Group theory, visualization, and mattress longevity

Lynne Kiesling

Steve Strogatz is a professor of applied mathematics at Cornell and a master of explaining abstract mathematical principles to non-mathematicians. He also posts occasionally on the New York Times’ Opinionator blog, and his post on Sunday was a real treat. Using the domestic conundrum of how to flip your mattress to maximize its longevity and inspired by a couple of recent publications, his delightful and clear post provides a wonderful introduction to group theory.

By looking into mattress math in some detail, I hope to give you a feeling for group theory more generally.  It’s one of the most versatile parts of mathematics. It underlies everything from the choreography of contra dancing and the fundamental laws of particle physics, to the mosaics of the Alhambra and their chaotic counterparts …

The mattress group also pops up in some unexpected places, from the symmetry of water molecules to the logic of a pair of electrical switches.  That’s one of the charms of group theory.  It exposes the hidden unity of things that would otherwise seem unrelated …

I’m fascinated with symmetry and spatial relationships of objects, so I relished this post, and I hope you do too.