The Early History of Counting | Hacker News Reader

The Early History of Counting

laphamsquarterly.org

61 pointsanarbadalov18 comments

> 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.

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 you can count 12 by using the thumb and counting the other 4 fingers

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?

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

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.

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

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.

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.

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?).

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.

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?

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".

> 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

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.

https://web.archive.org/web/20230823212730/https://www.lapha...

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).

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.

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.

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.

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