we saw that up here at this part of the curve-- let me do this in a different color. At this point of the curve in orange for any change-- when you do a change in your price since the prices are pretty high, that is a much lower percent change in price than the impact that you get on quantity. Because over here, although they look like they're close. Or I should say the absolute. For every 1 that down we move in price, we're moving 2 up quantity. But that 1 down in price is a very small percentage of price because our prices are high here. And it's a very large percentage of quantity right over here. So you get huge changes in percent quantity for very small changes in price in this part of the curve. So this part of the curve is elastic. Or you could say that its price elasticity for demand is greater than 1. You get larger changes in percent quantity for a given change in percent price. Now, these parts of the curve down here, we saw is the opposite's happening. You move 1 down, 1 unit down in price, you move 2 units to the right in quantity. But over here, price is a much lower. So this is a much larger percentage change in price. And this is a much smaller percentage change in quantity. So you get large percentage changes in price for small percentage change in quantity. That means that here, you are relatively inelastic. And then right over here, right at this point, right in this region, right over here, we saw that we had unit-- we were unit elastic right over there. So there's an interesting relationship going on. While we were, so while we were elastic, this part right over here, when we lowered price in this region. While we were elastic, when we lowered price, we got increases in revenue. So let me write this down. And this is generally, too, there's a couple of boundary cases on the math that make it a little bit, you can't make it absolutely true. But while we are elastic, at the elastic points of our demand curve, a decrease in price. Price goes down. Total revenue was going up. You do a price cut on this part of the demand curve, you get more revenue. Then, when you are at unit elasticity, what was happening? At unit elasticity, you were right at this point right over here. Right at this point over here. And roughly, when you do a price cut-- and I'm going to say this is roughly true-- your total revenue stays constant. But just right at that point, right when you're going through that unit elasticity point. And then finally, when you are inelastic when a large percent changes in price result and not so large percent change is in quantity demanded, then a price change going down resulted in lower total revenue. Resulted in total revenue going down. And this should, hopefully, make a little bit of intuitive sense. Because over here, this point, if given percent change in price, you were getting a larger percent change in quantity. So the percent in price went down. Your percent in quantity grew even more. So you made up any decrease in height with a increase in width. So your area increased. Down here, your decrease in percent price wasn't made up for a decrease in quantity. So when you made your rectangles little bit shorter, you didn't, we weren't able to compensate by growing the width as much. And so you actually had a lower area, lower total revenue.
Khan_Academy_AP_Microeconomics	Introduction_to_production_functions_AP_Microeconomics_Khan_Academy.txt	- [Instructor] You will hear the term production function thrown around in economic circles, and it might seem a little intimidating and a little mathy at first. But as you're about to see, it's a fairly basic idea. It's this idea that you could have these various inputs. Let's call this input number one, and then you have input number two. And you can keep going, and then you put them in, their inputs, into some type of process. And then that function, let's just call that f, that's going to describe how much output you can get given that input. We can also describe it a little bit more mathematically. Those of you who remember your Algebra Two might recognize this. Or we could say the output, it's often use the letter Q in economic circle, it's going to be a function, it's going to be a function of the various inputs. So I'll put input number one, input number two, and you could go, you could have as many inputs as is necessary to produce that good. And these inputs, if you wanted to categorize them, these are the classic factors of production that we would have talked about before. These would be, these would be your land, labor, capital, and entrepreneurship. And it doesn't have to be all of them, but each of these inputs would likely be factored as one of these. Now, this might still seem very abstract and very mathy. So to make things very tangible, let's give a, well, let's give a tangible example. Let's say that we're trying to make a bread toasting operation. So what we need to do is we take bread, we stick it in a toaster, and then once it's toast, we're done. And so what are our inputs there? Well, you're definitely going to need some bread, so let me draw some bread right over here, my best attempt at drawing bread. So that right over there, that is bread. You could call that input number one. Now you're also going to need a toaster, at least one toaster, or toasters I should say. And let's say the toasters that we use for this operation, they can toast four pieces of bread at a time, and it takes 10 minutes