4 ms·

The Early History of Counting

61 points by anarbadalov 3y ago

layer8 3y ago
https://web.archive.org/web/20230823212730/https://www.laphamsquarterly.org/roundtable/early-history-counting https://web.archive.org/web/20230823212730/https://www.lapha...
random3 3y ago
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
pkdpic 3y ago
> when the [notched] Lebombo bone was determined to be some 42,000 years old, it instantly became one of the most intriguing archaeological artifacts ever found. Not only does it put a date on when Homo sapiens started counting, it also marks the point at which we began to delegate our memories to external devices Awesome quick mind-expanding read. I always used to point out to art history students that evidence of painting [ground pigment stones] predates any actual preserved paintings / notches / engravings etc by a lot and even predates our speciation. https://en.m.wikipedia.org/wiki/Pigment#History https://en.m.wikipedia.org/wiki/Pigment#History We have no idea what humans and protohumans were painting for several hundred thousand years, maybe just our bodies for cooling benefits, maybe patterns, maybe counting marks. Who knows but fun to speculate on especially with such unfathomable stretches of time. Permaculture vibes. Always blows my mind.
irrational 3y ago
> Later, the surfaces of those bullae were impressed with the tokens to be sealed inside so that a bulla’s contents could be divined without having to break it open. Once it became apparent that the signs on the outside were as useful as the tokens on the inside, the tokens themselves became surplus to requirements My understanding is they continued to use bulla. They would create a clay version of a contract and then seal it inside of a clay "envelope". Then the contract would be replicated on the outside of the envelope. People could read the outside of the envelope to see what the contract stipulated, but if there was ever a disagreement (charges of the outside having been altered) then the envelope could be broken open to check the version inside to see if it matched the version on the outside.
FullyFunctional 3y ago
Great account, but ... > Whereas decimal gives rise to round numbers such as 1, 10, and 100 (or 10 squared), ... the author apparently doesn't get the irony of this. It's only "round" in base 10. Whichever system you use, will have its own "round" numbers (in my wheelhouse hex is spoken, so 0x800 is a fine round number).
- interfixus 3y ago
  It's not the author who doesn't get it. What is said is decimal gives rise to these round numbers, other bases yield other ones.
em500 3y ago
Using base-2, you could in theory count to 2^10 using 10 fingers. Unfortunately in practice many binary numbers or very difficult to represent on my fingers.
trebligdivad 3y ago
The book 'The Universal History of Numbers' by Georges Ifrah has a vast amount of detail on this from many civilisaitons. Some of it in incredible depth.

61 points by anarbadalov 3y ago

https://web.archive.org/web/20230823212730/https://www.laphamsquarterly.org/roundtable/early-history-counting https://web.archive.org/web/20230823212730/https://www.lapha...

random3 3y ago

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

pkdpic 3y ago

> when the [notched] Lebombo bone was determined to be some 42,000 years old, it instantly became one of the most intriguing archaeological artifacts ever found. Not only does it put a date on when Homo sapiens started counting, it also marks the point at which we began to delegate our memories to external devices Awesome quick mind-expanding read. I always used to point out to art history students that evidence of painting [ground pigment stones] predates any actual preserved paintings / notches / engravings etc by a lot and even predates our speciation. https://en.m.wikipedia.org/wiki/Pigment#History https://en.m.wikipedia.org/wiki/Pigment#History We have no idea what humans and protohumans were painting for several hundred thousand years, maybe just our bodies for cooling benefits, maybe patterns, maybe counting marks. Who knows but fun to speculate on especially with such unfathomable stretches of time. Permaculture vibes. Always blows my mind.

irrational 3y ago

> Later, the surfaces of those bullae were impressed with the tokens to be sealed inside so that a bulla’s contents could be divined without having to break it open. Once it became apparent that the signs on the outside were as useful as the tokens on the inside, the tokens themselves became surplus to requirements My understanding is they continued to use bulla. They would create a clay version of a contract and then seal it inside of a clay "envelope". Then the contract would be replicated on the outside of the envelope. People could read the outside of the envelope to see what the contract stipulated, but if there was ever a disagreement (charges of the outside having been altered) then the envelope could be broken open to check the version inside to see if it matched the version on the outside.

FullyFunctional 3y ago

Great account, but ... > Whereas decimal gives rise to round numbers such as 1, 10, and 100 (or 10 squared), ... the author apparently doesn't get the irony of this. It's only "round" in base 10. Whichever system you use, will have its own "round" numbers (in my wheelhouse hex is spoken, so 0x800 is a fine round number).

interfixus 3y ago
It's not the author who doesn't get it. What is said is decimal gives rise to these round numbers, other bases yield other ones.

em500 3y ago

Using base-2, you could in theory count to 2^10 using 10 fingers. Unfortunately in practice many binary numbers or very difficult to represent on my fingers.

trebligdivad 3y ago

The book 'The Universal History of Numbers' by Georges Ifrah has a vast amount of detail on this from many civilisaitons. Some of it in incredible depth.