Fields Medal Winner Manjul Bhargava On the Pythagorean Theorem Controversy 187
prajendran writes There were a lot of controversies generated at the Indian Science Congress earlier this month, including claims of ancient aircraft in India, the use of plastic surgery there, and ways to divine underground water sources using herbal paste on the feet. One argument that could be tested using some form of evidence was the assertion by Science Minister Harsh Vardhan that the Pythagorean theorem was discovered in India. Manjul Bhargava, a Princeton University professor of mathematics and a Fields Medal winner describes why the question is not defined well.
Divergent creation theory (Score:4, Insightful)
It could have been created in both places, it being a relatively simple law of mathematics that anyone pondering triangles is bound to discover soon enough.
There are other examples of things being invented in two separate places at roughly the same time. Why the need for bragging rights? Let the evidence do that.
Re: Divergent creation theory (Score:4, Insightful)
"Why the need for bragging rights?"
Because humans are petty little prideful bitches who use nationalism to compensate for insecurities and a lack of any real sense of self worth. This is the paleo-mathematical version of "whose dick is bigger".
Re: Divergent creation theory (Score:5, Interesting)
I know parent is trolling, but that's actually a real problem with real world consequences that they've been running into:
http://news.bbc.co.uk/2/hi/sou... [bbc.co.uk]
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Informative article there.
Yeah, I didn't even know length made a difference. Is that for real? I thought girth was the issue, and otherwise you just rolled 'em out as far as they would go.
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Does it really matter now? (Score:4, Insightful)
Pythagorean theorem was discovered in India
Nobody's going to change the name of it now, and there's no copyright royalties to be had on it.
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Instead, teach the joy of doing mathematics
Re: Does it really matter now? (Score:1)
Except you conveniently ignore the fact that modern "greek" identity is a fantasy built by British and German imperialists obsessed with Attic culture. Ask anyone in "Macedonia" 200 years ago what they were, and they would have one of two answers. "Turk" or "Roman." Definitely not "Greek," let alone "Macedonian."
Both Greeks' and Slavs' claims to be the true Macedonians are equally ridiculous. As far as claims based on the relationship of the language currently used go, then the Italians, French, Portuguese
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Re: Does it really matter now? (Score:1)
Greek was absolutely an identity during Roman times. Being Roman wasn't mutually exclusive with being Greek.
And the Romans saw themselves as the successors to Greek civilization. Even during Roman times the language of philosophy was still often Greek. The same way the intellectual elite used Latin in Europe during the middle ages.
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Well, Pythagorean theorem was discovered* in Greece by the Greek... Pythagora! (* provided the first recorded proof, so...)
Except for the fact that there is no recorded proof by Pythagoras, and indeed no evidence at all that he had one. What we have is simply a statement of the relationship - which was known to the Egyptians and Babylonians a millenia or two before.
As Manjul Bhargava observes (you did read TFA, didn't you?) if surviving recorded proof is the standard then the theorem is Chinese.
In no standard of evidence does Pythagoras get priority.
Re:Watch out for Disney (Score:5, Interesting)
Actually Disney would never argue for that, because they would be on the hook for billions of dollars in back copyright payments for all the works that they have "used" out of copyright.
Personally I feel that if a firm or body wants to make use of a copyright extension, then back payments would be applicable to people who's copyright would not have expired had that extension been in place when they made use of the work. So Disney for example would need to payout on Pinocchio as Carlo Collodi only died in 1890, so in 1940 it would still have been under copyright by modern standards.
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So how is extending the copyright on already existing works not an ex post facto law? Changing the terms for new copyrighted works would not be an ex post facto law, But a retroactive blanket change of the terms on already copyrighted works, many of which are decades old?
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Read my idea again, it is very specifically not ex post facto. Copyright extension is fine, but if you wish to make use of it then you have to consider your past actions. If you don't make use of it then you don't have to consider your past actions. As such it is not ex post facto as it does not change any pre-existing legal relationships.
I would note by your definition of ex post facto then any copyright extension as currently enacted is illegal in the U.S.A. because it changes the legal status of relation
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Dam I meant to point out that if you had bothered to read your wikipedia link you would note that the U.S. Supreme court has repeatedly ruled that ex post facto law is only prohibited for criminal law and not civil law. As copyright is civil law ex post facto effects of legislation is permitted.
he made a very good point (Score:3)
He made a very good point, it's all about perspective.
