Researchers Discover World of Mathematics in Crumpled Paper

Paper is an ideal model for studying other crumpling challenges, such as how DNA packs into a cell, or how best to cram a giant solar sail into a small satellite.

While working on his doctoral thesis at Harvard over the last few years, Omer Gottesman spent a lot of time at his desk crumpling sheets of paper, especially when he was stuck. He’d crumple a sheet, uncrumple it, stare into its depths, and think, "There must be something that would make all this mess look a little less messy."

Crumple, uncrumple, crumple. Sheet after sheet landed in the recycling bin, each one blank but for its chaotically creased geography. In time, a semblance of order emerged. Crumpled wads of paper are no doubt as old and commonplace as paper itself — "graves for failed theories," Mr. Gottesman, a physicist, has called them. But for him, the crumpled paper itself was the research.

The dynamics of crumpling are in play everywhere: in the initial unfolding of an insect’s wing; in the way DNA packs into a cell nucleus, in the challenge of how best to cram a giant solar sail into a small satellite so that it unfurls successfully. Scientists, in turn, devote considerable energy to deciphering, and trying to reduce, this complexity and disorder. Paper is an ideal model.

"Despite the apparent ease with which sheets of paper are crumpled and tossed away, crumpling dynamics are often considered a paradigm of complexity," Gottesman noted in a research paper published earlier this month in the journal Communications Physics.

"One of the key assumptions physicists make is that there are some universal properties that are shared between many disordered complicated systems," he said recently. "Studying one complicated system could teach us a lot about other systems as well." More information about mapping advanced physics of paper crumpling is available in the full article available online from the New York Times (Nov. 26, 2018)