though they must have seemed a curse, were in the long run a blessing to the development of cosmology, the study of the universe at large. Had the celestial motions been simple, it might have been possible to explain them solely in terms of the simple, poetic tales that characterized the early cosmologies. Instead, they proved to be so intricate and subtle that they could not be predicted accurately without eventually coming to terms with the physical reality of how and where the sun, moon, and planets actually move, in real, three-dimensional space. The truth is beautiful, but the beautiful is not necessarily true: However aesthetically pleasing it may have been for the Sumerians to imagine that the stars and planets swim back from west to east each dayvia a subterranean river beneath a flat earth, such a conception was quite useless when it came to determining when Mars would go into retrograde or the moon occult Jupiter.
Retrograde motion of Mars occurs when Earth overtakes the more slowly moving outer planet, making Mars appear to move backward in the sky.
Consequently the idea slowly took hold that an adequate model of the universe not only should be internally consistent, like a song or a poem, but should also make accurate predictions that could be tested against the data of observation. The ascendency of this thesis marked the beginning of the end of our cosmological childhood. Like other rites of passage into adulthood, however, the effort to construct an accurate model of the universe was a bittersweet endeavor that called for hard work and uncertainty and deferred gratification, and its devotees initially were few.
One was Eudoxus. He enters the pages of history on a summer day in about 385 B.C ., when he got off the boat from his home town of Cnidus in Asia Minor, left his meager baggage in cheap lodgings near the docks, and walked five miles down the dusty road to Plato’s Academy in the northwestern suburbs of Athens. The Academy was a beautiful spot, set in a sacred stand of olive trees, the original “groves of academe,” near Colonus, blind Oedipus’ sanctuary, where the leaves of the white poplars turned shimmering silver in the wind and the nightingales sang day and night. Plato’s mentor Socrates had favored the groves of academe, which even Aristophanes the slanderer of Socrates described lovingly as “all fragrant with woodbine and peaceful content.” 6
Beauty itself was the principal subject of study at the Academy, albeit beauty of a more abstract sort, LET NONE BUT GEOMETERS ENTER HERE , read the motto inscribed above the door, and great was the general enchantment with the elegance of geometrical forms. Geometry (
geo-metry
, “earth-measurement”) had begun as a practical affair, the method employed by the Egyptian rope-stretchers in the annual surveys by which they reestablished the boundaries of farmlands flooded by the Nile. But in the hands of Plato and his pupils, geometry had been elevated to the status approaching that of a theology. For Plato, abstract geometrical forms
were
the universe, and physical objects but their imperfect shadows. As he was more interested in perfection than imperfection, Plato wrote encomiums to the stars but seldom went out at night to study them.
He backed this view with an imposing personal authority. Plato was not only smart, but rich—an aristocrat, one of the “guardians”of Greek society, descended on his mother’s side from Solon the lawmaker and on his father’s from the first kings of Athens—and physically impressive;
Plato
, meaning “broad-shouldered,” was a nickname bestowed upon him by his gymnastics coach when as a youth he wrestled in the Isthmian Games. Eudoxus, we may assume, was suitably impressed. He was, however, a geometer in his own right—he was to help lay the foundations of Euclidean geometry and to define the “golden rectangle,” an elegant proportion that turns up everywhere from the Parthenon to the