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Parts of the Somnium were clearly autobiographical. The hero, for example, visits Tycho Brahe. He has parents who sell drugs. His mother consorts with spirits and daemons, one of whom eventually provides the means to travel to the moon. The Somnium makes clear to us, although it did not to all of Kepler’s contemporaries, that “in a dream one must be allowed the liberty of imagining occasionally that which never existed in the world of sense perception.” Science fiction was a new idea at the time of the Thirty Years’ War, and Kepler’s book was used as evidence that his mother was a witch.
In the midst of other grave personal problems, Kepler rushed to Württemberg to find his seventy-four-year-old mother chained in a Protestant secular dungeon and threatened, like Galileo in a Catholic dungeon, with torture. He set about, as a scientist naturally would, to find natural explanations for the various events that had precipitated the accusations of witchcraft, including minor physical ailments that the burghers of Württemberg had attributed to her spells. The research was successful, a triumph, as was much of the rest of his life, of reason over superstition. His mother was exiled, with a sentence of death passed on her should she ever return to Württemberg; and Kepler’s spirited defense apparently led to a decree by the Duke forbidding further trials for witchcraft on such slender evidence.
The upheavals of the war deprived Kepler of much of his financial support, and the end of his life was spent fitfully, pleading for money and sponsors. He cast horoscopes for the Duke of Wallenstein, as he had done for Rudolf II, and spent his final years in a Silesian town controlled by Wallenstein and called Sagan. His epitaph, which he himself composed, was: “I measured the skies, now the shadows I measure. Sky-bound was the mind, Earth-bound the body rests.” But the Thirty Years’ War obliterated his grave. If a marker were to be erected today, it might read, in homage to his scientific courage: “He preferred the hard truth to his dearest illusions.”
Johannes Kepler believed that there would one day be “celestial ships with sails adapted to the winds of heaven” navigating the sky, filled with explorers “who would not fear the vastness” of space. And today those explorers, human and robot, employ as unerring guides on their voyages through the vastness of space the three laws of planetary motion that Kepler uncovered during a lifetime of personal travail and ecstatic discovery.
The lifelong quest of Johannes Kepler, to understand the motions of the planets, to seek a harmony in the heavens, culminated thirty-six years after his death, in the work of Isaac Newton. Newton was born on Christmas Day, 1642, so tiny that, as his mother told him years later, he would have fit into a quart mug. Sickly, feeling abandoned by his parents, quarrelsome, unsociable, a virgin to the day he died, Isaac Newton was perhaps the greatest scientific genius who ever lived.
Even as a young man, Newton was impatient with insubstantial questions, such as whether light was “a substance or an accident,” or how gravitation could act over an intervening vacuum. He early decided that the conventional Christian belief in the Trinity was a misreading of Scripture. According to his biographer, John Maynard Keynes,
He was rather a Judaic Monotheist of the school of Maimonides. He arrived at this conclusion, not on so-to-speak rational or sceptical grounds, but entirely on the interpretation of ancient authority. He was persuaded that the revealed documents gave no support to the Trinitarian doctrines which were due to late falsifications. The revealed God was one God. But this was a dreadful secret which Newton was at desperate pains to conceal all his life.
Like Kepler, he was not immune to the superstitions of his day and had many encounters with mysticism. Indeed, much of Newton’s intellectual development can be attributed to this tension between rationalism and mysticism. At the Stourbridge Fair in 1663, at age twenty, he purchased a book on astrology, “out of a curiosity to see what there was in it.” He read it until he came to an illustration which he could not understand, because he was ignorant of trigonometry. So he purchased a book on trigonometry but soon found himself unable to follow the geometrical arguments. So he found a copy of Euclid’s Elements of Geometry, and began to read. Two years later he invented the differential calculus.
As a student, Newton was fascinated by light and transfixed by the Sun. He took to the dangerous practice of staring at the Sun’s image in a looking glass:
In a few hours I had brought my eyes to such a pass that I could look upon no bright object with neither eye but I saw the Sun before me, so that I durst neither write nor read but to recover the use of my eyes shut my self up in my chamber made dark three days together & used all means to divert my imagination from the Sun. For if I thought upon him I presently saw his picture though I was in the dark.
