The Clockwork Universe Part 4

[image]

Jupiter and nearby mysterious objects, as seen by Galileo The answer, Galileo came to see, was that four objects were in orbit around Jupiter. "I have discovered four planets, neither known nor observed by any one of the astronomers before my time," Galileo crowed. (He hurried to name the moons in honor of Cosimo de' Medici, Grand Duke of Tuscany, who swallowed the bait with gusto.) Here was a planetary system in miniature, and not a diagram or a mathematical hypothesis but an observable reality. Jupiter's moons were mini-Earths moving in orbit around a central body. Why could not the Earth itself be in orbit around a huge central body? And if the Earth, why not the other planets, too?

These were exhilarating, disorienting discoveries. The unsuspected vistas revealed by the telescope inspired a fair number of seventeenth-century thinkers to rejoice at this proof that G.o.d's creation was truly without bounds. It was only fitting that an infinite G.o.d should have created an infinite universe. What could be "more splendid, glorious, and magnificent than for G.o.d to have made the universe commensurate with his own immensity?" asked the Royal Society's Joseph Glanvill.

The gates to the cosmos had been thrown open, and optimists ran through and turned cartwheels in the vastness. "When the heavens were a little blue arch stuck with stars, methought the universe was too strait and close," exulted the French writer Bernard de Fontenelle, in an immensely popular account of the new doctrines called On the Plurality of Worlds On the Plurality of Worlds. "I was almost stifled for want of air; but now it is enlarged in height and breadth and a thousand vortexes taken in. I begin to breathe with more freedom, and I think the universe to be incomparably more magnificent than it was before."24 But the endless expanses that beckoned so invitingly to some induced a kind of trembling agoraphobia in others. Pascal spoke for all who found themselves horrified by a vision of the planets as specks of dust adrift in a black immensity. "The eternal silence of these infinite s.p.a.ces frightens me," he observed, and he seemed to view humankind on its lonely voyage as akin to a ship's crew adrift in an endless sea. "What is a man in the midst of infinity?" Pascal asked.

Decades before, Copernicus's pushing of the Earth off center stage had inspired similar questions and similar fears, but among a smaller audience. Galileo had far more impact. Anyone could look through a telescope, while almost no one could follow a mathematical argument. But whether Copernicus or Galileo took the role of narrator, the story was the same. The Earth was not the center of the universe but a run-of-the-mill planet in a random corner of the cosmos.

This stripping away of Earth's special status is always cited as a great a.s.sault on human pride. Freud famously contended, for example, that in the course of modern history three thinkers had dealt enormous blows to humankind's self-esteem. The three were Copernicus, Darwin, and Freud himself. Darwin had proved that humans are animals, and Freud that we are blind to our own motivations. But the first body blow had come from Copernicus, who had displaced mankind from his place of honor.

Freud had a key piece of the story almost exactly backward. Before Copernicus and Galileo, humans had had believed that they lived at the center of the universe, but in their minds the center was a shameful, degraded place, not an exalted one. The Earth was lowly in every sense, at the furthest possible remove from the heavens. Man occupied "the filth and mire of the world," wrote Montaigne, "the worst, lowest, most lifeless part of the universe, the bottom story of the house." believed that they lived at the center of the universe, but in their minds the center was a shameful, degraded place, not an exalted one. The Earth was lowly in every sense, at the furthest possible remove from the heavens. Man occupied "the filth and mire of the world," wrote Montaigne, "the worst, lowest, most lifeless part of the universe, the bottom story of the house."

In the cosmic geography of the day, heaven and h.e.l.l were actual places. h.e.l.l was not consigned to some vague location "below" but sat deep inside the Earth with its center directly beneath Jerusalem. The Earth was the center of the universe, and h.e.l.l was the center of the center. Galileo's adversary Cardinal Bellarmine spelled out why that was so. "The place of devils and wicked d.a.m.ned men should be as far as possible from the place where angels and blessed men will be forever. The abode of the blessed (as our adversaries agree) is Heaven, and no place is further removed from Heaven than the center of the earth."

Mankind had always occupied a conspicuous place in the universe, in other words, but it was a dangerous and exposed position rather than a seat of honor. Theologians through the ages had thought well of that arrangement precisely because it did not not puff up human pride. Humility was a virtue, they taught, and a home set amid "filth and mire" was nearly certain to have humble occupants. puff up human pride. Humility was a virtue, they taught, and a home set amid "filth and mire" was nearly certain to have humble occupants.

In a sense, Copernicus had done mankind a favor. By moving the Earth to a less central locale, he had moved humankind farther from harm's way. For religious thinkers, ironically, this was yet another reason to object to the new doctrine. Theologians found themselves contemplating a riddle-how to keep humanity in its place when its place had moved?

In time, they would come up with an answer. They would seize on a different aspect of the new astronomy, the vast expansion in the size of the universe. If the universe was bigger, then man was smaller. For theologians in search of a way to reconcile themselves to science's new teachings, a doctrine that seemed to belittle mankind was welcome news.

