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If we didn't have ten fingers would we care so much about decimals? They aren't particularly well suited to anything more than any other number system. Base 12

If we didn't have ten fingers would we care so much about decimals? They aren't particularly well suited to anything more than any other number system. Base 12 actually has a lot more going for it.

chriswarbo 3y ago
The best thing about SI is that it only has one unit per dimension, and no conversion factors between units (it is "coherent"). Unfortunately, this simplicity and elegance usually goes unappreciated; while people focus on arbitrary powers of ten (e.g. that 100 hundredths is one) http://www.chriswarbo.net/projects/units/metric_red_herring.html http://www.chriswarbo.net/projects/units/metric_red_herring.... PS: The SI unit of time is the "second"; which is actually a sexagesimal fraction (a "pars minuta secunda", AKA a second small part; which is a sixtieth of a "pars minuta", a sixtieth of an hour)
- evanb 3y ago
  Just appending 0s to change scale is true in any base. If you'd grown up in base 12 you'd write that 100 one-hundred-forty-fourths is one and that there's nothing particularly simple about A As (84 in your natural numerals), where A=9+1.
- zokier 3y ago
  That is somewhat idealistic view on SI, and even more so of the metric system. While SI is nominally coherent, it is in practice accomplished by having very awkward values for defining constants, and that factor is excluded from the coherence consideration. E.g. to convert from seconds to meters you need to use conversion factor c, which is very much not 1. I would also be very careful and not conflate metric and SI systems. There are all sorts whacky metric systems (although most of them historical) that are not nearly as clean as SI. And even SI historically has been messier than its today.
  - Armisael16 3y ago
    c is used in the definition of the meter, but you don’t remotely need to know that in day-to-day life. As long as the seven base units (length, time, mass, temperature, electric current, luminosity) end up with reasonable values the system is practically coherent. (are the values reasonable? well, human-scale capacitors and resistors seem pretty heavily skewed away from the center of the scale…)
  - chriswarbo 3y ago
    > e.g. to convert from seconds to meters you need to use conversion factor c, which is very much not 1. SI cannot "convert from seconds to meters", since it treats length and duration as separate dimensions. Any multiplier which turns a duration into a length must have dimension of length/duration (and hence SI units of meters/seconds); something with those units is a speed, not a conversion factor (which is dimensionless). That's not specific to any particular speed, whether c or otherwise.
    - zokier 3y ago
      My example was weak, but the greater point is that SIs coherence is oversold because it still requires many unnecessary (non-one) constant factors in equations; SI merely brushes the issue under the rug by labeling those as "fundamental" as if they are not almost completely arbitrary.
DeathArrow 3y ago
But we do have 10 fingers. And apart from that, base 10 is just about right. Not too small to be hard to comprehend, not too big to force your memory. Would it be easier for you if you are using base 2 or base 16?
- Eisenstein 3y ago
  I think having 1/4 and 1/3 be whole numbers would be more useful than being able to count on my fingers.
  - DeathArrow 3y ago
    Are 3 and 4 magical? Why not 1/2 and 1/5?
    - willis936 3y ago
      They're all magical because they are small. 12 is a highly factorable number and 10 is not. Ancient Greece was not ignorant of this fact. https://en.wikipedia.org/wiki/Highly_composite_number https://en.wikipedia.org/wiki/Highly_composite_number https://youtu.be/2JM2oImb9Qg https://youtu.be/2JM2oImb9Qg
    - Cockbrand 3y ago
      Well, 10 is only divisible by 2 and 5, while you can divide 12 by 2, 3, 4 and 6 (in the integer space, of course). So you can express more basic divisions without remainder.
    - jcranmer 3y ago
      It is easy to eyeball divisions of 2 and 3 by hand, and get results with high degrees of accuracy. A division of 4 can be accomplished by dividing by 2 twice. It is not easy to eyeball divisions of 5 by hand; you pretty much need to use a ruler for that to get results of tolerable accuracy.
  - chriswarbo 3y ago
    There are finger-counting methods for pretty much any base. Most are more efficient (capable of counting higher) than the base 10 approach of associating each finger with a digit https://en.wikipedia.org/wiki/Finger-counting https://en.wikipedia.org/wiki/Finger-counting
EdiX 3y ago
The duodecimal meme needs to die. Base 12 is not that much better than base 10. Yes it has more integer divisors (2, 3, 4, 6) than base 10 (2, 5) but there's only two reasons to care about that. The first one is to split a batch of something: there's more ways to split 12 of something than 10 of something, but you can use base 10 and still do things in batches of 12. The second reason is for easy divisibility checks, but for that all that matters is prime divisors. Base 12 and base 10 have the same number of prime divisors 2 and 3 versus 2 and 5. But base 10 has an interesting property here, because 10-1 is 9, which is a power of 3 you get somewhat easy divisibility rules for both 9 and 3. 12-1, on the other hand, is 11 which is prime so you only have a relatively uninteresting divisibility rule for 11. I think at best you can claim that 12 is about as good as 10. Base 60 would be strictly better than base 10 if it weren't for the fact that we can't easily memorize multiplication tables for base 60.
- shortrounddev2 3y ago
  >we can't easily memorize multiplication tables for base 60. I don't think anybody memorizes multiplication tables anymore. At least I wasn't taught that when I was in school (I'm 29)
  - EdiX 3y ago
    You would still have to memorize 60 different symbols. A base so large is unwieldy either way.
  - cl3misch 3y ago
    I think you do memorize them, albeit not consciously. The results of operations on small numbers are "cached" in your head while operations on large numbers are subdivided into more operations on smaller numbers, and so on. I guess OP meant that for a base-60 system we would have to do a lot of caching.
  - recursive 3y ago
    How do you calculate 5 * 7? With a calculator?
- 3y ago
bcye 3y ago
Base 10 isn't so special either, there are some cultures that used/are using base 8, counting the spaces between their fingers instead: https://en.wikipedia.org/wiki/Octal https://en.wikipedia.org/wiki/Octal

