To Explain the World: The Discovery of Modern Science

by Steven Weinberg

  The “natural scientists” of Geminus share some characteristics of today’s theoretical physicists, but with huge differences. Following Aristotle, Geminus sees the natural scientists as relying on first principles, including teleological principles: the natural scientist supposes that the heavenly bodies “are better as they are.” For Geminus it is only the astronomer who uses mathematics, as an adjunct to his observations. What Geminus does not imagine is the give-and-take that has developed between theory and observation. The modern theoretical physicist does make deductions from basic principles, but he uses mathematics in this work, and the principles themselves are expressed mathematically and are learned from observation, certainly not by considering what is “better.”

  In the reference by Geminus to the motions of planets “that revolve in parallel courses and those that wind along oblique circles” one can recognize the homocentric spheres rotating on tilted axes of the schemes of Eudoxus, Callippus, and Aristotle, to which Geminus as a good Aristotelian would naturally be loyal. On the other hand, Adrastus of Aphrodisias, who around AD 100 wrote a commentary on the Timaeus, and a generation later the mathematician Theon of Smyrna were sufficiently convinced by the theory of Apollonius and Hipparchus that they tried to make it respectable, by interpreting the epicycles and deferents as solid transparent spheres, like the homocentric spheres of Aristotle, but now not homocentric.

  Some writers, facing the conflict between the rival theories of the planets, threw up their hands, and declared that humans were not meant to understand celestial phenomena. Thus, in the mid–fifth century AD, in his commentary on the Timaeus, the Neoplatonist pagan Proclus proclaimed:16

  When we are dealing with sublunary things, we are content, because of the instability of the material which goes to constitute them, to grasp what happens in most instances. But when we want to know heavenly things, we use sensibility and call upon all sorts of contrivances quite removed from likelihood. . . . That this is the way things stand is plainly shown by the discoveries made about these heavenly things—from different hypotheses we draw the same conclusions relative to the same objects. Among these hypotheses are some which save the phenomena by means of epicycles, others which do so by means of eccentrics, still others which save the phenomena by means of counterturning spheres devoid of planets. Surely the god’s judgement is more certain. But as for us, we must be satisfied to “come close” to those things, for we are men, who speak according to what is likely, and whose lectures resemble fables.

  Proclus was wrong on three counts. He missed the point that the Ptolemaic theories that used epicycles and eccentrics did a far better job of “saving the phenomena” than the Aristotelian theory using the hypothesis of homocentric “counterturning spheres.” There is also a minor technical point: in referring to hypotheses “which save the phenomena by means of epicycles, others which do so by means of eccentrics” Proclus seems not to realize that in the case where an epicycle can play the role of an eccentric (discussed in footnote *), these are not different hypotheses but different ways of describing what is mathematically the same hypothesis. Above all, Proclus was wrong in supposing that it is harder to understand heavenly motions than those here on Earth, below the orbit of the Moon. Just the reverse is true. We know how to calculate the motions of bodies in the solar system with exquisite precision, but we still can’t predict earthquakes or hurricanes. But Proclus was not alone. We will see his unwarranted pessimism regarding the possibility of understanding the motion of the planets repeated centuries later, by Moses Maimonides.

  Writing in the first decade of the twentieth century, the physicist turned philosopher Pierre Duhem17 took the side of the Ptolemaics because their model fitted the data better, but he disapproved of Theon and Adrastus for trying to lend reality to the model. Perhaps because he was deeply religious, Duhem sought to restrict the role of science merely to the construction of mathematical theories that agree with observation, rather than encompassing efforts to explain anything. I am not sympathetic to this view, because the work of my generation of physicists certainly feels like explanation as we ordinarily use the word, not like mere description.18 True, it is not so easy to draw a precise distinction between description and explanation. I would say that we explain some generalization about the world by showing how it follows from some more fundamental generalization, but what do we mean by fundamental? Still, I think we know what we mean when we say that Newton’s laws of gravitation and motion are more fundamental than Kepler’s three laws of planetary motion. The great success of Newton was in explaining the motions of the planets, not merely describing them. Newton did not explain gravitation, and he knew that he had not, but that is the way it always is with explanation—something is always left for future explanation.

