Better than extended beta move

Instead of the extended graphic beta move (proposed here and declared still in beta version in the graphic lambda calculus tutorial) is to couple the Reidemeister 2  move R2 with the graphic beta move. Here is how it can be done.

Let us define, for any scale parameter \varepsilon \in \Gamma, the following versions of the application gate and abstraction gate:


Remark that when \varepsilon =1 we can recover the usual application gate


and the usual abstraction gate


The graphic beta move and the move R2 can be coupled into the following nice move:



This will be used for making clear where the space is encoded in graphic lambda calculus and how.  Of course, it has to do with emergent algebras, seen in graphic lambda calculus. If you want to get ahead of explanations and figure out by yourself then the following posts will help:


(in case you see adds here: they have nothing to do with me or with this blog)

Journal of uncalled advices

All the steps of the editorial process used by legacy publishers are obsolete. To see this, is enough to ask “why?”.

  1. The author sends the article to the publisher (i.e. “submits” it). Why? Because in the old days the circulation and availability of research articles was done almost exclusively by the intermediary of the publishers. The author had to “submit” (to) the publisher in order for the article to enter through the processing pipe.
  2. The editor of the journal seeks reviewers based on ___________ [please add your suggestions], which amounts to hunches, friends advice, basically thin air. Why? Because, in the days when we could pretend we can’t search for every relevant bit of information, there was no other way to feed our curiosity but from the publishing pipe.
  3. There are 2 reviewers who make reports. (With the author, that makes 3 readers of the article, statistically more than 50% of the readers the article will have,  once published.) Why? Because the pyramidal way of organization was, before the net era, the most adapted. The editor on top, delegates the work to reviewers, who call back the editor to inform him first, and not the author, about their opinion. The author worked, let’s say, for a year and the statistically insignificant number of 2 other people make an opinion on that work in … hours? days? maybe a week of real work? No wonder then that what exits through the publishing pipe is biased towards immediate applications, conformity of ideas and the glorified version of school homeworks.
  4. The editor, based solely on the opinion of 2 reviewers, decides what to do with the article. He informs the author, in a non-conversational way, about the decision. Why? Because again of the pyramidal organization way of thinking. The editor on top, the author at the bottom. In the old days, this was justified by the fact that the editor had something to give to the author, in exchange of his article: dissemination by the means of industrialized press.
  5. The article is published, i.e. a finite number of physical copies are typed and sent to libraries and particulars, in exchange for money. Why? Nothing more to discuss here, because this is the step the most subjected to critics by the OA movement.
  6. The reader chooses which of the published articles to read based on authority arguments. Why? Because there was no way to search, firsthand, for what the reader needs, i.e. research items of interest in a specific domain. There are two effects of this. (a) The raise of importance of the journal over the one of the article. (b) The transformation of research communication into vanity chasing.  Both effects were (again, statistically) enforced by poor science policy and by the private interests of those favoured by the system, not willing to  rock the boat which served them so well.

Given that the entire system is obsolete, what to do? It is, frankly, not our business, as researchers, to worry about the fate of legacy publishers, more than about, say, umbrella repairs specialists.

But, what to do, in these times of transition?  It is in my power to laugh a bit, at least, and maybe to make others, with real decision power, to think.

That is why I propose a Journal of Uncalled Advices, which would work as the spnetwork, only driven by publishers, as a journal.

  1. The editor searches in the arxiv, or elsewhere, article he likes, or he consider important.
  2. Makes a public call for reviews of the selected articles. He manages the place of the discussion.
  3. At some point a number of technical reports appear (the uncalled advices), collaboratively.
  4. The editor uses again his nose to separate opinion from technical reports and produces (writes) two final (for the journal)  articles about the research article. The opinion part could as well serve as vulgarization of the research article, the technical part could serve to the specialists and to the author.
  5. The two articles are sold by piece, for 6 months and then they are made public.
  6. The reader uses the journal articles as evidence and makes his own mind about the research article.


