Cosmos (29 page)

They did not advocate the free confrontation of conflicting points of view. Instead, like all orthodox religions, they practiced
a rigidity that prevented them from correcting their errors. Cicero wrote:

The Pythagoreans were fascinated by the regular solids, symmetrical three-dimensional objects all of whose sides are the same regular polygon. The cube is the simplest example, having six squares as sides. There are an infinite number of regular polygons, but only five regular solids. (The proof of this statement, a famous example of mathematical reasoning, is given in
Appendix 2
.) For some reason, knowledge of a solid called the dodecahedron having twelve pentagons as sides seemed to them dangerous. It was mystically associated with the Cosmos. The other four regular solids were identified, somehow, with the four “elements” then imagined to constitute the world; earth, fire, air and water. The fifth regular solid must then, they thought, correspond to some fifth element that could only be the substance of the heavenly bodies. (This notion of a fifth essence is the origin of our word
quintessence.)
Ordinary people were to be kept ignorant of the dodecahedron.

In love with whole numbers, the Pythagoreans believed all things could be derived from them, certainly all other numbers. A crisis in doctrine arose when they discovered that the square root of two (the ratio of the diagonal to the side of a square) was irrational, that √2 cannot be expressed accurately as the ratio of any two whole numbers, no matter how big these numbers are. Ironically this discovery (reproduced in
Appendix 1
) was made with the Pythagorean theorem as a tool. “Irrational” originally meant only that a number could not be expressed as a ratio. But for the Pythagoreans it came to mean something threatening, a hint that their world view might not make sense, which is today the other meaning of “irrational.” Instead of sharing these important mathematical discoveries, the Pythagoreans suppressed the knowledge of
and the dodecahedron. The outside world was
not to know.
^*
Even today there are scientists opposed to the popularization of science: the sacred knowledge is to be kept within the cult, unsullied by public understanding.

The Pythagoreans believed the sphere to be “perfect,” all points on its surface being at the same distance from its center. Circles were also perfect. And the Pythagoreans insisted that planets moved in circular paths at constant speeds. They seemed to believe that moving slower or faster at different places in the orbit would be unseemly; noncircular motion was somehow flawed, unsuitable for the planets, which, being free of the Earth, were also deemed “perfect.”

The pros and cons of the Pythagorean tradition can be seen clearly in the life’s work of Johannes Kepler (
Chapter 3
). The Pythagorean idea of a perfect and mystical world, unseen by the senses, was readily accepted by the early Christians and was an integral component of Kepler’s early training. On the one hand, Kepler was convinced that mathematical harmonies exist in nature (he wrote that “the universe was stamped with the adornment of harmonic proportions”); that simple numerical relationships must determine the motion of the planets. On the other hand, again following the Pythagoreans, he long believed that only uniform circular motion was admissible. He repeatedly found that the observed planetary motions could not be explained in this way, and repeatedly tried again. But unlike many Pythagoreans, he believed in observation and experiment in the real world. Eventually the detailed observations of the apparent motion of the planets forced him to abandon the idea of circular paths and to realize that planets travel in ellipses. Kepler was both inspired in his search for the harmony of planetary motion and delayed for more than a decade by the attractions of Pythagorean doctrine.

A disdain for the practical swept the ancient world. Plato urged astronomers to think about the heavens, but not to waste their time observing them. Aristotle believed that: “The lower sort are by nature slaves, and it is better for them as for all inferiors that they should be under the rule of a master.… The slave shares in his master’s life; the artisan is less closely connected with him, and only attains excellence in proportion as he becomes a slave. The meaner sort of mechanic has a special and separate slavery.” Plutarch wrote: “It does not of necessity follow that, if the work delight you with its grace, the one who wrought it is worthy of
esteem.” Xenophon’s opinion was: “What are called the mechanical arts carry a social stigma and are rightly dishonoured in our cities.” As a result of such attitudes, the brilliant and promising Ionian experimental method was largely abandoned for two thousand years. Without experiment, there is no way to choose among contending hypotheses, no way for science to advance. The anti-empirical taint of the Pythagoreans survives to this day. But why? Where did this distaste for experiment come from?

An explanation for the decline of ancient science has been put forward by the historian of science, Benjamin Farrington: The mercantile tradition, which led to Ionian science, also led to a slave economy. The owning of slaves was the road to wealth and power. Polycrates’ fortifications were built by slaves. Athens in the time of Pericles, Plato and Aristotle had a vast slave population. All the brave Athenian talk about democracy applied only to a privileged few. What slaves characteristically perform is manual labor. But scientific experimentation is manual labor, from which the slaveholders are preferentially distanced; while it is only the slaveholders—politely called “gentle-men” in some societies—who have the leisure to do science. Accordingly, almost no one
did science. The Ionians were perfectly able to make machines of some elegance. But the availability of slaves undermined the economic motive for the development of technology. Thus the mercantile tradition contributed to the great Ionian awakening around 600
B.C
., and, through slavery, may have been the cause of its decline some two centuries later. There are great ironies here.

