Tag Archives: biological computing

What if… it can be done? An update of an old fake news post

In May 2014 I made a fake news post (with the tag WHAT IF) called Autodesk releases Seawater. It was about this big name who just released a totally made up product called Seawater.

“SeaWater is a design tool for the artificial life based decentralized Internet of Things.”

In the post it is featured this picture

[source]

scoop-of-water-magnified-990x500… and I wrote:

“As well, it could be  just a representation of the state of the IoT in a small neighbourhood of you, according to the press release describing SeaWater, the new product of Autodesk.”

Today I want to show you this:

3_27_quine

or better go and look in fullscreen HD this video

The contents is explained in the post from the microblogging collection chemlambda

27 microbes. “This is a glimpse of the life of a community of 27 microbes (aka chemlambda quines). Initially the graph has 1278 nodes (atoms) and 1422 edges (bonds). There are hundreds of atoms refreshed and bonds made and broken at once.”

Recall that all this is done with the most simple algorithm, which turns chemlambda into an asynchronous graph rewrite automaton.

A natural development would be to go further, exactly like described in the Seawater post.

Because it can be done 🙂

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The Internet can be your pet

or  you could have a pet which embeds and run a copy of the whole Internet.

The story from this post  starts from this exploratory posting on Google plus from June 2nd, 2015, which zooms from sneakernet to sneakernet  delay-tolerant networking to  Interplanetary Internet to Nanonetworks to DNA digital data storage to molecular computers.

I’ll reproduce the final part, then I’ll pass to the Internet as you pet thing.

“At this stage things start to be interesting. There is this DNA digital data storage technique
http://en.wikipedia.org/wiki/DNA_digital_data_storage
which made the news recently by claiming that the whole content of the Net fits into a spoon of DNA (prepared so to encode it by the technique).

I have not been able to locate the exact source of that claim, but let’s believe it because it sounds reasonable (if you think at the scales involved).

It can’t be the whole content of the net, it must mean the whole passive content of the net. Data. A instant (?) picture of the data, no program execution.

But suppose you have that spoonful of DNA, how do you use it? Or what about also encoding the computers which use this data, at a molecular level.

You know, like in the post about one Turing Machine, Two Turing Machines https://plus.google.com/+MariusBuliga/posts/4T19daNatzt
if you want classical computers running on this huge DNA tape.

Or, in principle, you may be able to design a molecular google search …
molecule, which would interact with the DNA data to retrieve some piece of it.

Or you may just translate all programs running on all computers from all over the world into lambda calculus, then turn them into chemlambda molecules, maybe you get how much, a cup of molecular matter?

Which attention:
– it executes as you look at it
– you can duplicate it into two cups in a short matter of time, in the real world
– which makes the sneakernet simply huge related to the virtual net!

Which brings of course molecular computers proposal to the fore
http://chorasimilarity.github.io/chemlambda-gui/dynamic/molecular.html  ”

Let’s develop this a bit! (source)

The following are projections about the possible future of biochemical computations with really big data: the whole, global data produced and circulated by humans.

They are based on estimates of the information content in the biosphere from the article [1] and on a proposal for life like molecular computing.

Here are the facts. In [1] there are given estimates about the information content of DNA in the biosphere, which are used further.

One estimate is that there are about 5 X 10^11 tonnes of DNA, in a biomass of about 2 X 10^12 tonnes, which gives a proportion of DNA in biomass of about 1/40.

This can be interpreted as: in order to run the biochemical computations with 1g of DNA there are needed about 40g of biochemical machinery.

From the estimate that the biomass contains about 5 X 10^30 cells, it follows that 4g of DNA are contained (and thus run in the biochemical computation) in 10^13 cells.

The Internet has about 3 X 10^9 computers and the whole data stored is equivalent with about 5g of DNA [exact citation not yet identified, please provide a source].

Based on comparisons with the Tianhe-2 supercomputer (which has about 3 X 10^6 cores) it follows that the whole Internet processes in a way equivalent as a magnitude order to 10^3 such supercomputers.
From [1] (and from the rather dubious equivalence of FLOPS with NOPS)  we get that the whole biosphere has a power of 10^15 X 10^24 NOPS, which gives for 10^13 cells (the equivalent of 4g of DNA) about 10^17 NOPS. This shows that approximately the power of the biochemical computation of 4g of DNA (embedded in the biochemical machinery of about 160g) is of the same order with the power of computation of the whole internet.