  Because of their odd motions, the planets were useless as clocks or calendars or compasses. They were put to a different sort of use in Hellenistic times and afterward for purposes of astrology, a false science learned from the Babylonians.* The sharp modern distinction between astronomy and astrology was less clear in the ancient and medieval worlds, because the lesson had not yet been learned that human concerns were irrelevant to the laws governing the stars and planets. Governments from the Ptolemies on supported the study of astronomy largely in the hope that it would reveal the future, and so naturally astronomers spent much of their time on astrology. Indeed, Claudius Ptolemy was the author not only of the greatest astronomical work of antiquity, the Almagest, but also of a textbook of astrology, the Tetrabiblos.

  But I can’t leave Greek astronomy on this sour note. For a happier ending to Part II of this book, I’ll quote Ptolemy on his pleasure in astronomy:19

  I know that I am mortal and the creature of a day; but when I search out the massed wheeling circles of the stars, my feet no longer touch the Earth, but, side by side with Zeus himself, I take my fill of ambrosia, the food of the gods.

  PART III

  THE MIDDLE AGES

  Science reached heights in the Greek part of the ancient world that were not regained until the scientific revolution of the sixteenth and seventeenth centuries. The Greeks made the great discovery that some aspects of nature, especially in optics and astronomy, could be described by precise mathematical naturalistic theories that agree with observation. What was learned about light and the heavens was important, but even more important was what was learned about the sort of thing that could be learned, and how to learn it.

  Nothing during the Middle Ages, either in the Islamic world or in Christian Europe, compares with this. But the millennium intervening between the fall of Rome and the scientific revolution was not an intellectual desert. The achievements of Greek science were preserved and in some cases improved in the institutions of Islam and then in the universities of Europe. In this way, the ground was prepared for the scientific revolution.

  It was not only the achievements of Greek science that were preserved in the Middle Ages. We will see in medieval Islam and Christendom a continuation of the ancient debates over the role in science of philosophy, of mathematics, and of religion.

  9

  The Arabs

  After the collapse in the fifth century of the western Roman Empire, the Greek-speaking eastern half continued as the Byzantine Empire, and even increased in extent. The Byzantine Empire achieved a climactic military success during the reign of the emperor Heraclius, whose army in AD 627 in the battle of Nineveh destroyed the army of the Persian Empire, the ancient enemy of Rome. But within a decade the Byzantines had to confront a more formidable adversary.

  The Arabs were known in antiquity as a barbarian people, living in the borderland of the Roman and Persian empires, “that just divides the desert and the sown.” They were pagans, with a religion centered at the city of Mecca, in the settled portion of western Arabia known as the Hejaz. Starting at the end of the 500s, Muhammad, an inhabitant of Mecca, set out to convert his fellow citizens to monotheism. Meeting opposition, he and his acolytes fled in 622 to
Medina, which they then used as a military base for the conquest of Mecca and of most of the Arabian Peninsula.

  After Muhammad’s death in 632, a majority of Muslims followed the authority of four successive leaders headquartered at first at Medina: his companions and relatives Abu Bakr, Omar, Othman, and Ali. They are recognized today by Sunni Muslims as the “four rightly guided caliphs.” The Muslims conquered the Byzantine province of Syria in 636, just nine years after the battle of Nineveh, and then went on to seize Persia, Mesopotamia, and Egypt.