With that said, does it not sound like India reading a page from the book "stranger in a strange land"
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The only good point he made is that by mathematical standards the question is who proved the theorem. The rest of his interview is a pop-sci gobbledygook. Even a better question would be, "in what sense was it proved?" The first rigorous geometric theory was created by Euclid, who lived 200 years after Pythagoras. Did the Chinese have a theory, or did they just whip up some philosophical musings?
Re:he made a very good point (Score:5, Interesting)
The only good point he made is that by mathematical standards the question is who proved the theorem.
I disagree. Proofs aren't the only important element of mathematical creation/discovery. Conjectures are also crucial, and there are lots of important conjectures which are notable long before they're proved. The Pythagorean theorem is clearly one such, because it's extremely useful even if you can't prove it. For that matter, as noted by the article, the Egyptians found it very useful, and they not only didn't have a proof, they didn't even fully understand the relation. They merely knew that some certain combinations of proportions made right triangles... and then used that fact all over the place. The Babylonians also probably understood the principle, and the Pythagoreans likely learned it from them or the Egyptians.
In addition, even a proof is irrelevant if it just gets lost, or buried. Communication of proofs, especially as part of a systematic theory is even more important and -- as you correctly noted -- that achievement is indisputably Greek. How much of it was due to the Pythagorean mystics and how much to Euclid is a matter of much debate; some historians of mathematics argue that the Pythagoreans discovered essentially everything in the first two books of Elements. Euclid's main achievement with respect to the theorem may well have been mostly just to record it and remove all of the references to beans and the rest of the Pythagorean mysticism. What the truth is we'll likely never know, but the Greeks attributed the knowledge of the theorem to Pythagoras, which I think is quite meaningful.
All of these stages in the development, proof, formalization and dissemination of important ideas are crucial. The best point to be made here is that the question is inherently meaningless. Any attempt to pick an "origin" must fail because the theorem originated over millenia, and was likely independently discovered in different regions at different times. Even if it's a Chinese manuscript that contains the earliest proof, it seems unlikely that the Greeks got it from the Chinese, and it appears that the Chinese proof in question had little effect on history, Eastern or Western, while the Greek proof, alongside the rest of Elements, fundamentally shaped Western civilization.
That last claim may seem a little too strong, but it's not. Greek Mathematics didn't so much influence Greek philosophy as create it, and Greek philosophy similarly founded Western philosophy as a whole.
Plato's philosophy in particular, was essentially mathematical, and his notion of Forms, the central element of his ideas, is clearly an attempt to relate the pure, abstract beauty of geometry to the world as a whole, and to use it as a vehicle for understanding reality and man's relationship with it. Aristotle was, in many ways, the anti-Plato, but he also deeply honored mathematics. All of the rest of Western philosophy, including its deep influence on social and political structures, can be viewed, as Russell said, as a series of footnotes to Plato and Aristotle, they were that important. And a large part of the powerful influence of Greek ideas on Roman, medieval Christian, Renaissance and modern philosophy derived from the elegance and power of Greek mathematics. Although it wasn't often stated so clearly, the indisputable clarity and power of Greek mathematics impressed later generations and convinced them that the rest of Greek wisdom might well be equally profound.
The Pythagorean version, as presented by Euclid, mattered.
There may have been a half-dozen proofs of the Pythagorean theorem created, recorded and lost, in many locations around the world, perhaps long before Pythagoras. But none of them mattered. The one that did is the Greek proof, and the Greeks credited the Pythagoreans.
In the next Star Trek reboot (Score:2)
Chekov will probably be from India.
Chekov: "Ah, yes - Quatro-triticale!"
Kirk: "Does everyone know about this wheat but me?"
Chekov: "Not everyone, Captain - it was an Indian inwention!"
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Don't some Indian languages have the "w" sound but not the "v"? In that case, Chekov's accent would be correct (Russian has "v" but not "w").
Same old, same old (Score:1)
Some same, some different (Score:2)
Sure, the Hindu nationalist politician the other day who brought up the issue deserves your criticism, claiming that Indian mystics were flying to other planets centuries before the West was.
