Archive - Jul 21, 2008

Date

I Ching and math

My mom arrived in US. And brought me 3 books.
One of them is about I Ching and using hexagrams to solve xMO level math problems.
The hexagrams' Yin and Yang parts maps to 0 and 1, or -1 and 1 respectively.
It's quite easy to use the 0,1 to form a Boolean Algebra and then using that to solve Olympiad problems. Also it was shown to solve the game Nim and a few classic coloring problems.
1 and -1 can form a Abelian group(-1,1), solve another set of math problem.
A Boolean vector can represent graphs, solves yet another kind of math problem.
It also consist of some discrete probability things...
and more...

It's just using the I Ching terminology as a isomorphism to modern mathematics.
Quite interesting. It's not useful, but it proves a point. That I Ching's hexagrams' structure has many mathematical ideas that's considered quite modern.

This graph limited the mind of ancient Chinese mathematician. Sad.
If they have done mathematics just for the sake of it instead of using it for real application only, then maybe, we can have a lot more useful theorems.

In most dynasties, mathematicians have very low social status. But people who does I Ching have high status due to common people and philosophers believe I Ching is the answer to everything(like 42.) So Chinese mathematicians start to do math that related to I Ching, and rarely let themselves to do math outside the I Ching framework.

I hope I get a decent job doing math.

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