Tag Archives: computing with space

Space is that which is well typed

I’m about to reconsider my previous impression about types as only decorations over the artificial chemistry.
TLDR; Space is that which is well typed.

However well typed should only have a local meaning, as usual in chemlambda.


Where’s the ship? (lots of questions part II)

I explain in Lots of questions, part I how Plato and Brazil made me want to switch from math to biology.  Eventually it seems I ended in fundamentals of computing, but there is this strange phenomenon. I can’t figure it how it works, or why, or even if is widespread or rare. I think is widespread, but I don’t have clear evidence about it other than the old saying that people don’t change.

So Plato+Rio gives geometry+biology gives artificial chemistry+distributed computing.


I don’t get how this functions.

Makes no sense.

Now I have a hint that we are the computation,  we execute ourselves during our lifetime, our brains are just part of the seed, part of the program. We don’t really have billions of neurons and cells, everything is just the state of a computation.  Part of the seed is our genetic inheritance, other part of the seed is our geographical and more largely cultural inheritance. We are not separated from the external medium, there is no external medium, exactly like there is no me and the Net, only many actors interacting asynchonously and locally according to some protocols. In the case of real life the protocols are casted in   real molecules, at a finer scale only emerging phenomena of a much faster and wider computation going on, of a geometrical nature. But the principle is scale independent, that is how we manage space (perception and interaction) in our brains.

So we don’t change.

Take this blog, I make from time to time some counts. For the last 3 months gives this. There are 491 posts on chorasimilarity. In the last week 78 of them have been read, last month 219, last quarter 331. This series makes no sense unlese there are very long range relations between the posts, relations which are perceived by enough readers of this blog.

Oh, great!

Two mysteries. The first is that I have no idea why exactly there long time correlations arrive in my writing. The second mystery is why do you perceive them too.

So there is this strange phenomenon, which I can’t explain.

I remark though that there has to be something starts the new computation cycle, the new turn of spiral, the new chamber of the snail shell.

It is stimulation.

Last time was Plato and Rio.

I feel that I lack something in order to tell you more and for me to learn more in the absence of enough external stimuli.

I know I can build really new and also classical stuff, but I loose interest in time without stimuli. That is why I change every few years what I do. It is not rewarding for me to see that after I left a field somebody picks an idea and makes it stronger, it is not rewarding to see that I was right when nobody believed.  Maybe I just have a nose for good ideas which float in the air and I detect them before many others, but I don’t have the right spce and culture position to make them grow really big. You know, just an explorer who comes back home after a lonely expedition and tells you about blue seas and wide skies with strange constellations. Yeah, OK creep. But then, after some years the trend is to go to bath in those blue seas. And where is the creep? Just coming home, telling about that new jungle and the road from there to the clouds.

Stimulation. Trust. New worlds await. Need my ship, now.




Lots of questions, part I

There is a button for “publish”. So what?

I started this open notebook  with the goal to disseminate some of my work and ideas.  There are always many subjects to write about, this open notebook has almost 500 posts. Lately the rhythm of about a post every 3 days slowed down to a post a week.  I have not run out of ideas, or opinions. It is only that I don’t get anything in return.

I explain what I mean by getting something in return. I don’t believe that one should expect a compensation for the time and energy converted into a post. There are always a million posts to read.  There is not a lot of time to read them. It is costly in brain time to understand them, and probably, from the point of view of the reader, the result of this investment does not worth the effort.

So it’s completely unreasonable to think that my posts should have any treatment out of the usual.

Then, what can be the motivation to have an open notebook, instead of just a notebook? Besides vanity, there is not much.

But vanity was not my motivation, although it feels very good to have a site like this one. Here is why:   from the hits I can see that people read old posts as frequently as new posts. You have to agree that this is highly unusual for a blog. So, incidentally,  perhaps this is not a blog, doh.

I put vanity aside and I am now closer to the real motivations for maintaining this open notebook.

Say you have a new idea, product, anything which behaves like a happy virus who’s looking for hosts to multiply. This is pretty much the problem of any creator: to find hosts.  OK, what is available for a creator who is not a behemoth selling sugar solutions or other BRILLIANT really simple viruses like phones, political ideas, contents for lazy thinking trolls and stuff like this?

