UPDATE: The most recent addition to the material mentioned in the post is Find a Quine, which let you generate random 10 nodes graphs (there are 9 billion of them) and to search for new quines. They are rare, but today I found 3 (two all of them are shown as examples).Â If you find one, mail me the code (instructions on the page).

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The ease of use of the recently written chemlambda.js makes easier the sharing of past ideas (from the chemlambda collection) and as well of new ideas.

Here is some material and some new thoughts. Before this, just recall that the *new* work is in hapax. See what chemlambda has to do with hapax, especially towards the end.

The story of the first chemlambda quine, deduced from the predecessor of a Church number. Especially funny is that this time you are not watching an animation, it happens in front of you đź™‚

More quines and random eggs, if you want to go further in the subject of chemlambda quines.Â The eggs are 4-nodes graphs (there are 720 of them). They manifest an amazing variety of behaviour. I think that the most interesting is that there are quines and there are also graphs which have a reversible evolution, without being quines. Indeed, in chemlambda a quine is one which has a periodic evolution (thus is reversible) under the greedy algorithm of rewrites. But there is also the reversible, but not quine case, where you can reverse the evolution of a graph by picking a sequence of rewrites.

Finally, if you want to look also at famous animations, you have the feed the quine. This contains some quines but also some other graphs which featured in the chemlambda collection.

Most of all, come back to see more, because I’m going to update and update…

Categoricitis is the name of a disease which infects the predisposed fans of category theory, those which are not armed with powerfull mathematical antibodies. Show them some diagrams from the height of your academic tower, tell them you have answers for real problems and they will believe.

Yes, just another cryptocurrency story… Wait a moment, this one is different, because it is backed by strong mathematical authority! You’ll practically see all the actors from the GeekWire story mentioned in the posts linked further.

“Programmers, ventureÂ capitalists, blockchain enthusiasts, experts in software, finance, and mathematics: myriad perspectives from around the globe came to join in the dawn of a new internet. Letâ€™s just say, itâ€™s a lot to take in. This project is the real dealÂ â€“ the idea is revolutionary […]”

RChain is light years ahead of the industry. Why? It is upholding the principle of correct by constructionÂ with the depth and rigor of mathematics.â€ť

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Another one, in the same place: Pyrofex (archived). This is not a bombastic guestpost, it’s authored by Baez.

“Mike Stay is applying category theory to computation at a new startup called Pyrofex. And this startup has now entered a deal with RChain.”

Incidentally (but which fan reads everything?) in the same post Baez is candid about computation and category theory.

“When I first started, I thought the basic story would be obvious: people must be making up categories where the morphisms describe processes of computation.

But I soon learned I was wrong: […] the morphisms were equivalence classes of things going between data typesâ€”and this equivalence relation completely washed out the difference, between, say, a program that actually computes 237 Ă— 419 and a program that just prints out 99303, which happens to be the answer to that problem.

In other words, the actual process of computation was not visible in the category-theoretic framework.” [boldfaced by me]

(then he goes on to say that 2-categories are needed in fact, etc.)

In Applied Category Theory at NIST (archived) we read:

“The workshop aims to bring together two distinct groups. First, category theorists interested in pursuing applications outside of the usual mathematical fields. Second, domain experts and research managers from industry, government, science and engineering who have in mind potential domain applications for categorical methods.”

I never trusted these ideas. I had interactions with some of the actors in this storyÂ Â (example) (another example), basically around distributed GLC . Between 2013-2015, instead of writing programs the fans of GLCÂ practically killed the distributed Â GLC projectÂ because it was all the time presented in misleading terms of agents and processes, despite my dislike. Which made me write chemlambda, so eventually that was good.

[hype] GLC and chemlambda are sort of ideal Lisp machines which you can cut in half and they still work. But you have to renounce at semantics for that, which makes this description very different from the actual Lisp machines.Â [/hype]

This is a black and white formulation, so there certainly are exceptions. Feel free to contradict.

