The Science of Unpredictability | Los Alamos National LaboratoryDOE/LANL Jurisdiction Fire Danger Rating:Skip To ContentLANL Homemediapublications1663April 22, 2026The Science of UnpredictabilityA Nobel laureate, a brilliant programmer, and two unexpected discoveries—the rise of nonlinear dynamics at Los Alamos.Kyle Dickman, Science WriterDownload PDFIn 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.  “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.” 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. “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.” 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.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.  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.  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 becomes emergent, coupled, and sensitive,” Saxena says. “Tiny nudges can have enormous consequences.” “Chaos, in the scientific sense, isn’t randomness or disorder. It is deterministic unpredictability.” Two decades later, in the mid-1970s, came the Lab’s second major contribution to nonlinear science. That’s when a young theorist named Mitchell Feigenbaum left Virginia for Los Alamos. Soon after arriving, Feigenbaum began picking apart another nonlinear system, one that described how the state of a system at one moment determines its state in the next.  Feigenbaum was interested in systems governed by feedback, where outputs feed back into inputs. Such models appear everywhere, from population dynamics to electrical circuits. His questions were fundamental: when does orderly behavior break down, and how does regularity give way to irregular, unpredictable behavior? Is the transition smooth, or does it follow a deeper pattern? Famously too impatient to wait for time on the Lab’s supercomputers, Feigenbaum chased his intuition about chaos with a pencil and a programmable calculator.  Mitchell Feigenbaum, photographed years after his Los Alamos work, whose discovery of universal constants revealed how nonlinear systems transition to chaos.Chaos, in the scientific sense, isn’t randomness or disorder. It is deterministic unpredictability. As many nonlinear systems are pushed harder, they don’t slide smoothly into chaos. Instead, their regular behavior fractures in stages. The process, called period doubling, describes how a system that once repeated every cycle begins oscillating between two repeating states, then four, then eight, and so on. Feigenbaum noticed that each successive doubling occurred after a change in conditions about 4.67 times smaller than the one before it. Practically speaking, this meant that in short order, infinite bifurcations were squeezed into a finite range of conditions, making long-term prediction impossible.  “I called my parents that evening and told them that I had discovered something truly remarkable that, when I had understood it, would make me a famous man,” Feigenbaum later recalled. He did indeed become famous in certain scientific circles. “The behavior of a wide class of nonlinear systems was governed by the same numbers.” From tornado formation to dripping faucets, Feigenbaum had uncovered a universal rule that governs how systems march toward chaos.By 1980, Los Alamos was well known for its contribution to the field of nonlinear dynamics and founded the Center for Nonlinear Studies, the first institute of its kind. In the decades since, researchers there have shown that the same nonlinear mathematics appear in shockwave propagation, material failure, ocean-atmosphere coupling, earthquake rupture, and astrophysical explosions. “Once you recognize the mathematics,” Saxena says, “the connections become obvious. Everything is connected.”  Read from left to right, this bifurcation diagram shows how a simple system transitions from order to chaos. Regular behavior splits through repeated doubling until the diagram dissolves into a dense cloud of points, each representing a possible outcome sensitive to minute changes in conditions. The pattern reveals that chaos is not disorder, but structured, deterministic unpredictability.“I called my parents that evening and told them that I had discovered something truly remarkable that, when I had understood it, would make me a famous man.”  Saxena and others, are applying nonlinear ideas back to the field’s computational roots through studies of quantum materials. Their work focuses on designing topological materials that could enable new kinds of quantum conductors, sensors, and diagnostics—tools that could push computational science beyond the limits of classical models. If realized, these materials could form the basis of quantum computers designed to tackle problems classical computers struggle to represent at all, like the complex nonlinear systems that Fermi, Pasta, Ulam, and Tsingou first wrestled with 70 years ago. “Human creativity, intuition, and the scientific process remain our best tools for applying nonlinear ideas to the most complex problems we face,” says Saxena.People Also Ask: What is chaos theory? Chaos theory is the study of systems that follow precise rules but behave in unpredictable ways. In chaotic systems, tiny differences in starting conditions can grow rapidly over time, making long-term prediction impossible even though the underlying physics is fully deterministic. This sensitivity is often described by the “butterfly effect,” where a small disturbance can lead to large consequences elsewhere. Chaos theory does not describe randomness or disorder. Instead, it reveals hidden structure and patterns in complex systems, showing that the transition from orderly behavior to unpredictability often follows universal mathematical rules. These ideas are central to understanding weather, turbulent flows, heart rhythms, ecosystems, and many other natural and engineered systems. ShareStay up to dateSubscribe to 1663 magazine for expert insights on groundbreaking research initiatives and innovations advancing both national-security programs and basic science.Subscribe NowMore 1663 Stories1663 HomeWhat and Why: Los Alamos Discoveries80+ years of game-changing science and engineeringDiscovery of a LifetimeLos Alamos scientists measured the neutron lifetime with record accuracy.From Ghost Particle to Cosmic MessengerLos Alamos has a long legacy of neutrino scienceFission, Fusion, and the Data Behind BothDecades of Los Alamos discoveries, from the birth of fission to the edge of fusion.The Universe’s Brightest MysteryLos Alamos scientists turned nonproliferation instruments into tools of cosmic revelation.Big Change for Information ExchangeThe archive that rewired research and launched a revolutionPrevious12NextFollow usKeep up with the latest news from the Lab

