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Pythagorean Theorem proof in a 2100 year old Chinese book

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Re: Pythagorean Theorem proof in a 2100 year old Chinese book

#141

Post by E6300 »

good_vibes wrote: post #119
E6300 wrote: post #104

Earlier quoted context omitted.

"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.

Re: Pythagorean Theorem proof in a 2100 year old Chinese book

#142

Post by MichaelMoser123 »

jernfrost wrote: post #50

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.

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.

Re: Pythagorean Theorem proof in a 2100 year old Chinese book

#143

Post by averagewall »

jernfrost wrote: post #128
arjo129 wrote: post #105

Earlier quoted context omitted.

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 develo…

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 wou…

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.

Re: Pythagorean Theorem proof in a 2100 year old Chinese book

#144

Post by dang »

good_vibes wrote: post #61

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 t…

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

Re: Pythagorean Theorem proof in a 2100 year old Chinese book

#145

Post by agumonkey »

proteinbased wrote: post #94
sn41 wrote: post #58

Earlier quoted context omitted.

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…

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.

Re: Pythagorean Theorem proof in a 2100 year old Chinese book

#146

Post by _Codemonkeyism »

sn41 wrote: post #93
_Codemonkeyism wrote: post #86

Earlier quoted context omitted.

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…

"Ancient science is not the same as pseudoscience."

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

Re: Pythagorean Theorem proof in a 2100 year old Chinese book

#147

Post by nurettin »

sn41 wrote: post #58
jernfrost wrote: post #50

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…

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

Re: Pythagorean Theorem proof in a 2100 year old Chinese book

#148

Post by Confusion »

sn41 wrote: post #58
jernfrost wrote: post #50

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…

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.

Re: Pythagorean Theorem proof in a 2100 year old Chinese book

#149

Post by jernfrost »

iam-you wrote: post #138
jernfrost wrote: post #132

Earlier quoted context omitted.

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 prevent…

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.

Re: Pythagorean Theorem proof in a 2100 year old Chinese book

#150

Post by gus_massa »

y2kenny wrote: post #131
gus_massa wrote: post #47

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…

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.

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