But the Indian mathematician who won the Fields Medal, the mathematical equivalent of a Nobel Prize is the person were talking about today, and he gave a good discussion about what different aspects of the theorem were invented where and when. It was relatively short and sound-bitey, and there's a lot of history we r
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There seems to have been more communication between the different regions of Eurasia and Africa in ancient times than is generally realized. China traded as far away as Timbuktu, Marco Polo met Greek engineers in China, spices from India and Indonesia were used in Papal kitchens in the Vatican, tin from Britain was used in Greek bronze, African gold was used in Chinese coinage. Even jade from the Americas showed up in China and American pepper plants in Siam. If goods can travel then so can books and ide
British! (Score:3)
You heathen bastards!
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No, Jesus was Jewish.
God, OTOH, is well known to be an Englishman.
Mathematics is to universial to turn nationalistic (Score:2)
The key to understanding why the whole debate is doubtable and nationalistic from the beginning, is to understand that general mathematics is a universal science.
You cannot invent mathematics.
(Remark: This should also be true with physics, these physics inventors haven't even their free energy device running so well it could power their cell phone.)
Basic mathematics like pythagorean theorem is discovered,
and Pythagoras didn't invent it, he discovered that just some basic relationships but he wrote down a un
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You have to invent mathematics. It isn't a feature of the real world.
Consider Euclid, for example. He has postulates, axioms, and definitions, and proceeds to deduce interesting things from these. He made things up: he knew of no physical examples of points or lines or circles, just approximations. He looked at real-life dots and almost-straight lines and almost-perfect circles, abstracted them, and ran with it.
At that time, it was thought that geometry (earth-measure) was a description of reality,
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> Indians think of Judaism as that new fangled sect
> Hinduism is contemporary with the ancient Greek and Iranian religions.
Whenever you see a menorah. That's a remembrance of when that "new fangled sect" collided head on with that ancient Greek religion.
You seem to be a great confirmation that this is an Indian flavor of "Chekov-ism" we are seeing here.
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Nations are never great. Societies and cultures that choose to be free - free to think, free to choose, free to express, free to travel and study anything - are what history has shown to be great.
Any country that allows it's people to be truly free will eventually be great, and will be remembered as great. Sometimes people forget who and why a group of people came to be known as great, but as we forget and repeat history, we will re-learn.
The theorem part (Score:2)
According to The Fine Article, Indians have documentary evidence of knowledge of a few right triangles.
The Pythagorean theorem states a universal truth about all right triangles.
The difference is quite significant.
And of course, the theorem predates Pythagoras - the Pythagoreans just projected a whole lot of mysticism onto the result.
Re:The theorem part (Score:5, Informative)
That's not how I RTFA'ed. I saw it as
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It's not called a theorem without the proof.
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But, it's not generally true, because x, y must be
nonzero... and requiring primes does achieve that
distinction. A weak theorem is better than a false conjecture
Re: The theorem part (Score:2)
The thing that Pythagoras can be most accurately given credit for was the idea that ALL triangles, not just triangles with sides of integer relation, abided by the formula. Realizing this effectively posited that irrational numbers could exist. Everybody before that just worked in "triples" of integers.
The weird detail was that Pythagoras swore all his followers to secrecy about this fact, because he had a series of religious beliefs attached to integers and their ratios. He had at least one person kille
What have you done for me lately? (Score:2)
Spend less time on something that happens a long time ago and worry more about things like those call centers and your nifty new space program.
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" Indians are just good at science."
That perception exists in the West because the people from India that we tend to encounter are 3 or 4 standard deviations above the mean intelligence in a population of 1.2 billion.
Uh-huh. (Score:2, Insightful)
If someone else had discovered this theorem, it would have a different name -- unless there's an Indian named "Pythagoras" -- so checkmate Science Minister Harsh Vardhan.
In a nutshell... (Score:5, Interesting)
-- In India there is an undeniable and strong tendency to construct narratives of how everything good in the world was discovered in India. All Indians don't share this perspective, in fact it is shared by a minority, but er, that amounts to 150 million people or something.
-- This tendency is inward, not outward looking. This politician Harsh Vardhan is a fuck up, like a lot of Indian politicians. But generally this thinking is not directed at bragging to the rest of the world about how great India is, rather it is to nurse, heal, revive people's connections with their own trampled culture and history -- one that in recent times is increasingly being supplanted by a pseudo-western culture and western lifestyle. It's a way of telling people in India to give their intellectual heritage another chance.
