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101 [166] GALILEO
GALILEO [166] continually applied. From this it fol lowed, according to some medieval phi losophers, that the heavenly bodies, which were continually moving, had to be pushed along by the eternal labors of angels. A few even used such arguments to deduce the existence of God. On the other hand, some philosophers of the late Middle Ages, such as Buridan [108], held that constant motion required no force after the initial impulse. By that view God in creating the world could have given it a start and then let it run by itself forever after. If a continuous force were applied, said these philoso phers, the resulting motion would be come ever more rapid. Galileo’s experiments decided in favor of this second view and against Aristotle. Not only did the velocity of a falling ball increase steadily with time under the continuous pull of the earth, but the total distance it covered increased as the square of the time. He also showed that a body could move under the influence of two forces at one time. One force, applying an ini tial force horizontally (as the explosion of a gun), could keep a body moving horizontally at a constant velocity. An other force, applied constantly in a verti cal direction, could make the same body drop downward at an accelerated veloc ity. The two motions superimposed would cause the body to follow a para bolic curve. In this way Galileo was able to make a science out of gunnery. This concept of one body influenced by more than one force also explained how it was that everything on the sur face of the earth, including the atmo sphere, birds in flight, and falling stones, could share in the earth’s rotation and yet maintain their superimposed motions. This disposed of one of the most effec tive arguments against the theories of Copernicus [127] and showed that one need not fear that the turning and re volving earth would leave behind those objects not firmly attached to it. (Galileo’s proofs were all reached by the geometric methods of the Greeks. The application of algebra to geometry and the discovery of infinitely more pow erful methods of mathematical analysis than those at Galileo’s disposal had to await Descartes [183] and Newton [231]. Yet Galileo made do with what he had and his discoveries marked the beginning of the science of mechanics and served as the basis a century later for the three laws of motion propounded by Newton.) In his book on mechanics Galileo also dealt with the strength of materials, founding that branch of science as well. He was the first to show that if a struc ture increased in all dimensions equally it would grow weaker—at least he was the first to explain the theoretical basis for this. This is what is now known as the square-cube law. The volume in creases as the cube of linear dimensions but the strength only as the square. For that reason larger animals require pro portionately sturdier supports than small ones. A deer expanded to the size of an elephant and kept in exact proportion would collapse. Its legs would have to be thickened out of proportion for proper support. The success of Galileo and his succes sors, particularly Newton, in accounting for motion by pushes and pulls (“forces”) gave rise to the thought that everything in the universe capable of measurement could be explained on the basis of pushes and pulls no more com plicated in essence than the pushes and pulls of levers and gears within a ma chine. This mechanistic view of the uni verse was to gain favor until a new revo lution in science three centuries after Galileo showed matters to be rather more complicated than the mechanists had assumed. Yet Galileo was reluctant to de nounce Aristotelian physics too publicly. He waited for a safe opportunity to do so and this came with the nova of 1604 (the one usually associated with Kepler [169]). Galileo used the nova to argue against the Aristotelian notion of the im mutability of the heavens and, by impli cation, against the Aristotelian view gen erally.
