The most important scientific achievement in Western history is commonly ascribed to Nicolaus Copernicus, who on his death-bed published "Concerning the Revolutions of the Heavenly Spheres." Science historian Thomas Kuhn called the Polish-born astronomer's accomplishment the "Copernican Revolution." It represented a final break with the Middle Ages, a movement from religion to science, from dogma to enlightened secularism. What had Copernicus done to become the most important scientist of all time?
In school we learned that in the sixteenth century, Copernicus reformed the solar system, placing the sun, rather than the earth, at its center, correcting the work of the second-century Greek astronomer Ptolemy. By constructing his heliocentric system, Copernicus put up a fire wall between the West and East, between a scientific culture and those of magic and superstition.
Copernicus did more than switch the center of the solar system from the earth to the sun. The switch itself is important, but mathematically trivial. Other cultures had suggested it. Two hundred years before Pythagoras, philosophers in northern India had understood that gravitation held the solar system together, and that therefore the sun, the most massive object, had to be at its center. The ancient Greek astronomer Aristarchus of Samos had put forth a heliocentric system in the third century B.C. The Maya had posited a heliocentric solar system by A.D. 1000. Copernicus's task was greater. He had to repair the flawed mathematics of the Ptolemaic system.
Ptolemy had problems far beyond the fact that he chose the wrong body as the pivot point. On that, he was adhering to Aristotelian beliefs. A workable theory of universal gravitation had yet to be discovered. Thus hampered, Ptolemy attempted to explain mathematically what he saw from his vantage in Alexandria: various heavenly bodies moving around the earth. This presented problems.
Mars, for instance, while traveling across our sky, has the habit, like other planets, of sometimes reversing its direction. What's happening is simple: the earth outspeeds Mars as both planets orbit the sun, like one automobile passing another. How does one explain this in a geo-centric universe? Ptolemy came up with the concept of epicycles, circles on top of circles. Visualize a Ferris wheel revolving around a hub. The passenger-carrying cars are also free to rotate around axles connected to the outer perimeter of the wheel. Imagine the cars constantly rotating 360 degrees as the Ferris wheel also revolves. Viewed from the hub, a point on the car would appear to move backward on occasion while also moving forward with the motion of the wheel.
Ptolemy set the upper planets in a series of spheres, the most important of which was the "deferent" sphere, which carried the epicycle. This sphere was not concentric with the center of the earth. It moved at a uniform speed, but that speed was not measured around its own center, nor around the center of the earth, but around a point that Ptolemy called the "center of the equalizer of motion," later to be called the "equant." This point was the same distance from the center of the deferent as the distance of the deferent's center from the earth, but in the opposite direction. The result was a sphere that moved uniformly around an axis that passed not through its own center but, rather, through the equant.
The theory is confusing. No number of readings or constructions will help, because Ptolemy's scheme is physically impossible. The flaw is called the equant problem, and it apparently eluded the Greeks. The equant problem didn't fool the Arabs, and during the late Middle Ages Islamic astronomers created a number of theorems that corrected Ptolemy's flaws.
Copernicus confronted the same equant problem. The birth of Isaac Newton was a century away, so Copernicus, like Ptolemy and the Arabs before him, had no gravitation to help him make sense of the situation. Thus, he did not immediately switch the solar system from geo-centricity to heliocentricity. Instead, he first improved the Ptolemaic system, putting the view of the heavens from earth on a more solid mathematical basis. Only then did Copernicus transport the entire system from its earth-centered base to the sun. This was a simple operation, requiring Copernicus only to reverse the direction of the last vector connecting the earth to the sun. The rest of the math remained the same.
It was assumed that Copernicus was able to put together this new planetary system using available math, that the Copernican Revolution depended on a creative new application of classical Greek works such as Euclid's Elements and Ptolemy's Almagest. This belief began breaking down in the late 1950s when several scholars, including Otto Neugebauer, of Brown University; Edward Kennedy, of the American University of Beirut; Noel Swerdlow, of the University of Chicago; and George Saliba, of Columbia University, reexamined Copernicus's mathematics.
They found that to revolutionize astronomy Copernicus needed two theorems not developed by the ancient Greeks. Neugebauer pondered this problem: did Copernicus construct these theorems himself or did he borrow them from some non-Greek culture? Meanwhile, Kennedy, working in Beirut, discovered astronomical papers written in Arabic and dated before A.D. 1350. The documents contained unfamiliar geometry. While visiting the United States, he showed them to Neugebauer.
Neugebauer recognized the documents' significance immediately. They contained geometry identical to Copernicus's model for lunar motion. Kennedy's text was written by the Damascene astronomer Ibn al-Shatir, who died in 1375. His work contained, among other things, a theorem employed by Copernicus that was originally devised by another Islamic astronomer, Nasir al-Din al-Tusi, who lived some three hundred years before Copernicus.
