[Fis] Fwd: A new discussion session; Self-Other in Biology
Loet Leydesdorff
loet at leydesdorff.net
Mon Dec 26 05:53:15 CET 2022
https://urldefense.com/v3/__https://leydesdorff.net/hertzberger/hetty/25dec22.pdf__;!!D9dNQwwGXtA!TwhH4Dtpds5jfSZ8XLpZ8dKzmgVaEUXzLLBoWnn8-_z68rVMr66jPqob3e6veMx6v1MTVxllUYaPGu2f5oE$
Dear colleagues, family, and frineds
Pleiase, find a pdf ile at the webpage above.
This file is in DUtch.
The reference is::
Leydesorff, L. (2022). „Herr Obersturmbahnführer, gestatten Sie daß Ich
rede?. (https://urldefense.com/v3/__https://leydesdorff.net/hertzberger/hetty/25dec22.pdf__;!!D9dNQwwGXtA!TwhH4Dtpds5jfSZ8XLpZ8dKzmgVaEUXzLLBoWnn8-_z68rVMr66jPqob3e6veMx6v1MTVxllUYaPGu2f5oE$ ), 39 pp.
Comments are most welcome in this stage:
Best, Loet
PS. Given a health condition, I am no longer able to read and write
emails without mistakes. Please, consider using the telephone or skype.
Best, Loet
---------------------------------------------------------------------------------------------
"The Evolutionary Dynamics of Discusive Knowledge"
<https://urldefense.com/v3/__https://link.springer.com/book/10.1007/978-3-030-59951-5__;!!D9dNQwwGXtA!TwhH4Dtpds5jfSZ8XLpZ8dKzmgVaEUXzLLBoWnn8-_z68rVMr66jPqob3e6veMx6v1MTVxllUYaPmgC-yRI$ >(Open Access)
Professor emeritus, University of Amsterdam
------ Original Message ------
>From "joe.brenner en bluewin.ch" <joe.brenner en bluewin.ch>
To pedroc.marijuan en gmail.com
Cc fis en listas.unizar.es
Date 12/25/2022 10:05:10 PM
Subject Re: [Fis] Fwd: A new discussion session; Self-Other in Biology
>Dear Pedro, Dear All,
>
>Christmas is not even over and already a fascinating disagreement! In
>my system, Gödel is closer to reality because incompleteness is a
>feature of reality. Fixed points look pretty inert to me, and in
>biology??
>
>I believe since I don't have all the skills needed to be sure that
>fixed points eliminate the need for recursive functions but you have
>just gotten rid of another, probably real mental process. Recursion and
>anticipation, using dynamic forms of information, are what mind is
>about.
>
>I don't claim that mine is the "right" handle. I just plead for it to
>humbly accompany the story from computer science.
>
>Thank you and Happy New Year!
>>----Original Message----
>>From : pedroc.marijuan en gmail.com
>>Date : 25/12/2022 - 21:42 (E)
>>To : fis en listas.unizar.es
>>Subject : [Fis] Fwd: A new discussion session; Self-Other in Biology
>>
>>-------- Mensaje reenviado --------
>>Asunto: Re: [Fis] A new discussion session; Self-Other in Biology
>>Fecha: Fri, 23 Dec 2022 09:31:53 +0100
>>De: guillaume.bonfante <guillaume.bonfante en loria.fr>
>>Para: Louis Kauffman <loukau en gmail.com>, Markose, Sheri
>><scher en essex.ac.uk>
>>CC: Pedro C. Marijuán <pedroc.marijuan en gmail.com>, fis
>><fis en listas.unizar.es>,
>>guillaume.bonfante en mines-nancy.univ-lorraine.fr<guillaume.bonfante en mines-nancy.univ-lorraine.fr>,
>>mikhail.prokopenko en sydney.edu.au<mikhail.prokopenko en sydney.edu.au>,
>>Neil Gershenfeld <neil.gershenfeld en cba.mit.edu>, Koonin, Eugene
>>(NIH/NLM/NCBI) [E] <koonin en ncbi.nlm.nih.gov>, Oron Shagrir
>><oron.shagrir en gmail.com>,
>>Noson en sci.brooklyn.cuny.edu<Noson en sci.brooklyn.cuny.edu>, Friston,
>>Karl <k.friston en ucl.ac.uk>, John Mattick <j.mattick en unsw.edu.au>
>>
>>
>>Dear all,
>>
>>End of the year, and now some spare time. As a computer scientist, in
>>my opinion, Goedel's Incompleteness Theorem is touchy but not the
>>right handle. As some of you mentioned below, I think that fix-points
>>are much more promising.
>>
>>They have various forms. They exist at every layer of the arithmetical
>>hierarchy (you don't need to implement recursive functions). So, a
>>very flexible tool.
>>
>>All the best,
>>
>>Guillaume
>>
>>
>>Le 05/12/2022 à 00:25, Louis Kauffman a écrit :
>>>Dear Sheri,
>>>It would indeed be very helpful to have a zoom conversation about
>>>these themes.
>>>Please let me know when you would be available to have it.
>>>We could start with an hour meeting and discussion and then perhaps
>>>extend to a second meeting with some presentations.
>>>Included below is a slide show of mine that is a bit cryptic but does
>>>summarize some points of view.
>>>I have downloaded the papers you indicated in your email and will
>>>read them now.
>>>Very best,
>>>Lou
>>>
>>>
>>>
>>>>On Dec 5, 2022, at 2:53 PM, Markose, Sheri < scher en essex.ac.uk>
>>>>wrote:
>>>>
>>>>Dear Louis, Pedro and All –
>>>>
>>>>I apologize again for not attending to the comments as soon as they
>>>>appear. Autumn term is my very busy teaching term. Also, one of the
>>>>reasons why I got waylaid is that I had to urgently send in my
>>>>external examiner review of a Thesis of Adam Svahn (University of
>>>>Sydney) on 25 Nov. I was free to invite folk who I have had some
>>>>convos with on this topic and may be interested in the Foundations
>>>>of Information Systems online forum as participants and potential
>>>>leads on topics… I do this somewhat belatedly, my apologies again.
