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Yohanan Friedmann has reported that according to many modern historians and thinkers, the puritanical thought of Ahmad Sirhindi inspired the religious orthodoxy policy of Aurangzeb. Taxation policy. Shortly after coming to power, Aurangzeb remitted more than 80 long-standing taxes affecting all of his subjects. In 1679, Aurangzeb chose to re-impose "jizya", a military tax on non-Muslim subjects in lieu of military service, after an abatement for a span of hundred years, in what was critiqued by many Hindu rulers, family-members of Aurangzeb, and Mughal court-officials. The specific amount varied with the socioeconomic status of a subject and tax-collection were often waived for regions hit by calamities; also, Rajput and Maratha state officials, Brahmins, women, children, elders, the handicapped, the unemployed, the ill, and the insane were all perpetually exempted. The collectors were mandated to be Muslims. A majority of modern scholars reject that religious bigotry influenced the imposition; rather, realpolitik – economic constraints as a result of multiple ongoing battles and establishment of credence with the orthodox Ulemas – are held to be primary agents.
Aurangzeb also enforced a higher tax burden on Hindu merchants at the rate of 5% (as against 2.5% on Muslim merchants), which led to considerable dislike of Aurangzeb's economic policies; a sharp turn from Akbar's uniform tax code. According to Marc Jason Gilbert, Aurangzeb ordered the jizya fees to be paid in person, in front of a tax collector, where the non Muslims were to recite a verse in the Quran which referred to their inferior status as non Muslims. This decision led to protests and lamentations among the masses as well as Hindu court officials. In order to meet state expenditures, Aurangzeb had ordered increases in land taxes; the burden of which fell heavily upon the Hindu Jats. The reimposition of the jizya encouraged Hindus to flee to areas under East India Company jurisdiction, under which policies of religious sufferance and pretermissions of religious taxes prevailed. Aurangzeb issued land grants and provided funds for the maintenance of shrines of worship but also (often) ordered their destruction. Modern historians reject the thought-school of colonial and nationalist historians about these destruction being guided by religious zealotry; rather, the association of temples with sovereignty, power and authority is emphasized upon.
Whilst constructing mosques were considered an act of royal duty to subjects, there are also several "firmans" in Aurangzeb's name, supporting temples, "maths", chishti shrines, and gurudwaras, including Mahakaleshwar temple of Ujjain, a gurudwara at Dehradun, Balaji temple of Chitrakoot, Umananda Temple of Guwahati and the Shatrunjaya Jain temples, among others. Contemporary court-chronicles mention hundreds of temple which were demolished by Aurangzab or his chieftains, upon his order. In September 1669, he ordered the destruction of Vishvanath Temple at Varanasi, which was established by Raja Man Singh, whose grandson Jai Singh was believed to have facilitated Shivaji's escape. After the Jat rebellion in Mathura (early 1670), which killed the patron of the town-mosque, Aurangzeb suppressed the rebels and ordered for the city's Kesava Deo temple to be demolished, and replaced with an "Eidgah". In 1672–73, Aurangzeb ordered the resumption of all grants held by Hindus throughout the empire, though this was not followed absolutely in regions such as Gujarat, where lands granted in in'am to Charans were not affected. In around 1679, he ordered destruction of several prominent temples, including those of Khandela, Udaipur, Chittor and Jodhpur, which were patronaged by rebels.
In an order specific to Benaras, Aurangzeb invokes Sharia to declare that Hindus will be granted state-protection and temples won't be razed (but prohibits construction of any new temple); other orders to similar effect can be located. Eaton notes numerous new temples were built in other areas of the empire during this time. Richard Eaton, upon a critical evaluation of primary sources, counts 15 temples to have been destroyed during Aurangzeb's reign. Administrative reforms. Aurangzeb received tribute from all over the Indian subcontinent, using this wealth to establish bases and fortifications in India, particularly in the Carnatic, Deccan, Bengal and Lahore. Revenue. Aurangzeb's exchequer raised a record £100 million in annual revenue through various sources like taxes, customs and land revenue, "et al." from 24 provinces. He had an annual yearly revenue of $450 million, more than ten times that of his contemporary Louis XIV of France. Coins. Aurangzeb felt that verses from the "Quran" should not be stamped on coins, as done in former times, because they were constantly touched by the hands and feet of people. His coins had the name of the mint city and the year of issue on one face, and, the following couplet on other:
Law. In 1689, the second Maratha Chhatrapati (King) Sambhaji was executed by Aurangzeb. In a sham trial, he was found guilty of murder and violence, atrocities against the Muslims of Burhanpur and Bahadurpur in Berar by Marathas under his command. In 1675 the Sikh leader Guru Tegh Bahadur was arrested on orders by Aurangzeb, found guilty of blasphemy by a Qadi's court and executed. The 32nd Da'i al-Mutlaq (Absolute Missionary) of the Dawoodi Bohra sect of Musta'lī Islam Syedna Qutubkhan Qutubuddin was executed by Aurangzeb, then governor of Gujarat, for heresy; on 27 Jumadil Akhir 1056 AH (1648 AD), Ahmedabad, India. Military. It is reported that Aurangzeb always inspected his cavalry contingents every day, while testing his cutlasses sheep carcass, brought before him without the entrails and neatly bound up, in one strike. In 1663, during his visit to Ladakh, Aurangzeb established direct control over that part of the empire and loyal subjects such as Deldan Namgyal agreed to pledge tribute and loyalty. Deldan Namgyal is also known to have constructed a Grand Mosque in Leh, which he dedicated to Mughal rule.
In 1664, Aurangzeb appointed Shaista Khan subedar (governor) of Bengal. Shaista Khan eliminated Portuguese and Arakanese pirates from the region, and in 1666 recaptured the port of Chittagong from the Arakanese king, Sanda Thudhamma. Chittagong remained a key port throughout Mughal rule. In 1685, Aurangzeb dispatched his son, Muhammad Azam Shah, with a force of nearly 50,000 men to capture Bijapur Fort and defeat Sikandar Adil Shah (the ruler of Bijapur) who refused to be a vassal. The Mughals could not make any advancements upon Bijapur Fort, mainly because of the superior usage of cannon batteries on both sides. Outraged by the stalemate Aurangzeb himself arrived on 4 September 1686 and commanded the siege of Bijapur; after eight days of fighting, the Mughals were victorious. Only one remaining ruler, Abul Hasan Qutb Shah (the Qutbshahi ruler of Golconda), refused to surrender. He and his servicemen fortified themselves at Golconda and fiercely protected the Kollur Mine, which was then probably the world's most productive diamond mine, and an important economic asset. In 1687, Aurangzeb led his grand Mughal army against the Deccan Qutbshahi fortress during the siege of Golconda. The Qutbshahis had constructed massive fortifications throughout successive generations on a granite hill over 400 ft high with an enormous eight-mile long wall enclosing the city. The main gates of Golconda had the ability to repulse any war elephant attack. Although the Qutbshahis maintained the impregnability of their walls, at night Aurangzeb and his infantry erected complex scaffolding that allowed them to scale the high walls. During the eight-month siege the Mughals faced many hardships including the death of their experienced commander Kilich Khan Bahadur. Eventually, Aurangzeb and his forces managed to penetrate the walls by capturing a gate, and their entry into the fort led Abul Hasan Qutb Shah to surrender; he died after twelve years of Mughal imprisonment.
Mughal cannon making skills advanced during the 17th century. One of the most impressive Mughal cannons is known as the Zafarbaksh, which is a very rare "composite cannon", that required skills in both wrought-iron forge welding and bronze-casting technologies and the in-depth knowledge of the qualities of both metals. The "Ibrahim Rauza" was a famed cannon, which was well known for its multi-barrels. François Bernier, the personal physician to Aurangzeb, observed Mughal gun-carriages each drawn by two horses, an improvement over the bullock-drawn gun-carriages used elsewhere in India. During the rule of Aurangzeb, In 1703, the Mughal commander at Coromandel, Daud Khan Panni spent 10,500 coins to purchase 30 to 50 war elephants from Ceylon. Art and culture. Aurangzeb was noted for his religious piety; he memorized the entire Quran, studied hadiths and stringently observed the rituals of Islam, and "transcribe[d] copies of the Quran." Aurangzeb had a more austere nature than his predecessors, and greatly reduced imperial patronage of the figurative Mughal miniature.
Calligraphy. The Mughal Emperor Aurangzeb is known to have patronised works of Islamic calligraphy; the demand for Quran manuscripts in the "naskh" style peaked during his reign. Having been instructed by Syed Ali Tabrizi, Aurangzeb was himself a talented calligrapher in "naskh", evidenced by Quran manuscripts that he created. Architecture. Aurangzeb was not as involved in architecture as his father. Under Aurangzeb's rule, the position of the Mughal Emperor as chief architectural patron began to diminish. However, Aurangzeb did endow some significant structures. Catherine Asher terms his architectural period as an "Islamization" of Mughal architecture. One of the earliest constructions after his accession was a small marble mosque known as the Moti Masjid (Pearl Mosque), built for his personal use in the Red Fort complex of Delhi. He later ordered the construction of the Badshahi Mosque in Lahore, which is today one of the largest mosques in the Indian subcontinent. The mosque he constructed in Srinagar is still the largest in Kashmir. Aurangzeb had a palace constructed for himself in Aurangabad, which was extant till a few years ago.
Most of Aurangzeb's building activity revolved around mosques, but secular structures were not neglected. The Mubarak Manzil in Agra served as his riverside residence after his victory at Samugarh. The Bibi Ka Maqbara in Aurangabad, the mausoleum of Rabia-ud-Daurani, was constructed by his eldest son Azam Shah upon Aurangzeb's decree. Its architecture displays clear inspiration from the Taj Mahal. Aurangzeb also provided and repaired urban structures like fortifications (for example a wall around Aurangabad, many of whose gates still survive), bridges, caravanserais, and gardens. Aurangzeb was more heavily involved in the repair and maintenance of previously existing structures. The most important of these were mosques, both Mughal and pre-Mughal, which he repaired more of than any of his predecessors. He patronised the "dargahs" of Sufi saints such as Bakhtiyar Kaki, and strived to maintain royal tombs. Textiles. The textile industry in the Mughal Empire emerged very firmly during the reign of the Mughal Emperor Aurangzeb and was particularly well noted by Francois Bernier, a French physician of the Mughal Emperor. Francois Bernier writes how "Karkanahs", or workshops for the artisans, particularly in textiles flourished by "employing hundreds of embroiderers, who were superintended by a master". He further writes how "Artisans manufacture of silk, fine brocade, and other fine muslins, of which are made turbans, robes of gold flowers, and tunics worn by females, so delicately fine as to wear out in one night, and cost even more if they were well embroidered with fine needlework".
He also explains the different techniques employed to produce such complicated textiles as "Himru" (whose name is Persian for "brocade"), "Paithani" (whose pattern is identical on both sides), "Mushru" (satin weave) and how "Kalamkari", in which fabrics are painted or block-printed, was a technique that originally came from Persia. Francois Bernier provided some of the first, impressive descriptions of the designs and the soft, delicate texture of Pashmina shawls also known as "Kani", which were very valued for their warmth and comfort among the Mughals, and how these textiles and shawls eventually began to find their way to France and England. Foreign relations. Aurangzeb sent diplomatic missions to Mecca in 1659 and 1662, with money and gifts for the Sharif. He also sent alms in 1666 and 1672 to be distributed in Mecca and Medina. Historian Naimur Rahman Farooqi writes that, "By 1694, Aurangzeb's ardour for the Sharifs of Mecca had begun to wane; their greed and rapacity had thoroughly disillusioned the Emperor ... Aurangzeb expressed his disgust at the unethical behavior of the Sharif who appropriated all the money sent to the Hijaz for his own use, thus depriving the needy and the poor." According to English traveller named John Fryar, Aurangzeb also consider that despite his enormous power on land, it is cheaper to establish reciprocal relation with the naval forces of Portuguese empire to secure the sea interest of ships in Mughal territory, so he did not built an overtly massive naval forces.
Relations with Aceh. For decades, the Malabari Mappila Muslims which representing the Mughal empire are already patronized Aceh Sultanate. Aurangzeb, and his brother, Dara Shikoh, participated with Aceh trade and Aurangzeb himself also exchanging presents with the Sultan of Aceh in 1641. In that year, it is recorded the daughter of Iskandar Muda, Sultanah Safiatuddin, has presented Aurangzeb with eight elephants. When the VOC, or Dutch East India Company trying to disrupt the trade in Aceh to make their own Malaka trade lucrative, Aurangzeb threatened the Dutch with retaliation against any losses in Gujarat due to Dutch intervention. This effort were caused due to VOC realization that Muslim tradings were damaging to the VOC. The Firman issued by Aurangzeb caused the VOC to back down and allowed Indian sailors to pass into Aceh, Perak, and Kedah, without any restrictions. Relations with the Uzbek. Subhan Quli Khan, Balkh's Uzbek ruler was the first to recognise him in 1658 and requested for a general alliance, he worked alongside the new Mughal Emperor since 1647, when Aurangzeb was the Subedar of Balkh.