The Tusi couple, as the theorem is now called, solves a centuries-old problem that plagued Ptolemy and the other ancient Greek astronomers: how circular motion can generate linear motion. Picture a large sphere with a sphere half its size inside it, the smaller sphere contacting the larger at just one point. If the large sphere rotates and the small sphere revolves in the opposite direction at twice that speed, the Tusi couple dictates that the original point of tangency will oscillate back and forth along the diameter of the larger sphere. By setting the celestial spheres properly, this theorem explained how the epicycle could move uniformly around the equant of the deferent, and still oscillate back and forth toward the center of the deferent. All this could now be done by positing spheres moving uniformly around axes that passed through their centers, thus avoiding the pitfalls of Ptolemy's configurations. A rough analogy is a steam-engine piston, which moves back and forth as the wheel is turning.
A second theorem found in the Copernican system is the Urdi lemma, after the scientist Mu'ayyad al-Din al-'Urdi, who proposed it sometime before 1250. It simply states that if two lines of equal length emerge from a straight line at the same angles, either internally or externally, and are connected up top with another straight line, the two horizontal lines will be parallel. When the equal angles are external, all four lines form a parallelogram. Copernicus did not include a proof of the Urdi lemma in his work, most likely because the proof had already been published by Mu'ayyad al-Din al-'Urdi. Columbia's George Saliba speculates that Copernicus didn't credit him because Muslims were not popular in sixteenth-century Europe.
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Scholarship moved to Cairo and then to Cordoba and Toledo in Spain as the Muslim empire expanded into Europe. When the Christians recaptured Toledo in the twelfth century, European scholars descended upon the documents. They were interested in all Arabic documents? translations of Greek works but also original Arabic writings and Arabic translations of other cultures' manuscripts. Much of the scientific knowledge of the ancient world ? Greece as well as Babylonia, Egypt, India, and China ? was tunneled to the West through Spain. George Saliba has found that there was an intense traffic in Arabic manuscripts between Damascus and Padua during the early 1500s, and more and more scientific documents, written in Arabic, are being rediscovered in European libraries. Saliba has documented that many European scholars in the Renaissance were literate in Arabic. They read the Islamic papers and shared the information with their less literate colleagues.
One example is Copernicus, who studied at Padua. Saliba points out that if Copernicus did borrow from Islamic astronomers ? and the jury is still out ? he had good reason not to acknowledge his intellectual debt. It would have been impolitic, says Saliba, to mention Islamic science when the Ottoman Empire was at the door of Europe. Another European scholar who studied at Padua was William Harvey, who established the geometry of the human circulatory system in 1629, an-other landmark in science according to the AAAS's Science time line. A 1241 Arab document, notes Saliba, lays out the same geometry, including the crucial assertion that the blood must first travel through the lungs before passing through the heart, contrary to the opinion of the ancient Greek physician Galen and past medical scholarship.
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Both the Urdi lemma and the Tusi couple are, in the words of Saliba, "organically embedded within [Copernican] astronomy, so much so that it would be inconceivable to extract them and still leave the mathematical edifice of Copernican astronomy intact"
Map publishers sometimes insert fictitious islands or other features into their maps to trap plagiarists. Did Copernicus borrow al-Tusi's theorem without credit? There's no smoking gun, but it is suspicious that Copernicus's math contains arbitrary details that are identical to al-Tusi's. Any geometric theorem has the various points labeled with letters or numbers, at the discretion of the originator. The order and choice of symbols is arbitrary. The German science historian Willy Hartner noted that the geometric points used by Copernicus were identical to al-Tusi's original notation. That is, the point labeled with the symbol for alif by al-Tusi was marked A by Copernicus. The Arabic ba was marked B, and so on, each Copernican label the phonetic equivalent of the Arabic. Not just some of the labels were the same?almost all were identical.
There was one exception. The point designating the center of the smaller circle was marked as f by Copernicus. It was a z in Tusi's diagram. In Arabic script, however, a z in that hand could be easily mistaken for an f.
Johannes Kepler, who stretched Copernicus's circular planetary orbits into ellipses later in the century, wondered why Copernicus had not included a proof for his second "new" theorem, which was in fact the Urdi lemma. The obvious answer has eluded most historians because it is too damaging to our Western pride to accept: the new math in the Copernican Revolution arose first in Islamic, not European minds. From a scientific point of view, it's not important whether Copernicus was a plagiarist. The evidence is circumstantial, and certainly he could have invented the theorems on his own. There is no doubt, however, that two Arab astronomers beat him to the punch.
Note: The above article is an excerpt from "Lost Discoveries: The Ancient Roots of Modern Science - from the Babylonians to the Maya" by Dick Teresi. Simon & Shuster, 2002. |
