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Pythagorean Theorem proof in a 2100 year old Chinese book (fermatslibrary.com)
346 points by balele on March 24, 2017 | hide | past | favorite | 142 comments



From what I understand, the Chinese had often recorded many facts about nature and mathematics very early and accurately. However they never really created much laws. Laws of nature was a western invention. E.g. they observed accurately planetary movements, but never attempted to formulate the laws governing those movements. That sort of thinking was crucial for scientific thinking.


Maybe true. The emphasis was on calculations. For example, there was a heliocentric model in India [1], which was too complicated to come from a "simple" mechanical model, but was quite accurate.

But I think we should not be too eager to jump on to "science is only from laws" bandwagon. Courses on the philosophy of science take this dogma to absurd extremes, ignoring how current science is often done. There is enough science done today where the laws are only vague, but we do predict useful stuff from simulations - climate models and earthquake modelling being the most prominent - despite not having "simple" laws behind them. As Freeman Dyson often observes, physicists still don't have a good explanation of why a bicycle doesn't topple when in motion - but we've been riding them for a century and half [2].

I think trial-and-error, and simulations also count as sophisticated science.

It's more than a tad racist to insist that Egyptians, Babylonians, Chinese and Indians, as well as medieval Arab scientists were all child races incapable of truly knowing what they were doing.

[1] https://en.wikipedia.org/wiki/Nilakantha_Somayaji

[2] https://www.wired.com/1998/02/dyson/


Feyerabend's Against Method goes further: examining crucial discoveries in science reveals no pattern which could be called a scientific method. Everyone sort of freestyles it or does what works.

I think modern western science discounts other sources of knowledge, because it is not just a platonic ideal but a sort of politics of the scientists, which they need to justify the choices they make.


This is waffle. 'Western Science' is an abstraction. The 'official position of Western Science' is not an accredited publication as far as I know. More to the point, if you have criticisms of individual scientists (the ones who contribute to science [ i.e., people all nationalities and places on Earth) ] who 'discount other sources of knowledge' please be specific. They may or may not have a point. We can't know unless you specify.


Too much troll, didn't read


Even simulations are based on formulating rules or laws in which the different parts operate within. I think you are bringing up an awful lot of straw-men to counter my point. I never suggested one should be narrow minded about it, simply that by merely having observations, we don't really have science. IMHO science relies on having theories which we can formulate rules or laws from which makes it possible to make predictions. What else besides explaining things and making predictions is the point of science?

"It's more than a tad racist to insist that Egyptians, Babylonians, Chinese and Indians, as well as medieval Arab scientists were all child races incapable of truly knowing what they were doing."

What on earth are you rambling about? Were have I made even the faintest suggestion that that is the case? Different civilizations has invented different things and advanced at different levels and different times through our history. Pointing this out isn't racist with respect to other people. Is is racist against Europeans to suggest that Indians invented the zero and our numerals. Am I then suggesting that those stupid childish Europeans couldn't come up with even basic stuff like numerals themselves?

Is it racist to point out that native Americans didn't invent quantum mechanics?

Anyway I don't believe there is such a thing as human races, but there definitely are differences between various cultures and civilizations.

It is an undeniable fact that western civilization was the main driver of the scientific revolution. Should it then not be interesting to understand why it was that the west advanced so much further than the others. One of the key observations which helps understand this is the western preoccupation with formulating laws of nature early on.

How else can you explain how a relatively poor and backwater region of the world could end up eclipsing, far richer, more populous and advance regions such as the Arab world, China, India?


> native Americans didn't invent quantum mechanics

Maya's totally knew about quantum, how else could they have had novelty theory and predicted the 2012 timewave zero collapse? It's not like they had access to the I-Ching[0] to be able to model it like Terrence McKenna did.

... on that note, a bit more serious; this is as good an opportunity to randomly ask as any; can anyone explain to me (as far as pseudo-science goes, going along with all of the assumptions) what the basic reasoning is in Timewave Zero, how they got from the King Wen sequence (which is a certain permutation of the 64 I-Ching hexagrams, but afaik they just use it as a particular 64-element permutation compared to the original order, without taking into further account the symbology of the invididual hexagrams), and turned it into that fractal line graph they call the Timewave? There is an article on deoxy.org that appears to go into technical detail but when I read it and tried to reproduce, it doesn't really say how that step is done. OTOH apparently there's software (screenshots) that plot this graph, so there must be some kind of deterministic algorithm, but I haven't been able to find any docs about it.

[0] ... OR DID THEY??


Regarding bicycles, I feel compelled to share one of my favourite articles on wikipedia. [1] Still, I think the point you made is valid.

[1] https://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamic...


Pretty neat. There's also a TED talk about balance which was pretty amazing.

ps: I wonder if there's a skateboard dynamics.


"medieval Arab scientists"

Ibn_al-Haytham was one of the inventors of the "scientific method". https://en.wikipedia.org/wiki/Ibn_al-Haytham


At least as far as is quoted on that Wikipedia article, he gives a description of basic rigor, not the scientific method.

https://upload.wikimedia.org/wikipedia/commons/5/5c/The_Scie...


I totally uphold your idea. One more case, machine learning, especially deep learning, which lacks strict mathematical model and theoretical explanation, actually works pretty well on reality problems in fact. Maybe, it takes years for theorists to build a theoretical framework to explain, but it does not hinder us to exploit the technique.


You're spreading antiscientific misinformation with your claim that Freeman Dyson asserts that we don't have a good explanation for why bicycles don't topple. The linked article doesn't support that claim.

What Dyson says is that it's hard to design a technological artifact, like a bycicle, from scratch, using theory only. We know perfectly how and why it works, but it's very hard to design something the behavior of which is actually governed cleanly by the fundamental explanatory principles in predictable ways. That doesn't make the principles of the explanation wrong: it's recognizing that reality is incredibly messy. It's about how hard technology is, not about science.


Which is why it is so important that written knowledge survives civilizations, so that future generations can learn from the past.

With our current focus on digital media and "cloud", there won't be anything left in 2100 years for people to have a blick of what we are doing.


