Ptolemy's Almagest, the highest achievement of Greek geometrical planetary astronomy, was without rival for some fourteen centuries, until supplanted by Copernicus's De revolutionibus orbium coelestium after a.d. 1543. Yet, awe inspiring as the Almagest was, and indeed still is, it was far from complete or satisfactory, even by Ptolemy's own standards. Striving valiantly to save the phenomena, whatever the cost in additional circles, Ptolemy had drifted away from a simple planetary model toward an overly elaborate, Rube Goldberg-like monstrosity. (Goldberg, a cartoonist, drew weird contrivances performing simple tasks with many bizarre and unnecessary steps.) Even worse was Ptolemy's introduction of the equant point, a violation of uniform circular motion. Why then was the Copernican revolution, its necessity so evident, so long delayed in coming?
That no man of Ptolemy's genius again walked the Earth for many centuries might suffice as an explanation for the time lag. This sort of explanation is not in current fashion, however. Nor does it illuminate the problem. A hypothesis more open to investigation and more productive of further study is that a whole tradition of astronomy was interred shortly after Ptolemy and not soon resurrected. In the Islamic world, it was not pursued until nearly a millennium later; and in the Latin-reading West not until shortly before Copernicus.
The most obvious cause of disrupted astronomical activity, as well as most other activities of the Roman world, was the decline of that civilization. Also, interest shifted from traditional intellectual pursuits to service in the rapidly growing Christian religion.
This historical explanation presumes existence of an intellectual inertial force and, consequently, continuation of research in geometrical planetary astronomy until disrupted or diverted by an opposing force. We might, however, assume instead that a state of intellectual inattention is the natural state of affairs and then ask whether there were forces present to cause either continuation or revival of work in the astronomical tradition.
Neither historical approach—assuming inertial progress or a natural state of rest—need necessarily be exclusive. Indeed, it is difficult to place unambiguously in a single category all aspects of the long neglect of Ptolemy's Almagest.
In the West, the break in the Ptolemaic tradition runs deeper than a general and gradual decline of civilization, a decline so gradual that scientific activity in other fields continued sporadically for centuries. Greek science was distilled into handbooks, and it was primarily through this medium that the late Greek science of Alexandria became known to Latin readers. The Almagest, however, was written after the major incorporation of Greek handbook knowledge into Latin. Hence, Ptolemy's achievement was known in the West only by reputation until the twelfth century. Nor did later commentaries on Ptolemy's work by astronomers at Alexandria find their way immediately to the Latin-reading West.
Alexandria already had become a provincial city in the Roman Empire by Ptolemy's time, and in the second and third centuries a.d., political crises and almost incessant civil war in the Empire disrupted internal order and economic production. Among the casualties were the Museum and the Library. The major destruction of these centers of learning occurred in the fourth century when, under Emperor Constantine, Christianity triumphed in the Empire and pagan institutions were destroyed. In a.d. 392 the last fellow of the Museum was murdered by a mob and the Library was pillaged. Whatever may have remained was further damaged in the Arab conquest in the seventh century a.d.
Islam spread rapidly after Mohammed arrived in Medina in a.d. 622, conquering first Mecca, then the rest of the Arabian peninsula—east through what is now Iran, west through North Africa by a.d. 670, and across the Mediterranean to Spain in a.d. 711. This invasion of Europe was only blocked in a.d. 732 at the Battle of Tours. Not until a.d. 1248 were Cordoba and Seville retaken by Christians, and Granada did not fall until a.d. 1492.
Those conquered by Islam were to be left undisturbed in their way of life on condition that they pay tribute. The conquerors' initial intention was not to spread Islam but to substitute one elite for another and to return wealth, in the form of taxes, to the central treasury. Gradually, though, masters and subjects merged. The central administration moved to Damascus and then to Baghdad, vainly hoping to leave behind the tribal disputes and civil wars of the Arabian peninsula. By the middle of the tenth century a.d., the once-unified Islamic empire had collapsed irretrievably into independent fragments, none of which provided the continuity over many generations that had made possible Alexandrian advances in geometrical astronomy from Apollonius to Hipparchus to Ptolemy.
The Arabs enjoyed both a relatively high level of science and a firsthand acquaintanceship with Ptolemy's Almagest. Yet many Islamic scientists were more interested in Aristotelian physical science. For them, Ptolemy's system was little more than a convenient computing device. In Spain in the twelfth century a.d., ibn-Rushd (Averroes, as he was known in the West) and al-Bitruji (Alpetragius) rejected Ptolemy's astronomy of epicycles, eccentrics, and equants for a system of concentric spheres more in accordance with Aristotelian physics. Averroes wrote that there was nothing in the mathematical sciences that would lead us to believe that eccentrics and epicycles exist. . . . The astronomer must, therefore, construct an astronomical system such that the celestial motions are yielded by it and that nothing that is from the standpoint of physics impossible is implied. . . . Ptolemy was unable to set astronomy on its true foundations. . . . The epicycle and the eccentric are impossible. We must, therefore apply ourselves to a new investigation concerning that genuine astronomy whose foundations are principles of physics. . . . Actually, in our time astronomy is nonexistent; what we have is something that fits calculation but does not agree with what is. (Duhem, To Save the Phenomena, 31).