Conclusion until now: the whole Internet could be run in a “pet” living organism of about 200g. (Comparable to a rat.)

This conclusion holds only if there is a way to map silicon and TM based computers into biochemical computations.

There is a huge difference between these two realms, which comes from the fact that the Internet and our computers are presently built as a hierarchy, with multiple levels of control, while in the same time the biochemical computations in a living cell do not have any external control (and there is no programming).

It is therefore hard to understand how to map the silicon and TM based computations (which run one of the many computation paradigms embedded into the way we conceive programming as a discipline of hierarchical control) into a decentralized, fully asynchronous, in a ransom environment biochemical computation.

But this is exactly the proposal made in [2], which shows that in principle this can be done.

The details are that in [2] is proposed an artificial chemistry (instead of the real world chemistry) and a model of computation which satisfies all the requirements of biochemical computations.
(See very simple examples of such computations in the chemlambda collection https://plus.google.com/u/0/collection/UjgbX )

The final conclusion, at least for me, is that provided there is a way to map this (very basic) artificial chemistry into real chemical reactions, then one day you might have the whole Internet as a copy which runs in your pet.

[1] An Estimate of the Total DNA in the Biosphere,
Hanna K. E. Landenmark,  Duncan H. Forgan,  Charles S. Cockell,
http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1002168

[2] Molecular computers,
Marius Buliga, 2015
http://chorasimilarity.github.io/chemlambda-gui/dynamic/molecular.html

Suppose this. What then?

 I want to understand how a single molecule interacts with others, chemically. You have to agree that this is a worthy goal.
What I say is this. By using a collection of made up molecules and made up chemical reactions, I proved that by the stupid deterministic algorithm I can do anything and by experiment that it seems that if I design well the initial molecule then I can do anything I proposed myself doing, with the stupid random algorithm (a molecule which encounters randomly enzymes which rewrite it by chemical reactions). For me, the molecule is not the process, it is just a bunch of atoms and bonds. But I proved I can do anything with it, without any lab supervision.Which is relevant because any real cell does that. It has no supervision, nor goals, nor understanding, is nothing else than a collection of chemicals which interact randomly.

My hypothesis is the following. There is a transformation from the made up chemlambda molecules, which TRANSFORMS:
– node into real molecule
– port into real molecule
– bond into real molecule

and some other real molecules called here “enzymes”, one per any type of graph rewrite

such that

– graph rewrite G which replaces this configuration LT of two nodes and 1 bond  into that  RT configuration TRANSFORMS into  the chemical reaction between enzyme G and the transformation of LT into real chemicals, which gives the transformation of RT into real chemicals and the enzyme G (perhaps carrying away some other reaction products, to have conservation of # atoms)

The argument for that hypothesis is that the rewrites are so simple, compared with real chemistry of biomolecules, that there have to exist such reactions.

This is explained in the Molecular computers
http://chorasimilarity.github.io/chemlambda-gui/dynamic/molecular.html

Suppose that the hypothesis is confirmed. Either by identifying the TRANSFORM from scratch (i.e. by using chemistry knowledge to identify classes of reactions and chemicals which can model chemlambda), or by finding the enzymes G and the real molecules corresponding to node, port and bond in some fundamental biochemical processes (that would be even more wonderful).

Suppose this. What then?

Then, say I have the goal to design a molecule which does something inside a cell, when injected in the body. It does it by itself, in the cell medium. What it does can always (or in principle) be expressed as an algorithm, as a computation.

I use chemlambda and TRANSFORM to design the molecule and check that once I have it, it does the job. It is of course a problem to build it in reality, but for this I have the printer of Craig Venter, the digital biological converter https://youtu.be/DVL1nL3SU6I .

So I print it and that’s all. When injected in the body, once arrived in the cell, it does the job.

Other possibilities would open in the case some formalism like chemlambda (i.e. using individual molecules and rewrites, along with trivial random algorithms) is identified in real biochemistry. This would help enormously the understanding of biochemical processes, because instead of working empirically, like now when we work at the level of functions of molecules (knowing well that the same molecule does different things in different contexts and that molecule-function association is very fragile in biology), we might work inversely, from using functions as black boxes to being able to build functions. Even to go outside functions and understand chemistry as computation directly, not only as a random medium for encoding our theoretical notions of computation.