Chapter Eighteen.

Flies as Big as a Lamb The microscope came along a bit later than the telescope, but its discovery produced just as much amazement. Here, too, were new worlds, and this time teeming with life! The greatest explorer of these new kingdoms was an unlikely conquistador, a Dutch merchant named Antonie van Leeuwenhoek. He seems to have begun tinkering with lenses with no grander ambition than to check for defects in swatches of cloth.

Leeuwenhoek quickly moved beyond fabric samples. Peering through microscopes he built himself-more like magnifying gla.s.ses than what we think of as microscopes-he witnessed scenes that no one else had ever imagined. In a frenzy of excitement, he dashed off letters to the Royal Society, hundreds altogether, describing the "secret world" he had found. He thrilled at the living creatures in a drop of water scooped from a puddle and then found he did not even have to venture outdoors to find teeming, complex life. He put his own saliva under the microscope and "saw, with great wonder, that in the said matter there were many very little living animalcules, very prettily a-moving. The biggest sort had a very strong and swift motion, and shot through the spittle like a pike does through the water."

Hooke had been experimenting with microscopes of his own design for years. Leeuwenhoek's microscopes yielded clearer images, but on November 15, 1677, Hooke reported that he, too, had seen a great number of "exceedingly small animals" swimming in a drop of water. And he had witnesses. Hooke rattled off a list: "Mr. Henshaw, Sir Christopher Wren, Sir John Hoskyns, Sir Jonas Moore, Dr. Mapletoft, Mr. Hill, Dr. Croone, Dr. Grew, Mr. Aubrey, and diverse others." The roll call of names highlights just how shocking these findings were. The microscope was so unfamiliar, and the prospect of a tiny, living, hitherto invisible world so astonishing, that even an eminent investigator like Hooke needed allies. It would be as if, in our day, Stephen Hawking turned a new sort of telescope to the heavens and saw UFOs flying in formation. Before he told the world, Hawking might coax other eminent figures to look for themselves.

But Hooke and the rest of the Royal Society could not catch Leeuwenhoek. Endlessly patient, omnivorously curious, and absurdly sharp-eyed, he racked up discovery after discovery.25 Sooner or later, everything-pond water, blood, plaque from his teeth-found its way to his microscope slides. Leeuwenhoek jumped up from his bed one night, "immediately after e.j.a.c.u.l.a.t.i.o.n before six beats of the pulse had intervened," and raced to his microscope. There he became the first person ever to see sperm cells. "More than a thousand were moving about in an amount of material the size of a grain of sand," he wrote in amazement, and "they were furnished with a thin tail, about five or six times as long as the body... and moved forward owing to the motion of their tails like that of a snake or an eel swimming in water." Sooner or later, everything-pond water, blood, plaque from his teeth-found its way to his microscope slides. Leeuwenhoek jumped up from his bed one night, "immediately after e.j.a.c.u.l.a.t.i.o.n before six beats of the pulse had intervened," and raced to his microscope. There he became the first person ever to see sperm cells. "More than a thousand were moving about in an amount of material the size of a grain of sand," he wrote in amazement, and "they were furnished with a thin tail, about five or six times as long as the body... and moved forward owing to the motion of their tails like that of a snake or an eel swimming in water."26 Leeuwenhoek hastened to a.s.sure the Royal Society that he had obtained his sample "after conjugal coitus" (rather than "by sinfully defiling myself"), but he did not discuss whether Mrs. Leeuwenhoek shared his fascination with scientific observation. Leeuwenhoek hastened to a.s.sure the Royal Society that he had obtained his sample "after conjugal coitus" (rather than "by sinfully defiling myself"), but he did not discuss whether Mrs. Leeuwenhoek shared his fascination with scientific observation.

No matter. Others did. Even Charles II delighted in peering through microscopes and witnessing life in miniature. "His Majesty seeing the little animals, contemplated them in astonishment and mentioned my name with great respect," Leeuwenhoek wrote proudly. This was a development almost as striking as Leeuwenhoek's findings themselves. In the new world of science, a merchant who had never attended a university and knew only Dutch, not Latin, could make discoveries that commanded the attention of a king.

Both the microscope and the telescope fascinated the seventeenth century's intelligentsia, not just its scientists. The telescope tended to produce unwelcome musings on man's puniness, as we have seen, but the picture of worlds within worlds revealed by the microscope did not trouble most people. Pascal was an exception. The endless descent into microworlds-"limbs with joints, veins in these limbs, blood in these veins, humors in this blood, globules in these humors, gases in these globules"-left him queasy and afraid. Many a ten-year-old has delighted in an imaginary outward zoom that plays Pascal's voyage in reverse: I live at 10 Glendale Road in the town of Marblehead in the county of Ess.e.x in the state of Ma.s.sachusetts in the United States of America on the planet Earth in the Milky Way galaxy. I live at 10 Glendale Road in the town of Marblehead in the county of Ess.e.x in the state of Ma.s.sachusetts in the United States of America on the planet Earth in the Milky Way galaxy. Pascal's inward journey shared the same rhythm, but the dread in his tone stood the child's exhilaration on its head. Pascal's inward journey shared the same rhythm, but the dread in his tone stood the child's exhilaration on its head.

