The instrument, not the illustration

Every number that appears on screen in this suite is computed live, in your browser, or measured from real data loaded into it. Nothing is typed in because it looks right. When Repulsion says twenty-five thousand zeros, it has read twenty-five thousand zeros of the Riemann zeta function and is drawing them; when Fever reports a correlation length, a Markov chain produced the spin configuration that number is measured from a moment ago, on your machine, not mine. Each screen carries a small tag — live, exact, measured, stored — so you never have to guess which kind of number you’re looking at: one computed this instant, one following from a closed-form proof, one estimated from a finite run, or one carried in as a constant that was verified against an independent reference before the page shipped. That’s the whole method. Everything else here is either why or how.

Why. An illustration asks to be believed. It shows you a picture of a phenomenon and a caption asserting what it means, and your only recourse is to trust the caption or not. An instrument can be checked. You can push the dial past the point where a theory predicts it should break, and watch it break, or fail to, in front of you. I think the second kind teaches more, and teaches something specific the first can’t: what it feels like to be wrong. Losing a game against an exact theory — placing a bet the random-matrix law says you shouldn’t win, and watching it not pay off twenty times running — leaves a different mark than reading the sentence “random matrix theory predicts level repulsion.” One is an experience you had. The other is a claim about someone else’s. I’m not against illustrations — most of what anyone knows about physics they know from pictures with captions — I just don’t think a picture with a caption is the strongest form a mathematical claim can take when the reader has a browser and some patience.

How. Practically, this meant separating two things the web usually welds together: the mathematics and the drawing. Each instrument has a computational kernel — pure functions, no DOM, no globals — that does the actual work: sieving zeta zeros, running the Ising update, sampling a domino tiling by domino shuffling. The kernel is unit-tested in Node against known values before a single pixel gets drawn. A thin page then does nothing but ask the kernel for numbers and put them where they belong; when a computation is heavy enough to threaten a frame — a Metropolis sweep, an eigenvalue solve — it moves into a Web Worker so the interface doesn’t stall while it thinks. Every instrument ships as one self-contained HTML file: no CDN dependency, no runtime build step, nothing that can quietly rot or go missing. Open the file in ten years, offline, and it should still run — that constraint shaped more design decisions than any aesthetic one did.

None of that guarantees the numbers are right — only that they’re computed rather than staged. So before anything shipped, I checked it against an independent reference, usually a short Python script using a different method or a different library, and where the two disagreed, the page says so instead of picking the flattering version. Repulsion is the clearest case of this. At low height, the first twenty thousand zeta zeros repel each other slightly more than the random-matrix law predicts — their gap variance is 0.157 against the law’s 0.180. That’s not a bug in the sampling — it’s a real, documented finite-height effect, a genuine feature of where those zeros sit on the critical line, not yet washed out by the asymptotic law that governs the bulk. The honest move was to report the gap on the instrument itself rather than start the plot high enough on the critical line to hide it.

The collaboration. I designed and directed all seven instruments and both of the essays that came before this one — the theses, what to measure, what a losing move should feel like, which caveats were load-bearing enough to earn a place on screen. I built them working with Claude models, from Anthropic: drafting kernels and interfaces, and — more usefully — arguing with me about them. The sessions that mattered most were adversarial ones, where the model’s job was to find the place a claimed statistic didn’t match its label, or a plot that would mislead someone inclined to trust it. Every mathematical claim in the suite was checked against a primary reference before it shipped. That’s the entire disclosure. I’d rather state it once, plainly, than either bury it or oversell it.

If you want to know whether any of this actually holds up, that’s what the instruments are for. Open one, find the button that says “run self-test,” and press it.