When I happened to be living in the fort of Nandana in the land of India, I observed from a high mountain standing to the west of the fort, a large plain lying south of the mountain. It occurred to me that I should examine this method [a method described previously] there. So, from the top of the mountain, I made an empirical measurement of the contact between the Earth and the blue sky. I found that the line of sight [to the horizon] had dipped below the reference line [that is, the horizontal direction] by the amount 34 minutes of arc. Then I measured the perpendicular of the mountain [that is, its height] and found it to be 652.055 cubits, where the cubit is a standard of length used in that region for measuring cloth.*
From these data, al-Biruni concluded that the radius of the Earth is 12,803,337.0358 cubits. Something went wrong with his calculation; from the data he quoted, he should have calculated the radius as about 13.3 million cubits. (See Technical Note 16.) Of course, he could not possibly have known the height of the mountain to the accuracy he stated, so there was no practical difference between 12.8 million cubits and 13.3 million cubits. In giving the radius of the Earth to 12 significant figures, al-Biruni was guilty of misplaced precision, the same error that we saw in Aristarchus: carrying out calculations and quoting results to a much greater degree of precision than is warranted by the accuracy of the measurements on which the calculation is based.
I once got into trouble in this way. I had a summer job long ago, calculating the path of atoms through a series of magnets in an atomic beam apparatus. This was before desktop computers or pocket electronic calculators, but I had an electromechanical calculating machine that could add, subtract, multiply, and divide to eight significant figures. Out of laziness, in my report I gave the results of the calculations to eight significant figures just as they came from the calculating machine, without bothering to round them off to a realistic precision. My boss complained to me that the magnetic field measurements on which my calculation was based were accurate to only a few percent, and that any precision beyond this was meaningless.
In any case, we can’t now judge the accuracy of al-Biruni’s result that the Earth’s radius is about 13 million cubits, because no one now knows the length of his cubit. Al-Biruni said there are 4,000 cubits in a mile, but what did he mean by a mile?
Omar Khayyam, the poet and astronomer, was born in 1048 in Nishapur, in Persia, and died there around 1131. He headed the observatory at Isfahan, where he compiled astronomical tables and planned calendar reform. In Samarkand in central Asia he wrote about topics in algebra, such as the solution of cubic equations. He is best known to English-speaking readers as a poet, through the magnificent nineteenth-century translation by Edward Fitzgerald of 75 out of a larger number of quatrains written by Omar Khayyam in Persian, and known as The Rubaiyat. Unsurprisingly for the hardheaded realist who wrote these verses, he strongly opposed astrology.
The greatest Arab contributions to physics were made in optics, first at the end of the tenth century by Ibn Sahl, who may have worked out the rule giving the direction of refracted rays of light (about which more in Chapter 13), and then by the great al-Haitam (Alhazen). Al-Haitam was born in Basra, in southern Mesopotamia, around 965, but worked in Cairo. His extant books include Optics, The Light of the Moon, The Halo and the Rainbow, On Paraboloidal Burning Mirrors, The Formation of Shadows, The Light of the Stars, Discourse on Light, The Burning Sphere, and The Shape of the Eclipse. He correctly attributed the bending of light in refraction to the change in the speed of light when it passes from one medium to another, and found experimentally that the angle of refraction is proportional to the angle of incidence only for small angles. But he did not give the correct general formula. In astronomy, he followed Adrastus and Theon in attempting to give a physical explanation to the epicycles and deferents of Ptolemy.
An early chemist, Jabir ibn Hayyan, is now believed to have flourished in the late eighth or early ninth century. His life is obscure, and it is not clear whether the many Arabic works attributed to him are really the work of a single person. There is also a large body of Latin works that appeared in Europe in the thirteenth and fourteenth centuries attributed to a “Geber,” but it is now thought that the author of these works is not the same as the author of the Arabic works attributed to Jabir ibn Hayyan. Jabir developed techniques of evaporation, sublimation, melting, and crystallization. He was concerned with transmuting base metals into gold, and hence is often called an alchemist, but the distinction between chemistry and alchemy as practiced in his time is artificial, for there was then no fundamental scientific theory to tell anyone that such transmutations are impossible. To my mind, a distinction more important for the future of science is between those chemists or alchemists who followed Democritus in viewing the workings of matter in a purely naturalistic way, whether their theories were right or wrong, and those like Plato (and, unless they were speaking metaphorically, Anaximander and Empedocles), who brought human or religious values into the study of matter. Jabir probably belongs to the latter class. For instance, he made much of the chemical significance of 28, the number of letters in the alphabet of Arabic, the language of the Koran. Somehow it was important that 28 is the product of 7, supposed to be the number of metals, and 4, the number of qualities: cold, warm, wet, and dry.