  Their conquests introduced the Arabs to a more cosmopolitan world. For instance, the Arab general Amrou, who conquered Alexandria, reported to the caliph Omar, “I have taken a city, of which I can only say that it contains 6000 palaces, 4000 baths, 400 theatres, 12,000 greengrocers, and 40,000 Jews.”1

  A minority, the forerunners of today’s Shiites, accepted only the authority of Ali, the fourth caliph and the husband of Muhammad’s daughter Fatima. The split in the world of Islam became permanent after a revolt against Ali, in which Ali as well as his son Hussein was killed. A new dynasty, the Sunni Ummayad caliphate, was established at Damascus in 661.

  Under the Ummayads Arab conquests expanded to include the territories of modern Afghanistan, Pakistan, Libya, Tunisia, Algeria, and Morocco, most of Spain, and much of central Asia beyond the Oxus River. From the formerly Byzantine lands that they now ruled they began to absorb Greek science. Some Greek learning also came from Persia, whose rulers had welcomed Greek scholars (including Simplicius) before the rise of Islam, when the Neoplatonic Academy was closed by the emperor Justinian. Christendom’s loss became Islam’s gain.

  It was in the time of the next Sunni dynasty, the caliphate of the Abbasids, that Arab science entered its golden age. Baghdad, the capital city of the Abbasids, was built on both sides of the Tigris River in Mesopotamia by al-Mansur, caliph from 754 to 775. It became the largest city in the world, or at least the largest outside China. Its best-known ruler was Harun al-Rashid, caliph from 786 to 809, famous from A Thousand and One Nights. It was under al-Rashid and his son al-Mamun, caliph from 813 to 833, that translation from Greece, Persia, and India reached its greatest scope. Al-Mamun sent a mission to Constantinople that brought back manuscripts in Greek. The delegation probably included the physician Hunayn ibn Ishaq, the greatest of the ninth-century translators, who founded a dynasty of translators, training his son and nephew to carry on the work. Hunayn translated works of Plato and Aristotle, as well as medical texts of Dioscorides, Galen, and Hippocrates. Mathematical works of Euclid, Ptolemy, and others were also translated into Arabic at Baghdad, some through Syriac intermediaries. The historian Philip Hitti has nicely contrasted the state of learning at this time at Baghdad with the illiteracy of Europe in the early Middle Ages: “For while in the East al-Rashid and al-Mamun were delving into Greek and Persian philosophy, their contemporaries in the West, Charlemagne and his lords, were dabbling in the art of writing their names.”2

  It is sometimes said that the greatest contribution to science of the Abbasid caliphs was the foundation of an institute for translation and original research, the Bayt al-Hikmah, or House of Wisdom. This institute is supposed to have served for the Arabs somewhat the same function that the Museum and Library of Alexandria served for the Greeks. This view has been challenged by a scholar of Arabic language and literature, Dimitri Gutas.3 He points out that Bayt al-Hikmah is a translation of a Persian term that had long been used in pre-Islamic Persia for storehouses of books, mostly of Persian history and poetry rather than of Greek science. There are only a few known examples of works that were translated at the Bayt al-Hikmah in the time of al-Mamun, and those are from Persian rather than Greek. Some astronomical research, as we shall see, was going on at the Bayt al-Hikmah, but little is known of its scope. What is not in dispute is that, whether or not at the Bayt al-Hikmah, the city of Baghdad itself in the time of al-Mamun and al-Rashid was a great center of translation and research.

  Arab science was not limited to Baghdad, but spread west to Egypt, Spain, and Morocco, and east to Persia and central Asia. Participating in this work were not only Arabs but also Persians, Jews, and Turks. They were very much a part of Arab civilization and wrote in Arabic (or at least in Arabic script). Arabic then had something like the status in science that English has today. In some cases it is difficult to decide on the ethnic background of these figures. I will consider them all together, under the heading “Arabs.”