Relations with the Safavid dynasty. Safavid Iran and the Mughal Empire had long clashed over Kandahar, an outpost on the distant frontier of their two empires. Control of the city swung back and forth. Aurangzeb led two unsuccessful campaigns to recapture it 1649 and 1652. Mughal attempts died down after 1653 amidst internal rivalries. Upon ascending the throne, Aurangzeb was eager to obtain diplomatic recognition from the Safavids to bolster the legitimacy of his rule. Abbas II of Persia sent an embassy in 1661. Aurangzeb received the ambassador warmly and they exchanged gifts. A return embassy sent by Aurangzeb to Persia in 1664 was poorly treated. Tensions over Kandahar rose again. There were cross border raids, but hostilities subsided after Abbas II's death in 1666. Aurangzeb's rebellious son, Prince Akbar, sought refuge with Suleiman I of Persia. Suleiman rescued him from the Imam of Musqat, but refused to assist him in any military adventures against Aurangzeb. Relations with the French. In 1667, the French East India Company ambassadors Le Gouz and Bebert presented Louis XIV of France's letter which urged the protection of French merchants from various rebels in the Deccan. In response to the letter, Aurangzeb issued a "firman" allowing the French to open a factory in Surat.
Relations with the Sultanate of Maldives. In the 1660s, the Sultan of the Maldives, Ibrahim Iskandar I, requested help from Aurangzeb's representative, the Faujdar of Balasore. The Sultan wished to gain his support in possible future expulsions of Dutch and English trading ships, as he was concerned with how they might impact the economy of the Maldives. However, as Aurangzeb did not possess a powerful navy and had no interest in providing support to Ibrahim in a possible future war with the Dutch or English, the request came to nothing. Relations with the Ottoman Empire. Like his father, Aurangzeb was not willing to acknowledge the Ottoman claim to the caliphate. He often supported the Ottoman Empire's enemies, extending cordial welcome to two rebel Governors of Basra, and granting them and their families a high status in the imperial service. Sultan Suleiman II's friendly postures were ignored by Aurangzeb. The Sultan urged Aurangzeb to wage holy war against Christians. However, Aurangzeb were granted as patron of Sharif of Mecca, and sending the Sherif at that time with richly laden mission, which at that time were under the jurisdiction of Ottoman.
Relations with the English and the Anglo-Mughal War. In 1686, the East India Company, which had unsuccessfully tried to obtain a "firman" that would grant them regular trading privileges throughout the Mughal Empire, initiated the Anglo-Mughal War. This war ended in disaster for the English after Aurangzeb in 1689 dispatched a large fleet from Janjira that blockaded Bombay. The ships, commanded by Sidi Yaqub, were manned by Indians and Mappilas. In 1690, realising the war was not going favourably for them, the Company sent envoys to Aurangzeb's camp to plead for a pardon. The company's envoys prostrated themselves before the emperor, agreed pay a large indemnity, and promise to refrain from such actions in the future. In September 1695, English pirate Henry Every conducted one of the most profitable pirate raids in history with his capture of a Grand Mughal grab convoy near Surat. The Indian ships had been returning home from their annual pilgrimage to Mecca when the pirate struck, capturing the "Ganj-i-Sawai", reportedly the largest ship in the Muslim fleet, and its escorts in the process. When news of the capture reached the mainland, a livid Aurangzeb nearly ordered an armed attack against the English-governed city of Bombay, though he finally agreed to compromise after the Company promised to pay financial reparations, estimated at £600,000 by the Mughal authorities. Meanwhile, Aurangzeb shut down four of the English East India Company's factories, imprisoned the workers and captains (who were nearly lynched by a rioting mob), and threatened to put an end to all English trading in India until Every was captured. The Lords Justices of England offered a bounty for Every's apprehension, leading to the first worldwide manhunt in recorded history. However, Every successfully eluded capture.
In 1702, Aurangzeb sent Daud Khan Panni, the Mughal Empire's Subhedar of the Carnatic region, to besiege and blockade Fort St. George for more than three months. The governor of the fort Thomas Pitt was instructed by the East India Company to sue for peace. Relations with the Ethiopian Empire. Ethiopian Emperor Fasilides dispatched an embassy to India in 1664–65 to congratulate Aurangzeb upon his accession to the throne of the Mughal Empire. The delegation reportedly presented several valuable offerings to the Mughal Emperor, such as slaves, ivory, horses, a set of intricately adorned silver pocket pistols, a zebra and various other exotic gifts. François Bernier, describes the presents as consisting of: Relations with the Tibetans, Uyghurs, and Dzungars. After 1679, the Tibetans invaded Ladakh, which was in the Mughal sphere of influence. Aurangzeb intervened on Ladakh's behalf in 1683, but his troops retreated before Dzungar reinforcements arrived to bolster the Tibetan position. At the same time, however, a letter was sent from the governor of Kashmir claiming the Mughals had defeated the Dalai Lama and conquered all of Tibet, a cause for celebration in Aurangzeb's court.
Aurangzeb received an embassy from Muhammad Amin Khan of Chagatai Moghulistan in 1690, seeking assistance in driving out "Qirkhiz infidels" (meaning the Buddhist Dzungars), who "had acquired dominance over the country". Relations with the Czardom of Russia. Russian Czar Peter the Great requested Aurangzeb to open Russo-Mughal trade relations in the late 17th century. In 1696 Aurangzeb received his envoy, Semyon Malenkiy, and allowed him to conduct free trade. After staying for six years in India, and visiting Surat, Burhanpur, Agra, Delhi and other cities, Russian merchants returned to Moscow with valuable Indian goods. Rebellions. Traditional and newly coherent social groups in northern and western India, such as the Marathas, Rajputs, Hindu Jats, Pashtuns, and Sikhs, gained military and governing ambitions during Mughal rule, which, through collaboration or opposition, gave them both recognition and military experience. Jat rebellion. In 1669, Hindu Jats began to organise a rebellion that is believed to have been caused by the re-imposition of "jizya" and destruction of Hindu temples in Mathura. The Jats were led by Gokula, a rebel landholder from Tilpat. By the year 1670 20,000 Jat rebels were quelled and the Mughal Army took control of Tilpat, Gokula's personal fortune amounted to 93,000 gold coins and hundreds of thousands of silver coins.
Gokula was caught and executed. But the Jats once again attempted rebellion. Raja Ram Jat, in order to avenge his father Gokula's death, plundered Akbar's tomb of its gold, silver and fine carpets, opened Akbar's grave and dragged his bones and burned them in retaliation. Jats also shot off the tops of the minarets on the gateway to Akbar's Tomb and melted down two silver doors from the Taj Mahal. Aurangzeb appointed Mohammad Bidar Bakht as commander to crush the Jat rebellion. On 4 July 1688, Raja Ram Jat was captured and beheaded. His head was sent to Aurangzeb as proof of his beheading. However, after Aurangeb's death, Jats under Badan Singh later established their independent state of Bharatpur. Due to the Jat rebellion, the temples of Pushtimarg, Gaudiya, and Radha vallabh Vaishnavs in Braj were abandoned and their icons were taken to different regions or into hiding. Mughal–Maratha Wars. In 1657, while Aurangzeb attacked Golconda and Bijapur in the Deccan, the Hindu Maratha warrior, Shivaji, used guerrilla tactics to take control of three Adil Shahi forts formerly under his father's command. With these victories, Shivaji assumed de facto leadership of many independent Maratha clans. The Marathas harried the flanks of the warring Adil Shahis, gaining weapons, forts, and territory. Shivaji's small and ill-equipped army survived an all out Adil Shahi attack, and Shivaji personally killed the Adil Shahi general, Afzal Khan. With this event, the Marathas transformed into a powerful military force, capturing more and more Adil Shahi territories. Shivaji went on to neutralise Mughal power in the region.
In 1659, Aurangzeb sent his trusted general and maternal uncle Shaista Khan, the Wali in Golconda to recover forts lost to the Maratha rebels. Shaista Khan drove into Maratha territory and took up residence in Pune. But in a daring raid on the governor's palace in Pune during a midnight wedding celebration, led by Shivaji himself, the Marathas killed Shaista Khan's son and Shivaji maimed Shaista Khan by cutting off three fingers of his hand. Shaista Khan, however, survived and was re-appointed the administrator of Bengal going on to become a key commander in the war against the Ahoms. Aurangzeb next sent general Raja Jai Singh to vanquish the Marathas. Jai Singh besieged the fort of Purandar and fought off all attempts to relieve it. Foreseeing defeat, Shivaji agreed to terms. Jai Singh persuaded Shivaji to visit Aurangzeb at Agra, giving him a personal guarantee of safety. Their meeting at the Mughal court did not go well, however. Shivaji felt slighted at the way he was received, and insulted Aurangzeb by refusing imperial service. For this affront he was detained, but managed to effect a daring escape.
Shivaji returned to the Deccan, and crowned himself "Chhatrapati" or the ruler of the Maratha Kingdom in 1674. Shivaji expanded Maratha control throughout the Deccan until his death in 1680. Shivaji was succeeded by his son, Sambhaji. Militarily and politically, Mughal efforts to control the Deccan continued to fail. Aurangzeb's third son Akbar left the Mughal court along with a few Muslim Mansabdar supporters and joined Muslim rebels in the Deccan. Aurangzeb in response moved his court to Aurangabad and took over command of the Deccan campaign. The rebels were defeated and Akbar fled south to seek refuge with Sambhaji, Shivaji's successor. More battles ensued, and Akbar fled to Persia and never returned. In 1689, Aurangzeb's forces captured and executed Sambhaji. His successor Rajaram, later Rajaram's widow Tarabai and their Maratha forces fought individual battles against the forces of the Mughal Empire. Territory changed hands repeatedly during the years (1689–1707) of interminable warfare. As there was no central authority among the Marathas, Aurangzeb was forced to contest every inch of territory, at great cost in lives and money. Even as Aurangzeb drove west, deep into Maratha territory – notably conquering Satara – the Marathas expanded eastwards into Mughal lands – Malwa and Hyderabad. The Marathas also expanded further South into Southern India defeating the independent local rulers there capturing Jinji in Tamil Nadu. Aurangzeb waged continuous war in the Deccan for more than two decades with no resolution. He thus lost about a fifth of his army fighting rebellions led by the Marathas in Deccan India. He travelled a long distance to the Deccan to conquer the Marathas and eventually died at the age of 88, still fighting the Marathas.
Aurangzeb's shift from conventional warfare to anti-insurgency in the Deccan region shifted the paradigm of Mughal military thought. There were conflicts between Marathas and Mughals in Pune, Jinji, Malwa and Vadodara. The Mughal Empire's port city of Surat was sacked twice by the Marathas during the reign of Aurangzeb and the valuable port was in ruins. Matthew White estimates that about 2.5 million of Aurangzeb's army were killed during the Mughal–Maratha Wars (100,000 annually during a quarter-century), while 2 million civilians in war-torn lands died due to drought, plague and famine. Ahom campaign. In 1660 Mir Jumla II, the viceroy of Bengal, was ordered to recover the lost territories. The Mughals set out in November 1661. Within weeks they occupied the capital of Kuch Behar, which they annexed. Leaving a detachment to garrison it, the Mughal army began to retake their territories in Assam. Mir Jumla II advanced on Garhgaon, the capital of the Ahom kingdom, and reached it on 17 March 1662. The ruler, Raja Sutamla, had fled before his approach. The Mughals captured 82 elephants, 300,000 rupees in cash, 1000 ships, and 173 stores of rice.
On his way back to Dacca, in March 1663, Mir Jumla II died of natural causes. The battle of Saraighat was the last battle in the last major attempt by the Mughals to extend their empire into Assam. Though the Mughals managed to regain Guwahati briefly after a later Borphukan deserted it, the Ahoms wrested control in the battle of Itakhuli in 1682 and maintained it till the end of their rule. Satnami opposition. In May 1672, the Satnami sect, obeying the commands of an old toothless woman (according to Mughal accounts), organised a revolt in the agricultural heartlands of the Mughal Empire. The Satnamis were known to have shaved off their heads and even eyebrows and had temples in many regions of Northern India. They began a large-scale rebellion 75 miles southwest of Delhi. The Satnamis believed they were invulnerable to Mughal bullets and believed they could multiply in any region they entered. The Satnamis initiated their march upon Delhi and overran small-scale Mughal infantry units. Aurangzeb responded by organising a Mughal army of 10,000 troops, artillery, and a detachment of his imperial guards. Aurangzeb wrote Islamic prayers and drew designs that were sewn into the army's flags. His army crushed the Satnami rebellion.