>>>>
>>>>(i) The bulk of Adam Svahn’s work co-authored with
>>>>Mikhail Prokopenko (S & P) is already published and can be found
>>>>here
>>>>https://urldefense.com/v3/__https://doi.org/10.1162/artl_a_00370__;!!D9dNQwwGXtA!TwhH4Dtpds5jfSZ8XLpZ8dKzmgVaEUXzLLBoWnn8-_z68rVMr66jPqob3e6veMx6v1MTVxllUYaPheeRUxI$
>>>><https://urldefense.com/v3/__https://doi.org/10.1162/artl_a_00370__;!!D9dNQwwGXtA!R8lchYgfzUtRK_UvjczZjG4odrY4nCT90ap2vplSNdF7nmHYAjY30NMIkzAIZPRsIn5AxYjgQKn_X6p4BTG0vMTREdnb$>
>>>> and is relevant to our discussion. While we are still in the dark
>>>>about how the near universal genomic (ACGT/U) alphabets emerged, the
>>>>genome clearly manifests an unbroken chain of life with programs
>>>>encoded in these alphabets and their execution via gene expression
>>>>produce the somatic and phenotype identity of organisms. S & P share
>>>>objectives as those that I have given specifically re how
>>>>self-reference and negator operations known from Gödel (1931)
>>>>incompleteness theorems and undecidability thereof arise so the
>>>>software based genomic system is capable of endogenous novelty
>>>>production and evolvability.
>>>>
>>>>S& R give an interesting and plausible account of how RNA-push down
>>>>automata with their push and pop rules can produce limit cycle
>>>>dynamics or the extensively found repetitive motifs sometimes called
>>>>biological palindromes in the genome. They argue that a 2-stack
>>>>RNA-push down automata is necessary to produce reflexive structures
>>>>where the automata in addition to simply executing a program can use
>>>>the 2ndstack to reflect on codes and make changes to them.
>>>>
>>>>
>>>>(ii) Section 5 of S&P relates to undecidability as fixed
>>>>points of negation functions and has much in common Louis’s 15 Nov
>>>>email point 5 below ( I have scissored and pasted this in the email
>>>>trail below) on the ease with which self-negating Gödel sentences
>>>>can be created by logicians. However, biology unlike Gödel (and
>>>>other logicians) is not directly concerned about undecidability,
>>>>incompleteness, or whether a program halts. I have stuck my neck out
>>>>and said that Gödel machinery used by biology and the formidable
>>>>genomic self-referential general intelligence is to establish a hack
>>>>free agenda for the genome geared toward autonomous life.
>>>>
>>>>Thus, some further thought needs to be expended as to how the
>>>>negator operation naturally occurs in biology. I have stated it is
>>>>the bio malware or the viral software that Eugene Koonin et al have
>>>>said has been coextensive with life having provided the
>>>>copy/replicate program possibly in what the computer literature
>>>>calls Quines. The latter are distinct from online self-assembly of
>>>>somatic self which requires gene expression or machine execution as
>>>>in the ribosomal machines. To make out gene-codes that
>>>>self-assemble the organism have been changed/tampered with by
>>>>software of non-self other appears to be a pressing matter for
>>>>homeostasis which is clearly a bio-cybersecurity problem.
>>>>
>>>>(iii) The over 85% offline recording in the Thymic MHC
>>>>receptors of expressed genes in humans for example brings us to the
>>>>points made by Pedro in his 1 December email on Self and non-self
>>>>antigen recognition in Adaptive Immune System. Thank you Pedro for
>>>>the nugget of information of how the MHC receptors has two strips of
>>>> 8-10 amino acids residues for Class 1, mostly "self", and 13-18
>>>>amino acids residues for Class 2 for non-self. I did not know
>>>>this. I will read "Sensing the world and its dangers: An
>>>>evolutionary perspective in
>>>>neuroimmunology." By Aurora Krauset al. In, eLife 2021;10:e66706.
>>>>DOI: https://urldefense.com/v3/__https://doi.org/10.7554/eLife.66706__;!!D9dNQwwGXtA!TwhH4Dtpds5jfSZ8XLpZ8dKzmgVaEUXzLLBoWnn8-_z68rVMr66jPqob3e6veMx6v1MTVxllUYaP9-9QdGg$
>>>><https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=https*3a*2f*2fdoi.org*2f10.7554*2feLife.66706&c=E,1,mnuJARbiz5DP5j0H1X0ciBwcFLUNxlmdaZCNXX6tuWJ7oLj-36Vg9-Wauvxar1tDnTFYRaRF0eqlIxd2zzkL3LoskpUW1kBa2CHZaMqYUapU2iEi&typo=1__;JSUlJSU!!D9dNQwwGXtA!R8lchYgfzUtRK_UvjczZjG4odrY4nCT90ap2vplSNdF7nmHYAjY30NMIkzAIZPRsIn5AxYjgQKn_X6p4BTG0vN18TkB3$>.
>>>>
>>>> If you recall how the Recursive Fixed Point Theorem
>>>>which starts with a mirror mapping between online self-assembly
>>>>program execution, fg(g)) that have halted and create somatic
>>>>identity and the offline record of the
>>>> same in a 2- place function s (g, g) in the MHC
>>>>receptors creating the Thymic self. I say the first g from the left
>>>>in s (g, g) and changes thereof relate to what happens to self and
>>>>the second is self’s record of what
>>>> the other has done to self. So if the 2nd entry is
>>>>different from the first entry in s (g, g) it is off diagonal etc.
>>>>The non-self hostile other is a projection of self g ‘gene codes’
>>>>and those f ¬ ! which are reactive to the self g-
>>>> codes denoted as g¬. As we know an astronomic
>>>>number of potential indexes g¬ are generated by the RAG genes.
