v 6.30.00
28 Jan 2022
updated 28 Jan 2022

Complex Numbers

Needless to say, many denominations of coinage have come and gone in the British Isles over the past millennium or two, but the most recent pre-decimal UK versions displayed to the full the prevailing genius for dogged conservatism allied with open-minded flexibility. Or so we liked to think; foreign visitors thought otherwise.

DenominationSymbolNumerical base
Pound (libra)£10 (decimal)
Shilling (solidus)s or /20 (vigesimal)
Penny (denarius)d12 (duodecimal)
Ha'penny (half)½ d2 (binary/bicimal)
Farthing (fourth)¼ d2 (binary/bicimal)

There were furthermore

  • The ten-bob note (10/- = one half of a pound, resuscitated as the 50p coin)
  • (Just occasionally) the crown (5/- = one quarter of a pound)
  • The half-crown (2/6d = one-eighth of a pound)
  • The florin (2/- = one-tenth of a pound)
  • Plus the sixpence (6d = half a shilling)
  • And the threepence ("threppence" or "thruppence", 3d = quarter of a shilling)
  • And (a bit further back) the groat (4d = one third of a shilling)

And of course the guinea (21/-), which survived only in the fine-art auction room, the racing world, the hotel trade, and gentlemen's tailors or outfitters (remember the Mad Hatter, whose headgear was priced at 10/6 – half a guinea in fact, as per the Tenniel illustration).

I've always been deeply impressed that people in every walk of life, who professed a total inability at numerical matters, could nevertheless cope effortlessly with multiple-base arithmetic, allied to an intrinsic calculating ability (though the multiplication tables as such would have mystified them) – providing that the context related to money or perhaps mensuration. Think shopping in the market, or filling-in pools coupons, or measuring timber in imperial lengths.

Could the psychology of demotic arithmetic have deeper implications than simply the survival of the most intrinsically numerate? I leave that to better brains than mine.