Doubting Ptolemy
Ptolemy's models were essentially a mathematical system for predicting the positions of the planets. Yet in the Planetary Hypotheses he did try to fit the models into a cosmological system, the Aristotelian scheme of tightly nested spheres centered on the earth. He placed the nearest point of Mercury's path immediately beyond the most distant point of the moon's path; immediately beyond the farthest excursion of Mercury lay the nearest approach of Venus, and so on through the spheres for the sun, Mars, Jupiter and Saturn.
To reproduce the observed nonuniform motions of the planets, however, Ptolemy adopted two purely geometric devices in addition to the epicycle. First, he placed the deferent circles off-center with respect to the earth. Second, he made the ingenious assumption that the motion of celestial bodies was uniform not around the earth, nor around the centers of their deferents, but instead around a point called the equant that was opposite the earth from the deferent center and at an equal distance. Eccentric deferents and equants did a good job of representing the varying speeds with which planets are seen to move across the sky, but to some minds they were philosophically offensive.
The equant in particular was objectionable to philosophers who thought of planetary spheres as real physical objects, each sphere driven by the one outside it (and the outermost driven by the prime mover), and who wanted to be able to construct a mechanical model of the system. For example, as was pointed out by Maimonides, a Jewish scholar of the 12th century who worked in Spain and Cairo, the equant point for Saturn fell right on the spheres for Mercury. This was clearly awkward from a mechanical point of view. Furthermore, the equant violated the philosophical notion that heavenly bodies should be moved by a system of perfect circles, each of which rotated with uniform angular velocity about its center. To some purists even Ptolemy's eccentric deferents, which moved the earth away from the center of things, were philosophically unsatisfactory.
The Islamic astronomers adopted the Ptolemaic-Aristotelian cosmology, but eventually criticism emerged. One of the first critics was Ibn al-Haytham (Alhazen), a leading physicist of 11th-century Cairo. In his Doubts on Ptolemy he complained that the equant failed to satisfy the requirement of uniform circular motion, and he went so far as to declare the planetary models of the Almagest false.
Only one of Ibn al-Haytham's astronomical works, a book called On the Configuration of the World, penetrated into Latin Europe in the Middle Ages. In it he attempted to discover the physical reality underlying Ptolemy's mathematical models. Conceiving of the heavens in terms of concentric spheres and shells, he tried to assign a single spherical body to each of the Almagest's simple motions. The work was translated into Castilian in the court of Alfonso the Wise, and early in the 14th century from Castilian into Latin. Either this version or a Latin translation of one of Ibn al-Haytham's popularizers had a major influence in early Renaissance Europe. The concept of separate celestial spheres for each component of Ptolemy's planetary motions gained wide currency through a textbook, Theorica novae planetarum, written by the Viennese Georg Peurbach in about 1454.
Meanwhile, in the 12th century in the western Islamic region of Andalusia, the astronomer and philosopher Ibn Rushd (Averroes) gradually developed a somewhat more extreme criticism of Ptolemy. "To assert the existence of an eccentric sphere or an epicyclic sphere is contrary to nature...," he wrote. "The astronomy of our time offers no truth, but only agrees with the calculations and not with what exists." Averroes rejected Ptolemy's eccentric deferents and argued for a strictly concentric model of the universe.
An Andalusian comtemporary, Abu Ishaq al-Bitruji, actually tried to formulate such a strictly geocentric model. The results were disastrous. For example, in al-Bitruji's system Saturn could on occasion deviate from the ecliptic by as much as 26 degrees (instead of the required three degrees). As for the observed motions that led Ptolemy to propose the equant, they were completely ignored. In the words of one modern commentator, al-Bitruji "heaps chaos on confusion." Nevertheless, early in the 13th century his work was translated into Latin under the name Alpetragius, and from about 1230 on his ideas were widely discussed throughout Europe. Even Copernicus cited his order of the planets, which placed Venus beyond the sun.
