[HN Gopher] The Babylonians used Pythagorean ideas long before P...
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The Babylonians used Pythagorean ideas long before Pythagoras
Author : helsinkiandrew
Score : 129 points
Date : 2021-08-07 09:19 UTC (1 days ago)
(HTM) web link (www.economist.com)
(TXT) w3m dump (www.economist.com)
| pushpen99 wrote:
| copied/stolen from India/Hindus
| estaseuropano wrote:
| There is a huge swath of Indian comments here, claiming vaguely
| that all these are Indian ideas without any evidence to back
| this up. Would be curious to see some actual evidence.
|
| Not to forget that things can also be invented/discovered more
| than once independently.
| throw13579 wrote:
| Downvoting your post. Here on HN, we believe all worthwhile
| discoveries were made by white people plus a handful of races
| whose markets we're trying hard to break into.
| ummonk wrote:
| So Pythagoras likely didn't even formulate the theorem - he was
| more into numerology and only cared about sum of squares
| triplets, not the results about right triangles.
|
| On the other hand, we have strong evidence that the Babylonians
| understood and applied the "Pythagorean" theorem long before
| Pythagoras lived.
|
| Additionally, the first recorded explicit statement of the
| theorem is actually by the Indian writer Baudhayan, over a
| century before Pythagoras.
|
| The oldest extant proof of the theorem comes from Euclid. The
| proof commonly attributed to Pythagoras actually first shows up
| in the Chinese Zhoubi Suanjing, several centuries after
| Pythagoras.
|
| Quite simply, "Pythagorean theorem" is a major misnomer.
| Natsu wrote:
| Things get named after the person who popularized something,
| not generally after the first to discover it.
|
| It's called the Pythagorean theorem because that's where
| western people who called it that learned it from, the other
| things being unknown to them.
| yhoneycomb wrote:
| Whatever. Still a misnomer in my book. With that said, you
| are free to invent your definition of misnomer if you so
| desire.
| ummonk wrote:
| Explaining why a misnomer came about isn't an argument for
| why we should continue to perpetuate it.
| afarrell wrote:
| We should perpetuate it for at least 3 more years because
| we have way bigger epistemological fish to fry.
| toiletaccount wrote:
| yeah the babylonians are still a little sore about this
| misattribution
| jjoonathan wrote:
| Here's a reason: sharing, communication, and popularization
| are even more important than the underlying idea. The
| Babylonians can fight the Chinese, Egyptians, and 5 other
| claimants for the historical footnote of who figured it out
| first. I don't really care. If the Pythagoreans evangelized
| the concept at a critical juncture in the history of the
| discourse that eventually became my education, I think
| that's a fine reason to leave their name on the theorem.
|
| Of course, the Pythagorean theorem is a good springboard
| for discussing how this works, how attribution is often
| murky or flat out wrong, how evidence of various bits of
| math popped up far earlier in history than their official
| invention, yet remained sterile and ultimately went nowhere
| because they weren't shared, popularized, and expanded
| upon. Or it happened but stopped at cultural boundaries and
| didn't get to us by that path, so we give credit to the
| person who made that happen. In any case, receiving the
| idea is what we care about, not originating the idea. See:
| Euler did it first, Gauss did it first, ancient Indians did
| it first, ancient Chinese did it first, etc, etc.
| throw13579 wrote:
| Colonized Indians need to take control of their history like
| the Chinese did. Otherwise the appropriators will continue to
| have a field day.
| estaseuropano wrote:
| This is a 2000-year-precolonial issue though.
| ummonk wrote:
| My understanding is that some schools in India teach it as
| the "Pythagorean theorem" and others as the "Baudhayan
| theorem" - the choice of which term to use is definitely a
| colonial issue.
| jdkfglkjh34 wrote:
| https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy
| echopurity wrote:
| The great man theory almost always fails. The life of Pythagoras
| is largely myth. This theorem was most likely known and proven
| well before him. This is old news.
|
| https://link.springer.com/article/10.1057/jt.2009.16
| joemaller1 wrote:
| An uncomfortably large percentage of our population doesn't
| understand the theorem, no matter what it's called. But sure,
| let's quibble about the name.
| gremloni wrote:
| It's important because otherwise you keep getting the "white
| people made everything" argument.
| kgeist wrote:
| Did Pythagoras/Pythagoreans ever claim they invented all the
| things they discussed?