to do that, four slices in 10 minutes. Now you might say, well, aren't those going to be all of our inputs? But then the obvious question is that bread isn't just going to jump into the toaster on its own and then jump back out. Someone, there's going to be, needs to be some labor to operate this operation. So we're going to need some toaster operators, and let's say that they can process, they can process one slice per minute, one slice per minute. I know many of you all are thinking that you could do better than that, but try to do it all day, one slice per minute. Now based on this, if these are really all of the three inputs into producing the output toasted piece of bread, we could try to construct a production function here. So let's do that. So let's say then the output is going to be the number of slices of toasted bread. And it's going to be equal to, and I'm gonna write this as, well, I'm gonna make our production function as being the minimum of several values. And what you're going to see, it's going to be based on what's going to be our rate-limiting factor? And I want to get too much in the weeds with you on this, but just to help us understand, so it's going to be the minimum of, well, the amount of bread you have, so slices of bread, slices of bread. And why does that make sense? Well, you're only, the amount of toasted bread you can produce is always going to be limited by the amount of untoasted bread that you put into your process. If you only have 60 that's going in per hour here, well, then you can only produce a maximum of 60 right over here, and this is going to be per hour, per hour. So this is gonna be the slices of bread per hour. Now, our other input, how much toast can one toaster toast in one hour? Well, if they do four slices in 10 minutes, we'll multiply that time six to get to an hour. That's gonna be 24 slices per hour. So we could do 24 times the number of toasters, times the toasters. And then last but not least, how much bread or how many slices can one person process per hour? Well, it's going to be 60 slices per hour. So we'll do 60 times, times, let's call them workers, I was gonna call 'em toasters, but we are using that for the equipment, times the number of workers. And so it's worth, at this point, just pause this video and really process what's going on. What are the inputs here, and what are the outputs? Well, the inputs are right over here. This is the number of slices of bread per hour, the number of toasters we have at our disposal, the number of workers. Toasters you could view as capital. Workers you could view as labor. And now another interesting thing to think about, and we will talk a lot about this in economics, is what's going on in the long run and the short run? And production functions are useful for thinking about the long run in the short run because the short run is defined, the short run is defined as the situation in which at least one of your inputs is fixed. Let me write this down, at least, at least one input is fixed. Now, what does that mean in our bread toasting example right over here? Well, let's just say that we can, it's very easy to get slices of bread. If we have the capacity and we want to produce more bread, the slices of bread are, let's say it's just never our rate-limiting factor. So that part isn't fixed. But to get a new toaster, let's say these are special toasters, and you gotta order them and it takes a month. So let's say that there's a one-month lead time on this input, one month lead time. And let's say, for workers, there's just not a line of people ready to toast toast. You have to put a job posting out there, and you're going to have to interview people. And so let's say that it takes two weeks to hire someone, so two weeks to hire, or I guess you could also say two weeks to hire or to fire someone if you want to reduce capacity. Let's say it takes one month to either get a toaster or to remove a toaster. Well, in that case, the short run in this situation is a time period where at least one of the inputs is fixed. So pause this video, and think about what would be the short run in our situation? Well, the short run in our situation, the number of toasters we're going to have is going to be fixed for at least a month. So our short run, in this situation, is up to a month, so up to, up to a month. And then the other side of it, what would the long run be? Well, in the long run, by definition none of your inputs are fixed. You can change the number you have of any of these things. So our long run is going to be greater than one month in this example. Now, it's really worth noting that was just for this example. If we were talking about some type of automobile factory and the output is the number of automobiles produced per day or per month and then you have all these inputs, you would have your metal, you would have your labor, and then you would have the equipment for the factory itself, well, there, the long run, it might take another year or even two years or five years to build a factory. In that case, the long run would be the time period greater than amount it takes to build another factory. Usually, capital is the thing that is most fixed for the longest period of time, and that's why it made it hard for us to get our toasters. So I will leave ya there. This is just an introduction to the idea of a production function. But hopefully with our bread toasting example, it is not so intimidating.
