by Will Durant
A similar lag occurred in the acceptance of the Copernican astronomy. In Italy it might be studied and taught if presented as hypothesis rather than demonstrated fact;66 Giordano Bruno defended it, and Campanella already wondered whether the inhabitants of other planets thought themselves, as earthlings do, the center and purpose of all things.67 Generally, Protestant theologians vied with Catholic in denouncing the new system. Bacon and Bodin alike repudiated it.68 More surprising was its rejection by the greatest astronomer of the half century that followed Copernicus’ death (1543).
Tycho Brahe was born in 1546 in the then Danish province of Scania, now the southern extremity of Sweden. His father was a member of the Danish Council of State; his mother was mistress of the robes of the Queen. His rich Uncle Jorgen, disconsolately childless, abducted him, wheedled the parents into consent, and gave the boy every advantage of education. At thirteen Tycho entered the University of Copenhagen. According to Gassendi, he was drawn to astronomy when he heard a teacher discuss a forthcoming eclipse of the sun. He watched the eclipse come as predicted, and marveled at the science that had reached such prophetic power. He bought a copy of Ptolemy’s Almagest, pored over it to the neglect of other studies, and never abandoned the geocentric view there presented in the second century of our era.
At sixteen he was transferred to the University of Leipzig, where he studied law by day and the stars by night. He was warned that this regimen would lead to physical and nervous breakdown. Tycho persisted, and he spent his allowance on astronomical instruments. In 1565 his uncle died, leaving him a large fortune. After settling his business affairs, Tycho hurried to Wittenberg for more mathematics and astronomy; thence, driven by plague, to Rostock. There he fought a duel and had part of his nose cut off; he ordered a bright new nose of silver and gold and wore it the rest of his life. He dabbled in astrology and predicted the coming death of Suleiman the Magnificent, only to find that the Sultan had already died.69 After much travel in Germany he returned to Denmark, busied himself with chemistry, and was brought back to astronomy by discovering a new star in the constellation Cassiopeia (1572). His carefree observations of this transitory star and his account of it in his first publication, De nova Stella, gave him a European reputation, but shocked some great Danes, who considered authorship a form of exhibitionism incompatible with blue blood. Tycho confounded them by marrying a peasant girl. He seems to have felt that a simple housewife was the best mate for an absorbed astronomer and was the best match open to a man with a golden nose.
Dissatisfied with astronomical facilities in Copenhagen, he set out for Cassel, where Landgrave William IV had built (1561) the first observatory with a revolving roof, and Joost Bürgi had developed a pendulum clock which made possible an unprecedented accuracy in timing the observation and movements of stars. Fired with new zeal, Tycho went back to Copenhagen and interested Frederick II in projects for an observatory. The King gave him the island of Hveen (Venus) in the Sound, and a good pension. With this and his own means Tycho built there a castle and gardens which he called Uraniburg (Heavenly City), with living quarters, library, laboratory, several observatories, and a workshop to make his own instruments. He had no telescope; twenty-eight years were to pass before its invention; yet it was his observations that guided Kepler to epochal discoveries.
In twenty-one years at Hveen Tycho and his pupils gathered a body of data exceeding in extent and accuracy anything hitherto known. He took records of the sun’s apparent motion every day for many years. He was one of the first astronomers to allow for the refraction of light and the fallibility of observers and instruments; so he repeated the same observation time and again. He discovered and reduced to law the variations in the motion of the moon. His meticulous tracing of a comet in 1577 led him to the now universally accepted belief that comets, instead of being generated in the earth’s atmosphere, are true celestial bodies moving in fixed and regular courses. When Tycho published his catalogue of 777 stars, and marked them with loving care on the great celestial globe in his library, he had justified his life.