| [deleted]
| h2odragon wrote:
| Tomorrow, the newly formed "Estate of Pythagoras" corporation
| will begin selling shares in its upcoming lawsuits against
| "everybody who has ever used math" for IP infringement as
| appropriate in their many jurisdictions.
|
| No one will really bet big on it until Disney takes them over.
| contingencies wrote:
| Expounded in modern publication since at least _Weisheit und
| Wissenschajt: Studien zu Pythagoras, Philolaos, und Platon_
| (1962)
| Koshkin wrote:
| This is yet another evidence in favor of the idea that
| mathematics is not invented but discovered.
| oblak wrote:
| During a heated argument, a person I know argued that humanity
| advanced as fast as it did during the 19th century after aliens
| invented(!) electricity and gave it to us.
|
| Took me a while to process
| mojuba wrote:
| The aliens lost patience, I can understand them.
| ganzuul wrote:
| https://archive.is/DUZat
| codekilla wrote:
| Yes, but the point is the approach to _proof_ (proving this for
| all cases) that represented a paradigm shift in mathematics,
| largely attributed to Thales.
| sn41 wrote:
| The earliest known proof of Pythagorean theorem is due to
| Euclid. It is strange at all that any credit is attributed to
| Pythagoras, since Babylonians, Egyptians, Indians and Chinese
| all had discovered this [1]. And Pythagoras did not prove his
| theorem, to the best of our knowledge.
|
| [1] https://en.wikipedia.org/wiki/Pythagorean_theorem#History
| jules wrote:
| How would one discover the Pythagorean theorem without having
| a proof?
| tim333 wrote:
| You could draw a right angle triangle and notice that the
| squares match without being able to prove that.
| ttyprintk wrote:
| Also weird that (more generally) Euclid is only rarely
| mentioned by name, and more often nearly anonymously as the
| author of Elements. Yet, Pythagoras is named early and often.
| ashtonkem wrote:
| Euclid got Euclidean geometry, and that's not nothing.
| ardit33 wrote:
| Euclidian plane.... term is used all the time. Euclidian
| Geometry as well.
|
| His ideas have a large part in Math and Geometry
| thaumasiotes wrote:
| Pythagoras isn't named so much in his aspect as a
| mathematician. He's named because he is the center of a
| major Greek mystery cult. (The other major cult being
| centered around Orpheus.)
| Galanwe wrote:
| From what I remember from my epistemology courses, it's due
| to historiographical reasons: there are a lot of cross
| reference of the existence of Pythagoras from other texts,
| so his historical context and existence is well anchored.
| As for Euclid, apart from the Elements, there is pretty
| much no mention of him anywhere, which is even more
| troubling since the depth and reach of the Elements is
| massive and should have had an impact at the time. This led
| some people to think that Euclid may not be a person but a
| group of people.
|
| This is what I remember from courses 15 years ago, I may be
| wrong or outdated on the subject ;)
| ttyprintk wrote:
| This is close to what I was taught. I don't know ancient
| Greek, so I wonder if that language draws a distinction
| between singular and plural in the way "the author" of
| Elements is structured.
|
| Fwiw, I do recall that Pythagoras seems to have forbidden
| written records, so what survives are his followers'
| notes, who apparently gave him singular credit where we
| might expect a collaboration.
| thaumasiotes wrote:
| > I don't know ancient Greek, so I wonder if that
| language draws a distinction between singular and plural
| in the way "the author" of Elements is structured.
|
| I don't know what you mean by "in the way 'the author' of
| Elements is structured", but yes, Greek draws a
| distinction between singular and plural. (And dual,
| though to a lesser degree.)
| ttyprintk wrote:
| I think this is the most important point modern readers need to
| make.
|
| If we discover a proof earlier than Thales, regardless of
| whether it's Greek, we might revise the discovery of trig. But
| this is about certain triples being used practically in Babylon
| (who recorded everything) without any recorded interest in the
| relationship between triples.
|
| Because Greeks first recorded the important part --- the proof
| --- I think it's factual and not at all offensive to refer to
| Ancient Greek culture as influential in that recorded
| innovation in geometry.
|
| I've seen a movement to broadly give credit to other cultures
| for Pythagoras, but knowing about triples is just not enough to
| say that they promoted innovation leading to trig.
| babesh wrote:
| I think that there are several ideas that are both powerful
| and that people muddle when they talk about mathematics. Also
| the talk is often tinged with cultural pride.
|
| The ideas are conceptualization, generalization, and rigor.
|
| The Pythagorean triples are a conceptualization that for
| certain right triangles, the squares of the three sides obey
| a relationship.