Most people felt more fascination than fright, perhaps simply because we tend to feel powerful in proportion to our size. In any case, both telescope and microscope strengthened the case for G.o.d as designer. The ordinary world had already provided countless examples of G.o.d's craftsmanship. "Were men and beast made by fortuitous jumblings of atoms," Newton wrote contemptuously, "there would be many parts useless in them-here a lump of flesh, there a member too much." Now the microscope showed that G.o.d had done meticulous work even in secret realms that man had never known. Unlike those furniture makers, say, who lavished all their care on the front of their bureaus and desks but neglected surfaces destined to stay hidden, G.o.d had made every every detail perfect. detail perfect.

The heavens declared the glory of G.o.d, and so did fleas and flies and feathers. Man-made objects looked shoddy in comparison. Hooke examined the tip of a needle under a microscope, to test the aptness of the expression "as sharp as a Needle." He found not a perfect, polished surface but "large Hollows and Roughnesses, like those eaten in an Iron Bar by Rust and Length of Time." A printed dot on the page of a book told the same story. To the naked eye it looked "perfectly black and round," wrote Hooke, "but through the Magnifier it seemed grey, and quite irregular, like a great Splatch of London Dirt."

No features of the natural world were too humble to inspire rapt study. In some of the earliest experiments with microscopes, Galileo had tinkered with various designs. His astonishment reaches us across a gap four centuries wide. Galileo had seen "flies which look as big as a lamb," he told a French visitor, "and are covered all over with hair, and have very pointed nails by means of which they keep themselves up and walk on gla.s.s, although hanging feet upwards."

Many of the objects that came in for close examination were even less grand than houseflies. In April 1669 Hooke and the other members of the Royal Society gazed intently at a bit of fat and then at a moldy smear of bookbinder's paste, "which was found to have a fine moss growing on it." One early scientist who studied plants under the microscope marveled that "one who walks about with the meanest stick holds a piece of nature's handicraft which far surpa.s.ses the most elaborate... needlework in the world."

[image]

Robert Hooke's drawing of a fly's meticulously "designed" eyes Hooke published a lavish book called Micrographia Micrographia that featured such stunning ill.u.s.trations (by Hooke himself) as a twelve-by-eighteen-inch foldout engraving of a flea. The creature was, Hooke noted admiringly, "adorn'd with a curiously polish'd suit of sable Armour, neatly jointed." Another oversize ill.u.s.tration showed a fly's eyes, with some fourteen thousand facets or "pearls." Hooke went out of his way to justify lavishing attention on so lowly an insect. "There may be as much curiosity of contrivance and structure in every one of these Pearls, as in the eye of a Whale or Elephant," he wrote, and he noted that in any case G.o.d was surely up to such a task. "As one day and a thousand years are the same with him, so may one eye and ten thousand." that featured such stunning ill.u.s.trations (by Hooke himself) as a twelve-by-eighteen-inch foldout engraving of a flea. The creature was, Hooke noted admiringly, "adorn'd with a curiously polish'd suit of sable Armour, neatly jointed." Another oversize ill.u.s.tration showed a fly's eyes, with some fourteen thousand facets or "pearls." Hooke went out of his way to justify lavishing attention on so lowly an insect. "There may be as much curiosity of contrivance and structure in every one of these Pearls, as in the eye of a Whale or Elephant," he wrote, and he noted that in any case G.o.d was surely up to such a task. "As one day and a thousand years are the same with him, so may one eye and ten thousand."

Both telescope and microscope had opened up new worlds. The new vistas served to reinforce the belief that on every scale the universe was a flawless, harmonious, and unimaginably complex mechanism. G.o.d was a sculptor who could shape stars and planets and a craftsman with a delicacy of touch to shame the finest jeweler.

Chapter Nineteen.

From Earthworms to Angels If the thinkers of the seventeenth century had been content to see G.o.d as a superbly talented artist and craftsman, their homage might have taken a different form. Instead they looked at the marvelous sights revealed by the telescope and microscope and found new support for their favorite doctrine, that G.o.d was a mathematician.

They believed it already, thanks largely to their discoveries about the geometry of the cosmos, but they saw the new evidence as proving the case beyond the least possible doubt. In part this was because of the new sights themselves. Seen through the microscope, the least imposing objects revealed a geometer's shaping hand. One early scientist wrote an astonished hymn to grains of salt, which turned out to be "Cubes, Rhombs, Pyramids, Pentagons, Hexagons, Octagons" rendered "with a greater Mathematical Exactness than the most skilful Hand could draw them."