Khan_Academy_AP_Microeconomics	Inferior_goods_clarificationx.txt	I sensed some confusion coming out of the last video. And for your good, so I thought I would do another one. So let's make, let's assume that there's three cars in the market, and what I want to do with this is I sense that some people thought that I was suggesting that a car in general is an inferior good, and that's not what I was saying. I was saying, if we lived in a reality where everyone owned a car and a car was a necessity for life, and that is true in much of the developed world, I was saying that the cheapest car in the market might be considered an inferior good. And to think about that, let's just think about the entire population. So let's say this line, this line represents the entire population in our place, in our developed country, where everyone owns a car. And let's say, let's represent this car with a blue. So let's say maybe 1/3 of the people right now have that car. Now, let's say a good chunk of the people have this midsize sedan, this is probably the car that most people would like to have, it's a little bit safer, it's a little bit larger, it's a more powerful engine. And so this is where most people are sitting. And then you have this ultra, this kind of luxury, you have this luxury car, Rolls Royce maybe. And so that is a very small segment. So this end of the line is the poor, in our population. This is the rich right over here. So this is at some given income level, and maybe we could say this is true at a particular price point. But what we're going to talk about is the general impact on demand-- so on the entire curve at any given price point, always assuming that this is the most expensive, this is in between, and this is the least expensive. Now, what happens if income goes up from here? Well, the very poorest, they're not going to be able to necessarily just trade up to this midsize sedan yet, although they maybe have more income for other things or maybe they can get a nicer version of this. But for the most part, they're still going to be driving this car. But at kind of the boundary right over here, if the incomes do go up, there will be people who now could afford the mid-size car, and that's what they want. And so these people might start buying the midsize car. And then what will happen over here, well, maybe there's a few people at the boundary over here, they now have the money to afford this very expensive car, and it suits their tastes. And so they also, a very small proportion, also grows there. So what happened here? When income went up, the quantity demanded at a particular price point for this smallest car went down. But the demand for this midsize car went up, it took a much bigger chunk out of this blue than a chunk was taken out of it by the orange, and also the demand for this very expensive car went up. And that was at a particular price point, but assuming that this is the most expensive, this is the middle, and this is the cheapest expensive, this would be true of probably any price point. And so we have this phenomenon that when income went up, the quantity demanded at multiple price points for this car-- so let me draw its actual demand curve. So this car right over here, this is price, this over here is demand. If its old demand curve looked something like this, we're saying-- and maybe when we thought about this at first, we're thinking of the price point right over here, we notice when income went up, at that particular price point, the quantity demanded went down, and that'd be true pretty much any price point, assuming that this is always the cheapest car. So at any price point, you would have a decrease in demand. Remember, when we talk about a decrease in demand, we're talking about a shift of the entire curve, we're not talking about just one particular quantity. Now, there's another interesting question that was asked, and I think it was a very nice and subtle thing to think about. I keep drawing these shifting demand curves, and if at least I understand the question properly, the question is well, does the curve, when it shifts, does it necessarily shift perfectly or does sometimes it change? Does it shift more at one price point or another? And the simple answer is it can. In fact, in very few circumstances would it probably be a perfect shift. Depending on the price point you're at, it would probably shift a little bit different. So the actual shape of the curve might change while it's shifting. But anyway, going back to this, so we see this cheap car right here had the unusual property that when incomes went up, the demand curve shifted to the left. And that's why we call this an inferior good. These other two cars when-- so that's price, and this is demand-- these other two cars when income went up-- so if this was the demand curve at first-- when income went up, demand went up. The whole curve got shifted to the right, so they are normal. So these are normal goods.