Sikh opposition. The ninth Sikh Guru, Guru Tegh Bahadur, like his predecessors was opposed to forced conversion of the local population as he considered it wrong. Approached by Kashmiri Pandits to help them retain their faith and avoid forced religious conversions, Guru Tegh Bahadur sent a message to the emperor that if he could convert Teg Bagadur to Islam, every Hindu will become a Muslim. In response, Aurangzeb ordered arrest of the Guru. He was then brought to Delhi and tortured so as to convert him. On his refusal to convert, he was beheaded in 1675. In response, Guru Tegh Bahadur's son and successor, Guru Gobind Singh, further militarised his followers, starting with the establishment of Khalsa in 1699, eight years before Aurangzeb's death. In 1705, Guru Gobind Singh sent a letter entitled "Zafarnamah", which accused Aurangzeb of cruelty and betraying Islam. Guru Gobind Singh's formation of Khalsa in 1699 led to the establishment of the Sikh Confederacy and later Sikh Empire. Pashtun opposition. The Pashtun revolt in 1672 under the leadership of the warrior poet Khushal Khan Khattak of Kabul, was triggered when soldiers under the orders of the Mughal Governor Amir Khan allegedly molested a Parachi woman affiliated with the Safi in modern-day Kunar Province of Afghanistan. The Safi tribes retaliated against the soldiers. This attack provoked a reprisal, which triggered a general revolt of most of tribes. Attempting to reassert his authority, Amir Khan led a large Mughal Army to the Khyber Pass, where the army was surrounded by tribesmen and routed, with only four men, including the Governor, managing to escape.
Aurangzeb's incursions into the Pashtun areas were described by Khushal Khan Khattak as "Black is the Mughal's heart towards all of us Pathans". Aurangzeb employed the scorched earth policy, sending soldiers who massacred, looted and burnt many villages. Aurangzeb also proceeded to use bribery to turn the Pashtun tribes against each other, with the aim that they would distract a unified Pashtun challenge to Mughal authority, and the impact of this was to leave a lasting legacy of mistrust among the tribes. After that the revolt spread, with the Mughals suffering a near total collapse of their authority in the Pashtun belt. The closure of the important Attock-Kabul trade route along the Grand Trunk road was particularly disastrous. By 1674, the situation had deteriorated to a point where Aurangzeb camped at Attock to personally take charge. Switching to diplomacy and bribery along with force of arms, the Mughals eventually split the rebels and partially suppressed the revolt, although they never managed to wield effective authority outside the main trade route.
Rathore rebellion. Described as the "Rathore rebellion" (1679-1707), the conflict between Rajputs of Marwar and the Mughals started after the death of Jaswant Singh of Marwar, due to Aurangzeb's attempt to interfere in the succession of Marwar. On 23 July 1679, Aurangzeb made attempts to divide Marwar into two Rathore principalities, one held by Inder Singh Rathore and other by Ajit Singh. Aurangzeb also proposed that Ajit Singh should be raised as a Muslim and offered Jodhpur in return. The resistance to Mughal interference was started by the Rajput nobles under Durgadas Rathore and erupted into an all-out war between the Mughal empire and Rajputs of Marwar supported by Mewar Rajputs. It lasted for almost thirty years. The rebellion reached a climax after the death of Aurangzeb on 3 March 1707 and the capture of Jodhpur by the Rathores on 12 March 1707. Death. By 1689, the conquest of Golconda and Mughal victories in the south expanded the Mughal Empire to 4 million square kilometres, with a population estimated to be over 158 million. However, this supremacy was short-lived. Historian Jos Gommans says that "... the highpoint of imperial centralisation under emperor Aurangzeb coincided with the start of the imperial downfall."
Aurangzeb constructed a small marble mosque known as the Moti Masjid (Pearl Mosque) in the Red Fort complex in Delhi. However, his constant warfare, especially with the Marathas, drove his empire to the brink of bankruptcy just as much as the wasteful personal spending and opulence of his predecessors. The Indologist Stanley Wolpert says that: Even when ill and dying, Aurangzeb made sure that the populace knew he was still alive, for if they had thought otherwise then the turmoil of another war of succession was likely. He died at his military camp in Bhingar near Ahmednagar on 3 March 1707 at the age of 88, having outlived many of his children. He had only 300 rupees with him which were later given to charity as per his instructions and he prior to his death requested not to spend extravagantly on his funeral but to keep it simple. His modest open-air grave in Khuldabad, Aurangabad, Maharashtra expresses his deep devotion to his Islamic beliefs. It is sited in the courtyard of the shrine of the Sufi saint Shaikh Burhan-u'd-din Gharib, who was a disciple of Nizamuddin Auliya of Delhi.
Brown writes that after his death, "a string of weak emperors, wars of succession, and coups by noblemen heralded the irrevocable weakening of Mughal power". She notes that the populist but "fairly old-fashioned" explanation for the decline is that there was a reaction to Aurangzeb's oppression. Although Aurangzeb died without appointing a successor, he instructed his three sons to divide the empire among themselves. His sons failed to reach a satisfactory agreement and fought against each other in a war of succession. Aurangzeb's immediate successor was his third son Azam Shah, who was defeated and killed in June 1707 at the battle of Jajau by the army of Bahadur Shah I, the second son of Aurangzeb. Both because of Aurangzeb's over-extension and because of Bahadur Shah's weak military and leadership qualities, entered a period of terminal decline. Immediately after Bahadur Shah occupied the throne, the Maratha Empire – which Aurangzeb had held at bay, inflicting high human and monetary costs even on his own empire – consolidated and launched effective invasions of Mughal territory, seizing power from the weak emperor. Within decades of Aurangzeb's death, the Mughal Emperor had little power beyond the walls of Delhi.
Assessments and legacy. Aurangzeb's rule has been the subject of both praise and controversy. During his lifetime, victories in the south expanded the Mughal Empire to 4 million square kilometres, and he ruled over a population estimated to be over 158 million subjects. His critics argue that his ruthlessness and religious bigotry made him unsuitable to rule the mixed population of his empire. Some critics assert that the persecution of Shias, Sufis and non-Muslims to impose practices of orthodox Islamic state, such as imposition of sharia and "jizya" religious tax on non-Muslims, doubling of custom duties on Hindus while abolishing it for Muslims, executions of Muslims and non-Muslims alike, and destruction of temples eventually led to numerous rebellions. G. N. Moin Shakir and Sarma Festschrift argue that he often used political opposition as pretext for religious persecution, and that, as a result, groups of Jats, Marathas, Sikhs, Satnamis and Pashtuns rose against him. Multiple interpretations of Aurangzeb's life and reign over the years by critics have led to a very complicated legacy. Some argue that his policies abandoned his predecessors' legacy of pluralism and religious tolerance, citing his introduction of the "jizya" tax and other policies based on Islamic ethics; his demolition of Hindu temples; the executions of his elder brother Dara Shikoh, King Sambhaji of Maratha and Sikh Guru Tegh Bahadur and the prohibition and supervision of behaviour and activities that are forbidden in Islam such as gambling, fornication, and consumption of alcohol and narcotics. At the same time, some historians question the historical authenticity of the claims of his critics, arguing that his destruction of temples has been exaggerated, he paid for temple maintenance, and in the latter half of his reign employed significantly more Hindus, especially Marathas, in his imperial bureaucracy than his predecessors and opposed bigotry against Hindus and Shia Muslims in imperial service.
Muhammad Al-Munajjid has argued that the opinions from Islamic scholarly community towards Aurangzeb were positive because of the emperor's general attitude and actions, such as abolishing Bid'ah celebrations, musics, and the customs of bowing and kissing the ground which were done by his predecessors, practically adhering to the practice of Salafi while still held to Hanafite creed. Apparently this view of Aurangzeb were influenced by Muhammad Saleh Kamboh, who acted as his teacher. In Pakistan, author Haroon Khalid writes that, "Aurangzeb is presented as a hero who fought and expanded the frontiers of the Islamic empire" and "is imagined to be a true believer who removed corrupt practices from religion and the court, and once again purified the empire." The academic Munis Faruqui also opines that the "Pakistani state and its allies in the religious and political establishments include him in the pantheon of premodern Muslim heroes, especially lauding him for his militarism, personal piety, and seeming willingness to accommodate Islamic morality within state goals."
Muhammad Iqbal, considered the spiritual founder of Pakistan, admired Aurangzeb. Iqbal Singh Sevea, in his book on the political philosophy of the thinker, says that "Iqbal considered that the life and activities of Aurangzeb constituted the starting point of Muslim nationality in India". Maulana Shabbir Ahmad Usmani, in his funeral oration, hailed M.A. Jinnah, the founder of Pakistan, to be the greatest Muslim since Aurangzeb. Pakistani-American academic Akbar Ahmed described President Zia-ul-Haq, known for his Islamization drive, as "conceptually ... a spiritual descendent of Aurangzeb" because Zia had an orthodox, legalistic view of Islam. Muhammad Sayyid Tantawy, a grand mufti of Egypt, once called Aurangzeb as "A remnant of the Rightly-Guided Rashidun Caliphs", as appreciation of Aurangzeb commitment to Islam teaching. Beyond the individual appreciations, Aurangzeb is seminal to Pakistan's national self-consciousness, as historian Ayesha Jalal, while referring to the Pakistani textbooks controversy, mentions M. D. Zafar's "A Text Book of Pakistan Studies" where we can read that, under Aurangzeb, "Pakistan spirit gathered in strength", while his death "weakened the Pakistan spirit." Another historian from Pakistan, Mubarak Ali, also looking at the textbooks, and while noting that Akbar "is conveniently ignored and not mentioned in any school textbook from class one to matriculation", contrasts him with Aurangzeb, who "appears in different textbooks of Social Studies and Urdu language as an orthodox and pious Muslim copying the Holy Quran and sewing caps for his livelihood." This image of Aurangzeb is not limited to Pakistan's official historiography.
As of 2015, about 177 towns and villages of India have been named after Aurangzeb. Historian Audrey Truschke points out that Bharatiya Janta Party (BJP), Hindutva proponents and some others outside Hindutva ideology regard Aurangzeb as Muslim zealot in India. Jawaharlal Nehru wrote that, due to his reversal of the cultural and religious syncretism of the previous Mughal emperors, Aurangzeb acted "more as a Moslem than an Indian ruler", while Mahatma Gandhi was of the view that there was greater degree of freedom under Mughal rule than the British rule and asks that "in Aurangzeb's time a Shivaji could flourish. Has one hundred and fifty years of the British rule produced any Pratap and Shivaji?" Other historians also noting that there are Hindu temples built during Aurangzeb reign, while he also employed significantly more Hindus in his imperial bureaucracy than his predecessors did, opposed bigotry against Hindus and Shia Muslims. Literatures. Aurangzeb has prominently featured in the following books Personal life.
Full title. The epithet Aurangzeb means 'Ornament of the Throne'. His chosen title Alamgir translates to Conqueror of the World. Aurangzeb's full imperial title was: "Al-Sultan al-Azam wal Khaqan al-Mukarram Hazrat Abul Muzaffar Muhy-ud-Din Muhammad Aurangzeb Bahadur Alamgir I", "Badshah Ghazi", "Shahanshah-e-Sultanat-ul-Hindiya Wal Mughaliya". Aurangzeb had also been attributed various other titles including "Caliph of The Merciful", "Monarch of Islam", and "Living Custodian of God". Family. Consorts. Aurangzeb had at least 4 consorts in his harem, from which he fathered 6 sons and 6 daughters:
Alexandrine Alexandrine is a name used for several distinct types of verse line with related metrical structures, most of which are ultimately derived from the classical French alexandrine. The line's name derives from its use in the Medieval French "Roman d'Alexandre" of 1170, although it had already been used several decades earlier in "Le Pèlerinage de Charlemagne". The foundation of most alexandrines consists of two hemistichs (half-lines) of six syllables each, separated by a caesura (a metrical pause or word break, which may or may not be realized as a stronger syntactic break): o o o o o o \| o o o o o o o=any syllable; \|=caesura However, no tradition remains this simple. Each applies additional constraints (such as obligatory stress or nonstress on certain syllables) and options (such as a permitted or required additional syllable at the end of one or both hemistichs). Thus a line that is metrical in one tradition may be unmetrical in another. Where the alexandrine has been adopted, it has frequently served as the heroic verse form of that language or culture, English being a notable exception.
