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I agree with you, but think 16 would be a better base than 12 as it's binary reducible all the way down. It doesn't have a factor of three, which can be useful,

I agree with you, but think 16 would be a better base than 12 as it's binary reducible all the way down. It doesn't have a factor of three, which can be useful, but being able to natively understand and do math in a hex base would be such a boon, especially in the computer era. The Babylonians base 60 was quite a practical decision we partially inherited, but the metric 10 and Aztec 20 were probably just cavemen looking at their fingers (and toes). If you use your thumb to index the interphalangeal joints of your hand, you also get 16 which is super slick. A4 is a nice standard, but we really missed out on realizing base 16 metric.

Beltalowda 4y ago
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.
int_19h 4y ago
We're already long past the point where doing math in hex (or binary) is something that an average software engineer is likely to face. And outside of the industry, who ever cared?
- monopoliessuck 4y ago
  There's lots of practical implications to measuring in halfs indefinitely. See my response to the sister comment. Hex exists because binary switches are simple to manufacture and simple to reason about, but we've been halving measures since time immemorial and will continue to do so, even if our systems make it a bit difficult. Binary search trees aren't just base two because we liked the number. Base ten, on the other hand, is just a number we picked and it happens to check a few boxes too.

Beltalowda 4y ago

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.

int_19h 4y ago

We're already long past the point where doing math in hex (or binary) is something that an average software engineer is likely to face. And outside of the industry, who ever cared?

monopoliessuck 4y ago
There's lots of practical implications to measuring in halfs indefinitely. See my response to the sister comment. Hex exists because binary switches are simple to manufacture and simple to reason about, but we've been halving measures since time immemorial and will continue to do so, even if our systems make it a bit difficult. Binary search trees aren't just base two because we liked the number. Base ten, on the other hand, is just a number we picked and it happens to check a few boxes too.