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.