Most people learn how important shapes are in preschool. But in a commentary in the July 25, 2024 issue of the journal Nature Chemical Engineering, a University of Wisconsin-Madison chemical engineer encourages his colleagues to remember just how influential shape can be in natural and engineered systems.
Victor Zavala, the Baldovin-DaPra Professor of chemical and biological engineering at UW-Madison, penned the piece with his former PhD student Alexander D. Smith (PhD ChemE ’22).
Victor Zavala
“We’ve been doing a lot of work in data science over the last seven years or so. And one thing we’ve discovered is that shape plays a central role in understanding data and in understanding the behavior of complex systems,” Zavala says.
In the commentary, Zavala explains that systems are collections of components that are connected in a complex manner—for example, chemical processes, the human body, and even molecules, are systems. The connectivity of these systems defines their shape and such shape influences their efficiency, flexibility, and resilience.
For instance, the cardiovascular system in our bodies has a branched structure similar to the shape of trees. “The reason for this is because the body is trying to minimize energy while pumping blood to every single extremity of the body,” says Zavala. “It turns out that is the same shape trees use to deliver resources to their branches. And it’s even the way we’ve designed our power grid, natural gas and water delivery. They have a similar shape to try to achieve a universal goal: minimize energy.”
Many chemical processes have a “community-like” shape, which tightly connects clusters of components (such clusters are known as modules). The brain also has this type of shape, since neurons are arranged in regions that conduct well-defined functions. Even data, Zavala says, takes on a shape that can be used to shed light on things like molecular simulations, microscopy, spectra, time series, and more.
Emerging tools from mathematics, including graph theory, topology and geometry, are making it much easier to quantify the underlying shape of natural and engineered systems. Knowing the shape of a system makes it easier to understand and tweak its behavior.
Zavala says that understanding shape is an important skill that engineers should acquire, just as they are trained to use statistics to understand the randomness of systems; Zavala hopes that fellow researchers appreciate and draw on the full range of modern tools that allow them to characterize shapes or make decisions using shape.
Featured image caption: The branching shape of this maple tree on the UW-Madison campus is similar to the shape of systems in the human body, the power grid, water delivery and many others. Credit: Jeff Miller/UW-Madison.