Ever wondered what shaving cream, whipped topping, and the very structure of your cells have in common? Surprisingly, the answer lies in the secret logic of artificial intelligence, specifically, how everyday foam behaves. For years, scientists believed that foams, like glass, were static, with their tiny components locked in place. But new research is turning this understanding on its head. Engineers at the University of Pennsylvania have made a groundbreaking discovery: the internal motion of foam closely mirrors the mathematical principles behind deep learning, the engine that powers modern AI. This finding suggests a shared organizing principle across physical, biological, and computational systems. But here's where it gets controversial: Can something as simple as foam teach us about the very nature of learning itself?
Let's dive deeper. In a study published in the Proceedings of the National Academy of Sciences, researchers used computer simulations to track the movement of bubbles within a wet foam. The results were unexpected. Instead of settling into fixed positions, the bubbles were in constant motion, exploring numerous possible arrangements.
From a mathematical standpoint, this behavior closely resembles how deep learning works. During training, an AI system repeatedly adjusts its parameters—the information that defines what an AI "knows"—rather than locking into a single final state. This continuous adjustment allows AI to learn and adapt, much like the bubbles in the foam. "Foams constantly reorganize themselves," explains John C. Crocker, Professor in Chemical and Biomolecular Engineering (CBE) and the paper's co-senior author. "It's striking that foams and modern AI systems appear to follow the same mathematical principles. Understanding why that happens is still an open question, but it could reshape how we think about adaptive materials and even living systems."
Why is this so surprising? Because for a long time, scientists viewed foams through a very different lens. Foams often appear solid at a human scale, maintaining their shape and bouncing back after being squeezed. At the microscopic level, however, foams are "two-phase" materials, consisting of bubbles suspended in a liquid or solid background. Traditional theories treated foam bubbles like rocks rolling across an energy landscape, settling into the lowest energy positions. However, when researchers examined real foam data, they found a mismatch between theory and reality. The bubbles weren't behaving as predicted.
And this is the part most people miss: Solving this puzzle required a new approach, one that could describe systems that continue changing without ever settling into a single, fixed arrangement. Enter artificial intelligence. Modern AI systems learn by continuously adjusting numerical parameters during training. Early approaches aimed for a single optimal solution, but deep learning relies on optimization methods related to gradient descent. Over time, researchers realized that pushing models too far into the deepest possible solutions caused problems. Systems that fit their training data too precisely became fragile and performed poorly on new information. "The key insight was realizing that you don't actually want to push the system into the deepest possible valley," says Robert Riggleman, Professor in CBE and co-senior author of the paper. "Keeping it in flatter parts of the landscape, where lots of solutions perform similarly well, turns out to be what allows these models to generalize."
When the Penn team reexamined their foam data using this perspective, the similarity became clear. Foam bubbles don't settle into deep, stable positions. Instead, they continue moving within broad regions where many configurations are equally viable. The same mathematics that helps explain why deep learning works also captures what foams have been doing all along.
The implications of this research are far-reaching. By showing that foam bubbles move in ways similar to learning algorithms, the research encourages scientists to rethink how other complex systems behave. Crocker's team is now revisiting the cytoskeleton, the microscopic framework inside cells that supports life. Like foam, the cytoskeleton must continually reorganize while preserving its overall structure. "Why the mathematics of deep learning accurately characterizes foams is a fascinating question," says Crocker. "It hints that these tools may be useful far outside of their original context, opening the door to entirely new lines of inquiry."
This research, supported by the National Science Foundation, has opened a new door for understanding the world around us.
What do you think? Does this change how you view everyday materials? Could this lead to breakthroughs in material science or even medicine? Share your thoughts in the comments below!