>>>>
>>>> How the immune system identifies a yet to happen
>>>>attack by a novel non-self antigen requires the first part of the
>>>>fix point of the latter generated in the Thymic T-cell receptors to
>>>>sync with those generated in the
>>>> the peripheral MHC receptors when the said
>>>>expressed genes are attacked (like the lung tissue etc) in real
>>>>time. The latter is experientially generated and while the former
>>>>is a spectacular case of predictive coding. So
>>>> unless the T-cell receptor has cloned the index of
>>>>the novel bio-malware in advance via V(D) J, the AIS will not be
>>>>recognize the biomalware should it attack. I have said fixed point
>>>>for the software/algorithm f ¬ ! requires
>>>> the full use of say Rogers Second Recursion Theorem
>>>>and the Gödel Sentence thereof, viz. far more machinery
>>>>self-referential structures than in the original Gödel (1931)
>>>>formats.
>>>>
>>>>(iv) Finally, there is the problem that the information
>>>>processing for advanced code based systems is one akin to Formal
>>>>Systems of Theorems and non-Theorems. For this Raymond Smullyan’s
>>>>book of the same name is what gave me the idea that a tight grip
>>>>will be exerted with all inference based recursive reductions and
>>>>Gödel Sentences when some potential negations to theorems viz. the
>>>>halting self-assembly gene codes that generate the organism, are in
>>>>the offing. This self-referential genomic blockchain distributed
>>>>ledger of the unbroken chain of life has similarities with manmade
>>>>BCDL, but latter are not self-referential with individual nodes
>>>>being able to self-report attacks.
>>>>
>>>>Louis, I would love to have a zoom chat with you as it will be great
>>>>to sound you out more. You are right about the mindboggling variants
>>>>of self-reference ….
>>>>Ditto for many others who I hope to be in touch with soon.
>>>>
>>>>Many thanks again for the great comments.
>>>>
>>>>All best
>>>>
>>>>Sheri
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>From: Pedro C. Marijuán <pedroc.marijuan en gmail.com>
>>>>Sent: 01 December 2022 13:03
>>>>To: Markose, Sheri <scher en essex.ac.uk>; Louis Kauffman
>>>><loukau en gmail.com>
>>>>Cc: fis <fis en listas.unizar.es>;
>>>>guillaume.bonfante en mines-nancy.univ-lorraine.fr
>>>>Subject: Re: [Fis] A new discussion session
>>>>
>>>>Dear Sheri, Lou, and all discussants,
>>>>
>>>>It is a pity that this excellent discussion has taken place in
>>>>complicated academic weeks, as it has been caught in a sort of
>>>>"punctuated equilibrium" of longer stasis than activities in our
>>>>evolutionary list. Well, I have a couple of very brief comments:
>>>>
>>>>First, emphasizing that one of the references in Youri's last
>>>>messages should be obligated reading for biologically interested
>>>>parties: "Sensing the world and its dangers: An evolutionary
>>>>perspective in
>>>>neuroimmunology." By Aurora Krauset al. In, eLife 2021;10:e66706.
>>>>DOI: https://urldefense.com/v3/__https://doi.org/10.7554/eLife.66706__;!!D9dNQwwGXtA!TwhH4Dtpds5jfSZ8XLpZ8dKzmgVaEUXzLLBoWnn8-_z68rVMr66jPqob3e6veMx6v1MTVxllUYaP9-9QdGg$
>>>><https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=https*3a*2f*2fdoi.org*2f10.7554*2feLife.66706&c=E,1,mnuJARbiz5DP5j0H1X0ciBwcFLUNxlmdaZCNXX6tuWJ7oLj-36Vg9-Wauvxar1tDnTFYRaRF0eqlIxd2zzkL3LoskpUW1kBa2CHZaMqYUapU2iEi&typo=1__;JSUlJSU!!D9dNQwwGXtA!R8lchYgfzUtRK_UvjczZjG4odrY4nCT90ap2vplSNdF7nmHYAjY30NMIkzAIZPRsIn5AxYjgQKn_X6p4BTG0vN18TkB3$>.
>>>>In this vein, I will follow with the argument that the multicellular
>>>>self is a composite, an association with a microbial consortium that
>>>>probably was the big evolutionary cause to create a defense system
>>>>of such a great complexity. The innate immune system would
>>>>represent the evolutionary learning about those dangers, with scores
>>>>of different components and pattern recognition strategies...
>>>>
>>>>And second, about the adaptive immune system, it is where the
>>>>ongoing mostly formal discussion would apply (can we agree with
>>>>that?). Then, it seems that the core of this adaptive immune branch
>>>>is the Major Histocompatibility Complex molecule (MHC). This MHC
>>>>molecules of two major classes are highly complex (polygenic and
>>>>polymorphic) and they are in charge of presenting to lymphocyte T
>>>>cells the protein fragments churned out from the proteosomes inside
>>>>cells (fragments of variable lenght: 8-10 amino acids residues for
>>>>Class 1, mostly "self", and 13-18 amino acids residues for Class 2,
>>>>mostly "non self"). Then, the thymus is in charge of deactivating
>>>>the T cells loaded with self stuff. My point is that the defense in
>>>>front of the non-self is based on indirect products of protein
>>>>translation. This causes me some uneasiness, as protein translation
>>>>(see Youri's presentation months ago) introduces a layer of extra
>>>>complexity, not to speak the processing via proteosomes. Further,
>>>>with just 10 or 12 amino acids can we faithfully ascertain
>>>>algorithmic non-self provenance??
>>>>
>>>>Well, Sheri is far more acknowledged with all this stuff. And
>>>>perhaps Lou can say something about the formal distinguishability of
>>>>10-12 aa.
>>>>Best--Pedro
>>>>
>>>>
>>>>
>>>>
>>>>From: Louis Kauffman loukau en gmail.com
>>>>Sent: 15 November 2022 23:02
>>>>To: Markose, Sheri scher en essex.ac.uk
>>>>Cc: "Pedro C. Marijuán" pedroc.marijuan en gmail.com; fis
>>>>fis en listas.unizar.es;
>>>>guillaume.bonfante en mines-nancy.univ-lorraine.fr
>>>>Subject: Re: [Fis] A new discussion session
>>>>
>>>>Sheri,
>>>>I will try to respond to your letter about the post Goedel
>>>>structures by first quoting the last part of my previous letter that
>>>>discusses Goedelian ideas from the point of view of fixed points.