And Alpetragius wrote:
It is impossible to imagine numerous spheres with diverse motions for each planet, as Ptolemy assumed, or anything like it. . . . The assumptions and principles which he [Ptolemy] invented seemed to me a matter which I could not tolerate. I was not enthusiastic about his assumption—for example, that spheres eccentric to the center of the universe rotate about their eccenters, and that these centers rotate about other centers; that epicycles rotate about their centers . . . (Goldstein, Al-Bitruji, 59—60)
There would be little effort in Muslim Spain to develop further Ptolemy's geometrical astronomy. Nonetheless, the Islamic world did produce the most innovative addition to geometrical models of planetary motions achieved during the Middle Ages: the Tusi couple, a combination of uniform circular motions yielding net motion in a straight line.
In a.d. 1258 Mongol invaders under Hulagu Khan, a grandson of Genghis Khan, conquered Baghdad. Within a
Details of al-Tusi's relationship with Hulagu Khan are not without interest even today, many hundreds of years after the fact. The allegation that al-Tusi, a Shiite Muslim, persuaded Hulagu to continue his attack on Baghdad and destroy the Sunni Caliphate contributes to current enmity between Shiite and Sunni Muslims. History has its uses and misuses. Sometimes it is exploited, and even distorted, for partisan purposes.
Other anecdotes raise the issue of government support for science and the compromises scientists sometimes must make. Al-Tusi had converted to the faith of his Sunni patrons. Then, following Hulagu's victory over the Sunni Caliphate, al-Tusi, in a self-serving recantation, described himself as having earlier fallen into the power of the heretics, and only now was he rescued from that place and ordered to observe the stars by Hulagu. Al-Tusi also found it expedient to rewrite introductions to a number of works in which he had lavishly praised his earlier benefactors.
Al-Tusi is not the only scientist ever pressured by his patron. With the recent demise of the Soviet Union and the opening of previously secret archives, an outpouring of scholarship is underway on the moral dilemmas and compromises of Soviet scientists. Similar studies have been undertaken of scientists working under Nazi domination. Even American scientists have complained of being pressured not to speak out against an administration's policies and not to release scientific studies whose conclusions are contrary to an administration's political inclinations.
year of his military triumph, Hulagu granted to Nasir al-din al-Tusi, an outstanding scholar formerly under the patronage of the dynasty conquered by Hulagu, his wish for an observatory.
Different sources attribute initiative for an observatory to al-Tusi, to Hulagu, and to Hulagu's brother, Mangu. Mangu Khan had a strong interest in mathematics and astronomy and may have asked Hulagu to send him al-Tusi to help build an observatory in his own capital city in China. Astrology apparently was behind Hulagu's interest in an observatory, though as expenses mounted, he is reported to have begun to doubt the utility of predicting immutable events if nothing could be done to circumvent them anyway.
Al-Tusi's observatory was constructed at Maragha, in northwest Persia (now Iran). Some of the most renowned scientists of the time, from as far as China to the east and Spain to the west, moved there, and the observatory's library was reported to have 400,000 volumes. Recent excavations, however, have found space for far fewer books.
Working with assistants and new instruments at Maragha, within a dozen years al-Tusi produced a new table of the planets' positions. He also wrote the Al-Tadhkira, a Memoir on the Science of Astronomy. In it he explained: "The scientific exposition that we wish to undertake will be a summary account of [astronomy] presented in narrative form. The details are expounded and proofs of the validity of most of them are furnished in the Almagest. Indeed, ours would not be a complete science if taken in isolation from the Almagest for it is a report of what is established therein" (Ragep, Nasir al-Din al-Tusi's Memoir on Astronomy, 19).
Al-Tusi choose not to go into the geometrical proofs available in the Almagest, but instead to concentrate on the physical situation: "These then are models and rules that should be known. We have only stated them here; their geometric proofs are given in the Almagest. Restricting oneself to cir-
Funds from religious endowments helped finance the Maragha Observatory, which survived until at least a.d.1304 and possibly until a.d.1316, not only surviving Hulagu but spanning the reign of five or six more rulers as well. The administration of religious endowments often passed from father to son, and two of al-Tusi's sons succeeded him as director of the observatory.
