The mathematics of wobbly coffee tables

There’s nothing worse than getting the wobbly table at a coffeehouse and spilling a drink all over your lap. (Okay, okay, realistically, there are quite a lot of things worse than that. The rhetorical trick of saying “there’s nothing worse than …” is, when you think about, incredibly stupid because it implies you’ve done a comparative assessment of all possible bad things that could happen in life and selected the most genuinely ghastly, gruesome experience. But hey: As rhetorical tricks go, this one’s a classic! I’m sticking with it.)

Anyway. The point is, when you get stuck with a wobbly table, is there any way to un-wobble-ify it? Most people attempt to stick a matchbook or piece of napkin underneath the leg. But André Martin, a physicist at CERN, would use a different trick: He’d rotate the table, working under the assumption that the legs were all the same length and that ground would eventually yield up four areas at the same level — producing a perfectly stable table. He’s always able to find a good orientation. That got him wondering: Could he mathematically prove his technique will always work?

Thus was born “On The Stability of Four Feet Tables” (PDF link), Martin’s recent paper arguing the proof indeed exists: Rotate a round table for long enough and you will inevitably produce stability. Mind you, Martin makes several assumptions that may dice out your particular coffeehouse: The table must be round, its legs all perfectly even, and while the ground has any number of bumps, the inclination between any two points must never be more than 15%. As a story at news@Nature points out:

Whether it will help during the coffee breaks at CERN is another matter: the ground there might be too irregular. “The trouble with the terrace is that there is both grass and paving slabs,” Martin says.

The bigger problem is that, in my experience, the problem with wobbly tables is not that the ground is uneven, but the legs are uneven. Would Martin’s proof obtain for a table with uneven legs? Assuming the legs are off by a gradation of no more than 15%, would the bumps in the floor be able to compensate for the legs? And more to the point, would the damn coffeehouse owner go out and like, buy some damn tables with even legs? And while you’re at it, pal, turn off the Bob Dylan. There’s only so much Dylan anyone can take.

(Thanks to Steve Emrich for this one!)

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I'm Clive Thompson, the author of Smarter Than You Think: How Technology is Changing Our Minds for the Better (Penguin Press). You can order the book now at Amazon, Barnes and Noble, Powells, Indiebound, or through your local bookstore! I'm also a contributing writer for the New York Times Magazine and a columnist for Wired magazine. Email is here or ping me via the antiquated form of AOL IM (pomeranian99).

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