Galileo’s work made him unpopular at Pisa and he moved to a better position at Padua, in Venetian territory. (Venice was a region of considerable intellectual freedom at that time.) The new position
[166] GALILEO
GALILEO [166] paid three times the salary of the old one —though Galileo lived gaily and gen erously and was always in debt anyway. He was always in trouble, too, for he made himself unpopular with influential people. He had a brilliant and caustic wit and he could not resist using that wit to make jackasses—and therefore bitter enemies—of those who disagreed with him. Even as a college student, he had been nicknamed “the wrangler” because of his argumentativeness and noncon formity. He even refused to wear aca demic robes, though this cost him several fines. Besides he was so brilliant a lec turer that students flocked to hear him, coming in numbers as high as two thou sand, according to a possibly exaggerated report, while his colleagues mumbled away in empty halls, and nothing will in furiate colleagues more than that. In Padua, Galileo was corresponding with Kepler, and in this correspondence he admitted, as early as 1597, that he had come to believe in the theories of Copernicus, though he prudently re frained for a while from saying so pub licly. The execution of Bruno [157] in 1600 must have encouraged Galileo to continue refraining. In 1609, however, he heard that a mag nifying tube, making use of lenses, had been invented in Holland. Before six months had passed, Galileo had devised his own version of the instrument, one that had a magnifying power of thirty- two. He could adjust it in reverse, to serve as a microscope, and he observed insects by this means. However, it was as a telescope that he made best use of it. He turned it on the heavens. Thus began the age of telescopic astronomy. Using his telescope Galileo found that the moon had mountains and the sun had spots, which showed once again that Aristotle was wrong in his thesis that the heavens were perfect and that only on earth was there irregularity and disorder. Tycho Brahe [156] had already done that in his studies on his nova and his comet, and Fabricius [167] had done it in his studies of a variable star, but Galileo’s findings attacked the sun itself. (Other astronomers discovered the sun spots at almost the same time as Galileo —for indeed, very large spots can some times be made out with the naked eyes, when the sun’s brilliance is dimmed at the horizon, or by mist—and there was wrangling over priority, which made Galileo additional enemies. Galileo, how ever, whether he had priority in the dis covery or not, did more than merely see the spots. He used them to show that the sun rotated about its axis in twenty-seven days, by following individual spots around the sun. He even determined the orientation of the sun’s axis in that fash ion. (Nor did Galileo get off scot-free. His studies of the sun damaged his eyes, which had already suffered from infec tions in his youth, and in old age he went blind.) The stars, even the bright ones, re mained mere dots of light in the tele scope, while the planets showed as little globes. Galileo deduced from this that the stars must be much farther away than the planets and that the universe might be indefinitely large. Galileo also found that there were many stars in existence that could be seen by telescope but not by naked eye. The Milky Way itself owed its luminos ity to the fact that it was composed of myriads of such stars. More dramatically, he found that Ju piter was attended by four subsidiary bodies, visible only by telescope, that circled it regularly. Within a few weeks of observation he was able to work out the periods of each. Kepler gave these latter bodies the name of satellites and they are still known as the Galilean sat ellites. They are known singly by the mythological names of Io, Europa, Gan ymede, and Callisto. Jupiter with its sat ellites was a model of a Copemican sys tem—small bodies circling a large one. It was definite proof that not all astro nomical bodies circled the earth. Galileo observed that Venus showed phases entirely like those of the moon, from full to crescent, which it must do if the Copemican theory was correct. Ac cording to the Ptolemaic theory Venus would have to be a perpetual crescent. The discovery of the phases of Venus definitely demonstrated, by the way, the fact that planets shine by reflected sun
[166] GALILEO
GALILEO [166] light. Galileo discovered that the night side (that is, the dark portion) of the moon when the moon was less than full had a dim glow, which he explained as caused by light shining upon it from the earth (earthshine). It had been seen be fore but had been explained otherwise. Poseidonius [52] thought it was sunlight shining through a partly transparent moon. Reinhold [143] thought the moon’s surface was phosphorescent. Earthshine showed that earth, like the planets, gleamed in the sun, and re moved one more point of difference be tween the earth and the heavenly bodies. All these telescopic discoveries meant the final establishment of Copernicanism more than half a century after Coper nicus had published his book. Galileo announced his discoveries in special numbers of a periodical he called Sidereus Nuncius (“Starry Messenger”) and these aroused both great enthusiasm and profound anger. Aged Venetian aris tocrats clambered to the top of a tower in order to look