Feynman can counter this much better than I can,

"Feynman on pseudo science" https://vimeo.com/118188988


Ancient science is not the same as pseudoscience.

The problem with a lot of the ancient sources is the lack of proofs. What I am arguing is that lack of proofs in ancient mathematical texts doesn't mean that it is all bunkum, and the authors did not know what they were talking about.

I am not talking cultural relativism or "social science is a science" relativism.

Again, another example: Euler is the father of modern analysis, through his "Analysis of the Infinite" [1]. None of his proofs are rigorous according to modern standards. Do you think Feynman would've called Euler a fool?

[1] http://www.maa.org/press/periodicals/convergence/mathematica...


"Ancient science is not the same as pseudoscience."

Ancient science is science. Ancient pseudo science is ancient pseudo science.


Why bring racism to every comparison. They obviously weren't good at the kind of mathematics/science that leads to technological progress. So what?


I think you're being a little unfair to philosophy of science here, bearing in mind how poorly 'Leviathan and the air-pump' was received by actual scientists.


I didn't know "earthquake modeling" was a thing.


This is an interesting idea, even if it does play into the "exotic Oriental thinking" meme. I've seen this line of thinking usually attached with rubbish like "The Westerner wants to control the world, the Eastener only wants to explain it."

However I think that first making observations and then the crucial step of extrapolating and making predictions based on those is as good as any formally named 'law'.


Reading up on Copernicus, Kepler and astronomy gives a good idea I think about what I am getting at.

Extrapolation isn't that easy to do with e.g. astronomy. Orbits don't go in straight predictable lines. They are ellipses where the speed will vary depending on where you are in the orbit. Kepler found that the are covered per time unit was constant, thus implying that when the orbits were closer to the sun they would speed up.

I guess you could say extrapolation was what Kepler tried to do but it took him a lot of work to figure it out. The Chinese while very advance in many respect did not try doing that. What I've read is that they did not have the Judeo-Christian belief that the mind of God could be learned. The laws governing the motions of the heavens was assume inscrutable to the human mind.


Proofs were not always of the same rigor - what was once considered a proof may not be so by modern standards.

Now what this book shows is that 2100 years ago some level of proof was also a requirement in Chinese mathematics; this makes classical Greek/western thought look not quite as unique as it is portrayed.


You might be interested in (perhaps already know) of this book, which develops your idea in some detail: https://en.wikipedia.org/wiki/The_Beginning_of_Infinity


Yes, induction is what makes our progress possible.


[flagged]


Pointing out that western civilization did something isn't the same as claiming only people of western decent is capable of doing something.

Christopher Columbus, was a westerner and went to America. That is just stating a fact of something that happened. That doesn't imply that if Christopher Columbus had black skin it would have been an impossible feat for him to accomplish. Isaac Newton would not have been prevented from inventing calculus if he had slanted eyes.

"Are you saying they were just simply looking at effects without trying to understand causes" As a matter of fact, yes. Chinese astronomer e.g. as far as I know, recorded lots of details about the movements of celestial bodies, but never attempted to device laws governing these movements. The greeks did with their Ptolemaic world view even if they were screwed up. It gave a starting point for Copernicus and Kepler to improve on.

"are you saying their thinking wasn't scientific" Yes, I am. There is no racist undertone there, as much as you like to hunt for it. This was a product of the society and traditions they lived in, not their skin color, slant of eyes or whatever you might want to make a big deal about.

"This of the people who brought us writing and mathematics" Should get your facts straight before you try to belittle me. Mathematics isn't simply numerals. You can do mathematics just fine without indian/arabic numerals. More important for science, it was the greeks who made the first formal mathematical proofs.

And who do you presume are these people who "gave" us writing? Are you assuming writing came to Europe from India, China, Egypt or something?


I'm not presuming anything. writing came from Egypt, likely mathematics too, and where do you think the greeks get their knowledge from? Egypt. Obviously, they were creative in their own right, but that doesn't change the fact of where this stuff originated.


Show me some links, quotes, references or whatever that suggests the Egyptians did math before the Sumerians or Babylonians then. As far as I know the Greeks got knowledge both from Babylonians and Egyptians. Math like writing was developed independently many places. There is no proof to my knowledge that Egyptians was the original source of all this. When you make such an explicit claim, I think you ought to be able to back it up with something.

To my knowledge there was nothing special with Egyptian writing or mathematics. When I read about ancient math, I find much more interesting things to read about in the Babylonians and Sumerians. We still got the 60-based number system from the babylonians in our geometry and division of time.

The next stage in mathematics was clearly the Greeks, which advance ancient mathematics to a new level, with e.g. the way they did proofs etc.

Also the idea that an idea singularly originated in one place, strikes me as a rather simplistic understanding how how science and technology works. People almost never come up with an idea exclusively in a vacuum. One always builds on existing ideas in many increments and often many people derive at similar conclusions independently. If one looks at e.g. the light bulb or steam engine, it is very hard to point to one particular man or country having invented the light bulb. Too many people were involved in an infinite amount of small improvements.

It makes a lot more sense to talk about where did significant scientific progress happen. Who advanced the state of something the most. That often makes more sense than talking about who invented or discovered something.

It should not be very controversial that the advancement of modern science and mathematics has mainly been a western phenomenon. I don't mean to imply that people of western origin are superior, but that historical developments and accidents have culminated in giving a strong advantage to western nations from about 1500s onwards.

There are many good things about western culture I think one should not have to be ashamed of. The willingness for western culture to take a critical look at itself shows one of its strengths. I can think of any other civilization so ready to point out ones own weaknesses and wrongdoings as western civilization. Understanding your weakness is the key to growth and improvement.


So if I'm understanding correctly, this is evidence that about 300 years after the death of Pythagoras, his proof "travelled" over the silk road to China?


There’s evidence that the “Pythagorean Theorem” was known in Mesopotamia a millennium before Pythagoras. It was likely widely known in the ancient world.

The Greeks wrote their mathematical ideas in a different way than other cultures, so the answers to these questions aren’t completely clear-cut.