>>>>My letter was quite long, and it is possible to not get to the
>>>>second half.
>>>>Note also that the first half is based on a referential situation g
>>>>—> F where #g ——> Fg is what I call the Indicative Shift of g —> F.
>>>>This is formal and does not assume anythng other than arrow
>>>>structure.
>>>>With g —> F# we have #g —> F#g making F#g refer to its own name.
>>>>There is more to say herd and references that I cannot send to the
>>>>list, so I will get a dropbox for it and further discussion later
>>>>today.
>>>>Best,
>>>>Lou K.
>>>>
>>>>##########
>>>>It is a very interesting question whether such encoding or such
>>>>multiple relationships to context occur in biology. Here are some
>>>>remarks.
>>>>
>>>>1. In biology is is NORMALLY the case that certain key structures
>>>>have multiple interpretations and uses in various contexts.
>>>>The understanding of such multiple uses and the naming of them
>>>>requires an observer of the biology. Thus we see the action of a
>>>>cell membrane and we see the action of mitosis, and so on.
>>>>
>>>>2. There are implicit encodings in biology such as the sequence
>>>>codes in DNA and RNA and their unfoldment. To what extent do they
>>>>partake of the properties of Goedel coding?
>>>>
>>>>3. The use of the Goedel coding in the Incompleteness theorem
>>>>depends crucially on the relationship of syntax and semantic in the
>>>>formal system and in the mathematician’s interpretation of the
>>>>workings of that system. The Goedel argument depends upon the formal
>>>>system S being seen as a mathematical object that itself can be
>>>>studied for its properties and behavior.
>>>>When we speak of the truth of G, we are speaking of our assessment
>>>>of the possible behaviour of S, given its consistency. We are
>>>>reasoning about S just as Euclid reasons about the structure of
>>>>right triangle.
>>>>
>>>>4. In examining biological structures we take a similar position and
>>>>reason about what we know about them. Sufficiently complex
>>>>biological structures can be seen as modeled by certain logical
>>>>formal systems.
>>>>And then Goedelian reasoning can be applied to them. This can even
>>>>be extended to ourselves. Suppose that I am modeled correctly in my
>>>>mathematical reasoning by a SINGLE CONSISTENT FORMAL SYSTEM S.
>>>>Then “I” can apply the above proof of Goedel’s Therem to S and
>>>>deduce that G cannot be proven by S. Thus “I” have exceeded the
>>>>capabilities of S. Therefore it is erroneous to assume that my
>>>>mathematical reasoning is encapsulated by a single formal system S.
>>>>If I am a formal system, that system must be allowed to grow in
>>>>time. Such reasoning as this is subtle, but the semantics of the
>>>>relationship of mathematicians and the formal systems that they
>>>>study is subtle and when biology is brought in the whole matter
>>>>becomes exceedingly interesting.
>>>>
>>>>5. We man not need numbers to have these kinds of relationships. And
>>>>example is the Smullyan Machine that prints sequences of symbols
>>>>from the alphabet {~,P,R} on a tape. Sequences that begin with
>>>>P,~P,PR and ~PR are regarded as meaningful, with the meanings:
>>>>PX: X can be printed.
>>>>~PX: X cannot be printed.
>>>>PRX: XX can be printed.
>>>>~PRX: XX cannot be printed.
>>>>Here X is any string of the symbols {~,P,R}.
>>>>Thus PR~~P means that XX can be printed where X = ~~P. Thus PR~~P
>>>>means that ~~P~~P can be printed.
>>>>By printed we mean on one press of the button on the Machine, a
>>>>string of characters is printed.
>>>>IT IS ASSUMED THAT THE SMULLYAN MACHINE ALWAYS TELLS THE TRUTH WHEN
>>>>IT PRINTS A MEANINGFUL STATEMENT.
>>>>Then we have the
>>>>
>>>>Theorem. There are meaningful true strings that the Smullyan Machine
>>>>cannot print.
>>>>
>>>>This is a non-numerical analog of the Goedel Theorem. And the string
>>>>that cannot be printed is G = ~PR~PR.
>>>>For you see that G is meaningful and since G = ~PRX, G says that XX
>>>>cannot be printed. But X = ~PR and XX = ~PR~PR = G. So G says that G
>>>>cannot be printed.
>>>>If the machine were to print G, it would lie. And the machine does
>>>>not lie.
>>>>Therefore G is unprintable.
>>>>But this is what G says.
>>>>So we have established the truth of G and proved the Theorem.
>>>>
>>>>6. Examine this last paragraph 5. The Machine is like an organism
>>>>with a limitation. This limitation goes through the semantics of
>>>>reference. ~PRX refers to XX and so can refer to itself if we take X
>>>>= ~PR. ~PX refers to X and cannot refer to itself since it is longer
>>>>than X. In biological coding the DNA code is fundamentally smaller
>>>>or equal to the structure to which it refers.
>>>>Thus the self-reproduction of the DNA is possible since DNA = W+C
>>>>the convention of the Watson and Crick strand and each of W and C
>>>>can by themselves engage in an action to encode, refer to, the other
>>>>strand. W can produce a copy of C in the form W+C and C can produce
>>>>a copy of W in the form W+C each by using the larger environment.
>>>>Thus W+C refers to itself, reproduces itself by a method of encoding
>>>>quite similar to the self reference of the Smullyan Machine.
>>>>
>>>>7. Von Neuman devised a machine that can build itself. B is the von
>>>>Neuman machine and B.x —> X,x where x is the plan or blueprint or
>>>>code for and entity X. B builds X with given the blueprint x.
>>>>Then we have B,b —> B,b where b is the blueprint for B. B builds
>>>>itself from its own blueprint. I hope you see the analogy with the
>>>>Goedel code.
