Old Theories Rarely Die of Contradiction. They Stop Making New Things.

In 1969, Thomas Kuhn pulled a Princeton physics student named Jed Buchwald out of the lab and made him a research assistant. Fifty-two years later, Buchwald, now a historian and philosopher of science at Caltech, sits with Lex Fridman and says, quite calmly, that he does not think science advances the way Kuhn said it did. The two men kept arguing after Buchwald ran an institute at MIT and Kuhn, then in the philosophy department, came over for the talks. They were still arguing, in a sense, for the rest of Kuhn's life.

*The Structure of Scientific Revolutions* came out in 1962 with a picture that still dominates textbooks. Scientists form a community, work inside a "paradigm," and solve puzzles until they hit what Kuhn called anomalies that crack the frame. Then someone arrives with a different way of doing things, a revolution happens, and a new paradigm takes over. Buchwald knows that picture from the inside. He does not think history obeys it.

He once wrote a book on the origins of the wave theory of light, one of Kuhn's favorite examples. Kuhn thought the wave theory rose because Newton's particle view of light ran into a phenomenon it could not crack. The archives, Buchwald says, show that the phenomenon later had little to do with why wave optics won, and that the particle view could in fact explain many of the results attributed to waves, only clumsily and after the fact.

What the wave theory offered, especially after Augustin Fresnel deployed advanced calculus in France, was a chance to invent. Younger people who were becoming physicists in the 1820s through 1840s could design new devices, compute things they could not compute before, and open a vein in polarization, a phenomenon ironically discovered by Newtonians. Newton's scheme could accommodate those results once they existed. It could not generate them *de novo*, and for a twenty-year-old entering the field the choice was almost automatic: go where you can make new stuff.

Fridman wants to know whether paradigm shifts still exist. Buchwald says they do, only they are rarely as neat or as powerful as Kuhn first claimed, and late in life Kuhn himself was modifying the original scheme. Asked to split progress between lone geniuses and messy collaboration, Buchwald refuses a percentage. One, two, or three people are usually central when things begin to move, which does not make them solely responsible for what follows.

Galileo's work on motion is the usual test case. Others could adapt pieces of it without buying the whole scheme, and it spread because you could do new work with it. Descartes, a mechanical philosopher who thought the world was matter in motion, never thought much of Galileo's results and treated them as an approximation. One of Descartes's followers who then broke with him was Christiaan Huygens, older than Newton and, Buchwald says, one of the two greatest scientists of the seventeenth century.

Huygens used Galilean relations to build the first pendulum-governed clock, and even figured out a mathematically perfect timekeeper that did not, in practice, work. He and his brother ground lenses. When Fridman admits the name is hazy, Buchwald is blunt: after two years of physics you should know Huygens, because a fundamental principle in optics still carries his name. People remember equations and forget the human beings attached to them.

Fridman asks the counterfactual: if you removed Newton or Galileo, would science have stopped? Buchwald says that is not entirely incorrect, but he finds it hard to believe that without Galileo someone like Huygens would not have appeared, given the belief structure of the time and the state of mathematics. It would not have been the same. Things would still have evolved.

Fridman paints a lugubrious picture: from knocking rocks in caves to some future apocalypse, where on that arc is the twenty-first century? Below one percent, or nearly done? Buchwald first separates the question of whether civilization will die from the question of where science sits. Then he says he finds it hard to answer, because in the deepest philosophical sense he is not a realist.

Access to the inner workings of nature, he argues, is always mediated by the materials and instruments at hand. That does not mean he thinks the Standard Model or quantum electrodynamics is false; he would not dream of saying so. Those theories work, especially in huge accelerators and in cosmology, to an accuracy no physical theory had reached before. What he does not accept is Steven Weinberg's claim that through them we have probed the depths of reality.

He also does not think physics can keep doing what it has done for a hundred years. Nobody will keep building bigger and more expensive machines to rip particles apart, and physicists will turn to other unexplained features of the material world. You can argue that the Standard Model should in principle climb all the way to chemical reactions; chemists do not work that way. They use higher-level quantum mechanical relations, and the dream of one deep theory that explains everything, Buchwald thinks, only took its fullest form toward the end of the nineteenth century.

