The Mathematics of Five Pills on Edge
This morning as usual I dropped five pills into a tray, and I saw something I'd never seen in about six years of dropping the same five pills into the same tray: three of them had landed and stayed standing on edge. I'd see one pill landing that way many times and sometimes, very rarely, two standing that way. But three—never before.

All the pills are lying and standing just the way they fell from my hand. Pills A, C, and D are standing on edge (it's hard to see this in the case of pill D, but it definitely IS standing on edge). Pills B and E are lying on their sides.
As shown by the photo and the diagram below it, A's edge side is relatively wide, about three sixteenth of an inch, so it lands on its edge fairly often, about once every seven days. The edge sides of B and E are only one sixteenth inch wide, but their bodies are very large, so they almost never stand on edge when they fall, perhaps one time in fifty days. The edge sides of C and D are just as narrow, but their bodies are relatively small, so they land on edge pretty often, about one time in thirteen.
According to these rates of fall, the mathematics predict that pillls A, C, and D will all land standing on edge at the same time once in 1183 trials (7 x 13 x 13 = 1183). The event in the picture above took place after about 1095 trials (trials made every other day for about six years), so the mathematical prediction was pretty good.
Using these same figures, I can expect to see ALL FIVE PILLS land on edge one of these days. The mathematics say it's bound to happen at least once...in about 16,430 years.
That'll be something to write home about.

All the pills are lying and standing just the way they fell from my hand. Pills A, C, and D are standing on edge (it's hard to see this in the case of pill D, but it definitely IS standing on edge). Pills B and E are lying on their sides.
As shown by the photo and the diagram below it, A's edge side is relatively wide, about three sixteenth of an inch, so it lands on its edge fairly often, about once every seven days. The edge sides of B and E are only one sixteenth inch wide, but their bodies are very large, so they almost never stand on edge when they fall, perhaps one time in fifty days. The edge sides of C and D are just as narrow, but their bodies are relatively small, so they land on edge pretty often, about one time in thirteen.
According to these rates of fall, the mathematics predict that pillls A, C, and D will all land standing on edge at the same time once in 1183 trials (7 x 13 x 13 = 1183). The event in the picture above took place after about 1095 trials (trials made every other day for about six years), so the mathematical prediction was pretty good.
Using these same figures, I can expect to see ALL FIVE PILLS land on edge one of these days. The mathematics say it's bound to happen at least once...in about 16,430 years.
That'll be something to write home about.
Published on May 11, 2015 15:12
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