-- Honestly, most rational people don't give a damn about where the Pythagorus theorem was invented. I mean if it were an easily provable fact, then it might be an interesting piece of historical information, but given that it's ambiguous who cares, unless to stoke one's nationalist ego.
-- The Princeton mathematician who won the Fields Medal... which is like a Nobel prize except that it's given once every 4 years... is a reference because of his grasp of mathematics, not because he's Indian. If you think of him as "some Indian guy trying to pocket a laurel for his fatherland" then that's a strong statement about you, not about him.
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1) I think pretty much every country is guilty of this "it came from here" thing; it's simple national chauvinism. Some more than others - Russia, US, France, India, and China all spring to mind as particularly prone.
2) your last point is true; if anyone bothered to RTFA, he says essentially that it depends on your standard of evidence, really: if you're looking for the vaguest possible standard, then it probably was 'discovered' in Ancient Egypt. If you're ok with a partial standard, then India looks st
Stigler's law at work (Score:2)
There's a saying that the credit for a discovery goes to the last person who finds it. This is a variation of Stigler's law:
http://en.wikipedia.org/wiki/S... [wikipedia.org]
That's not strange. (Score:2)
Isn't it very likely that something very basic like the pythagorean theorem was discovered more then once? Probably several times in the region we now call India.
We know of the greeks because we got to copy their stuff before it was burned, but we burned thousands of equal amount of historical accounts, philosophy and science from other sources. We've had long-lasting cultures who mainly destroyed other cultures and all their records.
We were just lucky the romans thought that the greeks were cool. If that h
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Re:Umm, no. (Score:5, Interesting)
Or you could just RTFA and discover that the nice Indian mathematician had some cogent and logical things to say.
TL;DR - it's complicated.
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The nice Indian mathematician does bring up some nice cogent and logical things.
But he also leaves out some points which are fairly damning to the argument that the Indians had much to do with this. Many/most non-Indian historians of mathematics seem to believe that the key Indian document here was very likely based on earlier (non-Indian) traditions. In other words, it was just a copy of stuff from Mesopotamia.
I'll quote the wikipedia article on the Theorem (which in turn supplies full quotes from the sc
Re:Umm, no. (Score:5, Interesting)
The nice Indian mathematician does bring up some nice cogent and logical things.
But he also leaves out some points which are fairly damning to the argument that the Indians had much to do with this. Many/most non-Indian historians of mathematics seem to believe that the key Indian document here was very likely based on earlier (non-Indian) traditions. In other words, it was just a copy of stuff from Mesopotamia.
I'll quote the wikipedia article on the Theorem (which in turn supplies full quotes from the scholarly document if you hate wikipedia):
"Van der Waerden believed that "it was certainly based on earlier traditions". Boyer (1991) thinks the elements found in the ulba-stram may be of Mesopotamian derivation."
That makes any claims that India "discovered" the theorem really really weak by any definition I would think.
I have actually read Van der Waerden's books on Mespotamian mathematics and astronomy (I have copies of them at hand). His "belief" is not evidence of any kind. He is simply supposing, without any supporting evidence.
And Boyer, who wrote his history of mathematics 50 years ago (1991 is a reprint, he died in 1976), was no expert in ancient mathematics. He has been called the "Gibbon of Mathematics" which is a very good analogy, since Gibbon's work represents a compilation of everything known and believed about the Romans, written from the perspective of an 18th century European, complete with moral interpretations drawn from contemporary cultural viewpoints. It was a work that says at least as much about Gibbon and Europe of the time, as it does about the Romans. Similarly Boyer's beliefs represent the assumptions of a western scholar trained in the 1930s.
No one has yet shown any evidence at all that the suryas actually draw from Mesopotamian sources. Saying it doesn't make it true.
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Aesop's fables, Damascus steel - two things that firmly point to cultural exchange between India and Mediterranean & Mesopotamian lands. Saying the Suryas draw from Mesopotamian sources in light of other historical evidence lends credibility to that assertion.
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So proof that something is possible is proof that something *is*? Okay...
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I discovered a prize in a box of cracker jacks, therefore I must have invented it.