>>>>
>>>>8. I will stop here. The relationships with biology are very worth
>>>>discussing.
>>>>Before stopping it is worth remarking that the Maturana Uribe Varela
>>>>autopoeisis is an example of a system arising into a form of
>>>>self-reference that has a lifetime due to the probabilisitic
>>>>dynamics of its process.
>>>> ###############
>>>>Best,
>>>>Lou Kauffman
>>>>
>>>>
>>>>
>>>>El 15/11/2022 a las 21:19, Markose, Sheri escribió:
>>>>>Dear Louis, dear Colleagues -
>>>>>
>>>>>Louis has given an excellent exposition of Gödel Numbering (g.n)
>>>>>(your point number 2 on coding and semantics is giving me food for
>>>>>thought) , giving example of prime factorization and also of Gödel
>>>>>Sentence as one that states its own unprovability. Unlike
>>>>>statements like "this is false", GS is not paradoxical and in a
>>>>>consistent system it is a theorem with a constructive g.n. The
>>>>>latter in terms of the prime factorization format, it is indeed a
>>>>>Hilbert 10 Diophantine equation with no integer solutions. A
>>>>>remarkable achievement in maths, considering Gödel was only 23
>>>>>years of age .... But what has this got to do with Biology and
>>>>>novelty production, the objectives of the my FIS discussion ?
>>>>>
>>>>>In view of brevity and also urged by Pedro, I dropped a couple of
>>>>>paragraphs in my FIS kick off submission as to why we need to
>>>>>exceed Gödel (1931) and couch the Gödel Incompleteness Results and
>>>>>the Gödel Sentence with a fuller understanding of algorithms as
>>>>>encoded instructions and as machine executable codes, of the notion
>>>>>of recursive enumeration (re) and re sets that was developed in the
>>>>>Emil Post (1944). I hope Louis Kauffman can comment on the the
>>>>>application of the fuller Gödel-Turing -Post-Rogers framework
>>>>>mentioned in my FIS note and in my papers cited there.
>>>>>
>>>>>1. I have found the following statement by Joel Hamkins ( :
>>>>>https://urldefense.com/v3/__http://jdh.hamkins.org/wp-content/uploads/A-review-of-several-fixed-point-theorems-1.pdf__;!!D9dNQwwGXtA!TwhH4Dtpds5jfSZ8XLpZ8dKzmgVaEUXzLLBoWnn8-_z68rVMr66jPqob3e6veMx6v1MTVxllUYaPJEFRRO0$
>>>>><https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=http*3a*2f*2fjdh.hamkins.org*2fwp-content*2fuploads*2fA-review-of-several-fixed-point-theorems-1.pdf&c=E,1,bKIlk9p4sIB5v1zLhbA_VCdX_aoMSPljj6KZdLjCesxOjPwYqUF5PkC4wqvoWq0qqGndGHjZ6ELzpZ8IhqbUDEGNINdm7Da4GNcSgCn3k0us&typo=1__;JSUlJSUl!!D9dNQwwGXtA!R8lchYgfzUtRK_UvjczZjG4odrY4nCT90ap2vplSNdF7nmHYAjY30NMIkzAIZPRsIn5AxYjgQKn_X6p4BTG0vHnETe5i$>
>>>>>) useful as it makes an important observation that the original
>>>>>Gödel (1931) framework permits an encodable proposition to make
>>>>>statements about itself while Second Recursion Theorems (SRT) also
>>>>>called Fixed Point Theorems are needed “to construct
>>>>>programs/algorithms that refer to themselves”. The terms programs
>>>>>and algorithms will be used interchangeably.
>>>>>
>>>>>I choose Rogers Fixed Point Theorem of (total) computable functions
>>>>>starting with the staple I have already indicated Diag (g) (RHS of
>>>>>(8) below) is what Neil Gerschenfeld calls ribosomal self-assembly
>>>>>machines in gene expression where the program g builds the machine
>>>>>that runs g.
>>>>>
>>>>>
>>>>>II. The first requirement of a system to identify Fixed Points viz.
>>>>>self-referential constructions of algorithms/programs is (8) viz to
>>>>>identify what function/algorithm has altered the Diag (g).
>>>>>
>>>>>
>>>>><image001.png>
>>>>>
>>>>>When online gene expression takes place on RHS of (8), viz. these
>>>>>programs have halt commands and builds the somatic and phenotype
>>>>>identity of vertebrates online, the offline record of this is made
>>>>>in the Thymus that can not only represent the Thymic/immune self
>>>>>but also concatenate changes thereof.
>>>>>
>>>>>I have suggested that the Adaptive Immune System and the Mirror
>>>>>Neuron System have these structures in (8). And the domain of
>>>>>self-halting machines as in (8) are the Theorems of the system and
>>>>>a subset of Post (1944) Creative Set. The non-Theorems have codes
>>>>>say g¬ which cannot halt in a formal system that is consistent.
>>>>>To my mind, the embodiment via the physical self being
>>>>>self-assembled and an offline record of this on LHS of (8) is what
>>>>>fuses syntax and semantics.
>>>>>
>>>>>II. Once, (8) is in place, the Adaptive immune system has to
>>>>>identify novel negation software function f¬! of non-self
>>>>>antigens which is an uncountable infinite possibilities. Hence the
>>>>>close to astronomic search with V(D) J of 10 20 – 10 30 ) of
>>>>>non-self antigens that can hijack the self- assembly machines as
>>>>>recorded on RHS of (8). Only from knowledge of self can the
>>>>>hostile other, in the case of the AIS, be identified.
>>>>>
>>>>>
>>>>>III. Roger Fixed Point assures us that the indexes of the fixed
>>>>>point for f¬! be generated. I have cced Guillame Bonfante who I
>>>>>think was among the first (with coauthors, 2006) to suggest how SRT
>>>>>can be used to identify computer viruses. But they do not use the
>>>>>full force of Self-Ref and Self -Rep and only implicitly use Post
>>>>>Creative and Productive Sets. The index of the Godel Sentence for
>>>>>the fixed point will endogenously lie outside of Post listable or
>>>>>recusively enumerable set for Theorems and known non-Theorems.
