The Science of Unpredictability | Los Alamos National Laboratory<br>DOE/LANL Jurisdiction Fire Danger Rating:

April 22, 2026The Science of Unpredictability<br>A Nobel laureate, a brilliant programmer, and two unexpected discoveries—the rise of nonlinear dynamics at Los Alamos.<br>Kyle Dickman, Science Writer<br>Download PDF

In 1955, 26-year-old mathematician and programmer Mary Tsingou sat in a cool, windowless room in a Los Alamos technical area before a wall of droning electronics: MANIAC. One of the world’s first scientific computers, MANIAC hummed, blinked, and hammered out rows of numbers on a mechanical printer. Tsingou had written code for a first-of-its-kind numerical experiment—now known as the Fermi–Pasta–Ulam–Tsingou, or FPUT problem. Conceived years earlier by Enrico Fermi, John Pasta, and Stanislaw Ulam, the experiment would uncover a paradox that would reshape how scientists think about systems as varied as the atmosphere, fusion plasmas, the economy, and even the rhythms of the human heart.<br>“Fermi passed away in 1954 and never saw the full paradox his idea would uncover,” says Avadh Saxena, a physicist and Lab Fellow who studies nonlinear phenomena at Los Alamos. “But the results were a watershed moment. They showed that nonlinear systems behave in surprisingly stable and structured ways, even when intuition says they should fall apart.”<br>The MANIAC computer at Los Alamos, pictured with two programmers. MANIAC was used to run the numerical experiment that helped create the field of nonlinear dynamics. It became known as the Fermi–Pasta–Ulam–Tsingou (FPUT) problem.The simulation Tsingou coded and ran over a few years was a one-dimensional line of masses connected by springs, but Fermi added a small nonlinear change to the spring force. Simple, yet it captured the nonlinear interactions of atoms, a system too small for experiments to observe directly. Fermi had designed the model to probe a fundamental assumption among physicists at the time—that even if a system wasn’t perfectly linear, energy should still spread out and thermalize much the same way it does in linear systems. The thinking went that small nonlinearities wouldn’t change how energy flows. To test that assumption, Fermi introduced a small nonlinear term into the springs’ restoring force. By hand, Tsingou wrote out the code and algorithm to simulate the problem on MANIAC.<br>“We made flowcharts,” recalled Tsingou in later interviews. She is now in her nineties and still lives in Los Alamos. “Because when you’re debugging a problem, you want to know where you are so you can stop at different places and look at things. Like any project, you have some idea, but as you go along, you have to make adjustments and corrections, or you have to back up and try a different approach.”<br>Mary Tsingou, around the time she wrote the code for the Fermi–Pasta–Ulam–Tsingou (FPUT) problem.Running the simulation unfolded over years. But on that winter day, as Tsingou watched the machine clacking out the results, she saw that the energy initially spread into other modes—just as Fermi and his coauthors had expected. But then something extraordinary happened. Energy flowed back, almost perfectly, into the mode where it had started. It was as if the system remembered its initial state and returned to it. Instead of drifting inexorably toward equilibrium, Tsingou and her collaborators had demonstrated—numerically, and for the first time—that the natural world does not always behave according to the tidy expectations of linear dynamics. Nature is messy.<br>To appreciate the magnitude of this result, a refresher on what “linear” means is a good place to start. In a linear system, causes and effects scale proportionally: double the force, double the response. Such systems are orderly, predictable, and mathematically tractable. Our engineered world depends on linear relationships that explain how things like arches, bridges, and walls hold firm. But much of nature doesn’t play by these rules. In certain natural systems, energy not only fails to disperse evenly; it can be trapped, amplified, or assembled into coherent structures that arise out of apparent disorder.<br>One shining example of how discoveries unearthed by FPUT molded the modern world is solitons, stable packets of energy that travel without dispersing. Understanding solitons proved essential to the development of long-distance optical fiber communications, which depend on pulses of light that carry information across continents. Put more simply: it was essential for creating the internet.<br>Beyond eventually tangible technologies, the FPUT experiment revealed the power of simulation as a new kind of scientific tool, one capable of uncovering physical behavior that neither hand calculation nor experiments could reach. But it also forced science to reckon with a world where prediction, stability, and control look very different than what linear dynamics proposed. “Once you move beyond the simplest interactions, everything...