In 1588 Frederick II died. The new King was a boy of eleven; the regents who ruled him were not as patient with the pride, temper, and extravagance of Brahe as Frederick had been; soon the governmental grants ran low, and in 1597 they ceased. Tycho left Denmark and settled in Benatek Castle, near Prague, as the guest of Emperor Rudolf II, who looked to him for astrological predictions. Brahe imported his instruments and records from Hveen, and advertised for an assistant. Johann Kepler came (1600), and worked fitfully but devotedly for his difficult master. Just as Brahe was hoping to develop his massive accumulation of data into a reasoned theory of the heavens, he was struck down at table by a burst bladder. He lingered in pain for eleven days, and died (1601) mourning that he had not completed his work. The funeral orator said that he had “coveted nothing but time.”70
VIII. KEPLER: 1571–163O
It turned out well for science that Tycho moved to Prague, for there Kepler inherited his observations, and deduced from them the planetary laws that prepared for Newton’s theory of gravitation. From Brahe to Kepler to Newton and from Copernicus to Galileo to Newton are the basic and converging lines of modern astronomy.
Kepler was born at Weil, near Stuttgart, son of an army officer who repeatedly went off to war as preferable to domesticity. Returning at last, the father opened a tavern, in which Johann served as a waiter. The boy was sickly; smallpox crippled his hands and permanently impaired his vision. The Duke of Württemberg saw in him the possibility of a good preacher and paid for his education. At Tübingen Michael Maestlin, who as professor taught the Ptolemaic astronomy, privately converted Kepler to the Copernican theory, and the youth became so enthusiastic about the stars that he abandoned all thought of an ecclesiastical career.
After taking his degree he became a schoolmaster at Graz, in Styria, teaching Latin, rhetoric, and mathematics for 150 gulden a year, with free lodging, and adding twenty gulden by editing annually an astrological calendar. At twenty-five he married a woman of twenty-three who had buried one husband and divorced another; she brought him a dowry and a daughter; he added six children in due course. A year after his marriage he was forced as a Protestant to leave Graz (1597), for the new Archduke of Styria, Ferdinand, was a resolute Catholic who ordered all Protestant clergymen and teachers out of Styria. Kepler had given further offense by publishing Mysterium cosmographicum (1596), ardently advocating the Copernican system; hopefully he sent copies to Brahe and Galileo. After a year of despondent poverty he was saved by Tycho’s invitation to Prague. But Tycho was hard to get along with; there were difficulties with religion and bread; the wife developed epilepsy. Then Tycho died, and Kepler was appointed his successor, at five hundred florins a year.
Brahe had bequeathed his records to him, but not his instruments. Unable to buy the best, Kepler found himself driven to study Brahe’s observations rather than add to them. He could never have said with Newton, “I do not invent hypotheses”; on the contrary, his head hummed with them; “I have much store of fantasy.”71 His peculiar skill lay in testing hypotheses, and his wisdom lay in casting them aside when the consequences that he had mathematically deduced from them proved incompatible with the observed phenomena.72 In seeking to plot the orbit of Mars he tried seventy hypotheses through four years.
Finally (1604) he reached his basic and epochal discovery—that the orbit of Mars around the sun is an ellipse, not a circle as astronomers from Plato to and including Copernicus had supposed; only an elliptical orbit harmonized with the repeated observations of Brahe and others. Kepler’s agile mind leaped to the question, What if all the planetary orbits are elliptical? Rapidly he tested the idea with the recorded observations; it agreed with them almost completely. In a Latin treatise on the motions of Mars, Astronomia nova de motibus stellae Martis (1609), he published the first two of “Kepler’s laws”: first, each planet moves in an elliptical orbit, in which one focus is the sun; second, each planet moves more
rapidly when near the sun than when farther from it, and a radius drawn from the sun to the planet covers, in its motion, equal areas in equal times. Kepler ascribed the differences in planetary speed to the greater emanation of solar energy felt by the planet as it neared the sun; in this connection he evolved from Gilbert an idea of magnetic attraction closely akin to Newton’s theory of gravitation.