|
| The Pythagorean theorem is both 1. a generalization that that
| would be the case for all right triangles and 2. rigorously
| proved it. Furthermore, at least for the proof in The
| Elements, it was axiomatic rigor, proving this via a chain of
| logic starting from base concepts.
|
| Now to the cultural pride aspect. Many cultures came up with
| concepts in mathematics. Many cultures generalized. Many
| cultures were rigorous.
|
| The argument is/should really be that the Pythagorean theorem
| is on the far end of the rigorous, generalization axis. The
| better argument actually is that The Elements is.
|
| My personal take is that the Pythagorean theorem isn't, at
| least in the long span of mathematics history, an exemplar of
| conceptualization.
|
| And yes, there is some overlap and ambiguity with these ideas
| and you can argue about where the boundaries lie but I don't
| think we gain that much from that.
|
| If people don't think that other cultures conceptualized,
| generalized, and were rigorous, just look at The Art of War,
| Bhagavad Gita, etc...
| babesh wrote:
| Also, rigor was romantacized. With the exception of The
| Elements, very little math till the last maybe 200 years
| had that level of rigor. Newton and Leibniz sure didn't.
| ttyprintk wrote:
| This is one of my pet peeves, too, an obsession with
| referencing the first to try innovative math. Maybe
| Babylonian root finding is a simplified case of what we
| call Newton's method. The minimum level of rigor for a
| concept to go from theorem to proof is both human and
| philosophical. We get very little recognition for the
| mathematicians putting in the hard work, and detrimental
| recognition for concepts that don't exactly widen a field
| of math for innovation.
|
| Recent movements to revise the recognition of Pythagoras
| are doing the right thing when they acknowledge the path
| dependence of unbroken written communication of ideas is
| often mistaken for awarding prestige to a particular
| institution, educational tradition, or culture.
| ttyprintk wrote:
| About conceptualization, my understanding is that ancient
| Greek followers of religious leader Pythagoras realized
| that this was not only a relationship between length and
| area, but a formula for irrational numbers. This might be a
| claim without evidence, and would not be the first time
| Western education has tried that.
|
| Babylonians had no problem arriving at solutions to square
| roots, and a lot of their texts are yet undeciphered. If we
| find that Babylonians ruminated about irrational numbers,
| too, then we're talking about a major revision in the
| history of math. Until then, to me, the concepts in the
| Greek treatments are more innovative than the practical
| usage in Babylon.
|
| I think your take is supported if it turns out people have
| read way too much into the religion around Pythagoras. I
| think Pythagoras would be surprised to be famous for a
| proof when he'd rather be famous for musical scale or some
| weird ritualistic dance or something. In fact, as
| mathematicians we might be better served by later proofs,
| which is implied by your other points, I think.
| thaumasiotes wrote:
| > this is about certain triples being used practically in
| Babylon (who recorded everything)
|
| The difference isn't that Mesopotamia generated more records
| than other cultures. It's that Mesopotamian records become
| practically indestructible when burned.
|
| (This didn't help much in Babylon itself, which didn't burn.)
| hdjjhhvvhga wrote:
| Previous discussion:
| https://news.ycombinator.com/item?id=28062020
| dang wrote:
| Thanks! Macroexpanded:
|
| _Australian mathematician discovers applied geometry on
| 3,700-year-old tablet_ -
| https://news.ycombinator.com/item?id=28062020 - Aug 2021 (11
| comments)
| Mikeb85 wrote:
| So who's the Babylonian guy who we can name it after?
|
| Also, this has been well known for awhile.
| contradistinct wrote:
| Nothing is ever invented by the person it's named after [1].
|
| [1]: https://taylor.gl/blog/11
| ArtWomb wrote:
| Next up: the shocking discovery of a Vedic interpretation of
| quantum chromodynamics ;)
|
| https://www.sanskritimagazine.com/vedic_science/quantum-mech...
| hdjjhhvvhga wrote:
| I believe sites like these do a disservice to the ancient
| knowledge of Hindu people. There were many important
| discoveries, some unknown to the West for centuries, and still
| not having enough exposure (when you read math books, they
| start with Greeks, then maybe they gloss a bit over al-
| Khwarizmi and then jump right into the 17th century to all big
| names, as if nothing was happening for over a thousand years -
| well, a _lot_ was going on, just not in Europe).