If we didn't have ten fingers would we care so much about decimals? They aren't particularly well suited to anything more than any other number system. Base 12 actually has a lot more going for it.

chriswarbo 3y ago

The best thing about SI is that it only has one unit per dimension, and no conversion factors between units (it is "coherent"). Unfortunately, this simplicity and elegance usually goes unappreciated; while people focus on arbitrary powers of ten (e.g. that 100 hundredths is one) http://www.chriswarbo.net/projects/units/metric_red_herring.html http://www.chriswarbo.net/projects/units/metric_red_herring.... PS: The SI unit of time is the "second"; which is actually a sexagesimal fraction (a "pars minuta secunda", AKA a second small part; which is a sixtieth of a "pars minuta", a sixtieth of an hour)

evanb 3y ago
Just appending 0s to change scale is true in any base. If you'd grown up in base 12 you'd write that 100 one-hundred-forty-fourths is one and that there's nothing particularly simple about A As (84 in your natural numerals), where A=9+1.
zokier 3y ago
That is somewhat idealistic view on SI, and even more so of the metric system. While SI is nominally coherent, it is in practice accomplished by having very awkward values for defining constants, and that factor is excluded from the coherence consideration. E.g. to convert from seconds to meters you need to use conversion factor c, which is very much not 1. I would also be very careful and not conflate metric and SI systems. There are all sorts whacky metric systems (although most of them historical) that are not nearly as clean as SI. And even SI historically has been messier than its today.
- Armisael16 3y ago
  c is used in the definition of the meter, but you don’t remotely need to know that in day-to-day life. As long as the seven base units (length, time, mass, temperature, electric current, luminosity) end up with reasonable values the system is practically coherent. (are the values reasonable? well, human-scale capacitors and resistors seem pretty heavily skewed away from the center of the scale…)
- chriswarbo 3y ago
  > e.g. to convert from seconds to meters you need to use conversion factor c, which is very much not 1. SI cannot "convert from seconds to meters", since it treats length and duration as separate dimensions. Any multiplier which turns a duration into a length must have dimension of length/duration (and hence SI units of meters/seconds); something with those units is a speed, not a conversion factor (which is dimensionless). That's not specific to any particular speed, whether c or otherwise.
  - zokier 3y ago
    My example was weak, but the greater point is that SIs coherence is oversold because it still requires many unnecessary (non-one) constant factors in equations; SI merely brushes the issue under the rug by labeling those as "fundamental" as if they are not almost completely arbitrary.