Fridman presses on what a "theory of everything" even means. In today's physics it means unification of the laws; in antiquity it meant something looser, and even a completed unification would leave chemistry, minds, and societies unexplained. Buchwald would not push the phrase back that far. At best you reach the seventeenth century, because antiquity discussed the nature of the world without sharing the later faith that violently manipulating matter in a device tells you what nature is doing on its own.

That faith, he says, was first held by people we now call alchemists. The dream was not yet a single equation. It was the hope that by probing nature in artificially constructed ways we can find out what is going on deep down. That is the essence of experimental science: you have to mess with nature, then convince others that you have not produced a fake, artifactual behavior that fails in the wild.

Buchwald was taking graduate courses in general relativity as an undergraduate at Princeton when Kuhn "stole" him. Talking with Caltech colleagues such as Kip Thorne, he reports a working consensus that even the deepest laws we can divine may be unique to this universe as it formed at the Big Bang. String theory has been the mathematically inclined candidate for decades, good at accommodating things, still unable to generate experimental tests. "Before the Big Bang" may not mean anything, given the nature of time.

Why these laws? One answer is that if they were different we would not be here to ask, circular and still compelling. LIGO's gravitational-wave detectors, he and Fridman agree, are among the rare tools that can march us backward. Looking inside a black hole remains a dream. The larger human hunger, Fridman adds, is the key to how everything works, and Buchwald does not mock the hunger. He just will not confuse it with having arrived.

The disagreement with Weinberg, Buchwald says, is not about physics. Weinberg helped found the Standard Model. The question is older, and in one form it is Kant's: can we ever convince ourselves that we have come to grips with something not knowable through the senses, except in the most remote way through instruments? We can corral nature with mathematics and experimental structures. Whether any particular way of corralling will play itself out, he does not know. "It always has."

He often starts a history of science class by looking at a student and saying, "You are in fact a figment of my imagination." If a dragonfly looked at the same student, its nervous system would form a wholly different perceptual structure. Who is right, Buchwald or the dragonfly? The question, he thinks, is the wrong one. It is very difficult to get beyond the constructs our perceptual system leads us to, and the apparatus we build still delivers outputs we process with those same systems.

The classroom analogy is a laptop. He sends a paper, a student opens the PDF, and claims to be looking at the assigned text. No: the student is looking at a stream of light from a screen. Dragging that "page" with a mouse is not moving paper. It is moving a construct processed so that our habits of paper can still operate. Fridman then asks about consciousness, "for a friend." Buchwald laughs, admits he has read a fair bit of popular writing, and says he cannot really say much.

He is a materialist in the deepest sense: nothing is out there except material structures interacting, and he does not think the bottle of water on the table is conscious, though he adds that he cannot talk to it. He knows Fridman is conscious because they can interact, unless Fridman is a figment or a robot generating the illusion well enough for a conversation. Consciousness, whatever it is, must arise from some organizational structure of material elements. As neuroscience maps brain patterns onto behavior, we will get a better handle on associated activity, but we still cannot move from that activity to experience. Fridman wonders whether consciousness is an undiscovered law of physics that permeates matter; Buchwald says he would then have to stop drinking the water, because every sip would involve a little suffering.

Asked for the most beautiful moments in the history of science, Buchwald wants events that join conceptual and mathematical work with probing experiment. Among his favorites is the young Isaac Newton sending sunlight through a prism. The prevailing idea, going back to antiquity, was that colors are modifications or tints of white light: the colors are not in the sunlight. County fairs sold crude, bubbly prisms because they made pretty colors, which everyone took as white light being stained.

Newton, already a formidable mathematician, used the known laws of refraction to ask a question that ignored color. If you turn a prism to a particular angle, sunlight from a circular sun, through a small hole, should still make a circle on a distant wall. It does not; it makes a long image, which told him that sunlight contains different types of light. Very few people in Europe could have done that calculation.

When he published the paper, he barely described the procedure, just numbers. You would think, given his notes, that he used a measuring device to set the prism. He did not. He held it in his hand and twiddled. At the angle that should turn a circle into a circle, the image also moves most slowly, so a hand can home in without instruments. Buchwald calls this manipulative experimentation: using mathematical knowledge of a system's inaccuracies to reach exact conclusions despite the built-in problems of measurement.

