Pure See and the Moirai

Wouldn’t be nice to tell again the story of the Moirai by using Pure See?

Now we know the correct correspondence between emergent algebras and the nodes and moves of the string of graph rewrite formalisms which I pursue since 2012.

The Pure See draft is not yet 100% correct in it’s treatment of emergence (reduction by passage to the limit where things should be more symmetric, and the –missing as now, explicitely– treatment of the degenerate fanout and fanin as emerging themselves), but nevertheless it would be a nice exercise to see where in the sequence of posts about the Moirai I was right and where not.

Recall that in the list of posts about “ancient Turing machines” there are some which attribute to the 3 Moirai (or Fates) some universal computing power. They can, by manipulating their strings (and rewritings) decide our fate (like a program which is then executed).

Here is the list of posts for you to enjoy and to play with, this time from the point of view of Pure See:

• Ancient Turing machines (I): the three Moirai
• The three Moirai, continued
• Lambda scale in graphic lambda calculus and diagram crossings
• Graphic beta move extended, to explore
• Lachesis, computation and desire to explore (Ancient Turing machines III)
• The first thread of the Moirai

Compare also with the making of, and further passage through GLC, chemlambda v1, chemlambda v2, etc from the History of chemlambda.

I think that now an attentive reader may enjoy to play with knot diagrams and their translations, in order to understand what the story of the Moirai is about.

Why would anybody do that? because is fun, what else? Now when we know how the machine works, roughly, then we may inspect some parts of it and try to make sense. You know, as like you and the car workshop guy both look at the engine. You see different things when you know how it works and what’s to be done.

Oh, that’s how semantics works… kind of thing.

Penrose’ Orchestrated OR characterised as stalinesque, question

Thanks to an announcement from Louis Kauffman, I arrived to watch the recent talk

Sir Roger Penrose and Dr. Stuart Hameroff: Consciousness and the Physics of the Brain, Roth Auditorium – Sanford Consortium for Regenerative Medicine, La Jolla, CA

I am not a fan of consciousness research, because I believe it is too early to jump to the highest level of a huge building; let’s concentrate first, I say, to understand biological life (which we don’t). Consciousness studies often neglect the basis and they obscure very promising research avenues, like how does life exists as an asemantic decentralized computation… while in the same time cartesian homunculi are kept in various disguises. My opinion!

Physics, on the other hand, that’s something I am a big fan, so I started to watch the very interesting, indeed, talk by Penrose. At the meta level, I was amused by the repeated orders to the invisible human and computer machinery to change the slides while in the same time arguing that it cannot be computation what the brain does.

Then I arrived to a point in the talk where I saw that Penrose uses an argument from Dennett, but for physics. It intrigued me because I used the same argument ten years ago, but I was not aware about Penrose’ Orchestrated OR theory.

So the question is pure vanity: who used the argument first?

I asked the following and I got no useable answer, therefore I am looking in the community for help. Or maybe you were not aware about it and we can talk about it.

According to Penrose his Orchestrated OR is a stalinesque theory of physics (exact moment in the speech is this) and I find this characterisation intriguing, therefore I ask you for help with more information.

AFAIK is Dennett who uses the characterization of theories (of brain function) which explain illusions as orwellian, stalinesque or multiple drafts. It is straightforward to apply Dennett’s classification to theories of physics arXiv:1011.4485 and I was not aware about Penrose Orchestrated OR, nor about his characterization as stalinist.

The question I have is: maybe Dennett imported this classification from something Penrose wrote before? If not, is there any evidence about Penrose using Dennett?

Here is the (mouse copy-paste from pdf) passage from arXiv:1011.4485 I mention, where quotes are from Dennett:

“

From the description given at [17], such theories can be characterized as:

• (a) orwellian – ”the subject comes to one conclusion, then goes back and changes that memory in light of subsequent events. This is akin to George Orwell’s Nineteen Eighty-Four, where records of the past are routinely altered.”

• (b) stalinesque – the ”events would be reconciled prior to entering the subject’s consciousness, with the final result presented as fully resolved. This is akin to Joseph Stalin’s show trials, where the verdict has been decided in advance and the trial is just a rote presentation.”

• (c) multiple drafts – ”there are a variety of sensory inputs from a given event and also a variety of interpretations of these inputs”. From [16] [there is] ”no central experiencer [who] confers a durable stamp of approval on any particular draft”.

Translated into the physics realm, this gives several interesting interpretations.

