On Astrology -Carl Sagan- Cosmos Chapter 3

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  6. The Harmony of Worlds
  8. _____________________
  10. If we lived on a planet where nothing ever changed, there would be little to do. There would be nothing to figure out. There would be no impetus for science. And if we lived in an unpredictable world, where things changed in random or very complex ways, we would not be able to figure things out. Again, there would be no such thing as science. But we live in an in­between universe, where things change, but according to patterns, rules, or, as we call them, laws of nature. If I throw a stick up in the air, it always falls down. If the sun sets in the west, it always rises again the next morning in the east. And so it becomes possible to figure things out. We can do science, and with it we can improve our lives.
  12. Human beings are good at understanding the world. We always have been. We were able to hunt game or build fires only because we had figured something out. There was a time before television, before motion pictures, before radio, before books. The greatest part of human existence was spent in such a time. Over the dying embers of the campfire, on a moonless night, we watched the stars.
  14. The night sky is interesting. There are patterns there. Without even trying, you can imagine pictures. In the northern sky, for example, there is a pattern, or constellation, that looks a little ursine. Some cultures call it the Great Bear. Others see quite different images. These pictures are not, of course, really in the night sky; we put them there ourselves. We were hunter folk, and we saw hunters and dogs, bears and
  16.  young women, all manner of things of interest to us. When seventeenth­century European sailors first saw the southern skies they put objects of seventeenth century interest in the heavens ­ toucans and peacocks, telescopes and microscopes, compasses and the sterns of ships. If the constellations had been named in the twentieth century, I suppose we would see bicycles and refrigerators in the sky, rock­and­roll ‘stars’ and perhaps even mushroom clouds ­ a new set of human hopes and fears placed among the stars.
  18. Occasionally our ancestors would see a very bright star with a tail, glimpsed for just a moment, hurtling across the sky. They called it a falling star, but it is not a good name: the old stars are still there after the falling star falls. In some seasons there are many falling stars; in others very few. There is a kind of regularity here as well. Like the Sun and the Moon, stars always rise in the east and set in the west, taking the whole night to cross the sky if they pass overhead. There are different constellations in different seasons. The same constellations always rise at the beginning of autumn, say. It never happens that a new constellation suddenly rises out of the east. There is an order, a predictability, a permanence about the stars. In a way, they are almost comforting.
  20. Certain stars rise just before or set just after the Sun ­ and at times and positions that vary with the seasons. If you made careful observations of the stars and recorded them over many years, you could predict the seasons. You could also measure the time of year by noting where on the horizon the Sun rose each day. In the skies was a great calendar, available to anyone with dedication and ability and the means to keep records.
  22. Our ancestors built devices to measure the passing of the seasons. In Chaco Canyon, in New Mexico, there is a great roofless ceremonial kiva or temple, dating from the eleventh century. On June 21, the longest day of the year, a shaft of sunlight enters a window at dawn and slowly moves so that it covers a special niche. But this happens only around June 21. I imagine the proud Anasazi people, who described themselves as ‘The Ancient Ones,’ gathered in their pews every June 21, dressed in feathers and rattles and turquoise to celebrate the power of the Sun. They also monitored the apparent motion of the Moon: the twenty­eight higher niches in the kiva may represent the number of days for the Moon to return to the same position among the constellations. These people paid close attention to the Sun and the Moon and the stars. Other devices based on similar ideas are found at Angkor Wat in Cambodia; Stonehenge in England; Abu Simbel in Egypt; Chichén Itzá in Mexico; and the Great Plains in North America.
  24. Some alleged calendrical devices may just possibly be due to chance ­ an accidental alignment of window and niche on June 21, say. But there are other devices wonderfully different. At one locale in the American Southwest is a set of three upright slabs which were moved from their original position about 1,000 years ago. A spiral a little like a galaxy has been carved in the rock. On June 21, the first day of summer, a dagger of sunlight pouring through an opening between the slabs bisects the spiral; and on December 21, the first day of winter, there are two daggers of sunlight that flank the spiral, a unique application of the midday sun to read the calendar in the sky. Why did people all over the world make such an effort to learn astronomy? We hunted gazelles and antelope and buffalo whose migrations ebbed and flowed with the seasons. Fruits and nuts were ready to be picked in some times but not in others. When we invented agriculture, we had to take care to plant and harvest our crops in the right season. Annual meetings of far­flung nomadic tribes were set for prescribed times. The ability to read the calendar in the skies was literally a matter of life and death. The reappearance of the crescent moon after the new moon; the return of the Sun after a total eclipse; the rising of the Sun in the morning after its troublesome absence at night were noted by people around the world: these phenomena spoke to our ancestors of the possibility of surviving death. Up there in the skies was also a metaphor of immortality.
  26. The wind whips through the canyons in the American Southwest, and there is no one to hear it but us ­ a reminder of the 40,000 generations of thinking men and women who preceded us, about whom we know almost nothing, upon whom our civilization is based.
  28. As ages passed, people learned from their ancestors. The more accurately you knew the position and movements of the Sun and Moon and stars, the more reliably you could predict when to hunt, when to sow and reap, when to gather the tribes. As precision of measurement improved, records had to be kept, so astronomy encouraged observation and mathematics and the development of writing.
