When toast falls, what's more likely: Buttered side up or buttered side down?

July 29, 2005

Dear Cecil:

As a veteran consumer of butter, jam, and toast, I find it a continuing source of irritation that the side of the toast upon which I put the jam and butter is almost always the side that hits the kitchen floor when the toast slips off the plate. What I'm curious to know is, is there a statistically larger chance of the toast's falling on its buttered side rather than the plain side? Or is it merely my mind playing "the van is always at the corner" on me?

People in Denmark are just now noticing this, which has been the subject of rueful commentary elsewhere in the world since at least 1884? Time to get you guys up to speed:

1. Prodigious scientific resources (seriously) have been brought to bear on this phenomenon. Browsing through the literature from 1995 on I count six articles and a book.

2. By far the grandest conclusions to date have been drawn by UK physicist and science journalist Robert A.J. Matthews, who sees in tumbling toast a demonstration of Murphy's Law ("if anything can go wrong, it will") and by extension the ineluctable perversity of the universe. (Actually, he says "innate cussedness of the universe," which is to my mind too mild coming at the end of a paper [European Journal of Physics, 1995] that drags in the electronic fine structure constant, the mass of the proton, and the speed of light.)

3. Momentarily digressing, we note that Matthews attributes Murphy's Law to an honest-to-God person named Murphy, specifically U.S. Air Force captain Edward A. Murphy, whose assistant apparently hooked up the electrodes wrong during rocket-sled tests in 1949. Initially I was reluctant to credit this too-neat account because its source was a BBC-TV program, which admittedly was by the BBC but on the other hand was still TV. However, evidence turned up online squares with Matthews's take: while the basic proposition expressed by the law is ancient, Captain Murphy and associates may have given it its modern formulation.

4. According to popular belief, toast always falls butter side down because of the weight and aerodynamic properties of the butter. Orthodox scientific thought holds that popular belief is moronic and that toast falls butter side down only half the time, as a matter of chance; we think otherwise because we selectively remember the times when it happens--the "van is always at the corner" effect. The BBC seemingly confirmed OST by flinging toast into the air and noting the random distribution of results. However, according to Matthews, this merely reflects gormless journalists' failing to grasp the nub of the problem--you don't fling toast, it falls off your plate. In fact, he demonstrates, tipping off a table causes the falling toast to rotate on its way down; but since the average table is only 30 inches high, the toast doesn't have time to rotate 270 degrees from the horizontal before impact. As a moment's thought will show, toast that starts out butter side up and rotates between 90 and 270 degrees en route earthward is going to wind up butter side down. (The weight of the butter is a nonfactor.) A simple enough conclusion, but it takes Matthews 15 numbered equations to get there.

5. Matthews then launches into an ambitious effort to relate falling toast to the fundamental structure of the universe, the gist of which is that (a) bipedal creatures such as ourselves can't be more than three meters tall or we'd dash our brains out when falling due to mathematically demonstrable physical constraints; (b) the height of a table necessarily is about half human height and thus has an upper bound of 1.5 meters, which is within the gotta-fall-butter-side-down range; therefore, (c) toast falling butter side down is as much a manifestation of implacable physical laws as the orbits of the planets. This is the part where protons, the speed of light, etc come in, leading one to think: This guy has really been hitting the mai tais.

6. Impressive (if eccentric) as the foregoing is, a later paper (Bacon et al, American Journal of Physics, 2001) says Matthews and others reporting similar results have spent too much time noodling with equations and not enough time in the lab. (Key failing: inadequate consideration of toast slippage.) Experiments using video analysis software, "sophisticated modeling programs . . . to facilitate the numerical solution of nonlinear differential equations," and videotapes of actual falling toast (well, a plywood substitute for toast, the natural variability of the real thing rendering it unsuitable for precision work) show that butter-side-downness is far from the sure thing claimed by earlier investigators and may be closer to the 50-50 rate posited a priori by OST per #4 above.

7. In short, we're pretty much back where we started. You dream of the ultimo Theory of Everything? Bah. We can't get past toast.

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