Photo by Robert Ruggiero on Unsplash
In A Nutshell
- A physicist built a device from ordinary bars and springs that can count, store memory, and process information without any electronics.
- Each unit, called a hysteron, snaps between two stable positions and remembers which one it landed in, enabling basic digital-style computation through pure physical force.
- By adjusting where springs are attached, the same device can be reconfigured to perform different tasks, including counting mechanical cycles and telling odd numbers from even ones.
- The work points toward a future where materials sense and respond to their environment without chips, batteries, or a single line of code.
A handful of rigid bars, some off-the-shelf springs, and a steel rod might not look like much. But a physicist has shown that this deceptively simple setup can count, remember, and select between outcomes, all without a computer chip, battery, or line of code.
Joseph D. Paulsen, a physicist affiliated with St. Olaf College and Syracuse University, has built a mechanical system that can be reconfigured by adjusting physical parameters to perform basic computations using nothing more than physical forces. Published in Nature Communications, the work translates an abstract mathematical model long used to understand disordered materials like crumpled paper and demagnetized metals into a real, reconfigurable device. The result is a platform that could one day lead to materials that sense their environment and respond in precise, programmable ways, no electronics required.
At the center of the design is what physicists call a “hysteron,” the smallest possible unit of a phenomenon called hysteresis. Hysteresis is what happens when a system’s response depends not just on what’s happening to it right now, but on what happened to it before. A crumpled sheet of paper remembers being crumpled. A bent paperclip doesn’t spring back to its original shape. Paulsen’s work shows that these tiny memory-holding units can be built, linked together, and controlled with precision.
How Smart Materials Are Built From Bars That Flip Like Switches
Each hysteron is a rigid bar mounted on a central pivot, free to rotate between two hard stops, like a seesaw that can only rest at two angles. A spring connects the bar to a horizontal steel rod that slides freely on bearings, serving as the “global drive.” When the rod is pushed far enough in one direction, the spring pulls the bar past a tipping point and it snaps to its other position. This snap-and-hold behavior is what makes it a hysteron: the bar has two stable states, and which one it’s in depends on what happened before.
Matters escalate when multiple bars are connected with additional springs. By choosing whether the coupling springs run parallel or cross over each other, Paulsen can create two very different kinds of interactions. Parallel springs create a cooperative effect, encouraging neighboring bars to land in the same position. Crossed springs create a frustrated effect, pushing neighboring bars toward opposite positions. The strength of these interactions can be adjusted by sliding the attachment point of the coupling springs along the bars.
From Blueprint to Mechanical Computation
Paulsen derived a mathematical mapping that connects the physical setup directly to the abstract model theorists have used for decades. It shows that each bar’s influence on another is independent and proportional, and that forces from multiple coupling springs simply add together.
It also reveals something unusual: the interactions between bars are naturally “non-reciprocal,” meaning bar A’s influence on bar B doesn’t have to equal bar B’s influence on bar A. This asymmetry arises from geometric differences, including the range of motion each bar can access, and turns out to be necessary for some of the most interesting behaviors.
Working from that blueprint, Paulsen targeted three specific computational tasks. The first is a mechanical memory lock. Two coupled bars with crossed springs are confined to different angular ranges. A small push on the driving rod flips one bar into a new state, and when the rod returns, that bar stays put, latched in place. Only a much larger push releases it. This latching behavior had been predicted in models to explain how disordered solids form multiple memories; Paulsen’s experiment is a physical demonstration of a behavior previously seen only in simulations.
The second is a counting mechanism. A chain of bars coupled with crossed springs is staggered so that each full back-and-forth cycle of the driving rod irreversibly flips one bar in sequence, like dominoes falling in slow motion. In this configuration, a chain of six bars can count up to three full cycles.
The third and most sophisticated demonstration uses four coupled bars to distinguish between an even and an odd number of driving cycles. After an even number of cycles, the system settles into one arrangement; after an odd number, a different one. This “period-2” response had previously been found only in computer simulations. Paulsen achieved it in the lab by iteratively adjusting spring positions and stop angles, a process he describes as a form of hands-on learning.
Why These Simple Smart Materials Could Reshape Engineering
Other research groups have built mechanical devices that count or encode information, but each relies on a different, custom-built strategy. What separates Paulsen’s platform is its generality. Bars, springs, and a sliding rod can be reconfigured to perform all of these functions simply by adjusting where things are positioned. No parts need to be swapped out or redesigned.
Whether learning algorithms could eventually automate that reconfiguration, shifting the system between target behaviors the way neural networks are trained, remains an open question. So does the challenge of scaling to larger collections of bars. But the foundation is in place, and it was built from hardware that wouldn’t look out of place in a high school physics lab.
Paper Notes
Limitations
The paper acknowledges several open questions. While the interactions between mechanical hysterons are shown to be pairwise and linear, whether “mixed interactions,” where bar A’s influence on bar B is cooperative while B’s influence on A is frustrated, can be realized across all regions of the system’s parameter space requires further work. The period-2 counting behavior with four hysterons was achieved through an iterative manual adjustment process rather than a systematic algorithm, and whether a suitable learning algorithm could navigate between different target behaviors remains unsolved. The model also assumes sufficiently strong driving springs relative to coupling springs to maintain two stable states, and certain small-angle approximations break down at larger bar angles, though the exact model remains valid there.
Funding and Disclosures
The research was supported by Syracuse University research subsidy funds and St. Olaf College research subsidy funds. The work was conceived at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-2210452. The author declares no competing interests.
Publication Details
Title: Mechanical hysterons with tunable interactions of general sign | Author: Joseph D. Paulsen, Department of Physics, St. Olaf College, Northfield, MN, USA, and Department of Physics and BioInspired Institute, Syracuse University, Syracuse, NY, USA | Journal: Nature Communications (2026), 17:2799 | DOI: https://doi.org/10.1038/s41467-026-70913-2 | Data and Code Availability: Data and custom code are openly available in the figshare repository under a CC BY 4.0 license. | Received: 12 May 2025; Accepted: 5 March 2026