  30. But then, much later, another rather curious idea arose, an assault by mysticism and superstition into what had been largely an empirical science. The Sun and stars controlled the seasons, food, warmth. The Moon controlled the tides, the life cycles of many animals, and perhaps the human menstrual* period ­ of central importance for a passionate species devoted to having children. There was another kind of object in the sky, the wandering or vagabond stars called planets. Our nomadic ancestors must have felt an affinity for the planets. Not counting the Sun and the Moon, you could see only five of them. They moved against the background of more distant stars. If you followed their apparent motion over many months, they would leave one constellation, enter another, occasionally even do a kind of slow loop­the­loop in the sky. Everything else in the sky had some real effect on human life. What must the influence of the planets be? * The root of the word means ‘Moon.’
  32. In contemporary Western society, buying a magazine on astrology ­ at a newsstand, say ­ is easy; it is much harder to find one on astronomy. Virtually every newspaper in America has a daily column on astrology; there are hardly any that have even a weekly column on astronomy. There are ten times more astrologers in the United States than astronomers. At parties, when I meet people who do not know I am a scientist, I am sometimes asked, ‘Are you a Gemini?’ (chances of success, one in twelve), or ‘What sign are you?’ Much more rarely am I asked, ‘Have you heard that gold is made in supernova explosions?’ or ‘When do you think Congress will approve a Mars Rover?’
  34. Astrology contends that which constellation the planets are in at the moment of your birth profoundly influences your future. A few thousand years ago, the idea developed that the motions of the planets determined the fates of kings, dynasties, empires. Astrologers studied the motions of the planets and asked themselves what had happened the last time that, say, Venus was rising in the Constellation of the Goat; perhaps something similar would happen this time as well. It was a subtle and risky business. Astrologers came to be employed only by the State. In many countries it was a capital offense for anyone but the official astrologer to read the portents in the skies: a good way to overthrow a regime was to predict its downfall. Chinese court astrologers who made inaccurate predictions were executed. Others simply doctored the records so that afterwards they were in perfect conformity with events. Astrology developed into a strange combination of observations, mathematics and careful record­ keeping with fuzzy thinking and pious fraud.
  36.  But if the planets could determine the destinies of nations, how could they avoid influencing what will happen to me tomorrow? The notion of a personal astrology developed in Alexandrian Egypt and spread through the Greek and Roman worlds about 2,000 years ago. We today can recognize the antiquity of astrology in words such as disaster, which is Greek for ‘bad star,’ influenza, Italian for (astral) ‘influence’; mazeltov, Hebrew ­ and, ultimately, Babylonian ­ for ‘good constellation,’ or the Yiddish word shlamazel, applied to someone plagued by relentless ill­fortune, which again traces to the Babylonian astronomical lexicon. According to Pliny, there were Romans considered sideratio, ‘planetstruck.’ Planets were widely thought to be a direct cause of death. Or consider consider: it means ‘with the planets,’ evidently the prerequisite for serious reflection. John Graunt compiled the mortality statistics in the City of London in 1632. Among the terrible losses from infant and childhood diseases and such exotic illnesses as ‘the rising of the lights’ and ‘the King’s evil,’ we find that, of 9,535 deaths, 13 people succumbed to ‘planet,’ more than died of cancer. I wonder what the symptoms were.
  38. And personal astrology is with us still: consider two different newspaper astrology columns published in the same city on the same day. For example, we can examine the New York Post and the New York Daily News on September 21, 1979. Suppose you are a Libra ­ that is, born between September 23 and October 22. According to the astrologer for the Post, ‘a compromise will help ease tension’; useful, perhaps, but somewhat vague. According to the Daily News’s astrologer, you must ‘demand more of yourself,’ an admonition that is also vague but also different. These ‘predictions’ are not predictions; rather they are pieces of advice ­ they tell what to do, not what will happen. Deliberately, they are phrased so generally that they could apply to anyone. And they display major mutual inconsistencies. Why are they published as unapologetically as sports statistics and stock market reports?
  40. Astrology can be tested by the lives of twins. There are many cases in which one twin is killed in childhood, in a riding accident, say, or is struck by lightning, while the other lives to a prosperous old age. Each was born in precisely the same place and within minutes of the other. Exactly the same planets were rising at their births. If astrology were valid, how could two such twins have such profoundly different fates? It also turns out that astrologers cannot even agree among themselves on what a given horoscope means. In careful tests, they are unable to predict the character and future of people they knew nothing about except their time and place of birth.*
  42. * 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 Kenko, we read: The Yin­Yang 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.
  44. There is something curious about the national flags of the planet Earth. The flag of the United States has fifty stars; the Soviet Union and Israel, one each; Burma, fourteen; Grenada and Venezuela, seven; China, five; Iraq, three; São Tomé a Príncipe, two; Japan, Uruguay, Malawi, Bangladesh and Taiwan, the Sun; Brazil, a celestial sphere; Australia, Western Samoa, New Zealand and Papua New Guinea, the constellation of the Southern Cross; Bhutan, the dragon pearl, symbol of the Earth;
  46.  Cambodia, the Angkor Wat astronomical observatory; India, South Korea and the Mongolian Peoples’ Republic, cosmological symbols. Many socialist nations display stars. Many Islamic countries display crescent moons. Almost half of our national flags exhibit astronomical symbols. The phenomenon is transcultural, non­sectarian, worldwide. It is also not restricted to our time: Sumerian cylinder seals from the third millennium B.C. and Taoist flags in prerevolutionary China displayed constellations. Nations, I do not doubt, wish to embrace something of the power and credibility of the heavens. We seek a connection with the Cosmos. We want to count in the grand scale of things. And it turns out we are connected ­ not in the personal, small­scale unimaginative fashion that the astrologers pretend, but in the deepest ways, involving the origin of matter, the habitability of the Earth, the evolution and destiny of the human species, themes to which we will return.