But was the theorem proved?


It’s really hard to say. Cuneiform on clay tablets was mostly records of finished computations, with the scratch work done with some kind of physical manipulation of tokens or mentally, and most of the instruction and culture transmitted orally.

The Sumerian/Babylonian style of written records did not match, say, Euclid’s Elements. (They didn’t write books full of precise definitions and proofs. They didn’t leave behind textbooks, only problem sets and worked examples.) But note that neither did the style of the Pythagoreans necessarily, and the notion that Pythagoras or his disciples made a proof comes from written records from hundreds of years later.


From Wikipedia:

> Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases.


I was thinking the same thing. It's easy to forget just how much the ancient Greeks accomplished 2,500 years ago.


I always wonder myself when I get to read ancient manuscripts and get to compare with modern days.

As humans we always lived a kind of ups and downs, regarding use of technology, relationships among countries, how open/closed the societies used to be, how travelling was seen and so on.

For example, in the ancient world there was already a kind of Erasmus, as Greek medicine students used to spend a few years with Egyptian doctors before getting back home and start practising.


Or it was independently recreated.


It could've been used without being proved also


The diagrams on the pages shown basically serve as a proof.


It's familiar from hands-on science museums to see a particular case of the Pythagorean theorem illustrated concretely with diagrams or liquid on a rotating plexiglass panel... But surely those aren't proofs, just illustrations. A proof needs to abstract over all possible right-angle triangles.


Both diagrams are a proof over all right-angle triangles, if you know algebra. See the very first comment after the images.


Hmmm. Maybe I'm just used to the convincing generality of the similarity argument (from Euclid, via Polya): https://math.berkeley.edu/~giventh/papers/eu.pdf

But also, we can't trust geometrical diagrams: https://en.wikipedia.org/wiki/Missing_square_puzzle


My understanding is that the 3-4-5 relationship was known for a long, long time before Pythagorus. I think the ancient Egyptians knew of the relationship. But that's not the same thing as a proof: meaning, the fact has been integrated with the fundamentals of a wider body of knowledge.

I see the illustration, but I don't understand how that's a "proof."


>I see the illustration, but I don't understand how that's a "proof."

That's an illustration of the proof. Here is a more modern, animated example: https://upload.wikimedia.org/wikipedia/commons/2/29/Pythagor... The Chinese proof looks more like this one though: https://i.stack.imgur.com/Ylzhg.gif There is also explanation in the annotations.


It's mind blowing when I see a new image like that and it completely changes how I understand the topic. I wish I could find more of those.


Search for the phrase "proofs without words" [0, 1]. There's long been a column in Mathematics Magazine by that name featuring proofs in this style, and there is a book of the same title published by the Mathematical Association of America (which I think collects proofs from the magazine column). Lots of examples from other sources will also show up in a web search.

0. https://encrypted.google.com/search?hl=en&q=proofs%20without...

1. Image results: https://encrypted.google.com/search?q=proofs+without+words&n...


This reminds me of this children toy: https://zh.wikipedia.org/wiki/%E4%B8%83%E5%B7%A7%E6%9D%BF


Also, Pythagoras was ~2500 years ago, before this thing.


Exactly, by the time this book existed 2100 years ago, the idea should have been traveling all over the place anyway. It's not like ancient civilizations were not connected at all.


Yes, people travelled a lot, specially merchants, that is also how Alexandria got many of its manuscripts.

The biggest difference was that nothing was assured about the safety of the travel.


The 3-4-5 relationship is also merely a special case of the Pythagorean theorem, even if they had a proof that all such triangles are right triangles.


https://en.wikipedia.org/wiki/Pythagorean_theorem

> In India, the Baudhayana Sulba Sutra, the dates of which are given variously as between the 8th and 5th century BC, contains a list of Pythagorean triples discovered algebraically, a statement of the Pythagorean theorem, and a geometrical proof of the Pythagorean theorem for an isosceles right triangle.

https://en.wikipedia.org/wiki/Baudhayana_sutras

> A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.

> The lines are to be referring to a rectangle, although some interpretations consider this to refer to a square. In either case, it states that the square of the hypotenuse equals the sum of the squares of the sides.

> If this refers to a rectangle, it is the earliest recorded statement of the Pythagorean theorem.


It's generally understood that the theorem, and in particular the 1/1/2 and 3/4/5 integral triangles were known prehistorically and independently 'discovered' in several places. It's not possible to know what the earliest recorded statement was, because we only have tiny fragments (more commonly, fragments of copies of fragments of later documentation of oral traditions) of what actually was recorded that long ago. Finding such a statement only says that its the earliest we're aware of, and even then its always contingent on a variety of factors.

These sorts of discussions always seem to devolve into "10,000 generations ago, someone who lived near where some of my ancestors later lived might have known more mathematics than people who lived near where your ancestors lived." [The 'That means I'm better than you.' is usually not explicit] Which is boring.


Wouldn't something from that period be written with seal script? That script looks like modern Han characters with an archaic font - it's completely readable.


Seal script is significantly older than that. 2100 years ago is squarely in the middle of the Han dynasty, after the square script we are familiar with was already standardized.


Someone commented on the site that it's a 17th century reproduction.


Also while those are Han, the language is sophisticated to regular Chinese readers. I can't even make sense of the words (individually yes) as a native Chinese speaker.

A far as paper writing, I found [1] which said roughly 100 A.D. some paper production began.

[1]: http://www.chinaheritagequarterly.org/tien-hsia.php?searchte...


Can you make an annotated version? Nothing fancy, if you add the translation with paintbrush and host it in imgur, I'll be completely happy.


It's traditional chinese but it's a challenge. This is my best guess: http://imgur.com/a/rnXPW

Looks like they were using colour as variable/labels.


Thanks! I replied in my other comment, because I made a previous explanation attempt but after looking at your translation I think that it was wrong and I wanted to highlight the differences.

https://news.ycombinator.com/item?id=13953495


Keep in mind that the earliest copies of Euclid, Plato, etc, are often from several hundred or 1000 years later.


It's probably of value to note that that diagrams that everyone is talking about are not part of the original text.


