# Summer report 2018, part 1

In this report I intend to present explanations about the scientific evolution of the chemlambda project, more about the social context and about new projects (em and stochastic evolution). I shall also write about my motivations and future intentions.

On the evolution of the chemlambda project and social context.

Inception and initial motivations. This open notebook contains many posts wittnessing the inception of chemlambda. I started to learn about and understand some aspects of the theory of computation as a geometer. My goal was to understand the computational contents of working with the formalism of emergent algebras. I thought that basically any differential geometric computation reduces to a graph rewrite automaton, without passing through the usual road which is non-geometrical, i.e. reduction to cartesian numerical manipulations. The interest is obvious to me, although I discovered soon that it is not obvious to many. A preferred analogy which I used was the one concerning the fly and the researcher who tries to understand the visual system of the fly. The fly’s brain, a marvel of nature, does not work with, nor it contains a priori knowledge of cartesian geometry, while in the same time the explanations of the researcher are almost completely based on cartesian geometry considerations. Which is then the way of the fly’s brain? And why can it be explained by recourse to sophisticated (for a fly) abstractions?

That’s why I advanced the idea that there is an embedded mechanism in nature which makes abstractions concrete and runs them by the dumbest algorithm ever: random and local. In this sense, if all differential geometric computations can be executed by a graph rewrite automaton, by using only random rewrites, applied only locally (i.e. by using only a small number of nodes and arrows), then the fly’s brain way and the researcher brain way are simply the same, only the semantics (the researcher has) is different, being only a historical building based on centuries of inverse engineering techniques called geometry, physics, mathematics.

The emergent algebras formalism has actually two parts, the first which can be easily reduced to graph rewrites, the second one which concerns passing to the limit in a precise sense and therefore obtaining new, “emergent” rewrites and equivalences of rewrites. At that initial point I had nothing, not the pure graph rewrites formalism, nor the passing to the limit formalism, except some particular results (in metric geometry and intriguingly in some problems related to approximate groups, then a hot work of Tao and collaborators).

That is how GLC (graphic lambda calculus) appeared. It was, in retrospect, a particular formulation analoguous with interaction graphs, with the new ideas that it is applicable to geometry, via the fact that the emergent algebra rewrites are of the same kind as the interaction graphs rewrites. Interaction graphs are an old subject in CS, only that my point of view was completely different than the classical one. Where the functional programming wizards were interested in semantics, global, concepts and the power of humanly designed abstractions, I was interested into the minimal, machine (or fly’s brain) like, random and automatic aspects.

Because the approximate groups were a hot subject then, I embedded a little part of what I was thinking about into a grant collaboration financed locally. Recall that I was always an Open Science researcher, therefore I concentrated on openly (i.e. back then via arXiv) constructing the fundamentals from where particular applications on approximate groups would have been low hanging fruits. However, for what I believe are political reasons (I publicly expressed as usual my strong feelings against academic and political corruption, which debase me as a citizen of my country which I always loved very much), my grant funding was cancelled even if I did a lot of relevant work, by far the most publicly visible and original. Oh well, that’s life, I was never interested much in these political aspects.I learned the hard way a truth: my country has a great pool of talents which make me proud, but in the same time talent is here choked by a group of mediocre and opportunistic managers. They thrive not because their scientific talent, which is not inexistent, but only modest, they thrive because their political choices. This state of affairs created an inverted pyramid of power (as seen from the talent point of view).

I filed therefore  in my notebooks the problem of understanding how a linear dilation structure emerges  from an approximate group.  There was nothing to stop me to go full OS.

I wrote therefore the Chemical concrete machine paper because I meaned it: there should be a way to make a machine, the dumbest of all, which works like Nature. This was  an advance over GLC, because it had almost all rewrites local (excepting global fan-out) and because it advanced the idea of the dumbest algorithm and that the dumbest algorithm is the way the Nature works.

Moreover the interest in GLC soared and I had the ocasion to talk a lot with Louis Kauffman, a wonderful researcher which I always admired, the king of knot theory. There were also lots of CS guys interested into GLC and they tried to convince me that maybe GLC has the key to true decentralized computing. A project with some of them and with Louis (contained in this arXiv paper) was submitted to an american agency. Unfortunately, even if the theoretical basis was appreciated, the IT part was not well done, actually is was almost inexistent. My problem was that the ideas I advanced were not (even by Louis sometimes) accepted, I needed somebody (I am a mathematician, not a programmer, see?) to write some pretty simple programs and let them work to see if I’m right and semantics is just human BS or not.

For an an artificial life conference I wrote with Louis another presentation of chemlambda, after the GLC project was not accepted for US funding. The formalism was still not purely local. There, Louis presented his older and very interesting points of view about computation and knot theory. These were actually different than mine, because for me knot theory is yet another graph rewriting automaton (without a defined algorithm for functioning). Moreover, recall emergent algebras, I have not made Louis to be interested in my point of view that the Rademacher 3 move is emergent, not fundamental.

Louis Kauffman is the first programmer of chemlambda. Indeed, he succeded to make some reductions in chemlambda using Mathematica. I don’t have Mathematica, as I never use on my computers anything which is not open. I longed for somebody, a real programmer, to make those darned simple programs for chemlambda.

I was interested back then into understanding chemlambda quines and complex reductions. On paper that was very very hard to progress.

Also, I have not succeded to gather interest for the emergent algebras aspect. Chemlambda simplified the emergent algebra side by choosing a minimal set of nodes, some of them which had an emergent algebra interpretation, but nobody cared. It is hard though to find anybody familiar with modern metric geometry and analysis and also familiar with interaction nets.

After some depressing months I wrote the programs in two weeks and got the first chemlambda reduction made with a combination of awk programs and d3.js.  The final repository is here.

The version of chemlambda (call it v2) used is explained in the article Molecular computers. It is purely local.

From there my choice was to make chemlambda a flagship of Open Science. You know much of the story but you may not know how and why I built more that 400 chemlambda molecules. The truth is that behind the pretty animations, almost each molecule deserves a separate article, or otherwise stated, when you look at a chemlambda molecule in action you see a visual version of a mathematical proof.

The chemlambda formalism has been externally validated, first by chemlambda-py (which has though a rewrite wrongly implemented, but otherwise is OK) then by chemlambda-hask which is much more ambitious, being a platform for a haskell version.

As for the connection with knot theory you have the Zipper Logic article (though it is like chemlambda v1 not a purely local agorithm, but it can be easily made so by the same techniques as chemlambda v2).

I also used figshare for the chemlambda collection of simulations (which covers the animations shown in the chemlambda collection on G+, see them starting from an independent list).

As concerns the social communication aspects of this OS project, it was a huge success.