Khan_Academy_AP_Microeconomics	Total_consumer_surplus_as_area_Microeconomics_Khan_Academy.txt	Let's say you run an orange stand. And this right here, you could view this as either the demand curve for your orange stand or your marginal benefit curve, or really you could call it the willingness to pay, the first 100 pounds of oranges. Or that very 100th pound, someone would be willing to pay $3 per pound. But then the 101st pound would be a little bit less than that. So that's the willingness to pay, or the marginal benefit of that incremental pound. But let's say you decide to set the price at $2, and you are able to sell 300 oranges in that week. What I want to think about is, what is the total consumer surplus that your consumers got? And the way to think about consumer surplus is, how much benefit did they get above and beyond what they paid? So for example, the person who bought-- let's just think about the exact 100th pound. The 100th pound, they paid $2. They paid $2, but their benefit looks like it was, I don't know, $3.30. But they only paid $2. So their benefit on that one pound, their benefit, or I should say their consumer surplus, is going to be $3.30 minus a $2.30. So that person who bought that 100th-- not all the 100 pounds, just that 100th pound-- got a consumer surplus of $3.30 minus $2, which is a $1.30 consumer surplus. So if you wanted to figure out the entire consumer surplus, well, you just have to do it for all of the pounds. So that was 100th pound. So essentially, you could view this as the area of this little thing right over here. And let me zoom in, just to make sure you understand what's going on. That thing that I just drew, if we zoom in, will look something like this. It was one pound wide. And this right over here was $2. And then we had our marginal benefit curve, or our demand curve, sloping down like that. And this point right over here was $3.30. And so to figure out the consumer surplus for that pound we said, OK, for that pound they were willing to pay $3.30. The benefit to them was $3.30. But they only had to pay $2. So the height of this right over here was $1.30. And so the consumer surplus is $1.30 per pound times one pound. And so that's where we got the $1.30 consumer surplus. Now, we could do that for every one of the pounds. So we could do that for the 101st pound. Let me get a different color. The 101st pound, we would do it like that. Then the 102nd pound, we would do it like that. 103rd pound like that. We'd do it for the 99th pound like that. And so you could imagine if we wanted to find the total consumer surplus, what are we doing? Well, we're essentially just finding the area between our demand curve and this line where the price is equal to 2. So we're just going to sum up this area. And if you're familiar with calculus, you might know that you can actually make these things arbitrarily small. You don't have to take a one pound wide rectangle. You get a half a pound wide rectangle, or a quarter pound wide rectangle. Then you'll just have more rectangles. It doesn't matter so much if you have a linear demand curve, but if you had a non-linear demand curve then it would matter. You'd want to get smaller and smaller and smaller, or thinner and thinner and thinner rectangles, so you could get better and better approximations for the consumer surplus. But needless to say, what you're really doing-- especially if you get unbelievably thin rectangles, and you have an unbelievably high number of them-- you're really just estimating the area under the demand curve and above the price equals $2. And so if you want to know this consumer surplus-- and I really want you to understand why this was. I mean, just think about it for each pound. It was just how much more value that pound, whoever bought that pound, how much more value do they get relative to what they paid. And we're just summing that up across all of the pounds. So to really figure out the total consumer surplus, we just have to find this area of this blue area. And that's just finding the area of a triangle. So this right over here, you have a base of 300. This length right over here is 300 pounds. And then our height over here. And we can just use this as the area of a triangle, because this is a simple linear demand curve. We would actually have to use a little bit of calculus if this was a non-linear curve. But the height here is 2. So our area, the area between the demand curve and our price equals 2, is equal to 1/2 times base times height. 1/2 times the base, which is 300 pounds, times the height, which is $2 per pound. The pounds cancel out. 1/2 times 2 is 1, times 300 is 300. So we get 300. And all we're left with is dollars. So the total consumer surplus in this case is $300. And it really is just the area between the demand curve and this price equals 2 line right over there.

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.