The earliest major figure in the Arab medical/philosophical tradition was al-Kindi (Alkindus), who was born in Basra of a noble family but worked in Baghdad in the ninth century. He was a follower of Aristotle, and tried to reconcile Aristotle’s doctrines with those of Plato and of Islam. Al-Kindi was a polymath, very interested in mathematics, but like Jabir he followed the Pythagoreans in using it as a sort of number magic. He wrote about optics and medicine, and attacked alchemy, though he defended astrology. Al-Kindi also supervised some of the work of translation from Greek to Arabic.
More impressive was al-Razi (Rhazes), an Arabic-speaking Persian of the generation following al-Kindi. His works include A Treatise on the Small Pox and Measles. In Doubts Concerning Galen, he challenged the authority of the influential Roman physician and disputed the theory, going back to Hippocrates, that health is a matter of balance of the four humors (described in Chapter 4). He explained, “Medicine is a philosophy, and this is not compatible with renouncement of criticism with regard to the leading authors.” In an exception to the typical views of Arab physicians, al-Razi also challenged Aristotle’s teaching, such as the doctrine that space must be finite.
The most famous of the Islamic physicians was Ibn Sina (Avicenna), another Arabic-speaking Persian. He was born in 980 near Bokhara in central Asia, became court physician to the sultan of Bokhara, and was appointed governor of a province. Ibn Sina was an Aristotelian, who like al-Kindi tried to reconcile with Islam. His Al Qanum was the most influential medical text of the Middle Ages.
At the same time, medicine began to flourish in Islamic Spain. Al-Zahrawi (Abulcasis) was born in 936 near Córdoba, the metropolis of Andalusia, and worked there until his death in 1013. He was the greatest surgeon of the Middle Ages, and highly influential in Christian Europe. Perhaps because surgery was less burdened than other branches of medicine by ill-founded theory, al-Zahrawi sought to keep medicine separate from philosophy and theology.
The divorce of medicine from philosophy did not last. In the following century the physician Ibn Bajjah (Avempace) was born in Saragossa, and worked there and in Fez, Seville, and Granada. He was an Aristotelian who criticized Ptolemy and rejected Ptolemaic astronomy, but he took exception to Aristotle’s theory of motion.
Ibn Bajjah was succeeded by his student Ibn Tufayl (Abubacer), also born in Muslim Spain. He practiced medicine in Granada, Ceuta, and Tangier, and he became vizier and physician to the sultan of the Almohad dynasty. He argued that there is no contradiction between Aristotle and Islam, and like his teacher rejected the epicycles and eccentrics of Ptolemaic astronomy.
In turn, Ibn Tufayl had a distinguished student, al-Bitruji. He was an astronomer but inherited his teacher’
s commitment to Aristotle and rejection of Ptolemy. Al-Bitruji unsuccessfully attempted to reinterpret the motion of planets on epicycles in terms of homocentric spheres.
One physician of Muslim Spain became more famous as a philosopher. Ibn Rushd (Averroes) was born in 1126 at Córdoba, the grandson of the city’s imam. He became cadi (judge) of Seville in 1169 and of Córdoba in 1171, and then on the recommendation of Ibn Tufayl became court physician in 1182. As a medical scientist, Ibn Rushd is best known for recognizing the function of the retina of the eye, but his fame rests chiefly on his work as a commentator on Aristotle. His praise of Aristotle is almost embarrassing to read:
[Aristotle] founded and completed logic, physics, and metaphysics. I say that he founded them because the works written before him on these sciences are not worth talking about and are quite eclipsed by his own writings. And I say that he completed them because no one who has come after him up to our own time, that is, for nearly fifteen hundred years, has been able to add anything to his writings or to find any error of any importance in them.5
The father of the modern author Salman Rushdie chose the surname Rushdie to honor the secular rationalism of Ibn Rushd.