In 1666, at the age of twenty-three, Newton was an undergraduate at Cambridge University when an outbreak of plague forced him to spend a year in idleness in the isolated village of Woolsthorpe, where he had been born. He occupied himself by inventing the differential and integral calculus, making fundamental discoveries on the nature of light and laying the foundation for the theory of universal gravitation. The only other year like it in the history of physics was Einstein’s “Miracle Year” of 1905. When asked how he accomplished his astonishing discoveries, Newton replied unhelpfully, “By thinking upon them.” His work was so significant that his teacher at Cambridge, Isaac Barrow, resigned his chair of mathematics in favor of Newton five years after the young student returned to college.
Newton, in his mid-forties, was described by his servant as follows:
I never knew him to take any recreation or pastime either in riding out to take the air, walking, bowling, or any other exercise whatever, thinking all hours lost that were not spent in his studies, to which he kept so close that he seldom left his chamber unless [to lecture] at term time … where so few went to hear him, and fewer understood him, that ofttimes he did in a manner, for want of hearers, read to the walls.
Students both of Kepler and of Newton never knew what they were missing.
Newton discovered the law of inertia, the tendency of a moving object to continue moving in a straight line unless something influences it and moves it out of its path. The Moon, it seemed to Newton, would fly off in a straight line, tangential to its orbit, unless there were some other force constantly diverting the path into a near circle, pulling it in the direction of the Earth. This force Newton called gravity, and believed that it acted at a distance. There is nothing physically connecting the Earth and the Moon. And yet the Earth is constantly pulling the Moon toward us. Using Kepler’s third law, Newton mathematically deduced the nature of the gravitational force.* He showed that the same force that pulls an apple down to Earth keeps the Moon in its orbit and accounts for the revolutions of the then recently discovered moons of Jupiter in their orbits about that distant planet.
Things had been falling down since the beginning of time. That the Moon went around the Earth had been believed for all of human history. Newton was the first person ever to figure out that these two phenomena were due to the same force. This is the meaning of the word “universal” as applied to Newtonian gravitation. The same law of gravity applies everywhere in the universe.
It is a law of the inverse square. The force declines inversely as the square of distance. If two objects are moved twice as far away, the gravity now pulling them together is only one-quarter as strong. If they are over ten times farther away, the gravity is ten squared, 102 = 100 times smaller. Clearly, the force must in some sense be inverse—that is, declining with distance. If the force were direct, increasing with distance, then the strongest force would work on the most distant objects, and I suppose all the matter in the universe would find itself careening together into a single cosmic lump. No, gravity must decrease with distance, which is why a comet or a planet moves slowly when far from the Sun and faster when close to the Sun—the gravity it feels is weaker the farther from the Sun it is.
All three of Kepler’s laws of planetary motion can be derived from Newtonian principles
. Kepler’s laws were empirical, based upon the painstaking observations of Tycho Brahe. Newton’s laws were theoretical, rather simple mathematical abstractions from which all of Tycho’s measurements could ultimately be derived. From these laws, Newton wrote with undisguised pride in the Principia, “I now demonstrate the frame of the System of the World.”
Later in his life, Newton presided over the Royal Society, a fellowship of scientists, and was Master of the Mint, where he devoted his energies to the suppression of counterfeit coinage. His natural moodiness and reclusivity grew; he resolved to abandon those scientific endeavors that brought him into quarrelsome disputes with other scientists, chiefly on issues of priority; and there were those who spread tales that he had experienced the seventeenth-century equivalent of a “nervous breakdown.” However, Newton continued his lifelong experiments on the border between alchemy and chemistry, and some recent evidence suggests that what he was suffering from was not so much a psychogenic ailment as heavy metal poisoning, induced by systematic ingestion of small quantities of arsenic and mercury. It was a common practice for chemists of the time to use the sense of taste as an analytic tool.
