Group Theory In The Bed Room

Original source: SimoleonSense.com .

Nothing like a little late night math…

Introduction (Via Steven Strogatz)

My wife and I have different sleeping styles — and our mattress shows it.  She hoards the pillows, thrashes around all night long, and barely dents the mattress, while I lie on my back, mummy-like, molding a cavernous depression into my side of the bed.

Bed manufacturers recommend flipping your mattress periodically, probably with people like me in mind.  But what’s the best system?  How exactly are you supposed to flip it to get the most even wear out of it?

Brian Hayes explores this problem in the title essay of his recent book, “Group Theory in the Bedroom.”  Double entendres aside, the “group” in question here is a collection of mathematical actions — all the possible ways you could flip, rotate or overturn the mattress so that it still fits neatly on the bed frame.

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As these examples suggest, group theory bridges the arts and sciences.   It addresses something the two cultures share — an abiding fascination with symmetry.  Yet because it encompasses such a wide range of phenomena, group theory is necessarily abstract.  It distills symmetry to its essence.

Normally we think of symmetry as a property of a shape.  But group theorists focus more on what you can do to a shape — specifically, all the ways you can change it while keeping something else about it the same.  More precisely, they look for all the transformations that leave a shape unchanged, given certain constraints.  These transformations are called the “symmetries” of the shape.  Taken together they form a “group,” a collection of transformations whose relationships define the shape’s most basic architecture.

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