Naturally Ibn Rushd rejected Ptolemaic astronomy, as contrary to physics, meaning Aristotle’s physics. He was aware that Aristotle’s homocentric spheres did not “save the appearances,” and he tried to reconcile Aristotle with observation but concluded that this was a task for the future:
In my youth I hoped it would be possible for me to bring this research [in astronomy] to a successful conclusion. Now, in my old age, I have lost hope, for several obstacles have stood in my way. But what I say about it will perhaps attract the attention of future researchers. The astronomical science of our days surely offers nothing from which one can derive an existing reality. The model that has been developed in the times in which we live accords with the computations, not with existence.6
Of course, Ibn Rushd’s hopes for future researchers were unfulfilled; no one ever was able to make the Aristotelian theory of the planets work.
There was also serious astronomy done in Muslim Spain. In Toledo al-Zarqali (Arzachel) in the eleventh century was the first to measure the precession of the apparent orbit of the Sun around the Earth (actually of course the precession of the orbit of the Earth around the Sun), which is now known to be mostly due to the gravitational attraction between the Earth and other planets. He gave a value for this precession of 12.9" (seconds of arc) per year, in fair agreement with the modern value, 11.6" per year.7 A group of astronomers including al-Zarqali used the earlier work of al-Khwarizmi and al-Battani to construct the Tables of Toledo, a successor to the Handy Tables of Ptolemy. These astronomical tables and their successors described in detail the apparent motions of the Sun, Moon, and planets through the zodiac and were landmarks in the history of astronomy.
Under the Ummayad caliphate and its successor, the Berber Almoravid dynasty, Spain was a cosmopolitan center of learning, hospitable to Jews as well as Muslims. Moses ben Maimon (Maimonides), a Jew, was born in 1135 at Córdoba during this happy time. Jews and Christians were never more than second-class citizens under Islam, but during the Middle Ages the condition of Jews was generally far better under the Arabs than in Christian Europe. Unfortunately for ben Maimon, during his youth Spain came under the rule of the fanatical Islamist Almohad caliphate, and he had to flee, trying to find refuge in Almeira, Marrakesh, Caesarea, and Cairo, finally coming to rest in Fustat, a suburb of Cairo. There until his death in 1204 he worked both as a rabbi, with influence throughout the world of medieval Jewry, and as a highly prized physician to both Arabs and Jews. His best-known work is the Guide to the Perplexed, which takes the form of letters to a perplexed young man. In it he expressed his rejection of Ptolemaic astronomy as contrary to Aristotle:8
You know of Astronomy as much as you have studied with me, and learned from the book Almagest; we had not sufficient time to go beyond this. The theory that the spheres move regularly, and that the assumed courses of the stars are in harmony with observation, depends, as you are aware, on two hypotheses: we must assume either epicycles, or eccentric spheres, or a combination of both. Now I will show that each of these two hypotheses is irregular, and totally contrary to the results of Natural Science.
He then went on to acknowledge that Ptolemy’s scheme agrees with observation, while Aristotle’s does not, and as Proclus did before him, ben Maimon despaired at the difficulty of understanding the heavens:
But of the things in the heavens man knows nothing except a few mathematical calculations, and you see how far these go. I say in the words of the poet9 “The heavens are the Lord’s, but the Earth he has given to the sons of man”; that is to say, God alone has a perfect and true knowledge of the heavens, their nature, their essence, their form, their motion, and their causes; but He gave man power to know the things which are under the heavens.
Just the opposite turned out to be true; it was the motion of heavenly bodies that was first understood in the early days of modern science.
There is testimony to the influence of Arab science on Europe in a long list of words derived from Arabic originals: not only algebra and algorithm, but also names of stars like Aldebaran, Algol, Alphecca, Altair, Betelgeuse, Mizar, Rigel, Vega, and so on, and chemical terms like alkali, alembic, alcohol, alizarin, and of course alchemy.
