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Fields Medal Winner Manjul Bhargava On the Pythagorean Theorem Controversy
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.
First, I was thinking of a bunch of "Big Bang Theory" shows while reading the article.
Second, I would like to nominate this article for the Lifetime Achievement in Pedantry award.
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.
It is just that before being Greek, Pythagoras's soul was in India.
(and before then, in Babylone and Egypt.)
QED
Science that global warming deniers can accept!
The shepherds did so well protecting the flock that the sheep no longer believed that wolves existed.
I almost modded this funny, thinking it was a parody. Is the spam becoming aware of it's surroundings?
An Indian website hosts an article about an Indian mathematician who asks, "Did India discover Pythagoras theorem? A top mathematician answers" Gee, I wonder what his conclusion will be?
It seems the cradle of western civilization isn't close enough to India's back yard for most Indian's tastes. Given the opportunity, they'd re-write history. Anti-American sentiment, along with anti-western sentiment, runs deep, and maybe for good reason. But whatever that reason, Indian's perpetual desire to re-write history ad nauseam is growing a bit old. What next, an article about how an Indian, not a Greek documented and used calculus in the 3rd century BC, long before Newton?
It would be delightful if India could point to an original Indian version of Euclid's Elements, the oldest continuously used textbook in history. Such books shape minds for, well, eons, by teaching logical & rational thought. Seemed to work well for Abraham Lincoln, he carried around a copy in his saddle bag and studied it while traveling.
Instead of self-glorifying episodic re-writes, how about discussing continuous, progressive and well reasoned contributions to culture and civilization?
"Every time I see an adult on a bicycle, I no longer despair for the future of the human race." - H. G. Wells
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.
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"
if you see me, smile and say hello.
and clickbait.
from TFA, if you believe a theorem is true when it's proven, then it's a chinese theorem.
But really, all this guy us saying:
invented & experimented with: egypt
1st used as standard practice: india
proven as fact: china
Sounds like it's still an idea created in egypt, so the headline is misleading.
... knowledge exists whether we are aware of it or not. Trying to take "credit" for discovering things that were always there for anyone to find is pretty sad.
Pythagoras hacked Sony to suppress the truth
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 mathematical world built up by Pythagoras and his followers, and the existence of a number that could not be expressed as the ratio of two of God's creations (which is how they thought of the integers) jeopardized the cult's entire belief system.
Poor Hippasus was apparently drowned by the secretive Pythagoreans for broadcasting this important discovery to the outside world.
“He’s not deformed, he’s just drunk!”
Damn! The link between Pythagoras and Kim isn't so weak! Whoa! Reincarnation?
“He’s not deformed, he’s just drunk!”
If Disney has anything to do with it copyright will be restored for everything ever created then it might matter who discovered the Pythagorean theorem.
For explanation watch :)
https://www.youtube.com/watch?v=Ln5QgeCL1fs (Goodness Gracious Me skit)
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.
I knew that the Hermetic Order of the Golden Mickey was behind this!
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!"
#DeleteChrome
My experience w/Indians (that is, people who are from India) is that they believe pretty much anything they are told. I work with many, many highly educated Indians, and it is unbelievable the shit they'll believe in; even really daft shit like numerology and astrology...
Welcome to Indian/Hindu nationalism...government ministers often make outlandish claims about something having being invented in India.
Indoor plumbing, on the other hand...
It was created by God and brought to Earth by his son Jesus and he's British!
You heathen bastards!
No, no, Chekhov told me that it was inwented in Russia!
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 universal formula..
(And I think he also managed to geometrically proof the theorem. I'm not sure)
So even if you find some of these so called pythagorean relationships and use the numbers in your construction - then if you don't write down a formula you have no theorem at all. And however sometimes a library burnes down and papyrus with the theorem is lost.
But again mathematics is universial, so if a theorem is truely universal it can be rediscovered. And this is what's happening, some pupils and students have the capability to rediscover mathematical principles using just their education they received to a certain point, with having never heard about before. Brilliant!
The real genius idea is after discovering a numerical relationship to write down a "general" formula, this is what he did.
Discoveries are made sometime, and sometime they are forgotten. It is possible that Pythagoras is just a "late" inventor, but understand the indian minister you need to understand that he is a hindu nationalist, and as any nationalist, he believes in the superiority of his "peer group".
This reveals an inferiority complex nationalistic indians are worried that their country was and is a develloping country - aside from their huge steps in science and engineering.
They just have too put their name on everything and claim everything, it's just sad, because these people will not stop there, where science and philosophy would return to a more rational debate.
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.
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.
If you read Wikipedia, you'll notice many, many articles are being modified to credit the original discovery to somebody of Indian or Middle Eastern origin. Usually this is done without sources, and it is never elaborated on why these discoveries were subsequently lost for hundreds of years.
It feels like people are trying to attribute discoveries to boost the standing of their own people, rather than just accepting that many of these discoveries were utilized effectively much later by people outside of India and the Arab world. Is that so wrong in itself?
Which is all the more impressive considering that it was the current dear leader that invented mathematics, theorems, and the abstract concepts of proof and discovery.