The field of nonlinear dynamics originated from foundational work conducted at Los Alamos, driven by the exploration of potential paradoxes within physical systems. This trajectory began with the Fermi–Pasta–Ulam–Tsingou (FPUT) problem, an experiment designed to test the assumption that systems, even when non-linear, would thermalize similarly to linear systems. Mary Tsingou coded and ran a numerical simulation of this problem using the MANIAC computer, which revealed that the system exhibited unexpected behavior where energy flowed back into the initial mode, demonstrating that natural systems do not conform to the tidy expectations of linear dynamics. This discovery established that nonlinear systems can trap, amplify, or assemble energy into coherent structures, providing a crucial counterpoint to the classical understanding of linear relationships where causes and effects scale proportionally.

The implications of understanding nonlinearity extended beyond theoretical physics, yielding tangible technological advancements. The insights from the FPUT experiment led to the discovery of solitons, stable packets of energy that do not disperse, which proved essential for the development of long-distance optical fiber communications and the infrastructure of the internet. Furthermore, the work underscored the power of simulation as a scientific tool capable of uncovering physical behaviors inaccessible through purely analytical methods, forcing science to accept a reality where prediction and stability are governed by more complex principles than linear mechanics alone.

Later, in the mid-1970s, the focus shifted toward understanding the transition from orderly behavior to unpredictable states, catalyzed by the work of Mitchell Feigenbaum. Feigenbaum investigated systems governed by feedback, seeking to determine when regularity breaks down into irregularity. He discovered that chaos in the scientific sense is not randomness or disorder but rather deterministic unpredictability. This transition is characterized by period doubling, a process where a system's regular behavior fragments through successive halving of cycles, following universal mathematical rules. Feigenbaum demonstrated that these transitions are governed by universal constants, suggesting that the behavior of a wide class of nonlinear systems is governed by the same underlying mathematics.

Since these initial discoveries, Los Alamos has established a lasting legacy in nonlinear science, leading to the founding of the Center for Nonlinear Studies. Researchers have since applied these nonlinear mathematical concepts widely across various domains, including shockwave propagation, material failure, ocean-atmosphere coupling, and astrophysics, emphasizing that the underlying mathematical connections across these seemingly disparate fields are universally linked. Modern research continues to leverage these nonlinear ideas in computational science, focusing on designing topological materials to develop new quantum conductors and sensors. This work aims to push computational capabilities beyond classical models, potentially enabling quantum computers to address complex nonlinear problems that classical computation struggles to handle, reinforcing the view that human creativity and intuition remain indispensable in applying these advanced concepts to the most complex physical phenomena.