Nevertheless his prodigious intellectual powers persisted unabated. In 1696, the Swiss mathematician Johann Bernoulli challenged his colleagues to solve an unresolved issue called the brachistochrone problem, specifying the curve connecting two points displaced from each other laterally, along which a body, acted upon only by gravity, would fall in the shortest time. Bernoulli originally specified a deadline of six months, but extended it to a year and a half at the request of Leibniz, one of the leading scholars of the time, and the man who had, independently of Newton, invented the differential and integral calculus. The challenge was delivered to Newton at four P.M. on January 29, 1697. Before leaving for work the next morning, he had invented an entire new branch of mathematics called the calculus of variations, used it to solve the brachistochrone problem and sent off the solution, which was published, at Newton’s request, anonymously. But the brilliance and originality of the work betrayed the identity of its author. When Bernoulli saw the solution, he commented, “We recognize the lion by his claw.” Newton was then in his fifty-fifth year.
The major intellectual pursuit of his last years was a concordance and calibration of the chronologies of ancient civilizations, very much in the tradition of the ancient historians Manetho, Strabo and Eratosthenes. In his last, posthumous work, “The Chronology of Ancient Kingdoms Amended,” we find repeated astronomical calibrations of historical events; an architectural reconstruction of the Temple of Solomon; a provocative claim that all the Northern Hemisphere constellations are named after the personages, artifacts and events in the Greek story of Jason and the Argonauts; and the consistent assumption that the gods of all civilizations, with the single exception of Newton’s own, were merely ancient kings and heroes deified by later generations.
Kepler and Newton represent a critical transition in human history, the discovery that fairly simple mathematical laws pervade all of Nature; that the same rules apply on Earth as in the skies; and that there is a resonance between the way we think and the way the world works. They unflinchingly respected the accuracy of observational data, and their predictions of the motion of the planets to high precision provided compelling evidence that, at an unexpectedly deep level, humans can understand the Cosmos. Our modern global civilization, our view of the world and our present exploration of the Universe are profoundly indebted to their insights.
Newton was guarded about his discoveries and fiercely competitive with his scientific colleagues. He thought nothing of waiting a decade or two after its discovery to publish the inverse square law. But before the grandeur and intricacy of Nature, he was, like Ptolemy and Kepler, exhilarated as well as disarmingly modest. Just before his death he wrote: “I do not know what I may appear to the world; but to myself I seem to have been only like a boy, playing on the seashore, and diverting myself, in now and then finding a smoother pebble or a prettier shell than ordinary, while the great ocean of truth lay all undiscovered before me.”
*The root of the word means “Moon.”
*Skepticism about astrology and related doctrines is neither new nor exclusive to the West. For example, in the Essays on Idleness, written in 1332 by Tsurezuregusa of Kenko, we read:
The Yin-Yang teachings [in Japan] have nothing to say on the subject of the Red Tongue Days. Formerly people did not avoid these days, but of late—I wonder who is responsible for starting this custom—people have taken to saying things such as, “An enterprise begun on a Red Tongue Day will never see an end,” or, “Anything you say or do on a Red Tongue Day is bound to come to naught: you lose what you’ve won, your plans are undone.” What nonsense! If one counted the projects begun on carefully selected “lucky days” which came to nothing in the end, they would probably be quite as many as the fruitless enterprises begun on the Red Tongue days.
*Four centuries earlier, such a device was constructed by Archimedes and examined and described by Cicero in Rome, where it had been carried by the Roman general Marcellus, one of whose soldiers had, gratuitously and against orders, killed the septuagenarian scientist during the conquest of Syracuse.
*In a recent inventory of nearly every sixteenth-century copy of Copernicus’ book, Owen Gingerich has found the censorship to have been ineffective: only 60 percent of the copies in Italy were “corrected,” and not one in Iberia.
*By no means the most extreme such remark in medieval or Reformation Europe. Upon being asked how to distinguish the faithful from the infidel in the siege of a largely Albigensian city, Domingo de Guzmán, later known as Saint Dominic, allegedly replied: “Kill them all. God will know his own.”