India was always an advanced country. The invasion of Islamic hordes and the resulting internal civil wars let the Europeans Johny come late lies take over for 200 years and le to 200 years of stagnation. In the history of a 4000 year civilization 200 years is nothing. Indians think of Judaism as that new fangled sect which just came up recently with nothing to say of Judaism's sub sects Christianity and Islam. Hinduism is contemporary with the ancient Greek and Iranian religions.
Europe and the west is now having its civil wars with Islam and gone into navel gazing mode like the 16 and 17 century Indians and Indians have got their focus back. Soon India and China will be back in their rightful place - leading the world. Only about 50 years more left of the short 300 period aberration in Human history where the west has mattered more than India and China.
Before going further do a Google search for "Hindu Achievements in Exact Science" and skim through this book to see a brief list of achievements from the Indian Subcontinent. One link that works is: http://www.forum-transregional...
You should cross check the references to satisfy yourself and research other references.
There is really no doubt that ancient India (even starting around 2500 BC or earlier) had made a lot of discoveries and technology advances. The same is true of ancient China. Don't forget that over 4000 years have elapsed so, naturally, a lot of information will have been lost along the way. The state of our world today owes a lot to these ancient civilizations, along with others such as Egyptians etc.
We should also recognize that today's world is Greek-Roman-centric, believing that logical thought, technology etc. originated with them. That is what most of us are taught in elementary/high-school in N. America and Europe. So, obviously that is what we believe. While the Greeks/Romans did come up with a lot of original thought and discoveries they were not the first in everything they are credited with. Many of their "original" ideas were already over a 1000 years or more older having been developed in either China or India. Do a little research and you will find that there were highly developed civilizations in the Indian sub-continent and China.
How exactly did they get to be so advanced if they did not have advanced tools / technology / thinking etc. ? And all this many 1000's of years before the Greeks/Romans ?
One needs to also understand that the West (Europe / N. America) is the power center of the world currently. This further's the status-quo of what we are taught. However, just a little research & Googling will demonstrate that not everything we are taught is correct or the truth.
So, here is a bit of background on how we reached this state:
It has a huge amount to do with 200 years of British rule of India, who, during that time, came up with systematic methods at wiping out indigenous technology/ processes / knowledge / thought, to attempt at establishing the superiority of European (not American) thought & techniques during their occupation from the 1700's up to mid 1940's. It all boils down at trying to break the psyche & spirit of the people for obvious goals (to rule over them etc.). They had to do this because when they originally arrived on the Indian subcontinent they found a fairly advanced civilization. So, now they needed a method to convince their population back home that the "locals" were in need of "civilizing". They did such a good job that many Indian leaders of the late 1800's / 1900's actually started believing in the inferiority of Indian thought (and superiority of Europeans). Naturally, these leaders had a knock-on effect on the population. To an extent the British did a pretty thorough job at killing indigenous technology/medicine etc.
Additionally, on the religious side, in the 1800's / early 1900's there was a lot of revisionist history being written. Anything that did not fall in line with Christian dates "could not have happened". This resulted in dates in a lot of ancient Indian texts being re-written to suit the views of other people. A good example is the Aryan Invasion Theory and other ideas propagated by Karl Marx. The Indian's were then taught (by Europeans) that they did not understand their own history and were given the newly "revised" history. These history books continue to have influence today.
Everything stated above can easily be verified via some simple Google searches so I am not listing specific references.
So now the question is why is there a need for the Indian Science Congress to "crow" about their achievements ? After all who really cares ?
One answer would be that "because it is the truth". Another answer is that b
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 equations were Diophantus's trick, not Pythagoras's.
Bill Stewart
New Fast-Compression-only CPR http://preview.tinyurl.com/dy575ks
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,
Bill Stewart
New Fast-Compression-only CPR http://preview.tinyurl.com/dy575ks
yea, anyone that has done any building pretty much figures out the PT in short order just trying to make a building that is square. in fact you pretty much can not build a square building without at least a crued understanding of it. it was likly passed from mason to mason for a thousand years before anyone thought to formalize it and write it down. so, if you find the first square building, you found the source.
Cut them some slack on these recent claims, guys. Let's not forget that India brought us Knight Rider, breakdancing, and dressing up like a 70's pimp: https://www.youtube.com/watch?v=vLeUnINuxl0
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.
It must have been something you assimilated. . . .
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.
You can't invent anything, because all inventions are universal in the sense that someone could build them on some other planet given the same materials. Given the same problems, someone would eventually come up with the same solutions. They might be more or less useful, but that is true of inventions different places and situations on Earth. Maybe instead of trying to equate "invent" with a useless definition, it would be better to just understand what it actually means.
The real genius idea is after discovering a numerical relationship to write down a "general" formula, this is what he did.
The general relationship definitely existed in some cultures before Pythagoras, and the question many ask is if he was the first to provide a proof of it, but that is uncertain.
> 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.
A Pirate and a Puritan look the same on a balance sheet.
There is another article in /. that truly deserves the Lifetime Achievement in Pedantry Award
http://tech.slashdot.org/story...
