The Science of Plato: Astronomy

WHY SNAKES HAVE NO FEET

Sources

Planes. The Timaeus is not limited to mathematical cosmology. It also covers issues of astronomy, biology, and human physiology. In Plato’s astronomical scheme, for instance, a spherical earth lies at the center of a greater sphere of the heavens, on whose inner surface the stars are embedded like bright nails. As the outer sphere turns, the stars are carried around the earth in a daily rotation. The sun, moon, and the other planets revolve at different speeds around what is known as the ecliptic. If the earth’s equator is extended outward to the sphere of the fixed stars, it forms a plane called the celestial equator. The ecliptic is an imaginary circular plane tilted about twenty-three degrees to the celestial equator. The path of the sun along the ecliptic intersects the celestial equator at the fall and spring equinoxes, the two days each year when day and night have equal lengths.

Planetary Motion. It was well known in the ancient world that the planets sometimes move erratically. At times they seem to change speed—to speed up or slow down—in their revolution “around the earth,” and sometimes they even appear to move backward. One of Plato’s most significant contributions to astronomy was his claim that these apparently irrational movements could be explained by supposing that each planet moved on not one but several circular tracks. He proposed that planetary motion should be thought of as a combination of orbits within orbits, in which the clockwise turns of one track, for instance, would cause the adjacent track to move counterclockwise, and so on. This view, he felt, might result in the creation of a regular, geometrical model of what looked like highly irregular behavior. If successful, what better example could there be of discovering order behind disorder, and so of “saving the phenomena”? The impact of this notion on Greek and much of later western astronomy was to be profound.

Astronomy. It is indeed in the science of astronomy that the ancient Greeks made their greatest and most influential advances. Here more than in any other field of research, mathematical and mechanical models were constructed, applied, analyzed, challenged, then further refined and applied again in an effort to “save the phenomena.”

Turning Point. The fourth century b.c.e. marks a turning point in early astronomical work. Prior to this period, there was Anaximander’s sixth-century model. He had proposed a system in which sun, moon, and stars orbit a cylindrical earth on tracks whose diameters are respectively twenty-seven, eighteen, and nine times earth’s diameter. His theory clearly owes more to love of symmetry than any empirical observation Anaximander ever could have made.

Philolaos. The Pythagoreans, too, had speculated about the nature and shape of the heavens. Philolaos, a member of the group who lived in the last half of the fifth century, surprisingly theorized that the earth is not located at the center of the universe, but instead orbits around a “central fire.” He further theorized that another or “counter-earth” orbited the fire at a point always precisely opposite the position of the earth and was therefore never actually visible to us. He is said to have used its existence to explain why lunar eclipses happen more often than eclipses of the sun.

Practical Applications. The observation of the heavens also had practical value in the ancient world. To begin with, it was regularly carried out as part of such nontheoretical business as farming and navigation. For Greeks no less than for the BabyIonians long before them, constellations marked off cardinal points, provided means of keeping time, and also predicted seasonal change. A considerable body of oral, anonymous lore had developed on this basis and was used both for reckoning at sea and also to determine cycles of planting and harvest.

Calendars. The need for accurate civic and religious calendars likewise encouraged astronomical observation, since here precise counting was required to measure the terms of public offices and to establish the all-important dates of festivals in honor of the gods. This need was especially great given the fact that the ancient Greek world traditionally measured time on the basis of the phases of the moon. Such lunar calendars had months of roughly twenty-nine or thirty days, resulting in a twelve-month year about 348 days long. This lunar year had to be reconciled somehow with the somewhat greater number of days (365) that resulted when a year was measured by the course of the sun.

Intercalation. Around 432 b.c.e. Meton of Athens accurately calculated how many additional or intercalary days should be added to the lunar calendar over the course of a nineteen-year cycle in order to bring it into alignment with the solar calendar. One of his contemporaries, Euctemon, also measured the exact lengths of each of the four seasons, based on careful observations of the equinoxes and solstices. (The solstices, in June and December, are the two days on which the sun reaches its farthest northern and southern positions along the ecliptic.)

Irregularities. The primary aim of fourth-century Greek astronomy was the task set for it by Plato. In the Timaeus he had proposed that it should be possible to construct a rational, geometric account of the motion of the stars, sun, moon, and the five known planets (Mercury, Venus, Mars, Jupiter, and Saturn). From the viewpoint of an observer on earth, their movements exhibit both orderliness and also strange, puzzling irregularities. Plato’s challenge was to design a model that would save those irregularities by making them regular and rational.

Celestial Movement. In order to construct a geometric model that would precisely reproduce these movements, several different motions had to be taken into consideration:

(1) On the one hand, there is the steady, daily revolution of all the celestial bodies around the earth from east to west—or so it seemed, assuming a geocentric universe, namely one in which the earth rests unmoving at the center while all the other heavenly bodies turn around it;

(2) Over the course of many weeks and months of nights, the constellations also seem to follow a longer, slower orbital path from east to west. Some disappear from view at certain seasons, but then always reappear in roughly the same place in the sky at roughly the same time each year. Their imaginary track through the heavens forms the circle or belt called the zodiac;

(3) Further, the sun, moon, and planets themselves move in the opposite direction, from west to east, against the background of constellations. They all follow the same path—the tilted orbit known as the ecliptic—but they do so at varying speeds, ranging from a single month for the moon to nearly thirty years for the planet Saturn to make one zodiacal orbit;

(4) Most problematic of all were the “stations” and “retrograde” movements of the planets. The name planet in fact derives from the Greek verb planasthai, which means “to wander.” Unlike the sun, moon, and “fixed” stars, the planets moved irregularly and therefore required a special explanation. When observed over the length of a year, planets such as Mars seem to stop in the course of their normal, easterly movement through the zodiac and to hold still for several nights. They then appear to move backward (retrograde), east to west, sometimes for as long as a month, before continuing on an easterly course again.

Apparent Anomalies. Plato’s challenge to the students in his Academy, to the astronomers of his own and later generations, was to produce a systematic account of this peculiar and seemingly unsystematic motion. Here it is important to note Plato’s underlying assumption—characteristically Greek, and at the same time also characteristically scientific—that these anomalies are not real but instead only apparent. Behind those visible oddities, Plato believed, are movements that are actually uniform, orderly, and mathematically expressible. This assumption still motivates modern astronomy, along with all the other sciences of the West. The actual search for a solution to the problem of planetary motion as Plato had posed it in fact occupied Western astronomers for the next two thousand years.

Eudoxus of Cnidus. The challenge was taken up first by Plato’s own associate, the astronomer Eudoxus of Cnidus (circa 408-355 b.c.e.). He was indeed a gifted polymath with a rather broad range of interests. The tradition credits him with research on mathematics, geography, medicine, and music along with astronomy. Precious little of his work survives, however, and his writings are on the whole patched together from quotations found in the works of Aristotle and Simplicius, a scholar of the sixth century C.E.

Eudoxan Model. Eudoxus’s solution to the problem of how celestial bodies move was to propose not one but a whole series of four simple, circular movements for each of the planets, and three each for the sun and moon. The result is a highly ingenious geometrical model. Spheres within spheres within spheres move in complex, contrary rotations, like cogs in a machine, all perfectly regular and orderly. The combined movements all together produce the illusion of irregular, wandering planets.

WHY SNAKES HAVE NO FEET

In the following passage from his work Parts of Animals (circa 335 b.c.e.), Aristotle applies his classification of animals into blooded and bloodless, along with his notion of immanent teleology —the fact that every single thing in nature has an innate purpose—to explain why snakes have no feet:

The reason for the footlessness of snakes is that nature does nothing in vain but in every case looks out for the best possible arrangement for each thing, saving its special entity and essence. Besides, as we have said before, no blooded animal can move at more than four points [that is, they can have no more than four feet]. Clearly, those blooded animals that are disproportionately long in relation to the rest of their body, as are snakes, cannot have feet. For they are not the sort to have more than four—then they would be bloodless [such as insects, for instance]—but with two or four feet they would be practically immobile, so slow and useless the movement would have to be.

Source: Anthony Preus, Science and Philosophy in Aristotle’s Biological Works (HiicJesheim, Germany & New York: G. Olms, 1975).

