I have a drawer full of odd socks. Where do the missing socks go?
Christian Turner, Washington DC
Dear Mr Turner,
Like most investments in physical capital, your sock supply is depreciating. Depreciation happens. I suggest that you should work out how to minimise the damage, rather than questing after the lost socks.
The problem is simple: each half of a unique pair of socks is a perfect complement to the other half. The marginal value of the first sock is close to zero, unless you favour unconventional dress. The marginal value of the second sock is a matching pair of socks. The result of a lost sock is in fact the loss of two socks.
This problem also plagues machines: when one component fails, the entire machine may need to be scrapped. The solution is to make interchangeable parts, so that the damaged piece can be replaced. Interchangeability dates back at least to Gutenberg and the printing press in the 1450s, but formidable technical problems meant that interchangeability didn’t become common until the assembly lines of the early 20th century. Generations of engineers knew that the struggle across the centuries would eventually pay economic dividends. You, on the other hand, do not need to wait for some hard-won technological breakthrough. You should have no difficulty providing interchangeable parts for your sock drawer. Throw out your pre-industrial inventory, then go out and buy two dozen pairs of identical socks at once.
I personally find this method works extremely well. What you lose in sartorial flexibility you make up in a less wasteful pattern of sock depreciation, and a vastly quicker search of the sock drawer each morning. Your socks will still vanish mysteriously, but you are far less likely to ask metaphysical questions about the phenomenon.
Also published at ft.com.