Approximate lifetimes of Ionian and other Greek scientists between the seventh century
B.C
. and the fifth century. The decline of Greek science is indicated by the relatively few individuals shown after the first century
B.C.

Similar trends are apparent throughout the world. The high point in indigenous Chinese astronomy occurred around 1280, with the work of Kuo Shou-ching, who used an observational baseline of 1,500 years and improved both astronomical instruments and mathematical techniques for computation. It is generally thought that Chinese astronomy thereafter underwent a steep decline. Nathan Sivin believes that the reason lies at least partly “in increasing rigidity of elite attitudes, so that the educated were less inclined to be curious about techniques and less willing to value science as an appropriate pursuit for a gentleman.” The occupation of astronomer became a hereditary office, a practice inconsistent with the advance of the subject. Additionally, “the responsibility for the evolution of astronomy remained centered in the Imperial Court and was largely abandoned to foreign technicians,” chiefly the Jesuits, who had introduced Euclid and Copernicus to the astonished Chinese, but who, after the censorship of the latter’s book, had a vested interest in disguising and suppressing heliocentric cosmology. Perhaps science was stillborn in Indian, Mayan and Aztec civilizations for the same reason it declined in Ionia, the pervasiveness of the slave economy. A major problem in the contemporary (political) Third World is that the educated classes tend to be the children of the wealthy, with a vested interest in the status quo, and are unaccustomed either to working with their hands or to challenging conventional wisdom. Science has been very slow to take root.

Plato and Aristotle were comfortable in a slave society. They offered justifications for oppression. They served tyrants. They taught the alienation of the body from the mind (a natural enough ideal in a slave society); they separated matter from thought; they divorced the Earth from the heavens—divisions that were to dominate Western thinking for more than twenty centuries. Plato, who believed that “all things are full of gods,” actually used the metaphor of slavery to connect his politics with his cosmology. He is said to have urged the burning of all the books of Democritus (he had a similar recommendation for the books of Homer), perhaps because Democritus did not acknowledge immortal souls or immortal
gods or Pythagorean mysticism, or because he believed in an infinite number of worlds. Of the seventy-three books Democritus is said to have written, covering all of human knowledge, not a single work survives. All we know is from fragments, chiefly on ethics, and secondhand accounts. The same is true of almost all the other ancient Ionian scientists.

In the recognition by Pythagoras and Plato that the Cosmos is knowable, that there is a mathematical underpinning to nature, they greatly advanced the cause of science. But in the suppression of disquieting facts, the sense that science should be kept for a small elite, the distaste for experiment, the embrace of mysticism and the easy acceptance of slave societies, they set back the human enterprise. After a long mystical sleep in which the tools of scientific inquiry lay moldering, the Ionian approach, in some cases transmitted through scholars at the Alexandrian Library, was finally rediscovered. The Western world reawakened. Experiment and open inquiry became once more respectable. Forgotten books and fragments were again read. Leonardo and Columbus and Copernicus were inspired by or independently retraced parts of this ancient Greek tradition. There is in our time much Ionian science, although not in politics and religion, and a fair amount of courageous free inquiry. But there are also appalling superstitions and deadly ethical ambiguities. We are flawed by ancient contradictions.

The Platonists and their Christian successors held the peculiar notion that the Earth was tainted and somehow nasty, while the heavens were perfect and divine. The fundamental idea that the Earth is a planet, that we are citizens of the Universe, was rejected and forgotten. This idea was first argued by Aristarchus, born on Samos three centuries after Pythagoras. Aristarchus was one of the last of the Ionian scientists. By this time, the center of intellectual enlightenment had moved to the great Library of Alexandria. Aristarchus was the first person to hold that the Sun rather than the Earth is at the center of the planetary system, that all the planets go around the Sun rather than the Earth. Typically, his writings on this matter are lost. From the size of the Earth’s shadow on the Moon during a lunar eclipse, he deduced that the Sun had to be much larger than the Earth, as well as very far away. He may then have reasoned that it is absurd for so large a body as the Sun to revolve around so small a body as the Earth. He put the Sun at the center, made the Earth rotate on its axis once a day and orbit the Sun once a year.

It is the same idea we associate with the name of Copernicus,
whom Galileo described as the “restorer and confirmer,” not the inventor, of the heliocentric hypothesis.
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For most of the 1,800 years between Aristarchus and Copernicus nobody knew the correct disposition of the planets, even though it had been laid out perfectly clearly around 280
B.C
. The idea outraged some of Aristarchus’ contemporaries. There were cries, like those voiced about Anaxagoras and Bruno and Galileo, that he be condemned for impiety. The resistance to Aristarchus and Copernicus, a kind of geocentrism in everyday life, remains with us: we still talk about the Sun “rising” and the Sun “setting.” It is 2,200 years since Aristarchus, and our language still pretends that the Earth does not turn.