[Fis] [External Email] Re: CODE DISCUSSION. A Slice of Life

[Stanley N Salthe]

Joseph -- Perhaps the world needs more poetry -- woven by words of course.
STAN

On Sun, Sep 26, 2021 at 4:02 AM joe.brenner en bluewin.ch <
joe.brenner en bluewin.ch> wrote:

> Dear Pedro, Dear Louis,
>
> I think that both your approaches are necessary and that the proper
> ontological priority has been given to Pedro's. I see Louis' approach as a
> formal, epistemic description of a low-dimensional "slice" through a
> complex much higher-dimensional reality, dynamic and changing.
>
> The question of the locus of meaning then disappears: meaning is in the
> conjunction of ourselves AND the biological entity. We are both separated
> and not separated from such entiities, and self-reference is never only
> reference to "self". I thus tend to discard some of the simpler and
> simplest concepts exactly because they fail to reflect reality and our
> relationships to it.
>
> Of course "simple structures" can be enfolded in more complex systems (the
> "that you describe", referring to Pedro) is superfluous), but this is like
> saying the number two can be enfolded in complex systems. The result is
> that use of what Louis calls the simplest references can be misleading
> unless it is explicitly stated, as Louis does, that they refer to models
> only. I just am afraid that the message tends to get lost. A system can be
> rich and consistent enough to do arithmetic bot nothing else.
>
> The world needs that something else very badly, without distractions.
>
> Thank you and best wishes,
>
> Joseph
>
>
>
> ----Message d'origine----
> De : loukau en gmail.com
> Date : 26/09/2021 - 06:21 (E)
> À : pcmarijuan.iacs en aragon.es
> Cc : fis en listas.unizar.es
> Objet : Re: [Fis] CODE DISCUSSION. Recursion & ANNOUNCEMENT
>
> Dear Pedro,
> (This copy is sent to fis list.)
> A comment on your comment.
> I do not, in making examples, claim that one must restrict one’s formalism
> to the form of those examples.
> The examples are intended to highlight conceptual aspects of the
> discussion.
> The objection that a given formalism is not complete can always be made,
> particularly if the formalism is believed to be consistent and is rich
> enough to do arithmetic (Goedel).
> Therefore, I do not attempt to produce complete formal systems.
> I intend to produce the simplest formal system that illustrate the ideas I
> am discussing.
>
> The issue that I am addressing in my previous two letters is the issue of
> the cybernetics of
>
> Meaning giving rise to Syntax
> and
> Syntax giving rise to Meaning.
>
> We understand this issue from the point of view of distinctions made by
> observers who themselves are part of the systems being observed.
> When one takes the point of view of human cognition, meaning has a large
> role.
> When one looks at molecular biology we see a fantastic array of
> syntactical behaviour and it is very difficult to see the locus of meaning
> except in ourselves as scientific observers of the biology.
> And yet we are ourselves such biological systems.
> This leads to a host of questions and many discussions.
> To look at the simplest references such as
> 2x —> xx
> and so 22 —> 22 giving self-reference,
> is helpful in gaining an understanding of these issues.
> Next simpler formalisms such as the von Neumann building machine
> B,x —> X,x
> whence
> B,b —> B,b
> are structures that can be enfolded in the more complex systems that you
> describe, and indeed the variety of ways that this can happen is part and
> parcel of the discussion.
> For example, it is very significant that molecular biology, in order to
> achieve self-replication of DNA in the context of cellular systems must
> overcome a host of complex topological and geometrical problems that a
> logician would never imagine from the abstractions of self-reference above.
> Best,
> Lou
>
> On Sep 24, 2021, at 5:17 AM, Pedro C. Marijuan < pcmarijuan.iacs en aragon.es>
> wrote:
>
> Dear All,
> Let me, first of all, announce an interesting e-conference organized by
> the journal *Information* (one of the official sponsors of the past IS4SI
> meeting).
> -----------------------------------------------------------------------------------------
>
> It is the 1st International Electronic Conference on Information
> (IECI2021),
> the deadline of which is approaching *: * **October 8th**.
