7 ms·

It makes no sense that our base has only 2 and 5 as factors. It is a stupid decision that can't be explained by rationality. The base 12 system is way better.

It makes no sense that our base has only 2 and 5 as factors. It is a stupid decision that can't be explained by rationality. The base 12 system is way better. It has 2 3 4 6 as factors. It's so good we use it everywhere. 2x12 hours, 12 eggs, 12 doughnuts, 12 months, 60 minutes, 12 inches. A base to be good needs many factors without being unwieldy. 10 is stupid as it skip the most useful ones 3 and 4. Nobody ever need to divide anything by 5. The perfect measurement system would be SI with base 12.

ecopoesis 10y ago
Base 10 can be explained rationally. Look at your hands. See those pointed bits? Count them. Now do you understand why use base 10?
- jcranmer 10y ago
  Look at your knuckles. You have 8 knuckles. Therefore, use base 8. You can put each finger in an up, down, or medial state, except the two thumbs which give only up or down. That gives base 28. You can count binary on your fingers as a positional number system. That's base 2. Base 10 is not the only base that's usable on our dexterous digits.
  - dragonwriter 10y ago
    > Look at your knuckles. You have 8 knuckles. If you have all fingers on one hand, the thumb of the other hand, and the last joint of each of the remaining fingers removed, sure. But 28 is the usual number of knuckles.
raattgift 10y ago
Why 12 and not 2, 1 or 1890? The choice of the number of values per position is entirely arbitrary, and almost the entire reason why you prefer twelve over ten is that twelve has more prime factors AND is close to ten. Six has the same number of prime factors as twelve; so does twenty-four. "Nobody ever need to divide anything by 5" So, what is left after you remove your "2 3 4 6 as factors" from your example up there of 60? If you work 35 or 40 hours in a week, how many hours should you expect to work on a work day?
- dredmorbius 10y ago
  Multiples of primes can be handy. 12 = 2 * 2 * 3, which gives subdivisions of 1/2, 1/3, 1/4, and 1/6. Other possibly useful values might be 30 (235) or 210 (2357), which has factors of all the primes lower than 10. The Babylonian system, based on 12, 30, 60, 120, 180, and 360 (223, 235, 2235, 2^3 * 3 * 5, and 2^3 * 3^2 * 5 respectively) have multiple useful subdivisions. Base-ten decimal is fun, but produces non-finite values when fractional values are considered: 1/3 = 0.333..., 2/3 = 0.666..., etc. Systems in which those fractions are inherently supported, and for which by Benford's law you're likely to see the divisors 2 - 9 fairly frequently (https://en.m.wikipedia.org/wiki/Benford%27s_law https://en.m.wikipedia.org/wiki/Benford%27s_law), this can be convenient. Particularly in an age of rulers, protractors, compases, and no digital electronic computors.
knz 10y ago
Isn't one of the main benefits of metric the ability to quick convert between the various scales? Converting between say 1.4m to mm is a lot easier than 4.5ft to inches. Or answering questions like how many square metres are in 5.2 hectares (vs square feet in acres). Arbitrary measurements of eggs and doughnuts (don't forget gallons) are not great examples - no one buys them for that precise amount, they buy them because that is what they are available in. I've never understood why some Americans are so stubborn about the metric system. The rest of the world has essentially made the switch for various reasons but arguably the most advanced nation on earth can't?
- recursive 10y ago
  If our number system had 12 digits, then you could apply powers of 12 by just moving the decimal point in exactly the same way.
  - knz 10y ago
    Yes, but base 10 is the common language we use today. And mm to m, is a lot easier than in to ft...
    - recursive 10y ago
      In base 10 that's all true. The comment you replied to proposed using base 12 instead. If your arguments are based on the assumption that we can only use base 10, then you can't really make an argument against base 12. It seems your arguments are constructed on the assumptions that contradict the proposal.
- gamegoblin 10y ago
  Using order-of-magnitude prefixes to scale up and down units is orthogonal to base. Things just look strange if you refer to other bases in base 10. Consider base-2 prefixes (now being known as kibi, mebi, gibi, etc) 1 kibibyte = 1024 bytes 1 mebibyte = 1048576 bytes These don't look like nice round numbers because I am representing scaling of a base 2 number in base 10. It's more clear if I say: 1 kibibyte = 10000000000 1 mebibyte = 100000000000000000000 1 gibibyte = 1000000000000000000000000000000 Each further prefix just adds 10 zeros to the binary value. Just like metric prefixes add zeros. One kilometer would still equal 1000 meters. But that 1000 is now in base 12, not in base 10. So rather than 10^3 it's now 12^3. But that just seems strange because you grew up with base 10. Eggs and doughnuts and many other things are measured in 12 because of its historical utility. It allows you to say things like "I'd like a quarter of dozen" and "a third of a dozen" which are not possible with 10. Extending a bit further, if you want division by 2, 3, 4, and 5 you can go up to base 60. The Babylonians (among others) did this and nowadays we have 60 seconds in a minute, 60 minutes in an hour, 6 * 60 degrees in a circle, etc: https://en.wikipedia.org/wiki/Sexagesimal https://en.wikipedia.org/wiki/Sexagesimal

ecopoesis 10y ago

Base 10 can be explained rationally. Look at your hands. See those pointed bits? Count them. Now do you understand why use base 10?