>>>>>
>>>>>IV. From these Gödel Sentences produced in the immune-cognitive
>>>>>systems, the explicit use of Post (1944) Theorems indicates how
>>>>>novel antibodies cannot be produced in the absence of the Gödel
>>>>>Sentence which allows a biotic element to self-report it is under
>>>>>attack.
>>>>>
>>>>>V. In conclusion, while it has become fashionable for some like
>>>>>Jurgen Schmidhuber to claim that there can be endogenous self
>>>>>improving recursive novelty (he calls them Gödel machines) , the
>>>>>Gödel Logic says that the original theorems and self-codes are kept
>>>>>unchanged/hack free and novelty is produced only in response to
>>>>>adversarial attacks of self codes. So the AIS story is somatic
>>>>>hypermutation so that nothing in the genome changes. As to how the
>>>>>germline itself changes, needs more investigation, in Biosystems
>>>>>paper, I suggest something very briefly.
>>>>>
>>>>>So thankyou all again for your in depth comments and interest.
>>>>>
>>>>>Best Regards
>>>>>
>>>>>Sheri
>>>>>
>>>>>-----Original Message-----
>>>>>From: Fis < fis-bounces en listas.unizar.es> On Behalf Of Louis
>>>>>Kauffman
>>>>>Sent: 08 November 2022 00:13
>>>>>To: "Pedro C. Marijuán" < pedroc.marijuan en gmail.com>
>>>>>Cc: fis < fis en listas.unizar.es>
>>>>>Subject: Re: [Fis] A new discussion session
>>>>>
>>>>>CAUTION: This email was sent from outside the University of Essex.
>>>>>Please do not click any links or open any attachments unless you
>>>>>recognise and trust the sender. If you are unsure whether the
>>>>>content of the email is safe or have any other queries, please
>>>>>contact the IT Helpdesk.
>>>>>
>>>>>Dear Pedro,
>>>>>Here are some comments about Goedel numbering and coding.
>>>>>
>>>>>It is interesting to think about Goedel numbering in a biological
>>>>>context.
>>>>>Actually we are talking about how a given entity has semantics that
>>>>>can vary from context to context.
>>>>>It is not simply a matter of assigning a code number. If g —> F is
>>>>>the relation of a Goedel number g to a statement F, then we have
>>>>>two contexts for F.
>>>>>1. F as a well formed formula in a formal system S.
>>>>>2. g as a number in either a number system for an observer of S or
>>>>>g as a number in S, but g, as a representative for F can be
>>>>>regarded in the system S with the meanings so assigned.
>>>>>Thus we have produced by the assignment of Goedel numbers a way for
>>>>>a statement F to exist in the semantics of more than one context.
>>>>>This is the key to the references and self-references of the
>>>>>Goedelian situations.
>>>>>
>>>>>Lets look at this more carefully. Recall that there is a formal
>>>>>system S and that to every well formed formula in S, there is a
>>>>>code number g = g(S). The code number can be produced in many ways.
>>>>>For example, one can assign different index numbers n(X) to each
>>>>>distinct generating symbol in S. Then with an expression F regarded
>>>>>as an ordered string of symbols, one can assign to F the product of
>>>>>the prime numbers, in their standard order, with exponents the
>>>>>indices of the sequence of characters that compose F. For example,
>>>>>g(~ x^2 = 2) = 2^{n(~)} 3^{n(x)}5^{n(^)}7^{n(2)}11^{n(=)}13^{n(2)}.
>>>>>From such a code, one can retrieve the original formula in a unique
>>>>>way.
>>>>>The system S is a logical system that is assumed to be able to
>>>>>handle logic and basic number theory. Thus it is assumed that S can
>>>>>encode the function g: WFFS(S) —> N where N denotes the natural
>>>>>numbers.
>>>>>And S can decode a number to find the corresponding expression as
>>>>>well. It is assumed that S as a logical system, is consistent.
>>>>>
>>>>>With this backgound, let g —> F denote the condition that g = g(F).
>>>>>Thus I write a reference g —> F for a mathematical discussion of S,
>>>>>to indicate that g is the Goedel number of F.
>>>>>
>>>>>Now suppose that F(x) is a formula in S with a free variable x.
>>>>>Free variables refer to numbers. Thus if I write x^2 = 4 then this
>>>>>statement can be specialized to 2^2 = 4 with x =2 and the
>>>>>specialization is true.
>>>>>Or I can write 3^2 = 4 and this is a false statement. Given F(x)
>>>>>and some number n, I can make a new sentence F(n).
>>>>>Now suppose that
>>>>>g —> F(x).
>>>>>Then we can form F(g) and this new statement has a Goedel number.
>>>>>Let #g denote the Goedel number of F(g).
>>>>>#g —> F(g).
>>>>>This # is a new function on Goedel numbers and also can be encoded
>>>>>in the system S. I will abbreviate the encoding into S by writing
>>>>>#n for appropriate numbers n handled by S.
>>>>>Then we can consider
>>>>>F(#x) and it has a Goedel number
>>>>>h —> F(#x)
>>>>>And we can shift that to
>>>>>#h —> F(#h).
>>>>>This is the key point.
>>>>>Now we have constructed a number #h so that F(#h) discusses its own
>>>>>Goedel number.
>>>>>
>>>>>This construction allows the proof of the Goedel Incompleteness
>>>>>Theorem via the sentence B(x) that states
>>>>>B(x) = “The statement with Goedel number x is provable in S.”
>>>>>(This can also be encoded in S.)
>>>>>
>>>>>We then construct
>>>>>h—> ~B(#x)
>>>>>and
>>>>>#h —> ~B(#h)
>>>>>and obtain the statement
>>>>>G= ~B(#h).
>>>>>G states the unprovability of the Goedel decoding of #h.
>>>>>But the Goedel decoding of #h is the statement G itself.
>>>>>Thus G states its own unprovability.