> We are kindly invited to submit an abstract:
> https://sciforum.net/user/submission/create/503
> In any case, they deserve our support: let us help promote their 1st
> International Electronic Conference on Information.
> ----------------------------------------------------------------------------------------
>
>
> Then, answering to Lou (and acknowledging other philosophical arguments),
> there is an additional point that could be relevant:  heterogeneity.
> Maybe I am wrong, but when I read the mssg below, my impression is that we
> are only considering a kind of homogeneous alphabets, that can grow via
> recursion, but that cannot go beyond the formal confines of that
> alphabet-world.
>
> Machine codes in computers (and the cascade of codes built upon them) are
> ultimately due to the physical heterogeneity of their processing
> architectures. I mean, CPU, ALU, Central memory, peripherics, etc. are
> structurally different and the strings of 0s and 1s circulating within the
> system do need codes (*addresses*) so that they can circulate via the
> central bus towards the specific component-architecture. This is the final
> meaning of computer codes: matching between heterogeneous processing
> architectures--and ascending upon multiple levels so that languages, etc.
> can be designed.
>
> In the biological world something similar occurs: we have sequential
> architectures (DNA & RNA) based on complementarity, structural
> architectures (membranes, cytoskeletons) based on identity, and a general
> "diluted" processing architecture (enzymes and proteins) based on
> supplementarity. Whatever function we may observe implies multiple ups and
> downs, back and forth, among these architectures and they need the
> recognition of quite specific motives arranged in well organized sets. Once
> the biological genetic code was in place, some complexity addicts
> (eukaryotes) progressively developed more and more codes & complex
> functions----and finally here we are. The final meaning of biological
> codes, like in computers, would be matching between heterogeneous
> architectures. About what agents helped in the code multiplication of
> eukaryotes, the response nowadays looks clear and clear: viruses and their
> complex retinue in the now internalized RNA world. See Luis Villarroel: *
> ex virus omnia.*
>
> So, there are formal, logical, philosophical, semiotic arguments to make
> about codes--OK, but if they do not consider this real world aspect of
> heterogeneity of processing architectures am afraid they will be of limited
> usefulness to approach the reliance of computers and living beings on
> codes.
>
> Best regards,
> --Pedro
>
> El 22/09/2021 a las 19:29, Louis Kauffman escribió:
>
> Dear Joseph,
>
> (I am sending this again without graphics so it can end up on fis.)
>
> The RD construction is very general, but we have articulated it with
> particular models.
>
> One starts with a domain where distinctions can be made and there is a
> notion of locality.
> In that domain one makes distinctions about given entities
> and replaces the entities by the corresponding signs of distinction.
> These signs amalgamate to become new entities to be distinguished at the
> next round.
>
> Lest this seem abstract, look again at the model.
> <RD.png>
> The sign = is an amalgamation of empty word on left and empty word on
> rght.
> The sign ] is amalgamation of empty word on left and  vertical bar | on
> rght.
> The sign [] is amalgamation of vertical bar | on left and  empty word on
> rght.
> The sign O is meant to be a box and so is an amalgamation of vertical bar
> on left and right.
>
> The point is that the alphabet arises by the amalgamations of previous
> distinctions and so new symbolic entities arise from the process of
> distinguishing by these rules.
> After the body of this email, I will show you how the two dimensional RD
> alphabet arises.
>
> This level of model includes notions of language and description in a very
> elementary formal framework.
> I have not included a logical language or a language that even begins to
> have self-reference and ordinary reference. Thus meta-levels and thinking
> about thinking are not fully reflected in this small model.
> But the action of the model gives one the opportunity to reflect on these
> larger issues. I am in the business of finding significant minimal
> models.
> These models are not going to be complete articulations of the whole
> situation of thinking about thinking or
> reflecting on reflecting. They are intended as ways to help thinking about
> that.
>
> Note also that the RD above engages in “mitosis” or “self-replication”. It
> does so without a reflective level. This is of interest
> for thinking about coding in biology and in thinking about what coding
> would mean in physical situations “below” biology.