  48. Modern popular astrology runs directly back to Claudius Ptolemaeus, whom we call Ptolemy, although he was unrelated to the kings of the same name. He worked in the Library of Alexandria in the second century. All that arcane business about planets ascendant in this or that solar or lunar ‘house’ or the ‘Age of Aquarius’ comes from Ptolemy, who codified the Babylonian astrological tradition. Here is a typical horoscope from Ptolemy’s time, written in Greek on papyrus, for a little girl born in the year 150: ‘The birth of Philoe. The 10th year of Antoninus Caesar the lord, Phamenoth 15 to 16, first hour of the night. Sun in Pisces, Jupiter and Mercury in Aries, Saturn in Cancer, Mars in Leo, Venus and the Moon in Aquarius, horoscopus Capricorn.’ The method of enumerating the months and the years has changed much more over the intervening centuries than have the astrological niceties. A typical excerpt from Ptolemy’s astrological book, the Tetrabiblos, reads: ‘Saturn, if he is in the orient, makes his subjects in appearance dark­skinned, robust, black­haired, curly­ haired, hairy­chested, with eyes of moderate size, of middling stature, and in temperament having an excess of the moist and cold.’ Ptolemy believed not only that behavior patterns were influenced by the planet’s and the stars but also that questions of stature, complexion, national character and even congenital physical abnormalities were determined by the stars. On this point modern astrologers seem to have adopted a more cautious position.
  50. But modern astrologers have forgotten about the precession of the equinoxes, which Ptolemy understood. They ignore atmospheric refraction, about which Ptolemy wrote. They pay almost no attention to all the moons and planets, asteroids and comets, quasars and pulsars, exploding galaxies, symbiotic stars, cataclysmic variables and X­ray sources that have been discovered since Ptolemy’s time. Astronomy is a science ­ the study of the universe as it is. Astrology is a pseudoscience ­ a claim, in the absence of good evidence, that the other planets affect our everyday lives. In Ptolemy’s time the distinction between astronomy and astrology was not clear. Today it is.
  52. As an astronomer, Ptolemy named the stars, listed their brightnesses, gave good reasons for believing that the Earth is a sphere, set down rules for predicting eclipses and, perhaps most important, tried to understand why planets exhibit that strange, wandering motion against the background of distant constellations. He developed a predictive model to understand planetary motions and decode the message in the skies. The study of the heavens brought Ptolemy a kind of ecstasy. ‘Mortal as I am,’ he wrote, ‘I know that I am born for a day. But when I follow at my pleasure the serried multitude of the stars in their circular course, my feet no longer touch the Earth. . .’
  54. Ptolemy believed that the Earth was at the center of the universe; that the Sun, Moon, planets and stars went around the Earth. This is the most natural idea in the
  56.  world. The Earth seems steady, solid, immobile, while we can see the heavenly bodies rising and setting each day. Every culture has leaped to the geocentric hypothesis. As Johannes Kepler wrote, ‘It is therefore impossible that reason not previously instructed should imagine anything other than that the Earth is a kind of vast house with the vault of the sky placed on top of it; it is motionless and within it the Sun being so small passes from one region to another, like a bird wandering through the air.’ But how do we explain the apparent motion of the planets ­ Mars, for example, which had been known for thousands of years before Ptolemy’s time? (One of the epithets given Mars by the ancient Egyptians was sekded­ef em khetkhet, which means ‘who travels backwards,’ a clear reference to its retrograde or loop­the­loop apparent motion.) Ptolemy’s model of planetary motion can be represented by a little machine, like those that, serving a similar purpose, existed in Ptolemy’s time.* The problem was to figure out a ‘real’ motion of the planets, as seen from up there, on the ‘outside,’ which would reproduce with great accuracy the apparent motion of the planets, as seen from down here, on the ‘inside.’
  58. * 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.
  60. The planets were imagined to go around the Earth affixed to perfect transparent spheres. But they were not attached directly to the spheres, but indirectly, through a kind of off­center wheel. The sphere turns, the little wheel rotates, and, as seen from the Earth, Mars does its loop­the­loop. This model permitted reasonably accurate predictions of planetary motion, certainly good enough for the precision of measurement available in Ptolemy’s day, and even many centuries later. Ptolemy’s aetherial spheres, imagined in medieval times to be made of crystal, are why we still talk about the music of the spheres and a seventh heaven (there was a ‘heaven,’ or sphere for the Moon, Mercury, Venus, the Sun, Mars, Jupiter and Saturn, and one more for the stars). With the Earth the center of the Universe, with creation pivoted about terrestrial events, with the heavens imagined constructed on utterly unearthly principles, there was little motivation for astronomical observations. Supported by the Church through the Dark Ages, Ptolemy’s model helped prevent the advance of astronomy for a millennium. Finally, in 1543, a quite different hypothesis to explain the apparent motion of the planets was published by a Polish Catholic cleric named Nicholas Copernicus. Its most daring feature was the proposition that the Sun, not the Earth, was at the center of the universe. The Earth was demoted to just one of the planets, third from the Sun, moving in a perfect circular orbit. (Ptolemy had considered such a heliocentric model but rejected it immediately; from the physics of Aristotle, the implied violent rotation of the Earth seemed contrary to observation.) It worked at least as well as Ptolemy’s spheres in explaining the apparent motion of the planets. But it annoyed many people. In 1616 the Catholic Church placed Copernicus’ work on its list of forbidden books ‘until corrected’ by local ecclesiastical censors, where it remained until 1835.* Martin Luther described him as ‘an upstart astrologer . . . This fool wishes to reverse the entire science of astronomy. But Sacred Scripture tells us that Joshua commanded the Sun to stand still, and not the Earth.’ Even some of Copernicus’ admirers argued that he had not really believed in a Sun­centered universe but had merely proposed it as a convenience for calculating the motions of the planets.
