4 ms·

I've once heard the base 12/base 60 system is derived from how people used to count with their fingers long ago: 1 hand has a thumb and four other fingers, ea

I've once heard the base 12/base 60 system is derived from how people used to count with their fingers long ago: 1 hand has a thumb and four other fingers, each consisting of 3 parts. So you point with your thumb to one of these 3 times 4=12 parts. If you run out of numbers, you take your other hand an put up a finger, then start counting from 1 with the other hand again. 5 fingers give you 5 times 12=60 possible combinations. No idea why they didn't do the thumb + 12 positions stuff with the other hand, which would have given 12 times 12=144 possibilities. Speculation: Maybe there was no need as such high numbers didn't appear in practice?.

cesaref 6y ago
Base 60 was used by the babylonians. They were big into astrological observations, and so I think their influence affected time and angle calculations. The numbers 12, 60 and 360 that occur in our time and angle calculations are interestingly factorials divided by 2. (4! = 24, 5! = 120, 6! = 720). Since larger factorials have both 2 and 4 as factors, they have 2^3 as part of their factorisation, and by the time you get to 6! you introduce another factor of 2, so it's not a big loss dropping one of those power of 2, you still have a huge range of factors and hence ease when working with fractions with these numbers. Attempts to replace degrees with base 10 (gradians) appears to be slow on the uptake, with radians being a more natural measurement (but who wants irrational angles in everyday life) so I think we're stuck with degrees.
- krick 6y ago
  There was an attempt to replace 24h system by 10h system around the same time metric system was introduced (French Republican Revolution), as a part of (much better, IMO) French Republican Calendar. Unfortunately, it didn't gain enough momentum and was cancelled after not so long. Babylonians inherited base-60 from sumerians. AFAIK, there is no real consensus why exactly it was base-60 with sumerians. One hypothesis is exactly what hyperman1 is telling us. Also, don't quote me on that, but I seem to remember hearing that 360° might have been introduced not because of divisibility specifically, but because of the size of the sun. Not sure how plausible is that, but, notably, angular diameter of the sun is ≈0.5°. So I might believe it is related, but if I'm not mistaken 5/12/60-numeric systems seem to be much older than 360°.
Jedd 6y ago
Interesting, but the fact that a sequence of finger positions indicates a number sounds risky in a blink and you get the wrong result kind of way. When we travelled to China years ago we were advised to learn the one-handed 1-10 gestures[1] which we were assured was in common use there, and solves one of the basic problems of asking for specific quantities of things without language. I guess that if you had an agreed endian (LSH / MSH?) you could represent all integers from 0-110 in a single two-handed gesture. Obviously, with 10 fingers, you could also represent 0-1023 by holding up various digits - and that's needing only two states per finger. How quickly or easily others would be able to read that representation is a different question. Plus most of us would need some training exercises to recover finger independence of pinky and ring. [1] https://en.wikipedia.org/wiki/Chinese_number_gestures https://en.wikipedia.org/wiki/Chinese_number_gestures
- xxs 6y ago
  >Obviously, with 10 fingers, you could also represent 0-1023 Some numbers would be outright banned, e.g. 132

cesaref 6y ago

Base 60 was used by the babylonians. They were big into astrological observations, and so I think their influence affected time and angle calculations. The numbers 12, 60 and 360 that occur in our time and angle calculations are interestingly factorials divided by 2. (4! = 24, 5! = 120, 6! = 720). Since larger factorials have both 2 and 4 as factors, they have 2^3 as part of their factorisation, and by the time you get to 6! you introduce another factor of 2, so it's not a big loss dropping one of those power of 2, you still have a huge range of factors and hence ease when working with fractions with these numbers. Attempts to replace degrees with base 10 (gradians) appears to be slow on the uptake, with radians being a more natural measurement (but who wants irrational angles in everyday life) so I think we're stuck with degrees.

krick 6y ago
There was an attempt to replace 24h system by 10h system around the same time metric system was introduced (French Republican Revolution), as a part of (much better, IMO) French Republican Calendar. Unfortunately, it didn't gain enough momentum and was cancelled after not so long. Babylonians inherited base-60 from sumerians. AFAIK, there is no real consensus why exactly it was base-60 with sumerians. One hypothesis is exactly what hyperman1 is telling us. Also, don't quote me on that, but I seem to remember hearing that 360° might have been introduced not because of divisibility specifically, but because of the size of the sun. Not sure how plausible is that, but, notably, angular diameter of the sun is ≈0.5°. So I might believe it is related, but if I'm not mistaken 5/12/60-numeric systems seem to be much older than 360°.

Jedd 6y ago

Interesting, but the fact that a sequence of finger positions indicates a number sounds risky in a blink and you get the wrong result kind of way. When we travelled to China years ago we were advised to learn the one-handed 1-10 gestures[1] which we were assured was in common use there, and solves one of the basic problems of asking for specific quantities of things without language. I guess that if you had an agreed endian (LSH / MSH?) you could represent all integers from 0-110 in a single two-handed gesture. Obviously, with 10 fingers, you could also represent 0-1023 by holding up various digits - and that's needing only two states per finger. How quickly or easily others would be able to read that representation is a different question. Plus most of us would need some training exercises to recover finger independence of pinky and ring. [1] https://en.wikipedia.org/wiki/Chinese_number_gestures https://en.wikipedia.org/wiki/Chinese_number_gestures

xxs 6y ago
>Obviously, with 10 fingers, you could also represent 0-1023 Some numbers would be outright banned, e.g. 132