Re:Umm, no. (Score:5, Informative)
It's complicated, but the arguments for each can be summarized:
First known indication of knowledge of the relation for integer-sided triangles (Pythagorean triples) - 2,500 BC in Egypt
First known general statement of relation - ca. 1,800 BC in Mesopotamia
First known general statement of relation with respect to right triangles - ca. 800 BC in India
First known rigourous proof of the relation - ca. 1046 to 256 BC in China
(Pythagoras, who may or may not have had a proof - ca. 570 to 495 BC in Greece)
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Just what, pray tell, has the US done to India that was so goddamn bad?
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US betrayed India to the Chinese. The CIA was sending terrorists into tibet from Indian soil and when China invaded India in retaliation US abandoned India and said you are on your own. Indians don't forget that the US is not a friend in need.
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Aren't you guys allies with Pakistan, the enemy of India?
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we pay pakistan not to go full-blown batshit insane.
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There are a couple of reasons.
1. The USA provided significant material support to Pakistan prior to and during the Indo-Pakistani wars which were to some extent seen as a cold war proxy conflict between the USA and USSR; this support and military cooperation continues in various forms, so India is naturally wary of American actions in the region. Although the cold war is for the most part over and the relationship between Russia and the USA has warmed substantially, India and Pakistan are still constantly a
Re: Umm, no. (Score:5, Insightful)
"The USA was a major force in dismantling colonialization. The exceptions to this seem to have been through the involvement of Wall Street anglophiles (or just plain agents of the British) "
Hmm. James Monroe, Teddy Roosevelt, William McKinley, William Randolph Hearst, General Pershing and Commodore Perry, all Anglophiles...
Ask the Spanish-speakers of the Western Hemisphere about the US commitment to anti-colonialism.
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Ask the Spanish-speakers of the Western Hemisphere about the US commitment to anti-colonialism.
That's a joke right? Because nobody speaks Spanish any more.
Re: Umm, no. (Score:2)
As an Angelino, I can assure you that many, many people still speak Spanish.
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The US started to get a distaste for classic colonialism early in the 20th Century, although it largely disregarded US messing in Latin America.
Woodrow Wilson's Fourteen Points, which formed the basis for the treaties ending WWI, were largely anti-colonialist, and many colonies were put on a somewhat different legal system, which implied that the colonial rule would be temporary.
Before WWII, the only colony in Asia that had a firm independence date was the Philippines. This is thought to have had a lo
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Panama, Puerto Rico followed pretty much the same path as the Phillipines. It was a post Spanish-American war thing.
Every June my neighborhood is host to a huge Puerto Rican Independence festival, where all the descendants of Puerto Ricans come back to the old neighborhood and celebrate the end of their dependence from Spain.
I can't wait to see the party they'll throw when they are finally truly independent.
Re: Umm, no. (Score:2)
The US doesn't operate colonies like 19th century Britain (although it does have some outright colonial possessions like Puerto Rico and the Marshalls). The US operates an empire much more like 16th century Britain, where local control is maintained by friendly satraps who are nominally independent but do not exercise true sovereignty, and resources (mostly oil, but also cheap labor) are expropriated by factorist enterprises, nowadays called "corporations."
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Obviously, those Indians are just driving home the point that events cannot possibly be attributed to a country that didn't exist at the time, thereby proving something about time and continuity, right?
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TIL Pythagoras was American.
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If you knew anything about building construction, you would know that the first humans that built an accurately square large structure must have known Pythagorean Theorem as it is the simplest and only way to set out the structure. Although they might not have expressed the theory directly, they certainly expressed it in the shape of the structure. It is starting to look like there was in fact ice age civilisations that collapsed as a result of the deluge resulting from the end of the last ice age and like
Don't need theory to get right angles (Score:2)
You don't need the Pythagorean Theorem to construct a right angle. You don't even need the theorem to know that a 3-4-5 triangle has a right angle. It's a nice explanation of why those proportions get you a right angle, but that's a different issue; once you know you want a right angle, and a triangle with integer-proportion sides so you can easily reproduce it, trial and error will get you there. Furthermore, the classical geometric proof doesn't automatically give you integer solutions; Diophantine equ
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One of the real values of Euclid's Elements is the insistence on proof of everything, which is part of what differentiates it from much of Classical Greek "science"; assertions like Aristotle's claim that heavy objects fall faster than light ones weren't good enough. And it's not like the Pythagoreans weren't mystics either; there's a story that one of their deep dark secrets was the irrationality of sqrt(2), which really annoyed them because it showed that their mathematically perfect universe wasn't.