  62.  * In a recent inventory of nearly every sixteenth­century 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.
  64. The epochal confrontation between the two views of the Cosmos ­ Earth­ centered and Sun­centered ­ reached a climax in the sixteenth and seventeenth centuries in the person of a man who was, like Ptolemy, both astrologer and astronomer. He lived in a time when the human spirit was fettered and the mind chained; when the ecclesiastical pronouncements of a millennium or two earlier on scientific matters were considered more reliable than contemporary findings made with techniques unavailable to the ancients; when deviations, even on arcane theological matters, from the prevailing doxological preferences, Catholic or Protestant, were punished by humiliation, taxation, exile, torture or death. The heavens were inhabited by angels, demons and the Hand of God, turning the planetary crystal spheres. Science was barren of the idea that underlying the phenomena of Nature might be the laws of physics. But the brave and lonely struggle of this man was to ignite the modern scientific revolution.
  66. Johannes Kepler was born in Germany in 1571 and sent as a boy to the Protestant seminary school in the provincial town of Maulbronn to be educated for the clergy. It was a kind of boot camp, training young minds in the use of theological weaponry against the fortress of Roman Catholicism. Kepler, stubborn, intelligent and fiercely independent, suffered two friendless years in bleak Maulbronn, becoming isolated and withdrawn, his thoughts devoted to his imagined unworthiness in the eyes of God. He repented a thousand sins no more wicked than another’s and despaired of ever attaining salvation.
  68. But God became for him more than a divine wrath craving propitiation. Kepler’s God was the creative power of the Cosmos. The boy’s curiosity conquered his fear. He wished to learn the eschatology of the world; he dared to contemplate the Mind of God. These dangerous visions, at first insubstantial as a memory, became a lifelong obsession. The hubristic longings of a child seminarian were to carry Europe out of the cloister of medieval thought.
  70. The sciences of classical antiquity had been silenced more than a thousand years before, but in the late Middle Ages some faint echoes of those voices, preserved by Arab scholars, began to insinuate themselves into the European educational curriculum. In Maulbronn, Kepler heard their reverberations, studying, besides theology, Greek and Latin, music and mathematics. In the geometry of Euclid he thought he glimpsed an image of perfection and cosmic glory. He was later to write: ‘Geometry existed before the Creation. It is co­eternal with the mind of God . . . Geometry provided God with a model for the Creation . . . Geometry is God Himself.’ In the midst of Kepler’s mathematical raptures, and despite his sequestered life, the imperfections of the outside world must also have molded his character. Superstition was a widely available nostrum for people powerless against the miseries of famine, pestilence and deadly doctrinal conflict. For many, the only certainty was the stars, and the ancient astrological conceit prospered in the courtyards and taverns of fear­haunted Europe. Kepler, whose attitude toward astrology remained ambiguous all his life, wondered whether there might be hidden patterns underlying the apparent chaos of daily life. If the world was crafted by God, should it not be examined closely? Was not all of creation an expression of the harmonies in the mind of God? The book of Nature had waited more than a millennium for a reader.
  72. In 1589, Kepler left Maulbronn to study for the clergy at the great university in Tübingen and found it a liberation. Confronted by the most vital intellectual currents of
  74.  the time, his genius was immediately recognized by his teachers ­ one of whom introduced the young man to the dangerous mysteries of the Copernican hypothesis. A heliocentric universe resonated with Kepler’s religious sense, and he embraced it with fervor. The Sun was a metaphor for God, around Whom all else revolves. Before he was to be ordained, he was made an attractive offer of secular employment, which ­ perhaps because he felt himself indifferently suited to an ecclesiastical career ­ he found himself accepting. He was summoned to Graz, in Austria, to teach secondary school mathematics, and began a little later to prepare astronomical and meteorological almanacs and to cast horoscopes. ‘God provides for every animal his means of sustenance,’ he wrote. ‘For the astronomer, He has provided astrology.’ Kepler was a brilliant thinker and a lucid writer, but he was a disaster as a classroom teacher. He mumbled. He digressed. He was at times utterly incomprehensible. He drew only a handful of students his first year at Graz; the next year there were none. He was distracted by an incessant interior clamor of associations and speculations vying for his attention. And one pleasant summer afternoon, deep in the interstices of one of his interminable lectures, he was visited by a revelation that was to alter radically the future of astronomy. Perhaps he stopped in mid­sentence. His inattentive students, longing for the end of the day, took little notice, I suspect, of the historic moment.
