Full explainer:
Sixty has twelve divisors, more than any smaller number, so an hour splits into thirds, quarters, fifths and sixths of whole minutes. (The 24 hours are Egyptian; Greek astronomers divided them in sixties, the Babylonian way: Neugebauer, The Exact Sciences in Antiquity, p. 81.)
• A seventh of an hour is 8 minutes 34 2/7 seconds; in base 60 its places repeat forever: 0;8,34,17,8,34,17,… Seven does not divide sixty, and no whole-number base ends every fraction (1/n ends exactly when every prime factor of n divides the base).
• In decimals a third repeats (0.333…); in base 12 thirds end (0.4) but fifths repeat (0.2497 2497…); base 60 ends both, but with a separate sign per digit it means 60 digits and 3,541 facts to learn (60 signs + 1,770 addition and 1,711 multiplication facts, each pair once), against 91 in base 10.
• The full video scores 60, 10, 12, 72 and 6 on dividing, learning and length, over 1,891 weightings, and answers whether we should switch.
Every number computed in Tungsten:
Animation drawn in Tungsten; narration by ElevenLabs.
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