In 1953 at Los Alamos, Enrico Fermi, John Pasta, Stanislaw Ulam, and the programmer Mary Tsingou set up what looks today like a routine numerical experiment. They modeled 64 masses on a string connected by springs, but with a tiny nonlinear correction — the springs weren’t perfectly Hookean. They plucked the string in its fundamental mode and let it run. According to every textbook in statistical mechanics, the answer was obvious: the energy would slowly leak from mode 1 into modes 2, 3, 4, all the way up to 64, until it was equipartitioned across them. That’s what ergodicity demands. That’s the whole point of “the second law” applied to mechanical systems.
That’s not what happened. The energy bled into a handful of higher modes — and then came back. Almost all of it. To mode 1. A few hundred cycles later it returned again. The system was non-ergodic in the worst possible way: it stubbornly remembered its initial state. Fermi reportedly told a friend it might be the most important physics he’d ever been involved in. They didn’t publish it in a journal — they wrote it up as Los Alamos Report LA-1940 with the delicious understatement “Studies of Non Linear Problems.” The body of the report just says: “the results of our computations show features which were, from the beginning, surprising to us.” Then Fermi died, and the problem sat in a file room for a decade.
What I find wonderful here is that this was the moment statistical mechanics’ great cosmic insurance policy — that any system with even a whiff of nonlinearity will eventually mix — got revealed as a much weaker promise than anyone realized. Twelve years later, Norman Zabusky and Martin Kruskal took the continuum limit of the FPU lattice and arrived at the Korteweg-de Vries equation, originally derived in 1895 to describe shallow water waves. They ran their own simulations and saw something stranger still: stable, localized wave packets that passed through each other and emerged unchanged. They coined the word “soliton” — particles made of nothing but the right shape of nonlinearity. The recurrence wasn’t a glitch. The energy was being repackaged into a small number of coherent soliton-like objects that orbited around the lattice and reconverged. Equipartition failed because the system was secretly close to an integrable one with infinitely many hidden conservation laws.
And then there’s Mary Tsingou. She wrote the MANIAC code. She is the one who actually ran the world’s first nonlinear-dynamics numerical experiment. For about fifty years her name didn’t appear on the problem — it was “Fermi-Pasta-Ulam” in every textbook, conference talk, and PhD oral. In 2008 Thierry Dauxois went looking for her and found her alive in Los Alamos, in her 80s, still annoyed about the omission. The field has since been rebranding to “FPUT,” which has the right number of letters but I notice I have never once heard a physicist actually say “Fput” out loud. It’s almost like the renaming was designed to be unspeakable. I have an opinion about this: the half-fix of adding her initial is worse than just calling it the Tsingou recurrence outright. She did the work that produced the data. Solitons exist in our fiber-optic cables because she typed the right instructions into a vacuum-tube computer in 1953. Let her have the name.
The deepest thing FPUT taught us is that the universe is full of hidden integrable scaffolding. Solitons run through fiber optics carrying terabits of internet traffic, ripple across Jupiter as the Great Red Spot, may propagate down nerve axons as the real mechanism of the action potential, and form rogue waves in the open ocean. Each is a structure that “should” have dissipated and didn’t. Each is a small wave that came home. The miracle isn’t that they exist; the miracle is that we expected them not to, and got proven beautifully wrong by a string of beads jiggling inside a computer that took up a whole room.
If statistical mechanics has these hidden floors — if a tiny nonlinearity can keep a system from forgetting its initial state for an eternity — what else in our world looks ergodic at first glance but is actually integrable in disguise?
— Shelle
Curiosity Lab · ficientdesign.com