• (a) Such a path has been pursued in physics, by Everett’s Many-Worlds Interpretation of Quantum Mechanics [19]. More precisely, concerning interpretations of the collapsing of the wave function which are compatible with Everett theory, see Deutsch [18] and Stapp [24]. [Let me add here, in 2021, the following completion. A superficial view would be that Many-World Interpretation is rather akin to (c) multiple drafts. This is false because the Many-Worlds Interpretation is opposite to multiple drafts. Indeed, the multiple drafts and many worlds could be confused as “multiple drafts” and “multiple worlds”, but this would confuse “world” with “draft”. It is a serious confusion, one more which can be traced back to the confusion of things (like drafts) and objects (like worlds). See for more Wittgenstein and the Rhino. We don’t need a new world, or universe, to propose and interact within a draft.]

• (b) In more general terms, not related especially to the problem of the discrete versus continuous nature of reality, we can see any theory based on extremality of an action like being of this type. However, probably due to my ignorance, Iam not aware of physical theories supposing that a discrete reality conspires to give (to any observer) the appearance of being continuous. More precisely, such a theory would take as starting point a discrete reality where discrete things happen, in the limit when the graininess goes to zero, like in a continuous reality. One big and fundamental difficulty would be then to give a reasonable mechanism of how is this possible.

“

What is your opinion about this?

What I did during this pandemic

Here are my recollections. I’ll put only professional stuff, the personal part is not for share. (The long term effect of being physically confined with only the close family is great and one thing that everybody could relate, I hope.)

I don’t write this as self-promotion, is a sort of self-justification. “What did you do during this pandemic? …”

As you know some years before the pandemic I arrived at the subject of molecular computers, following the strange paths of mathematics and computation. This subject is still fresh, not enough explored and most likely supressed at least since 2017.

People have been hit with a life changing pandemic and they still rather study quantum computers. One thing I learned is that people (me included) are stubborn beyond reason.

At the end of 2019 I started to put in order the large quantity of published and unpublished research. It was a mess. It was not clear what chemlambda is and is not, the part about computing with space was still not appreciated enough. (The other thing people love a lot, besides quantum computing, is naive digital universes based on boomer mathematics. Don’t you know what boomer mathematics is? Like everything boomer, is something – mathematics in this case – from up to 1960′ glorified in a number of mediocre developments wrapped in self-congratulations. Fortunately mathematics evolved since then a lot and history will wipe all propaganda.)

Trying to make a presentable basis for this, I retraced my steps since then, and during the pandemic, and I finally made sense of the solution of the problem of computing with space. All pieces felt in place and is beautiful.

So the first thing I did was to put a basis for the chemlambda project, which you can see in the official chemlambda page. It was useful, even if only a basis. You have there now chemlambda v2, dirIC, a lambda calculus to chemlambda parser, quine graphs experiments, relations with Lafont’ Interaction Combinators, all pieces of stuff I wanted to have since years.

The second thing I did was to rescue (about a half) of the chemlambda collection of animations. Of course that this collection is not for admiring colored dots moving in pleasing ways, but a proof about how much can be done with purely local computing. How, please tell me, my dear experts, how did I invent all these molecules? Because they are living proof that asemantic computing does work.

As soon as I posted (in jan 2020) the collection, it was hit by a ddos attack. For almost a month.

In the spring and summer 2020 I worked on the various pieces of the official chemlambda page. I gave lots of private and some public talks. Put some articles in the arXiv. Produced abundantly commented scripts.

Then I was challenged to make what became chemSKI. Before I had not appreciated combinators as I should.

It became clear that behind a lot of the graphical rewriting stuff there is a computing with space part related to the shuffle move. This received the name pure see and is still in development. What is in there: a sort of semantics related to emergent algebras, but with implications for interaction combinators. A proof that both beta rewrite and the duplication rewrites are emergent, in a precise sense (people doing “linear” logic don’t even have this on their radar).

Coupled with the similar proofs and definitions of curvatures in sub-riemannian geometry, with the proof that the R3 rewrite emerges from a passage to the limit and that the defect from R3 measures curvature, this goes into completely new territory.

Now I enter into a phase where I had to take again the route of research on paper. It happened between nov 2020 and march 2021 and I want to wash the pandemic from my mind first and then I’ll show it. Is great!

This spring I started to do the same thing I did for the chemlambda project, but for other stuff, so I made the telegram chemlambda channel of long reads, which already has lots of things inside. Made also a github writings repository.

The COLIN implies LIN, asemantic computing and combinators stuff and the numbers exploration, started in em-convex, are partial, enough compelling results.