Click on the link above and read for yourself on how much fun it is to be inside the Indian military
Muchas Gracias, Señor Edward Snowden !
-- 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.
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 really don't know about how much communication there was between different regions (so for instance, did Pythagoras and Euclid learn about it from people who'd traveled to India, such as Alexander the Great's armies or random merchants or traveling scholars? Or did they base their work on what the Egyptians had done?) There's also a lot we don't know about what was developed in each region, because only bits of it survived into the historical record. It's not like Pythagoras was the first person in the West to see a triangle; his original work was a follow-on to already known things that he'd learned.
Science does work that way, after all - we need to keep communication as open as possible so people can benefit from it.
Bill Stewart
New Fast-Compression-only CPR http://preview.tinyurl.com/dy575ks
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 intelligent.
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.
"Every time I see an adult on a bicycle, I no longer despair for the future of the human race." - H. G. Wells
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...
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 hadn't been the case, all that would have been destroyed as well.
... They have been infected with the classic italian propensity of laying claim to all of humanity's achievements they had no involvement with whatsoever. What's next, claiming all the world envies them?
I am an Indian and I don't give a fuck about whether it was an Indian that wrote down the first comprehensive statement of the Pythagorean theorem. The theorem would be as profound irrespective of where it originated. I am sick of my country's politicians gloating over an imaginary past full of glory to make up for the utter shambles that Indian science has been in over the past 50 years. I wonder if any these morons can even complete a Pythagorean triplet given the two of the numbers in one. Indian politicians boasting about imaginary science of the past is our version of buying a slick sports car to compensate for some of our insecurities.
Can't make a square without PT? Are you people high or just idiots?
Gimme a piece of string and I'll make right angles as much as you want. With no PT.
You can't invent anything...
Perhaps, but if anything can be invented, mathematics is surely one of them. Mathematics is nothing but a set of symbols and some rules for manipulating them. Anyone can make a new branch of math. Some kinds of math are nothing but an abstract structure, existing only in the mind of the mathematician, with no relationship to anything in the real world, and no known application. In other words, they're completely made up. If that doesn't count as an invention, then yeah, nothing does.
Let me know when India invents sanitation.
The dude who wrote "Was God a Skywalker"?
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Actually, you can build a square building without having *any* knowledge of the Pythagorean Theorem. You simply need the ability to measure a linear distance, and *compare* a linear distance. You don't even need to know what the linear distance being compared *is*.
You need:
A) Four equal lengths of whatever you're going to use to mark where to put the walls of the building.
B) A sufficiently long length of string.
To make a square:
1) Lay out the 4 lengths, end to end, so that they form a closed loop.
2) Put one end of the string on a corner
3) Stretch the string to the opposite corner, and mark where it falls.
4) Put the first end of the string at the adjacent corner
5) Stretch the string to the opposite corner, and mark where it falls.
6) Fold the string such that the two marks overlap.
7) Cut the string at the fold
8) Adjust the 4 lengths such that the cut string stretches from one corner to the opposite corner.
Congratulations, you have a square marked out for your building.
If you can measure angles, it's even easier, and you *still* don't need the PT.
You need:
A) Four equal lengths of whatever you're going to use to mark where to put the walls of the building.
B) A sufficiently long length of string.
To make a square:
1) Lay out the 4 lengths, end to end, so that they form a closed loop.
2) Measure one angle
3) Adjust until that angle is 90 degrees.
Congratulations you have a square.
Note: These instructions assume your marking lengths (A) are rigid. If they are not (such as being made of string themselves), it's a *bit* trickier, because you have to keep the lengths taught, but the process is fundamentally the same.
You're not from the US, are you?
You can't appreciate the beauty of it until you read it in the original Klingon.
You are in a maze of twisty little passages, all alike.
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!
Average Intelligence is a Scary Thing
> 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.
He's not "Indian". He's Canadian-American of Indian descent: http://en.wikipedia.org/wiki/M...
I, too, am very proud of how the first single cell organisms survived to become multicellular. You go, Eoarchean awesome cells! At some point, don't we just have to call history the past and move on to create our own future??? If we humans want to continue to survive, we are going to have to start thinking much more about the future, and dwelling less on attributions of the past. Don't get me wrong, it is good to know what happened and learn from it. But, once you find your historical sources have run out and you are basing your conclusions on millionth hand anecdotal evidence, it is time to let the past be the past.
I'm very sorry for the down-mod. I really thought my reply would have gotten you off the hook. I even *showed my work*.
C'mon people. Work with me here
“He’s not deformed, he’s just drunk!”
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, just like arithmetic. Many philosophers set themselves a goal of proving things about the world in a similar manner. Eventually, we figured out that we could invent other geometries, and much later that pretty much everything interesting has non-Euclidean geometries.
"When you have eliminated the unacceptable, whatever is left, however improbable, must be the truthiness" - Holmes
The formula is fact, it's part to math/reality not the ancient who's best remembered for it.
End of March we will see evidence that the Pythagorean Theory is actually 0.0001% off.