COMPUTING SCIENCE
Group Theory in the Bedroom
An insomniac's guide to the curious mathematics of mattress flipping
Brian Hayes
Sleepers Awake
In the morning, when I Googled "mattress flipping," I
learned that I'm not the only one who's been obsessing about this
silly business. Linda Cobb, The Queen of Clean®, recommends
flipping on a seasonal schedule—side-to-side in spring and
fall, and end-over-end in summer and winter. Or maybe it's the other
way around; I forget. A Web site called eHow, which promises
"Clear Instructions on How To Do (just about) Everything"
offers the following counsel: "Rotate your mattress twice a
year, or more often if instructed by the manufacturer. Flip it over
completely after the first six months. Then, after another six
months, flip it over and turn it so that the head is at the foot of
the bed." Is that clear? What would it mean to flip it over
incompletely? And what's the difference, exactly, between
rotating, flipping and turning? Does the final instruction to flip
and turn do anything that couldn't be achieved with a
single motion?
Another Web page, Phyl's Furniture Facts, takes on the task of
defining some of this terminology: "Flipping means to turn it
over while rotating means to make a 1/4 turn of the mattress while
it lies flat on the bed." (I tried the quarter turn, but it
didn't look very comfortable.)
Versions of the illustration reproduced at right appear on dozens of
Web sites. When I first saw this diagram, I thought for a fleeting
moment that I had found my golden rule. A quarter turn, a flip,
another quarter turn—"AND THERE YOU ARE.... Turned Over
and End to End as well!" Maybe this was the magic formula. But
no: A quick experiment with a small model of a mattress—I used
a paperback book—showed that the elaborate sequence of
operations in the diagram has exactly the same effect as a half turn
end-over-end. (But the more-complicated procedure may be worth
following anyway, especially in a room with a low ceiling.)
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