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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)

#61

Post by moshun »

botanical wrote: post #55
somenameforme wrote: post #39

Earlier quoted context omitted.

Oh how can you skip the most fun tale of them all. [1] Its authenticity is dubious, but there's probably at least parts of truth in it. In a nutshell, Pythagoras started a cult based around numbers, and the pseudo-divine purity of rational numbers - of which everything can be represented. Hippasus, a member of said cult, however managed to compellingly demonstrate that the square root of 2 could not be a rational num…

The wiki page says he drowned: https://en.wikipedia.org/wiki/Hippasus

was drowned was the version I heard in school.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#63

Post by frankplow »

botanical wrote: post #55
somenameforme wrote: post #39

Earlier quoted context omitted.

Oh how can you skip the most fun tale of them all. [1] Its authenticity is dubious, but there's probably at least parts of truth in it. In a nutshell, Pythagoras started a cult based around numbers, and the pseudo-divine purity of rational numbers - of which everything can be represented. Hippasus, a member of said cult, however managed to compellingly demonstrate that the square root of 2 could not be a rational num…

The wiki page says he drowned: https://en.wikipedia.org/wiki/Hippasus

It also says “one writer even has Pythagoras himself "to his eternal shame" sentencing Hippasus to death by drowning, for showing "that 2√2 is an irrational number”.”

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#64

Post by n4r9 »

orra wrote: post #60
saithound wrote: post #5

Every 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…

> It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. [...] whereas the Greeks definitely did (we don't know whether Pythagoras himself did it Wait, really? I thought the proofs back then were geometric, so only proved specific instances. And so it wasn't until algebra, maybe trig, was discovered it was properly proven?

There are fully general and valid geometric proofs, eg http://mathandmultimedia.com/wp-content/uploads/2010/02/pyth...

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#65

Post by tjbiddle »

botanical wrote: post #55
somenameforme wrote: post #39

Earlier quoted context omitted.

Oh how can you skip the most fun tale of them all. [1] Its authenticity is dubious, but there's probably at least parts of truth in it. In a nutshell, Pythagoras started a cult based around numbers, and the pseudo-divine purity of rational numbers - of which everything can be represented. Hippasus, a member of said cult, however managed to compellingly demonstrate that the square root of 2 could not be a rational num…

The wiki page says he drowned: https://en.wikipedia.org/wiki/Hippasus

It says he drowned... assumed because of the reason OP gave. Besides, moot point giving you're referencing Wikipedia to begin with.

> Hippasus is sometimes credited with the discovery of the existence of irrational numbers, following which he was drowned at sea. Pythagoreans preached that all numbers could be expressed as the ratio of integers, and the discovery of irrational numbers is said to have shocked them. However, the evidence linking the discovery to Hippasus is unclear.

> Pappus merely says that the knowledge of irrational numbers originated in the Pythagorean school, and that the member who first divulged the secret perished by drowning.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#66

Post by dr_dshiv »

somenameforme wrote: post #39
dr_dshiv wrote: post #10

Pythagoras was specifically known for accumulating the wisdom of diverse cultures—supposedly he met Thales, was initiated as Egyptian priest in Hermopolis, spent time in Babylon after being captured, and was initiated into every mystery cult he could. And as a boy on his home island of Samos, he would have been exposed to the building of the largest stone temple in Ancient Greece (to Hera) and the incredible engineer…

Oh how can you skip the most fun tale of them all. [1] Its authenticity is dubious, but there's probably at least parts of truth in it. In a nutshell, Pythagoras started a cult based around numbers, and the pseudo-divine purity of rational numbers - of which everything can be represented. Hippasus, a member of said cult, however managed to compellingly demonstrate that the square root of 2 could not be a rational num…

I don’t know of any ancient sources claiming that Pythagoras killed Hippasus. Seems unlikely to me! In any case, Hippasus was a fascinating figure:

“Aristoxenus (Fr. 90 Wehrli = DK I 109. 31 ff.) reports that Hippasus prepared four bronze disks of equal diameters, whose thicknesses were in the given ratios, and it is true that, if free hanging disks of equal diameter are struck, the sound produced by, e.g., a disk half as thick as another will be an octave apart from the sound produced by the other disk (Burkert 1972a, 377). Hippasus, thus, may be the first person to devise an experiment to show that a physical law can be expressed mathematically (Zhmud 2012a, 310).” [1]

Also in [2] this experiment is claimed to be the first documented scientific experiment in history. After all, Hippasus took a mathematical model for a physical phenomenon (how consonance relates to the mathematical ratios of a musical string) and tests the generalization of that model in a another physical medium (viz. bronze chimes with the same ratios 1:2 and 2:3 make the octave and fifth).

I wish they’d put this stuff in elementary math books when kids learn about Pythagoras.

[1] https://plato.stanford.edu/entries/pythagoreanism/#hippasus

[2] https://www.sciencedirect.com/science/article/pii/S240587262...

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#67

Post by bagels »

Diogenes said that Pythagoras hated beans: “One should abstain from fava beans, since they are full of wind and take part in the soul, and if one abstains from them one’s stomach will be less noisy and one’s dreams will be less oppressive and calmer.”

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#68

Post by usrusr »

saithound wrote: post #5

Every 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…

Why would you need numbers for right angles? You need a straight line and a string.

But I agree with the second paragraph: there's a huge difference between a procedure that is handed down as part of "this is how we estimate a building project" and a theorem that is declared universal truth and base for all kinds of other theorems. Even if they are exactly the same thing.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#70

Post by MrBuddyCasino »

dr_dshiv wrote: post #10

Pythagoras was specifically known for accumulating the wisdom of diverse cultures—supposedly he met Thales, was initiated as Egyptian priest in Hermopolis, spent time in Babylon after being captured, and was initiated into every mystery cult he could. And as a boy on his home island of Samos, he would have been exposed to the building of the largest stone temple in Ancient Greece (to Hera) and the incredible engineer…

> The relationship between math and spirituality was very strong back then!

On Seymour Cray:

Another favorite pastime was digging a tunnel under his home; he attributed the secret of his success to "visits by elves" while he worked in the tunnel: "While I'm digging in the tunnel, the elves will often come to me with solutions to my problem." [0]

[0] https://en.wikipedia.org/wiki/Seymour_Cray

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