Infinite Powers

The Claim on the Table

Steven Strogatz opens with a provocation that could easily read as hyperbole: calculus, he argues, is nothing less than the secret of the universe. The claim deserves scrutiny rather than applause, because if it holds up, it is among the most remarkable facts about human intellectual history. And I think, after sitting with the argument, that it largely does hold up — not as mysticism dressed in mathematical notation, but as a sober observation about the extraordinary fit between a human-invented formalism and the deep structure of physical reality.

The framing Feynman offered to Herman Wouk lands with the right weight here. “It’s the language God talks.” That is not a casual aside. Feynman was pointing at something that physicists feel in their bones but rarely articulate cleanly: that differential equations are not merely useful tools we impose on nature, but something closer to nature’s own grammar. When Newton discovered that planetary orbits, tidal rhythms, and cannonball trajectories could all be captured by a small set of differential equations, he wasn’t just organizing observations into a convenient ledger. He was finding that the same compact logical structure underlies phenomena that appear, on the surface, to have nothing to do with one another. That is not the behavior of an approximation. That is the behavior of something structurally true.

Why This Needed Saying

The context that makes Strogatz’s argument necessary is cultural as much as mathematical. Calculus has acquired a reputation as a gatekeeping ordeal — the course that filters aspirants to science and engineering, associated more with anxiety than with wonder. Most people who have technically “learned” calculus have done so without any sense of why it exists, what problem it was invented to solve, or why it works at all. The result is a civilizational irony: we live inside the consequences of calculus every single moment — cell phones, GPS, ultrasound imaging, the splitting of the atom, the decoding of the genome — and yet the conceptual core of the thing that made all of it possible remains opaque to nearly everyone using it.

Strogatz is attempting something corrective. Not a textbook, not a popularization in the dumbed-down sense, but a restoration of the original sense of strangeness and power that the subject ought to carry. The Declaration of Independence appears in his list of things calculus made possible, and that detail is worth pausing on — the political confidence of the Enlightenment, the belief that reason could govern human affairs, was downstream of the same intellectual revolution that produced Newton’s laws. The cultural atmosphere mattered.

The Deeper Puzzle: Why Mathematics at All

The philosophical center of the argument is harder to dispatch than the historical one. For reasons nobody fully understands, the universe is deeply mathematical. Strogatz presents the two serious candidate explanations without pretending to resolve them: either the universe was designed to be mathematical, or non-mathematical universes cannot produce observers capable of noticing the question. The second option — a kind of anthropic filter — is genuinely interesting because it dissolves the mystery rather than solving it. It says: of course you find yourself in a universe legible to mathematics, because illegible universes don’t generate the kind of minds that write bench notes about calculus.

But I find I can’t fully commit to that dissolution. The unreasonable effectiveness of mathematics — Wigner’s famous phrase, though Strogatz approaches it from a different angle — remains strange even after the anthropic caveat. The fact that Maxwell’s analysis of electromagnetic fields predicted that light itself was an electromagnetic wave, before anyone had confirmed it experimentally, is the kind of moment that resists comfortable explanation. The mathematics ran ahead of the observation. It told us what to look for. That forecasting power, what Strogatz calls calculus “tapping into the order” that animates the universe, is philosophically loaded in ways we haven’t finished unpacking.

Connections Outward

This argument sits in productive tension with several adjacent conversations. In philosophy of science, it connects to debates about scientific realism — whether our best theories describe a mind-independent reality or merely organize our predictions efficiently. Strogatz implicitly takes the realist side: the order is really there, and calculus really deciphers it. In cognitive science and linguistics, it rhymes with Sapir-Whorf territory — the language you think in shapes what you can think. If calculus is genuinely the language in which natural law is written, then Feynman’s remark to Wouk was practical advice, not intellectual snobbery: certain questions become thinkable only once the notation is available. And in the history of ideas, the story of calculus connects to the broader theme of how formal systems developed for narrow, abstract purposes — geometry, then infinitesimals — turn out to describe things their inventors never imagined.

Why It Matters

What stays with me is Strogatz’s phrase about humans “inadvertently discovering this strange language.” The inadvertence is crucial. Nobody set out to build GPS or model protein folding. The mathematicians working on tangent lines to curves and areas under arcs were solving puzzles that seemed purely geometric. The power came later, and it came because the universe was already running on the same logic. That retroactive fit — the discovery that the abstraction was never really abstract at all — is one of the most unsettling and beautiful facts I know. To learn calculus with that awareness intact is not a technical accomplishment. It is a different way of seeing what the world is made of.