See more about this at the chemlambda index
http://chorasimilarity.github.io/chemlambda-gui/index.html

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A citizen science project on autonomous computing molecules

 Wanted: chemists, or people who work(ed) with chemical molecules databases!
[update:  github.io version]
The  chemlambda project proposes the following. Chemlambda is a model of computation based on individual molecules, which compute alone, by themselves (in a certain well defined sense). Everything is formulated from the point of view of ONE molecule which interacts randomly with a family of enzymes.
So what?
Bad detail: chemlambda is not a real chemistry, it’s artificial.
Good detail: it is Turing universal in a very powerful sense. It does not rely on boolean gates kind of computation, but on the other pillar of computation which led to functional programming: lambda calculus.
So instead of molecular assemblies which mimic a silicon computer hardware, chemlambda can do sophisticated programming stuff with chemical reactions. (The idea that lambda calculus is a sort of chemistry appeared in the ALCHEMY (i.e. algorithmic chemistry) proposal by Fontana and Buss. Chemlambda is far more concrete and simple than Alchemy, principially different, but it nevertheless owes to Alchemy the idea that lambda calculus can be done chemically.)
From here,  the following reasoning.
(a) Suppose we can make this chemistry real, as explained in the article Molecular computers.  This looks reasonable, based on the extreme simplicity of chemlambda reactions. The citizen science part is essential for this step.
(b) Then is is possible to take further Craig Venter’s Digital Biological Converters (which already exist) idea and enhance it to the point of being able to “print” autonomous computing molecules. Which can do anything (amenable to a computation, so literary anything). Anything in the sense that they can do it alone, once printed.
The first step of such an ambitious project is a very modest one: identify the ingredients in real chemistry.
The second step would be to recreate with real chemistry some of the examples which have been already shown as working, such as the factorial, or the Ackermann function.
Already this second step would be a huge advance over the actual state of the art in molecular computing. Indeed, compare a handful of boolean gates with a functional programming like computation.
If it is, for example, a big deal to build with DNA some simple assemblies of boolean gates, then surely it is a bigger deal to be able to compute the Ackermann function (which is not primitive recursive, like the factorial) as the result of a random chemical process acting on individual molecules.
It looks perfect for a citizen science project, because what is missing is a human distributed search in existing databases, combined with a call for realization of possibly simple proofs of principles chemical experiments based on an existing simple and rigorous formalism.
Once these two steps are realized, then the proof of principle part ends and more practical directions open.
Nobody wants to compute factorials with chemistry, silicon computers are much better for this task. Instead, chemical tiny computers as described here are good for something else.
If you examine what happens in this chemical computation, then you realize that it is in fact a means towards self-building of chemical or geometrical structure at the molecular level. The chemlambda computations are not done by numbers, or bits, but by structure processing. Or this structure processing is the real goal!
Universal structure processing!
In the chemlambda vision page this is taken even further, towards the interaction with the future Internet of Things.

Notes for “Internet of things not Internet of objects”

1.   Kevin Ashton  That ‘Internet of things’ thing

Conventional diagrams of the Internet include servers and routers and so on, but they leave out the most numerous and important routers of all: people.
The problem is, people have limited time, attention and accuracy—all of which means they are not very good at capturing data about things in the real world.
Comments:
  • not things, objects!  Ashton writes about objects.
  • people are not good at capturing data, so let’s filter (i.e. introduce a bottleneck) the data for them, thank you!
  • however, people arrive to gather around  ideas and to discuss  despite the fact that “conventional diagrams of the Net leave out people”.
  • By having public discussions around an “idea” people arrive to filter creatively the information dump without resorting to artificial bottlenecks.  Non-human bottleneck stifle discussions!

Replaced further:

  • things by objects
  • ideas by things.
We’re physical, and so is our environment. Our economy, society and survival aren’t based on things or information—they’re based on objects. You can’t eat bits, burn them to stay warm or put them in your gas tank. Things and information are important, but objects matter much more. Yet today’s information technology is so dependent on data originated by people that our computers know more about things  than objects.
This looks like the credo of the Internet of Objects!
Do we want this?
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2.     What are, for people, things and objects?

