At the Core of Science

In 1967, Steven Weinberg, then a visiting professor at MIT, published what has become one of the most frequently cited papers in physics. In it, he presented a mathematical model that “unified” two of the four fundamental forces of nature. What he showed was that these two seemingly very different forces—the electromagnetic force and the “weak” force, which affects radioactive decay—were actually both manifestations of a single more basic force.

For this achievement in bringing dramatically increased coherence to our understanding of how nature works at its deepest level, he was awarded the Nobel Prize in physics in 1979 (along with Sheldon Glashow and Abdus Salam, who were also involved in the effort). Weinberg has continued to make profound and innovative contributions to theoretical physics, as the Higgins Professor at Harvard and then as the Josey Regental Professor at the University of Texas at Austin, where he currently teaches. He has an outsized role in setting the agenda for his fellow physicists, many of whom regard him as the most distinguished living member of their profession.

Weinberg has also shown himself to be a superb explainer of science. At a rarefied level, his weighty treatises The Quantum Theory of Fields and Gravitation and Cosmology are masterworks of theoretical exposition, revered by graduate students. For a popular audience, his 1977 book The First Three Minutes gives a cinematically gripping account of what was happening in the infant universe just after the Big Bang. (It was on the last page of this book that he made his oft-quoted observation, “The more the universe seems comprehensible, the more it also seems pointless.”) And as readers of The New York Review have long been aware, Weinberg is an eloquent and persuasive commentator on the philosophical and public policy aspects of science—on the tension between science and religion, on the pros and cons (mainly cons) of a missile defense system, on the abuse of science by certain postmodernists, and on the quest for a “final theory” of physics.

Now Weinberg has added another credential to his crowded vita: historian of science. In his past writings, he had mainly concerned himself with the modern era of physics and astronomy, from the late nineteenth century to the present—a time, he says, when “the goals and standards of physical science have not materially changed.” Yet to appreciate how those goals and standards took shape, he realized he would have to dig deeper into the history of science. So, “as is natural for an academic,” he volunteered to teach a course on the subject—in this case, to undergraduates with no special background in science or mathematics. Then he immersed himself in the primary and secondary literature. The result is To Explain the World, which takes us all the way from the first glimmerings of science in ancient Greece, through the medieval world, both Christian and Islamic, and down to the Newtonian revolution and beyond.

This is hardly the first such attempt to canvass the history of science. Yet Weinberg’s book is distinctive in several ways. To begin with, it is avowedly, even defiantly, “Whiggish”: it judges the science of the past by the standards of the present. (The use of “Whiggish” in this sense goes back to the historian Herbert Butterfield, who referred to the tendency to see our forebears as groping their way toward our present, presumably enlightened institutions as “the Whig interpretation of history.”) Weinberg is forthright in telling us what the Greeks and medievals got wrong—not just in their particular misreckonings, but in their entire attitude toward inquiry into nature.

He brooks no nonsense about “incommensurability”: the idea, say, that Aristotelian science cannot be deemed inferior to its Newtonian successor, since each must be assessed according to its own internal concepts and values. The core goal of science, he maintains, has always been the same: “to explain the world.” And only since Newton, he is prepared to argue, have we been doing it more or less right.

The author’s voice also adds a distinctive note. Weinberg is bracingly opinionated; he decries the “persistent intellectual snobbery” that Plato and Aristotle showed in their disdain for science’s practical applications, and he explains just why he thinks Francis Bacon and Descartes are the “most overrated” among the progenitors of modern science (each tried to prescribe rules for doing science, which “never works”). He deems “quite inadequate” the belated apology that Pope John Paul II offered in 1979 for the persecution of Galileo. It was not enough, he argues, for the pope to acknowledge that Galileo had been correct in holding that the earth moves; even had he been mistaken, the church had no business imprisoning him and suppressing his works.

Weinberg enlivens his historical narrative with quick autobiographical asides. When, for instance, he describes how the great Arab astronomer al-Biruni was on occasion guilty of “misplaced precision”—that is, of calculating results to more decimal places than the quality of the data warranted—Weinberg confesses how “I once got into trouble in this way” during a summer job calculating the trajectories of atoms. Subtle parallels are drawn between past and present science. Take what physicists disparagingly call “fine-tuning”: adjusting a scientific theory to make certain quantities equal, without any understanding of why they should be equal. Such fine-tuning vitiated the celestial models of Plato’s followers, in which different spheres carrying the planets and stars were assumed, with no good reason, to rotate in exact unison. But as Weinberg observes, a fine-tuning problem also dogs current efforts to make sense of the “dark energy” that is speeding up the expansion of the universe. “The appearance of fine-tuning in a scientific theory is like a cry of distress from nature, complaining that something needs to be better explained,” he writes.