I don't know Chinese, but I don't like the explanation in English at the side. I think that both diagrams are part of the same proof, not two independent proofs. I agree with the first comment by Martin Cohen http://disq.us/p/1h6y5qx

> The way I read it is that the first diagram says that(a+b)^2 = 4(ab/2)+c^2 and the second says that c^2 = 4(ab/2)+(a-b)^2. Both of these simplify to c^2 = a^2+b^2.

I only have a small proposed stylistic change that is to keep the are of the triangles as unknown values, let's call it T. So the first diagram shows that (a+b)^2 = 4T + c^2 and the second that c^2 = 4T + (a-b)^2. And simplifying you get simplify to c^2 = a^2 + b^2.

Is there a transcript and translation of the Chinese text?


I made this for another comment. Here you go: http://imgur.com/a/rnXPW


Thanks!

Copy of your previous comments in other thread for context:

> Also while those are Han, the language is sophisticated to regular Chinese readers. I can't even make sense of the words (individually yes) as a native Chinese speaker.

> It's traditional chinese but it's a challenge. This is my best guess:

> Looks like they were using colour as variable/labels.

--

Most of my previous guess is wrong :( .

In the second diagrams, they use that the area of the triangles is 6, they are not ignoring the number.

In both pages they ignore the outer triangles. They are not painted in neither graph. If they were using "my" solution I'd expect that the outer triangles in the first diagram were painted with the same color as the inner triangles in the second diagram.

The first diagram makes no sense. It looks like a graphic to show a numerical equality, but the geometric properties give no insight of the numerical properties. Perhaps it was a usual writing style?

There is no 49 in the first graphic (nor in the second) so my previous explanation doesn't fit with the text.

--

My second unsupported attempt of translation is:

[Second diagram]

The area of each red triangle is 6 [because 4 * 3 / 2 = 6].

The side of the inner yellow square is 1 [because 4 - 3 = 1], so the area is 1 [ 1 * 1 = 1].

The area of the [rotated] square is the sum of the four red triangles and the small yellow square, it is 25 [because 6 + 6 + 6 + 6 + 1 = 25].

So the side of the [rotated] square is 5.

Then the sides of the triangle at the bottom are 3, 4, 5.

[First diagram]

If we subtract the area of a square with side 5 and a square of side 3 [painted in cyan], we get the area [painted in yellow] that is 16.

[Notice that 16 is the area of a square of side 4, that we never draw here.]

--

My current opinion:

The second diagram is a proof that in a right triangle with legs 3 and 4, the hypotenuse is 5. I think that this can be extended to any other Pythagorean triple, but one at a time. This doesn't look like a general proof for all of them. This looks more like the verification of an example than a general proof.

The first diagram is an auxiliary construction for the second diagram. It's not very enlightling.

The explanation of the side added in Fermat's library is no a transcript or an explanation of the proof in the main text. It's another proof of the Pythagorean Theorem with a somewhat similar graphic, but it's unrelated.


I couldn't translate the middle left vertical sentence on the first diagram because it's a bit too faded. (It said something about the corner...) There's also references about 'this layer/level' all over the place that make me think there may be some paper folding involve but it could simply mean 'this layer is solid yellow' and so on.


I know you can use the second diagram to prove the theorem, but it requires an algebraic argument (the other two squares aren't shown). Unless the text says something pretty interesting, this looks more like a proof just for a 3,4,5 triangle.

The first diagram I can't get my head round at all, or is it proving something different?


The first and second diagrams are similar, just using the 'outside' vs 'inside' deconstruction.

If we label the sides a=3, b=4, and c=5 :

The first diagram shows that the big outer square of length (a+b) equals the area of the 4 triangles plus the rotated square of side c. (a+b)^2 = 2ab + c^2

[I'm not sure why they drew an inner 3x3 square on its own].

The second diagram puts the same four triangles inside the rotated square of side c, which leaves an extra smaller square of side (b-a) inside.

c^2 = 2ab + (b-a)^2


Yeah, the inner square is confusing.


The top comment after the images of the two diagrams explains how the 1st diagram is another algebraic proof, similar to the 2nd diagram.


It was true then...

http://abstrusegoose.com/376

However paper itself was invented around the same time. How come bookbinding already existed then?


Ah, Stigler's Law of Eponymy


Why not 2500 years ago!?


Couldn't have said it better myself. I think about this stuff a lot, how much ancient and modern overlap, how much Eastern and western overlap, yet how people still want to divide everything.

"The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift." - Albert Einstein

"The people in the Indian countryside don’t use their intellect like we do, they use their intuition instead, and the intuition is far more developed than in the rest of the world… Intuition is a very powerful thing, more powerful than intellect, in my opinion. That’s had a big impact on my work.

Western rational thought is not an innate human characteristic, it is learned and it is the great achievement of Western civilization. In the villages of India, they never learned it. They learned something else, which is in some ways just as valuable but in other ways is not. That’s the power of intuition and experiential wisdom." - Steve Jobs

Carl Sagan was really keen on seeing 'the bigger picture' too, can't find the particular quote I was looking for. Maybe later.


We detached this subthread from https://news.ycombinator.com/item?id=13953887 and marked it off-topic.


These divisions are very important. As long as mystical beliefs towards Eastern thought are used to cause real harm through herbal remedies and supplements, the public must be taught to give it less importance. Among critical thinkers, it is valuable to look for similarities in scientific histories.


Last I checked homeopathy was western. i think your bias towards eastern medicine would be better founded if you were to say faith healing rather than eastern. Within eastern medicine one also finds people who used early forms of experimentation to derive working cures. Examples of working medical cures include boswellia used to treat bursitis, artemisin used to treat malaria. Also both Chinese and Indians had developed anaesthetic before Europeans. Similarly the procedure of rhinoplasty was developed in India. When the British came in western surgeons studied the technique and took it back to Europe. In fact hygiene was a critical part of the ayurvedic surgeons life well before Europeans realized the importance of hygiene in surgery. Of course there are a lot bogus stuff in eastern cures as well but in the west you have stuff like homeopathy. I think the key take away is that you cannot divide by east and west. We are after all human and each culture has their own contribution to the face of the earth.