What if I don’t want to sell ideas, but instead I want to find those rare people with similar interests?

I don’t want to entertain anybody, instead that’s a small fishing net in the big sea.

OK, this was the initial idea. That compared to the regular ways, meaning writing academic articles, going to conferences, etc, there might be more chances to talk with interesting people if I go fishing in the high seas, so to say.

These are my expectations. That I might find interesting people to work with, based on common passions, and to avoid the big latency of the academic world, so that we can do really fast really good things now.

I know that it helps a lot to write simple. To dilute the message. To appeal to authority, popularity, etc.

But I expect that there is a small number of you guys who really think as fast as I do. And then reply to me, simultaneously to Marius.Buliga@imar.ro and Marius.Buliga@gmail.com .

Now that my expectations are explained, let’s look at the results. I have to put things in context a bit.

This site was called initially lifeinrio@wordpress.com . I wanted to start a blog about how is it to live in Rio with wife and two small kids. Not a bad subject, but I have not found the time for that side project, because I was just in the middle of an epiphany. I wanted to switch fields, I wanted to move from pure and applied mathematics to somewhere as close as possible to biology and neuroscience. But mind you that I wanted also to bring with me the math. Not to make a show of it, but to use the state of mind of a mathematician in these great emerging fields. So, instead of writing about my everyday life experiences, I started to write to everybody I found on the Net who was not (apparently) averse to mathematics and who was also somebody in neuroscience. You can imagine that my choices were not very well informed, because these fields were so far from what I knew before. Nevertheless I have found out interesting people, telling them about why I want to switch. Yes, why? Because of the following  reasons: (1) I am passionate about making models of reality, (2) I’m really good at finding unexpected points of view, (3) I learn very fast, (4) I understood that pure or applied math needs a challenge beyond the Cold War ones (i.e. theories of everything, rocket science, engineering).  OK, I’ll stop here with the list, but there were about 100 more reasons, among them being to understand what space is from the point of the view of a brain.

I got fast into pretty weird stuff. I started to read philosophy, getting hooked by Plato. Not in the way the usual american thinker does. They believe that they are platonic but they are empiricists, which is exactly the poor (brain) version of platonism. I shall stop giving kicks to empiricists, because they have advanced science in many ways in the last century.  Anyway empiricism looks more and more like black magic these days. Btw, have you read anything by Plato? If you do, then try to go to the source. Look for several sources,  you are not a good reader of ancient Greek.  Take your time, compare versions, spell the originals (so to say), discover the usual phenomenon that more something is appreciated, more shit inside.

Wow, so here is it a mathematician who wants to move to biology, and he uses Plato as a vehicle. That’s perhaps remarkabl…y stupid to do, Marius. What happened, have you ran out of the capacity to do math? Are you out in the field where people go when they can’t stand no more the beauty and hardness of mathematics? Everybody knows, since that guy who wrote with Ramanujan and later, after R was dead, told us that mathematics is for young people. (And probably white wealthy ones.)

No, what happened was that the air of Rio gave me the guts I have lost during the education process. Plato’s Timaeus spoke to me in nontrivial ways, in particular. I have understood that I am really on the side of geometers, not on the side of language people. And that there is more chance to understand brains if we try to model what the language people assume it works by itself, the low level, non rational processes of the brain. Those who need no names, no language, those highly parallel ones. For those, I discovered, there was no math to apply.  You may say that for example vision is one of the most studied subjects and that really there is a lot of maths already used for that. But if you say so then you are wrong.  There is no model of vision up to now, which explains how biological vision works without falling into the internal or external homunculus fallacies. If you look to computer vision, you know, you can do anything with computers, provided you have enough of them and enough time. There is a huge gap between computer vision and biological vision, a fundamental one.

OK, when I returned home to Bucharest I thought what if I reuse the lifeinrio.wordpress.com and transform it into chorasimilarity.worpress.com? This word chorasimilarity is made of “chora”, which is the feminine version of “choros”, which means place or space. Plato invented the “chora” as a term he used in his writings. “Similarity” was because of my background in math: I was playing with “emergent algebras”, which I invented previously of going on the biology tangent. In fact these emergent algebras made me think first that it is needed a new math, and that maybe they are relevant for biological vision.

I stop a bit to point to the post Scale is a place in the brain, which is about research on grid cells and place cells (research which just got a Nobel in medicine in 2014).