But the renewed emphasis on G.o.d-the-mathematician came mostly by way of a different, stranger path. One of the seventeenth century's most deeply held beliefs had to do with the so-called great chain of being. The central idea was that all the objects that had ever been created-grains of sand, chunks of gold, earthworms, lions, human beings, devils, angels-occupied a particular rank in a great chain that extended from the lowest of the low to the hem of G.o.d's garment. Nearby ranks blended almost insensibly into one another. Some fish had wings and flew into the air; some birds swam in the sea.

It was a fantastically elaborate system, though it strikes modern ears as more akin to a magical realist fantasy than a guide to everyday life. Purely by reasoning, the intellectuals of the seventeenth century believed, they could draw irrefutable conclusions about the makeup of the world. Angels, for example, were as real as oak trees. Since G.o.d himself had fashioned the great chain, it was necessarily perfect and could not be missing any links. So, just as there were countless creatures reaching downward downward from humans to the beasts, there had to be countless steps leading from humans to the beasts, there had to be countless steps leading upward upward from humans to G.o.d. QED. from humans to G.o.d. QED.

That made for a lot of angels. "We must believe that the angels are there in marvelous and inconceivable numbers," one scholar wrote, "because the honor of a king consists in the great crowd of his va.s.sals, while his disgrace or shame consists in their paucity. Thousands of thousands wait on the divine majesty and tenfold hundreds of millions join in his worship."

Each link had its proper place in the hierarchy, king above n.o.ble above commoner, husband above wife above child, dog above cat, worm above oyster. The lion was king of beasts, but every every domain had a "king": the eagle among birds, the rose among flowers, the monarch among humans, the sun among the stars. The various kingdoms themselves had specific ranks, too, some lower and some higher-stones, which are lifeless, ranked lower than plants, which ranked lower than sh.e.l.lfish, which ranked lower than mammals, which ranked lower than angels, with innumerable other kingdoms filling all the ranks in between. domain had a "king": the eagle among birds, the rose among flowers, the monarch among humans, the sun among the stars. The various kingdoms themselves had specific ranks, too, some lower and some higher-stones, which are lifeless, ranked lower than plants, which ranked lower than sh.e.l.lfish, which ranked lower than mammals, which ranked lower than angels, with innumerable other kingdoms filling all the ranks in between.

In a hierarchical world, the doctrine had enormous intuitive appeal. Those well placed in the pecking order embraced it, unsurprisingly, but even those stuck far from the top made a virtue of "knowing one's place." Almost without exception, scholars and intellectuals endorsed the doctrine of the all-embracing, immutable great chain. To say that things might be different was to suggest that they could be better. This struck nearly everyone as both misguided-to attack the natural order was to shake one's fist at the tide-and blasphemous. Since G.o.d was an infinitely powerful creator, the world necessarily contained all possible things arranged in the best possible way. Otherwise He might have done more or done better, and who would presume to venture such a criticism?

As usual, Alexander Pope summarized conventional wisdom in a few succinct words. No one ever had less reason to endorse the status quo than Pope, a hunchbacked, dwarfish figure who lived in constant pain. He strapped himself each day into a kind of metal cage to hold himself upright. Then he took up his pen and composed perfectly balanced couplets on the theme that G.o.d has His reasons, which we limited beings cannot fathom. "Whatever is, is right."

The great chain had a long pedigree, and from the beginning the idea that the world was jam-packed had been as important as the idea that it was orderly. Plato had decreed that "nothing incomplete is beautiful," as if the world were a stamp alb.u.m and any gap in the collection an affront. By the 1600s this view had long since hardened into dogma. If it was possible to do something, G.o.d would do it. Otherwise He would be selling himself short. Today the cliche has it that we use only 10 percent of our brains. For a thousand years philosophers and naturalists wrote as if to absolve G.o.d from that charge. "The work of the creator would have been incomplete if aught could be added to it," one French scientist declared blithely. "He has made all the vegetable species which could exist. All the minute gradations of animality are filled with as many beings as they can contain."

This was also the reason, thinkers of the day felt certain, that G.o.d had created countless stars and planets where the naked eye saw only the blackness of s.p.a.ce. G.o.d had created infinitely many worlds, one theologian and Royal Society member explained, because only a populous universe was "worthy of an infinite CREATOR, whose Power Power and and Wisdom Wisdom are without bounds and measures." are without bounds and measures."

But why did that all-powerful creator have to be a mathematician? Gottfried Leibniz, the German philosopher who took all knowledge as his domain, made the case most vigorously. The notion of a brim-full universe provided Leibniz the opening he needed. Leibniz was as restless as he was brilliant, and, perhaps predictably, he believed in an exuberantly creative G.o.d. "We must say that G.o.d makes the greatest number of things that he can," Leibniz declared, because "wisdom requires variety."