jcranmer 10y ago
Look at your knuckles. You have 8 knuckles. Therefore, use base 8. You can put each finger in an up, down, or medial state, except the two thumbs which give only up or down. That gives base 28. You can count binary on your fingers as a positional number system. That's base 2. Base 10 is not the only base that's usable on our dexterous digits.
- dragonwriter 10y ago
  > Look at your knuckles. You have 8 knuckles. If you have all fingers on one hand, the thumb of the other hand, and the last joint of each of the remaining fingers removed, sure. But 28 is the usual number of knuckles.

raattgift 10y ago

Why 12 and not 2, 1 or 1890? The choice of the number of values per position is entirely arbitrary, and almost the entire reason why you prefer twelve over ten is that twelve has more prime factors AND is close to ten. Six has the same number of prime factors as twelve; so does twenty-four. "Nobody ever need to divide anything by 5" So, what is left after you remove your "2 3 4 6 as factors" from your example up there of 60? If you work 35 or 40 hours in a week, how many hours should you expect to work on a work day?

dredmorbius 10y ago
Multiples of primes can be handy. 12 = 2 * 2 * 3, which gives subdivisions of 1/2, 1/3, 1/4, and 1/6. Other possibly useful values might be 30 (235) or 210 (2357), which has factors of all the primes lower than 10. The Babylonian system, based on 12, 30, 60, 120, 180, and 360 (223, 235, 2235, 2^3 * 3 * 5, and 2^3 * 3^2 * 5 respectively) have multiple useful subdivisions. Base-ten decimal is fun, but produces non-finite values when fractional values are considered: 1/3 = 0.333..., 2/3 = 0.666..., etc. Systems in which those fractions are inherently supported, and for which by Benford's law you're likely to see the divisors 2 - 9 fairly frequently (https://en.m.wikipedia.org/wiki/Benford%27s_law https://en.m.wikipedia.org/wiki/Benford%27s_law), this can be convenient. Particularly in an age of rulers, protractors, compases, and no digital electronic computors.

knz 10y ago

Isn't one of the main benefits of metric the ability to quick convert between the various scales? Converting between say 1.4m to mm is a lot easier than 4.5ft to inches. Or answering questions like how many square metres are in 5.2 hectares (vs square feet in acres). Arbitrary measurements of eggs and doughnuts (don't forget gallons) are not great examples - no one buys them for that precise amount, they buy them because that is what they are available in. I've never understood why some Americans are so stubborn about the metric system. The rest of the world has essentially made the switch for various reasons but arguably the most advanced nation on earth can't?

recursive 10y ago
If our number system had 12 digits, then you could apply powers of 12 by just moving the decimal point in exactly the same way.
- knz 10y ago
  Yes, but base 10 is the common language we use today. And mm to m, is a lot easier than in to ft...
  - recursive 10y ago
    In base 10 that's all true. The comment you replied to proposed using base 12 instead. If your arguments are based on the assumption that we can only use base 10, then you can't really make an argument against base 12. It seems your arguments are constructed on the assumptions that contradict the proposal.
gamegoblin 10y ago
Using order-of-magnitude prefixes to scale up and down units is orthogonal to base. Things just look strange if you refer to other bases in base 10. Consider base-2 prefixes (now being known as kibi, mebi, gibi, etc) 1 kibibyte = 1024 bytes 1 mebibyte = 1048576 bytes These don't look like nice round numbers because I am representing scaling of a base 2 number in base 10. It's more clear if I say: 1 kibibyte = 10000000000 1 mebibyte = 100000000000000000000 1 gibibyte = 1000000000000000000000000000000 Each further prefix just adds 10 zeros to the binary value. Just like metric prefixes add zeros. One kilometer would still equal 1000 meters. But that 1000 is now in base 12, not in base 10. So rather than 10^3 it's now 12^3. But that just seems strange because you grew up with base 10. Eggs and doughnuts and many other things are measured in 12 because of its historical utility. It allows you to say things like "I'd like a quarter of dozen" and "a third of a dozen" which are not possible with 10. Extending a bit further, if you want division by 2, 3, 4, and 5 you can go up to base 60. The Babylonians (among others) did this and nowadays we have 60 seconds in a minute, 60 minutes in an hour, 6 * 60 degrees in a circle, etc: https://en.wikipedia.org/wiki/Sexagesimal https://en.wikipedia.org/wiki/Sexagesimal