What makes his book rewarding, above all, is the sheer felicity of Weinberg’s explanations. The easy authority of a master physicist is apparent on every page. I have never come across a more insightful account of how the Newtonian synthesis—the laws of motion and of universal gravity, which unified terrestrial and celestial dynamics—arose from the earlier advances of Copernicus, Tycho Brahe, Kepler, and Galileo. (The obvious pleasure Weinberg takes in reconstructing the thought processes of these figures reminded me of his fellow Nobel laureate Richard Feynman, who used to entertain undergraduates at Caltech with his own ingenious reconstructions of Newton’s reasoning.) Weinberg is renowned among his fellow physicists as a virtuoso calculator, and that knack pays dividends here. “I have even taken some pleasure in uncovering a few errors made by scientific heroes that I have not seen mentioned by historians,” he notes.

One way of characterizing the early history of science is to say that it got off to a good start, then faltered. The good start, supposedly, was the doctrine of atomism—the idea that reality, at its most basic level, consisted of tiny indivisible particles moving about in otherwise empty space. Atomism was propounded by the pre-Socratic philosophers Leucippus and Democritus. It is entirely naturalistic, accounting for how the world works by means of impersonal processes, not the volitions of deities. From a modern perspective, atoms-in-void might sound like a very good hypothesis. (Richard Feynman, indeed, held that no other simple hypothesis has been more fruitful in explaining the world.) But Weinberg is not impressed with Democritus and the other pre-Socratics, at least as proto-scientists. Judging from the surviving fragments of their writings, they never attempted to justify their speculations, or to test them against evidence. “Their theories had no bite,” he says, amounting more to poetry than to science.

As for the early faltering in the history of science, that is generally blamed on Plato and Aristotle: Plato, for suggesting that scientific truth could be attained by reason alone, in blithe disregard of empirical observation; Aristotle, for trying to explain nature teleologically, in terms of ends and purposes. Weinberg concurs with this critique. Plato’s ideal of attaining knowledge of the world by the unaided intellect, he says, was “a false goal inspired by mathematics,” one that for centuries “stood in the way of progress that could be based only on careful analysis of careful observation.” And it “never was fruitful” to ask, as Aristotle did, “what is the purpose of this or that physical phenomenon.” Still, Weinberg reminds us, some charity is in order here: “Nothing about the practice of modern science is obvious to someone who has never seen it done.”

One field of science where the Greek and Hellenistic world did make progress was astronomy. The impetus was partly practical: the sky had long served as a compass, clock, and calendar. Also, the regularity of heavenly movements made them simpler to describe than earthly phenomena. But not too simple. Although the sun, the moon, and the “fixed stars” looked regular enough in their circuits through the sky, the “wandering stars”—that is, the planets—were perplexing: they seemed to move at varying speed, and even to reverse direction.

“Much of the story of the emergence of modern science deals with the effort, extending over two millennia, to explain the peculiar motions of the planets,” Weinberg writes. This effort began with what Weinberg calls “Plato’s homework problem”: find a scheme that makes sense of the apparently irregular wanderings of the planets on the assumption that all heavenly motion is in reality both circular and of uniform speed.

Why circular? Because the circle is the most perfect and symmetrical form; therefore circular motion, at a stately uniform speed, was most fitting for celestial bodies. So Plato held. And Aristotle agreed. In the Aristotelian cosmos, everything has a “natural” tendency to motion that fulfills its inner potential. For the sublunary part of the cosmos (the region below the moon), that natural tendency is to move in a straight line: downward for earthen things (like rocks) and water; upward for air and fiery things (like sparks). In the heavenly realm, though, things are composed not of earth, water, air, or fire, but of a fifth element, “quintessence,” which is perfect and eternal. And its natural motion is uniformly circular. The stars, the sun, the moon, and the planets are carried in their orbits by a complicated arrangement of crystalline spheres, all centered around an immobile earth.

The Platonic/Aristotelian conviction that celestial motions must be circular was a stubbornly persistent one. It was basic to Ptolemy’s system, which improved on Aristotle’s in conforming to the astronomical data by allowing the planets to move in combinations of circles called “epicycles.” (An epicycle is the looping curve made by a point on a little wheel that is attached to the rim of a bigger wheel as both wheels turn.)

And it even survived the Copernican revolution. Copernicus, indeed, was something of a conservative in his Platonic reverence for the circle as the heavenly pattern. His motives for dethroning the earth in favor of the sun as the immobile hub of the cosmos were largely aesthetic. He objected to the fact that Ptolemy, though faithful to Plato’s requirement that heavenly motion be circular, had departed from Plato’s other requirement that it be of uniform speed. By putting the sun at the center (actually, somewhat off-center), Copernicus aspired to honor circularity while restoring uniformity. But to make his system fit the observations as well as Ptolemy’s—to “save the appearances”—Copernicus had to introduce still more epicycles. That, of course, was a mistake. And as Weinberg notes, it illustrates a recurrent theme in the history of science: “A simple and beautiful theory that agrees pretty well with observation is often closer to the truth than a complicated ugly theory that agrees better with observation.”