You are trivializing the significant difference modern western science based medicine and earlier medicine. Of course people could come up with all sorts of practical solutions to various ailments and conditions through trial, error and observations. That however does not make it scientific. There is no scientific theory in you Chinese and Indian examples on which to make predictions and explanations. One example would be e.g. germ theory. It allows one to make predictions about things not yet observed. It helps explain why washing your hands is good. Now you can learn this from practical observations, but if you have no idea that the reason is due to germs being removed, then it prevents you from experimenting with and finding alternative cleaning agents or practices.


Western medicine is often found by trial and error too. Scientists perform tests of thousands of compounds just in case one of them happens to do something that might turn out to be useful. Some drugs are used to treat different diseases than what they were originally developed for because we noticed that patients with those other diseases mysteriously showed improvements. I can't think of which off the top of my head but perhaps a heart medicine that stopped baldness.

The key difference is western medicine is tested objectively, while traditional medicines are based on belief. A million people getting sick and taking a treatment and recovering doesn't mean the treatment does any good, but they'll believe it does because everyone else believes it too.


You're just arguing to argue. I didn't see any cognitive dissonance created in his comment.


It should be noted as well that the concept of the "Eastern" is also Western in origin.

A good read about this is Orientalism by Edward Said.


Exactly. I believe it is possible to synthesize the logic of the West and the intuition of the East.


Big Pharm and meat-based diet do a lot more harm to the entire biosphere and individuals than Ayurvedic medicine and yoga. Don't even get me started.

I don't know much about Eastern medicine outside of India to be honest. One exception: Chinese people buy tiger bone Viagra, elephant tusk art, rhino horn something, and shark fin soup.

I was born Hindu but became closer to Buddhist as I learned more about the scientific revolution and how it built the modern world.


Meat is unarguably bad, but the pharmaceuticals industry is the closest thing we have to a miracle factory. It has spared us from the miseries of polio, tuberculosis, smallpox, AIDS, surgery without anaesthetic and a thousand other horrors. Diseases that were once death sentences are now treatable with medications that cost pennies. Countless millions of lives have been saved by vaccination.

Ayurvedic medicine clearly does more harm than good. It has never been shown to be significantly more effective than placebo. Ayurveda poses a major risk of heavy metal poisoning, due to the pseudoscientific theories of rasa shastra.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2755247/


Not all ayurvedic medicine require heavy metals. There are herbs like boswellia (now also an allopathic drug) that genuinely do what they are supposed to do. Ayurveda, prevented black death in India. Granted there is a lot of bs out there that gets passed of but there are parts that do work. Distilling these parts is important. I think the lack of quality control in eastern medicine is what has given it a bad name. Granted we don't have antibiotics or anti cancer drugs but there were surgical procedures like rhinoplasty that were successfully carried out. Of course any medicine that is 2000 years old is going to be nowhere near what modern medicine is because we have had 2000 years to evolve it. Reason why easterners set store by it is it provided a bit more protection than what the doctors of medieval Europe could do. 1000years is a long time and lots changes, sadly eastern medicine didn't.


I should explain more clearly that I am all for Western and Eastern medicine finding a middle path. What I am against and referring to is how agribusiness, poor nutrition, clever marketing, and healthcare (mostly disease-care) create a lot of needless suffering. A lot of prescriptions are only there to take care of health problems that could have been prevented with proper nutrition and a more integrated, instead of reductionist, model for medicine.

I think I should explain my thoughts on HN a little clearer going forward.


> Big Pharm and meat-based diet do a lot more harm to the entire biosphere and individuals than Ayurvedic medicine and yoga.

Cars kill more people per year than heroin, therefore heroin is healthier than cars.

Let's wait until pseudo-scientific treatments become multi-billion dollar industries and then we'll talk about what does more harm to what.


I'm not talking about pseudo-scientific anything dude.

1.) A meat-based diet is directly linked to higher cancer rates.

"The World Health Organization has determined that dietary factors account for at least 30 percent of all cancers in Western countries and up to 20 percent in developing countries. When cancer researchers started to search for links between diet and cancer, one of the most noticeable findings was that people who avoided meat were much less likely to develop the disease. Large studies in England and Germany showed that vegetarians were about 40 percent less likely to develop cancer compared to meat eaters."

http://www.pcrm.org/health/cancer-resources/diet-cancer/fact...

2.) A meat-based diet is directly linked to clearing wild habitat for more farm animals.

"Both the meat-based average American diet and the lactoovovegetarian diet require significant quantities of nonrenewable fossil energy to produce. Thus, both food systems are not sustainable in the long term based on heavy fossil energy requirements. However, the meat-based diet requires more energy, land, and water resources than the lactoovovegetarian diet. In this limited sense, the lactoovovegetarian diet is more sustainable than the average American meat-based diet.

The major threat to future survival and to US natural resources is rapid population growth. The US population of 285 million is projected to double to 570 million in the next 70 y, which will place greater stress on the already-limited supply of energy, land, and water resources. These vital resources will have to be divided among ever greater numbers of people."

http://ajcn.nutrition.org/content/78/3/660S.full

3.) U.S. eats more meat than any nation on Earth and also has the most expensive health care in the world too, 20% of the GPD. We have a society whose delusions cause diseases and destruction around the world. If I was wrong, there wouldn't be so many brilliant scientists, doctors, artists, and entrepreneurs on this same train of thought.

4.) Yoga, meditation, plant-based diet have all played a major part in creating the modern world including computers and the internet. If people don't have discernment to know true from false, that is their shortcoming and not Dharma. ;)


You have not addressed my counter-argument. I'm not interested in defending "meat-based diets". I'm simply attacking your pseudo-medicine.

> We have a society whose delusions cause diseases and destruction around the world. If I was wrong, there wouldn't be so many brilliant scientists, doctors, artists, and entrepreneurs on this same train of thought.

Argumentum ad populum.

> Yoga, meditation, plant-based diet have all played a major part in creating [...] computers and the internet.