Here is a depiction of a thing [source]:

Germanische-ratsversammlung_1-1250x715

A thing  was the governing assembly  made up of the free people of the community, meeting in a place called a thingstead.
(“thing” in Germanic societies,  “res” for Romans, etc.)
Heidegger (The Thing):

Near to us are what we usually call things. The jug is a thing. What is a jug? We say: a vessel.  As a jug, the vessel is something self-sustained,  self-supporting, or independent.

An independent, self-supporting thing may become an object if we place it before us.

An object is a reification of a thing.
[Kenneth Olwig: “Heidegger, Latour and The Reification of Things:The Inversion and Spatial Enclosure of the Substantive Landscape of Things – the Lake District Case”, Geografiska Annaler: Series B 2013 Swedish Society for Anthropology and Geography]
An object is therefore real,  but all about thing and thingstead is lost.
Reification generally refers to making something real…
Reification (computer science), making a data model for a previously abstract concept.
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3.  An example of a thing and some of it’s reifications:
Quotes  and images from here:
On 20 May 1515, an Indian rhinoceros arrived in Lisbon from the Far East.
After a relatively fast voyage of 120 days, the rhinoceros was finally unloaded in Portugal, near the site where the Manueline Belém Tower was under construction. The tower was later decorated with gargoyles shaped as rhinoceros heads under its corbels.[11]
A rhinoceros had not been seen in Europe since Roman times: it had become something of a mythical beast, occasionally conflated in bestiaries with the “monoceros” (unicorn), so the arrival of a living example created a sensation.
The animal was examined by scholars and the curious, and letters describing the fantastic creature were sent to correspondents throughout Europe. The earliest known image of the animal illustrates a poemetto by Florentine Giovanni Giacomo Penni, published in Rome on 13 July 1515, fewer than eight weeks after its arrival in Lisbon.
Nashorn.2

Valentim Fernandes, , saw the rhinoceros in Lisbon shortly after it arrived and wrote a letter describing it to a friend in Nuremberg in June 1515.  A second letter of unknown authorship was sent from Lisbon to Nuremberg at around the same time, enclosing a sketch by an unknown artist. Dürer saw the second letter and sketch in Nuremberg. Without ever seeing the rhinoceros himself, Dürer made two pen and ink drawings,[23] and then a woodcut was carved from the second drawing, the process making the print a reversed reflection of the drawing.[19][24]

The German inscription on the woodcut, drawing largely from Pliny’s account,[13] reads:

On the first of May in the year 1513 AD [sic], the powerful King of Portugal, Manuel of Lisbon, brought such a living animal from India, called the rhinoceros. This is an accurate representation. It is the colour of a speckled tortoise,[25] and is almost entirely covered with thick scales. It is the size of an elephant but has shorter legs and is almost invulnerable. It has a strong pointed horn on the tip of its nose, which it sharpens on stones. It is the mortal enemy of the elephant. The elephant is afraid of the rhinoceros, for, when they meet, the rhinoceros charges with its head between its front legs and rips open the elephant’s stomach, against which the elephant is unable to defend itself. The rhinoceros is so well-armed that the elephant cannot harm it. It is said that the rhinoceros is fast, impetuous and cunning.[26]
Comment: you can see here a thing taking shape.
Durer_drawing
Despite its errors, the image remained very popular,[5] and was taken to be an accurate representation of a rhinoceros until the late 18th century.
The pre-eminent position of Dürer’s image and its derivatives declined from the mid-to-late-18th century, when more live rhinoceroses were transported to Europe, shown to the curious public, and depicted in more accurate representations.
Until the late 1930s, Dürer’s image appeared in school textbooks in Germany as a faithful image of the rhinoceros;[6] in German the Indian rhinoceros is still called the Panzernashorn, or “armoured rhinoceros”. It remains a powerful artistic influence, and was the inspiration for Salvador Dalí‘s 1956 sculpture, Rinoceronte vestido con puntillas (Rhinoceros dressed in lace), which has been displayed at Puerto Banús, in Marbella, since 2004.
Dalí.Rinoceronte
Comment: that is an object! You can stick an RFID to it and it has clear GPS coordinates.
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4.     Bruno Latour (From Realpolitik to Dingpolitik, or How to Make Things Public), writing about “object-oriented democracy”:

Who is to be concerned? What is to be considered? How to represent the sites where people meet to discuss their matters of concern?

How does the Internet of Objects respond to these questions about things and thingsteads?