Leibniz immediately proceeded to demonstrate his own wisdom by making the same point in half a dozen varied ways. Even if you were wealthy beyond measure, Leibniz asked, would you choose "to have a thousand well-bound copies of Virgil in your library"? "To have only golden cups"? "To have all your b.u.t.tons made of diamonds"? "To eat only partridges and to drink only the wine of Hungary or of Shiraz"?

Now Leibniz had nearly finished. Since G.o.d loved variety, the only question was how He could best ensure it. "To find room for as many things as it is possible to place together," wrote Leibniz, G.o.d would employ the fewest and simplest laws of nature. That That was why the laws of nature could be written so compactly and why they took mathematical form. "If G.o.d had made use of other laws, it would be as if one should construct a building of round stones, which leave more s.p.a.ce unoccupied than that which they fill." was why the laws of nature could be written so compactly and why they took mathematical form. "If G.o.d had made use of other laws, it would be as if one should construct a building of round stones, which leave more s.p.a.ce unoccupied than that which they fill."

So the universe was perfectly ordered, impeccably rational, and governed by a tiny number of simple laws. It was not enough to a.s.sert a.s.sert that G.o.d was a mathematician. The seventeenth century's great thinkers felt they had done more. They had proved it. that G.o.d was a mathematician. The seventeenth century's great thinkers felt they had done more. They had proved it.

The scientists of the 1600s felt that they had come to their view of G.o.d by way of argument and observation. But they were hardly a skeptical jury, and their argument, which seemed so compelling to its original audience, sounds like special pleading today. Galileo, Newton, Leibniz, and their peers leaped to the conclusion that G.o.d was a mathematician largely because they they were mathematicians-the aspects of the world that intrigued them were those that could be captured in mathematics. Galileo found that falling objects obey mathematical laws and proclaimed that were mathematicians-the aspects of the world that intrigued them were those that could be captured in mathematics. Galileo found that falling objects obey mathematical laws and proclaimed that everything everything does. The book of nature is written in the language of mathematics, he wrote, "and the characters are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth." does. The book of nature is written in the language of mathematics, he wrote, "and the characters are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth."

The early scientists took their own deepest beliefs and ascribed them to nature. "Nature is pleased with simplicity," Newton declared, "and affects not the pomp of superfluous causes." Leibniz took up the same theme. "It is impossible that G.o.d, being the most perfect mind, would not love perfect harmony," he wrote, and he and many others happily spelled out different features of that harmony. "G.o.d always complies with the easiest and simplest rules," Galileo a.s.serted.

"Nature does not make jumps," Leibniz maintained, just as Einstein would later insist that "G.o.d does not play dice with the universe." We attribute to G.o.d those traits we most value. "If triangles had a G.o.d," Montesquieu would write a few decades later, "he would have three sides."

Newton and the others would have scoffed at such a notion. They were describing G.o.d's creation, not their own. Centuries later, a cla.s.sically minded revolutionary like Einstein would still hold to the same view. In an essay on laws of nature, the mathematician Jacob Bronowski wrote about Einstein's approach to science. "Einstein was a man who could ask immensely simple questions," Bronowski observed, "and what his life showed, and his work, is that when the answers are simple too, then you hear G.o.d thinking."

For a modern-day scientist like Bronowski, this was a rhetorical flourish. Galileo, Newton, and the other great men of the seventeenth century could have expressed the identical thought, and they would have meant it literally.

Chapter Twenty.

The Parade of the Horribles When Galileo and Newton looked at nature, they saw simplicity. That was, they declared, G.o.d's telltale signature. When their biologist colleagues looked at nature, they saw endless variety. That was, they announced, G.o.d's telltale signature.

Each side happily cited one example after another. The physicists pointed out that as the planets circle the sun, for instance, they all travel in the same direction and in the same plane. The biologists presented their own eloquent case, notably in a large and acclaimed book t.i.tled The Wisdom of G.o.d Manifested in the Works of Creation. The Wisdom of G.o.d Manifested in the Works of Creation. The "vast Mult.i.tude of different Sorts of Creatures" testified to G.o.d's merits, the naturalist John Ray argued, just as it would show more skill in a manufacturer if he could fashion not simply one product but "Clocks and Watches, and Pumps, and Mills and [Grenades] and Rockets." The "vast Mult.i.tude of different Sorts of Creatures" testified to G.o.d's merits, the naturalist John Ray argued, just as it would show more skill in a manufacturer if he could fashion not simply one product but "Clocks and Watches, and Pumps, and Mills and [Grenades] and Rockets."

Strikingly, no one saw any contradiction in the views of the two camps. In part this reflected a division of labor. The physicists focused on the elegance of G.o.d's aesthetics, the biologists on the range of His inventiveness. Both sides were bound by the shared conviction, deeper than any possible division, that G.o.d had designed every feature of the universe. For the physicists, that view led directly to the idea that G.o.d was a mathematician, and progress. For biologists, it led down a blind alley and made the discovery of evolution impossible.