When Emperor Rudolf died (1612) Kepler moved to Linz, and again he lived by teaching school. His wife having passed away, he married a poor orphan girl. In providing his new home with wine he was fascinated by the difficulty of measuring the contents of a cask with curved sides; the essay that he published on the problem helped to prepare the discovery of infinitesimal calculus.
After puzzling for ten years over the relation between the speed of a planet and the size of its orbit, Kepler published, in his book The Harmony of the World (1619), his third law: the square of the time of revolution of a planet around the sun is proportioned to the cube root of its mean distance from the sun. (For example: Mars’s time of revolution is demonstrably 1.88 times that of the earth; the square of this is 3.53; the cube root of this is 1.52; i.e., the mean distance of Mars from the sun will be 1.52 times that of the earth from the sun.) Kepler was so overjoyed by having reduced the behavior of the planets to such order and regularity that he likened each orbital speed to a note on a musical scale, and concluded that the combined motions make a “harmony of the spheres,” which, however, is audible only to the “soul” of the sun. Kepler mingled mysticism with his science, illustrating again Goethe’s generous saying that a man’s defects are the faults of his time, while his virtues are his own. We can forgive the pride that wrote, in the preface to The Harmony of the World:
What I promised my friends in the title of this book…. what, sixteen years ago, I urged as a thing to be sought—that for which I joined Tycho Brahe, … to which I have devoted the best part of my life—I have at length brought to light. … It is not eighteen months since the unveiled sun … burst upon me. Nothing holds me; I will indulge my sacred fury. … If you forgive me, I rejoice; if you are angry I can bear it. The die is cast, the book is written, to be read either now or by posterity, I care not which; it may well wait a century for a reader, as God has waited six thousand years for a discoverer!73
In an Epitome of the Copernican Astronomy (1618–21) Kepler showed how his laws supported, clarified, and amended the Copernican system. “I have attested it as true in my inmost soul,” he said, “and I contemplate its beauty with incredible and ravishing delight.”74 The treatise was placed on the Index of Prohibited Books because it argued that the Copernican theory had been proved. Kepler, a pious Protestant, was not disturbed. For a while he enjoyed prosperity and acclaim. His salary as Imperial astronomer was generally paid. From faraway Britain James I invited him (1620) to come and adorn the English court, but Kepler refused, saying that he would suffer from being cooped up in an island.75
He shared the prevailing belief in witchcraft. His mother was charged with practicing it; witnesses alleged that their cattle, or they themselves, had become ill because Frau Kepler had touched them; one witness swore that her eight-year-old daughter had been made ill by Mother Kepler’s witchery, and she threatened to kill the “witch” if she did not at once cure the girl. The accused woman denied all guilt, but she was arrested and chained in a cell. Kepler fought for her at every stage of the proceedings. The state’s attorney proposed that a confession be drawn from her by torture. She was taken to the torture chamber and was shown the instruments to be used upon her; she still asserted her innocence. After thirteen months’ imprisonment she was released, but she died soon afterward (1622).
This tragedy, and the impact of the spreading war, darkened Kepler’s final years. In 1620 Linz was occupied by Imperialist troops, and its inhabitants neared starvation. Through all the chaos he continued his labor of formulating the observations of Brahe, others, and himself, in the Rudolphine tables (1627), which catalogued and charted 1,005 stars and remained standard for a century. In 1626 he moved to Ulm. His Imperial salary fell far in arrears, and he was hard pressed to feed his family. He applied to Wallenstein for employment as astrologer; he was engaged, and for some years he followed the general, casting horoscopes for him and publishing astrological almanacs. In 1630 he went to Regensburg to appeal to the Diet for the arrears of his salary. The effort consumed his last physical resources; he was seized with fever and died within a few days (November 15, 1630), in the fifty-ninth year of his age. All traces of his grave were swept away by the war.