Know
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Unfortunately all you have is square or rectangular foundation and none of the tools use to create them. Take a careful thought for social economies though and understand at which stage accuracy starts to count and square is required in large structures rather than just sort of square.
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To construct a square one only requires four right angles and a chosen length of side.
A right angle can be devised with common tools without resort to the symbolic representations of mathematics. String, pins, and marker is all you need.
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There are lots of ways to get right angles with simple tools that don't require knowing the Pythagorean theorem (including the use of 3-4-5 triangles, which work fine even if you don't know that they're one solution of a large class of problems.) Back when I was taking drafting and wood shop in junior high school, the way you got a right angle was "Use a T-Square and #2 pencil", not "Calculate the area of the square on the hypotenuse."
And ~2500 years later, when the condo I live in was built, Pythagoras's
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You're either a troll or a moron, pardon my French. The simplest way to construct a square is to take a piece of string, fold it into four identical lengths, and tie it into a ring. Now take four people and pull at the corners until the four sides are taut.
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I set out industrial buildings fuckwit and yeah 3,4,5 is exactly how you do it with string or actually braided wire because string stretches to much and that stretch makes a huge difference between varying lengths of string and even wind plays a role in that and after that you check the diagonals and then you go away and before you do anything you check it all again. Tape measure are also a pain because of course sun light will vary the length of your tape, requiring repeated short measures rather than lon
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I'm a moron too. I can't see how your string method assures right angles? Please enlighten me.
Yeah, me too. I keep getting a rhombus.
~Loyal
Re: Umm, no. (Score:5, Interesting)
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The British-Indian comedians of Goodness Gracious Me had a recurring sketch about "Mr. Everything comes from India", who would argue (mostly with his son that) everything came from India. Not only the things that actually are from India, like shampoo and verandas, but Shakespeare, the Mona Lisa ("Son, this is Mina Losa, a Gujarati washerwoman from Bhavnagar!"), John Travolta, Superman and the British royal family.
I think all nationalisms have some people like that.
Re: Umm, no. (Score:5, Interesting)
That's the problem I've seen with Indian workers as well, and several people I've worked with have seen it too. It seems to be a real problem, because they will not say no to their bosses - about anything. If they're given a task beyond their skillset, they say yes anyway because saying no would be disrespectful (or so I understand).
On one occasion, I was hired to spend a day working with the IT manager of a company in Dallas - to find what was happening with their network performance. I found (poorly configured) routers everywhere. Triple, quadruple, quintuple NAT, cross linked networks - dueling DHCP servers. It was a mess. It turned out that their IT manager managed to graduate his Indian university with a computer science degree and yet knew virtually nothing about anything. When his boss said add another router - he said yes.
I left after turning those routers into switches and restoring the performance they were missing, but not the performance they could have had if they'd put it together with the right parts to begin with.
I was paid in cash, by the IT manager - so I suspect that I was paid out of his pocket to save his job.
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We were recently looking for a new developer and thus put out the feelers - the number of Indian applications we got via agencies was high, but what was more surprising was the number of those applicants who were able to get multiple degrees in the subject from Indian universities in less time than it would take to achieve one degree in a western university (we are talking 2 degrees in a 2 year timespan, when one degree in the UK typically takes 3 years). Now why would that ring warning bells?
Oh, and the n
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I have hired some top people from India. I have also worked with some developers out of India that were extremely... not top people. So, your mileage may vary, I guess.
There do seem to be lots of Indian development groups that will pound out the fastest, sloppiest mess possible to meet a deadline. But I wouldn't put that down to being Indian, I'd say it is more a function of attempting to be an ultra-low-cost vendor. What is it they say about fast, good and cheap?
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There are plenty of top-notch people working American IT companies from India and similar non-Western places, because I work with a bunch of them (in the U.S.). Hiring anyone is simply a matter of figuring out how to filter out the posers, the Dunning-Kruger experts and the BS artists, and there are plenty of those to go around.
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I'm a racist (as usual) says the anonymous coward (Marc, is that you?) who can't accept that I'm not the only one to experience this phenomenon. I've worked with a few very intelligent Indian IT workers, and I love Indian culture (especially the food, mmm-mmm - makhani chicken). I think it's sad that some institutions pushing students out the door without the skills they need are giving a bad reputation to an entire race of people.
