Wildberger, hypergroups, groups and computer programs

[Andrius Kulikauskas]

Hi Kirby, Joe and all,

I recall discussion of group theory and trying to make sense of it in
terms of computer program instructions.

I started reading a related article by Norman Wildberger, "Finite group
theory for a (future) computer"
http://web.maths.unsw.edu.au/~norman/papers/FiniteGroupTheoryComputer.pdf

He is boldly pursuing novel positions in foundations of mathematics,
geometry, trigonometry.
http://web.maths.unsw.edu.au/~norman/index.html

And his videos are watchable and informative:
http://web.maths.unsw.edu.au/~norman/YouTube.htm

I wrote to him today because I'm curious if my work on "implicit math"
(based on how we figure things out in our minds) may be relevant, and
also because I'm looking for insights into the different kinds of
geometry. He has a video series on Universal Hyperbolic Geometry.

As an aside, I realized yesterday that exponentiation is a nice example
of nonassociativity. For example:
1,000,000 = (10^2)^3 whereas 10^(2^3) = 1,000,000,000

Mike, Michel, thank you for your great letters about your questions! I
look forward to responding.

Andrius

Andrius Kulikauskas
m...@ms.lt
+370 607 27 665

[kirby urner]

On Mon, Jul 18, 2016 at 7:50 AM, Andrius Kulikauskas <m...@ms.lt> wrote:

 

And his videos are watchable and informative:
http://web.maths.unsw.edu.au/~norman/YouTube.htm

Thanks Andrius.

I've been checking the videos.

Regarding WildTrig2, I'd be interested in further exploring this interpretation of the Pythagorean Theorem:

https://youtu.be/3GU9mGyxz04

http://www.grunch.net/synergetics/quadray/pythag2.gif

We have too few proofs in this form.

More context, going back to the 1990s:

 

I wrote to him today because I'm curious if my work on "implicit math" (based on how we figure things out in our minds) may be relevant, and also because I'm looking for insights into the different kinds of geometry.  He has a video series on Universal Hyperbolic Geometry.

As an aside, I realized yesterday that exponentiation is a nice example of nonassociativity.  For example:
1,000,000  =  (10^2)^3 whereas 10^(2^3) = 1,000,000,000

Mike, Michel, thank you for your great letters about your questions! I look forward to responding.

Andrius

Andrius Kulikauskas
m...@ms.lt
+370 607 27 665

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[kirby urner]

More context, going back to the 1990s:

http://www.grunch.net/synergetics/quadarea.html