This is probably the most absurd statement I've read all week.


[flagged]


"Your" as in "the one you brought up".

What does history or the Bay Area have to do with this discussion?


What did I bring up again? I'm confused what this about at this point. I feel like you are trying to create cognitive dissonance where there is none.

Read these: https://www.amazon.com/What-Dormouse-Said-Counterculture-Per...

https://www.amazon.com/Counterculture-Cyberculture-Stewart-N...


I'm talking about Ayurveda. To recap: you claimed that meat-based diets and pharmaceuticals cause more harm (in absolute terms) than Ayurveda, and I countered that the comparison is invalid because Ayurveda is practiced at a scale that's simply incomparable.


> 4.) Yoga, meditation, plant-based diet have all played a major part in creating the modern world including computers and the internet. If people don't have discernment to know true from false, that is their shortcoming and not Dharma. ;)

I was interested in your argument about meat and then I got to this, which immediately unraveled any point you had for me.

Investments in military technology played a major part in creating the modern world including computers and the Internet. That hippies were so intimately involved at a few important points is more a reflection of the time period and culture than causality, more an observation of the type of people drawn to the work for a season. Stating that we have the existence we have in large part because of yoga and meditation and not eating meat is so revisionist and misguided that I don't even know how to dispute it. I'm sorry, but that's just blatantly ridiculous because it's such a complete inversion of the actual truth.

That you take it further and imply someone is defective and invoke Dharma for believing otherwise is quite something. You should really bring it down a bit if you want your point to make sense, because you're coming across as far more arrogant than I think you intend.


Your missing the forest for the trees. I find many of the comments to my original comment to be very reductionist and misguided.

Semantics. What I typed, how he reacted, how I reacted, and now your reaction. We are so far from my original thought that I don't know how to respond. In fact, I think I'm going to stop here because I am wasting time talking about nothing of consequence.


Modern medicine, big Pharma and meat based diets are orthogonal to each other. Modern medicine has saved hundreds of millions of lives, while alternative medicine is leading people astray and ruining lives every day.

Sorry for the harsh words, but I've seen the damage, and I am tired of how alternative medicine is handled with silk gloves and shown infinite respect, in the name of being open minded.


A, you're wrong. Diet, healthcare, and pharmaceuticals are very interconnected. Also, adding pollution and climate change in there as well when you count land/water use and greenhouse gases produced by factory farming. Add advertising and lobbying in there as well, it's so effective you still think you're right.

B, the original comment was focused on taking what works from both and leaving the rest behind. You're making the same mistake as a billion other people...clinging to the paradigm you are currently in thinking there is nothing beyond it.

C, I'm tired of people thinking they are smart because they used the word 'orthogonal' and say things like 'sorry for the harsh words bro', which doesn't apply in this context and this is a pretty typical reddit/HN thread. Do you have any original insights into any of this or are you just gonna drop more vocab words and 'harsh words'?


anecdotal but had chronic sinusitis , allopathy mentioned only surgery as last option and that would also comeback after 5 to 6 years added sleep apnea. 3 months of regular Ayurveda and 12 days intense treatment. No issues now and very happy.


Any ideas of it's authentic? China is hyper nationalist so I'm initially skeptical. Might be as fictitous as their GDP figures or sovereignty over Taiwan.


We detached this subthread from https://news.ycombinator.com/item?id=13952573 and marked it off-topic.

The first question was fine of course but the political flamebait in the rest predictably took over.


> Any ideas of it's authentic?

It is. And it's nothing new and well-known[1]. OP is Fermats library's high resolution picture of the 17th century reproduction.

[1] https://en.wikipedia.org/wiki/Zhoubi_Suanjing


2100 years is still younger than Pythagoras's proof, so I don't see an obvious motivation for fabricating it.


Making sweeping statements like this on controversial topics without substantiation usually leads to flame war, as evident here.


When you want to like Taiwan more but then notice their view of Tibet is just as twisted

District 13


Both sides of that conflict were chock full of assholes.


> hyper nationalist

Says Americans, biggest lovers on this planet for their own national flag. /s


Swing and a miss.


> sovereignty over Taiwan

This is the claim that China and Taiwan should reunite since the PRC drove the Nationalist Party out of mainland China. It isn't fictitious, it's merely a political wish to merge the two from the PRC side. Similarly, some Nationalists in Taiwan are happy to take back mainland China, as much as the country is divided on whether Taiwan should remain as it is, or should declare its full independence.


The GP is talking about the straight-faced lie that the PRC peddles in international circles that Taiwan is a province of the mainland government. It is the international equivalent of putting their hands on their ears and shouting "LA LA LA I CAN'T HEAR YOU!", and about as legitimate as Mexico's claim to Texas.


I've ended dates over this with Chinese girls. Inevitably they condescend to me about how "I'm just an American" that "can't understand the complicated situation," but that I should rest assured that "Taiwan is not a country, it is a Chinese province." Never mind the fact that I lived there, documented the sunflower protests, speak the language... As opposed to these girls that hadn't even visited the nation. Because they can't. Because you need a special visa. To enter this "non-country."


I've just told older Chinese that the Taiwanese don't want to be a part of China and they tend to give it another thought.


Did you say "prove it, take the plane there", and how did they respond to the fact that you need a special visa?


"it's complicated" usually. At that point I'm usually already done though.


Doesn't the PRC's claim on Taiwan boil down to a combination of right-of-conquest ("Taiwan belonged to the Republic of China, we beat up the Republic of China, therefore Taiwan is ours") and Just Because? ("The PRC is the only legitimate Chinese government because the PRC says so")

I'm very skeptical of purely historical claims of sovereignty. If the people of Taiwan legitimately vote to join the PRC, that's their right, but the PRC has no legitimate right to demand it.


It must be clarified that mainland of China is also part of ROC according to ROC government[1]. In fact, the mainland and taiwan are in war, just like the Union and Confederacy in American civil war, even if there is not military conflicts right now. More interestingly, ROC actually claims larger territory than PRC (for example, part of Mongolia). It is ROC's constitution, not PRC's government, demands taiwan is part of China. Though it's not the People's Republic of China. And guess what, according to ROC's constitution, mainland China is "enemy occupied area". Therefore people in mainland China does not have right to vote, or legitimately declare independence.