Scope of the term. The term "alexandrine" may be used with greater or lesser rigour. Peureux suggests that only French syllabic verse with a 6+6 structure is, strictly speaking, an alexandrine. Preminger "et al". allow a broader scope: "Strictly speaking, the term 'alexandrine' is appropriate to French syllabic meters, and it may be applied to other metrical systems only where they too espouse syllabism as their principle, introduce phrasal accentuation, or rigorously observe the medial caesura, as in French." Common usage within the literatures of European languages is broader still, embracing lines syllabic, accentual-syllabic, and (inevitably) stationed ambivalently between the two; lines of 12, 13, or even 14 syllables; lines with obligatory, predominant, and optional caesurae. French. Although alexandrines occurred in French verse as early as the 12th century, they were slightly looser rhythmically, and vied with the "décasyllabe" and "octosyllabe" for cultural prominence and use in various genres. "The alexandrine came into its own in the middle of the sixteenth century with the poets of the Pléiade and was firmly established in the seventeenth century." It became the preferred line for the prestigious genres of epic and tragedy. The structure of the classical French alexandrine is
o o o o o S \| o o o o o S (e) S=stressed syllable; (e)=optional "mute e" Classical alexandrines are always rhymed, often in couplets alternating masculine rhymes and feminine rhymes, though other configurations (such as quatrains and sonnets) are also common. Victor Hugo began the process of loosening the strict two-hemistich structure. While retaining the medial caesura, he often reduced it to a mere word-break, creating a three-part line ("alexandrin ternaire") with this structure: o o o S \| o o ¦ o S \| o o o S (e) \|=strong caesura; ¦=word break The Symbolists further weakened the classical structure, sometimes eliminating any or all of these caesurae. However, at no point did the newer line "replace" the older; rather, they were used concurrently, often in the same poem. This loosening process eventually led to "vers libéré" and finally to "vers libre". English. In English verse, "alexandrine" is typically used to mean "iambic hexameter": /="ictus", a strong syllabic position; ×="nonictus" ¦=often a mandatory or predominant caesura, but depends upon the author
Whereas the French alexandrine is syllabic, the English is accentual-syllabic; and the central caesura (a defining feature of the French) is not always rigidly preserved in English. Though English alexandrines have occasionally provided the sole metrical line for a poem, for example in lyric poems by Henry Howard, Earl of Surrey and Sir Philip Sidney, and in two notable long poems, Michael Drayton's "Poly-Olbion" and Robert Browning's "Fifine at the Fair", they have more often featured alongside other lines. During the Middle Ages they typically occurred with heptameters (seven-beat lines), both exhibiting metrical looseness. Around the mid-16th century stricter alexandrines were popular as the first line of poulter's measure couplets, fourteeners (strict iambic heptameters) providing the second line. The strict English alexandrine may be exemplified by a passage from "Poly-Olbion", which features a rare caesural enjambment (symbolized codice_1) in the first line: <poem style="margin-left:2em"> Ye sacred Bards, that to ¦ your harps' melodious strings
Sung Heroes' deeds (the monuments of Kings) And in your dreadful verse the prophecies, The agèd world's descents, and genealogies; (lines 31-34) </poem> The Faerie Queene by Edmund Spenser, with its stanzas of eight iambic pentameter lines followed by one alexandrine, exemplifies what came to be its chief role: as a somewhat infrequent variant line in an otherwise iambic pentameter context. Alexandrines provide occasional variation in the blank verse of William Shakespeare and his contemporaries (but rarely; they constitute only about 1% of Shakespeare's blank verse). John Dryden and his contemporaries and followers likewise occasionally employed them as the second (rarely the first) line of heroic couplets, or even more distinctively as the third line of a triplet. In his "Essay on Criticism", Alexander Pope denounced (and parodied) the excessive and unskillful use of this practice: <poem style="margin-left:2em"> Then at the last and only couplet fraught With some unmeaning thing they call a thought,
A needless Alexandrine ends the song, That, like a wounded snake, drags its slow length along. (lines 354-357) </poem> Other languages. Spanish. The Spanish "verso alejandrino" is a line of 7+7 syllables, probably developed in imitation of the French alexandrine. Its structure is: o o o o o S o \| o o o o o S o It was used beginning about 1200 for "mester de clerecía" (clerical verse), typically occurring in the "cuaderna vía", a stanza of four "alejandrinos" all with a single end-rhyme. The "alejandrino" was most prominent during the 13th and 14th centuries, after which time it was eclipsed by the metrically more flexible "arte mayor". Juan Ruiz's Book of Good Love is one of the best-known examples of "cuaderna vía", though other verse forms also appear in the work. Dutch. The mid-16th-century poet Jan van der Noot pioneered syllabic Dutch alexandrines on the French model, but within a few decades Dutch alexandrines had been transformed into strict iambic hexameters with a caesura after the third foot. From the Low Countries the accentual-syllabic alexandrine spread to other continental literatures.
German. Similarly, in early 17th-century Germany, Georg Rudolf Weckherlin advocated for an alexandrine with free rhythms, reflecting French practice; whereas Martin Opitz advocated for a strict accentual-syllabic iambic alexandrine in imitation of contemporary Dutch practice — and German poets followed Opitz. The alexandrine (strictly iambic with a consistent medial caesura) became the dominant long line of the German baroque. Polish. Unlike many similar lines, the Polish alexandrine developed not from French verse but from Latin, specifically, the 13-syllable goliardic line: Latin goliardic: o o o s S s s \| o o o s S s Polish alexandrine: o o o o o S s \| o o o s S s s=unstressed syllable Though looser instances of this (nominally) 13-syllable line were occasionally used in Polish literature, it was Mikołaj Rej and Jan Kochanowski who, in the 16th century, introduced the syllabically strict line as a vehicle for major works. Czech. The Czech alexandrine is a comparatively recent development, based on the French alexandrine and introduced by Karel Hynek Mácha in the 19th century. Its structure forms a halfway point between features usual in syllabic and in accentual-syllabic verse, being more highly constrained than most syllabic verse, and less so than most accentual-syllabic verse. Moreover, it equally encourages the very different rhythms of iambic hexameter and dactylic tetrameter to emerge by preserving the constants of both measures:
iambic hexameter: s S s S s S \| s S s S s S (s) dactylic tetrameter: S s s S s s \| S s s S s s (s) Czech alexandrine: o o s S s o \| o o s S s o (s) Hungarian. Hungarian metrical verse may be written either syllabically (the older and more traditional style, known as "national") or quantitatively. One of the national lines has a 6+6 structure: o o o o o o \| o o o o o o Although deriving from native folk versification, it is possible that this line, and the related 6-syllable line, were influenced by Latin or Romance examples. When employed in 4-line or 8-line stanzas and rhyming in couplets, this is called the Hungarian alexandrine; it is the Hungarian heroic verse form. Beginning with the 16th-century verse of Bálint Balassi, this became the dominant Hungarian verse form. Modern references. In the comic book "Asterix and Cleopatra", the author Goscinny inserted a pun about alexandrines: when the Druid Panoramix ("Getafix" in the English translation) meets his Alexandrian (Egyptian) friend the latter exclaims "Je suis, mon cher ami, \|\| très heureux de te voir" at which Panoramix observes "C'est un Alexandrin" ("That's an alexandrine!"/"He's an Alexandrian!"). The pun can also be heard in the theatrical adaptations. The English translation renders this as "My dear old Getafix \|\| I hope I find you well", with the reply "An Alexandrine".
Analog computer An analog computer or analogue computer is a type of computation machine (computer) that uses physical phenomena such as electrical, mechanical, or hydraulic quantities behaving according to the mathematical principles in question ("analog signals") to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude (digital signals). Analog computers can have a very wide range of complexity. Slide rules and nomograms are the simplest, while naval gunfire control computers and large hybrid digital/analog computers were among the most complicated. Complex mechanisms for process control and protective relays used analog computation to perform control and protective functions. Analog computers were widely used in scientific and industrial applications even after the advent of digital computers, because at the time they were typically much faster, but they started to become obsolete as early as the 1950s and 1960s, although they remained in use in some specific applications, such as aircraft flight simulators, the flight computer in aircraft, and for teaching control systems in universities. Perhaps the most relatable example of analog computers are mechanical watches where the continuous and periodic rotation of interlinked gears drives the second, minute and hour needles in the clock. More complex applications, such as aircraft flight simulators and synthetic-aperture radar, remained the domain of analog computing (and hybrid computing) well into the 1980s, since digital computers were insufficient for the task.
Timeline of analog computers. Precursors. This is a list of examples of early computation devices considered precursors of the modern computers. Some of them may even have been dubbed 'computers' by the press, though they may fail to fit modern definitions. The Antikythera mechanism, a type of device used to determine the positions of heavenly bodies known as an orrery, was described as an early mechanical analog computer by British physicist, information scientist, and historian of science Derek J. de Solla Price. It was discovered in 1901, in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, and has been dated to , during the Hellenistic period. Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later. Many mechanical aids to calculation and measurement were constructed for astronomical and navigation use. The planisphere was first described by Ptolemy in the 2nd century AD. The astrolabe was invented in the Hellenistic world in either the 1st or 2nd centuries BC and is often attributed to Hipparchus. A combination of the planisphere and dioptra, the astrolabe was effectively an analog computer capable of working out several different kinds of problems in spherical astronomy.
The sector, a calculating instrument used for solving problems in proportion, trigonometry, multiplication and division, and for various functions, such as squares and cube roots, was developed in the late 16th century and found application in gunnery, surveying and navigation. The planimeter was a manual instrument to calculate the area of a closed figure by tracing over it with a mechanical linkage. The slide rule was invented around 1620–1630, shortly after the publication of the concept of the logarithm. It is a hand-operated analog computer for doing multiplication and division. As slide rule development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as transcendental functions such as logarithms and exponentials, circular and hyperbolic trigonometry and other functions. Aviation is one of the few fields where slide rules are still in widespread use, particularly for solving time–distance problems in light aircraft. In 1831–1835, mathematician and engineer Giovanni Plana devised a perpetual-calendar machine, which, through a system of pulleys and cylinders, could predict the perpetual calendar for every year from AD 0 (that is, 1 BC) to AD 4000, keeping track of leap years and varying day length.
The tide-predicting machine invented by Sir William Thomson in 1872 was of great utility to navigation in shallow waters. It used a system of pulleys and wires to automatically calculate predicted tide levels for a set period at a particular location. The differential analyser, a mechanical analog computer designed to solve differential equations by integration, used wheel-and-disc mechanisms to perform the integration. In 1876 James Thomson had already discussed the possible construction of such calculators, but he had been stymied by the limited output torque of the ball-and-disk integrators. Several systems followed, notably those of Spanish engineer Leonardo Torres Quevedo, who built various analog machines for solving real and complex roots of polynomials; and Michelson and Stratton, whose Harmonic Analyser performed Fourier analysis, but using an array of 80 springs rather than Kelvin integrators. This work led to the mathematical understanding of the Gibbs phenomenon of overshoot in Fourier representation near discontinuities. In a differential analyzer, the output of one integrator drove the input of the next integrator, or a graphing output. The torque amplifier was the advance that allowed these machines to work. Starting in the 1920s, Vannevar Bush and others developed mechanical differential analyzers.
Modern era. The Dumaresq was a mechanical calculating device invented around 1902 by Lieutenant John Dumaresq of the Royal Navy. It was an analog computer that related vital variables of the fire control problem to the movement of one's own ship and that of a target ship. It was often used with other devices, such as a Vickers range clock to generate range and deflection data so the gun sights of the ship could be continuously set. A number of versions of the Dumaresq were produced of increasing complexity as development proceeded. By 1912, Arthur Pollen had developed an electrically driven mechanical analog computer for fire-control systems, based on the differential analyser. It was used by the Imperial Russian Navy in World War I. Starting in 1929, AC network analyzers were constructed to solve calculation problems related to electrical power systems that were too large to solve with numerical methods at the time. These were essentially scale models of the electrical properties of the full-size system. Since network analyzers could handle problems too large for analytic methods or hand computation, they were also used to solve problems in nuclear physics and in the design of structures. More than 50 large network analyzers were built by the end of the 1950s.
World War II era gun directors, gun data computers, and bomb sights used mechanical analog computers. In 1942 Helmut Hölzer built a fully electronic analog computer at Peenemünde Army Research Center as an embedded control system ("mixing device") to calculate V-2 rocket trajectories from the accelerations and orientations (measured by gyroscopes) and to stabilize and guide the missile. Mechanical analog computers were very important in gun fire control in World War II, the Korean War and well past the Vietnam War; they were made in significant numbers. In the period 1930–1945 in the Netherlands, Johan van Veen developed an analogue computer to calculate and predict tidal currents when the geometry of the channels are changed. Around 1950, this idea was developed into the Deltar, a hydraulic analogy computer supporting the closure of estuaries in the southwest of the Netherlands (the Delta Works). The FERMIAC was an analog computer invented by physicist Enrico Fermi in 1947 to aid in his studies of neutron transport. Project Cyclone was an analog computer developed by Reeves in 1950 for the analysis and design of dynamic systems. Project Typhoon was an analog computer developed by RCA in 1952. It consisted of over 4,000 electron tubes and used 100 dials and 6,000 plug-in connectors to program. The MONIAC Computer was a hydraulic analogy of a national economy first unveiled in 1949.
Computer Engineering Associates was spun out of Caltech in 1950 to provide commercial services using the "Direct Analogy Electric Analog Computer" ("the largest and most impressive general-purpose analyzer facility for the solution of field problems") developed there by Gilbert D. McCann, Charles H. Wilts, and Bart Locanthi. Educational analog computers illustrated the principles of analog calculation. The Heathkit EC-1, a $199 educational analog computer, was made by the Heath Company, US . It was programmed using patch cords that connected nine operational amplifiers and other components. General Electric also marketed an "educational" analog computer kit of a simple design in the early 1960s consisting of two transistor tone generators and three potentiometers wired such that the frequency of the oscillator was nulled when the potentiometer dials were positioned by hand to satisfy an equation. The relative resistance of the potentiometer was then equivalent to the formula of the equation being solved. Multiplication or division could be performed, depending on which dials were inputs and which was the output. Accuracy and resolution was limited and a simple slide rule was more accurate. However, the unit did demonstrate the basic principle.