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Fields Medal Winner, not just the politician (Score:5, Informative)
I'll give the Indian politician the amount of credit it was due, along with mystical spacecraft flying to other planets and such. But this article by a guy who won the bloody Fields Medal not only deserves a lot more credibility before reading it, but also after - he talks about the discoveries of various parts of the idea in different parts of the world. And Indian and Arab mathematicians did contribute a huge amount to culture and civilization; you can't even claim they made zero contributions without using the zero they contributed,
Re:Umm, yes. (Score:2)
Good, let's reason instead of rhetoric. What specifically do you object to in the linked article? Because unless you point out verifiable issues, I'm using it next time I explain how stupid people can't stand information that contradicts their understanding.
Including your knee jerk response here as an exhibit, of course.
Ground rule, please keep to the specifics in the article, and not some straw man.
And please, don't start sentences with filler words. This may sound impossible, but it makes you sound less i
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While that's an admirable thought, the reality is that modern mathematics owes very little to the prehistoric findings pre ca 1500. The breakthroughs that transformed mathematics into the tool we use today occurred mostly in Europe during the Renaissance period and later. Perhaps the only significant (*) contribution before then is Euclid's tour de force (
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Pythagoras hacked Sony to suppress the truth [storyofmathematics.com]
Pythagoras imposed his quasi-religious philosophies... about never urinating towards the sun...
when Pythagoras’s student Hippasus tried to calculate the value of [square root of] 2, he found that it was not possible to express it as a fraction, thereby indicating the potential existence of a whole new world of numbers, the irrational numbers (numbers that can not be expressed as simple fractions of integers). This discovery rather shattered the elegant mathe
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Damn! The link between Pythagoras and Kim isn't so weak! Whoa! Reincarnation?
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Pythagoras imposed his quasi-religious philosophies... about never urinating towards the sun...
That was a translation error. What he actually said is you don't piss against the wind.
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Pythagoras imposed his quasi-religious philosophies... about never urinating towards the sun...
That was a translation error. What he actually said is you don't piss against the wind.
Where are my mod points when I need them!
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You can't appreciate the beauty of it until you read it in the original Klingon.
Re:I dno't know. (Score:5, Funny)
If you are going to nominate for lifetime achievement in pedantry I would go Slashdot.org instead if just one article.
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You call it pedantry, but I'm proud as fuck about things that my ancestors did without any input whatsoever from me personally. You go, ancient awesome guys!
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Indeed.
I may testify that it is called Pythagorean merely because of the path via which the theory's proof got popularised in the western world. No more no less.
This does not make any other discovery paths any less or more important, just parallel efforts (and Chinese are certain to have had many parallel discoveries).
However, when somebody comes to contest the ordering and aetiology of events he better comes with proof about it; that kind of proof is yet lacking or weak at best.
The ancient greek world tend
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Maybe you should try discovering something new (mathematical or scientific) that will be useful for thousands of years, then come back and tell us it was so easy that you don't deserve any credit.
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But would they still be easily accessible? What if the people who knew them died and the artifacts, such as paper and hard disks, that had a recording of these truths were destroyed. Then these small group of people would have to spend hundreds/thousands of years to rediscover these truths again.
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Sounds kind of strange - America is not the only country in the west and as a brit I learned that the basic concepts of algorithms and algebra were invented in the arab world, although the actual forms that we use today were developed in the 19th century. The eastern front was where nazis were sent to die (from the historical documentry Allo Allo probably), and stirrups came west with the Mongols who used them as a decisive military advantage.
So you could equally conclude that American education is uniquely
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The GGP was just beating on a strawman. He should have been ignored.
Re: "They" believe anything (Score:2)
There was really only one Jewish Zombie, and he's really just an excuse to have a protracted discourse on Neo-Platonism.
Hinduism is a beautiful system of beliefs but strains of it can be REALLY overloaded with a lot of superstition and naturalistic garbage... Christianity has different problems- its idealism and anti-humanism for a start- but it's attachment to weird pseudoscience isn't generally one of them.
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The dude who wrote "Was God a Skywalker"?
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Indoor plumbing, on the other hand...
Actually, the Indus Valley civilization seems to have had the first proper sewage systems, so ...