Almost nobody else was doing anything like that, and the combination of calculation and craft lasted well into the nineteenth century, when the foundations of optics, electricity, electrodynamics, and hydrodynamics were laid by people who were both talented mathematicians and good with their hands. Enrico Fermi, Fridman notes, was among the last who could do both, and he built a device with rather large positives and negatives. The prism paper also made Newton an enemy. Robert Hooke, the Royal Society's weekly demonstrator and the author of *Micrographia*, with its first depictions of a fly's eye, read Newton's account and had a double reaction: anything correct, he already knew, and anything he did not know was probably wrong.

Newton was born in 1642 near Grantham in England, in a house that still stands and that his mother later died in. His father died before he was born. His mother remarried a Reverend Smith, who took her a few miles away and left the boy with his grandmother, an abandonment Newton resented for life. As a child he was clever with kites, sometimes hanging candles on them and terrifying the neighbors at night. Buchwald cannot think of a physicist or natural philosopher he has studied who did not, as a child, like making things.

His mother wanted him to take over the family's yeoman farm. Stories say he was bad at it; one has him sitting in a field while the cows come home without him. Relatives and local dignitaries, seeing that he had been reading, got him to Cambridge as a subsizer, a student who cleaned the bedpans of richer boys. That did not last. He absorbed Descartes and the new ways of thinking, kept student notebooks, and built the foundations of a mathematics for processes that change continuously: the calculus.

The notebooks split the work. *Philosophical Questions* takes up reality and perception; the *Waste Book* takes up motion and collisions. He also copied the traditional curriculum, the neo-scholastic world rebuilt from Aristotle by Thomas Aquinas. Buchwald, wearing a blue shirt, likes to ask students where the blue is. They say the shirt, then retreat to photons, retinas, and percepts. Yes, he says: the blue is an artifact of our perceptual system. It is not out there.

That is not how the world was thought about into the sixteenth century, when qualities were in things and a working sense was supposed to deliver them as they are. The break becomes most visible in Descartes: the world's qualities are shapes, sizes, motions, maybe hard particles, not colors, sounds, smells, or softness. Newton would disagree with Descartes on much, but he picked up that break very strongly, and it underlies his later skepticism toward the evidence of the senses. To separate colors in the world from colors produced by the eye, the young Newton stuck a stick under his lower eyelid, pushed on the eyeball, and watched colored circles move. Buchwald always tells students not to do this.

Hooke was argumentative, an expert mechanic, and convinced that real knowledge of nature comes through carefully constructed devices. He also gave Newton stimulations that mattered later. A wealthy Danzig brewer, Hevelius, had built an observatory on top of his brewery and, working with his wife, produced a star catalog he claimed was unprecedentedly accurate, without using a telescope as a measuring device. Hooke said it was impossible: stars in an eyepiece are dots, and the naked eye cannot be that good.

At two successive Royal Society meetings he marched the members into the courtyard, pasted a card of black and white stripes on a wall, and had each man walk back until the stripes blurred. From distance and angle he computed the best human visual acuity. The number came out ten or more times worse than Hevelius had claimed, so Hevelius, Hooke concluded, was a fraud. Years later Buchwald reduced Hevelius's coordinates against modern NASA tables and found they were even more accurate than claimed. The Society sent young Edmond Halley to Danzig; Halley wrote back that he could not believe it, until Hevelius taught him the method and he matched the precision.

Hooke was right and wrong. He was wrong for the right reasons and right for the wrong reasons. What he had measured is what we now call 20/20 vision, the limit for static stripes. Hevelius was watching a bright star move past a pointer. Human eyes, like a frog's, are far more sensitive to motion than to a still fly on a string, and our acuity for distinguishing motion is five or more times better. The lesson is not that Hooke ran a sloppy experiment. He ran a good one on the wrong target, a mistake that still shows up in experimental design.

The apple story, Buchwald says, is not true, and it was not a different fruit; his colleague Simon Schaffer once said on television that "the role of fruit in the history of science has been vastly exaggerated." The real shift in Newton's thinking about motion came in correspondence with Hooke, who suggested a way of injecting time that let Newton solve problems he had not been set up to compute. Mechanical philosophers wanted a chain of contacts between Earth and Moon, while Hooke, with Christopher Wren, gestured at a magnetic-like direct relation. Newton would not have cared about the vague picture; he cared once he saw a mathematical way to work with force-like effects at a distance. After the *Principia*, Hooke claimed credit for the hint, and Newton dismissed it as a picayune idea.