Analog computer designs were published in electronics magazines. One example is the PEAC (Practical Electronics analogue computer), published in "Practical Electronics" in the January 1968 edition. Another more modern hybrid computer design was published in "Everyday Practical Electronics" in 2002. An example described in the EPE hybrid computer was the flight of a VTOL aircraft such as the Harrier jump jet. The altitude and speed of the aircraft were calculated by the analog part of the computer and sent to a PC via a digital microprocessor and displayed on the PC screen. In industrial process control, analog loop controllers were used to automatically regulate temperature, flow, pressure, or other process conditions. The technology of these controllers ranged from purely mechanical integrators, through vacuum-tube and solid-state devices, to emulation of analog controllers by microprocessors. Electronic analog computers. The similarity between linear mechanical components, such as springs and dashpots (viscous-fluid dampers), and electrical components, such as capacitors, inductors, and resistors is striking in terms of mathematics. They can be modeled using equations of the same form.
However, the difference between these systems is what makes analog computing useful. Complex systems often are not amenable to pen-and-paper analysis, and require some form of testing or simulation. Complex mechanical systems, such as suspensions for racing cars, are expensive to fabricate and hard to modify. And taking precise mechanical measurements during high-speed tests adds further difficulty. By contrast, it is very inexpensive to build an electrical equivalent of a complex mechanical system, to simulate its behavior. Engineers arrange a few operational amplifiers (op amps) and some passive linear components to form a circuit that follows the same equations as the mechanical system being simulated. All measurements can be taken directly with an oscilloscope. In the circuit, the (simulated) stiffness of the spring, for instance, can be changed by adjusting the parameters of an integrator. The electrical system is an analogy to the physical system, hence the name, but it is much less expensive than a mechanical prototype, much easier to modify, and generally safer.
The electronic circuit can also be made to run faster or slower than the physical system being simulated. Experienced users of electronic analog computers said that they offered a comparatively intimate control and understanding of the problem, relative to digital simulations. Electronic analog computers are especially well-suited to representing situations described by differential equations. Historically, they were often used when a system of differential equations proved very difficult to solve by traditional means. As a simple example, the dynamics of a spring-mass system can be described by the equation formula_1, with formula_2 as the vertical position of a mass formula_3, formula_4 the damping coefficient, formula_5 the spring constant and formula_6 the gravity of Earth. For analog computing, the equation is programmed as formula_7. The equivalent analog circuit consists of two integrators for the state variables formula_8 (speed) and formula_2 (position), one inverter, and three potentiometers. Electronic analog computers have drawbacks: the value of the circuit's supply voltage limits the range over which the variables may vary (since the value of a variable is represented by a voltage on a particular wire). Therefore, each problem must be scaled so its parameters and dimensions can be represented using voltages that the circuit can supply —e.g., the expected magnitudes of the velocity and the position of a spring pendulum. Improperly scaled variables can have their values "clamped" by the limits of the supply voltage. Or if scaled too small, they can suffer from higher noise levels. Either problem can cause the circuit to produce an incorrect simulation of the physical system. (Modern digital simulations are much more robust to widely varying values of their variables, but are still not entirely immune to these concerns: floating-point digital calculations support a huge dynamic range, but can suffer from imprecision if tiny differences of huge values lead to numerical instability.)
The precision of the analog computer readout was limited chiefly by the precision of the readout equipment used, generally three or four significant figures. (Modern digital simulations are much better in this area. Digital arbitrary-precision arithmetic can provide any desired degree of precision.) However, in most cases the precision of an analog computer is absolutely sufficient given the uncertainty of the model characteristics and its technical parameters. Many small computers dedicated to specific computations are still part of industrial regulation equipment, but from the 1950s to the 1970s, general-purpose analog computers were the only systems fast enough for real time simulation of dynamic systems, especially in the aircraft, military and aerospace field. In the 1960s, the major manufacturer was Electronic Associates of Princeton, New Jersey, with its 231R Analog Computer (vacuum tubes, 20 integrators) and subsequently its EAI 8800 Analog Computer (solid state operational amplifiers, 64 integrators). Its challenger was Applied Dynamics of Ann Arbor, Michigan.
Although the basic technology for analog computers is usually operational amplifiers (also called "continuous current amplifiers" because they have no low frequency limitation), in the 1960s an attempt was made in the French ANALAC computer to use an alternative technology: medium frequency carrier and non dissipative reversible circuits. In the 1970s, every large company and administration concerned with problems in dynamics had an analog computing center, such as: Construction. An analog computing machine consists of several main components: On the patch panel, various connections and routes can be set and switched to configure the machine and determine signal flows. This allows users to flexibly configure and reconfigure the analog computing system to perform specific tasks. Patch panels are used to control data flows, connect and disconnect connections between various blocks of the system, including signal sources, amplifiers, filters, and other components. They provide convenience and flexibility in configuring and experimenting with analog computations.
Patch panels can be presented as a physical panel with connectors or, in more modern systems, as a software interface that allows virtual management of signal connections and routes. Output devices in analog machines can vary depending on the specific goals of the system. For example, they could be graphical indicators, oscilloscopes, graphic recording devices, TV connection module, voltmeter, etc. These devices allow for the visualization of analog signals and the representation of the results of measurements or mathematical operations. These are just general blocks that can be found in a typical analog computing machine. The actual configuration and components may vary depending on the specific implementation and the intended use of the machine. Analog–digital hybrids. Analog computing devices are fast; digital computing devices are more versatile and accurate. The idea behind an analog-digital hybrid is to combine the two processes for the best efficiency. An example of such hybrid elementary device is the hybrid multiplier, where one input is an analog signal, the other input is a digital signal and the output is analog. It acts as an analog potentiometer, upgradable digitally. This kind of hybrid technique is mainly used for fast dedicated real time computation when computing time is very critical, as signal processing for radars and generally for controllers in embedded systems.
In the early 1970s, analog computer manufacturers tried to tie together their analog computers with a digital computers to get the advantages of the two techniques. In such systems, the digital computer controlled the analog computer, providing initial set-up, initiating multiple analog runs, and automatically feeding and collecting data. The digital computer may also participate to the calculation itself using analog-to-digital and digital-to-analog converters. The largest manufacturer of hybrid computers was Electronic Associates. Their hybrid computer model 8900 was made of a digital computer and one or more analog consoles. These systems were mainly dedicated to large projects such as the Apollo program and Space Shuttle at NASA, or Ariane in Europe, especially during the integration step where at the beginning everything is simulated, and progressively real components replace their simulated parts. Only one company was known as offering general commercial computing services on its hybrid computers, CISI of France, in the 1970s.
The best reference in this field is the 100,000 simulation runs for each certification of the automatic landing systems of Airbus and Concorde aircraft. After 1980, purely digital computers progressed more and more rapidly and were fast enough to compete with analog computers. One key to the speed of analog computers was their fully parallel computation, but this was also a limitation. The more equations required for a problem, the more analog components were needed, even when the problem wasn't time critical. "Programming" a problem meant interconnecting the analog operators; even with a removable wiring panel this was not very versatile. Implementations. Mechanical analog computers. Throughout history, many types of mechanical analog computers have been invented. These ranged from simple devices (like planimeters) to complex fire-control systems that guided WWII naval guns. Practical mechanical analog computers of any significant complexity used rotating shafts to carry variables from one mechanism to another. Cables and pulleys were used in a Fourier synthesizer, a tide-predicting machine, which summed the individual harmonic components. Another category, not nearly as well known, used rotating shafts only for input and output, with precision racks and pinions. The racks were connected to linkages that performed the computation. At least one U.S. Naval sonar fire control computer of the later 1950s, made by Librascope, was of this type, as was the principal computer in the Mk. 56 Gun Fire Control System.
These computers often employed precision miter-gear differentials (pairs of bevel gears arranged to produce the sum or difference of two shaft rotations) to transmit variables between computing elements. The Ford Instrument Mark I Fire Control Computer, for example, contained approximately 160 miter-gear differentials. Integration with respect to another variable was done by a rotating disc driven by one variable. Output came from a pick-off device (such as a wheel) positioned at a radius on the disc proportional to the second variable. (A carrier with a pair of steel balls supported by small rollers worked especially well. A roller, its axis parallel to the disc's surface, provided the output. It was held against the pair of balls by a spring.) Arbitrary functions of one variable were provided by cams, with gearing to convert follower movement to shaft rotation. Functions of two variables were provided by three-dimensional cams. In one good design, one of the variables rotated the cam. A hemispherical follower moved its carrier on a pivot axis parallel to that of the cam's rotating axis. Pivoting motion was the output. The second variable moved the follower along the axis of the cam. One practical application was ballistics in gunnery.
Coordinate conversion from polar to rectangular was done by a mechanical resolver (called a "component solver" in US Navy fire control computers). Two discs on a common axis positioned a sliding block with pin (stubby shaft) on it. One disc was a face cam, and a follower on the block in the face cam's groove set the radius. The other disc, closer to the pin, contained a straight slot in which the block moved. The input angle rotated the latter disc (the face cam disc, for an unchanging radius, rotated with the other (angle) disc; a differential and a few gears did this correction). Referring to the mechanism's frame, the location of the pin corresponded to the tip of the vector represented by the angle and magnitude inputs. Mounted on that pin was a square block. Rectilinear-coordinate outputs (both sine and cosine, typically) came from two slotted plates, each slot fitting on the block just mentioned. The plates moved in straight lines, the movement of one plate at right angles to that of the other. The slots were at right angles to the direction of movement. Each plate, by itself, was like a Scotch yoke, known to steam engine enthusiasts.
During World War II, a similar mechanism converted rectilinear to polar coordinates, but it was not particularly successful and was eliminated in a significant redesign (USN, Mk. 1 to Mk. 1A). Multiplication was done by mechanisms based on the geometry of similar right triangles. Using the trigonometric terms for a right triangle, specifically opposite, adjacent, and hypotenuse, the adjacent side was fixed by construction. One variable changed the magnitude of the opposite side. In many cases, this variable changed sign; the hypotenuse could coincide with the adjacent side (a zero input), or move beyond the adjacent side, representing a sign change. Typically, a pinion-operated rack moving parallel to the (trig.-defined) opposite side would position a slide with a slot coincident with the hypotenuse. A pivot on the rack let the slide's angle change freely. At the other end of the slide (the angle, in trig. terms), a block on a pin fixed to the frame defined the vertex between the hypotenuse and the adjacent side.
At any distance along the adjacent side, a line perpendicular to it intersects the hypotenuse at a particular point. The distance between that point and the adjacent side is some fraction that is the product of "1" the distance from the vertex, and "2" the magnitude of the opposite side. The second input variable in this type of multiplier positions a slotted plate perpendicular to the adjacent side. That slot contains a block, and that block's position in its slot is determined by another block right next to it. The latter slides along the hypotenuse, so the two blocks are positioned at a distance from the (trig.) adjacent side by an amount proportional to the product. To provide the product as an output, a third element, another slotted plate, also moves parallel to the (trig.) opposite side of the theoretical triangle. As usual, the slot is perpendicular to the direction of movement. A block in its slot, pivoted to the hypotenuse block positions it. A special type of integrator, used at a point where only moderate accuracy was needed, was based on a steel ball, instead of a disc. It had two inputs, one to rotate the ball, and the other to define the angle of the ball's rotating axis. That axis was always in a plane that contained the axes of two movement pick-off rollers, quite similar to the mechanism of a rolling-ball computer mouse (in that mechanism, the pick-off rollers were roughly the same diameter as the ball). The pick-off roller axes were at right angles.
A pair of rollers "above" and "below" the pick-off plane were mounted in rotating holders that were geared together. That gearing was driven by the angle input, and established the rotating axis of the ball. The other input rotated the "bottom" roller to make the ball rotate. Essentially, the whole mechanism, called a component integrator, was a variable-speed drive with one motion input and two outputs, as well as an angle input. The angle input varied the ratio (and direction) of coupling between the "motion" input and the outputs according to the sine and cosine of the input angle. Although they did not accomplish any computation, electromechanical position servos (aka. torque amplifiers) were essential in mechanical analog computers of the "rotating-shaft" type for providing operating torque to the inputs of subsequent computing mechanisms, as well as driving output data-transmission devices such as large torque-transmitter synchros in naval computers. Other readout mechanisms, not directly part of the computation, included internal odometer-like counters with interpolating drum dials for indicating internal variables, and mechanical multi-turn limit stops.
Considering that accurately controlled rotational speed in analog fire-control computers was a basic element of their accuracy, there was a motor with its average speed controlled by a balance wheel, hairspring, jeweled-bearing differential, a twin-lobe cam, and spring-loaded contacts (ship's AC power frequency was not necessarily accurate, nor dependable enough, when these computers were designed). Electronic analog computers. Electronic analog computers typically have front panels with numerous jacks (single-contact sockets) that permit patch cords (flexible wires with plugs at both ends) to create the interconnections that define the problem setup. In addition, there are precision high-resolution potentiometers (variable resistors) for setting up (and, when needed, varying) scale factors. In addition, there is usually a zero-center analog pointer-type meter for modest-accuracy voltage measurement. Stable, accurate voltage sources provide known magnitudes. Typical electronic analog computers contain anywhere from a few to a hundred or more operational amplifiers ("op amps"), named because they perform mathematical operations. Op amps are a particular type of feedback amplifier with very high gain and stable input (low and stable offset). They are always used with precision feedback components that, in operation, all but cancel out the currents arriving from input components. The majority of op amps in a representative setup are summing amplifiers, which add and subtract analog voltages, providing the result at their output jacks. As well, op amps with capacitor feedback are usually included in a setup; they integrate the sum of their inputs with respect to time.
Integrating with respect to another variable is the nearly exclusive province of mechanical analog integrators; it is almost never done in electronic analog computers. However, given that a problem solution does not change with time, time can serve as one of the variables. Other computing elements include analog multipliers, nonlinear function generators, and analog comparators. Electrical elements such as inductors and capacitors used in electrical analog computers had to be carefully manufactured to reduce non-ideal effects. For example, in the construction of AC power network analyzers, one motive for using higher frequencies for the calculator (instead of the actual power frequency) was that higher-quality inductors could be more easily made. Many general-purpose analog computers avoided the use of inductors entirely, re-casting the problem in a form that could be solved using only resistive and capacitive elements, since high-quality capacitors are relatively easy to make. The use of electrical properties in analog computers means that calculations are normally performed in real time (or faster), at a speed determined mostly by the frequency response of the operational amplifiers and other computing elements. In the history of electronic analog computers, there were some special high-speed types.
Nonlinear functions and calculations can be constructed to a limited precision (three or four digits) by designing function generators—special circuits of various combinations of resistors and diodes to provide the nonlinearity. Typically, as the input voltage increases, progressively more diodes conduct. When compensated for temperature, the forward voltage drop of a transistor's base-emitter junction can provide a usably accurate logarithmic or exponential function. Op amps scale the output voltage so that it is usable with the rest of the computer. Any physical process that models some computation can be interpreted as an analog computer. Some examples, invented for the purpose of illustrating the concept of analog computation, include using a bundle of spaghetti as a model of sorting numbers; a board, a set of nails, and a rubber band as a model of finding the convex hull of a set of points; and strings tied together as a model of finding the shortest path in a network. These are all described in Dewdney (1984).
Components. Analog computers often have a complicated framework, but they have, at their core, a set of key components that perform the calculations. The operator manipulates these through the computer's framework. Key hydraulic components might include pipes, valves and containers. Key mechanical components might include rotating shafts for carrying data within the computer, miter gear differentials, disc/ball/roller integrators, cams (2-D and 3-D), mechanical resolvers and multipliers, and torque servos. Key electrical/electronic components might include: The core mathematical operations used in an electric analog computer are: In some analog computer designs, multiplication is much preferred to division. Division is carried out with a multiplier in the feedback path of an Operational Amplifier. Differentiation with respect to time is not frequently used, and in practice is avoided by redefining the problem when possible. It corresponds in the frequency domain to a high-pass filter, which means that high-frequency noise is amplified; differentiation also risks instability.
Limitations. In general, analog computers are limited by non-ideal effects. An analog signal is composed of four basic components: DC and AC magnitudes, frequency, and phase. The real limits of range on these characteristics limit analog computers. Some of these limits include the operational amplifier offset, finite gain, and frequency response, noise floor, non-linearities, temperature coefficient, and parasitic effects within semiconductor devices. For commercially available electronic components, ranges of these aspects of input and output signals are always figures of merit. Decline. In the 1950s to 1970s, digital computers based on first vacuum tubes, transistors, integrated circuits and then micro-processors became more economical and precise. This led digital computers to largely replace analog computers. Even so, some research in analog computation is still being done. A few universities still use analog computers to teach control system theory. The American company Comdyna manufactured small analog computers. At Indiana University Bloomington, Jonathan Mills has developed the Extended Analog Computer based on sampling voltages in a foam sheet. At the Harvard Robotics Laboratory, analog computation is a research topic. Lyric Semiconductor's error correction circuits use analog probabilistic signals. Slide rules are still used as flight computers in flight training.
Resurgence. With the development of very-large-scale integration (VLSI) technology, Yannis Tsividis' group at Columbia University has been revisiting analog/hybrid computers design in standard CMOS process. Two VLSI chips have been developed, an 80th-order analog computer (250 nm) by Glenn Cowan in 2005 and a 4th-order hybrid computer (65 nm) developed by Ning Guo in 2015, both targeting at energy-efficient ODE/PDE applications. Glenn's chip contains 16 macros, in which there are 25 analog computing blocks, namely integrators, multipliers, fanouts, few nonlinear blocks. Ning's chip contains one macro block, in which there are 26 computing blocks including integrators, multipliers, fanouts, ADCs, SRAMs and DACs. Arbitrary nonlinear function generation is made possible by the ADC+SRAM+DAC chain, where the SRAM block stores the nonlinear function data. The experiments from the related publications revealed that VLSI analog/hybrid computers demonstrated about 1–2 orders magnitude of advantage in both solution time and energy while achieving accuracy within 5%, which points to the promise of using analog/hybrid computing techniques in the area of energy-efficient approximate computing. In 2016, a team of researchers developed a compiler to solve differential equations using analog circuits.
Analog computers are also used in neuromorphic computing, and in 2021 a group of researchers have shown that a specific type of artificial neural network called a spiking neural network was able to work with analog neuromorphic computers. In 2021, the German company anabrid GmbH began to produce THE ANALOG THING (abbreviated THAT), a small low-cost analog computer mainly for educational and scientific use. The company is also constructing analog mainframes and hybrid computers. Practical examples. These are examples of analog computers that have been constructed or practically used: Analog (audio) synthesizers can also be viewed as a form of analog computer, and their technology was originally based in part on electronic analog computer technology. The ARP 2600's Ring Modulator was actually a moderate-accuracy analog multiplier. The Simulation Council (or Simulations Council) was an association of analog computer users in US. It is now known as The Society for Modeling and Simulation International. The Simulation Council newsletters from 1952 to 1963 are available online and show the concerns and technologies at the time, and the common use of analog computers for missilry.
Audio Audio most commonly refers to sound, as it is transmitted in signal form. It may also refer to:
Minute and second of arc A minute of arc, arcminute (abbreviated as arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of a degree. Since one degree is of a turn, or complete rotation, one arcminute is of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth's circumference is very near . A minute of arc is of a radian. A second of arc, arcsecond (abbreviated as arcsec), or arc second, denoted by the symbol , is a unit of angular measurement equal to of a minute of arc, of a degree, of a turn, and (about ) of a radian. These units originated in Babylonian astronomy as sexagesimal (base 60) subdivisions of the degree; they are used in fields that involve very small angles, such as astronomy, optometry, ophthalmology, optics, navigation, land surveying, and marksmanship. To express even smaller angles, standard SI prefixes can be employed; the milliarcsecond (mas) and microarcsecond (μas), for instance, are commonly used in astronomy. For a two-dimensional area such as on (the surface of) a sphere, "square arcminutes" or "seconds" may be used.
Symbols and abbreviations. The prime symbol () designates the arcminute, though a single quote (U+0027) is commonly used where only ASCII characters are permitted. One arcminute is thus written as 1′. It is also abbreviated as arcmin or amin. Similarly, double prime (U+2033) designates the arcsecond, though a double quote (U+0022) is commonly used where only ASCII characters are permitted. One arcsecond is thus written as 1″. It is also abbreviated as arcsec or asec. In celestial navigation, seconds of arc are rarely used in calculations, the preference usually being for degrees, minutes, and decimals of a minute, for example, written as 42° 25.32′ or 42° 25.322′. This notation has been carried over into marine GPS and aviation GPS receivers, which normally display latitude and longitude in the latter format by default. Common examples. In general, by simple trigonometry, it can be derived that the angle subtended by an object of diameter or length at a distance is given by the following expression: One arcminute () is the approximate distance two contours can be separated by, and still be distinguished by, a person with 20/20 vision. The average apparent diameter of the full Moon is about , or .
One arcsecond () is the angle subtended by: Also notable examples of size in arcseconds are: One milliarcsecond () is about the size of a half dollar (), seen from a distance equal to that between the Washington Monument and the Eiffel Tower (around ). One microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth. One nanoarcsecond is about the size of a nickel () on the surface of Neptune as observed from Earth. History. The concepts of degrees, minutes, and seconds—as they relate to the measure of both angles and time—derive from Babylonian astronomy and time-keeping. Influenced by the Sumerians, the ancient Babylonians divided the Sun's perceived motion across the sky over the course of one full day into 360 degrees. Each degree was subdivided into 60 minutes and each minute into 60 seconds. Thus, one Babylonian degree was equal to four minutes in modern terminology, one Babylonian minute to four modern seconds, and one Babylonian second to (approximately 0.067) of a modern second.
Uses. Astronomy. Since antiquity, the arcminute and arcsecond have been used in astronomy: in the ecliptic coordinate system as latitude (β) and longitude (λ); in the horizon system as altitude (Alt) and azimuth (Az); and in the equatorial coordinate system as declination (δ). All are measured in degrees, arcminutes, and arcseconds. The principal exception is right ascension (RA) in equatorial coordinates, which is measured in time units of hours, minutes, and seconds. Contrary to what one might assume, minutes and seconds of arc do not directly relate to minutes and seconds of time, in either the rotational frame of the Earth around its own axis (day), or the Earth's rotational frame around the Sun (year). The Earth's rotational rate around its own axis is 15 minutes of arc per minute of time (360 degrees / 24 hours in day); the Earth's rotational rate around the Sun (not entirely constant) is roughly 24 minutes of time per minute of arc (from 24 hours in day), which tracks the annual progression of the Zodiac. Both of these factor in what astronomical objects you can see from surface telescopes (time of year) and when you can best see them (time of day), but neither are in unit correspondence. For simplicity, the explanations given assume a degree/day in the Earth's annual rotation around the Sun, which is off by roughly 1%. The same ratios hold for seconds, due to the consistent factor of 60 on both sides.
The arcsecond is also often used to describe small astronomical angles such as the angular diameters of planets (e.g. the angular diameter of Venus which varies between 10″ and 60″); the proper motion of stars; the separation of components of binary star systems; and parallax, the small change of position of a star or Solar System body as the Earth revolves about the Sun. These small angles may also be written in milliarcseconds (mas), or thousandths of an arcsecond. The unit of distance called the parsec, abbreviated from the parallax angle of one arc second, was developed for such parallax measurements. The distance from the Sun to a celestial object is the reciprocal of the angle, measured in arcseconds, of the object's apparent movement caused by parallax. The European Space Agency's astrometric satellite Gaia, launched in 2013, can approximate star positions to 7 microarcseconds (μas). Apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red giant with a diameter of 0.05″. Because of the effects of atmospheric blurring, ground-based telescopes will smear the image of a star to an angular diameter of about 0.5″; in poor conditions this increases to 1.5″ or even more. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1″. Techniques exist for improving seeing on the ground. Adaptive optics, for example, can produce images around 0.05″ on a 10 m class telescope.
Space telescopes are not affected by the Earth's atmosphere but are diffraction limited. For example, the Hubble Space Telescope can reach an angular size of stars down to about 0.1″. Cartography. Minutes (′) and seconds (″) of arc are also used in cartography and navigation. At sea level one minute of arc along the equator equals exactly one geographical mile (not to be confused with international mile or statute mile) along the Earth's equator or approximately . A second of arc, one sixtieth of this amount, is roughly . The exact distance varies along meridian arcs or any other great circle arcs because the figure of the Earth is slightly oblate (bulges a third of a percent at the equator). Positions are traditionally given using degrees, minutes, and seconds of arcs for latitude, the arc north or south of the equator, and for longitude, the arc east or west of the Prime Meridian. Any position on or above the Earth's reference ellipsoid can be precisely given with this method. However, when it is inconvenient to use base-60 for minutes and seconds, positions are frequently expressed as decimal fractional degrees to an equal amount of precision. Degrees given to three decimal places ( of a degree) have about the precision of degrees-minutes-seconds ( of a degree) and specify locations within about . For navigational purposes positions are given in degrees and decimal minutes, for instance, the Needles Lighthouse is at 50°39′44.2″N 1°35′30.5″W.
Property cadastral surveying. Related to cartography, property boundary surveying using the metes and bounds system and cadastral surveying relies on fractions of a degree to describe property lines' angles in reference to cardinal directions. A boundary "mete" is described with a beginning reference point, the cardinal direction North or South followed by an angle less than 90 degrees and a second cardinal direction, and a linear distance. The boundary runs the specified linear distance from the beginning point, the direction of the distance being determined by rotating the first cardinal direction the specified angle toward the second cardinal direction. For example, "North 65° 39′ 18″ West 85.69 feet" would describe a line running from the starting point 85.69 feet in a direction 65° 39′ 18″ (or 65.655°) away from north toward the west. Firearms. The arcminute is commonly found in the firearms industry and literature, particularly concerning the precision of rifles, though the industry refers to it as minute of angle (MOA). It is especially popular as a unit of measurement with shooters familiar with the imperial measurement system because 1 MOA subtends a circle with a diameter of 1.047 inches (which is often rounded to just 1 inch) at 100 yards ( at or 2.908 cm at 100 m), a traditional distance on American target ranges. The subtension is linear with the distance, for example, at 500 yards, 1 MOA subtends 5.235 inches, and at 1000 yards 1 MOA subtends 10.47 inches.
