How to count in base 33

You might think that with ten fingers, decimal or perhaps base 5 or 20 would be the only feasible bases in human culture. Not so:

The Yupno… have a counting system that enumerates the nostrils, eyes, nipples, belly button and climaxes in 31, for ‘left testicle’, 32, ‘right testicle’ and 33 ‘penis’.

Women of the Yupno tribe would not answer researchers’ questions so it is not clear what number system they use.

Counting systems can also become very elaborate:

In the eight century the Northumbrian theologian the Venerable Bede presented a system to count to a million, which was one part arithmetic, one part jazz hands… higher orders were expressed by moving the hands up and down the body – with a rather unpriestly image to represent 90,000: ‘grasp your loins with the left hand, the thumb towards the genitals’, Bede wrote.

I am well aware of the date but this is no hoax, but instead an extract from the first chapter of “Alex’s Adventures in Numberland” by Alex Bellos – or Alexander, as a numerologist strongly advises. The first chapter also discusses whether animals can count, explains that numbers have different qualities (ordinality and cardinality pose different challenges to chimps), and examines remote tribes with no words for “five” or more. Every page was a revelation.

The second chapter is about geometry and is not nearly so interesting but is still pretty good. It includes an explanation of the origins of the term “hypoteneuse”, so what’s not to like? I strongly suspect that the book would have been well worth buying, had the publishers not sent me a free copy anyway.

Tim Harford’s blog

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Tim, also known as the Undercover Economist, writes about the economics of everyday life.