Category Archives: Uncategorized

What is a chemlambda quine?

UPDATE 3: I made a landing page for my pages to play and learn.

UPDATE 2: And now there is Fractalize!

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).  If you find one, mail me the code (instructions on the page).


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.

A video tutorial about how to use the rest of new demos.

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 🙂

More quines and random eggs, if you want to go further in the subject of chemlambda quines.  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…

Plato, Orwell, Stalin & her exploratory cries

If you google

Plato Orwell Stalin “her exploratory cries”

this uniquely identifies an article I wrote back in in 2010, the year when I discovered  that I have to go in a new direction (for me).

[UPDATE: no longer true, Google  adapted  and now it points  to a number of my pages where there is none of the words searched…]

There are  two different ideas in that article:

  • the hypothesis that (Nature/ brains) use the same mechanism for (building/understanding) space. In today words: space (is/can be understood as)  a semantic (i.e. a decoration by local rules ) of a graph rewrite automaton. Nature runs the automaton probably by sampling from hamiltonian evolution (which does not compute) perturbed by dissipation (and the computer is in the information of the gap from hamiltonian evolution). Brains and more basically living cells run by chemistry, a toy model of the computation model is chemlambda. Those mechanisms are the same, the computer is in the information gap.
  • 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 🙂

Blockchain categoricitis 2, or life as an investor and a category theory fan

… or the unreasonable effectiveness of category theory in blockchain investments.

A year ago I wrote the post Blockchain categoricitis and now I see my prediction happening.

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.

Case in point: RChain. See Boom, bust and blockchain: RChain Cooperative’s cryptocurrency dreams dissolve into controversy.

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.


Guestpost at John Baez blog: RChain (archived)

“Programmers, venture 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. 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.”


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 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.”

and we see an animation from the post  “Correct-by-construction Casper | A Visualization for the Future of Blockchain Consensus“.


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]



Stats of perennial posts

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
  • 2011 (1), 2012 (4), 2013 (5), 2014 (2), 2015 (0), 2016 (1), 2017 (0), 2018 (3), 2019 (4)
  1. (2013) Graphic lambda calculus
  2. (2012) Conversion of lambda calculus terms into graphs
  3. (2011) The Cartesian Theater: philosophy of mind versus aerography
  4. (2012) Introduction to graphic lambda calculus
  5. (2019) Graphic lambda calculus and chemlambda (I)
  6. (2012) Right angles everywhere (I)
  7. (2014) Chemlambda
  8. (2019) Universality of interaction combinators and chemical reactions
  9. (2018) Diagrammatic execution models (Lambda World Cadiz 2018) compared with chemlambda
  10. (2012) Right angles everywhere (II), about the gnomon
  11. (2019) Graphic lambda calculus and chemlambda (II)
  12. (2014) The price of publishing with arXiv
  13. (2016) SciHub and patent wars
  14. (2013) Teaser: B-type neural networks in graphic lambda calculus (I)
  15. (2013) The Y combinator in graphic lambda calculus and in the chemical concrete machine
  16. (2019) Kaleidoscope
  17. (2013) A machine for computing the Ackermann function in graphic lambda calculus
  18. (2013) Dictionary from emergent algebra to graphic lambda calculus (II)
  19. (2018) I deleted Facebook, Twitter and entered the Invisible College
  20. (2018) Projects for 2019 and a challenge


  • 407 posts accessed, i.e. 62% of all posts up to 2018
  • 20% from same year, 15% of posts from same year in the top 20
  • 2011 (3), 2012 (3), 2013 (5), 2014 (3), 2015 (0), 2016 (1), 2017 (1), 2018 (4)
  1. (2013) Graphic lambda calculus
  2. (2012) Conversion of lambda calculus terms into graphs
  3. (2011) The Cartesian Theater: philosophy of mind versus aerography
  4. (2014) Chemlambda
  5. (2018) Diagrammatic execution models (Lambda World Cadiz 2018) compared with chemlambda
  6. (2011) Gromov’s Ergobrain
  7. (2013) Cartesian method, scientific method and counting problems
  8. (2013) A machine for computing the Ackermann function in graphic lambda calculus
  9. (2012) Right angles everywhere (II), about the gnomon
  10. (2012) Introduction to graphic lambda calculus
  11. (2014) The price of publishing with arXiv
  12. (2013) Teaser: B-type neural networks in graphic lambda calculus (I)
  13. (2014) Distributed GLC
  14. (2018) John Baez’ Applied Category Theory 2019 post uses my animation without attribution [updated]
  15. (2018) What about arXiv/figshare/zenodo and the EU copyright reform?
  16. (2011) How not to get bored, by reading Gromov and Tao
  17. (2017) Chemical Sneakernet
  18. (2018) I deleted Facebook, Twitter and entered the Invisible College
  19. (2016) Open peer review is something others should do, Open science is something you could do
  20. (2013) Example: decorations of S,K,I combinators in simply typed graphic lambda calculus


  • 454 posts accessed, i.e.  73% of all posts up to 2017
  • 20% from same year, 23% of posts from same year in the top 20
  • 2011 (3), 2012 (3), 2013 (5), 2014 (5), 2015 (0), 2016 (0), 2017 (4)
  1. (2013) Graphic lambda calculus
  2. (2017) The price of publishing with GitHub, Figshare, G+, etc
  3. (2011) The Cartesian Theater: philosophy of mind versus aerography
  4. (2012) Conversion of lambda calculus terms into graphs
  5. (2014) Chemlambda
  6. (2014) Distributed GLC
  7. (2013) Cartesian method, scientific method and counting problems
  8. (2017) Chemlambda for the people (with context)
  9. (2014) The price of publishing with arXiv
  10. (2012) Introduction to graphic lambda calculus
  11. (2012) Right angles everywhere (II), about the gnomon
  12. (2011) Gromov’s Ergobrain
  13. (2014) How to use chemlambda for understanding DNA manipulations
  14. (2013) A machine for computing the Ackermann function in graphic lambda calculus
  15. (2013) Unlimited detail is a sorting algorithm
  16. (2011) How not to get bored, by reading Gromov and Tao
  17. (2013) Hewitt Actor Model, lambda calculus and graphic lambda calculus
  18. (2014) Zipper logic
  19. (2017) More experiments with Open Science
  20. (2017) Back to the drawing board: all strings

Category theory is not a theory, here’s why: [updated]

Category theory does not make predictions.

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


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.


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.