*The proof of this statement can be found in Appendix 2.
*Some examples are still to be seen in the Graz armory.
*Brahe, like Kepler, was far from hostile to astrology, although he carefully distinguished his own secret version of astrology from the more common variants of his time, which he thought conducive to superstition. In his book Astronomiae Instauratae Mechanica, published in 1598, he argued that astrology is “really more reliable than one would think” if charts of the position of the stars were properly improved. Brahe wrote: “I have been occupied in alchemy, as much as by the celestial studies, from my 23rd year.” But both of these pseudosciences, he felt, had secrets far too dangerous for the general populace (although entirely safe, he thought, in the hands of those princes and kings from whom he sought support). Brahe continued the long and truly dangerous tradition of some scientists who believe that only they and the temporal and ecclesiastical powers can be trusted with arcane knowledge: “It serves no useful purpose and is unreasonable, to make such things generally known.” Kepler, on the other hand, lectured on astronomy in schools, published extensively and often at his own expense, and wrote science fiction, which was certainly not intended primarily for his scientific peers. He may not have been a popular writer of science in the modern sense, but the transition in attitudes in the single generation that separated Tycho and Kepler is telling.
*Sadly, Newton does not acknowledge his debt to Kepler in his masterpiece the Principia. But in a 1686 letter to Edmund Halley, he says of his law of gravitation: “I can affirm that I gathered it from Kepler’s theorem about twenty years ago.”
HEAVEN AND HELL
The doors of heaven and hell are adjacent and identical.
—Nikos Kazantzakis, The Last Temptation of Christ
The Earth is a lovely and more or less placid place. Things change, but slowly. We can lead a full life and never personally encounter a natural disaster more violent than a storm. And so we become complacent, relaxed, unconcerned. But in the history of Nature, the record is clear. Worlds have been devastated. Even we humans have achieved the dubious technical distinction of being able to make our own disasters, both intentional and inadvertent. On the landscapes of other planets where the record
s of the past have been preserved, there is abundant evidence of major catastrophes. It is all a matter of time scale. An event that would be unthinkable in a hundred years may be inevitable in a hundred million. Even on the Earth, even in our own century, bizarre natural events have occurred.
In the early morning hours of June 30, 1908, in Central Siberia, a giant fireball was seen moving rapidly across the sky. Where it touched the horizon, an enormous explosion took place. It leveled some 2,000 square kilometers of forest and burned thousands of trees in a flash fire near the impact site. It produced an atmospheric shock wave that twice circled the Earth. For two days afterward, there was so much fine dust in the atmosphere that one could read a newspaper at night by scattered light in the streets of London, 10,000 kilometers away.
The government of Russia under the Czars could not be bothered to investigate so trivial an event, which, after all, had occurred far away, among the backward Tungus people of Siberia. It was ten years after the Revolution before an expedition arrived to examine the ground and interview the witnesses. These are some of the accounts they brought back:
Early in the morning when everyone was asleep in the tent, it was blown up into the air, together with the occupants. When they fell back to Earth, the whole family suffered slight bruises, but Akulina and Ivan actually lost consciousness. When they regained consciousness they heard a great deal of noise and saw the forest blazing round them and much of it devastated.
I was sitting in the porch of the house at the trading station of Vanovara at breakfast time and looking towards the north. I had just raised my axe to hoop a cask, when suddenly … the sky was split in two, and high above the forest the whole northern part of the sky appeared to be covered with fire. At that moment I felt a great heat as if my shirt had caught fire.… I wanted to pull off my shirt and throw it away, but at that moment there was a bang in the sky, and a mighty crash was heard. I was thrown on the ground about three sajenes away from the porch and for a moment I lost consciousness. My wife ran out and carried me into the hut. The crash was followed by a noise like stones falling from the sky, or guns firing. The Earth trembled, and when I lay on the ground I covered my head because I was afraid that stones might hit it. At that moment when the sky opened, a hot wind, as from a cannon, blew past the huts from the north. It left its mark on the ground.…