through one of his tele scopes and see ships, otherwise invisible, far out at sea. He was the best lensmaker in Europe at the time and built a num ber of telescopes. He sent them all over Europe (one reaching Kepler) so that others might confirm his findings. Both Venice and Florence offered him lucra tive positions. To the annoyance of the Venetians, Galileo chose to travel to his beloved Florence. Galileo visited Rome in 1611, where he was greeted with honor and delight, though not everyone was happy. The thought of imperfect heavens, of invisi ble objects shining there, and, worst of all, of the Copemican system enthroned and the earth demoted from its position as center of the universe was most un settling. Galileo also rather unwisely ven tured to write a book giving his views on the Bible and generally discussing theo logical subjects to the offense of theolo gians. Galileo’s conservative opponents persuaded Pope Pius V to declare Coper nicanism a heresy, and Galileo was forced into silence in 1616. Intrigue continued. Now Galileo’s friends, now his enemies seemed to have gained predominance. In 1632 Galileo was somehow persuaded that the pope then reigning (Urban VIII) was friendly and would let him speak out. He there fore published his masterpiece, Dialogue on the Two Chief World Systems, in which he had two people, one represent ing the view of Ptolemy [64] and the other the view of Copernicus, present their arguments before an intelligent lay man. (Amazingly enough, despite his long friendship with Kepler, Galileo did not mention Kepler’s modification of Co pernicus’ theory, a modification that improved it beyond measure—but then, Kepler’s work was appreciated by virtu ally no one at the time.) Galileo of course gave the Copemican the brilliant best of the battle. The pope was persuaded that Simplicio, the char acter who upheld the views of Ptolemy in the book, was a deliberate and insult ing caricature of himself. The book was all the more damaging to those who felt themselves insulted, because it was writ ten in vigorous Italian for the general public (and not merely for the Latin- learned scholars) and was quickly trans lated into other languages—even Chi nese! Galileo was brought before the Inqui sition on charges of heresy (his indis creet public statements made it easy to substantiate the charge) and on June 22, 1633, was forced to renounce any views that were at variance with the Ptolemaic system. Romance might have required a heroic refusal to capitulate, but Galileo was nearly seventy and he had the exam ple of Bruno to urge him to caution. He recanted and was condemned to a pen ance of psalm recitations each week for three years—and, of course, to refrain from further heresy. Legend has it that when he rose from his knees, having completed his renunci ation, he muttered, “Eppur si muove!” (“And yet it moves,” referring to the earth.) This was indeed the verdict given by the world of scholarship, and the silencing of Galileo for the remaining few years of his old age (during which —in 1637—he made his last astro nomical discovery, that of the slow sway ing or “libration” of the moon as it revolves) was an empty victory for the
[167] FÀBRICIUS KEPLER
conservatives. When he died they won an even shallower victory by refusing him burial in consecrated ground. The Scientific Revolution begun with Copernicus had been opposed for nearly a century at the time of Galileo’s trial, but by then the fight was lost. The revo lution not only existed, but had pre vailed, although, to be sure, there re mained pockets of resistance. Harvard, in the year of its founding (1636), re mained firmly committed to the Ptole maic theory. Galileo’s Dialogue was not removed from the Roman Catholic Index of pro hibited books until 1835. In 1965, Pope Paul VI, on a visit to Pisa, spoke highly of Galileo— an even clearer admission that on this issue the church had been in the wrong. [167] FABRICIUS, David (fa-brish'- ee-us) German astronomer Born: Esens, Ostfriesland, March 9, 1564
Died: Osteel, Ostfriesland, May 7, 1617
The surname is a Latinized version of Goldschmidt. Fabricius, a Protestant minister, was a friend of Tycho Brahe [156] and Kepler [169], He was one of the first to join Galileo [166] in using the telescope for astronomical research but he could never bring himself to accept Kepler’s elliptical orbits. He insisted on Plato’s [24] circles. His best-known discovery came in the time of naked-eye astronomy, for in 1596 he observed a star that Bayer [170] later named Omicron Ceti and found to show periodic variations in brightness. Hevelius [194], a half century later, named it Mira (“wonderful”). It was the first variable star to be discovered. The mere existence of a star varying in brightness was another blow to the or thodox Aristotelian view that the heavens were perfect and unchanging. Fabricius was murdered by one of his parishioners, who was apparently a thief and whom Fabricius had threatened to expose. [168] LIPPERSHEY, Hans (lip'er-shee) German-Dutch optician Born: Wesel, Germany, about 1570
