3 ms·

Can you provide a reference for this? I'd like to know the reasoning.

• kinghajj 16y ago
  The Wikipedia article on duodecimal should give enough reasoning.
• btilly 16y ago
  The reasoning is that when we divide something evenly, we usually want to divide it into a small number of parts. 12 divides evenly into small parts better than 10 does, and so more often provides a convenient division. For instance if we assume that half the time we need to divide into halves, 1/4 of the time into thirds, 1/8 into quarters and so on, then over 90% of the time you wish to split something into 1/2, 1/3, 1/4, 1/6 or 1/12. All of which are trivial in a duodecimal system. By contrast only 56% of the time do you wish to split into the similarly easy 1/2, 1/5 or 1/10 in decimal. Even if we say that 1/4 and 1/8 are OK in decimal, we still wind up with inconvenient repeating fractions over 3 times as often as duodecimals do.
  • Dove 16y ago
    This seemed pedantic and silly to me until I read the reasoning in the wikipedia article. After all, we use numbers to do far more things than division, don't we? However, I was impressed by the far-reaching implications of this fact. The regularity of the base 12 times table was particularly compelling. You know how easy the 2's and 5's row is to learn on the times table, right? There's an obvious pattern that's easy to memorize? Lots of numbers are like that in base 12.
• petewarden 16y ago
  A slight tangent, but I recently ran across a fascinating theory on the origin of base-12 systems. If you use your thumb as a marker, you can touch four finger joints on each hand for a total of 12 positions. I tried it and it's a surprisingly natural way of keeping count. Here's the source paper: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babyl...
  • Dove 16y ago
    Hmm. That is a very natural way to count quite high on your fingers. But it seems unlikely as the origin of the Babylonian system cited. The 60 symbols are written in base 10; if it grew out of a culture that counted to twelve on their fingers, I'd expect to see five groups of twelve, not six groups of ten. I can think of a more natural explanation. When I am counting something on my fingers (in the conventional way), I often want a way to store the tens digit. Perhaps the Babylonians did, too. That the tens digit is drawn as two groups of three is suggestive that whatever method they used stored a trinary and a binary state. So, when I count off (palms up), I get to ten on the thumb of my right hand. It has a little more dexterity than my other fingers and can store more states. It's pretty straightforward to get to six by leaving it bent/straight and pointing out/up/in. It's natural to do while counting, too. (Bent and pointing in is a little uncomfortable if I want to use the other fingers, but then . . . you don't ever need to actually store 'six').
  • caf 16y ago
    If you use the tip of each finger as well, you can count in hex to 0xff with two hands ;)
    • what 16y ago
      You can count to 1023 in binary using both hands.
  • eitally 16y ago
    Anecdotal evidence of real life application: my mother (Indian/Pakistani, born in the '40s) counts this way. I never asked, but presumably she was either taught by her parents or in school.