Emergent algebras are about similarity. They make visible that behind is hidden an abstract graph rewrite system. Which in turn can be made concrete by transforming it into chemistry. An artificial chemistry.  But also, perhaps, a real one. Or, the brain is most of it chemistry. Do you see how everything gets in place?  Chora is just chemistry in the brain. Being universal, it is not surprising that we distilled, us humans, a notion of space from that.

There is a lot of infrastructure to build in order to link all these in a coherent way.

How space is born (0)

This opens a new series of posts, which will turn us back to the “computing with space” theme, the main interest here at chorasimilarity.

Look again at the move R2 of graphic lambda calculus.



The epsilon and mu are, originally, elements of a commutative group. Suggestions have been made repeatedly that the commutative group can be anything.

The epsilon and mu are port names, just like the red 1, 2, 3 from the figure.

In the more recent drawing conventions (not that that matters for the formalism) the port names are in blue.

Here is again the same move, but without the epsilon and mu.


Of course, the green node is the fanout, in the chemlambda version.

Yes, eventually, everything is related to everything in this open notebook.

In the next posts I shall take it step by step.










From a stain on the wall to five visual languages

Do you know about the “stain on the wall”  creativity technique of Leonardo da Vinci? Here is a quote [source used]:

I will not forget to insert into these rules, a new theoretical invention for knowledge’s sake, which, although it seems of little import and good for a laugh, is nonetheless, of great utility in bringing out the creativity in some of these inventions.    This is the case if you cast your glance on any walls dirty with such stains or walls made up of rock formations of different types.  If you have to invent some scenes, you will be able to discover them there in diverse forms, in diverse landscapes, adorned with mountains, rivers, rocks, trees, extensive plains, valleys, and hills. You can even see different battle scenes and movements made up of unusual figures,  faces with strange expressions,  and myriad things which you can  transform into a complete and proper form constituting part of similar walls and rocks. These are like the sound of bells, in whose tolling, you hear names and words that your imagination conjures up.

I propose to you  five graphical formalisms, or visual languages, towards the goal of “computing with space”.

They all come from a “stain on the wall”,  reproduced here  (is the beginning of the article What is a space? Computations in emergent algebras and the front end visual system, arXiv:1009.5028),  with  some links  to more detailed explanations and related material which I invite you to follow.

Or better, to threat them as  a stain on the wall. To share, to dream about, to create, to discuss.

In mathematics “spaces” come in many flavours. There are vector spaces, affine spaces, symmetric spaces, groups and so on. We usually take such objects as the stage where the plot of reasoning is laid. But in fact what we use, in many instances,are properties of particular spaces which, I claim, can be seen as coming from a particular class of computations.

There is though a “space” which is “given” almost beyond doubt, namely the physical space where we all live. But as it regards perception of this space, we know now that things are not so simple. As I am writing these notes, here in Baixo Gavea, my eyes are attracted by the wonderful complexity of a tree near my window. The nature of the tree is foreign to me, as are the other smaller beings growing on or around the tree.  I can make some educated guesses about what they are: some are orchids, there is a smaller, iterated version of the big tree. However, somewhere in my brain, at a very fundamental level, the visible space is constructed in my head, before the stage where I a capable of recognizing and naming the objects or beings that I see.


The five visual languages are to be used with the decentralized computing model called Distributed GLC.  They point to different aspects, or they try to fulfil different goals.

They are:



Take a better look at the knotted S combinator (zipper logic VI)

Continuing from  Knot diagrams of the SKI (zipper logic V) , here are some  more drawings of the S combinator which was described in the last post by means of crossings:




Seen like this, it looks very close to the drawings from section 5 of  arXiv:1103.6007.

I am not teasing you,  but many things are now clear exactly because of all these detours. There is a lot to write and explain now, pretty much straightforward and a day after day effort to produce something  which describes well the end of the journey. When in fact the most mysterious creative part is the journey.


Assembling the puzzle of computing with space (I)

A lot of material has accumulated, it is time to start assembling the puzzle.

Let’s look first what we have:

These are the pieces of the puzzle.


Today I want to show you that the extended beta move can be done in a formalism which is made by chemlambda with dilation nodes added,  and with the local emergent algebra moves added.