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gjm comments on Open thread, Oct. 26 - Nov. 01, 2015 - Less Wrong Discussion
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Comments (106)
I think the small base argument dominates the large base argument for most use cases.
The main place the 'too many digits' argument carries weight, I think, is divisibility. It's handy to be able to express a third as a single number instead of a sequence that consumes every bit you can give it. With 60, you have short representations of halves, thirds, quarters, fifths, sixths, tenths, twelfths, fifteenths, twentieths, thirtieths, and sixtieths.
You pay for that in having a larger alphabet, of course, which the Babylonians cheated on by using tallies (really, you should think of the Babylonian system as alternating places of (0-9) ones and (0-5) tens).
Hmm, that is interesting. It's also neat that it looks like truncation is a pretty natural form of rounding.
Yes, I agree that the allegedly-sexagesimal notation of the Babylonians is better thought of as a sort of compound alternating-base system. That seems inelegant enough to me that it's not at all obvious that 60 is a better choice than, say, 12.
Note, by the way, that the same things get terminating expansions in base 30 as do in base 60, it's just that some of them take longer to terminate. (Just as fractions like 1/16 terminate in base 10, just more slowly than they do in base 4, 8, or 16.)