Torsor rewrites

With the notation conventions from em-convex, there are 3 pairs of torsor rewrites.  A torsor, figured by a fat circle here, is a term T of type  T: E \rightarrow E \rightarrow E \rightarrow E

with the rewrites:

t1

and

t2

Finally, there is a third pair of rewrites which involve terms of the form \circ A for A: N

t3

The rewrite T3-1 tells that the torsor is a propagator for \circ A, the rewrite T3-2 is an apparently weird form of a DIST rewrite.

Now, the following happen:

  • if you add the torsor rewrites to em-convex then you get a theory of topological groups which have a usual, commutative smooth structure, such that the numbers from em-convex give the structure of 1-parameter groups
  • if you add the torsor rewrites to em, but without the convex rewrite then you get a more general theory, which is not based on 1-parameter groups,  because the numbers from em-convex give a structure more general
  • if you look at the emergent structure from em without convex, then you can define torsor terms whch satisfy the axioms, but of course there is no em-convex axiom.

Lots of fun, this will be explained in em-torsor soon.

 

 

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Authors: hodl your copyright or be filtered

For me this is the only sane reaction to the EU Copyright Directive. The only thing to do is to keep your copyright. Never give it to another. You can give non-exclusive rights of dissemination, but not the copyright of your work.

So: if you care about your piece of work then hodl copyright, if you don’t care about it (produced it to satisfy a job demand, for example) then proceed as usual, is trash anyway.

For my previous comments see this and this.

If you have other ideas then share them.

 

The second Statebox Summit – Category Theory Camp uses my animation

with attribution.

UPDATE: the post was initially written as a reaction to the fact that the Open Science project chemlambda needs attribution when some product related to it is used (in this case an animation obtained from a dodecahedron molecule which produces 4 copies; it works because it is a Petersen graph). As it can be seen in the comments everything was fixed with great speed, thank you Jelle. Here’s the new page look

Screenshot from 2018-09-09 15:18:06.png

Wishing the best to the participants, I’d like to learn more about Holochain in particular.

The rest of the post follows. It may be nice because it made me think about two unrelated little facts: (1) I was noticed before about the resemblance between chemlambda molecules and the “vajra chains” (2) well, I CHING hexagrams structure and rewrites are close to the two families of chemlambda rewrites, especially as seen in the “genes” shadow of a molecule. So putting these two things together, stimulated to find an even more halucinatory application of chemlambda, I arrived to algorithmic divination. Interested? Write to me!

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I hope they’ll fix this, the animation is taken probably from the slides I prepared for TED Chemlambda for the people (html+js).

Here’s a gif I made from what I see today Saturday 20:20 Bucharest time.

test_s

Otherwise I’m interested in the subject and open to discussions, if any which is not category theory PR, but of substance.

UPDATE: second thoughts

  • the halucinatory power of chemlambda manifests again 🙂
  • my face is good enough for a TED conference (source), now my animation is good for a CT conference, but not my charming personality and ideas
  • here is a very lucrative idea, contact me if you like it,  chemlambda OS research could be financed from that: I was notified about the resemblance between chemlambda molecules and the vajra chains of awareness, therefore what about making an app which would use chemlambda as a divination tool? Better than a horoscope, if well made, huge market. I can design some molecules and the algorithm for divination.