This brief survey leaves us with a question: why was it specifically those who practiced medicine, such as Ibn Bajjah, Ibn Tufayl, Ibn Rushd, and ben Maimon, who held on so firmly to the teachings of Aristotle? I can think of three possible reasons. First, physicians would naturally be most interested in Aristotle’s writings on biology, and in these Aristotle was at his best. Also, Arab physicians were powerfully influenced by the writings of Galen, who greatly admired Aristotle. Finally, medicine is a field in which the precise confrontation of theory and observation was very difficult (and still is), so that the failings of Aristotelian physics and astronomy to agree in detail with observation may not have seemed so important to physicians. In contrast, the work of astronomers was used for purposes where correct precise results are essential, such as constructing calendars; measuring distances on Earth; telling the correct times for daily prayers; and determining the qibla, the direction to Mecca, which should be faced during prayer. Even astronomers who applied their science to astrology had to be able to tell precisely in what sign of the zodiac the Sun and planets were on any given date; and they were not likely to tolerate a theory like Aristotle’s that gave the wrong answers.
The Abbasid caliphate came to an end in 1258, when the Mongols under Hulegu Khan sacked Baghdad and killed the caliph. Abbasid rule had disintegrated well before that. Political and military power had passed from the caliphs to Turkish sultans, and even the caliph’s religious authority was weakened by the founding of independent Islamic governments: a translated Ummayad caliphate in Spain, the Fatimid caliphate in Egypt, the Almoravid dynasty in Morocco and Spain, succeeded by the Almohad caliphate in North Africa and Spain. Parts of Syria and Palestine were temporarily reconquered by Christians, first by Byzantines and then by Frankish crusaders.
Arab science had already begun to decline before the end of the Abbasid caliphate, perhaps beginning about AD 1100. After that, there were no more scientists with the stature of al-Battani, al-Biruni, Ibn Sina, and al-Haitam. This is a controversial point, and the bitterness of the controversy is heightened by today’s politics. Some scholars deny that there was any decline.10
It is certainly true that some science continued even after the end of the Abbasid era, under the Mongols in Persia and then in India, and later under the Ottoman Turks. For instance, the building of the Maragha observatory in Persia was ordered by Hulegu in 1259, just a year after his sacking of Baghdad, in gratitude for the help that he thought that astrologers had given him in his conquests. Its founding director, the astronomer al-Tusi, wrote about spherical geometry (the geometry obeyed by great circles on a spherical su
rface, like the notional sphere of the fixed stars), compiled astronomical tables, and suggested modifications to Ptolemy’s epicycles. Al-Tusi founded a scientific dynasty: his student al-Shirazi was an astronomer and mathematician, and al-Shirazi’s student al-Farisi did groundbreaking work on optics, explaining the rainbow and its colors as the result of the refraction of sunlight in raindrops.
More impressive, it seems to me, is Ibn al-Shatir, a fourteenth-century astronomer of Damascus. Following earlier work of the Maragha astronomers, he developed a theory of planetary motions in which Ptolemy’s equant was replaced with a pair of epicycles, thus satisfying Plato’s demand that the motion of planets must be compounded of motions at constant speed around circles. Ibn al-Shatir also gave a theory of the Moon’s motion based on epicycles: it avoided the excessive variation in the distance of the Moon from the Earth that had afflicted Ptolemy’s lunar theory. The early work of Copernicus reported in his Commentariolus presents a lunar theory that is identical to Ibn al-Shatir’s, and a planetary theory that gives the same apparent motions as the theory of al-Shatir.11 It is now thought that Copernicus learned of these results (if not of their source) as a young student in Italy.
Some authors have made much of the fact that a geometric construction, the “Tusi couple,” which had been invented by al-Tusi in his work on planetary motion, was later used by Copernicus. (This was a way of mathematically converting rotary motion of two touching spheres into oscillation in a straight line.) It is a matter of some controversy whether Copernicus learned of the Tusi couple from Arab sources, or invented it himself.12 He was not unwilling to give credit to Arabs, and quoted five of them, including al-Battani, al-Bitruji, and Ibn Rushd, but made no mention of al-Tusi.
To Explain the World: The Discovery of Modern Science Page 12