In addition to devastating personal consequences for individuals and families, these restrictions have had profound ramifications for scientific communication and collaboration. The numbers of international students enrolling at U.S. universities dropped by 7 percent in 2017, after reaching a record high in 2016. Postdoctoral scholars find it increasingly difficult to secure visas to work in U.S. laboratories. And the work of multinational scientific research teams has been disrupted in the wake of anti-Muslim and anti-immigrant legislation.
International scientific collaboration may seem like a recent phenomenon, a late-20th-century product of the Internet and ease of global travel. But international communication and exchange of ideas have been a defining feature of science since at least the Middle Ages. The modern scientific order was built on international exchange — and if the United States continues to prohibit such collaboration, its role as a leader in science and medicine will be in serious jeopardy.
Nowhere are the global roots of scientific discovery more apparent than in the work of one of the most famous scientific heroes in the Western canon, Nicolaus Copernicus. In the 16th century, he became the first man since antiquity to propose that the sun, not Earth, was the (near) center of the cosmos and that Earth and all the other planets rotated around the sun.
This has long been recognized as one of the greatest scientific advances of all time, and heliocentrism — the recognition that the sun, rather than Earth, is the center of the solar system — is frequently associated with the beginnings of modern science. What is less well known is that Copernicus’s work would have been impossible without the contributions of astronomers and mathematicians in the Islamic world.
To understand Copernicus’s accomplishment, and his debt to Muslim scientists, it is essential to understand three fundamental tenets of astronomy in his day. The first of these was that astronomy was a quantitative, not a qualitative, subject. Astronomers needed to be able to calculate where a celestial object (like a planet) had been at a particular time in the past and where it would be at a particular time in the future. To do this, they used geometrical models of the motion of each celestial body.
The second tenet was that all motion in the heavens was uniform and circular. Therefore, all of the geometrical models used to calculate and predict the positions of planets had to be combinations of circular motions.
And, finally, it was axiomatic that all planets and the stars were embedded in solid, transparent spheres that rotated around Earth. They did not move through “space” in the modern sense. Ideally, the geometrical models that allowed prediction of planetary positions could be imagined as real, physical, three-dimensional spheres rotating around Earth. But it was widely recognized that it was perfectly possible to construct geometrical models that had predictive accuracy but were physically impossible. Copernicus challenged none of these fundamental tenets of astronomy, but he was deeply concerned with producing accurate geometrical models that also represented the real, physical structure of the cosmos.
Copernicus’s recognition that the sun was at the center of planetary motion did not automatically lead to more accurate predictions of planetary positions. He still had to come up with geometrical models for each planet and the moon, and these models had to consist of combinations of circles. Had he failed to produce these models, no astronomer would have been interested in his hypothesis that the sun was the center of the cosmos. His book would have faded rapidly into obscurity instead of becoming a starting point for modern physics and cosmology. And it is in these new, highly accurate geometrical models that his debt to Islamic scientists is so great.
For 1,400 years before Copernicus, astronomers used the work of Claudius Ptolemy (who lived in Alexandria, Egypt, during the 2nd century) as the basis for their calculations. But Ptolemy’s main innovation left astronomers with a difficult problem. Ptolemy assumed that all planets moved on circles rotating at constant speed. To make his models more accurate, he allowed some circles to rotate around their geometrical centers, but others did not.
In his planetary models, Ptolemy introduced a point some distance from the geometrical center, which he called the equant. He made this the center of uniform motion — in other words, an observer sitting at the equant point would see the planets cross equal arcs of sky in equal times.
This device worked well. Ptolemy’s mathematical models permitted accurate predictions of planetary positions and eclipses of the sun and moon. But while it worked, it was hard to imagine these models being the actual physical structure of the planetary spheres. To many astronomers, it just didn’t make sense for a circle to rotate about a point that was not its center. This slip in logic was Ptolemy’s equant problem, and European scientists made little headway in solving it. In fact, Copernicus may have been the first European since antiquity to really understand the problem.
Not so in the Islamic world. In the 13th century, a young man in Persia had a different idea. Nasir al-Din al-Tusi invented a method of combining two circular motions to produce a straight line. Adding this device to Ptolemy’s models made all circles rotate about their centers and avoided using the equant. The modern name for this two-circle device is the “Tusi couple.”
Tusi survived the Mongol conquest of the Abbasid Caliphate, the destruction of Baghdad and the slaughter of its inhabitants in 1258. He was already so famous that he was recruited by the conquerors as an astrology adviser. In return, he asked the new Mongol rulers to support the construction of a large astronomical observatory at Maragha in Persia. Many scientists came to work there, including the Syrian Muʾayyad al‐Dīn al‐Urdi. He helped build the instruments, one of which was four stories high. He also devised another way of solving the equant problem.
Urdi’s method introduced no new circles but redefined the distances between Earth, the center of the largest circle and the point that had been the equant. Three centuries later, around 1510, Copernicus used variants of Tusi’s method to do the work of the equant when he first presented his theory. But he switched to Urdi’s method in the major book for which he is remembered, “On the Revolutions of the Celestial Orbs,” published in 1543.
The new ideas introduced by Tusi and Urdi were developed by later Muslim astronomers, especially Alaʾ al‐Din ibn al‐Shatir, the astronomer responsible for determining the timing of religious events at the Omayyad Mosque in Damascus, Syria. He introduced new mathematical models for two problem cases, the moon and the planet Mercury. Ibn al‐Shatir’s models used complex combinations of circles, including Tusi couples, and Copernicus borrowed those models in “On the Revolutions.”
The astronomical techniques developed at Maragha began to arrive in Europe around 1300 when Gregory Chioniades traveled from Byzantium to Tabriz to study astronomy. After the Ottoman conquest of Constantinople in 1453, the sultan gathered astronomers to his new capital, bringing with them the methods of Tusi, Urdi and Shatir. The most important was Ali al‐Qushji from Samarkand. He advocated a key idea found in Copernicus — that astronomy was capable of determining the structure of the cosmos without starting from physics. He even acknowledged the possibility that Earth might rotate, although he continued to make Earth the center of the cosmos in his own models.
Diagrams showing methods like the Tusi couple arrived in the Vatican archives no later than 1475, two years after Copernicus was born in Poland, and one year after Qushji died in Istanbul. But the most likely route of transmission to Copernicus is a Jewish scholar from Istanbul, recently discovered by Robert Morrison of Bowdoin College. Moses Galeano visited Venice while Copernicus was finishing his education next door in Padua. Galeano’s later works show that he knew all the astronomy borrowed by Copernicus, who used the methods and ideas of Tusi, Urdi, Shatir and Qushji, but without naming any of them.
In the first 70 years after his death, only about a dozen people accepted Copernicus’s proposal that the sun, not Earth, was the center of planetary motions. But hundreds accepted the new models he introduced. The mathematics — most of it Islamic — was the reason most people read his book. Only later did heliocentrism gain any traction.
The science that descended from Copernicus — the origins of modern Western science — is the product of international, multilingual, multicultural exchange and collaboration, with a special debt to Muslims. Restrictions on such exchange will ultimately damage science. We did not get where we are on our own. We would not have got here at all without Muslim scientists. And we still need each other.