Since many modern telescopic sights are adjustable in half (), quarter () or eighth () MOA increments, also known as "clicks", zeroing and adjustments are made by counting 2, 4 and 8 clicks per MOA respectively. For example, if the point of impact is 3 inches high and 1.5 inches left of the point of aim at 100 yards (which for instance could be measured by using a spotting scope with a calibrated reticle, or a target delineated for such purposes), the scope needs to be adjusted 3 MOA down, and 1.5 MOA right. Such adjustments are trivial when the scope's adjustment dials have a MOA scale printed on them, and even figuring the right number of clicks is relatively easy on scopes that "click" in fractions of MOA. This makes zeroing and adjustments much easier: Another common system of measurement in firearm scopes is the milliradian (mrad). Zeroing an mrad based scope is easy for users familiar with base ten systems. The most common adjustment value in mrad based scopes is mrad (which approximates MOA). One thing to be aware of is that some MOA scopes, including some higher-end models, are calibrated such that an adjustment of 1 MOA on the scope knobs corresponds to exactly 1 inch of impact adjustment on a target at 100 yards, rather than the mathematically correct 1.047 inches. This is commonly known as the Shooter's MOA (SMOA) or Inches Per Hundred Yards (IPHY). While the difference between one true MOA and one SMOA is less than half of an inch even at 1000 yards, this error compounds significantly on longer range shots that may require adjustment upwards of 20–30 MOA to compensate for the bullet drop. If a shot requires an adjustment of 20 MOA or more, the difference between true MOA and SMOA will add up to 1 inch or more. In competitive target shooting, this might mean the difference between a hit and a miss.
The physical group size equivalent to "m" minutes of arc can be calculated as follows: group size = tan() × distance. In the example previously given, for 1 minute of arc, and substituting 3,600 inches for 100 yards, 3,600 tan() ≈ 1.047 inches. In metric units 1 MOA at 100 metres ≈ 2.908 centimetres. Sometimes, a precision-oriented firearm's performance will be measured in MOA. This simply means that under ideal conditions (i.e. no wind, high-grade ammo, clean barrel, and a stable mounting platform such as a vise or a benchrest used to eliminate shooter error), the gun is capable of producing a group of shots whose center points (center-to-center) fit into a circle, the average diameter of circles in several groups can be subtended by that amount of arc. For example, a "1 MOA rifle" should be capable, under ideal conditions, of repeatably shooting 1-inch groups at 100 yards. Most higher-end rifles are warrantied by their manufacturer to shoot under a given MOA threshold (typically 1 MOA or better) with specific ammunition and no error on the shooter's part. For example, Remington's M24 Sniper Weapon System is required to shoot 0.8 MOA or better, or be rejected from sale by quality control.
Rifle manufacturers and gun magazines often refer to this capability as "sub-MOA", meaning a gun consistently shooting groups under 1 MOA. This means that a single group of 3 to 5 shots at 100 yards, or the average of several groups, will measure less than 1 MOA between the two furthest shots in the group, i.e. all shots fall within 1 MOA. If larger samples are taken (i.e., more shots per group) then group size typically increases, however this will ultimately average out. If a rifle was truly a 1 MOA rifle, it would be just as likely that two consecutive shots land exactly on top of each other as that they land 1 MOA apart. For 5-shot groups, based on 95% confidence, a rifle that normally shoots 1 MOA can be expected to shoot groups between 0.58 MOA and 1.47 MOA, although the majority of these groups will be under 1 MOA. What this means in practice is if a rifle that shoots 1-inch groups on average at 100 yards shoots a group measuring 0.7 inches followed by a group that is 1.3 inches, this is not statistically abnormal.
The metric system counterpart of the MOA is the milliradian (mrad or 'mil'), being equal to of the target range, laid out on a circle that has the observer as centre and the target range as radius. The number of milliradians on a full such circle therefore always is equal to 2 × × 1000, regardless the target range. Therefore, 1 MOA ≈ 0.2909 mrad. This means that an object which spans 1 mrad on the reticle is at a range that is in metres equal to the object's linear size in millimetres (e.g. an object of 100 mm subtending 1 mrad is 100 metres away). So there is no conversion factor required, contrary to the MOA system. A reticle with markings (hashes or dots) spaced with a one mrad apart (or a fraction of a mrad) are collectively called a mrad reticle. If the markings are round they are called mil-dots. In the table below conversions from mrad to metric values are exact (e.g. 0.1 mrad equals exactly 10 mm at 100 metres), while conversions of minutes of arc to both metric and imperial values are approximate. Human vision.
In humans, 20/20 vision is the ability to resolve a spatial pattern separated by a visual angle of one minute of arc, from a distance of twenty feet. A 20/20 letter subtends 5 minutes of arc total. Materials. The deviation from parallelism between two surfaces, for instance in optical engineering, is usually measured in arcminutes or arcseconds. In addition, arcseconds are sometimes used in rocking curve (ω-scan) x ray diffraction measurements of high-quality epitaxial thin films. Manufacturing. Some measurement devices make use of arcminutes and arcseconds to measure angles when the object being measured is too small for direct visual inspection. For instance, a toolmaker's optical comparator will often include an option to measure in "minutes and seconds".
Alberto Giacometti Alberto Giacometti (, , ; 10 October 1901 – 11 January 1966) was a Swiss sculptor, painter, draftsman and printmaker, who was one of the most important sculptors of the 20th century. His work was particularly influenced by artistic styles such as Cubism and Surrealism. Philosophical questions about the human condition, as well as existential and phenomenological debates played a significant role in his work. Beginning in 1922, he lived and worked mainly in Paris but regularly visited his hometown Borgonovo to see his family and work on his art. Around 1935, he gave up on his Surrealist influences to pursue a more deepened analysis of figurative compositions. Giacometti wrote texts for periodicals and exhibition catalogues and recorded his thoughts and memories in notebooks and diaries. His critical nature led to self-doubt about his own work and his self-perceived inability to do justice to his own artistic vision. His insecurities nevertheless remained a powerful motivating artistic force throughout his entire life.
Between 1938 and 1944 Giacometti's sculptures had a maximum height of seven centimeters (2.75 inches). Their small size reflected the actual distance between the artist's position and his model. In this context he self-critically stated: "But wanting to create from memory what I had seen, to my terror the sculptures became smaller and smaller". After World War II, Giacometti created his most famous sculptures: his extremely tall and slender figurines. These sculptures were subject to his individual viewing experience—between an imaginary yet real, a tangible yet inaccessible space. In Giacometti's whole body of work, his painting constitutes only a small part. After 1957, however, his figurative paintings were equally as present as his sculptures. The almost monochrome paintings of his late work do not refer to any other artistic styles of modernity. Early life. Giacometti was born in Borgonovo, Switzerland, the eldest of four children of Giovanni Giacometti, a well-known post-Impressionist painter, and Annetta Giacometti-Stampa. He was a descendant of Protestant refugees escaping the inquisition. Coming from an artistic background, he was interested in art from an early age and was encouraged by his father and godfather.
Alberto attended the Geneva School of Fine Arts. His brothers Diego (1902–1985) and Bruno (1907–2012) would go on to become artists and architects as well. Additionally, his cousin Zaccaria Giacometti, later professor of constitutional law and chancellor of the University of Zurich, grew up together with them, having been orphaned at the age of 12 in 1905. Career. In 1922, he moved to Paris to study under the sculptor Antoine Bourdelle, an associate of Rodin. It was there that Giacometti experimented with Cubism and Surrealism and came to be regarded as one of the leading Surrealist sculptors. Among his associates were Miró, Max Ernst, Picasso, Bror Hjorth, and Balthus. Between 1936 and 1940, Giacometti concentrated his sculpting on the human head, focusing on the sitter's gaze. He preferred models he was close to—his sister and the artist Isabel Rawsthorne (then known as Isabel Delmer). This was followed by a phase in which his statues of Isabel became stretched out; her limbs elongated. Obsessed with creating his sculptures exactly as he envisioned through his unique view of reality, he often carved until they were as thin as nails and reduced to the size of a pack of cigarettes, much to his consternation. A friend of his once said that if Giacometti decided to sculpt you, "he would make your head look like the blade of a knife".
During World War II, Giacometti took refuge in Switzerland. There, in 1946, he met Annette Arm, a secretary for the Red Cross. They married in 1949. After his marriage his tiny sculptures became larger, but the larger they grew, the thinner they became. For the remainder of Giacometti's life, Annette was his main female model. His paintings underwent a parallel procedure. The figures appear isolated and severely attenuated, as the result of continuous reworking. He frequently revisited his subjects: one of his favourite models was his younger brother Diego, with whom he shared his studio in Paris. Later years. In 1958 Giacometti was asked to create a monumental sculpture for the Chase Manhattan Bank building in New York, which was beginning construction. Although he had for many years "harbored an ambition to create work for a public square", he "had never set foot in New York, and knew nothing about life in a rapidly evolving metropolis. Nor had he ever laid eyes on an actual skyscraper", according to his biographer James Lord. Giacometti's work on the project resulted in the four figures of standing women—his largest sculptures—entitled "Grande femme debout" I through IV (1960). The commission was never completed, however, because Giacometti was unsatisfied by the relationship between the sculpture and the site, and abandoned the project.
In 1962, Giacometti was awarded the grand prize for sculpture at the Venice Biennale, and the award brought with it worldwide fame. Even when he had achieved popularity and his work was in demand, he still reworked models, often destroying them or setting them aside to be returned to years later. The prints produced by Giacometti are often overlooked but the catalogue raisonné, "Giacometti – The Complete Graphics and 15 Drawings by Herbert Lust" (Tudor 1970), comments on their impact and gives details of the number of copies of each print. Some of his most important images were in editions of only 30 and many were described as rare in 1970. In his later years Giacometti's works were shown in a number of large exhibitions throughout Europe. Riding a wave of international popularity, and despite his declining health, he traveled to the United States in 1965 for an exhibition of his works at the Museum of Modern Art in New York. As his last work he prepared the text for the book "Paris sans fin", a sequence of 150 lithographs containing memories of all the places where he had lived.
Artistic analysis. Regarding Giacometti's sculptural technique and according to the Metropolitan Museum of Art: "The rough, eroded, heavily worked surfaces of Three Men Walking (II), 1949, typify his technique. Reduced, as they are, to their very core, these figures evoke lone trees in winter that have lost their foliage. Within this style, Giacometti would rarely deviate from the three themes that preoccupied him—the walking man; the standing, nude woman; and the bust—or all three, combined in various groupings"."" In a letter to Pierre Matisse, Giacometti wrote: "Figures were never a compact mass but like a transparent construction". In the letter, Giacometti writes about how he looked back at the realist, classical busts of his youth with nostalgia, and tells the story of the existential crisis which precipitated the style he became known for. "[I rediscovered] the wish to make compositions with figures. For this I had to make (quickly I thought; in passing), one or two studies from nature, just enough to understand the construction of a head, of a whole figure, and in 1935 I took a model. This study should take, I thought, two weeks and then I could realize my compositions...I worked with the model all day from 1935 to 1940...Nothing was as I imagined. A head, became for me an object completely unknown and without dimensions."
Since Giacometti achieved exquisite realism with facility when he was executing busts in his early adolescence, Giacometti's difficulty in re-approaching the figure as an adult is generally understood as a sign of existential struggle for meaning, rather than as a technical deficit. Giacometti was a key player in the Surrealist art movement, but his work resists easy categorization. Some describe it as formalist, others argue it is expressionist or otherwise having to do with what Deleuze calls "blocs of sensation" (as in Deleuze's analysis of Francis Bacon). Even after his excommunication from the Surrealist group, while the intention of his sculpting was usually imitation, the end products were an expression of his emotional response to the subject. He attempted to create renditions of his models the way he saw them, and the way he thought they ought to be seen. He once said that he was sculpting not the human figure but "the shadow that is cast". Scholar William Barrett in "Irrational Man: A Study in Existential Philosophy" (1962), argues that the attenuated forms of Giacometti's figures reflect the view of 20th century modernism and existentialism that modern life is increasingly empty and devoid of meaning. "All the sculptures of today, like those of the past, will end one day in pieces...So it is important to fashion one's work carefully in its smallest recess and charge every particle of matter with life."
A 2011–2012 exhibition at the Pinacothèque de Paris focused on showing how Giacometti was inspired by Etruscan art. "Walking Man" and other human figures. Giacometti is best known for the bronze sculptures of tall, thin human figures, made in the years 1945 to 1960. Giacometti was influenced by the impressions he took from the people hurrying in the big city. People in motion he saw as "a succession of moments of stillness". The emaciated figures are often interpreted as an expression of the existential fear, insignificance and loneliness of mankind. The mood of fear in the period of the 1940s and the Cold War is reflected in this figure. It feels sad, lonely and difficult to relate to. Death. Giacometti died in 1966 of heart disease (pericarditis) and chronic obstructive pulmonary disease at the Kantonsspital in Chur, Switzerland. His body was returned to his birthplace in Borgonovo, where he was interred close to his parents. With no children, Annette Giacometti became the sole holder of his property rights. She worked to collect a full listing of authenticated works by her late husband, gathering documentation on the location and manufacture of his works and working to fight the rising number of counterfeited works. When she died in 1993, the Fondation Giacometti was set up by the French state.
