Some updates, for things to come and plans.

1. Pure See is a relative of lambda calculus, in the sense that it is Turing universal, is very simple, but it does not use abstraction, application, let as primitives. It is a programming language built overÂ commutative emergent algebras, i.e. those with the shuffle trick, or equivalently with the algebraic properties of em-convex (but mind that em-convex still uses lambda and application operations; these are not needed).

I plan to make a parser for Pure See very soon.

2. This means that Pure See is as commutative as lambda calculus. Or, the general theory that I have in mind is non-commutative. And emergent, in the sense of emergent algebras.

Before going full non-commutative, one has to realize the beta rewrite as emergent. This is true, in the same way as associativity is emergent in the equational theory of emergent algebras, or the way to realize Reidemeister 3 rewrite from R1 and R2 (and a passage to the limit). The fact that beta is emergent is what makes Pure See to work and answers to the question: do emergent algebras compute? Yes, they do, because in the most uninteresting situation, the commutative one, we can implement lambda calculus with commutative emergent algebras.

3. The first non-coomutative case is the Heisemberg group, described as a non-commutative emergent algebra. I have since a long time the description. The shuffle trick becomes something else. Means that beta rewrite and DIST rewrites change into something more interesting. The whol eformalism actually becomes something else.

I thought that the general non-commutative case is in principle far more complex than the Heisenberg case. It was also unsatisfying that I had no explanation for the reason why Heisenberg groups appear in physics. What’s special about them?

Now I know, they are logically unavoidable (again in the frame of emergent algebras).

So I still play with this new point of view and I wonder what to do next.

The wise thing would be to carefully explain, in a legacy way, all this body of work. My initial plan was to base this explanations on a backbone of openly communicated programs and demos, so that the article versions would be a skin of the whole description. Who wants to read betdime stories has the article. Who wants more has the programs. Who wants all thinks about all this.

With the DDOS or whatever is it,Â it becomes harder to use independent ways of sharing.

Or should I jump directly to the non-commutative case?

Or somebody really started to make molecular computers?Â If so,Â it would be, short time span, the most interesting thing.

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