God In The Equation Page 3

  If the sphere of stars defines the outer limits of existence, as Aristotle argued, then it must have a definite extent. Thus Greek cosmology initiated a new way to evaluate the extent of God's glory, calculating the size of the universe. The answer depends on the number of spheres and on how tightly the various spheres could be packed together. Efficient packing became a lot more difficult when Claudius Ptolemaeus, better known as Ptolemy, attached small secondary circular motions onto the large circles marked out by the planets as they moved across the sky. These “epicycles” required considerable maneuvering room between spheres. Epicycles further compromised the geometric elegance of Eudoxus' system, but they did do a much better job at predicting planetary motions. The Islamic astronomer al-Farghani, writing in the ninth century B.C., estimated the minimum possible size for the solar system assuming all the parts were arranged as compactly as possible. By his reasoning, Saturn lies at a distance of about twenty thousand Earth radii, or about eighty million miles. He was off by just a factor of ten, which has to count as a major coincidence considering he was working from an entirely erroneous model.

  But what if the Earth circles the sun rather than the other way around? The Pythagoreans had proposed that fire, not earth, should lie at the center. Although Aristotle had derided the idea, Aristarchus of Samos went further and proposed a sun-centered universe around 280 B.C. This heliocentric, or sun-centered, model did not attract much of a following at the time, as it seemed to contradict both logic and common sense. Even the most casual sky gazer knows that the stars appear immobile relative to one another throughout the year. As long as the Earth is motionless, there is no problem. In fact, the unchanging appearance of the stars was one of Aristotle's key arguments that the Earth does not move. If the Earth swings around the sun, however, its change in position must slightly distort the constellations and make some stars appear to grow brighter and dimmer over the course of the year. No such variations are seen, so either the heliocentric model is wrong or else the distances to the stars are enormous compared with the size of the Earth's orbit around the sun. It is hard to fault the ancient Greeks for failing to appreciate the vast gulf between the planets and the starry firmament. Astronomers now know that the nearest star, a faint red sun named Proxima Centauri, lies some 267,000 times farther away than the sun; its apparent back-and-forth motion is 300 times too small to be seen by the naked eye. The incredible emptiness of empty space is why perspective effects are completely invisible.

  So the Aristotelian system reigned supreme in the Western world, refined by Islamic astronomers and reiterated in the teachings of medieval universities, until it faced an unlikely challenger, a Polish scholar named Nicolaus Copernicus. Around 1510, Copernicus resurrected the sun-centered universe in an unpublished work, Commentariolus, which he shared with a few friends. He developed these ideas at much greater length in his book De Revolutionibus, published shortly before his death in 1543. He had delayed making his views publicly known, fearing that it would arouse the wrath of the Catholic Church: after all, Joshua commanded the sun, not the Earth, to stop moving during his battle at Jericho. But Copernicus was no iconoclast, at least not an intentional one.

  As a sign of faith, Copernicus dedicated his book to Pope Paul III and preemptively defended his ideas against rabble-rousers who would quote the Bible to attack ideas that, he believed, lay outside the bounds of religion. “If there should chance to be any mathematicians who, ignorant in mathematics yet pretending to skill in that science, should dare, upon the authority of some passage of Scripture wrested to their purpose, to condemn and censure my hypothesis, I value them not, and scorn their inconsiderate judgment,” he wrote. And, like his predecessors, he bowed before the majesty of the sphere and believed Plato's dictum that the planets followed uniform circular motion. But he wasn't satisfied with the philosophy or the aesthetics of the geocentric arrangement of the heavens. By placing the sun in the middle, Copernicus eliminated some of the unappealing epicycles from Ptolemy's cosmic model. He also created a more unified scheme by giving Mercury and Venus full orbits around the sun, granting them equal status with the other planets. In the Earth-centered models, these two were customarily constrained in their motions to explain why they always appear close to the sun in the sky. Moreover, the heliocentric system dispensed with the variable motions introduced by Ptolemy, so Copernicus could even claim that he was trying to return to the uniformity that was a hallmark of Aristotle's physics.

  Still, all of these arguments couldn't disguise the Copernican system's radical perspective on the place of humanity in the universe. By locating the sun at the center, Copernicus removed us from a specially privileged location and declared that logic trumped the needs of religion or philosophy. In what could be considered compensation, he placed us in motion among the celestial spheres, twining our destiny more closely with that of the stars. No longer was the earthly realm distinct from the ether. Now, studying the physical nature of the Earth offered the possibility of insight into the cosmic spheres, as both participated in the same circular dance. And while putting the sun at the middle shrank the sizes of the planetary orbits—the distance to Saturn in this new scheme was about forty million miles—the stars now had to be incredibly far away in order to appear motionless. In fact, the rotation of the Earth eliminated entirely the need for a finite sphere of fixed stars rotating once every twenty-four hours. It was quite possible, Copernicus reflected, that the universe could be boundless.