  76. There were only six planets known in Kepler’s time: Mercury, Venus, Earth, Mars, Jupiter and Saturn. Kepler wondered why only six? Why not twenty, or a hundred? Why did they have the spacing between their orbits that Copernicus had deduced? No one had ever asked such questions before. There were known to be five regular or ‘platonic’ solids, whose sides were regular polygons, as known to the ancient Greek mathematicians after the time of Pythagoras. Kepler thought the two numbers were connected, that the reason there were only six planets was because there were only five regular solids, and that these solids, inscribed or nested one within another, would specify the distances of the planets from the Sun. In these perfect forms, he believed he had recognized the invisible supporting structures for the spheres of the six planets. He called his revelation The Cosmic Mystery. The connection between the solids of Pythagoras and the disposition of the planets could admit but one explanation: the Hand of God, Geometer.
  78. Kepler was amazed that he ­ immersed, so he thought, in sin ­ should have been divinely chosen to make this great discovery. He submitted a proposal for a research grant to the Duke of Württemberg, offering to supervise the construction of his nested solids as a three­dimensional model so that others could glimpse the beauty of the holy geometry. It might, he added, be contrived of silver and precious stones and serve incidentally as a ducal chalice. The proposal was rejected with the kindly advice that he first construct a less expensive version out of paper, which he promptly attempted to do: ‘The intense pleasure I have received from this discovery can never be told in words . . . I shunned no calculation no matter how difficult. Days and nights I spent in mathematical labors, until I could see whether my hypothesis would agree with the orbits of Copernicus or whether my joy was to vanish into thin air.’ But no matter how hard he tried, the solids and the planetary orbits did not agree well. The elegance and grandeur of the theory, however, persuaded him that the observations must be in error, a conclusion drawn when the observations are unobliging by many other theorists in the history of science. There was then only one man in the world who had access to more accurate observations of apparent planetary positions, a self­exiled Danish nobleman who had accepted the post of Imperial Mathematician in the Court of the Holy Roman Emperor, Rudolf II. That man was Tycho Brahe. By chance, at Rudolf’s suggestion, he had just invited Kepler, whose mathematical fame was growing, to join
  80.  him in Prague. A provincial schoolteacher of humble origins, unknown to all but a few mathematicians, Kepler was diffident about Tycho’s offer. But the decision was made for him. In 1598, one of the many premonitory tremors of the coming Thirty Years’ War engulfed him. The local Catholic archduke, steadfast in dogmatic certainty, vowed he would rather ‘make a desert of the country than rule over heretics.’* Protestants were excluded from economic and political power, Kepler’s school was closed, and prayers, books and hymns deemed heretical were forbidden. Finally the townspeople were summoned to individual examinations on the soundness of their private religious convictions, those refusing to profess the Roman Catholic faith being fined a tenth of their income and, upon pain of death, exiled forever from Graz. Kepler chose exile: ‘Hypocrisy I have never learned. I am in earnest about faith. I do not play with it.’ * 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.’
  82. Leaving Graz, Kepler, his wife and stepdaughter set out on the difficult journey to Prague. Theirs was not a happy marriage. Chronically ill, having recently lost two young children, his wife was described as ‘stupid, sulking, lonely, melancholy.’ She had no understanding of her husband’s work and, having been raised among the minor rural gentry, she despised his impecunious profession. He for his part alternately admonished and ignored her, ‘for my studies sometimes made me thoughtless; but I learned my lesson, I learned to have patience with her. When I saw that she took my words to heart, I would rather have bitten my own finger than to give her further offense.’ But Kepler remained preoccupied with his work. He envisioned Tycho’s domain as a refuge from the evils of the time, as the place where his Cosmic Mystery would be confirmed. He aspired to become a colleague of the great Tycho Brahe, who for thirty­five years had devoted himself, before the invention of the telescope, to the measurement of a clockwork universe, ordered and precise. Kepler’s expectations were to be unfulfilled. Tycho himself was a flamboyant figure, festooned with a golden nose, the original having been lost in a student duel fought over who was the superior mathematician. Around him was a raucous entourage of assistants, sycophants, distant relatives and assorted hangers­on. Their endless revelry, their innuendoes and intrigues, their cruel mockery of the pious and scholarly country bumpkin depressed and saddened Kepler: ‘Tycho . . . is superlatively rich but knows not how to make use of it. Any single instrument of his costs more than my and my whole family’s fortunes put together.’ Impatient to see Tycho’s astronomical data, Kepler would be thrown only a few scraps at a time: ‘Tycho gave me no opportunity to share in his experiences. He would only, in the course of a meal and, in between other matters, mention, as if in passing, today the figure of the apogee of one planet, tomorrow the nodes of another . . . Tycho posesses the best observations . . . He also has collaborators. He lacks only the architect who would put all this to use.’ Tycho was the greatest observational genius of the age, and Kepler the greatest theoretician. Each knew that, alone, he would be unable to achieve the synthesis of an accurate and coherent world system, which they both felt to be imminent. But Tycho was not about to make a gift of his life’s work to a much younger potential rival. Joint authorship of the results, if any, of the collaboration was for some reason unacceptable. The birth of modern science ­ the offspring of theory and observation ­ teetered on the precipice of their mutual mistrust.