>>>>>Therefore, S being consistent, cannot prove G.
>>>>>
>>>>>By making these arguments we have have proved that G cannot be
>>>>>proved by S.
>>>>>Thus we have shown that G is in fact true.
>>>>>We have shown that there are true statements in number theory
>>>>>unprovable by system S..
>>>>>##########################
>>>>>
>>>>>The above is a very concise summary of the proof of Goedel’s
>>>>>Incompleteness Theorem, using Goedel number encoding.
>>>>>
>>>>>It is a very interesting question whether such encoding or such
>>>>>multiple relationships to context occur in biology. Here are some
>>>>>remarks.
>>>>>
>>>>>1. In biology is is NORMALLY the case that certain key structures
>>>>>have multiple interpretations and uses in various contexts.
>>>>>The understanding of such multiple uses and the naming of them
>>>>>requires an observer of the biology. Thus we see the action of a
>>>>>cell membrane and we see the action of mitosis, and so on.
>>>>>
>>>>>2. There are implicit encodings in biology such as the sequence
>>>>>codes in DNA and RNA and their unfoldment. To what extent do they
>>>>>partake of the properties of Goedel coding?
>>>>>
>>>>>3. The use of the Goedel coding in the Incompleteness theorem
>>>>>depends crucially on the relationship of syntax and semantic in the
>>>>>formal system and in the mathematician’s interpretation of the
>>>>>workings of that system. The Goedel argument depends upon the
>>>>>formal system S being seen as a mathematical object that itself can
>>>>>be studied for its properties and behavior.
>>>>>When we speak of the truth of G, we are speaking of our assessment
>>>>>of the possible behaviour of S, given its consistency. We are
>>>>>reasoning about S just as Euclid reasons about the structure of
>>>>>right triangle.
>>>>>
>>>>>4. In examining biological structures we take a similar position
>>>>>and reason about what we know about them. Sufficiently complex
>>>>>biological structures can be seen as modeled by certain logical
>>>>>formal systems.
>>>>>And then Goedelian reasoning can be applied to them. This can even
>>>>>be extended to ourselves. Suppose that I am modeled correctly in my
>>>>>mathematical reasoning by a SINGLE CONSISTENT FORMAL SYSTEM S.
>>>>>Then “I” can apply the above proof of Goedel’s Therem to S and
>>>>>deduce that G cannot be proven by S. Thus “I” have exceeded the
>>>>>capabilities of S. Therefore it is erroneous to assume that my
>>>>>mathematical reasoning is encapsulated by a single formal system S.
>>>>>If I am a formal system, that system must be allowed to grow in
>>>>>time. Such reasoning as this is subtle, but the semantics of the
>>>>>relationship of mathematicians and the formal systems that they
>>>>>study is subtle and when biology is brought in the whole matter
>>>>>becomes exceedingly interesting.
>>>>>
>>>>>5. We man not need numbers to have these kinds of relationships.
>>>>>And example is the Smullyan Machine that prints sequences of
>>>>>symbols from the alphabet {~,P,R} on a tape. Sequences that begin
>>>>>with P,~P,PR and ~PR are regarded as meaningful, with the meanings:
>>>>>PX: X can be printed.
>>>>>~PX: X cannot be printed.
>>>>>PRX: XX can be printed.
>>>>>~PRX: XX cannot be printed.
>>>>>Here X is any string of the symbols {~,P,R}.
>>>>>Thus PR~~P means that XX can be printed where X = ~~P. Thus PR~~P
>>>>>means that ~~P~~P can be printed.
>>>>>By printed we mean on one press of the button on the Machine, a
>>>>>string of characters is printed.
>>>>>IT IS ASSUMED THAT THE SMULLYAN MACHINE ALWAYS TELLS THE TRUTH WHEN
>>>>>IT PRINTS A MEANINGFUL STATEMENT.
>>>>>Then we have the
>>>>>
>>>>>Theorem. There are meaningful true strings that the Smullyan
>>>>>Machine cannot print.
>>>>>
>>>>>This is a non-numerical analog of the Goedel Theorem. And the
>>>>>string that cannot be printed is G = ~PR~PR.
>>>>>For you see that G is meaningful and since G = ~PRX, G says that XX
>>>>>cannot be printed. But X = ~PR and XX = ~PR~PR = G. So G says that
>>>>>G cannot be printed.
>>>>>If the machine were to print G, it would lie. And the machine does
>>>>>not lie.
>>>>>Therefore G is unprintable.
>>>>>But this is what G says.
>>>>>So we have established the truth of G and proved the Theorem.
>>>>>
>>>>>6. Examine this last paragraph 5. The Machine is like an organism
>>>>>with a limitation. This limitation goes through the semantics of
>>>>>reference. ~PRX refers to XX and so can refer to itself if we take
>>>>>X = ~PR. ~PX refers to X and cannot refer to itself since it is
>>>>>longer than X. In biological coding the DNA code is fundamentally
>>>>>smaller or equal to the structure to which it refers.
>>>>>Thus the self-reproduction of the DNA is possible since DNA = W+C
>>>>>the convention of the Watson and Crick strand and each of W and C
>>>>>can by themselves engage in an action to encode, refer to, the
>>>>>other strand. W can produce a copy of C in the form W+C and C can
>>>>>produce a copy of W in the form W+C each by using the larger
>>>>>environment. Thus W+C refers to itself, reproduces itself by a
>>>>>method of encoding quite similar to the self reference of the
>>>>>Smullyan Machine.
>>>>>
>>>>>7. Von Neuman devised a machine that can build itself. B is the von
>>>>>Neuman machine and B.x —> X,x where x is the plan or blueprint or
>>>>>code for and entity X. B builds X with given the blueprint x.
>>>>>Then we have B,b —> B,b where b is the blueprint for B. B builds
>>>>>itself from its own blueprint. I hope you see the analogy with the
>>>>>Goedel code.
>>>>>
>>>>>8. I will stop here. The relationships with biology are very worth
>>>>>discussing.