  Centuries earlier, Saint Augustine had warned that the church should not endorse theories of the material world, lest it find itself on the losing end of the argument. All the same, prominent Catholic theologians and Protestant leaders, including both Pope Paul V and Martin Luther, argued against Copernicus. The church was hardly alone in rejecting any change in scientific tradition. Aristotelian philosophers recoiled from the Copernican system, and Tycho Brahe, probably the greatest observational astronomer in the pretelescopic era, dismissed it as absurd. They found it hard to let go of the spiritual and philosophical certainty of a known scientific system. Copernicus remained true to the cult of the circle, but his view of the universe contained a baffling new mystical element that we would now call inertia. In the heliocentric model, the Earth is constantly on the move. What propels it? And why then don't we all fly off? By setting the Earth in motion, Copernicus eliminated the heavenly ether as the propulsive force. He had to assume that some unknown factor keeps the universe running in smooth harmony.

  Despite the reactionary responses to Copernicus, the scientific assault on the cosmos advanced sharply within a single lifetime. In 1609, Galileo Galilei turned his crude spyglasses skyward and witnessed sight after sight that didn't accord with the church-sanctioned cosmology. His discoveries are now part of every student's education, a triumphant retelling of the rise of the sci/religious faith during a time when it was surrounded by nonbelievers. Galileo saw that Jupiter is attended by four little stars—the satellites lo, Europa, Ganymede, and Callisto—that clearly follow paths around it, not around the Earth. Venus shows a cycle of phases like those of the moon, something that could happen only if Venus orbits around the sun, not the Earth. Furthermore, the sun has dark spots and the moon is covered with craters, physical flaws that undermined the alleged perfection of the heavens. Old-time religion faced a serious threat: a clever, outspoken, prominent thinker who was armed with a telescope.

  Galileo's observations forced him to set aside his early doubts and proved to him that the Copernican system was correct. In fact, he became something of a Copernican zealot. His vehement attacks on the “Peripatetics” who did not believe in the motion of the Earth stirred up enmity within the church and ultimately led to the banning of De Revolutionibus in 1616. He stirred the pot further in his famous 1632 Dialogue, a mock discussion in which the supporter of the heliocentric system clearly gained the upper hand while the conservative doubter, tellingly named Simplicio, came off as something of a buffoon. The Vatican, unamused, ultim
ately called Galileo before the Inquisition, where seven of the ten cardinals sitting in judgment decided against him. Ironically, Pope Urban VIII was a former friend who had invited Galileo to write his book in part to demonstrate that the church was not repressing intellectual inquiry in Italy. Despite Galileo's follies, the church ended up looking increasingly irrelevant, and these episodes ultimately fostered more liberal religious interpretations that could accommodate the new astronomical ideas sweeping across Europe.

  While Galileo undermined Aristotelian cosmology from the observational side, the German astronomer Johannes Kepler undermined its mechanisms, Kepler, fastidious in his thinking and his habits—today we might call him neurotic—performed a meticulous analysis of the motions of Mars that had been compiled by his mentor and tormentor, Tycho Brahe. So it happened that Tycho, who railed against Copernicus, indirectly spawned an even more extreme cosmological revision. Kepler fully embraced the Copernican system but found the discrepancies between the predicted and actual positions of Mars intolerable. He also hated the thicket of spheres on spheres and epicycles on epicycles. After a manic search for harmony, Kepler did a shocking thing: he replaced circles with ellipses, elongated shapes somewhat like the outline of an egg. Immediately all the observations fell into place and the solar system adhered to what he considered a much purer geometrical simplicity.

  Continuing this theme, Kepler associated each planet with a perfect geometric solid. When he pictured how these solids would fit if one were nested inside another, he believed he could account for the observed spacing of the planets. Geometry functioned as the mystical element that kept order in his universe; he treated the concentric solids both as physical objects and as metaphorical expressions of Christian theology, with the sun at rest in the middle, representing God the Father, the creator of motion. Despite its overtly religious inspiration, Kepler's math helped destroy the old spherical cosmology and thereby separate astronomy from church doctrine. Kepler quietly made another revision to his planetary system that further aided in this disentanglement. Early on he had proposed that the planets were moved by souls, continuing a tradition extending all the way back to Aristotle, but in later editions of his Mysterium Cosmogmphicum he rejected this animistic interpretation. He recognized that the speed at which planets move varies according to their distance from the sun, which hardly seemed the attribute of an independent soul. So he switched from a spiritual to a material explanation: “When I considered that this moving cause weakened with distance, and that the sun's light too is attenuated with distance from the sun, I came to the conclusion that this is some kind of force. . .”

  The demise of the spheres and the corruption of the celestial orbs opened up a whole new domain to scientific inquiry. As long as planets existed on their crystal shells composed of unearthly elements, mingling among angels and souls, the question of why the heavens moved was one for philosophers and theologians. Perhaps Aristotle was right when he asserted that it is the nature of ether to proceed in perfect circles, with the whole system set in motion by an Unmoved Mover. Even the Copernican system could possibly work this way. But Kepler's free-range ellipses were another matter entirely. They dispensed entirely with the planetary spheres, so the old appeal to divine circular motion made no sense. Kepler proposed instead that some kind of force keeps the planets moving in their paths. This idea necessarily introduced a new question. What kind of force can reach through space and cause elliptical orbits? Kepler had no convincing answer.