His function in the history of astronomy was to mediate between Copernicus and Newton. He advanced beyond Copernicus by replacing circular with elliptical orbits, by abandoning eccentrics and epicycles, and by placing the sun not at the center of a circle but at one focus of an ellipse. By these changes he freed the Copernican system from many of the difficulties that had almost justified Tycho Brahe in rejecting it; through him the heliocentric view now won a rapidly widening acceptance. He transformed what had been a brilliant guess into a hypothesis worked out in impressive mathematical detail. He provided Newton with the planetary laws that led to the theory of gravitation. While keeping his religious faith fervent and undiminished, he revealed the universe as a structure of law, as a cosmos of order in which the same laws ruled the earth and the stars. “My wish,” he said, “is that I may perceive the God whom I find everywhere in the external world in like manner within me.”76
IX. GALILEO: 1564–1642
1. The Physicist
Galileo Galilei was born at Pisa on the day of Michelangelo’s death (February 18, 1564), in the same year as Shakespeare. His father was a cultured Florentine, who shared in teaching him Greek, Latin, mathematics, and music. Not for nothing was Galileo an almost exact contemporary of Monteverdi (1567–1643); music was one of his perennial consolations, especially in his blind old age; he played the organ creditably and the lute well. He liked to draw and paint, and sometimes he regretted that he had not become an artist. In that wonderful Italy of his youth the flame of the Renaissance still burned, inspiring men to be complete. He mourned that he could not design a temple, carve a statue, paint a portrait, write poetry, compose music, guide a ship;77 he longed to do all of these; and we feel, as we contemplate him, that he lacked only time. Such a man, under different accidents, could have been any kind of great man. Whether by nature or by circumstance, he turned in boyhood to making and playing with machines.
At seventeen he was sent to the University of Pisa to study medicine and philosophy. A year later he made his first scientific discovery—that the swings of a pendulum, regardless of their width, take equal times. By lengthening or shortening the arm of a pendulum he could retard or quicken the rate of oscillation until it synchronized with his pulse; by this “pulsilogia” he could accurately measure his heartbeat.
About this time he discovered Euclid. He overheard a tutor teaching geometry to the pages of the Grand Duke of Tuscany; the logic of mathematics seemed to him immeasurably superior to the Scholastic and Aristotelian philosophy that he had received in the classroom; clandestinely, with Euclid’s Elements in his hand, he followed the lessons of the instructor to the pages. The tutor took an interest in him and taught him privately. In 1585 Galileo left the University of Pisa without taking a degree, moved to Florence, and, under the tutor’s guidance, gave himself with passion to mathematics and mechanics. A year later he invented a hydrostatic balance to measure the relative weights of metals in an alloy, and won the praise of the Jesuit Clavius for an essay on the center of gravity in solid bodies. Meanwhile his father’s means ran out, and Galileo faced the obligation to earn his own bread. He applied for teaching posts at Pisa, Florence, and Padua; he was rejected as too young. In 1589, as he and a friend were planning to seek their fortunes in Constantinople and the East, they heard that the chair of mathematics at Pisa had fallen vacant. Galileo applied for it in forlorn hope; he was still only twenty-five. He was given
a three-year appointment, at sixty scudi per year. On this he could starve, but he could show his mettle.
He was mettlesome enough, for he began at once, from his professorial chair, a war on the physics of Aristotle. According to the Greek “the downward movement of a mass of gold or lead, or of any other body endowed with weight, is quicker in proportion to its size.”78 Lucretius79 and Leonardo da Vinci80 expressed the same view. Even in antiquity Hipparchus (c. 130 B.C.) had questioned the opinion of Aristotle “on bodies carried downward through weight”; and Joannes Philoponus (533 A.D.), commenting on Aristotle, thought that the difference in time of fall between two objects one of which is twice the weight of the other will be “either none at all or imperceptible.”81 Here we come upon a famous and disputed story. It appears first in an early biography of Galileo, written by his friend Vincenzo Viviani in 1654 (twelve years after Galileo’s death), and claiming to be founded on Galileo’s own verbal account: