Read Coming of Age in the Milky Way Online
Authors: Timothy Ferris
Tags: #Science, #Philosophy, #Space and time, #Cosmology, #Science - History, #Astronomy, #Metaphysics, #History
Coming of Age in the Milky Way (4 page)
The phrase to “save the appearances” is Plato’s, and its ascension via the Ptolemaic universe marked a victory for Platonic idealism and a defeat for empirical induction. Plato shared with his teacher Socrates a deep skepticism about the ability of the human mind to comprehend nature by studying objects and events. As Socrates told his friend Phaedrus while they strolled along the Ilissus, “I can’t as yet ‘know myself,’ as the inscription at Delphi enjoins, and so long as that ignorance remains it seems to me ridiculous to inquire into extraneous matters.”
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Among these “extraneous matters” was the question of the structure of the universe.
Aristotle loved Plato, who seems not entirely to have returned his devotion; their differences went beyond philosophy, and sounded to the depths of style. Plato dressed plainly, while Aristotle wore tailored robes and gold rings and expensive haircuts. Aristotle cherished books; Plato was wary of men who were too bookish.
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With a touch of irony that has survived the centuries, Plato called Aristotle “the brain.”
Aristotle, for all his empirical leanings, never lost his attachment to the beauty of Plato’s immortal geometrical forms. His universe of lucid spheres was a kind of heaven on earth, where his spirit and Plato’s might live together in peace. Neither science nor philosophy has yet succeeded where Aristotle failed. Consequently his ghost and Plato’s continue to contend, on the pages of the philosophical and scientific journals and in a thousand laboratories and schoolrooms. When philosophers of science today wrestle with
such questions as whether subatomic particles behave deterministically, or whether ten-dimensional spacetime represents the genuine architecture of the early universe or is instead but an interpretive device, they are in a sense still trying to make peace between old broadshoulders and his bright brash student, “the brain.”
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This phenomenon, called the precession of the equinoxes, was known to the ancient Greeks and may have been discovered even earlier. Georgio de Santillana, in his book
Hamlet’s Mill
, identifies it with the ancient myth of Amlodhi (later Hamlet), the owner of a giant salt grinder that sank to the bottom of the sea while being transported by ship. The mill has ground on ever since, creating a whirlpool that slowly twists the heavens. Whether or not it describes precession, the myth of Hamlet’s mill certainly endures; I first heard it at the age of nine, in a rural schoolyard in Florida, from a little girl who was explaining why the ocean is salty.
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By Eudoxus’ day, all educated Greeks accepted that the earth was spherical, on the strength of such evidence as the shape of the shadow it casts on the moon during lunar eclipses.
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In Plato’s
Phaedrus
, Socrates recounts an old story of how the legendary King Thamus of Egypt had declined the god Theuth’s offer to teach his subjects how to write. “What you have discovered is a recipe not for memory, but for reminder,” says King Thamus. “And it is no true wisdom that you offer your disciples, but only its semblance, for by telling them of many things without teaching them you will make them seem to know much, while for the most part they know nothing, and as men filled, not with wisdom, but with the conceit of wisdom, they will be a burden to their fellows.” This remains one of the most prophetic denunciations of the perils of literacy ever enunciated—although, of course, it is thanks to the written word that we know of it.
R
AISING
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AND
L
OWERING
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R
OOF
Aristarchus of Samos supposed that the heavens remained immobile and that the earth moved through an oblique circle, at the same time turning about its own axis.
—Plutarch
Now see that mind that searched and made
All Nature’s hidden secrets clear
Lie prostrate prisoner of night.—Boethius
T
he earth-centered universes of Eudoxus, Aristotle, Callippus, and Ptolemy were small by today’s standards. Ptolemy’s appears to have been the most generous. Certainly he thought it grand, and he liked to remark, with an astronomer’s fondness for wielding big numbers, that in his universe the earth was but “a point” relative to the heavens. And, indeed, it was enormous by the standards of a day when celestial objects were assumed to be small and to lie close at hand; Heraclitus and Lucretius thought the sun was about the size of a shield, and Anaxagoras the atomist
was banished for impiety when he suggested that the sun might be larger than the Peloponnesus. Nevertheless, the Ptolemaic universe is estimated to have measured only some fifty million miles in radius, meaning that it could easily fit inside what we now know to be the dimensions the earth’s orbit around the sun.
The diminutive scale of these early models of the cosmos resulted from the assumption that the earth sits, immobile, in the center of the universe. If the earth does not move, then the stars do: The starry sphere must rotate on its axis once a day in order to bring the stars trooping overhead on schedule, and the larger the sphere, the faster it must rotate. Were such a cosmos very large, the speed mandated for the celestial sphere would become unreasonably high. The stars of Ptolemy’s universe already were obliged to hustle along at better than ten million miles per hour, and were the celestial sphere imagined to be a hundred times larger it would have to be turning faster than the velocity of light. One did not have to be an Einstein, or even to know the velocity of light, to intuit that
that
was too fast—a point that had begun to worry cosmologists by the sixteenth century. All geocentric, immobile-earth cosmologies tended to inhibit appreciation of the true dimensions of space.
To set the earth in motion would be to expand the universe, a step that seemed both radical and counterintuitive. The earth does not
feel
as if it is spinning, nor does the observational evidence suggest any such thing: Were the earth turning on its axis, Athens and all its citizens would be hurtling eastward at a thousand miles per hour. If so, the Greeks reasoned, gale-force easterlies ought constantly to sweep the world, and broad jumpers in the Olympics would land in the stands well to the west of their jumping-off points. As no such effects are observed, most of the Greeks concluded that the earth does not move.