Two centuries pa.s.sed between Newton's theory of gravity and Darwin's theory of evolution. How could that be? Newton's work bristled with mathematics and focused on remote, unfamiliar objects like planets and comets. Darwin's theory of evolution dealt in ordinary words with ordinary things like pigeons and barnacles. "How extremely stupid not to have thought of that!" Thomas Huxley famously grumbled after first reading Darwin's Origin of Species. Origin of Species. No one ever scolded himself for not beating Newton to the No one ever scolded himself for not beating Newton to the Principia. Principia.

The "easier" theory proved harder to find because it required abandoning the idea of G.o.d the designer. Newton and his contemporaries never for a moment considered rejecting the notion of design. The premise at the heart of evolution is that living creatures have inborn, random differences; some of those random variations happen to provide an advantage in the struggle for life, and nature favors those variations. That focus on randomness was unthinkable in the seventeenth century. Even Voltaire, the greatest skeptic of his day, took for granted that where there was a design, there was a designer. No thinker of that age, no matter how brilliant, could imagine an alternative. "It is natural to admit the existence of a G.o.d as soon as one opens one's eyes," Voltaire wrote. "It is by virtue of an admirable art that all the planets dance round the sun. Animals, vegetables, minerals-everything is ordered with proportion, number, movement. n.o.body can doubt that a painted landscape or drawn animals are works of skilled artists. Could copies possibly spring from an intelligence and the originals not?"

Newton, blinded by his faith in intelligent design, argued in the same vein. In a world where randomness was a possibility, he scoffed, we'd be beset with every variety of jury-rigged, misshapen creature. "Some kinds of beasts might have had but one eye, some more than two."

The problem was not simply that for Newton and the others "randomness" conveyed all the horror of "anarchy." Two related beliefs helped rule out any possibility of a seventeenth-century Darwin. The first was the a.s.sumption that every feature of the world had been put there for man's benefit. Every plant, every animal, every rock existed to serve us. The world contained wood, the Cambridge philosopher Henry More explained, because otherwise human houses would have been only "a bigger sort of beehives or birds' nests, made of contemptible sticks and straw and dirty mortar." It contained metal so that men could a.s.sault one another with swords and guns, rather than sticks, as they enjoyed the "glory and pomp" of war.

The second a.s.sumption that blinded Newton and his contemporaries to evolution was the idea that the universe was almost brand-new. The Bible put creation at a mere six thousand years in the past. Even if someone had conceived of an evolving natural world, that tiny span of time would not have offered enough elbow room. Small changes could only transform one-celled creatures into daffodils and dinosaurs if nature had eons to work with. Instead, seventeenth-century scientists took for granted that trees and fish, men and women, dogs and flowers all appeared full-blown, in precisely the form they have today.

Two hundred years later, scientists still clung to the same idea. In the words of Louis Aga.s.siz, Darwin's great Victorian rival, each species was "a thought of G.o.d."

Chapter Twenty-One.

"Shuddering Before the Beautiful"

The seventeenth century's faith that "all things are numbers" originated in ancient Greece, like so much else. The Greek belief in mathematics as nature's secret language began with music, which was seen not as a mere diversion but as a subject for the most intense study. Music was the great exception to the general rule that the Greeks preferred to keep mathematics untainted by any connection with the everyday world.

Pluck a taut string and it sounds a note. Pluck a second string twice as long as the first, Pythagoras found, and the two notes are an octave apart. Strings whose lengths form other simple ratios, like 3 to 2, sound other harmonious intervals.27 That insight, the physicist Werner Heisenberg would say thousands of years later, was "one of the truly momentous discoveries in the history of mankind." That insight, the physicist Werner Heisenberg would say thousands of years later, was "one of the truly momentous discoveries in the history of mankind."

Pythagoras believed, too, that certain numbers had mystical properties. The world was composed of four elements because 4 was a special number. Such notions never lost their hold. Almost a thousand years after Pythagoras, St. Augustine explained that G.o.d had created the world in six days because 6 is a "perfect" number. (In other words, 6 can be written as the sum of the numbers that divide into it exactly: 6 = 1 + 2 + 3.)28 The Greeks felt sure that nature shared their fondness for geometry. Aim a beam of light at a mirror, for example, and it bounces off the mirror at the same angle it made on its incoming path. (Every pool player knows that a ball hit off a cushion follows the same rule.) [image]

When light bounces off a mirror, the two marked angles are equal.

What looked like a small observation about certain angles turned out to have a big payoff-of the infinitely many paths that the light beam might take on its journey from a a to a mirror to to a mirror to b b, the path it actually does take is the shortest one possible. And there's more. Since light travels through the air at a constant speed, the shortest shortest of all possible paths is also the of all possible paths is also the fastest fastest.

Even if light obeyed a mathematical rule, the rule might have been messy and complicated. But it wasn't. Light operated in the most efficient, least wasteful way possible. This was so even in less straightforward circ.u.mstances. Light travels at different speeds in different mediums, for instance, and faster in air than in water. When it pa.s.ses from one medium to another, it bends.