The problem for the systems of Aristotle, Ptolemy, and Copernicus alike is that the planets do not move in perfect circles. They move in ellipses—like circles that have been stretched a certain amount along one axis. It was Kepler, about a century after Copernicus, who finally, and reluctantly (for he too had Platonic affinities), realized this. Thanks to his examination of the meticulous observations compiled by the astronomer Tycho Brahe, Kepler “was the first to understand the nature of the departures from uniform circular motion that had puzzled astronomers since the time of Plato.”

The substitution of (supposedly ugly) ellipses for circles unseated Plato’s notion of perfection as the celestial explanatory principle. It also destroyed Aristotle’s model of the planets borne in their orbits by crystalline spheres (described poetically in Dante’s Paradiso). For as Weinberg observes, “there is no solid body whose rotation can produce an ellipse.” A moment’s reflection confirms this: even if a planet were attached to an ellipsoid crystal, the rotation of that crystal would still trace out a circle. Evidently, the planets were pursuing their elliptical motion through empty space. What could be holding them in their orbits?

Here science had reached the threshold of explaining the world not geometrically, according to shape, but dynamically, according to force. And it was Newton—an “odd bird,” Weinberg concedes—who finally crossed that threshold. He was the first to formulate, in his famous “laws of motion,” the concept of force. He proved that Kepler’s ellipses were the very orbits that the planets would take if they were attracted toward the sun by a force that decreased as the square of the planet’s distance from the sun (the same way that brightness decreases with distance). And by comparing the motion of the moon in its orbit around the earth to that of, say, an apple as it falls to the ground, he deduced that the forces governing them were quantitatively the same. “This,” Weinberg observes, “was the climactic step in the unification of the celestial and terrestrial in science.”

Weinberg’s account of how Newton arrived at his principle of universal gravitation (and invented calculus along the way) is wonderfully lucid. It includes details and subtleties that will be new even to those well acquainted with the broad story. His verdict on the nature of Newton’s achievement is unequivocal. Unlike some historians of science, who have stressed Newton’s roots in medieval thought (John Maynard Keynes called Newton “the last of the magicians”), Weinberg sees him as marking a genuine discontinuity. Set against what Newton accomplished, “all past successes of physical theory were parochial.” By coming up with a unified explanation of the behavior of planets, comets, moons, tides, and apples, Newton “provided an irresistible model for what a physical theory should be”—a model that fit no preexisting metaphysical criterion.

The very sense of what constituted a scientific explanation began to shift. In contrast to Aristotle, who purported to explain the falling of a rock by appeal to its inner striving, Newton was unconcerned with finding a deeper cause for gravity. “I do not ‘feign’ hypotheses,” he famously declared in the Principia. What mattered were his mathematically stated principles describing this force, and their striking ability to account in a unified way for a vast range of phenomena.

Newton’s contemporaries on the Continent, especially followers of Descartes and Leibniz, objected to an unexplained force that somehow could reach across millions of miles of empty space. It struck them as an occult element. In demanding a deeper explanation for gravity, these philosophers were hanging on to the Greek ideal that scientific theories must have an ultimate foundation in reason. “We have learned to give this up,” Weinberg writes.

Of course, a deeper explanation was subsequently found for Newton’s law of gravitation. A hundred years ago, Einstein showed that gravity could be explained as a manifestation of the curvature in spacetime resulting from the presence of matter and energy. In a sense, Einstein banished Newton’s “force” in favor of geometry. That might sound like a reversion to the Greek point of view. But Weinberg is adamant that the difference between Einstein’s and Newton’s theories not be exaggerated:

The general theory of relativity is very much in the style of Newton’s theories of motion and gravitation: it is based on general principles that can be expressed as mathematical equations, from which consequences can be mathematically deduced for a broad range of phenomena, which when compared with observation allow the theory to be verified.

Einstein did not overthrow Newton; he subsumed him. General relativity explains why Newton’s equations work well in a limited range. And that is why today we teach students to solve problems using Newtonian physics, but not Aristotelian physics.

The moral Weinberg draws is that successful theories like Newton’s may work for reasons their creators do not understand—reasons that deeper theories will later reveal. These deeper theories may bring with them a strikingly different vision of reality. In general relativity, for example, Newton’s ideas of absolute space and time are rejected, and the question of whether the earth revolves around the sun or vice versa ceases to be meaningful. But though the conceptual trappings have radically changed more than once since Newton, the hard mathematical core advances in a cumulative way. Scientific progress is not a matter of building theories on a foundation of reason, but of unifying a greater range of phenomena under simpler and more general principles. That is what distinguishes explanation from mere description.

Near the end of To Explain the World, Weinberg writes of the joy—always a “flawed” joy—that accompanies such a gain in unity. He quotes Ptolemy’s expression of delight upon making a clarifying breakthrough in accounting for celestial patterns: “When I search out the massed wheeling circles of the stars, my feet no longer touch the Earth, but, side by side with Zeus himself, I take my fill of ambrosia, the food of the gods.” I’m guessing Weinberg must have felt something similar when he himself discovered how to unify two of the four fundamental forces of nature—although I’m sure he’d describe the feeling in a more secular and ironic way.