The problem was that the Greeks had only half the concept of inertia. They understood that objects at rest tend to remain at rest—a context we retain today when we speak of an “inert object” and mean that it is immobile—but they did not realize that objects in motion, including broad jumpers and the earth’s atmosphere, tend to remain in motion. This more complete conception of inertia would not be achieved until the days of Galileo and Newton. (Even with amendments by Einstein and intimations of others by the developing superunified theories, plenty of mystery remains in the
idea of inertia today.) Its absence was a liability for the ancient Greeks, but it was not the same thing as the religious prejudice to which many schoolbooks still ascribe the motives of rational and irrational geocentrists alike.
If one goes further and imagines that the earth not only spins on its axis but orbits the sun, then one’s estimation of the dimensions of the cosmos must be enlarged even more. The reason for this is that if the earth orbits the sun, then it must alternately approach and withdraw from one side of the sphere of stars—just as, say, a child riding a merry-go-round first approaches and then recedes from the gold ring. If the stellar sphere were small, the differing distance would show up as an annual change in the apparent brightness of stars along the zodiac; in summer, for instance, when the earth is on the side of its orbit closer to the star Spica, its proximity would make Spica look brighter than it does in winter, when the earth is on the far side of its orbit. As no such phenomenon is observed, the stars must be
very
far away, if indeed the earth orbits the sun.
The astonishing thing, then, given their limited understanding of physics and astronomy, is not that the Greeks thought of the universe in geocentric terms, but that they did not
all
think of it that way. The great exception was Aristarchus, whose heliocentric cosmology predated that of Copernicus by some seventeen hundred years.
Aristarchus came from Samos, a wooded island near the coast of Asia Minor where Pythagoras, three centuries earlier, had first proclaimed that all is number. A student of Strato of Lampsacus, the head of the Peripatetic school founded by Aristotle, Aristarchus was a skilled geometer who had a taste for the third dimension, and he drew, in his mind’s eye, vast geometrical figures that stretched not only across the sky but out into the depths of space as well. While still a young man he published a book suggesting that the sun was nineteen times the size and distance of the moon; his conclusions were quantitatively erroneous (the sun actually is four hundred times larger and farther away than the moon) but his methods were sound.
It may have been this work that first led Aristarchus to contemplate a sun-centered cosmos: Having concluded that the sun was larger than the earth, he would have found that for a giant sun to orbit a smaller earth was intuitively as absurd as to imagine that
a hammer thrower could swing a hammer a hundred times his own weight. The evolution of Aristarchus’ theory cannot be verified, however, for his book proposing the heliocentric theory has been lost. We know of it from a paper written in about 212 B.C. by Archimedes the geometer.
In a small, heliocentric universe, the earth would be much closer to a summer star like Spica in summer than in winter, making Spica’s brightness vary annually. As there is no observable annual variation in the brightness of such stars, Aristarchus concluded that the stars are extremely distant from the earth.
Archimedes’ paper was titled “The Sand Reckoner,” and its purpose was to demonstrate that a system of mathematical notation he had developed was effective in dealing with large numbers. To make the demonstration vivid, Archimedes wanted to show that he could calculate even such a huge figure as the number of grains of sand it would take to fill the universe. The paper, addressed to
his friend and kinsman King Gelon II of Syracuse, was intended as but a royal entertainment or a piece of popular science writing. What makes it vitally important today is that Archimedes, wanting to make the numbers as large as possible, based his calculations on the dimensions of the most colossal universe he had ever heard of—the universe according to the novel theory of Aristarchus of Samos.
Archimedes, a man of strong opinions, had a distaste for loose talk of “infinity,” and he begins “The Sand Reckoner” by assuring King Gelon that the number of grains of sand on the beaches of the world, though very large, is not infinite, but can, instead, be both estimated and expressed:
I will try to show you, by means of geometrical proofs, which you will be able to follow, that, of the numbers named by me … some exceed not only the number of the mass of sand equal in magnitude to the earth filled up in the way described, but also that of a mass equal in magnitude to the universe.
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Continuing in this vein, Archimedes adds that he will calculate how many grains of sand would be required to fill, not the relatively cramped universe envisioned in the traditional cosmologies, but the much larger universe depicted in the new theory of Aristarchus:
Aristarchus of Samos brought out a book consisting of certain hypotheses, in which it appears, as a consequence of the assumptions made, that the universe is many times greater [in size] than that now so called. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same center as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.
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Here Archimedes has a problem, for Aristarchus is being hyperbolic when he says that the size of the universe is as much larger than the orbit of the sun as is the circumference of a sphere to its center. “It is easy to see,” Archimedes notes, “that this is impossible;
for, since the center of the sphere has no magnitude, we cannot conceive it to bear any ratio whatever to the surface of the sphere.”
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To plug hard numbers into Aristarchus’ model, Archimedes therefore takes Aristarchus to mean that the ratio of the size of the earth to the size of the universe is comparable to that of the orbit of the earth compared to the sphere of stars. Now he can calculate. Incorporating contemporary estimates of astronomical distances, Archimedes derives a distance to the sphere of stars of, in modern terminology, about six trillion miles, or one light-year.
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