Look at the drawing below and imagine a lifeguard at a a rather than a flashlight. If a lifeguard standing on the beach at rather than a flashlight. If a lifeguard standing on the beach at a a sees a person drowning at sees a person drowning at b b, where should she run into the water? It's tricky, because she's much slower in the water than on land. Should she run straight toward the drowning man? Straight to a point at the water's edge directly in front of the flailing man?

[image]

Light bends as it pa.s.ses from air into water.

Curiously, this riddle isn't in the least tricky for light, which "knows" exactly the quickest path to take. "Light acts like the perfect lifeguard," physicists say, and over the centuries they've formulated a number of statements about nature's efficiency, not just to do with light but far more generally. The eighteenth-century mathematician who formulated one such principle proclaimed it, in the words of the historian Morris Kline, "the first scientific proof of the existence and wisdom of G.o.d."

Light's remarkable behavior was only one example of the seventeenth century's favorite discovery, that if a mathematical idea was beautiful it was virtually guaranteed to be useful. Scientists ever since Galileo and Newton have continued to find mysterious mathematical connections in the most unlikely venues. "You must have felt this, too," remarked the physicist Werner Heisenberg, in a conversation with Einstein: "the almost frightening simplicity and wholeness of the relationships which nature suddenly spreads out before us and for which none of us was in the least prepared."

For the mathematically minded, the notion of glimpsing G.o.d's plan has always exerted a hypnotic pull. The seduction is twofold. On the one hand, delving into the world's mathematical secrets gives a feeling of having one's hands on nature's beating heart; on the other, in a world of chaos and disaster, mathematics provides a refuge of eternal, unchallengeable truths and perfect order.

The intellectual challenge is immense, and the difficulty of the task makes the pursuit even more obsessive. In Vladimir Nabokov's novel The Defense The Defense, Aleksandr Luzhin is a chess grand master. He speaks of chess in just the way that mathematicians think of their field. While pondering a move and lighting a cigarette, Luzhin accidentally burns his fingers. "The pain immediately pa.s.sed, but in the fiery gap he had seen something unbearably awesome-the full horror of the abysmal depths of chess. He glanced at the chessboard, and his brain wilted from unprecedented weariness. But the chessmen were pitiless; they held and absorbed him. There was horror in this, but in this also was the sole harmony, for what else exists in the world besides chess?"

Mathematicians and physicists share that pa.s.sion, and unlike chess players they take for granted that they are grappling with nature's deepest secrets. (The theoretical physicist Subrahmanyan Chandrasekhar, a pioneer in the study of black holes, spoke of "shuddering before the beautiful.") They sustain themselves through the empty years with the unshakable belief that the answer is out there, waiting to be found. But mathematics is a cruel mistress, indifferent to the suffering of those who would woo her. Only those who themselves have wandered lost, wrote Einstein, know the misery and joy of "the years of searching in the dark for a truth that one feels but cannot express; the intense desire and the alternations of confidence and misgiving, until one breaks through to clarity and understanding."

The abstract truths that enticed Einstein and his fellow scientists occupy a realm separate from the ordinary world. That gulf between the everyday world and the mathematical one has, many times through the centuries, served as a lure rather than a barrier. When he was a melancholy sixteen-year-old, the modern-day philosopher and mathematician Bertrand Russell recalled many years later, he used to go for solitary walks "to watch the sunset and contemplate suicide. I did not, however, commit suicide, because I wished to know more of mathematics."

A deep dive into mathematics has special appeal, for it serves at the same time as a way to flee the world and to impose order on it. "Of all escapes from reality," the mathematician Gian-Carlo Rota observed, "mathematics is the most successful ever.... All other escapes-s.e.x, drugs, hobbies, whatever-are ephemeral by comparison." Mathematicians have withdrawn from the dirty, dangerous world, they believe, and then, by thought alone, they have added new facts to the world's store of knowledge. Not just new facts, moreover, but facts that will stand forever, unchallengeable. "The certainty that [a mathematician's] creations will endure," wrote Rota, "renews his confidence as no other pursuit." It is heady, seductive business.

Perhaps this accounts for the eagerness of so many seventeenth-century intellectuals to look past the wars and epidemics all around them and instead to focus on the quest for perfect, abstract order. Johannes Kepler, the great astronomer, barely escaped the religious battles later dubbed the Thirty Years' War. One close colleague was drawn and quartered and then had his tongue cut out. For a decade his head, impaled on a pike, stood on public display next to the rotting skulls of other "traitors."