  84.  In the remaining eighteen months that Tycho was to live, the two quarreled and were reconciled repeatedly. At a dinner given by the Baron of Rosenberg, Tycho, having robustly drunk much wine, ‘placed civility ahead of health,’ and resisted his body’s urgings to leave, even if briefly, before the baron. The consequent urinary infection worsened when Tycho resolutely rejected advice to temper his eating and drinking. On his deathbed, Tycho bequeathed his observations to Kepler, and ‘on the last night of his gentle delirium, he repeated over and over again these words, like someone composing a poem: “Let me not seem to have lived in vain . . . Let me not seem to have lived in vain.” ’
  86. After Tycho’s death, Kepler, now the new Imperial Mathematician, managed to extract the observations from Tycho’s recalcitrant family. His conjecture that the orbits of the planets are circumscribed by the five platonic solids was no more supported by Tycho’s data than by Copernicus’. His ‘Cosmic Mystery’ was disproved entirely by the much later discoveries of the planets Uranus, Neptune and Pluto ­ there are no additional platonic solids* that would determine their distances from the Sun. The nested Pythagorean solids also made no allowance for the existence of the Earth’s moon, and Galileo’s discovery of the four large moons of Jupiter was also discomfiting. But far from becoming morose, Kepler wished to find additional satellites and wondered how many satellites each planet should have. He wrote to Galileo: ‘I immediately began to think how there could be any addition to the number of the planets without overturning my Mysterium Cosmographicum, according to which Euclid’s five regular solids do not allow more than six planets around the Sun . . . I am so far from disbelieving the existence of the four circumjovial planets that I long for a telescope, to anticipate you, if possible, in discovering two around Mars, as the proportion seems to require, six or eight round Saturn, and perhaps one each round Mercury and Venus.’ Mars does have two small moons, and a major geological feature on the larger of them is today called the Kepler Ridge in honor of this guess. But he was entirely mistaken about Saturn, Mercury and Venus, and Jupiter has many more moons than Galileo discovered. We still do not really know why there are only nine planets, more or less, and why they have the relative distances from the Sun that they do. (See Chapter 8.)
  88. * The proof of this statement can be found in Appendix 2.
  90. Tycho’s observations of the apparent motion of Mars and other planets through the constellations were made over a period of many years. These data, from the last few decades before the telescope was invented, were the most accurate that had yet been obtained. Kepler worked with a passionate intensity to understand them: What real motion of the Earth and Mars about the Sun could explain, to the precision of measurement, the apparent motion of Mars in the sky, including its retrograde loops through the background constellations? Tycho had commended Mars to Kepler because its apparent motion seemed most anomalous, most difficult to reconcile with an orbit made of circles. (To the reader who might be bored by his many calculations, he later wrote: ‘If you are wearied by this tedious procedure, take pity on me who carried out at least seventy trials.’)
  92. Pythagoras, in the sixth century B.C., Plato, Ptolemy and all the Christian astronomers before Kepler had assumed that the planets moved in circular paths. The circle was thought to be a ‘perfect’ geometrical shape and the planets, placed high in the heavens, away from earthly ‘corruption,’ were also thought to be in some mystical sense ‘perfect’ Galileo, Tycho and Copernicus were all committed to uniform circular
  94.  planetary motion, the latter asserting that ‘the mind shudders’ at the alternative, because ‘it would be unworthy to suppose such a thing in a Creation constituted in the best possible way.’ So at first Kepler tried to explain the observations by imagining that the Earth and Mars moved in circular orbits about the Sun. After three years of calculation, he believed he had found the correct values for a Martian circular orbit, which matched ten of Tycho’s observations within two minutes of arc. Now, there are 60 minutes of arc in an angular degree, and 90 degrees, a right angle, from the horizon to the zenith. So a few minutes of arc is a very small quantity to measure ­ especially without a telescope. It is one­fifteenth the angular diameter of the full Moon as seen from Earth. But Kepler’s replenishable ecstasy soon crumbled into gloom ­ because two of Tycho’s further observations were inconsistent with Kepler’s orbit, by as much as eight minutes of arc: Divine Providence granted us such a diligent observer in Tycho Brahe that his observations convicted this . . . calculation of an error of eight minutes; it is only right that we should accept God’s gift with a grateful mind . . . If I had believed that we could ignore these eight minutes, I would have patched up my hypothesis accordingly. But, since it was not permissible to ignore, those eight minutes pointed the road to a complete reformation in astronomy. The difference between a circular orbit and the true orbit could be distinguished only by precise measurement and a courageous acceptance of the facts: ‘The universe is stamped with the adornment of harmonic proportions, but harmonies must accommodate experience.’ Kepler was shaken at being compelled to abandon a circular orbit and to question his faith in the Divine Geometer. Having cleared the stable of astronomy of circles and spirals, he was left, he said, with ‘only a single cartful of dung,’ a stretched­out circle something like an oval.
  96. Eventually, Kepler came to feel that his fascination with the circle had been a delusion. The Earth was a planet, as Copernicus had said, and it was entirely obvious to Kepler that the Earth, wracked by wars, pestilence, famine and unhappiness, fell short of perfection. Kepler was one of the first people since antiquity to propose that the planets were material objects made of imperfect stuff like the Earth. And if planets were ‘imperfect,’ why not their orbits as well? He tried various oval­like curves, calculated away, made some arithmetical mistakes (which caused him at first to reject the correct answer) and months later in some desperation tried the formula for an ellipse, first codified in the Alexandrian Library by Apollonius of Perga. He found that it matched Tycho’s observations beautifully: ‘The truth of nature, which I had rejected and chased away, returned by stealth through the back door, disguising itself to be accepted . . . Ah, what a foolish bird I have been!’
