It needs to be renamed as the Tablet Theorem.
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Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
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Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#12Actual paper from 2009: https://link.springer.com/article/10.1057/jt.2009.16 Link above is clickbait blogspam (like most things on IFLScience)
The journal is named „Journal of Targeting, Measurement and Analysis for Marketing“, which may be the scientific equivalent of a clickbait blogspam site (but I haven’t checked more deeply).
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#13Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. The Egyptians used Pythagorean triples to measure right angles way before the birth of Pythagoras. But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylo…
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Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#14Earlier quoted context omitted.
> Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. I don't see why that was necessary. You can get pretty far with eyeballing it and custom cutting to fit.
A "you" can, and many individual "you"s presumably did that, to general satisfaction. But the implicit assumption you made is that eyeballing and cutting is easy, while triangles are hard, even though it's the other way around, especially with stone age tools. But we're talking about groups of people, "they", who all build a lot. Such groups tend to have a few people who make these observations, and then the observat…
>A "you" can, and many individual "you"s presumably did that, to general satisfaction
I was chatting with the person that was in charge of marking the fields for the local youth soccer league. I volunteered to help one weekend, and one of the first things he asked was if I knew what a 3/4/5 triangle was since it was the only way to know you'll be squared. I never did figure out to what level he was dead panning his joke or if he was even meaning for it to be a joke. Either way, I laughed.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#15How did he live for so long?!
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#16How did he live for so long?!
The earlier drafts of the proof were rejected by editors. He had to fight.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#17Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. The Egyptians used Pythagorean triples to measure right angles way before the birth of Pythagoras. But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylo…
Proofs are of course the gold standard. But even if others discovered the rule, their contribution should not be held to be trivial.
A modern analogy: today, people are very happy to use LLMs and Transformers without anyone "proving" that they work. Right now, philosophically, they are at the level of empirical observations (perhaps not even that). Does that mean that today's AI researchers should get no credit when at a later date? I am not sure. Empirical discovery of a rule is also no trivial thing.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#18> The Pythagorean Theorem is arguably the most famous statement in mathematics, and the fourth most beautiful equation.
Just out of curiosity, which equations are considered the top three “most beautiful?”
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#19Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. The Egyptians used Pythagorean triples to measure right angles way before the birth of Pythagoras. But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylo…
Proofs are of course the gold standard. But even if others discovered the rule, their contribution should not be held to be trivial. A modern analogy: today, people are very happy to use LLMs and Transformers without anyone "proving" that they work. Right now, philosophically, they are at the level of empirical observations (perhaps not even that). Does that mean that today's AI researchers should get no credit when…
Pointing out that it's not a theorem doesn't mean it's been trivialized.
If there's no proof, it's not a theorem, by definition. That doesn't make empirical observations worthless -- far from it!
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#20Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. The Egyptians used Pythagorean triples to measure right angles way before the birth of Pythagoras. But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylo…
> Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. I don't see why that was necessary. You can get pretty far with eyeballing it and custom cutting to fit.
> I don't see why that was necessary. You can get pretty far with eyeballing it and custom cutting to fit.
i'm not saying at all that I know the answer, but eyeballing and cutting is good for a patio, but on a ziggurat or pyramid scale it seems you don't do so much eyeballing or cutting, and more planning how much material and how many slaves you're going to need for how long, and where to put the doors so the passageways will meet up, that sort of thing.