Should Autistics Invent Math Instead of Learning It?

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byakuugan
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20 Jun 2017, 12:11 pm

I invented a lot of Algebra, Trig, and Calculus when I was in elementary school and didn't know of any math beyond division.
I was discouraged after finding out that most of my mathematical discoveries had already been thought of, and were included in various textbooks.
I was diagnosed with Asperger's Syndrome near the end of Junior High, and was supposed to be sent to a special High School for autistic people, but I ended up being sent to a neurotypical community college instead.
I took the 3 calculus classes, but lost interest in learning more math after realizing that most of the students and teachers only cared about memorization and passing the classes, rather than deriving and appreciating the material.
I took up professional chess, and only recently started getting back into mathematics as a way to teach chess concepts more concretely.
I then decided that chess would be a good way to teach math concepts more intuitively, so I started my own math curriculum that uses chess as a teaching tool.
For example:
The knight represents the eight Gaussian Integers:
(2 + i), (2 – i), (-2 + i), (-2 – i), (1 + 2i), (1 – 2i), (-1 + 2i), (-1 – 2i)
The camel represents the eight Gaussian Integers:
(3 + i), (3 – i), (-3 + i), (-3 – i), (1 + 3i), (1 – 3i), (-1 + 3i), (-1 – 3i)
The zebra represents the eight Gaussian Integers:
(3 + 2i), (3 – 2i), (-3 + 2i), (-3 – 2i), (2 + 3i), (2 – 3i), (-2 + 3i), (-2 – 3i)
The giraffe represents the eight Gaussian Integers:
(4 + i), (4 – i), (-4 + i), (-4 – i), (1 + 4i), (1 – 4i), (-1 + 4i), (-1 – 4i)
The antelope represents the eight Gaussian Integers:
(4 + 3i), (4 – 3i), (-4 + 3i), (-4 – 3i), (3 + 4i), (3 – 4i), (-3 + 4i), (-3 – 4i)

I finished the first two videos in my math curriculum
https://www.youtube.com/watch?v=9covKtfM-O0
https://www.youtube.com/watch?v=eRA5u3F_KcY

I am interested to know if my videos provided more intuition than what you might have learned in school.
My videos are specifically designed for: low-functioning autistics, people with learning disabilities, intuitive non-mathematical people, and high-functioning autistics with little education.



starkid
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20 Jun 2017, 12:33 pm

I doubt that many people will know what zebra, camel, etc. mean. Those aren't widely known names for chess pieces.



byakuugan
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20 Jun 2017, 1:09 pm

That is why I want to make chess variants into mainstream sports, but many people tend to get bored with turn-based chess, so turning judochess (and variants) into mainstream sports would be more realistic, with something like a dance dance revolution pad instead of a mouse/touchpad/touchscreen, since most people prefer physical sports.
If there was a dance dance revolution judochess variant with camels, zebras, etc. then the next generation will have an extremely intuitive understanding of trigonometry and number theory.



starkid
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20 Jun 2017, 1:39 pm

byakuugan wrote:
If there was a dance dance revolution judochess variant with camels, zebras, etc. then the next generation will have an extremely intuitive understanding of trigonometry and number theory.

I'm sure that depends on individual learning style and would not help everyone; learning through metaphor or analogy isn't intuitive for some people. Actually, I'm not sure that an "intuitive" understanding of math is a good idea or even possible. I suppose it depends on what exactly you mean by "intuitive."



Chichikov
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20 Jun 2017, 2:22 pm

I get the concept, and I suppose it's interesting, but you're dealing with a small subset of people. I've been around chess for 30 years and I'll hold my hand up and admit I've never heard of any of the chess pieces you've mentioned, I had to google them. So within a minute of your video I was already confused because I don't have intuitive knowledge of what a "zebra" can do. I can look at a chess board and without thinking know what a knight can do but not a zebra, giraffe or yazoo. So your videos are already only appealing to people with good knowledge of that type of chess, for everyone else they're just instantly confused.

You probably know about numberphile, but if you don't have a look at their videos (YouTube) and see how they talk about and present maths problems to see if you can pick up any tips. I can follow most numberphile videos, but I couldn't follow any of yours. I might be outside your target audience though.



Dear_one
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20 Jun 2017, 8:14 pm

Feynman invented some of his own math as a boy, and later was celebrated for his eponymous diagrams. Newton is famous for inventing calculus during a school break, and Euler developed a formula that was first just a curiosity, but is now the key to calculating safe columns. My own math, used to pioneer in flexible structures, is a mashup adapted from several sources. It works, despite my overall mathematical ignorance.
If you wish to popularize anything, you will probably have to limit your vocabulary, and allow only one term that might need a definition per presentation. For most people, a mathematical formula is as slow to read as music being decoded and written as word instructions. I'd try to describe a relationship in general terms as an interesting story before showing how it works exactly.