|
| However, some people exaggerate in the other direction, I'm not
| sure if this is just a Hindu thing or a more global phenomenon,
| but there is a limit of what you can explain using Vedas, at
| least as far as science is concerned. (Metaphysics is something
| different, but this a completely different discussion.)
| Xplune13 wrote:
| I agree. As an Indian it is just sad that there are people
| that do this. The effect of such articles is actually the
| loss of faith in the real findings of those ancient people
| caused by exaggerated claims presented in these articles.
|
| There are so many actual great things and findings written in
| those texts, but it seems like people are either in the ship
| of "Everything is in Vedas" or "All this isn't worth
| researching". The lack of interest in researching these
| ancient texts caused by these 2 extreme sides is
| disheartening.
| newyankee wrote:
| Per this source, in their own words Fibonacci credits
| Indian mathematician for his series. There is a great deal
| of disservice done to Eastern sources in the history of
| Science & Mathematics which is mostly because modern
| versions of these mostly skipped these places.
|
| https://trueindologytwitter.wordpress.com/2020/03/31/indian
| -...
| Xplune13 wrote:
| No doubt about it. There are A LOT of things that aren't
| credited correctly in the modern world, but these
| articles that I referenced aren't helping the situation
| at all. On the contrary, they're worsening the state all
| these topics are in with their exaggerated claims which
| make people question the integrity of the real work
| itself.
|
| There should be thorough studies about Indology (at least
| in far greater number than there are right now) without
| all these click-baity articles associated with it.
| throw13579 wrote:
| A lot of math theorems might have been stolen /
| 'appropriated' from here: https://en.wikipedia.org/wiki/Keral
| a_school_of_astronomy_and...
| estaseuropano wrote:
| The wiki article you link states 1) no direct evidence of a
| link or that their ideas were known beyond Kerala exists
| and 2) they might also have worked off ideas NY Islamic
| scholars. Really not sure what the specific claim or
| evidence you have is to give credit for 'many ideas' to
| this group.
| Falandafa2021 wrote:
| Peter kingsley talks about this in both reality and a story
| that will pierce where you dive deep into the hidden
| connection between Pythagoreans and mystical traditions
| leading back to the mountains of Tibet.
|
| The teachings of Falan Dafa also discusses this claiming that
| the earth and human civilizations has gone through cycles of
| destruction and renewal with the last period occuring in the
| time of the ice age where a small surviving group of mystics
| in Tibetan mountains managed to survive which matches up with
| the flood stories across cultures and recent scientific
| discoveries outlined by people like Graham Handcock.
| dragonelite wrote:
| I don't think you need big cycles of destruction and
| renewal like those guys claims. Perfect example was what
| happened in Europe when the western roman empire
| disintegrated.
|
| The whole knowledge transfer chain from master to student
| got disrupted. So much so that the institutional knowledge
| base got eroded and people forgot how to do/maintain
| products. Maybe because you a cluster of smaller empires no
| one could finance those prestige projects, without those
| big projects the knowledge transfer chain will also be
| disrupted.
|
| This me just thinking up loud and accepting the shit I
| learned 10~15 years ago and haven't used in a long time
| have simple been forgotten. Human memory is extremely
| fragile, so the invention of paper must have been super
| important to keep those knowledge transfer chain going over
| the millennia.
| rishikeshs wrote:
| :P
| 8note wrote:
| The last sentence reads like a joke about how his equation was
| improved by Dirac to consider the speed of light
| throw13579 wrote:
| https://en.wikipedia.org/wiki/Cultural_appropriation
| etothepii wrote:
| I don't know if it's true but we were always taught in the
| History of Maths course at Cambridge[1] that Pythagoras did not
| exist, or at least there was no evidence of a specific person
| called Pythagoras. Further if you followed the footnotes in most
| any research on the subject (especially claims that the Egyptians
| or Babylonians knew the theorem) you almost always end up at a
| loose end.
|
| [1] https://www.ice.cam.ac.uk/about-us/staff-
| profiles/tutor/pier...
| tim333 wrote:
| For what it's worth Wikipedia has him as a real person living
| 570 - c. 495 BC, son of Mnesarchus, a gem-engraver on the
| island of Samos, who travelled to Croton about 530 BC and set
| up some kind of school there.
| spoonjim wrote:
| It might be the mathematical equivalent of Winston
| Churchill... a person who definitely existed, but who didn't
| say 90% of the famous _bon mots_ attributed to him. It might
| have been that if you wanted your ideas to spread you had to
| attribute them to "Pythagoras."
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