that's quite a feet

It's tabloid innumeracy time again. Have a look at this Daily Mail story about some canoe-footed freak who sent off for a pair of slippers off the internet, one a size 13 and the other a size 14½. He got the size 13 one back all right, or so the story goes, but there was a decimal point mix-up with the other one and he ended up with a size 1450 slipper! Which is seven feet long! Those crazy inscrutable Chinese.

Now I know what you're thinking, because it's what I was thinking - why would a decimal point mix-up result in a size 1450 slipper? A size 145 one, sure, but how and why would they have slipped the extra zero in? And while there isn't a strict linear relationship between shoe sizes, surely common sense dictates that a ratio of 100 between the shoe sizes would have resulted in a ratio of more than seven (if we assume, and let's do that for the moment, that the proper size one would have been about a foot long) between the slippers?

Time to pop over to Wikipedia for the lowdown on how UK shoe sizes are calculated. It turns out that the length difference between successive shoe sizes is a barleycorn, or a third of an inch, and that an adult size 1 shoe will fit a foot 8⅔ inches long. The upshot of which is that given either the shoe size S or the foot length L (in inches) you can calculate the other by plugging it into one of the following formulae:

• S = 3L - 25
• L = (S + 25)/3

So if you had a foot that was exactly a foot long, you would take a size 11 shoe. Similarly, a size 14.5 shoe would fit a foot (14.5 + 25)/3 = 13.2 inches long.

So what of the claim in the original story? Well, let's plug some numbers into the formulae and see what falls out. A seven-foot slipper is 84 inches long, which means it corresponds to shoe size 227. On the other hand, a size 145 slipper is 56.7 inches long, or about 4 feet 9 inches. Stick an extra factor of ten into the mix, though, and you find that a size 1450 slipper is 491.7 inches long, or a fraction under 41 feet. Considerably bigger than the one in the picture, clearly.

So pretty much none of the numbers in the Mail's story bear any resemblance to reality. It seems most likely that what they've got hold of here is a publicity stunt for a shoe-related website, combined that with a failure to do even the most basic checking of either the facts or the sanity of the numbers being thrown around, and vomited up this pointless abomination onto the page.