People are going to use the Internet of Objects as an Internet of Things. How can we help them (us!) by designing a thing-friendly Internet of Things?

My guess and proposal is to try to put space (i.e. thingstead) into the IoT.  By design.
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5.   Not the RFID space.  Not the GPS space.  This may be useful for the goal of inhuman optimization, but will not promote by itself the conversation needed to have around things and their reifications, the objects.
People are going to divert the ways of the IoT, designed with  this lack of appetite for human communication, as they succeeded previously!
For understanding why RFID and GPS  are not sufficient, let’s imagine, like Borges, that the world is a library.
  • RFID – name of the book
  • GPS – place on the shelf
Is this enough for me, reader, who wants to retrieve (and discuss with other readers about) a book without knowing it’s title, nor it’s position on a shelf?
No!  I have to call a librarian (the bottleneck), an inhuman and very efficient one, true,  who will give me a list of possible titles and who will fetch the book from the right shelf. I don’t have direct access to the library, nor my friends which may have different ideas about the possible titles and shelves where the book might be.
The librarian will optimize the book-searching and book-fetching, will optimize all this not for me, or for you, or for our friends, but for a bayesian individual in a bayesian society. (see Bayesian society)
What I would like is to have access to my library (in the big Universal Library) and to be able to share my spatial competences of using my library with my friends. That means a solution for the following problem, which  Mark Changizi  mentions in relation to e-books (but I think is relevant instead for the human IoT)

The Problem With the Web and E-Books Is That There’s No Space for Them

My personal library serves as extension of my brain. I may have read all my books, but I don’t remember most of the information. What I remember is where in my library my knowledge sits, and I can look it up when I need it. But I can only look it up because my books are geographically arranged in a fixed spatial organization, with visual landmarks. I need to take the integral of an arctangent? Then I need my Table of Integrals book, and that’s in the left bookshelf, upper middle, adjacent to the large, colorful Intro Calculus book.

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6.  What else?  These notes are already rich enough, therefore please be free to stop reading, if you feel like.
Actually, this is a technical problem: how to create space where there is none, without using arbitrary names (RFID) or global (but arbitrary) coordinates (GPS)?
It is the same problem which we encounter in neuroscience: how the brain makes sense of space without using any external geometrical expertise? how to explain the “brain as a geometry engine” (as Koenderink) when there is no rigorous  model of computation for this brain behaviour?
There may be a point in holding that many of the better-known brain processes are most easily understood in terms of differential geometrical calculations running on massively parallel processor arrays whose nodes can be understood quite directly in terms of multilinear operators (vectors, tensors, etc).
In this view brain processes in fact are space.
I have two proposals for this, which go far beyond explanations which may fit into a post.  I put them  here only for the sake of giving an explanation of the motivations I have, and maybe for inviting the interested people to gather for discussing about these things.
It is about “computing with space”, which is the middle name of this blog.  The first name, chorasimilarity, is made by gluing Plato’s notion of space “chora” with  (self-)”similarity”, which is, I believe the essence of transforming space from a “vessel” into a self-sustaining, self-supporting thingstead.
The first proposal is to concentrate on completely asynchronous, purely local  models of distributing computing as a low-level basis for the architecture of a true IoT.
For example: mesh networks. (Thank you Peter Waaben.)
I know of only one model of computation which satisfy the previously mentioned demands and also  solves the problem of putting space into the Net:
It is based on actors which gather in an agora to discuss things that matter.  Literally!
But there is long way to  arrive to a proof of principle, at least, for such a space-rich IoT, which brings me to the second proposal, which (may) be too technical for this post, alluded here: A me for space.
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Model of computation vs programming language in molecular computing

An interesting discussion (?) started in the comments of this John Baez  G+ post concerns differences between “model of computation” and “programming language” denominations (in that post, in particular, for Petri nets).

I reproduce here what I think that are relevant bits for this discussion and later, after possibly several updates, I shall try to write something useful by using these bits.

1.  Turing machine and lambda calculus are both models of computation, but lambda calculus is also  a programming language and Turing machine is not.

2. Zachariah Hargis makes the point of comparing this model of computation  vs  programming language distinction as related to the one  made by Leibniz between calculus ratiocinator  and  lingua characteristica. (Among other references, note to self to explore further.)