Islamic traditionalists farther west, and thus free of the Mongol hegemony, criticized al-Tusi for transferring "the endowments of religious schools, mosques, and the hospices attached to them, making them his personal property . . . He also established schools for the heretics. . . . Finally he taught magic, for he was a sorcerer who worshipped idols" (Ragep, Nasir al-Din al-Tusi's Memoir on Astronomy, 19).
One historian has interpreted al-Tusi's diversion of religious endowments, normally devoted to institutions of charity and public assistance such as mosques, madrases (schools), and hospitals, to the operation of the observatory as an indication of the integration and harmonization of the observatory with Muslim culture and civilization. There were observatories at Maragha, Samarquand, Baghdad, and other places.
Not all was harmonious, however. The Istanbul observatory, built in a.d. 1577, would be torn down shortly after its completion, the attempt to pry into the secrets of nature suspected of having brought on misfortunes. In the wake of the famous comet of a.d. 1577, there had followed in quick order plague, defeats of Turkish armies, and the deaths of several important persons.
cles is sufficient in the entirety of this science for whoever studies the proofs. However, one who attempts to understand the principles of the motions must know the configuration of the bodies" (Ragep, Nasir al-Din al-Tusi's Memoir on Astronomy, 19).
The principle behind al-Tusi's innovative combination of uniform circular motions to produce motion in a straight line, the Tusi couple, is simply described. A straight-line motion can be produced by rolling (at any speed) a small circle within a large circle, with the planet fixed to the circumference of the rolling, smaller circle, provided that the diameter of the large circle is precisely twice the diameter of the small circle.
Al-Tusi's small circle, however, did not—indeed, could not—roll around in the large circle. Medieval Islamic astronomy aimed to produce a realistic physical model, not merely a mathematical formulation or fiction. Following Aristotle's physics, there could be no void in the heavens. Thus the large circle must be filled with some sort of celestial material, which would be torn apart by a small circle moving through it. Furthermore, after passage of the small circle, the celestial material would have had to be mended back together.
Instead, al-Tusi had both circles rotate, the small one twice as fast as the large one and in the opposite direction. This is mathematically equivalent to the small circle rolling at any speed in the large circle and avoids any possible collision of the planet and the small circle with celestial material filling the large circle.
Figure 12.1: Straight Line Motion from Circular Motion. A combination of uniform circular motions can be devised to produce motion in a straight line.
a: First, imagine (above) a circle of diameter d rolling on a flat surface. A planet fixed to the circle moves halfway around the circle as the circle rolls a distance of half its circumference (^d/2), and completes a circuit as the circle rolls a distance ^d.
b: Next (above), curve the flat surface into a circle of diameter D, with D = 2d. (The new circle is twice the size of the original circle.) Roll the small circle inside the large circle. A point on the small circle will come back into contact with the circumference of the large circle after one complete turn of the small circle. This occurs after the small circle moves a distance ^d (its circumference) around the large circle, or half way around the large circle (^d = ^D/2).
c: Finally, as the small circle rolls around the inside of the large circle, a point (planet) on the small circle constantly falls along a straight line, which is also a diameter of the large circle (in this case, the vertical diameter). Three positions of the small circle are shown above. Intermediate positions also place the planet on the same straight line. The net result is to convert uniform circular motion into seemingly straight-line motion.
After formulating the version of his geometrical construction with circles, al-Tusi later created a version composed of spheres. Clearly, he was aiming at a physically plausible, Aristotelian cosmology with uniformly rotating spheres.
Al-Tusi's geometrical innovation commands attention in its own right. Furthermore, it is at the center of a historical mystery. Did Copernicus borrow this device for use in his own revolutionary astronomy?
It is not unknown in the history of science for identical problems and identical considerations to impel scientists in identical directions. General similarity is not conclusive proof that Copernicus borrowed a particular geometrical construction from an earlier source rather than that he independently discovered it. Geometrical drawings by al-Tusi and Copernicus, however, are strikingly similar, even sharing the same alphabetical letters (Arabic and Roman equivalents)!
Few Europeans could read Arabic, but Arabic and Persian astronomical writings were translated into Byzantine Greek and carried to Italy. The Vatican library also contains a Greek text of around a.d. 1300 on theoretical astronomy inspired by Islamic astronomy and incorporating the Tusi couple. Copernicus, in Rome in a.d.1500, might have seen it. Furthermore, other Greek and Latin materials using the Tusi couple were circulating in Italy when Copernicus studied there.
The likely connection between al-Tusi and Copernicus came to light at the end of the nineteenth century with the translation of sections of an a.d. 1389 manuscript of al-Tusi's book in the Bibliothèque Nationale in Paris. The astronomer-historian J.L.E. Dreyer, in his 1906 History of the Planetary Systems from Thales to Kepler, discussed al-Tusi's geometrical device and noted, somewhat cryptically and in a footnote: "Compare Copernicus, De revolutionibus, III, 4"
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