[Algebra and NKS] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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Algebra and NKS
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Posted by: nonono
Can we apply nks to beta algebra? This question engraved in my head after I have read Beta Algebra by Algirdas Javtokas. The author investigates algebraic structure with infinitely many identity elements (!) (he calls it – beta group). The idea looks pretty simple and somehow it catches attention. Why? I don’t know, maybe because of craziness of the thought or charm of unexpectedness. What do you think about that?
You can find this book here:
http://www.amazon.com/gp/product/14...5Fencoding=UTF8
Posted by: Todd Rowland
It is nice to see original ideas in algebra at such a basic level.
There might be some connections with NKS, though admittedly I don't know much about beta algebra, beyond what is in the online article.
One way is to give representations to the beta algebras. For an analogy, one can represent the dihedral group by the symmetries of the polygon, giving the abstract group some concrete reason for its existence.
It could be possible to define a binary cellular automaton operator, which would represent certain beta algebras. It also could be possible that some of the simple NKS rules can be thought of as representations.
As noted in NKS, there are actually many undiscovered mathematics.
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