  As a rough approximation, we can identify two different scientific traditions that divided the Arab savants. On one hand, there were real mathematicians and astronomers who were not much concerned with what today we would call philosophy. Then there were philosophers and physicians, not very active in mathematics, and strongly influenced by Aristotle. Their interest in astronomy was chiefly astrological. Where they were concerned at all with the theory of the planets, the philosopher/physicians favored the Aristotelian theory of spheres centered on the Earth, while the astronomer/mathematicians generally followed the Ptolemaic theory of epicycles and deferents discussed in Chapter 8. This was an intellectual schism that, as we shall see, would persist in Europe until the time of Copernicus.

  The achievements of Arab science were the work of many individuals, none of them clearly standing out from the rest as, say, Galileo and Newton stand out in the scientific revolution. What follows is a brief gallery of medieval Arab scientists that I hope may give some idea of their accomplishments and variety.

  The first of the important astronomer/mathematicians at Baghdad was al-Khwarizmi,* a Persian born around 780 in what is now Uzbekistan. Al-Khwarizmi worked at the Bayt al-Hikmah and prepared widely used astronomical tables based in part on Hindu observations. His famous book on mathematics was Hisah-al-Jabr w-al-Muqabalah, dedicated to the caliph al-Mamun (who was half Persian himself). From its title we derive the word “algebra.” But this was not really a book on what is today called algebra. Formulas like the one for the solution of quadratic equations were given in words, not in the symbols that are an essential element of algebra. (In this respect, al-Khwarizmi’s mathematics was less advanced than that of Diophantus.) From al-Khwarizmi we also get our name for a rule for solving problems, “algorithm.” The text of Hisah al-Jabr w-al-Muqabalah contains a confusing mixture of Roman numerals; Babylonian numbers based on powers of 60; and a new system of numbers learned from India, based on powers of 10. Perhaps the most important mathematical contribution of al-Khwarizmi was his explanation to the Arabs of these Hindu numbers, which in turn became known in Europe as Arabic numbers.

  In addition to the senior figure of al-Khwarizmi, there were collected in Baghdad a productive group of other ninth-century astronomers, including al-Farghani (Alfraganus),* who wrote a popular summary of Ptolemy’s Almagest and developed his own version of the planetary scheme described in Ptolemy’s Planetary Hypotheses.

  It was a major occupation of this Baghdad group to improve on Eratosthenes’ measurement of the size of the Earth. Al-Farghani in particular reported a smaller circumference, which centuries later encouraged Columbus (as mentioned in an earlier footnote) to think that he could survive an ocean voyage westward from Spain to Japan, perhaps the luckiest miscalculation in history.

  The Arab who was most influential among European astronomers was al-Battani (Albatenius), born around 858 BC in northern Mesopotamia. He used and corrected Ptolemy’s Almagest, making more accurate measurements of the ~23½° angle between the Sun’s path through the zodiac and the celestial equator, of the lengths of the year and the seasons, of the precession of the equinoxes, and of the positions of stars. He introduced a trigonometric quantity, the sine, from India, in place of the closely related chord used and calculated by Hipparchus. (See Technical Note 15.) His work was frequently quoted by Copernicus and Tycho Brahe.

  The Persian astronomer al-Sufi (Azophi) made a discovery whose cosmological significance was not recognized until the twentieth century. In 964, in his Book of the Fixed Stars, h
e described a “little cloud” always present in the constellation Andromeda. This was the earliest known observation of what are now called galaxies, in this case the large spiral galaxy M31. Working at Isfahan, al-Sufi also participated in translating works of Greek astronomy into Arabic.

  Perhaps the most impressive astronomer of the Abbasid era was al-Biruni. His work was unknown in medieval Europe, so there is no latinized version of his name. Al-Biruni lived in central Asia, and in 1017 visited India, where he lectured on Greek philosophy. He considered the possibility that the Earth rotates, gave accurate values for the latitude and longitude of various cities, prepared a table of the trigonometric quantity known as the tangent, and measured specific gravities of various solids and liquids. He scoffed at the pretensions of astrology. In India, al-Biruni invented a new method for measuring the circumference of the Earth. As he described it:4