4 ms·

I'd argue that the bones 42,000 years ago, mark the first "writing". Likely counting predates that in verbal/sign form. I don't understand how one could get to

I'd argue that the bones 42,000 years ago, mark the first "writing". Likely counting predates that in verbal/sign form. I don't understand how one could get to 12 counting finger joints on one hand. I count 14 or 15 :) Edit: better explanation on wikipedia https://en.wikipedia.org/wiki/Duodecimal https://en.wikipedia.org/wiki/Duodecimal you can count 12 by using the thumb and counting the other 4 fingers

gumby 3y ago
My ma learned to do arithmetic this way as a kid and still uses it.
- riffraff 3y ago
  Does she count up to 12 on one hand but up to five on the other? This always confused me about the 60 explanation. It seems to me either you count up to 12 on both hands 24 or 144), or you might as well use the fingers of one hand to point to the joints on the other, thus getting 14 * 5. And the five itself is suspicious: you can count to 6 * 12 not 5 * 12, since you can raise 0..5 fingers.
  - 082349872349872 3y ago
    I think it more likely that ranchers count their animals (moving through a gate?) on fingers (and wind up with base-5 à la Yan Tan Tethera or base-10) while bakers count stationary things in nice rectangles (and wind up with base-6 or base-12), so base-60 was just a reconciliation (have hot dog packs and hot dog bun packs reconciled yet?).
  - gumby 3y ago
    Sexagesimal was quite common because it’s so useful (lots of factors). 144 wouldn’t be as handy, I think. Because of all the factors, in many cases it’s easier to do calculations in base 60 (or 12) in your head, in particular for human scale things where factors like 2/3 make sense. I do this every day without thinking about it. Base 10 is pretty lame.
  - yencabulator 3y ago
    Use a finger on your right hand to point to a joint/pad on your left hand (not including the left thumb). First, your right index finger goes through 12 values, then your right middle finger goes through the next 12 values, and so on. 5*12 = 60.
    - riffraff 3y ago
      But why not include the thumb? If you count using the thumb it makes sense, but if you use the other hand why would you skip it?
      - yencabulator 3y ago
        Maybe because base-60 has some numerological property that makes it easier to use than base-72? All I can think of off-hand is that 60/5=12 while you can't divide 72 evenly by 5. 72 wins at dividing by 8 & 9, but it might be more rare to split a pile of things into that many. 60's divisors connect more neatly back to base-10, but that's probably a modern era concern, not valid back then. Also, your thumb has one fewer exposed joint/pad -- the base sort of blends in with the palm, the final joint is much further down -- so they might have felt it's "different".
abdullahkhalids 3y ago
There are three fleshy parts on each finger. Four fingers on each hand. Use thumb to point at each fleshy part in sequence to count from 1-12. This is what I do for counting/addition. However, recently getting into music. Now, add a fourth count on each finger (point with thumb at the fleshy part on the palm just below each finger), to get a 16 count on one hand.
em500 3y ago
This is already concisely explained in the article The Mesopotamians’ unique counting method is thought to come from a mix of a duodecimal system that used the twelve finger joints of one hand and a quinary system that used the five fingers of the other. By pointing at one of the left hand’s twelve joints with one of the right hand’s five digits, or, perhaps, by counting to twelve with the thumb of one hand and recording multiples of twelve with the digits of the other, it is possible to represent any number from 1 to 60. How is the long winded Wikipedia article a better explanation?
- random3 3y ago
  I'm not able to descipher how it works from that fragment. This on wikipedia is clear, however: > Using the thumb as a pointer, it is possible to count to 12 by touching each finger bone, starting with the farthest bone on the fifth finger, and counting on

gumby 3y ago

My ma learned to do arithmetic this way as a kid and still uses it.

riffraff 3y ago
Does she count up to 12 on one hand but up to five on the other? This always confused me about the 60 explanation. It seems to me either you count up to 12 on both hands 24 or 144), or you might as well use the fingers of one hand to point to the joints on the other, thus getting 14 * 5. And the five itself is suspicious: you can count to 6 * 12 not 5 * 12, since you can raise 0..5 fingers.
- 082349872349872 3y ago
  I think it more likely that ranchers count their animals (moving through a gate?) on fingers (and wind up with base-5 à la Yan Tan Tethera or base-10) while bakers count stationary things in nice rectangles (and wind up with base-6 or base-12), so base-60 was just a reconciliation (have hot dog packs and hot dog bun packs reconciled yet?).
- gumby 3y ago
  Sexagesimal was quite common because it’s so useful (lots of factors). 144 wouldn’t be as handy, I think. Because of all the factors, in many cases it’s easier to do calculations in base 60 (or 12) in your head, in particular for human scale things where factors like 2/3 make sense. I do this every day without thinking about it. Base 10 is pretty lame.
- yencabulator 3y ago
  Use a finger on your right hand to point to a joint/pad on your left hand (not including the left thumb). First, your right index finger goes through 12 values, then your right middle finger goes through the next 12 values, and so on. 5*12 = 60.
  - riffraff 3y ago
    But why not include the thumb? If you count using the thumb it makes sense, but if you use the other hand why would you skip it?
    - yencabulator 3y ago
      Maybe because base-60 has some numerological property that makes it easier to use than base-72? All I can think of off-hand is that 60/5=12 while you can't divide 72 evenly by 5. 72 wins at dividing by 8 & 9, but it might be more rare to split a pile of things into that many. 60's divisors connect more neatly back to base-10, but that's probably a modern era concern, not valid back then. Also, your thumb has one fewer exposed joint/pad -- the base sort of blends in with the palm, the final joint is much further down -- so they might have felt it's "different".

abdullahkhalids 3y ago

There are three fleshy parts on each finger. Four fingers on each hand. Use thumb to point at each fleshy part in sequence to count from 1-12. This is what I do for counting/addition. However, recently getting into music. Now, add a fourth count on each finger (point with thumb at the fleshy part on the palm just below each finger), to get a 16 count on one hand.

em500 3y ago

This is already concisely explained in the article The Mesopotamians’ unique counting method is thought to come from a mix of a duodecimal system that used the twelve finger joints of one hand and a quinary system that used the five fingers of the other. By pointing at one of the left hand’s twelve joints with one of the right hand’s five digits, or, perhaps, by counting to twelve with the thumb of one hand and recording multiples of twelve with the digits of the other, it is possible to represent any number from 1 to 60. How is the long winded Wikipedia article a better explanation?

random3 3y ago
I'm not able to descipher how it works from that fragment. This on wikipedia is clear, however: > Using the thumb as a pointer, it is possible to count to 12 by touching each finger bone, starting with the farthest bone on the fifth finger, and counting on