[1] https://commons.wikimedia.org/wiki/File:ROC_Administrative_a...


China lodged a formal complaint and warned of the "destr[uction of] Sino-US ties" because the US president admitted that the Taiwanese president spoke to him. If there's a reasonable party in all this, it is definitely not China. https://www.theguardian.com/world/2016/dec/03/china-donald-t...


We are incredibly off topic, but I think it's a bit reductionist to call China unreasonable. China is, above all, pragmatic. The Taiwan situation is a farce, but the Communist Party has reasons to believe it necessary. Party sovereignty and legitimacy are based on defending Chinese independence and restoring national grandeur (强国梦) after colonial humiliation. Any change on the Taiwan issue could cause both separatist and nationalist forces to escalate out of control, potentially destabilizing the entire country.

China really doesn't want to find out what might happen if countries start recognizing Taiwanese independence, so the US president poking at that bubble is seen as a threat. China responds with assertive words because fighting with words is better than fighting a war.


There's a lot of political will in Taiwan to change the constitution, but China has threatened war if that occurs, and the US is very lukewarm on it.

So it's not as if the ROC is free to amend their own constitution - as doing so would negatively affect their national security. It's safer for them to keep up the ridiculous notion that they have sovereignty over Mongolia and parts of the Russian far east.


It would be rather peculiar if during the American Civil War the Confederates had retreated to something like Cuba and remained there to this day.


There's a community of Confederate descendants in Brazil. Most of them have assimilated but a few live in ancestral lands. There's an annual festival and everything.

https://en.wikipedia.org/wiki/Confederados https://www.vice.com/en_us/article/welcome-to-americana-braz...

There were also settlements in Belize and Mexico apparently. None of them lay claim to being independent nations and owning mainland US though.

The ROC as I see it retreated into an enclave of the former whole China and was never fully vanquished from Chinese land. So it's really more like if the Union stopped fighting after the Confederacy was defeated in all but one breakaway state. Even more accurately, since the PRC were the rebels, it'd be like the Confederates took over all the Union states except, say, Pennsylvania and then the war came to a halt. The Pennsylvania redoubt of the US would still be the US and may or may not make claims to the rest of the formerly united United States.

But what do I know about the situation? I'm just an American.


Descriptions of all possible points of view are presented in the Wikipedia article "Political status of Taiwan" [1]. Among these is the (fringe) theory that based on various post-WWII treaties, the US currently holds sovereignty over Taiwan [2] (a view not endorsed by the US government, by the way).

[1] https://en.wikipedia.org/wiki/Political_status_of_Taiwan

[2] https://en.wikipedia.org/wiki/Political_status_of_Taiwan#Arg...


I worry that China is outcompeting us.


Please don't do this here.


Who gives a shit? It is almost always Americans making such statements, obsessed as they are about being number one. If Chine gets richer and more technologically advance that would be good for them and good for us westerners. It is not a zero sum game.

Although to be realistic I don't think China will ever outcompete the US. Not because I don't want them to, but simply because so many fundamentals count in Americas favor and against China. China is facing a demographic catastrophe. The US can easily grow its population with immigration and has plenty of land and natural resources to do so.


I agree with the non zero-sum point, however...

China is facing a demographic catastrophe.

Strongly disagree. The view on the ground in China is great. Almost everyone has their material needs exceeded, many sectors of infrastructure are second to none, education and internationalization of tastes is increasing, and the society is generally very safe. E-vehicles and e-commerce are everywhere. Rent a bicycle for nothing. Visit the tropics, Himalayas, desert or snow with a cheap domestic flight. Cuisine is arguably the most extensive in the world. Mobile payments are ubiquitous. Internet is cheap to free and literally you can get a signal anywhere. Yes, of course like anywhere it's not perfect, but it's really a far cry from America's stagnant and elitist education system, crumbling or monopolistically privatized infrastructure (eg. transport, medicine), and widespread opiate, gun and race problems.

(FYI: minimum wage in most Chinese cities for an unskilled foreigner with any kind of get up and go is 200CNY/hr (~USD$28/hr) these days... a great many western workers are on less than half of that, and would do very well to migrate.)

so many fundamentals count in Americas favor

I would like to hear what these are supposed to be. Having elite universities doesn't count if you rent them out to all comers, default English doesn't count if more people speak it overseas, VC doesn't count if it's easier to get elsewhere, and land isn't needed if your population is already happy to urbanize with extreme density. China owns the world's supply chain and manufacturing, has a highly efficient centralized form of government that can get huge or long term projects done without recourse to political terms, and leads the world in output and deployment scale of renewable energy systems (hydro, solar), modern transport infrastructure, robotics, internet, mobile payment and e-vehicles. Those are some pretty big fundamentals, too. From my perspective all the US really has are systemic global financial and communications surveillance capabilities and a big fat army. Their diplomatic trajectory is nothing to write home about, either.


>China is facing a demographic catastrophe.

you didn't refute that. you just said "life on the ground today is good." That's why its called a cliff. Things are pretty good right up to the moment you fall off.

>FYI: minimum wage in most Chinese cities for an unskilled foreigner with any kind of get up and go is 200CNY/hr

But that's not the same thing as minimum wage. Many many Chinese people earn less than that. When you're a Chinese person you can't just hit up your mate on wechat for some bullshit English teaching job whenever you want beer money.


There's really no need to refute a statement which goes directly against sustained personal observation, especially when it is made without producing any actual evidence.

Obviously not everyone earns the same, then again local people tend to have more money than even wealthy foreigners at the high end, and at the low end at least tend to benefit from free housing, familial support networks, and do not have to fund international travel to maintain ties to home.

Furthermore, downvoting because you don't agree with someone is considered bad form.


> (FYI: minimum wage in most Chinese cities for an unskilled foreigner with any kind of get up and go is 200CNY/hr (~USD$28/hr) these days... a great many western workers are on less than half of that, and would do very well to migrate.)

