the second idea is that as concerns brains, biological vision definitely is the creation of a geometry engine, as Koenderink write, but more specifically because there should be some universal form of computation which comes from the (formalization of) exploration of space via multiple drafts or maps. There’s where emergent algebras come into play, but this part is not yet completely clear, because until now I am not sure in all details that I succeded to prove that emergent algebras are universal, either in sense of Turing or Lafont.

That and the collapsing of the wave function is an orwellian theory and the minimal action principle is stalinesque, if we apply to physics the classification of Dennett of theories of biological vision.

Somewhere in the text you’ll find as well “her exploratory cries”. And a mutant army of bats 🙂

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, venturecapitalists, blockchain enthusiasts, experts in software, finance, and mathematics: myriad perspectives from around the globe came to join in the dawn of a new internet. Let’s just say, it’s a lot to take in. This project is the real deal – the idea is revolutionary […]”

RChain is light years ahead of the industry. Why? It is upholding the principle of correct by construction with the depth and rigor of mathematics.”

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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 types—and this equivalence relation completely washed out the difference, between, say, a program that actually computes 237 × 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 story (example) (another example), basically around distributed GLC . Between 2013-2015, instead of writing programs the fans of GLC practically killed the distributed GLC project 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. [/hype]

How perennial is this blog? I took the top 20 directly accessed posts in each year, for 2017, 2018 and 2019 up to Feb 10.

Conclusion:from the 665 posts from this blog (666 with this one)

in each year only 20% of the top 20 posts are from the same year. So this blog is not read as a news source, it ages well.

73% of all posts available ever were accessed directly in 2017, 62% in 2018 and already 20% in the first month and 1/2 of 2019. Because 2019 just started, it follows that at least 60% of all posts since 2011 are read every year.

Also, 2015 and 2016 are not well represented in top 20, probably because of the chemlambda collection. Sad, because there are many other things here than chemlambda, for example posts about OA and OS.

Here is the data. Mind that the data probably represents only post read by people who don’t use blockers, as seen via the stats page of the blog. Helas, I would like to know what is the real situation, while in the same time I advice everybody to use blockers, as I do. As an author, I do need a bit a love though, indulge me.

2019 (up to Feb 10):

134 posts accessed, i.e. 20% of all posts up to 2019

20% from same year, 30% of posts from same year in the top 20

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 something 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. 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 🙂 Category theory seems modular enough for them. A tool for abstraction, too, something they are trained in. And — why don’t you recognize? — with that eternal polish of mathematics, but without the effort.

This is exploited cynically by good public communicators with a creativity problem. 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. 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. As you know my banner is “can do anything”. 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.