>>>>>Before stopping it is worth remarking that the Maturana Uribe
>>>>>Varela autopoeisis is an example of a system arising into a form of
>>>>>self-reference that has a lifetime due to the probabilisitic
>>>>>dynamics of its process.
>>>>>
>>>>>Very best,
>>>>>Lou Kauffman
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>_______________________________________________
>>>>>Fis mailing list
>>>>>Fis en listas.unizar.es
>>>>>https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=http*3a*2f*2flistas.unizar.es*2fcgi-bin*2fmailman*2flistinfo*2ffis&c=E,1,1A1lgz03IPLQ2hs74kfiKoMaeMUB45427CkA4or9aZPmd25ZxHPE88KK0k9wHh7-Un8A9g25n5WMXHIu8yhAyMhiouezvcso3GGs3inouA,,&typo=1__;JSUlJSUlJQ!!D9dNQwwGXtA!TwhH4Dtpds5jfSZ8XLpZ8dKzmgVaEUXzLLBoWnn8-_z68rVMr66jPqob3e6veMx6v1MTVxllUYaPA_uS6GI$
>>>>><https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=http*3a*2f*2flistas.unizar.es*2fcgi-bin*2fmailman*2flistinfo*2ffis&c=E,1,1A1lgz03IPLQ2hs74kfiKoMaeMUB45427CkA4or9aZPmd25ZxHPE88KK0k9wHh7-Un8A9g25n5WMXHIu8yhAyMhiouezvcso3GGs3inouA,,&typo=1__;JSUlJSUlJQ!!D9dNQwwGXtA!R8lchYgfzUtRK_UvjczZjG4odrY4nCT90ap2vplSNdF7nmHYAjY30NMIkzAIZPRsIn5AxYjgQKn_X6p4BTG0vHlkTv5Q$>
>>>>>----------
>>>>>INFORMACIN SOBRE PROTECCIN DE DATOS DE CARCTER PERSONAL
>>>>>
>>>>>Ud. recibe este correo por pertenecer a una lista de correo
>>>>>gestionada por la Universidad de Zaragoza.
>>>>>Puede encontrar toda la informacin sobre como tratamos sus datos en
>>>>>el siguiente enlace:
>>>>>https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=https*3a*2f*2fsicuz.unizar.es*2finformacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas&c=E,1,fozeJ_L1c5tT22-_XAnl69C5WGhrrENGO-y2mO0uH3X4Bbm3EnwS5CaEussDHCR05GDKiVPAM9G4jQaY0kVhqsc4vdv55TdLJ2956rnsNTuETjVx&typo=1__;JSUlJQ!!D9dNQwwGXtA!TwhH4Dtpds5jfSZ8XLpZ8dKzmgVaEUXzLLBoWnn8-_z68rVMr66jPqob3e6veMx6v1MTVxllUYaPdiobMug$
>>>>><https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=https*3a*2f*2fsicuz.unizar.es*2finformacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas&c=E,1,fozeJ_L1c5tT22-_XAnl69C5WGhrrENGO-y2mO0uH3X4Bbm3EnwS5CaEussDHCR05GDKiVPAM9G4jQaY0kVhqsc4vdv55TdLJ2956rnsNTuETjVx&typo=1__;JSUlJQ!!D9dNQwwGXtA!R8lchYgfzUtRK_UvjczZjG4odrY4nCT90ap2vplSNdF7nmHYAjY30NMIkzAIZPRsIn5AxYjgQKn_X6p4BTG0vJLaKpZp$>
>>>>>Recuerde que si est suscrito a una lista voluntaria Ud. puede darse
>>>>>de baja desde la propia aplicacin en el momento en que lo desee.
>>>>>https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=http*3a*2f*2flistas.unizar.es&c=E,1,3TvXH92hrTfzt-a8xmVthnhgYDIEoQe6-G0P6rC6QRkjfvtNsCmkhdLTIB3yp7fRPc9B_8iQu5fWOkBGz-j3blB0p3sUtmf6XMK2hwJsC8gB1kGLD5vipYwnBGfi&typo=1__;JSUl!!D9dNQwwGXtA!TwhH4Dtpds5jfSZ8XLpZ8dKzmgVaEUXzLLBoWnn8-_z68rVMr66jPqob3e6veMx6v1MTVxllUYaP47puIqs$
>>>>><https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=http*3a*2f*2flistas.unizar.es&c=E,1,3TvXH92hrTfzt-a8xmVthnhgYDIEoQe6-G0P6rC6QRkjfvtNsCmkhdLTIB3yp7fRPc9B_8iQu5fWOkBGz-j3blB0p3sUtmf6XMK2hwJsC8gB1kGLD5vipYwnBGfi&typo=1__;JSUl!!D9dNQwwGXtA!R8lchYgfzUtRK_UvjczZjG4odrY4nCT90ap2vplSNdF7nmHYAjY30NMIkzAIZPRsIn5AxYjgQKn_X6p4BTG0vDDD0K5c$>
>>>>>----------
>>>>
>>>>
>>>>
>>>><~WRD0001.jpg>
>>>><https://urldefense.com/v3/__https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient__;!!D9dNQwwGXtA!R8lchYgfzUtRK_UvjczZjG4odrY4nCT90ap2vplSNdF7nmHYAjY30NMIkzAIZPRsIn5AxYjgQKn_X6p4BTG0vNvQg6vb$>
>>>>Libre de virus.https://urldefense.com/v3/__http://www.avast.com__;!!D9dNQwwGXtA!TwhH4Dtpds5jfSZ8XLpZ8dKzmgVaEUXzLLBoWnn8-_z68rVMr66jPqob3e6veMx6v1MTVxllUYaP4AxzeY8$
>>>><https://urldefense.com/v3/__https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient__;!!D9dNQwwGXtA!R8lchYgfzUtRK_UvjczZjG4odrY4nCT90ap2vplSNdF7nmHYAjY30NMIkzAIZPRsIn5AxYjgQKn_X6p4BTG0vNvQg6vb$>
>>>>
>>>
>>
>>
>
>
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