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Can't divide 16 by 3 though; the nice thing about 12 is that you get nice natural numbers for many common divisors: >>> 12/2, 12/3, 12/4, 12/5, 12/6, 12/7, 1

Can't divide 16 by 3 though; the nice thing about 12 is that you get nice natural numbers for many common divisors: >>> 12/2, 12/3, 12/4, 12/5, 12/6, 12/7, 12/8 (6.0, 4.0, 3.0, 2.4, 2.0, 1.7142857142857142, 1.5) >>> 16/2, 16/3, 16/4, 16/5, 16/6, 16/7, 16/8 (8.0, 5.333333333333333, 4.0, 3.2, 2.6666666666666665, 2.2857142857142856, 2.0) With base-12, only 7 is awkward (and that's probably okay as it's not that common) and the non-natural numbers of 2.4 and 1.5 when dividing by 5 and 8 are still fairly easy to deal with. Dividing by the common figures of 2, 3, and 4 gives nice numbers. Base-16 has the "infinite number problem" for 3 and 6 that base-10 has, and only 2, 4, and 8 give natural numbers. This is probably why there are 12 months and why people used "a dozen" for a long time.

monopoliessuck 4y ago
Sure and I agree with you, except base 16 is binary reducible all the way down which isn't a small thing. The Imperial or US standard systems of measure rounded the horses on halving in an awkward way because halving is intuitive. 1/2, 1/8, 1/16, 1/32 of an inch etc. and it's proven very useful. Splitting a meter into ten is less useful than splitting it in half and that half into half. Base ten doesn't half indefinitely across units bases. 1000cm, 500cm, 125cm, 62.5cm, 31.25, 15.625, 7.8125, 3.90625, 1.953125, 0.9765625... 4096cm, 2048cm, 1024cm, 512cm, 256, 128, 64, 32, 16, 8, 4, 2, 1 (which of course looks a lot better in base 16 notation) 1000, 800, 400, 200, 100, 80, 40, 20, 10, 8, 4, 2, 1 We could have had the best of both worlds. When SI was getting standardized there was a proposal for extra glyphs for base 12 and 16 that would have obviated our overloading of A-F too. Measuring in 1/256 of an inch would have been crazy simple while also getting the other metric goodies, IMO.

monopoliessuck 4y ago

Sure and I agree with you, except base 16 is binary reducible all the way down which isn't a small thing. The Imperial or US standard systems of measure rounded the horses on halving in an awkward way because halving is intuitive. 1/2, 1/8, 1/16, 1/32 of an inch etc. and it's proven very useful. Splitting a meter into ten is less useful than splitting it in half and that half into half. Base ten doesn't half indefinitely across units bases. 1000cm, 500cm, 125cm, 62.5cm, 31.25, 15.625, 7.8125, 3.90625, 1.953125, 0.9765625... 4096cm, 2048cm, 1024cm, 512cm, 256, 128, 64, 32, 16, 8, 4, 2, 1 (which of course looks a lot better in base 16 notation) 1000, 800, 400, 200, 100, 80, 40, 20, 10, 8, 4, 2, 1 We could have had the best of both worlds. When SI was getting standardized there was a proposal for extra glyphs for base 12 and 16 that would have obviated our overloading of A-F too. Measuring in 1/256 of an inch would have been crazy simple while also getting the other metric goodies, IMO.