Died: Middelburg, Netherlands, about 1619 Lippershey was a lens grinder who sold spectacles, the one device for which lenses were commonly used in those days. One of his apprentices, while pass ing away an idle moment in 1608, adjusted two lenses before his eyes and found that distant objects seemed closer. Startled, he told Lippershey, who mounted such lenses in tubes and at tempted to sell them (the first tele scopes) to the Dutch government. Rec ognizing the use of the instrument in warfare, the government tried to keep it secret. Hearing rumors of such a device, however, Galileo [166] in Italy quickly constructed one and turned it upon the heavens, revolutionizing astronomy rather than warfare. [169] KEPLER, Johann German astronomer Born: Weil der Stadt, Württem berg, December 27, 1571 Died: Regensburg, Bavaria, No vember 15, 1630 In his youth, Kepler, the son of a pro fessional soldier (who deserted his fam ily) and grandson of a man who had served as mayor of the family’s home town, was cursed with a sickly consti tution. An attack of smallpox, when he was three, crippled his hands and weak ened his eyes. This made it necessary for him to have a religious education, for he seemed fit for no post more strenuous than that of minister. He studied at the University of Tü bingen, where he was scapegoated by the other students, and where he was con verted to Copernicanism. He graduated in 1588 and earned a master’s degree in 1591. His brilliance in mathematics was soon recognized, and by 1594 all thought of the ministry was abandoned and he was teaching science at the Uni versity of Graz in Austria. In 1597, he
[169] KEPLER
KEPLER [169] married and in this way eventually gained five children and fourteen years of unhappiness. There was a strong strain of mysticism in Kepler. An astronomy professor in those days was expected to cast horo scopes, and Kepler threw himself into that form of work. He was no faker but studied the Greek astronomers carefully in an attempt to make a real science out of astrology as Cardano [137] had done nearly a century before. In this he failed, as Cardano had. Again like Cardano, Kepler attempted to use astrological techniques to solve biblical mysteries. He tried to work out the date of creation, for instance, and found it to be 3992 b . c . In later life Kepler seemed rather apologetic about his ability as an astrolo ger, but there is no question that it was more valued by his patrons than his achievements in science. He cast horo scopes for Emperor Rudolf and in later years for the imperial general, Albrecht von Wallenstein, earning him their pro tection, although he was a Protestant and the times were those of the Thirty Years’ War, during which religious ha treds were strong. In 1598 religious disputes (well in ad vance of the climactic quarrel of the Thirty Years’ War) were intense in Graz, and Kepler felt it advisable to leave. He accepted a position at Prague with the aged Tycho Brahe [156], with whom he had been in correspondence for some time. On Tycho’s death in 1601 Kepler inherited the invaluable data that the older man had collected over the years, including his careful observations of the apparent motion of the planet Mars.
Kepler set about trying to devise a sys tem of the heavens based on these obser vations. He was spurred on by the ap pearance of another nova (“Kepler’s star”) on September 30, 1604, not quite as bright as Tycho’s star, but spectacular enough. In his work, however, Kepler was side tracked by his interest in mystic notions dating back to the Greeks. He believed firmly in the “music of the spheres” first propounded by Pythagoras [7] and his followers and even tried to work out the exact notes sounded by each planet in its motions. (Earth, he said, sounded the notes “mi,” “fa,” “mi,” indicating it to be the abode of misery, /amine and misery.)
He also felt the influence of Plato [24], for he tried to fit the five Platonic solids into the planetary scheme of things. The book in which he advanced this notion, published in 1596, was what first inter ested Tycho Brahe in Kepler. In working out his regular-solid theory of the planets, he circumscribed an octa hedron about the sphere of Mercury and placed the sphere of Venus through its vertices. An icosahedron was circum scribed about the sphere of Venus and the sphere of earth was placed through its vertices. And so on. He spent a tremendous amount of time working it all out in the hope of ac counting exactly for the relative dis tances from the sun of the various planets. He finally realized by 1595 he couldn’t adjust the various solids and spheres properly. Nevertheless, he did not give up. It oc curred to him at last that nothing he could do with spheres would fit Tycho’s data, and he began to search for some noncircular curve that would fit. First, he tried an egg-shaped oval without suc cess, and then he settled on the ellipse. The ellipse, a curve first studied by Apollonius [49], resembles a flattened circle. A circle has a diameter that is fixed in length however it is drawn, but an ellipse’s diameter (a straight line drawn through its center) varies in length according to its position. The longest diameter is the major axis, the shortest the minor axis. The flatter the ellipse, the greater the proportionate difference in length between major and minor axis and the greater its “eccen tricity.” (The eccentricity of a circle is zero; it is not flattened at all.) Along the major axis are two points called foci at equal distances from the center. The foci have this property: if from each focus a straight line is drawn to the same point on the curve of the el lipse, the sum of the two lines is always equal to the length of the major axis. 1 0 6
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