Rotating Spheres. In his solution, each of the four spheres assigned to a planet produces one element of its total movement. To understand how it works, imagine the earth surrounded by four concentric, turning spheres; these constitute the system of a single planet—Mars, for instance. The planet itself rides along the equator of the smallest or innermost sphere (D), but its overall movement is also a result of the motions of each of the three increasingly larger ones (C, B, and A). Their motions are as follows: the largest and outermost sphere (A) turns from east to west once every twenty-four hours on an axis that runs north to south. This motion accounts for how, to a terrestrial observer, Mars seems to orbit the earth at just that speed. Modern astronomy, of course, now correctly attributes this to Earth’s own rotation. The next sphere (B) rotates far more slowly and in the opposite direction, west to east, against the backdrop of the constellations. It turns once every twenty-two months, since this period is the actual time it takes Mars to complete one circuit through the zodiac. Rather than being perfectly north-south, the axis of this second sphere is tilted a little, at right angles to the ecliptic. This detail helps account for apparent changes in the speed and position of Mars at various times over the course of two years. As for the motions of the two innermost spheres (C and D), these are the most important. Eudoxus designed them to account for the bizarre stations and retrograde movements that drew so much scientific attention to the planets in the ancient world. After all, this is what had motivated Plato’s demand for a rational solution in the first place. By tilting the axes of these two spheres at certain specific angles to each other, and by making them rotate in opposite directions at equal speeds, Eudoxus produced the appearance of a curving movement called a hippopede, or “horse-fetter.”

Planetary Paths. The hippopede is a path shaped like a figure eight. As Mars moves back and forth along it, the planet makes a looping motion. This configuration combines with its slow, easterly movement along the zodiacal track and the fast east-west spin of its daily rotation to create the illusion of a planet that periodically stops, stands still, goes back, and then moves again. From the fixed point of an astronomer on earth, the model Eudoxus proposed seemed to answer Plato’s challenge successfully.

Mathematical Theory. The Eudoxan solution is a remarkably imaginative leap. It moves from erratic, irregular sensory data to a vision of the uniform and orderly events that can explain them. Moreover, it is a leap of the mind more than the eye, an astonishing stretch of the imagination, guided by rules of geometry. It is a feat of sheer mathematical theorizing, for in the absence of telescopes and other tools for measurement it completely lacked empirical support.

Revisions. The model has many weaknesses. In particular, it could not account for changes in planetary brightness. From observation, any given planet regularly gets dimmer at certain times of year, then brighter again—a fact which modern astronomy explains in terms of its varying distance from earth. Nonetheless, the model designed by Eudoxus established the standard pattern for addressing the question of how planets move. Later astronomers tinkered with his geometry, adding or subtracting orbital paths in ever more ingenious and intricate combinations to produce the observed effect. Eudoxus had proposed a total of twenty-seven spheres as the minimum number necessary to replicate the apparent movements of the planets. They were increased to thirty-four by Callippus of Cyzicus, an astronomer who lived around 330 b.c.e. Aristotle added an additional twenty-two spheres, to bring the total number up to fifty-six. Heraclides of Pontus (fl. 350 b.c.e.) complicated the model even further by proposing a theory of “epicycles.” According to this approach, the planets Venus and Mercury actually orbit the sun while the sun itself orbits the earth. He is also credited with the striking minority view that the earth itself rotates on an axis while the surrounding heavens stay at rest!

Elliptical Model. The strange movements of the planets remained a central problem for astronomy for nearly two millennia after Plato had first made it a scientific challenge. In fact, not until the seventeenth century were models in which the planets move around inside perfectly circular spheres finally abandoned. They were then replaced by a model in which their orbits are instead elliptical. The one who proposed this new shape was none other than the great German scientist Johannes Kepler (1571-1630), one of the founders of modern astronomy. The various solutions to Plato’s problem indeed changed over time, and new tools—such as the telescope, first used after 1609—brought the heavens ever closer to the eye. What never changed, however, was the demand that had first been expressed by the ancient Greeks. The observable phenomena far in the sky, above and around the earth, had to be “saved” by constructing models of the universe that conformed to laws of geometry. The orderliness of those far distant worlds was first dreamed of in the mathematical imagination of ancient Greeks.

Sources

D. R. Dicks, Early Greek Astronomy to Aristotle (Ithaca, N.Y.: Cornell University Press, 1970).

David C. Lindberg, The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600 b.c.e. to c.e. 1450 (Chicago: University of Chicago Press, 1992).

Samuel Sambursky, The Physical World of the Greeks (New York: Macmillan, 1956).