Coming of Age in the Milky Way (13 page)
Read Coming of Age in the Milky Way Online
Authors: Timothy Ferris
Tags: #Science, #Philosophy, #Space and time, #Cosmology, #Science - History, #Astronomy, #Metaphysics, #History
But these experiments, which form the basis for the myth of the Leaning Tower, served to verify rather than to instigate Galileo’s thesis. More important were his “thought experiments,” the careful thinking through of procedures that he could not actually carry out. To be sure, Galileo recognized, as he put it, that “reason must step in” only “where the senses fail us.” But since he lived in
a time when the senses were aided by none but the most rudimentary experimental apparatus—he had, for instance, no timepiece more accurate than his pulse—Galileo found that reason had to step in rather often. In the words of Albert Einstein, the greatest all-time master of the thought experiment, “The experimental methods of Galileo’s disposal were so imperfect that only the boldest speculation could possibly bridge the gaps between empirical data.”
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Consequently it was more by thinking than by experimentation that Galileo arrived at new insights into the law of falling bodies.
His reasoning went something like this: Suppose that a cannonball takes a given time—say, two pulse beats—to fall from the top of a tower to the ground. Now saw the cannonball in half, and let the two resulting demiballs fall. If Aristotle is right, each demiball, since it weighs only half as much as the full cannonball, should fall more slowly than did the original, full-size cannonball. If, therefore, we drop the two demiballs side by side, they should descend at an identical, relatively slow velocity. Now tie the demiballs together, with a bit of string or a strand of hair. Will this object, or “system,” in Galileo’s words, fall fast, as if it knew it were a reconstituted cannonball, or slowly, as if it still thought of itself as consisting of two half cannonballs?
Galileo phrased his
reductio ad absurdum
this way, in his
Dialogues Concerning Two New Sciences
:
[Were Aristotle right that] a large stone moves with a speed of, say, eight while a smaller moves with a speed of four, then when they are united, the system will move with a speed of less than eight; but the two stones when tied together make a stone larger than that which before moved with a speed of eight. Hence the heavier body moves with less speed than the lighter; an effect which is contrary to [Aristotle’s] supposition. Thus you see how, from your assumption that the heavier body moves more rapidly than the lighter one, I infer that the heavier body moves more slowly.
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This line of reasoning pointed directly to the second major question facing post-Copernican physics, that of inertia. If a cannonball and a feather fall at the same rate in a vacuum, then what is the difference between them? There must be
some
difference: The cannonball, after all, weighs more than the feather, will make more of an impression if dropped on one’s head from atop the Leaning
Tower, and is harder to kick along the ground. We would say today that the feather and the cannonball have differing
mass
, and that the amount of their mass determines their
inertia
—their tendency to resist changes in their state of motion. It is precisely because the heavier object possesses greater inertia that it takes longer for gravity to get it going, which is why it falls no faster than the lighter object. But these are Newtonian conceptions, unknown to Galileo, who had to make his way on his own.
Galileo’s thought experiment: According to Aristotle, if a one-pound cannonball falls a given distance in a given time (1), then if the ball is cut in half, each half-pound ball should fall less far in the same interval (2). But, reasoned Galileo, what happens if the two half-balls are attached, by a thread or a stick (3)? Thus was Aristotle’s physics of falling bodies reduced to absurdity.
Aristotle had defined half of the concept of inertia, that bodies at rest tend to remain at rest. This was sufficient for dealing with an immobile Earth, but was of no use in explicating the physics of
an earth in motion in a Copernican universe. Galileo groped his way toward the other half of the concept—that bodies in motion tend to remain in motion, i.e., that the cannonball’s inertial mass makes it just as difficult to stop as to start. Sometimes he came close, as in his charming comparison of the residents of planet Earth with voyagers aboard a ship:
Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully … have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.
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But here Galileo bogged down. He was still a captive of Aristotle’s erroneous supposition that the behavior of objects results from an internal tendency, or “desire,” rather than simply from their inertial mass and the application of force:
I seem to have observed that physical bodies have physical inclination to some motion (as heavy bodies downward), which motion is exercised by them through an intrinsic property and without need of a particular external mover, whenever they are not impeded by some obstacle. And to some other motion they have a repugnance (as the same heavy bodies to motion upward), and therefore they never move in that manner unless thrown violently by an external mover. Finally, to some movements they are indifferent, as are these same heavy bodies to horizontal motion, to which they have neither inclination … or repugnance…. And therefore, all external impediments removed, a heavy body on a spherical surface concentric with
the earth will be indifferent to rest and to movements toward any part of the horizon. And it will maintain itself in that state in which it has once been placed; that is, if placed in a state of rest, it will conserve that; and if placed in movement toward the west (for example) it will maintain itself in that movement.
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Some of these words anticipate Newton’s explanation of inertia; bodies “placed in movement” tend to remain in motion, those “at rest” to remain at rest. Others remain ensnared in Aristotle’s dusty web, as when Galileo asserts that objects have an inherent “inclination” or “repugnance” for certain sorts of motion. Galileo never really freed himself of confusion on this point, and his “law” of falling bodies, stated in 1604 and often called the first law of classical physics, was fraught with error.