3. Chemical reaction networks (CRNs)  is one fundamental ingredient of molecular computing, no matter what formalization of CRNs is used. Don’t believe that all “computational part” of a CRN is a Petri net (because it is often very important which are concretely the molecules and reactions involved in the CRN, not only the abstract number of species and reaction rates between those).

4. Petri nets, as used in chemistry, are a tool for getting quantitative information from CRNs, once the CRNs are designed by other means. Petri nets might be useful for thinking about CRNs, but not necessary for designing CRNs.

5.  CRNs  which are designed by using, or embody in some sense lambda calculus is a much more interesting path towards a “programming language”, and a classical one (Fontana and Buss Algorithmic chemistry), than the more studied engineering style implementation of imperative programming and by force copy-paste of TM thinking into bio computing.

6. Among the specifications for a “programming language for chemistry” are the following:

  • (a) geometrical (in particular no use of currying, along more obvious features as being parallel, asynchronous, the latter being achievable already by many well known, non exotic programming languages),
  • (b) purely syntactic (in particular no names management, nor input-output signalling),
  • (c) (maybe an aspect of (b), but not sure)  no use of evaluation in computation (strategy).

(The chemical concrete machine satisfies these requirements and moreover it contains lambda calculus, thus showing that  such a “language” is possible. However, the chemical concrete machine is based on a made-up, artificial chemistry, thus it provides only a proof of principle for the existence of such a “language”. Or is it?  Biochemists help is needed to identify, or search for real chemical reactions which could be used for implementing the chemical concrete machine in reality.)

7. The problem of tacit axioms in history of the Church-Turing thesis might be especially relevant for biochemists, and it could also be mentioned as an argument in favour of making a distinction between “model of computation” and “programming language”:  any model of computation uses some tacit axioms, while a programming language does not (only at the semantic level concerning making (human) sense about the results and ways of functioning of the programming language  such tacit axioms are used in this case). For biochemists, to not use such tacit axioms is a must  when they try to find scientifically valid explanations. CS does well when ignoring these, in most of the cases.

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Neurons know nothing, however …

… they know surprisingly much, according to the choice of definition of “neural knowledge”. The concrete definition which I adopt is the following:  the knowledge of a neuron at a given moment is the collection (multiset) of molecules it contains. The knowledge of a synapse is the collection of molecules present in respective axon, dendrite and synaptic cleft.

I take the following hypotheses for a wet neural network:

  • the neural network is physically described as a graph with nodes being the neurons and arrows being the axon-dendrite synapses. The network is built from two ingredients: neurons and synapses. Each synapse involves three parts: an axon (associated to a neuron), a synaptic cleft (associated to a local environment) and a dendrite (associated to a neuron).
  • Each of the two ingredients of a neural network, i.e. neurons and synapses, as described previously, function by associated chemical reaction networks, involving the knowledge of the respective ingredients.
  • (the most simplifying hypothesis)  all molecules from the knowledge of a neuron, or of a synapse, are of two kinds: elements of MOLECULES or enzyme  names from the chemical concrete machine.

The last hypothesis seem to introduce knowledge with a more semantic flavour by the backdoor. That is because, as explained in  arXiv:1309.6914 , some molecules (i.e. trivalent graphs from the chemical concrete machine formalism) represent lambda calculus terms. So, terms are programs, moreover the chemical concrete machine is Turing universal, therefore we end up with a rather big chunk of semantic knowledge in a neuron’s lap. I intend to show you this is not the case, in fact a neuron, or a synapse does not have (or need to) this kind of knowledge.

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Before giving this explanation, I shall explain in just a bit more detail how the wet neural network,  which satisfies those hypotheses, works.  A physical neuron’s behaviour is ruled by the chemistry of it’s metabolic pathways. By the third hypothesis these metabolic pathways can be seen as graph rewrites of the molecules (more about this later). As an effect of it’s metabolism, the neuron has an electrical activity which in turn alters the behaviour of the other ingredient, the synapse. In the synapse act other chemical reaction networks, which are amenable, again by the third hypothesis, to computations with the chemical concrete machine. As an effect of the action of these metabolic pathways, a neuron communicates with another neuron. In the process the knowledge of each neuron (i.e. the collection of molecules) is modified, and the same is true about a synapse.