In May 2007 the executor of his widow's estate, former French foreign minister Roland Dumas, was convicted of illegally selling Giacometti's works to a top auctioneer, Jacques Tajan, who was also convicted. Both were ordered to pay €850,000 to the Alberto and Annette Giacometti Foundation. Legacy. Exhibitions. Giacometti's work has been the subject of numerous solo exhibitions including the High Museum of Art, Atlanta (1970); Centre Pompidou, Paris (2007–2008); Pushkin Museum, Moscow "The Studio of Alberto Giacometti: Collection of the Fondation Alberto et Annette Giacometti" (2008); Kunsthal Rotterdam (2008); Fondation Beyeler, Basel (2009); Buenos Aires (2012); Kunsthalle Hamburg (2013); Pera Museum, Istanbul (2015); Tate Modern, London (2017); Vancouver Art Gallery, "Alberto Giacometti: A Line Through Time" (2019); National Gallery of Ireland, Dublin (2022). The National Portrait Gallery, London's first solo exhibition of Giacometti's work, "Pure Presence" opened to five star reviews on 13 October 2015 (to 10 January 2016, in honour of the fiftieth anniversary of the artist's death).
From April 2019, the Prado Museum in Madrid, has been highlighting Giacometti in an exhibition. Public collections. Giacometti's work is displayed in numerous public collections, including: Art foundations. The Fondation Alberto et Annette Giacometti, having received a bequest from Alberto Giacometti's widow Annette, holds a collection of circa 5,000 works, frequently displayed around the world through exhibitions and long-term loans. A public interest institution, the Foundation was created in 2003 and aims at promoting, disseminating, preserving and protecting Alberto Giacometti's work. The Alberto-Giacometti-Stiftung established in Zürich in 1965, holds a smaller collection of works acquired from the collection of the Pittsburgh industrialist G. David Thompson. Notable sales. According to record Giacometti has sold the two most expensive sculptures in history. In November 2000 a Giacometti bronze, "Grande Femme Debout I", sold for $14.3 million. "Grande Femme Debout II" was bought by the Gagosian Gallery for $27.4 million at Christie's auction in New York City on 6 May 2008.
"L'Homme qui marche I", a life-sized bronze sculpture of a man, became one of the most expensive works of art, and at the time was the most expensive sculpture ever sold at auction. It was in February 2010, when it sold for £65 million (US$104.3 million) at Sotheby's, London. "Grande tête mince", a large bronze bust, sold for $53.3 million just three months later. "L'Homme au doigt" ("Pointing Man") sold for $126 million (£81,314,455.32), or $141.3 million with fees, in Christie's May 2015, "Looking Forward to the Past" sale in New York City. The work had been in the same private collection for 45 years. As of now it is the most expensive sculpture sold at auction. After being showcased on the BBC programme "Fake or Fortune", a plaster sculpture, titled "Gazing Head", sold in 2019 for half a million pounds. In April 2021, Giacometti's small-scale bronze sculpture, Nu debout II (1953), was sold from a Japanese private collection and went for £1.5 million ($2 million), against an estimate of £800,000 ($1.1 million).
Other legacy. Giacometti created the monument on the grave of Gerda Taro at Père Lachaise Cemetery. According to a lecture by Michael Peppiatt at Cambridge University on 8 July 2010, Giacometti, who had a friendship with author/playwright Samuel Beckett, created a tree for the set of a 1961 Paris production of "Waiting for Godot". Giacometti and his sculpture "L'Homme qui marche I" appear on the former 100 Swiss franc banknote. In 2001 he was included in the exhibition held at the National Portrait Gallery, London. Giacometti's sculptural style has featured in advertisements for various financial institutions, starting in 1987 with the "Shoes" ad for Royal Bank of Scotland directed by Gerry Anderson. The 2017 movie "Final Portrait" retells the story of his friendship with the biographer James Lord. Giacometti is played by Geoffrey Rush.
Anthem An anthem is a musical composition of celebration, usually used as a symbol for a distinct group, particularly the national anthems of countries. Originally, and in music theory and religious contexts, it also refers more particularly to short sacred choral work (still frequently seen in Sacred Harp and other types of shape note singing) and still more particularly to a specific form of liturgical music. In this sense, its use began in English-speaking churches; it uses English language words, in contrast to the originally Roman Catholic 'motet' which sets a Latin text. Etymology. "Anthem" is derived from the Greek ("antíphōna") via Old English . Both words originally referred to antiphons, a call-and-response style of the singing. The adjectival form is "anthemic". History.
The anthem developed as a replacement for the Catholic "votive antiphon" commonly sung as an appendix to the main office to the Blessed Virgin Mary or other saints. Notable composers of liturgical anthems: historic context. During the Elizabethan period, notable anthems were composed by Thomas Tallis, William Byrd, Tye, and Farrant but they were not mentioned in the Book of Common Prayer until 1662 when the famous rubric "In quires and places where they sing here followeth the Anthem" first appears. Early anthems tended to be simple and homophonic in texture, so that the words could be clearly heard. During the 17th century, notable anthems were composed by Orlando Gibbons, Henry Purcell, and John Blow, with the verse anthem becoming the dominant musical form of the Restoration. In the 18th century, famed anthems were composed by Croft, Boyce, James Kent, James Nares, Benjamin Cooke, and Samuel Arnold. In the 19th century, Samuel Sebastian Wesley wrote anthems influenced by contemporary oratorio which stretch to several movements and last twenty minutes or longer. Later in the century, Charles Villiers Stanford used symphonic techniques to produce a more concise and unified structure. Many anthems have been written since then, generally by specialists in organ music rather than composers, and often in a conservative style. Major composers have usually written anthems in response to commissions and for special occasions: for instance Edward Elgar's 1912 "Great is the Lord" and 1914 "Give unto the Lord" (both with orchestral accompaniment); Benjamin Britten's 1943 "Rejoice in the Lamb" (a modern example of a multi-movement anthem, today heard mainly as a concert piece); and, on a much smaller scale, Ralph Vaughan Williams's 1952 "O Taste and See" written for the coronation of Queen Elizabeth II. With the relaxation of the rule, in England at least, that anthems should only be in English, the repertoire has been greatly enhanced by the addition of many works from the Latin repertoire.
Types. The word "anthem" is commonly used to describe any celebratory song or composition for a distinct group, as in national anthems. Further, some songs are artistically styled as anthems, whether or not they are used as such, including Marilyn Manson's "Irresponsible Hate Anthem", Silverchair's "Anthem for the Year 2000", and Toto's "Child's Anthem". National anthem. A national anthem (also state anthem, national hymn, national song, etc.) is generally a patriotic musical composition that evokes and eulogizes the history, traditions, and struggles of a country's people, recognized either by that state's government as the official national song, or by convention through use by the people. The majority of national anthems are marches or hymns in style. The countries of Latin America, Central Asia, and Europe tend towards more ornate and operatic pieces, while those in the Middle East, Oceania, Africa, and the Caribbean use a simpler fanfare. Some countries that are devolved into multiple constituent states have their own official musical compositions for them (such as with the United Kingdom, Russian Federation, and the former Soviet Union); their constituencies' songs are sometimes referred to as national anthems even though they are not sovereign states.
Flag anthem. A flag anthem is generally a patriotic musical composition that extols and praises a flag, typically one of a country, in which case it is sometimes called a national flag anthem. It is often either sung or performed during or immediately before the raising or lowering of a flag during a ceremony. Most countries use their respective national anthems or some other patriotic song for this purpose. However, some countries, particularly in South America, use a separate flag anthem for such purposes. Not all countries have flag anthems. Some used them in the past but no longer do so, such as Iran, China, and South Africa. Flag anthems can be officially codified in law, or unofficially recognized by custom and convention. In some countries, the flag anthem may be just another song, and in others, it may be an official symbol of the state akin to a second national anthem, such as in Taiwan. Sports anthem. Many pop songs are used as sports anthems, notably including Queen's "We Are the Champions" and "We Will Rock You", and some sporting events have their own anthems, most notably including UEFA Champions League.
Shared anthems. Although anthems are used to distinguish states and territories, there are instances of shared anthems. "Nkosi Sikelel' iAfrika" became a pan-African liberation anthem and was later adopted as the national anthem of five countries in Africa including Zambia, Tanzania, Namibia and Zimbabwe after independence. Zimbabwe and Namibia have since adopted new national anthems. Since 1997, the South African national anthem has been a hybrid song combining new English lyrics with extracts of "Nkosi Sikelel' iAfrika" and the former state anthem "Die Stem van Suid-Afrika". For North and South Korea, the folk song "Arirang" is considered a shared anthem for both countries. For example, it was played when the two Koreas marched together during the 2018 Winter Olympics. "Hymn to Liberty" is the longest national anthem in the world by length of text. In 1865, the first three stanzas and later the first two officially became the national anthem of Greece and later also that of the Republic of Cyprus. "Forged from the Love of Liberty" was composed as the national anthem for the short-lived West Indies Federation (1958–1962) and was adopted by Trinidad and Tobago when it became independent in 1962.
"Esta É a Nossa Pátria Bem Amada" is the national anthem of Guinea-Bissau and was also the national anthem of Cape Verde until 1996. "Oben am jungen Rhein", the national anthem of Liechtenstein, is set to the tune of "God Save the King/Queen". Other anthems that have used the same melody include "Heil dir im Siegerkranz" (Germany), "Kongesangen" (Norway), "My Country, 'Tis of Thee" (United States), "Rufst du, mein Vaterland" (Switzerland), "E Ola Ke Alii Ke Akua" (Hawaii), and "The Prayer of Russians". The Estonian anthem "Mu isamaa, mu õnn ja rõõm" is set to a melody composed in 1848 by Fredrik (Friedrich) Pacius which is also that of the national anthem of Finland: " (" in Swedish). It is also considered to be the ethnic anthem for the Livonian people with lyrics "Min izāmō, min sindimō" ("My Fatherland, my native land"). "Hey, Slavs" is dedicated to Slavic peoples. Its first lyrics were written in 1834 under the title "Hey, Slovaks" ("Hej, Slováci") by Samuel Tomášik and it has since served as the ethnic anthem of the Pan-Slavic movement, the organizational anthem of the Sokol physical education and political movement, the national anthem of Yugoslavia and the transitional anthem of the State Union of Serbia and Montenegro. The song is also considered to be the second, unofficial anthem of the Slovaks. Its melody is based on Mazurek Dąbrowskiego, which has also been the anthem of Poland since 1926, but the Yugoslav variation is much slower and more accentuated.
Between 1991 and 1994 "Deșteaptă-te, române!" was the national anthem of both Romania (which adopted it in 1990) and Moldova, but in the case of the latter it was replaced by the current Moldovan national anthem, "Limba noastră". Between 1975 and 1977, the national anthem of Romania "E scris pe tricolor Unire" shared the same melody as the national anthem of Albania "Himni i Flamurit", which is the melody of a Romanian patriotic song "Pe-al nostru steag e scris Unire". The modern national anthem of Germany, "Das Lied der Deutschen", uses the same tune as the 19th- and early 20th-century Austro-Hungarian imperial anthem "Gott erhalte Franz den Kaiser". The "Hymn of the Soviet Union", was used until its dissolution in 1991, and was given new words and adopted by the Russian Federation in 2000 to replace an instrumental national anthem that had been introduced in 1990. "Bro Gozh ma Zadoù", the regional anthem of Brittany and, "Bro Goth Agan Tasow", the Cornish regional anthem, are sung to the same tune as that of the Welsh regional anthem "Hen Wlad Fy Nhadau", with similar words.
For parts of states. Some countries, such as the former Soviet Union, Spain, and the United Kingdom, among others, are held to be unions of several "nations" by various definitions. Each of the different "nations" may have their own anthem and these songs may or may not be officially recognized; these compositions are typically referred to as regional anthems though may be known by other names as well (e.g. "state songs" in the United States). Austria. In Austria, the situation is similar to that in Germany. The regional anthem of Upper Austria, the "Hoamatgsang" (), is notable as the only (official) German-language anthem written – and sung – entirely in dialect. Belgium. In Belgium, Wallonia uses "Le Chant des Wallons" and Flanders uses "De Vlaamse Leeuw". Brazil. Most of the Brazilian states have official anthems. Minas Gerais uses an adapted version of the traditional Italian song "Vieni sul mar" as its unofficial anthem. During the Vargas Era (1937–1945) all regional symbols including anthems were banned, but they were legalized again by the Eurico Gaspar Dutra government.
Canada. The Canadian province of Newfoundland and Labrador, having been the independent Dominion of Newfoundland before 1949, also has its own regional anthem from its days as a dominion and colony of the UK, the "Ode to Newfoundland". It was the only Canadian province with its own anthem until 2010, when Prince Edward Island adopted the 1908 song "The Island Hymn" as its provincial anthem. Czechoslovakia. Czechoslovakia had a national anthem composed of two parts, the Czech anthem followed by one verse of the Slovak one. After the dissolution of Czechoslovakia, the Czech Republic adopted its own regional anthem as its national one, whereas Slovakia did so with slightly changed lyrics and an additional stanza. Germany. In Germany, many of the Länder (states) have their own anthems, some of which predate the unification of Germany in 1871. A prominent example is the Hymn of Bavaria, which also has the status of an official anthem (and thus enjoys legal protection). There are also several unofficial regional anthems, like the "Badnerlied" and the "Niedersachsenlied".

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