  98. Kepler had found that Mars moves about the Sun not in a circle, but in an ellipse. The other planets have orbits much less elliptical than that of Mars, and if Tycho had urged him to study the motion of, say, Venus, Kepler might never have discovered the true orbits of the planets. In such an orbit the Sun is not at the center but is offset, at the focus of the ellipse. When a given planet is at its nearest to the Sun, it speeds up. When it is at its farthest, it slows down. Such motion is why we describe the planets as forever falling toward, but never reaching, the Sun. Kepler’s first law of planetary motion is simply this: A planet moves in an ellipse with the Sun at one focus. In uniform circular motion, an equal angle or fraction of the arc of a circle is covered in equal times. So, for example, it takes twice as long to go two­thirds of the way around a circle as it does to go one­third of the way around. Kepler found
  100.  something different for elliptical orbits: As the planet moves along its orbit, it sweeps out a little wedge­shaped area within the ellipse. When it is close to the Sun, in a given period of time it traces out a large arc in its orbit, but the area represented by that arc is not very large because the planet is then near the Sun. When the planet is far from the Sun, it covers a much smaller arc in the same period of time, but that arc corresponds to a bigger area because the Sun is now more distant. Kepler found that these two areas were precisely the same no matter how elliptical the orbit: the long skinny area, corresponding to the planet far from the Sun, and the shorter, squatter area, when the planet is close to the Sun, are exactly equal. This was Kepler’s second law of planetary motion: Planets sweep out equal areas in equal times. Kepler’s first two laws may seem a little remote and abstract: planets move in ellipses, and sweep out equal areas in equal times. Well, so what? Circular motion is easier to grasp. We might have a tendency to dismiss these laws as mere mathematical tinkering, something removed from everyday life. But these are the laws our planet obeys as we ourselves, glued by gravity to the surface of the Earth, hurtle through interplanetary space. We move in accord with laws of nature that Kepler first discovered. When we send spacecraft to the planets, when we observe double stars, when we examine the motion of distant galaxies; we find that throughout the universe Kepler’s laws are obeyed.
  102. Many years later, Kepler came upon his third and last law of planetary motion, a law that relates the motion of various planets to one another, that lays out correctly the clockwork of the solar system. He described it in a book called The Harmonies of the World. Kepler understood many things by the word harmony: the order and beauty of planetary motion, the existence of mathematical laws explaining that motion ­ an idea that goes back to Pythagoras ­ and even harmony in the musical sense, the ‘harmony of the spheres.’ Unlike the orbits of Mercury and Mars, the orbits of other planets depart so little from circularity that we cannot make out their true shapes even in an extremely accurate diagram. The Earth is our moving platform from which we observe the motion of the other planets against the backdrop of distant constellations. The inner planets move rapidly in their orbits ­ that is why Mercury has the name it does: Mercury was the messenger of the gods. Venus, Earth and Mars move progressively less rapidly about the Sun. The outer planets, such as Jupiter and Saturn, move stately and slow, as befits the kings of the gods.
  104. Kepler’s third or harmonic law states that the squares of the periods of the planets (the times for them to complete one orbit) are proportional to the cubes of their average distance from the Sun; the more distant the planet, the more slowly it moves, but according to a precise mathematical law: P 2 = a 3 , where P represents the period of revolution of the planet about the Sun, measured in years, and a the distance of the planet from the Sun measured in ‘astronomical units.’ An astronomical unit is the distance of the Earth from the Sun. Jupiter, for example, is five astronomical units from the Sun, and a 3 = 5 x 5 x 5 =125. What number times itself equals 125? Why, 11, close enough. And 11 years is the period for Jupiter to go once around the Sun. A similar argument applies for every planet and asteroid and comet. Not content merely to have extracted from Nature the laws of planetary motion, Kepler endeavored to find some still more fundamental underlying cause, some influence of the Sun on the kinematics of worlds. The planets sped up on approaching the Sun and slowed down on retreating from it. Somehow the distant planets sensed the Sun’s presence. Magnetism also was an influence felt at a distance, and in a stunning anticipation of the idea of universal gravitation, Kepler suggested that the underlying cause was akin to magnetism:
  106.  My aim in this is to show that the celestial machine is to be likened not to a divine organism but rather to a clockwork . . . , insofar as nearly all the manifold movements are carried out by means of a single, quite simple magnetic force, as in the case of a clockwork [where] all motions [are caused] by a simple weight.
  108. Magnetism is, of course, not the same as gravity, but Kepler’s fundamental innovation here is nothing short of breathtaking: he proposed that quantitative physical laws that apply to the Earth are also the underpinnings of quantitative physical laws that govern the heavens. It was the first nonmystical explanation of motion in the heavens; it made the Earth a province of the Cosmos. ‘Astronomy,’ he said ‘is part of physics.’ Kepler stood at a cusp in history; the last scientific astrologer was the first astrophysicist.
