Chorasimilarity
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Gradually when I put stuff on telegra.ph, I'll share it here. Subjects are #molecular #computing #lambdacalculus #ai #alife #openscience #openaccess #vision #mathematics #philosophy
I just want to bring to your attention where pure see is going, if you were intrigued by the Substitution is objective (lI) post.
In case you wonder why "substitution is objective" this is in the sense used for "objective" in my posts.
But as concerns pure see I said that it is a formalism interesting enough, like linear logic, however it is just a shadow of a larger, noncommutative one.
It is then natural to structure it in such a way that it holds as much as possible in the general case.
So where is it going? It has emergent algebra as a model, but there are two other different models. The "commutativity" name comes from an emergent algebra characterization in the presence of the algebraic version of SHUFFLE, the only rewrite schema of pure see.
In the more general case all fits into a map making formalism, which has algebraic and topological parts, with the topological part usually left aside until the whole range of the algebraic side is clear.
Or it turns out that the more profound mathematically is to start from the topological side, which will make clear why the algebraic side is like it is.
And so new algebraic structure appears, like the dual side of map making hinted in the linked chorasimilarity post.
On a personal note the complete math was done on paper while I was more than worried about the bout of Bell's palsy which hit me in jan. So is good to stay more on paper, I was so happy that it worked that I had to make the sibylline https://chorasimilarity.wordpress.com/2021/02/12/maps-are-intrinsic-charts-are-model-theoretic/
Almost half a year ago I asked about an example of an unknown structure described here https://mbuliga.github.io/colin/colin.pdf and today I got an answer involving artificial intelligence in the text https://mathoverflow.net/q/391530 Is the kind of answer I really have to think about. Update: is not clear though if the example given responds to the question. Update 2: I proved that there are no such examples for emergent algebras, see https://chorasimilarity.wordpress.com/2021/06/02/colin-implies-lin/ That is surprising and unexpected.