  But Isaac Newton did. The iconic British scientist solved the problem of planetary motion and redefined the place of God in the universe by rejecting, at long last, the ancient Aristotelian divisions between heaven and Earth. Historian Richard S. Westfall once described Newton's intellectual might as something beyond normal human comprehension. Consider the agony many of us experienced as students when we attempted to master calculus. Newton invented the foundations of calculus one year out of college. His personality was a mix of arrogance, brooding privacy, and alchemical obsessions. The calculus he created remained hidden in a drawer for years because Newton had no desire to place himself in the public eye. Likewise, his greatest notion and his greatest book came about only because of a bitter dispute with a scientific and the ceaseless nagging of Edmond Halley, the British astronomer who studied the bright comet that bears his name. Without those prods, Newton might never have written the text that catapulted science toward its sci/religious destiny.

  The book was the Mathematical Principles of Natural Philosophy, better known by its shortened Latin title, Principia, published in 1687. The notion was the law of universal gravitation. The familiar tale that Newton had a sudden flash of inspiration after being conked on the head with an apple was probably invented to help keep the attention of high school physics students. True or not, this tiny anecdote contains a concise summary of what is so revelatory and downright magical in Newton's mathematical description of gravity. It is not just a practical explanation of the motion of a cannonball through the air or of that apple falling from the tree. It is also a manifesto of cosmic interconnectedness. Universal gravitation extends forever, so the force that pulls on the apple also holds the moon in orbit about the Earth and links one bit of the cosmos with every other. Gravity, like God, touches every piece of creation. Understand gravity, and God is pushed to the extremes, as a Creator and as a moral force, but not as an active participant in physical reality. This is Newton's other apple: the fruit of the tree of knowledge that sends man out of God's protected acres.

  Universal gravitation provided a desperately needed replacement for the ether and Aristotle's crystalline spheres. It also made explicit what was implicit in Copernicus's revolutionary cosmology: The laws of heaven are the laws of the Earth, and vice versa. When Newton applied his theory of gravity to the planets, he found that they naturally yielded elliptical motion and the laws of planetary motion that Kepler had found. Newton's equations also allowed a universe of any size. The force of gravity falls off in proportion to the square of the distance, but there seemed no ultimate limit to its range. The pull of the planets held on to their moons; the sun's powerful attraction, in turn, kept the planets in line. The process could keep going to larger and larger scales without end. Newton showed the way to banish the angels from the observable universe, and so divorce cosmology from theology.

  For all his successes, Newton never managed to pin down the ultimate nature of the spooky attraction that could travel unfettered through empty space and pull disparate worlds together. “I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy,” he wrote in Principia. And we now know that Newton's understanding of gravity was not complete. It is hopeless for explaining extreme phenomena such as black holes. Yet he attained such a close approximation of reality that his formulas are still good enough to send men to the moon or to measure the mass of a distant galaxy. More than two centuries passed before Einstein, the high prophet of modern cosmology, managed to improve on Newton's work and bring science to the pinnacle of sublime knowledge. Einstein's general relativity linked gravity, space, and time into a seamless whole. This connection completely erased Aristotle's division between earth and ether, and the religious division between heaven and hell. In Einstein's cosmology, we are unified with the spirit of the universe.

  Many of Einstein's beliefs about the religious spirit of science grew directly out of his predecessor's ideas and attitudes. Newton placed great value on economy of explanation: “Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things,” he wrote. And he saw his science as a kind of divine inquiry. He viewed the cosmos as the handiwork of God, and God as the ultimate gravitational “cause” that had eluded him. Formulating the rules of gravity, then,
allowed Newton a small window into the mind of the Creator. He attempted to exploit his scientific ideas in order to know the size and form of the whole universe, trusting that the physical truths that hold here must hold everywhere. Newton, like Einstein, found himself responsible for the well-being of the universe as a result.

  Newton believed that gravity acted instantly across any distance. In the post-Copernican world, it was clear that those distances could well be endless. Elliptical orbits were the order of the solar system. What, Newton wondered as if he were chatting with God, is the order of the universe as a whole? Initially he pictured the cosmos as a finite cluster of matter, encompassing ourselves and all the stars that we can see, surrounded by an infinite void. The unbounded extent of the universe was an essential part of Newton's world-view, because he deeply believed that the Lord must be infinite and eternal, “existing always and everywhere.” After completing the Principia in 1687, however, he began to suspect that his clustered universe would not be stable. Gravity would pull and pull until every part of the cluster accumulated into a single mass; it might take a great deal of time, but eventually it would happen. This premonition of collapse was the first hint that the entire universe might change over time.