Calculus, in Buchwald's telling, is a set of techniques for investigating continuous mathematical functions rather than discrete counting numbers. Geometers already had limited methods for areas under curves and tangents. Young Newton, staring at a polynomial expansion, saw that it could be generalized, arrived at the binomial theorem, and used small increments to discover that finding areas and finding tangents are reciprocal operations. His version worked with small increments and continuous flows. Physicists still write a dot over a variable for a rate of change; that dot is Newton's.

He did not publish it, and when Gottfried Leibniz visited London, heard about the work, and developed the form of calculus the world actually uses, a three-hundred-year fight began over how independently he had done it. Leibniz's admirers insist on complete independence; Newton, as president of the Royal Society, convened a panel that concluded Leibniz had taken everything. About twenty-five years ago Domenico Bertoloni Meli, now at Indiana, got hold of a Leibniz manuscript, the *Tentamen*, an attempted alternative to Newtonian mechanics. Meli argued that Leibniz had reverse-engineered the *Principia* and cooked it backwards to get the results he wanted.

Most historians of mathematics, Buchwald says, do not agree. His friend Michael Nauenberg, a physicist at UC Santa Cruz who died a couple of years before the interview, had supporting evidence that could not get past referees, including at a technical journal Buchwald co-edits. Buchwald remains suspicious. Fridman asks why Newton attracts these dramas and Einstein does not. Buchwald does not think theft is that common. The Newton-Hooke-Leibniz fights sit at the beginning of science as something other than an aristocratic pastime, in a period still inventing rules so that disagreement would not end with a sword.

Competition, he says, is almost always good for science and often painful for the people. During the French Revolution the École Polytechnique trained François Arago and Jean-Baptiste Biot, who came back from a metric-system expedition to a feud over credit that turned polarization into a battlefield. In 1815 a young army engineer, Augustin Fresnel, passed through Paris; Arago, seeing a weapon, installed him at the observatory and fed him problems that undercut Biot paper after paper. Fresnel knew he was being used, wrote his brother that he did not want the fight, and kept producing because Arago kept pushing.

Why was Newton a complicated man? He had a hard childhood, was self-contained and solitary, and, once famous, moved to London in the 1690s as warden and then master of the Mint. Coinage was riddled with counterfeiting. He sent investigators after the forgers and saw at least one famous operator, Chaloner, to the gallows. Buchwald suspects the special anger came from nasty things Chaloner had said about him in Parliament. Even so, at Cambridge, without wealth, he attracted people who recognized how smart he was, including Humphrey Newton, a roommate who became a kind of secretary.

As far as we know he had no relationships with women or men except formal ones; the closest woman was his niece Catherine Barton, who ran his London household and married John Conduitt, later a keeper of Newton's legacy. During a modern pandemic Fridman wants the story of the plague years. Buchwald notes there was no Zoom, and it would not have mattered: Humphrey said Newton might as well have been lecturing to the walls. As Lucasian professor, succeeding in practice Isaac Barrow, who gave up the chair after recognizing the younger man's genius, Newton had only to lecture now and then and deposit the notes, whether anyone was there or not. Those deposited notes, including the optical lectures, are how we now read him.

The so-called *annus mirabilis* is 1666, when Newton was about twenty-four, two years after arriving at Cambridge at eighteen. Calculus and the optical discoveries date to that stretch, though the notebooks show a lot already in motion. Buchwald likes to ask his twenty-one-year-old physics and chemistry students, especially over Zoom, whether they know what Newton produced when he was their age and an epidemic sent him home. He thinks Newton could have done the work staying at Cambridge. It is true, though, that the prism experiments on the wall were done in the room you can still visit, with an apple tree in the garden that is not the original tree but cuttings, because four hundred years is too long for the original to last.

The *Principia* is a powerful work in itself, not just a date in a timeline. Book One states Newton's laws of motion and asks, geometrically, what force directed to a fixed point will make a body follow a given curve, using limiting ratios of line segments rather than the algebraic calculus. Book Two develops hydrostatics, a little hydrodynamics, and the concept of pressure. Book Three applies Book One to the solar system, which can be solved exactly only for two bodies; the Moon's motion, repeating among the stars every nineteen years, a fact the Babylonians knew, forced Newton into approximations that later French mathematicians such as Laplace would systematize. Alan Shapiro's annotated edition of Newton's optical notes, Buchwald adds, shows the same mind still joining experiment to mathematics in the work published as the *Opticks* in 1704.