Galileo might have made more progress in understanding inertia and gravitation had he collaborated with Kepler. Kepler, too, had only part of the answer; he, like Galileo, thought of inertia chiefly as a tendency of objects to remain at rest, and, consequently, he conceived of gravity as having not only to hold planets in thrall to the sun but also to tug them along in their orbits. But he was ahead of Galileo in some ways, as when he proposed that the gravitational attraction of the moon is responsible for the tides. Galileo dismissed Kepler’s theories of gravity as mere mysticism. “I am … astonished at Kepler,” he wrote. “… Despite his open and acute mind, and though he has at his fingertips the motions attributed to the earth, he has nevertheless lent his ear and his assent to the moon’s dominion over the waters, to occult properties, and to such puerilities.”
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The differences between the two men were pronounced. Galileo was an urbane gentleman who loved wine (which he described as “light held together by moisture”), women (he had three children by his mistress, Marina Gamba), and song (he was an accomplished musician). Kepler sneezed when he drank wine, had little luck with women, and heard his music in the stars. The deep organ-tones of religiosity and mysticism that resounded through Kepler’s works struck Galileo as anachronistic and more than a bit embarrassing. Kepler suspected as much, and pled with Galileo to please “not hold against me my rambling and my free way of speaking about nature.” Galileo never answered his letter. Einstein remarked near the end of his life that “it has always hurt me to
think that Galilei did not acknowledge the work of Kepler…. That, alas, is vanity,” Einstein added. “You find it in so many scientists.”
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Nowhere is Galileo’s disdain for Kepler more painful to recount than in the matter of the telescope. Kepler was by this time recognized as the most accomplished astronomer in the world, and his enthusiastic endorsement of Galileo’s
Starry Messenger
had helped stave off criticism by those who dismissed the telescope as a kalei-doscopelike toy that produced not magnification but illusion. (This was not an entirely unreasonable suspicion; Galileo’s early telescopes produced spurious colors, and they presented such a dim image, in so narrow a field of view, that it was not immediately obvious that they magnified at all.) But astronomy hereafter would require telescopes, and Kepler, though he understood the optical principles involved much better than Galileo did, could not obtain lenses of quality in Prague. With his customary earnestness and lack of restraint, Kepler wrote to Galileo in 1610, asking him for a telescope or at least a decent lens, “so that at last I too can enjoy, like yourself, the spectacle of the skies.”
O telescope, instrument of much knowledge, more precious than any scepter! … How the subtle mind of Galileo, in my opinion the first philosopher of the day, uses this telescope of ours like a sort of ladder, scales the furthest and loftiest walls of the visible world, surveys all things with his own eyes, and, from the position he has gained, darts the glances of his most acute intellect upon these petty abodes of ours—the planetary spheres I mean—and compares with keenest reasoning the distant with the near, the lofty with the deep.
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Galileo ignored Kepler’s entreaties. Possibly he feared that his observations might be eclipsed by what an astronomer of Kepler’s abilities could accomplish if he, too, had a telescope at hand. In any event, he had other fish to fry. He was busy parlaying his rapidly growing celebrity into a position at Cosimo de’ Medici’s court in Tuscany. He passed the request along to Cosimo’s ambassador, who advised him to, by all means, send the estimable Kepler a spyglass. Galileo instead told Kepler that he had no telescopes to spare, and that to make a new one would require too much time. Meanwhile, he was making presents of telescopes to
royal patrons whose favor might advance his career. One of the beneficiaries of Galileo’s gifts, the elector of Cologne, summered in Prague that year and loaned Kepler his telescope. For one month, Kepler could gaze with delight at the craters of the moon and the stars of the Milky Way. Then the elector left town, taking the telescope with him.
Just when Galileo might have done the most to help bring physics to a Copernican maturity, he instead diverted his efforts to a quixotic campaign aimed at converting the Roman Catholic Church to the Copernican cosmology. Politics did not suit him, and soon he was demanding, like any blustering campaigner, that Copernicanism be accepted for little better reason than that he said it was correct. The old anti-Aristotelian was asking to be regarded as the new Aristotle, urging that it was now acceptable to ignore the planets in favor of the decree of a book, so long as the book was his own.
His situation grew more precarious when he abandoned the Venetian Republic for the glittering court at Tuscany, where he was named chief mathematician and philosopher to the grand duke. His friend Giovanni Sagredo warned him that he was making a mistake. “Who knows what the infinite and incomprehensible events of the world may cause if aided by the impostures of evil and envious men,” he wrote Galileo in a letter from the Levant, where he was serving as the Venetian consul. “… I am very much worried by your being in a place where the authority of the friends of the Jesuits counts heavily.”
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But Galileo could resist neither the glory nor the wealth of the Medician court, nor the prospect of being relieved of his teaching duties at Padua: “I deem it my greatest glory to be able to teach princes,” he wrote. “I prefer not to teach others.”
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The initial reaction against Galileo’s campaign came less from priests than from pedants. The reactionaries whom the world remembers for their obstinate refusal to look through his telescope —“pigeons” and “blockheads” as Galileo called them—were not clerics but professors, and they were worried less about impiety than about threats to their academic authority. The Church, initially, was more tolerant. The Vatican praised Galileo’s research with the telescope and honored him with a day of ceremonies at the Jesuit Roman College, and when a Dominican monk named Thommaso Caccini preached a sermon against Galileo in Florence,
he was promptly rebuked by the preacher general of the Dominican Order, Father Luigi Maraffi, who apologized to Galileo for the fact that he was sometimes obliged “to answer for all the idiocies that thirty or forty thousand brothers may or do actually commit.”
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