I intend to post something inspired by the comics. I’m not ready just yet. Until then, though, I’d like to share a neat article published in Nature. It’s about paper.
In particular, it’s about how paper crumples. When paper is crumpled, and flattened out again, it looks different. When it’s crumpled and flattened out again, it looks even more different. But you reach a point where crumping and flattening the paper stops making it look all that different. A model for the fragmentation kinetics of crumpled thin sheets, by Jovana Andrejevic, Lisa M Lee, Shmuel M Rubinstein, and Chris H Rycroft, tries to explain the process.
The skeptical reader might say this is obvious. They’re invited to write a simulation that takes a set of fold lines and predicts which sides of the paper are angled out and which are angled in. The skeptical reader may also ask who cares about paper. It’s paper because many mathematics problems start from the kinds of things one sets one’s hands on. Anyone who’s seen a crack growing across their sidewalk, though — or across their countertop, or their grandfather’s desk — realizes there are things we don’t understand about how things break. And why they break that way. And, more generally, there’s a lot we don’t understand about how complicated “natural” shapes form. The big interest in this is how long molecules crumple up. The shapes of these govern how they behave, and it’d be nice to understand that more.
The New York Times has an article explaining the paper, with more of the story of what the research is and why it’s important. This if you don’t feel comfortable reading formulas about compaction ratios or skipping over formulas to get to text again.