At the other end of the Islamic world a fresh critique of the Ptolemaic mechanisms was undertaken in the 13th century by Nasir al-Din al-Tusi. One of the most prolific Islamic polymaths, with 150 known treatises and letters to his credit, al-Tusi also constructed a major observatory at Maragha (the present-day Maragheh in Iran).
Al-Tusi found the equant particularly dissatisfactory. In his Tadhkira ("Memorandum") he replaced it by adding two more small epicycles to the model of each planet's orbit. Through this ingenious device al-Tusi was able to achieve his goal of generating the nonuniform motions of the planets by combinations of uniformly rotating circles. The centers of the deferents, however, were still displaced from the earth. Two other astronomers at the Maragha observatory, Mu'ayyad al-Din al-'Urdi and Qutb al-Din al-Shirazi, offered an alternative arrangement, but this system too retained the philosophically objectionable eccentricity.
Finally a completely concentric rearrangement of the planetary mechanisms was achieved by Ibn al-Shatir, who worked in Damascus in about 1350. By using a scheme related to that of al-Tusi, Ibn al-Shatir succeeded in eliminating not only the equant but also certain other objectionable circles from Ptolemy's constructions. He thereby cleared the way for a perfectly nested and mechanically acceptable set of celestial spheres. (He described his work thus: "I found that the most distinguished of the later astronomers had adduced indisputable doubts concerning the well-known astronomy of the spheres according to Ptolemy. I therefore asked Almighty God to give me inspiration and help me to invent models that would achieve what was required, and God--may He be praised and exalted--did enable me to devise universal models for the planetary motions in longitude and latitude and all other observable features of their motions, models that were free from the doubts surrounding previous ones.") Yet Ibn al-Shatir's solution, along with the work of the Maragha astronomers, remained generally unknown in medieval Europe.
Influence on Copernicus?
Ibn al-Shatir's forgotten model was rediscovered in the late 1950's by E. S. Kennedy and his students at the American University of Beirut. The discovery raised an intriguing question. It was quickly recognized that the Ibn al-Shatir and Maragha inventions were the same type of mechanism used by Copernicus a few centuries later to eliminate the equant and to generate the intricate changes in the position of the earth's orbit. Copernicus, of course, adopted a heliocentric arrangement, but the problem of accounting for the slow but regular changes in a planet's orbital speed remained exactly the same. Since Copernicus agreed with the philosophical objections to the equant--like some of his Islamic predecessors, he apparently believed celestial motions were driven by physical, crystalline spheres--he too sought to replace Ptolemy's device. In a preliminary work, the Commentariolus, he employed an arrangement equivalent to Ibn al-Shatir's. Later, in De revolutionibus, he reverted to the use of eccentric orbits, adopting a model that was the sun-centered equivalent of the one developed at Maragha.
Could Copernicus have been influenced by the Maragha astronomers or by Ibn al-Shatir? No Latin translation has been found of any of their works or indeed of any work describing their models. It is conceivable that Copernicus saw an Arabic manuscript while he was studying in Italy (from 1496 to 1503) and had it translated, but this seems highly improbable. A Greek translation of some of the al-Tusi material is known to have reached Rome in the 15th century (many Greek manuscripts were carried west after the fall of Constantinople in 1453), but there is no evidence that Copernicus ever saw it.
Scholars are currently divided over whether Copernicus got his method for replacing the equant by some unknown route from the Islamic world or whether he found it on his own. I personally believe he could have invented the method independently.
Nevertheless, the whole idea of criticizing Ptolemy and eliminating the equant is part of the climate of opinion inherited by the Latin West from Islam. The Islamic astronomers would probably have been astonished and even horrified by the revolution started by Copernicus. Yet his motives were not completely different from theirs. In eliminating the equant, and even in placing the planets in orbit around the sun, Copernicus was in part trying to formulate a mechanically functional system, one that offered not only a mathematical representation but also a physical explanation of planetary motions. In a profound sense he was simply working out the implications of an astronomy founded by Ptolemy but transformed by the Islamic astronomers. Today that heritage belongs to the entire world of science.
by Owen Gingerich.
Scientific American, April 1986 v254 p74(10) COPYRIGHT Scientific American Inc.
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