They give a bit more context in this video. (from 2017)
By the way, I got that link from an article in The Guardian, and I can't find anything in either of those two articles that really adds on top of what was known in 2017. It could just be hard for a layperson to understand, and so was oversimplified?
TLDW is that researchers have known for decades that this tablet showed the Babylonians knew the Pythagorean Theorem for 1000 years before Pythagoras was born. So, that part isn't new.
They seem to be saying that what's new is that they understand each line of this tablet describes a different right triangle, and that due to the Babylonians counting in base 60, they can describe many more right triangles for a unit length than we can in base 10.
They feel like this can have many uses in things like surveying, computing, and in understanding trigonometry.
My take is that this was a very interesting discovery, but that they probably felt pressure to figure out a way to describe it as useful in the modern world. But we've known about the useful parts of this discovery for forever. Our clocks are all base 60. And our computers are binary, not base 10, just to start with.
We overvalue trying to make every advance in knowledge immediately useful. Knowledge can be good for its own sake.
"Having many more right triangles for a unit length" would have an incredible benefit in constructing enormous triangly things.
Instead becoming more acute about triangly things... we were more obtuse and went base ten
Well yeah, who's got 60 fingers? I mean sure, there's Fingers Georg, but that guy's weird.
People used to count 12 knuckles times 5 fingers for a total base 60.
Using only 5+5 fingers is the dumbed down version.
Wasn't it the Sumerians that did use base 60 and just went to counting knuckles and joints to get to the base 60 system ... never fully understood it when I read about it either
Sumerians and Babylonians used the same cuneiform writing system with a base of 6Γ10, but it seems like they also used to count to 60 as 12Γ5... and what we're left with, is the simplified 5+5=10.
Some days I wonder what would be different if weβd evolved with six fingers on each hand.
We've evolved with 14 knuckles on each hand... and a brain that struggles to keep 7 elements at once in operating memory. You can also count up to 1023 with just 10 fingers (in binary). It's not a lack of fingers problem.
I'm not sure what problem you're referring to. I mean if we naturally leant towards base 12, I wonder what would be different, if anything?
The problem is our brains have a limited operating memory. People can (unless disabled) easily track 1 o 2 items at once, even 3, 4, 5... and start losing track somewhere around 6 or 7; 8 is considered exceptional.
That's why kids don't generally use their fingers to count 2+2, but start using them for "harder" operations like 4+4.
Base 10 is already past our brain's limits... but we're kind of fine with it because we can use our fingers (think of it as evolving at a time before formal education when most people were illiterate).
Base 60 is also past our brain's limits, but it's easily divisible into easy to track 1, 2, 3, 4, 5, or 6 pieces (aka $lcm(1..6)$), which makes it highly useful. The Babylonians still used to write it down as base 6Γ10, and it was common to count on knuckles and fingers as 12Γ5.
The uneducated populace picked up the easiest part of the two: 5+5.
if we naturally leant towards base 12
If we had 12 fingers, we could've as easily ended up using base 12, only thing different would be 1/3 would equal exactly 0.4, while 1/5 would equal 0.24972497... oh well, we'd manage.
If our brains could track 12 items at once however, then we could benefit from base $lcm(1..12)$ or 27720. That... is hard to imagine, because we can't track 11 items at once; otherwise 27720 would jump out as "obviously" divisible by 11, 9, or 7.
That's very interesting. Thank you for giving us your insight on this.
They give a bit more context in this video. (from 2017)
By the way, I got that link from an article in The Guardian, and I can't find anything in either of those two articles that really adds on top of what was known in 2017. It could just be hard for a layperson to understand, and so was oversimplified?
TLDW is that researchers have known for decades that this tablet showed the Babylonians knew the Pythagorean Theorem for 1000 years before Pythagoras was born. So, that part isn't new.
They seem to be saying that what's new is that they understand each line of this tablet describes a different right triangle, and that due to the Babylonians counting in base 60, they can describe many more right triangles for a unit length than we can in base 10.
They feel like this can have many uses in things like surveying, computing, and in understanding trigonometry.
My take is that this was a very interesting discovery, but that they probably felt pressure to figure out a way to describe it as useful in the modern world. But we've known about the useful parts of this discovery for forever. Our clocks are all base 60. And our computers are binary, not base 10, just to start with.
We overvalue trying to make every advance in knowledge immediately useful. Knowledge can be good for its own sake.
"Having many more right triangles for a unit length" would have an incredible benefit in constructing enormous triangly things.
Instead becoming more acute about triangly things... we were more obtuse and went base ten
Well yeah, who's got 60 fingers? I mean sure, there's Fingers Georg, but that guy's weird.
People used to count 12 knuckles times 5 fingers for a total base 60.
Using only 5+5 fingers is the dumbed down version.
Wasn't it the Sumerians that did use base 60 and just went to counting knuckles and joints to get to the base 60 system ... never fully understood it when I read about it either
Here is a demonstration
https://mathsciencehistory.com/2021/11/09/count-to-60-with-your-phalanges/
Sumerians and Babylonians used the same cuneiform writing system with a base of 6Γ10, but it seems like they also used to count to 60 as 12Γ5... and what we're left with, is the simplified 5+5=10.
Also, we shall remember that:
π ππ°π πππ ππ πππ΅ π πππ π ππ π ππ π΅π€ πππ π¬πΎπ
Now Iβm wondering why the Babylonians didnβt have giant triangle shaped orbital habitats.
Base 60 is based.
They can math.
Base 12 is a good compromise between math and meat imo
One, two, three, four, five, six, seven, eight, nine, to market, stayed home.
Some days I wonder what would be different if weβd evolved with six fingers on each hand.
We've evolved with 14 knuckles on each hand... and a brain that struggles to keep 7 elements at once in operating memory. You can also count up to 1023 with just 10 fingers (in binary). It's not a lack of fingers problem.
I'm not sure what problem you're referring to. I mean if we naturally leant towards base 12, I wonder what would be different, if anything?
The problem is our brains have a limited operating memory. People can (unless disabled) easily track 1 o 2 items at once, even 3, 4, 5... and start losing track somewhere around 6 or 7; 8 is considered exceptional.
That's why kids don't generally use their fingers to count 2+2, but start using them for "harder" operations like 4+4.
Base 10 is already past our brain's limits... but we're kind of fine with it because we can use our fingers (think of it as evolving at a time before formal education when most people were illiterate).
Base 60 is also past our brain's limits, but it's easily divisible into easy to track 1, 2, 3, 4, 5, or 6 pieces (aka $lcm(1..6)$), which makes it highly useful. The Babylonians still used to write it down as base 6Γ10, and it was common to count on knuckles and fingers as 12Γ5.
The uneducated populace picked up the easiest part of the two: 5+5.
If we had 12 fingers, we could've as easily ended up using base 12, only thing different would be 1/3 would equal exactly 0.4, while 1/5 would equal 0.24972497... oh well, we'd manage.
If our brains could track 12 items at once however, then we could benefit from base $lcm(1..12)$ or 27720. That... is hard to imagine, because we can't track 11 items at once; otherwise 27720 would jump out as "obviously" divisible by 11, 9, or 7.
That's very interesting. Thank you for giving us your insight on this.