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UPDATE: As I’m watching Gromov on probability, symmetry, linearity, the first part:

I can’t stop noticing several things:

he repeatedly say “we don’t compute”, “we don’t make computations”

he rightly say that the classical mathematical notation hides the real thing behind, like for example by using numbers, sets, enumerations (of states for ex.)

and he clearly thinks that category theory is a more evolved language than the classical.

Yes, my opinion is that indeed the category theory language is more evolved than classical. But there is an even more evolved stage: computation theory made geometrical (or more symmetric, without the need for states, enumerations, etc).

Category theory is some kind of trap for those mathematicians who want to say somethingÂ is computable or something is, or should be an algorithm, but they don’t know how to say it correctly. Corectly means without the burden of external, unnatural bagagge, like enumeration, naming, evaluations, etc. So they resort to category theory language, because it allows them to abstract over sets, enumerations, etc.

There is no, yet, a fully geometrical version of computation theory.

What Gromov wants is to express himself in that ideal computation theory, but instead he only has category theory language to use.

Gromov computes and then he says this is not a computation.

Grothendieck, when he soaks the nut in the water, he lets the water compute. He just build a computer and let it run.Â He reports the results, that’s what classical mathematical language permits.

That’s the problem with category theory, it does not compute, properly, just reports the results of it.

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As concerns the real way humans use category theory…

Mathematicians use category theory as a tool, or as a notation, or as a thought discipline, or as an explanation style. Definitely useful for the informed researcher! Or a life purpose for a few minds.

All hype for the fans of mathematics, computer science or other sciences. To them, category theory gives the false impression of understanding. Deep inside, the fan of science (who does not want/have time/understands anything of the subject) feels that all creative insights are based on a small repertoire of simple (apparently) tricks. Something that the fan can do, something which looks science-y, without the effort.

Then, there are the programmers, wonderful clever people who practice a new science and long for recognition from the classics đź™‚ Category theory seems modular enough for them. A tool for abstraction, too, something they are trained in.Â And — why don’t you recognize? — with that eternal polish of mathematics, but without the effort.

This is exploited cynically by goodÂ public communicators with a creativity problem.Â The recipe is: explain. Take an older, difficult creation, wash it with category theory and present it as new.

Unexpectedly and somehow contrary to my fresh posting about my plans for 2019, during the week of Jan 7-12, 2019 a new project appeared, which is temporary named Kaleidoscope. [Other names, until now: kaleidos, morphoo. Other suggestions?]

This post marks the appearance of the project in my log. I lost some time for a temporary graphical label of it:

I have the opinion that new, very promising projects need a name and a label, as much as an action movie superhero needs a punchline and a mask.

So what is the kaleidoscope? It is as much about mechanical computers (or physically embedded computation) as it is about graph rewrite systems and about space in the sense of emergent algebras and about probabilities. It is a physics theory, a computation model and a geometry in the same time.

What can I wish more, research wise?

Yes, so it deserves to be tried and verified in all details and this takes some time. I do hope that it will survive to my bugs hunt so that I can show it and submit it to your validation efforts.

Now, here is a list of projects which are almost done on paper and which deserve attention or reserve some surprises for 2019. Then a challenge for you, dear creative reader.

I mentioned Hydrogen previously. This is a project to build a realistic hydrogen atom purely in software. This means that I need a theory (a lambda calculus like) for state spaces, then for quantum mechanics and finally for a hydrogen atom.

Space is of special interest (and needed to build hydrogen), a lambda calculus for space is proposed in the em project. Now I am particularly fascinated by numbers.

The needs project is a bridge towards chemlambda.Â It’s entirely written, in pieces, it is about permutation automata. Only the main routine is public.

And what would life be without luck, aka computable probabilities? This is the least advanced project, for the moment it covers some parts of classical mechanics, but it is largely feasible and a pleasure to play with it in the year to come.

I have a strong feeling that these projects look very weird to you, so I have a proposal and a challenge. The proposal for you is to ask for details. I am willing to give as much as (or perhaps more than) you need.

The challenge is the following.Â As you know my banner is “can do anything”.Â So let’s test it:

propose a subject of research where you are stuck. Or better, you want to change the world (in a good way).

I’ll do something about it as quick as possible, if you get me interested.