As concerns chemical reactions between molecules, in the chemical concrete machine formalism there is only one type of reactions which are admissible, namely the reaction between a molecule and an enzyme. Recall that if (some of the) molecules are like lambda calculus terms, then (some of the) enzymes are like names of reduction steps and the chemical reaction between a molecule and an enzyme is assimilated to the respective reduction step applied to the respective lambda calculus term.

But, in the post  SPLICE and SWITCH for tangle diagrams in the chemical concrete machine    I proved that in the chemical concrete machine formalism there is a local move, called SWITCH

chem_switch

which is the result of 3 chemical reactions with enzymes, as follows:

chem_switch_2

Therefore, the chemical concrete machine formalism with the SWITCH move added is equivalent with the original formalism. So, we can safely add the SWITCH move to the formalism and use it for defining chemical reactions between molecules (maybe also by adding an enzyme, or more, for the SWITCH move, let’s call them \sigma).  This mechanism gives chemical reactions between molecules with the form

A + B + \sigma \rightarrow C + D + GARB

where $\latex A$ and B are molecules such that by taking an arrow from A and another arrow from B we may apply the \sigma enzyme and produce the SWITCH move for this pair of arrows, which results in new molecules C and D (and possibly some GARBAGE, such as loops).

In conclusion, for this part concerning possible chemical reactions between molecules, we have enough raw material for constructing any chemical reaction network we like. Let me pass to the semantic knowledge part.

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Semantic knowledge of molecules. This is related to evaluation and it is maybe the least understood part of the chemical concrete machine. As a background, see the post  Example: decorations of S,K,I combinators in simply typed graphic lambda calculus , where it is explained the same phenomenon (without any relation with chemical metaphors) for the parent of the chemical concrete machine, the graphic lambda calculus.

Let us consider the following rules of decorations with names and types:

chem_decor_1

If we consider decorations of combinator molecules, then we obtain the right type and identification of the corresponding combinator, like in the following example.

chem_decor_2

For combinator molecules, the “semantic knowledge”, i.e. the identification of the lambda calculus term from the associated molecule, is possible.

In general, though, this is not possible. Consider for example a 2-zipper molecule.

chem_decor_3

We obtain the decoration F as a nested expression of A, D, E, which enough for performing two beta reductions, without knowing what A, D, E mean (without the need to evaluate A, D, E). This is equivalent with the property of zippers, to allow only a certain sequence of graphic beta moves (in this case two such moves).

Here is the tricky part: if we look at the term F then all that we can write after beta reductions is only formal, i.e. F  reduces to (A[y:=D])[x:=E], with all the possible problems related to variable names clashes and order of substitutions. We can write this reduction but we don’t get anything from it, it still needs further info about relations between the variables x, y and the terms A, D, E.

However, the graphic beta reductions can be done without any further complication, because they don’t involve any names, nor of variables, like x, y, neither of terms, like A, D, E, F.

Remark that the decoration is made such that:

  • the type decorations of arrows are left unchanged after any move
  • the terms or variables decorations (names elsewhere “places”) change globally.

We indicate this global change like in the following figure, which is the result of the sequence of the two possible \beta^{+} moves.

chem_decor_4

Therefore, after the first graphic beta reduction, we write  A'= A[y:=D] to indicate that A' is the new, globally (i.e. with respect to the whole graph in which the 2-zipper is a part) obtained decoration which replaces the older A, when we replace y by D. After the second  graphic beta reduction we use the same notation.

But such indication are even misleading, if, for example, there is a path made by arrows outside the 2-zipper, which connect the arrow decorated by D with the arrow decorated by y.  We should, in order to have a better notation, replace D by D[y:=D], which gives rise to a notation for a potentially infinite process of modifying D. So, once we use graphs (molecules) which do not correspond to combinators (or to lambda calculus terms), we are in big trouble if we try to reduce the graphic beta move to term rewriting, or to reductions in lambda calculus.

In conclusion for this part: decorations considered here, which add a semantic layer to the pure syntax of graph rewriting, cannot be used as replacement the graphic molecules, nor should reductions be equated with chemical reactions, with the exception of the cases when we have access to the whole molecule and moreover when the whole molecule is one which represents a combinator.

So, in this sense, the syntactic knowledge of the neuron, consisting in the list of it’s molecules, is not enough for deducing the semantic knowledge which is global, coming from the simultaneous decoration of the whole chemical reaction network which is associated to the whole neural network.