>
> Let me give here another example: the audio-active sequences studied by
> John Horton Conway.
> 1
> 11 - read “one one” and it describes the line above.
> 21- read “two ones” and it describes the line above.
> 1211- read “one two, one one” and it describes the line above.
> 111221- read “three ones, two two’s, one one” and it describes the line
> above.
> 312211- read “one three, two two’s, one one” and it describes the line
> above.
> …
> This recursion is an example of "describing describing" and the coding
> issues are somewhat different from the RD.
> We retain locality of interaction and have a fixed alphabet that is less
> iconic. Counting is needed at the descriptive level.
> This recursion requires more structure to run, but it is very very
> interesting.
> Note that 22 is the only self-referential sequence.
>
> Note also that we could write nx —> xx…x (n x’s) meaning that nx describes
> xx…x.
> In the audio active line we would have
> xxxx…x
> nx
>
> as in
> 777
> 37.
>
> So we have nx —> xx…x
> and 2x —> xx
> and so
> 22 —> 22.
>
> This pattern fits into the whole of 20th century logic since Russell.
> Let me tender persuasions.
> Russell:  Rx = ~xx
> This is the definition of the Russell set if you take AB to mean “B is a
> member of A” and ~ is “not”.
> Then: RR = ~ RR is the Russell paradox.
> In this formalism, the Russell paradox becomes the production of a fixed
> point for negation.
>
> Church and Curry generalized this to an abstract formalism (lambda
> calculus) where they could write
> gx = F(xx) for an arbitrary F.
> Then
> gg = F(gg) and we produce a fixed point for F.
> This is exactly how we got to the self reference of 22 by
> 2x —> xx
> 22 —> 22
> where here equality is replaced  by reference.
>
> The notion of replacement of reference is integral to Goedelian
> self-refefrence.
> g ——> P(x) now interpreted as “g is the Goedel number of the proposition
> P(x) with free variable x.
> Then let #g be the Goedel number of P(g) so that
> #g —> P(g).
> Let the language be rich enough so that # is an operation in the language.
> h —> P(#x)
> Then
> #h—> P(#h)
> and P(#h) talks about its own Goedel number.
> Then with Goedel let ~B(x) mean that “there is no proof of the statement
> with Goedel number x.
> Then with
> h —> ~B(#x)
> #h —> ~B(#h)
> and we have produced the proposition ~B(#h) that asserts its own
> unprovability!
> This is the core of Goedel’s incompleteness Theorem.
>
> I hope you see that we have arrived Goedel’s Theorem on a track leading
> directly from the self-reference of 22, by way of the Russell Paradox.
> All this comes from the capacity of language to speak about language and
> thinking to think about thinking.
> Goedel in fact shows us that all formalisms that we build that are rich
> enough and are consistent will be incomplete.
> So there is no intent here to create complete formalisms.
> I want to look at how the simplest non trivial formalisms behave, and how
> even very similar ones such as the RD and the audio activity are related to
> each other and to
> the larger issues of reference, self reference  and the generation of such
> dialogues at all levels.
>
> Note also how small formalisms can summarize wide ideas.
> The von Neumann Universal Building Machine B acts as follows.
> B,x —> X,x.
> Give B a blueprint x and B will produce X (the entity described by the
> blueprint).
> Hence if b is the blueprint for B, then B can build itself!
> B,b —> B,b.
> This is another variant of 2x —> xx so 22—> 22.
>
> Another thing that happened in the 20th century is that everyone got
> frightened about Rx =~xx giving RR = ~ RR,
> and the story I am telling here of the central role of reference and
> self-reference is still not fully appreciated by mathematical practitioners
> such as
> economists and even physicists.
> Very best,
> Lou
>
>
>
> _______________________________________________
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> --
> -------------------------------------------------
> Pedro C. Marijuán
> Grupo de Bioinformación / Bioinformation Group
> pcmarijuan.iacs en aragon.eshttp://sites.google.com/site/pedrocmarijuan/
> -------------------------------------------------
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