UPDATE:  The following older posts are relevant



My post ended here, in case there is something added after the end of the post, it’s an example of uncalled adds.

New tutorials, spread!

Have you noticed?  There are now, available on this open notebook, two tutorials:

After some tinkering, I arrived at the following logo for graphic lambda calculus and derivative works (like the chemical concrete machine):


We see here a double helix, which is in fact formed by a lambda and another lambda upside down, which could also be a Y.

You would do me a favour to spread the word about these tutorials, or better, to use them.  I put a link to the graphic lambda calculus tutorial on reddit, and a g+ post about the chemical concrete machine tutorial here.  There’s also a tweet about it:

I am looking for a place where I can put a part of the contents of this blog (which is rather big), namely the various series of connected posts, which contain a lot of work and time invested. I am thinking about github, but I am not so sure.  The thing with the blog format, besides it is still not loved by  those who made their career by ISI bean counting,  is that it is too linear. This can be repaired by links, however.

Where does the chemical concrete machine naturally sits

The more I learn about biological computing, like, in a random order, about:

the more it seems that the chemical concrete machine fits naturally into this. Yes, it is partly a garage lab version of this thread of research, but on the other side it has certain advantages, mainly the following one. It is a “pure” graph rewriting system, freed from any 1D thinking conventions. It is true that in order to compute with it on a silicon computer one needs to rewrite it by adding lots of things on top (for example bigraphs may be a way to formalize a model of computation with graphs, in silico, where we need to manage reaction sites, labels of input and output arrows), not because they are natural, but because of the need to make a humanly comprehensive discourse about that (which brings all the effects of the cartesian disease, see the conclusion of this post) .

Soon, after the start of the academic year, an article will be available on arxiv (and submitted to publication, although I am more and more skeptical about this way of research communication, starting with the ’90s) . There are so many directions of development for the chemical concrete machine, also in parallel with graphic lambda calculus, and also with the initial path, computing with space (i.e. the computational content of emergent algebras).

I don’t feel anymore that what I write here is too abstract for the “applied” researchers in biological computing. No, it turns out some of you have already seen this kind of stuff. The only question is: “does the chemical concrete machine brings anything new”?  I think it does, because, as nature, is geometrical and not discourse based.

In conclusion, I look forward for collaborations, academic or not. As you might have noticed, I spend a lot of time with this open notebook/blog for trying to stir open, free share of ideas in fundamental research, which might be also very concretely relevant for the real world. Needless to say I shall benefit from such collaborations, but the converse is also true, if you excuse my self-promotional impulse (again, I heard that the net is not subtle, which I doubt, but let’s suppose so). The idea is that if I can do it alone, then imagine what could we do together.

UPDATE: What do you think about this logo for the chemical concrete machine?


Types and places

Simply typed graphic lambda calculus    is an added layer of decorations with types  over graphic lambda calculus, described by the following rules:


See  Example: decorations of S,K,I combinators in simply typed graphic lambda calculus   for the compatibility with simply typed lambda calculus.

Compared with the purity of graphic lambda calculus,  types (at least of this kind) seem a step back. However, graphic lambda calculus has also the emergent algebra sector, see  arXiv:1305.5786 [cs.LO] section 5, and also here the series

The starting point of the research subject on “computing with space” is to try to understand the computational content of emergent algebras arXiv:0907.1520 [math.RA]. This has lead to graphic lambda calculus, passing by decorated binary trees and decorated tangle diagrams, until the non-decorated formalism of graphic lambda calculus. This formalism is not yet completely finished; indeed, the extended graphic beta move,  arXiv:1302.0778 [math.GT], especially section 8,   which mixes the emergent algebra part with the purely logic part, is still in beta stage.

Therefore, I’m coming back to the decorated version and remark that, as concerns the two gates which appear in the emergent algebra sector, they can be decorated with places:


Places form an emergent algebra. Types form a free magma (for well decorated graphs).