  110. Not given to quiet understatement, Kepler assessed his discoveries in these words: With this symphony of voices man can play through the eternity of time in less than an hour, and can taste in small measure the delight of God, the Supreme Artist . . . I yield freely to the sacred frenzy . . . the die is cast, and I am writing the book ­ to be read either now or by posterity, it matters not. It can wait a century for a reader, as God Himself has waited 6,000 years for a witness. Within the ‘symphony of voices,’ Kepler believed that the speed of each planet corresponds to certain notes in the Latinate musical scale popular in his day ­ do, re, mi, fa, sol, la, ti, do. He claimed that in the harmony of the spheres, the tones of Earth are fa and mi, that the Earth is forever humming fa and mi, and that they stand in a straightforward way for the Latin word for famine. He argued, not unsuccessfully, that the Earth was best described by that single doleful word. Exactly eight days after Kepler’s discovery of his third law, the incident that unleashed the Thirty Years’ War transpired in Prague. The war’s convulsions shattered the lives of millions, Kepler among them. He lost his wife and son to an epidemic carried by the soldiery, his royal patron was deposed, and he was excommunicated by the Lutheran Church for his uncompromising individualism on matters of doctrine. Kepler was a refugee once again. The conflict, portrayed by both the Catholics and the Protestants as a holy war, was more an exploitation of religious fanaticism by those hungry for land and power. In the past, wars had tended to be resolved when the belligerent princes had exhausted their resources. But now organized pillage was introduced as a means of keeping armies in the field. The savaged population of Europe stood helpless as plowshares and pruning hooks were literally beaten into swords and spears.*
  112. * Some examples are still to be seen in the Graz armory.
  114. Waves of rumor and paranoia swept through the countryside, enveloping especially the powerless. Among the many scapegoats chosen were elderly women living alone, who were charged with witchcraft. Kepler’s mother was carried away in the middle of the night in a laundry chest. In Kepler’s little hometown of Weil der Stadt, roughly three women were tortured and killed as witches every year between 1615 and 1629. And Katharina Kepler was a cantankerous old woman. She engaged in disputes that annoyed the local nobility, and she sold soporific and perhaps
  116.  hallucinogenic drugs as do contemporary Mexican curanderas. Poor Kepler believed that he himself had contributed to her arrest.
  118. It came about because Kepler wrote one of the first works of science fiction, intended to explain and popularize science. It was called the Somnium, ‘The Dream.’ He imagined a journey to the Moon, the space travelers standing on the lunar surface and observing the lovely planet Earth rotating slowly in the sky above them. By changing our perspective we can figure out how worlds work. In Kepler’s time one of the chief objections to the idea that the Earth turns was the fact that people do not feel the motion. In the Somnium he tried to make the rotation of the Earth plausible, dramatic, comprehensible: ‘As long as the multitude does not err .... I want to be on the side of the many. Therefore, I take great pains to explain to as many people as possible.’ (On another occasion he wrote in a letter, ‘Do not sentence me completely to the treadmill of mathematical calculations ­ leave me time for philosophical speculations, my sole delight.’*)
  120. * 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 Mechonica, 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.
  122. With the invention of the telescope, what Kepler called ‘lunar geography’ was becoming possible. In the Somnium, he described the Moon as filled with mountains and valleys and as ‘porous, as though dug through with hollows and continuous caves,’ a reference to the lunar craters Galileo had recently discovered with the first astronomical telescope. He also imagined that the Moon had its inhabitants, well adapted to the inclemencies of the local environment. He describes the slowly rotating Earth viewed from the lunar surface and imagines the continents and oceans of our planet to produce some associative image like the Man in the Moon. He pictures the near contact of southern Spain with North Africa at the Straits of Gibraltar as a young woman in a flowing dress about to kiss her lover ­ although rubbing noses looks more like it to me.
  124. Because of the length of the lunar day and night Kepler described ‘the great intemperateness of climate and the most violent alternation of extreme heat and cold on the Moon,’ which is entirely correct. Of course, he did not get everything right. He believed, for example, that there was a substantial lunar atmosphere and oceans and inhabitants. Most curious is his view of the origin of the lunar craters, which make the Moon, he says, ‘not dissimilar to the face of a boy disfigured with smallpox.’ He argued correctly that the craters are depressions rather than mounds. From his own observations he noted the ramparts surrounding many craters and the existence of central peaks. But he thought that their regular circular shape implied such a degree of order that only intelligent life could explain them. He did not realize that great rocks falling out of the sky would produce a local explosion, perfectly symmetric in all
  126.  directions, that would carve out a circular cavity ­ the origin of the bulk of the craters on the Moon and the other terrestrial planets. He deduced instead ‘the existence of some race rationally capable of constructing those hollows on the surface of the Moon. This race must have many individuals, so that one group puts one hollow to use while another group constructs another hollow.’ Against the view that such great construction projects were unlikely, Kepler offered as counterexamples the pyramids of Egypt and the Great Wall of China, which can, in fact, be seen today from Earth orbit. The idea that geometrical order reveals an underlying intelligence was central to Kepler’s life. His argument on the lunar craters is a clear foreshadowing of the Martian canal controversy (Chapter 5). It is striking that the observational search for extraterrestrial life began in the same generation as the invention of the telescope, and with the greatest theoretician of the age.
  128. 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.
  130. In the midst of other grave personal problems. Kepler rushed to Württemberg to find his seventy­four­year­old 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. Sky­bound was the mind, Earth­bound 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.
  132. The lifelong quest of Johannes Kepler, to understand the motions of the planets, to seek a harmony in the heavens, culminated thirty­six 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.
  134.  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 so­to­speak 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.
  136. 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.
  138. 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.
  140. In 1666, at the age of twenty­three, 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.
  142. Newton, in his mid­forties, 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.
  144.  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.
  146. * 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.’
  148. 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.
  150. 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 one­quarter as strong. If they are moved ten times farther away, the gravity is ten squared, 10 2 = 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 careering 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.
  152. 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.’
  154. 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 seventeenth­century 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.
  156.  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 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 fifty­fifth 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.
  158. 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.’
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