Where does data fit? Buchwald would rather not define "the scientific method." Humans have been making the world repeat itself for as long as there have been humans. He prefers to talk about the considered manipulation of artificial structures to produce results that can be joined to schemes for building other devices and making predictions. Astronomical data obtained without that loop still counts. The modern idea of data, though, smuggles in statistics.

Imagine a millimeter ruler and a mark on paper. You align one end and the other falls between ticks, so you guess. Five minutes later you guess again. After many trials, asked for the best estimate, you average. Why? The central limit theorem, a piece of statistics not really developed until the 1750s, 1760s, and 1770s. Newton died in 1727. The intuition, Buchwald says, was not really there yet.

Huygens, a skilled mechanic who also fought Hooke over a spring watch, left optical notes at Leiden University. His theory needed four constants measured well enough to predict other quantities, so he made measurement after measurement. When he calculated, and when he published at the end of his life, he gave one number: not an average, but the trial he was most confident in after practice. Publishing six numbers and combining them would have looked, to contemporaries, like not knowing what you were doing, and Buchwald grants that older method an inkling of value, because statistics is not a solvent for every problem.

Alchemy used to be written off as mysticism, which is not entirely untrue and is substantially untrue. Alchemists pursued chrysopoeia, turning cheap materials into valuable ones, and along the way learned complex amalgams, glass alembics, and heat-driven decomposition, with cryptic formulas that have mostly turned out to be real recipes under code names. By Newton's time the work had merged with mechanical philosophy: if matter is particles, perhaps chemical processes can rearrange them, which is not so stupid, Buchwald notes, unless you count cold fusion. Newton spent more of the late 1670s on those manipulations than on anything except optics, and William Newman at Indiana has reproduced the shiny "star regulus" Newton described.

Newton was deeply religious, not unusually so for the age, and he found solace in a governing, abstract, rule-making, exacting deity. Buchwald thinks his conviction that you can figure things out had a great deal to do with the belief that this rule-maker does not act arbitrarily. He was an anti-Trinitarian, holding that Christ was endowed with powers rather than possessing a divine being, and he did not think miracles had continued after Christ or that Old Testament wonders happened in the literal way told. Like nearly everyone, he thought creation was about six thousand years ago, 4004 BCE if you follow Bishop Ussher, and that did not interfere with the astronomy: he was watching the brilliant construction a perfect entity had produced.

If you dropped Newton into a conversation with Einstein about spacetime and general relativity, Buchwald says, he would sit in shock and have no idea what Einstein was talking about. A better experiment is to take a Newton in his forties, not a man in his mid-eighties, keep Einstein offstage, and put him on a railroad, then show him sparks, a live wire, a clicking telegraph, and a telephone receiver for a couple of months. After that, walk him through 1890s laboratories, simpler devices first, with extra time on optics. He was brilliant, and bit by bit he would begin to see; dump him in front of Einstein and his eyes would glaze over.

The compressed history that makes Newton-to-Einstein look short is, Buchwald says, totally wrong. The distance is huge, in fundamental conceptions, mathematical structures, experimental devices, and the organization of science. Fridman asks how much of the world you have to load in from age five, including experiences that do not look like physics, in order to have ideas that push science forward. Buchwald's answer is yes: the railroad, the steam engine, and the Watt engine evolved largely independently of contemporary theories of heat, even though Watt knew the chemist Joseph Black. What they were not independent of was a practice of manufacturing devices that do novel things, plus a growing premium on calculating efficiency.

Fridman, rereading Einstein's 1905 papers on the photoelectric effect, Brownian motion, special relativity, and E=mc², wants to know how evolution produces that kind of concentrated genius. Buchwald notes that both Newton and Einstein had precedents, and that Einstein's donated brain, sliced after death, showed nothing unusual to the eye. He recalls a story from his student days of a young woman on the autism spectrum who could not speak or read affect, yet could hear Chopin once and run variations at the piano. Some aspect of mind can tune into a corner of reality and master it, and every once in a while that corner is physics, though how that happens, he says, who knows. The episode closes with a line from Kuhn: the answers you get depend on the questions you ask.