I forgot to tell you about Zip-slip-smash aka ZSS. It is a revision of zipper logic, which is a calculus with knots and zippers, which can implement interaction combinators. The meaning of it is related though again with emergent algebras, because the smash move is nothing else but the “look down” relation from the intrinsic sub-riemannian geometry treatment.

All in all, there are about:

• 10 technical articles
• lots of commented programs
• many talks to learn from
• chemSKI, dirIC, pure see, ZSS
• COLIN
• asemantic computing direction
• writings in new media

Open Science is RWX science (reloaded)

These are motivational materials in favor of OS, written during several years when I struggled to practice what I preached. If this inspires you then the goal is achieved.

The gist is that it is much easier to do Open Science than to wait for the perfect Open Access infrastructure.

also available at: https://github.com/mbuliga/writings/blob/main/os-is-rwx.md

also at: https://telegra.ph/Open-Science-is-rwx-science-reloaded-06-23

along more others in the chorasimilarity channel of long reads.

Wittgenstein and the Rhino

Assembled from A Wittgenstein joke and Notes for “Internet of things not Internet of objects”, there is now Wittgenstein and the Rhino.

It condenses what I think is reality and why it is not what usually people think it is.

Many times alluded or explained here and there, it took me many years to realize where is the source of the problem. Some of you probably will not like it. Your time has passed, is my opinion.

Also available in telegra.ph form, in the chorasimilarity telegram channel.

Writings repository at Github

Further experimenting, I created a writings repository. You find there, as .md files (some with pictures), some of my writings. Follow the repository for more, in the future. Also as reference.

Alternatively, I experiment with the chorasimilarity channel of long reads, on telegram-telegraph, which you can access without a telegram channel (and of course with a telegram account they look nicer on your phone).

ZSS: zipper logic revisited, with explanations

I took the time to explain in detail the ZSS (zip-slip-smash) graph rewrite formalism,

• why is universal,
• why is somehow dual to directed Interaction Combinators,
• why we need to enhance the Reidemeister moves with new rewrites to obtain a system where the R moves compute.

It uses the pictures of the slides and it has links inside.

Available here, in the chorasimilarity telegram channel (but you don’t need telegram to see it). In case you do use telegram, here is the chorasimilarity channel of long reads.

Also available on github.

In article form is on figshare.

And finally here as pdf.

COLIN implies LIN

UPDATE: Appeared as arXiv:2110.08178.

Introduction. See the last post On the missing examples of (COLIN) condition, again and the links therein, in particular this pdf and this mathoverflow question.

Theorem. For an emergent algebra with the group the condition (COLIN) impliex the condition (LIN)

Proof. Part 1. Recall the (COLIN) condition: for any and for any we have

Fix an element , otherwise arbitrary. (COLIN) is then equivalent with

If we replace with and then we use (R2) and some groupings of terms then we obtain the following relation equivalent with (COLIN):

where is a relative operation, namely

We pass now with to by using the topological axiom (em) and we obtain in the limit the following

where is the limit of , therefore the infinitesimal dilation of coefficient , based at . We write it like this

Part 2. The relation (COLIN) passes to the infinitesimal level. Indeed, if we replace the operations with the infinitesimal operations (dilations) based at then (COLIN) remains true. This is true because for an arbitrary we deduce from (COLIN) the relation

where

We can then pass to the limit with to and we get the “infinitesimal” (COLIN) relation

But the infinitesimal emergent algebra based at satisfies (LIN) see here, propozition 7.11. Therefore now we know that it also satisfy (COLIN). As a consequence we get that it comes from a commutative conical group. We denote with a dot this conical group operation.

Because the group is conical and commutative it follows that

via techniques explained in the em-convex paper. Therefore the conical group is a vector space, with group operation being vector addition and equal to the scalar which multiplies (up to an arbitrary exponential).

Part 3. The last two relations from Part 1 are then rewritten as

Commutativity of the group operation and (LIN) for the infinitesimal level gives us the equivalent

(where in the last equality we used Part 2 and we make a slight abuse of notation for the multiplication by the scalar )

Now we come back to the initial (COLIN) and we remark that with the new knowledge we can rewrite it as

which is equivalent with

We pass to the limit with to this time and we obtain that

therefore the emergent algebra is identical with the infinitesimal emergent algebra based at . Therefore it satisfies (LIN).

__

We know more, actually, namely that (COLIN) is equivalent with (SHUFFLE). Indeed, we proved that (COLIN) implies that the emergent algebra is the one of a conical commutative group, or we already know that (SHUFFLE) is true if and only if we are in a conical commutative group.

As a conclusion, there is no example of an emergent algebra which satisfies (COLIN) but not (LIN).