As I’m sure is the case in your house, socks go missing on a regular basis. You’re sure that every night a PAIR of socks goes into the linen basket, and that when the washing is done ALL its contents go in the machine, but, once things are dried and ready to go back in the drawers and wardrobes, some sock somewhere will be missing its partner.
Now, to try to limit this problem I have an odd-sock box. When I find a sock without a partner, it gets checked against the contents of the odd-sock box, to see if it’s a match. If it is, then great, we have recovered a pair; if it’s not, then it goes in the box. And so the contents of the odd sock box sometimes increase in number, and sometimes decrease. But mostly the contents increase.
One would of thought that if there are (say) ten odd socks in the odd-sock box, then there are ten rogue socks scattered around the house somewhere. Let’s face it, socks only ENTER the house in pairs (I’m fairly certain on this point) and only LEAVE it again in pairs, so by the law of continuity the total contents of the house should remain pairable. So where are they? I further hypothesize then that the chances of me finding a rogue sock (e.g. under a bed, on top of a bookcase, under the cat bowl etc) should be directly proportional to the number of rogue socks there are – the more rogue socks, the greater the chance of stumbling on one. Moreover, the rate of loss of socks, I suggest, is roughly constant – after all, I tend to put the same number of socks on my feet every day, so why would I be more likely to lose one one day as opposed to the next.
So we can construct a differential equation for the number of rogue socks in the house – the rate of increase of rogue socks is equal to a constant (for the loss part) minus another constant times the total number lost (for the re-discovery) part. A bit of maths tells me then that I would expect the number of rogue socks to eventually reach a limit, when the rate of loss equals the rate of discovery, and approach that limit exponentially, rather like the voltage across a charging capacitor.
Alas, experimental data suggests that there is no sign of such a limit being reached. The contents of the odd-sock box seems to be growing linearly.
My new hypothesis, which I shall need to test, is that we have a sock eating monster in the house. Evidence for this hypothesis, I admit, is currently thin, but it would certainly explain why the cat suddenly leaps two feet in the air without warning (on being startled by the sock monster), or, in the middle of the night, runs up and down the corridor several times (being chased by the sock monster). Unfortunately, there’s also the nagging question of why the sock monster hasn’t learned to raid the sock box when it feels a bit peckish, but let’s ignore that one.
Next step is to construct a sock-monster trap (at least the bait will be easy to procure) and wait…