Kepler came from a village in Germany where dozens of women had been burned as witches during his lifetime. His mother was charged with witchcraft and, at age seventy-four, chained and imprisoned while awaiting trial. She had poisoned a neighbor's drink; she had asked a grave digger for her father's skull, to make a drinking goblet; she had bewitched a villager's cattle. Kepler spent six years defending her while finishing work on a book called The Harmony of the World. The Harmony of the World. "When the storm rages and the shipwreck of the state threatens," he wrote, "we can do nothing more worthy than to sink the anchor of our peaceful studies into the ground of eternity." "When the storm rages and the shipwreck of the state threatens," he wrote, "we can do nothing more worthy than to sink the anchor of our peaceful studies into the ground of eternity."

Chapter Twenty-Two.

Patterns Made with Ideas For the Greeks, the word mathematics mathematics had vastly different a.s.sociations than it does for most of us. Mathematics had almost nothing to do with adding up columns of numbers or figuring out how long it would take Bob and Tom working together to paint a room. The aim of mathematics was to find eternal truths-insights into the abstract architecture of the world-and then to prove their validity. "A mathematician, like a painter or poet, is a maker of patterns," wrote G. H. Hardy, an acclaimed twentieth-century mathematician and an ardent proponent of the Greek view. "If his patterns are more permanent than theirs, it is because they are made with ideas." had vastly different a.s.sociations than it does for most of us. Mathematics had almost nothing to do with adding up columns of numbers or figuring out how long it would take Bob and Tom working together to paint a room. The aim of mathematics was to find eternal truths-insights into the abstract architecture of the world-and then to prove their validity. "A mathematician, like a painter or poet, is a maker of patterns," wrote G. H. Hardy, an acclaimed twentieth-century mathematician and an ardent proponent of the Greek view. "If his patterns are more permanent than theirs, it is because they are made with ideas."

Let's take a few minutes to look at the kind of thing Greek mathematicians accomplished, because it was their example-and the way they interpreted their success-that inspired their intellectual descendants in the seventeenth century. (One of Newton's a.s.sistants could recall only one occasion when he had seen Newton laugh. Someone had made the mistake of asking Newton what use it was to study Euclid, "upon which Sir Isaac was very merry.") The Greeks had looked for their "permanent patterns" in the world of mathematics. Seventeenth-century scientists set out with the same goal except that they expanded their quest to the world at large.

They found mathematics on all sides. When Isaac Newton directed a beam of light through a prism, he marveled at the rainbow on his wall. No one could miss either the beauty or the order in that familiar spectacle, but it was the interplay between the two that so intrigued Newton. "A naturalist would scarce expect to see ye science of those colours become mathematicall," he wrote, "and yet I dare affirm that there is as much certainty in it as in any other part of Opticks."

For the Greeks the notion of "proof"-not a claim or a likelihood but actual proof beyond a doubt-was fundamental. A proof in mathematics is a demonstration or an argument. It starts with a.s.sumptions and moves, step by step, to a conclusion. But unlike ordinary arguments-who was the greatest president? who makes the best pizza in Brooklyn?-mathematical arguments yield irrefutable, permanent, universally acknowledged truths. Of all the shapes you can make with a piece of string Of all the shapes you can make with a piece of string, a circle encloses the biggest area. a circle encloses the biggest area. The list of prime numbers never ends. The list of prime numbers never ends.29 If three points aren't in a straight line If three points aren't in a straight line, there is a circle that pa.s.ses through all three. there is a circle that pa.s.ses through all three. Everyone who can follow the argument sees that it must be so. Everyone who can follow the argument sees that it must be so.

Like other arguments, proofs come in many varieties. Mathematicians have individual, recognizable styles, just as composers and painters and tennis players do. Some think in pictures, others in numbers and symbols. The Greeks preferred to think pictorially. Take the Pythagorean theorem, for instance, perhaps the most famous theorem of them all. The theorem involves a right triangle-a triangle where one angle is 90 degrees-and relates the lengths of the various sides. In the simplest right triangle, one side is 3, another 4, and the longest 5. Many centuries before the birth of Christ, some unknown genius stared at those numbers-3, 4, 5-and saw something that astonished him.

It's easy to draw a triangle with a side 3 inches long and a side 4 inches long and a third side that's short (at left, below), or a triangle with a side 3 inches long and a side 4 inches long and a third side that's long (at right, below). But if the angle between the 3-inch side and the 4-inch one is not just any angle but 90 degrees, then the length of the third side turns out to be precisely 5. So the puzzle pieces that our unknown genius turned over and over in his mind were these: 3, 4, 5, 90 degrees. What tied those numbers together?

[image]

No doubt he drew endless right triangles and measured the sides. Nearly always the longest side would be a seemingly random number, no matter how carefully the two short sides were chosen. Even in the simplest case-a triangle where the two short sides were both 1 inch long-the third side didn't look simple at all. A shade more than 1 inches, not even anything that lined up with the divisions on a ruler.

Perhaps he stuck with his experiments long enough to draw the right triangle with short sides 5 and 12. Set a ruler in place to draw the third side and then measure it. Success at last-the long side is precisely 13 inches long, so here is another right triangle with all three sides respectable whole numbers.