DeathArrow 3y ago

But we do have 10 fingers. And apart from that, base 10 is just about right. Not too small to be hard to comprehend, not too big to force your memory. Would it be easier for you if you are using base 2 or base 16?

Eisenstein 3y ago
I think having 1/4 and 1/3 be whole numbers would be more useful than being able to count on my fingers.
- DeathArrow 3y ago
  Are 3 and 4 magical? Why not 1/2 and 1/5?
  - willis936 3y ago
    They're all magical because they are small. 12 is a highly factorable number and 10 is not. Ancient Greece was not ignorant of this fact. https://en.wikipedia.org/wiki/Highly_composite_number https://en.wikipedia.org/wiki/Highly_composite_number https://youtu.be/2JM2oImb9Qg https://youtu.be/2JM2oImb9Qg
  - Cockbrand 3y ago
    Well, 10 is only divisible by 2 and 5, while you can divide 12 by 2, 3, 4 and 6 (in the integer space, of course). So you can express more basic divisions without remainder.
  - jcranmer 3y ago
    It is easy to eyeball divisions of 2 and 3 by hand, and get results with high degrees of accuracy. A division of 4 can be accomplished by dividing by 2 twice. It is not easy to eyeball divisions of 5 by hand; you pretty much need to use a ruler for that to get results of tolerable accuracy.
- chriswarbo 3y ago
  There are finger-counting methods for pretty much any base. Most are more efficient (capable of counting higher) than the base 10 approach of associating each finger with a digit https://en.wikipedia.org/wiki/Finger-counting https://en.wikipedia.org/wiki/Finger-counting

EdiX 3y ago

The duodecimal meme needs to die. Base 12 is not that much better than base 10. Yes it has more integer divisors (2, 3, 4, 6) than base 10 (2, 5) but there's only two reasons to care about that. The first one is to split a batch of something: there's more ways to split 12 of something than 10 of something, but you can use base 10 and still do things in batches of 12. The second reason is for easy divisibility checks, but for that all that matters is prime divisors. Base 12 and base 10 have the same number of prime divisors 2 and 3 versus 2 and 5. But base 10 has an interesting property here, because 10-1 is 9, which is a power of 3 you get somewhat easy divisibility rules for both 9 and 3. 12-1, on the other hand, is 11 which is prime so you only have a relatively uninteresting divisibility rule for 11. I think at best you can claim that 12 is about as good as 10. Base 60 would be strictly better than base 10 if it weren't for the fact that we can't easily memorize multiplication tables for base 60.

shortrounddev2 3y ago
>we can't easily memorize multiplication tables for base 60. I don't think anybody memorizes multiplication tables anymore. At least I wasn't taught that when I was in school (I'm 29)
- EdiX 3y ago
  You would still have to memorize 60 different symbols. A base so large is unwieldy either way.
- cl3misch 3y ago
  I think you do memorize them, albeit not consciously. The results of operations on small numbers are "cached" in your head while operations on large numbers are subdivided into more operations on smaller numbers, and so on. I guess OP meant that for a base-60 system we would have to do a lot of caching.
- recursive 3y ago
  How do you calculate 5 * 7? With a calculator?
3y ago

bcye 3y ago

Base 10 isn't so special either, there are some cultures that used/are using base 8, counting the spaces between their fingers instead: https://en.wikipedia.org/wiki/Octal https://en.wikipedia.org/wiki/Octal