Quoting wages is meaningless if you don't also mention cost of living.


Depends on location and expectations, generally speaking in second or third tier cities usually 5000/month outgoings is comfortable, ie. breakeven from 25 hours/month (6 hours/week).


Nothing wrong with worrying and wanting your home country to be the best either. Worrying leads to motivation which leads to competition which benefits everyone.


> Who gives a shit? It is almost always Americans making such statements, obsessed as they are about being number one.

Are you guys seriously not getting the joke? I don't usually buy into the stereotype that Hacker News is utterly humorless, but you're not making it easy.


According to this editorial, China will be the global tech leader soon (if it isn't already):

http://www.scmp.com/business/global-economy/article/2081771/...


Who is "us"?


This is what we call a "joke," playing on some Westerners' fears of modern Chinese global economic power.


[flagged]


We've banned this account for repeatedly violating the HN guidelines. Nationalist politics are off-topic and unwelcome here, and the incivility you've been displaying is not acceptable.

Posting like this will eventually get your main account banned as well.


> All said, calling India a nation of idiots at this point would be a compliment.

If I could, I would have downvoted you just for this statement. Although everything else is "good facts"

I have read so many books from Gandhi, but cannot find a connection to his thoughts/principles - in a normal scenario. What makes sense is this statement (used in India): "Mazboori ka naam Mahatma Gandhi.” i.e When you are helpless, act like Mahatma Gandhi. And that makes perfect sense because India's population was weak and helpless against the British rulers.

For other people, who don't want to dig-down the national anthem in English - here it is from the all knowing Wikipedia. The first two lines are enough to offend India's democracy - yet its the national anthem

I am going to write to the Indian authorities - unfortunately, at the best they'll change the translation and brainwash with bad history again.

----

Source: https://en.wikipedia.org/wiki/Jana_Gana_Mana

You are the ruler (directing the nation for farewell) of the hearts of all peoples,

Dispenser of India's fortune.

Thy name rouses the hearts of the Punjab, Sindh, Gujarat, and Maratha,

Of the Dravida, and Odisha and Bengal.

It echoes in the hills of Vindhyas and,

Himalayas, mingles in the music of the

Yamuna and the Ganga and is chanted by

the waves of the Indian Sea.

We pray for your blessings,

and sing by your praise,

The saving of all people

waits in thy hand.

You are the dispenser of India's fortune,

Victory, victory, victory to thee.[7]

----


Except for a couple sentences in the beginning, your message is entirely off-topic.


Could you expand on the brainwashing claims a bit more, i'd be excited to hear them. Not meant in a negative way, just curios.

I was always under the impression Ghandhi is seen in positive light, even in China.


Don't you think that's a bit strange ? The dude was helping the massacre the Bantus in Africa and suddenly becomes a "messiah" in a few years after returning to India ? I mean that is a miracle [1]. I wish historical figures were reassessed every few years in light of contemporary ethics, but this never happens with those the establishment wants you to see in positive light.

His antics are well-documented (with lots of references here).

https://sringeribelur.wordpress.com/2015/07/23/gandhi-articl...

He probably single-handedly delayed India's independence by ~20-30 years (was't that convenient).

[1] Okay that was a bit of an exaggeration since the Liberal movement essentially believed that it was the burden of the white race to civilize the barbarians (to paraphrase John Locke). Indians were I guess A-san (3rd class ? Or may be 2nd back in those days)... which is what Gandhi too believed.


Oh, well, i need to adjust my view then. Thanks for your reply, very insightful indeed!


Don't be too enamored. These are fairly standard right wing talking points in India. From his comments on Gandhi and Pythagoras one can easily infer that he is a supporter of Narendra Modi and Hindu supremacy.

Pythagoras' school provided the earliest documented proof of the theorem, but the result was possibly known as early as 3000 BC.

As for Gandhi, he grew up in a strictly birth based hierarchical society and he pretty much accepted social and racial hierarchies until his thoughts evolved circa 1913. Most of Gandhi's racist quotes come from before 1910.


Exercise in dealing with such "Exhibit A"'s:

> Pythagoras' school provided the earliest documented proof of the theorem, but the result was possibly known as early as 3000 BC.

Actually there is no known evidence Pythagoras or his school had any relation to the theorem. Much of it is word-of-mouth legend (and even then not particularly informative).

It's amusing when the same people accept legends from Europe as canonical, while treating similar historical data in India as literally non-existent.

> Don't be too enamored. These are fairly standard right wing talking points in India. From his comments on Gandhi and Pythagoras one can easily infer that he is a supporter of Narendra Modi and Hindu supremacy.

> As for Gandhi, he grew up in a strictly birth based hierarchical society and he pretty much accepted social and racial hierarchies until his thoughts evolved circa 1913. Most of Gandhi's racist quotes come from before 1910.

I guess the Native Americans too were "supremacists". How about the Bantus, don't forget them, man! ... These narratives get mind-numbingly boring; much as it does to hear of the BJP as some great establishment challengers. Eesh, don't you sheep read anything other than the Hindu's editorials ? In any case, this has typically been the talking point of the status quo-ists and pro-establishment ones for .. what 300 years ?

I'd not keep my hopes up with such creatures though since they have neither the afflictions of reading nor of reason. Social creatures will exploit the status-quo for maximum gain, and anyone who claims we (even in the occident) don't live in a hierarchical society are naive fools not worth arguing with.


> Actually there is no known evidence Pythagoras or his school had any relation to the theorem.

https://books.google.com/books?id=Cf9Rj_ADZU4C&pg=PA29&lpg=P...


You basically prove my point.

Your "proof" is some admirer claiming this guy discovered it [1] ? You realize, even if this were true, he'd (atleast) be third in the game. Also where pray tell me where is this glorious "proof" you were bandying about earlier ?

"Legend", you might want to look up the word. Or may be words are not quite for the big-mouthed ? ggrks man!

[1] https://www.quora.com/How-did-Pythagoras-arrive-at-the-Pytha...




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