Sometimes I think about things too much.

In my head there’s the concept of wallet entropy which is a measure of how fragmented the currency in your wallet currently is. So if you’ve just touched down in a foreign country and all your currency is in a small number of large denominations then you have very low wallet entropy, and of course a high wallet entropy results from an excess of shrapnel[1].

Money transactions are, naturally, entropy transforming properties (though unlike thermodynamic entropy there is no energy gradient to traverse. That would be fun – a wallet which gave off heat when you combined five 20p pieces into a £1 coin…). For example, you are buying lunch and the total comes to £3.64 – you pay with a £5 note. Now the most efficient change you could be given is a £1 coin, a 20p coin, a 10p coin a 5p coin and a 1p coin. Your wallet entropy has just sky-rocketed!

A wallet exothermic process (so to speak) would be one where, for instance, you paid for goods totalling £5.10 with a £10 and a 10p piece, to be given a £5 note as change.

Some transactions maintain entropy whilst nevertheless changing the wallet’s value. If you give a £1 coin and get a 50p coin back then your wallet entropy has remained constant.

For me, the entropy seems to be cyclic – sometimes I’m working hard to get my entropy up (because I know I’ll need change for car parking for example), other times getting it down to avoid my wallet becomming too bloated to fit nicely in my pocket.

I suspect there is actually a wallet entropy equilibrium which I am constantly circling wherein you have enough entropy for small payments where notes aren’t accepted but not so much that your wallet becomes unusable.

In fact that’s probably a universal property – if you have lots of change in your wallet and you’re at a shop where they’re low on change, you are likely to pay in smaller denominations (and so, more coins) to equalise the entropy between the two of you as much as possible.

Till tomorrow, I hope.

Mark

  1. This might just be a British English expression for the lowest coin denominations like 1p and 2p pieces. [↩]