Self-Reference (and its relative Absence) as a Fundamental Issue

  • Self-Reference (and its relative Absence) as a Fundamental Issue

    Posted by Gary on December 12, 2023 at 9:23 pm

    I have recently been re-reading ‘The Laws of Form’ (LofF) by George Spencer Brown (GSB) and papers related to it, and thinking a lot about ‘reentry into the form’ and ‘self-reference.’ It seems to me that we might make a useful distinction between left and right hemispheres, in this general context. With regard to the left hemisphere, with its connection to ‘Chronos’ (ie. digital time that is fundamentally discontinuous), and the way it relates to time as a sequence of distinct, separate ‘frames’, one might conclude the distinct lacking of the capacity for continuous self-reference and thus, in its nominalistic focus on making distinctions (ie. ‘indicating’) via focal attention between what ‘is’ and what ‘is not’, it would be having real problems with antimonies and paradoxes like the Russellian ‘Liar Paradox’, and, being mired in language-encoded thought, get ‘stuck’ in the binary logic that sees everything as either one pole or the other. This is the nature of Charles Sanders Peirce’s category of ‘Secondness’ which he called ‘Necessitarianism’. For the left hemisphere, classical logic with the Law of Excluded Middle and the Law of NonContradiction in full effect. In this context, antimonies are fundamentally unresolvable and their ‘poles’ are incommensurable. There is no possibility of Peircean ‘Thirdness’ or ‘mediation’. This would correspond to the first ten chapters of LofF in which GSB develops his ‘calculus of indication’ based on the act of distinction. Which is something the left hemisphere is good at. One might imagine this response of the left hemisphere, in its dream of achieving absolute certainty, to a posed antimony between two diametrically opposing interpretations of a statement like ‘This statement is FALSE’: “Give me a break! This is my worst nightmare… If it is True then it is False (A), and if it is False then it is True (B). So now: which is it? It has to be one or the other!…. HELP!!!” Russell got to this point and threw in the towel along with Whitehead in their approach to analytical mathematics. It is clearly a ‘dead end’. Not so, says GSB in Chapter 11 in which, in introducing ‘Equations of the Second Degree’ in his Calculus of Indication, he runs into a similar paradox in which the unmarked state is equal to the marked state (E3, p 48). What to do? GSB engages his right hemisphere and comes up with a solution: Reentry. An ‘Imaginary state’ of the form which is neither marked nor unmarked but BOTH. And TIME. So that now alternation is possible. Which now allows for an oscillation between the two poles opening up the possibility of mediation. He calls this, in Chapter 12 title, ‘Re-entry into the Form.’ This is the ‘magic sauce’ or the ‘super-power; that the Right Hemisphere brings to the situation. And this possibility of continuous self-reference, or–as Robert Rosen in his relational biology would call the underlying feature, ‘closed causal loops’–is THE characteristic that differentiates living ‘organisms’ from fabricated ‘mechanisms’. It is the central constant factor which may well connect all of the natural universe together as the underpinning of ‘primary consciousness’–as distinguished from the ‘meta-consciousness’ that the reflective ability that the left hemisphere brings to the table by way of language providing the human species-specific capacity for communication regarding what it feels like to be a conscious creature. So we benefit very significantly from this ‘super-power’ as well.

    But what is the primary ‘super-power’? The capacity to observe and reflect or the capacity to experience directly? The capacity of the inspecting spectator or of the performing actor?

    With regard to the centrality of continuous self-reference in the autonomy of living, self-sustaining organisms, Francisco Varela pushed the idea further into a full calculus of self-reference based on GSB’s fundamental insight…


    So, there are two contributing elements to human understanding: the ‘line’ and the ‘circle’. The first being in a dimension of 1 and the second being in a dimension of 2. The ‘line’ being left hemispheric, and the ‘circle’ being right hemispheric. And what is necessary is a way to mediate between these two fundamental operational structures–to translate between them. So that they can keep each other fully informed. But how do you compress dimension 2 into dimension 1 and vice versa? Holographic representation.


    Niels Hoffmann replied 3 weeks, 2 days ago 3 Members · 11 Replies
  • 11 Replies
  • sjahari hollands

    December 14, 2023 at 8:06 pm

    Interesting Post. It seems to me that we are in a continuous dance between the 1 and the 2 and that we find truth, beauty, creativity when the two are in balance, toggling back and forth. The actor on stage is totally in the present moment, while simultaneously having the script tucked in there somewhere in the background.

    • Gary

      December 25, 2023 at 6:37 pm

      Yes, I fully agree. Both are necessary for survival but the circle takes precedence over the line. Self-reference is fundamental and necessary for the functioning of the organism.

      • Gary

        December 25, 2023 at 7:26 pm

        What is a key issue is the requirement for the use of imaginary numbers in addition to real numbers (ie. ‘complex‘ numbers) in the mathematical modeling of the dynamics of a self-referential organism (see seminal paper by Francisco Varela titled ‘A Calculus of Self-Reference’), in G Spencer-Brown’s ‘Laws of Form‘ to allow for ‘Re-entry into the Form‘ (ie. self-reference) in the description of a calculus of indication that governs the process of ‘distinction’, and in quantum physics, where the use of complex numbers is necessary in the Schrödinger Wave Equation and in the quantum Hilbert Space (in classical mechanics this is not necessary and only real numbers are required!). So what is the basic difference between quantum physics and classical physics? In quantum physics, natural systems are modeled as ‘complex’ organisms that include ‘closed causal loops’ operating on a dynamical continuum, while in classical mechanics, natural systems are modeled as ‘simple’ mechanisms that comply with the mechanistic formalism, NOT as organisms. This all comes from the work of theoretical/relational biologist, Robert Rosen (author of ‘Life Itself‘ and ‘Essays on Life Itself‘). What is the bottom line? That all natural systems are ‘complex’ organisms that manifest ‘Rosennian complexity‘ due to the fact that they include ‘closed causal loops‘ operating on a dynamical continuum, which means that they are NOT computable, NOT algorithmic, NOT simulable, and NOT strictly deterministic. While mechanisms that comply with the mechanistic formalism which are subject to an ‘ontology of states‘–which organisms are NOT subject to. In other words, in the mechanistic formalism, there is the possibility of partitioning the system into ‘states’ and the ‘laws’ that govern them. But for an organism, this is NOT possible. Organisms are NOT subject to an ‘ontology of states’. This distinction has HUGE implications. It means that living Organisms as naturally occurring autopoietic, self-sustaining systems, can be shown, using the mathematical theory of categories, to be fundamentally, categorically different from fabricated Mechanisms. And that <i class=””>the semantic description of living Organisms EXCEEDS the syntactic description, whereas the semantic description of fabricated Mechanisms is EQUIVALENT to the syntactic description–for mechanisms, if you know the structure, you can predict the function; but for organisms, this is not possible. This is analogous to the distinction between the function of ‘natural language’ versus ‘computer language’. The meaning of a statement in ‘natural language’ is CONTEXT-DEPENDENT. The meaning of a statement in ‘computer language’ must be CONTEXT-INDEPENDENT. For a living Organism, meaning is mediated by context. For a fabricated Mechanism, meaning is independent of context. Or, you could say, for a Mechanism, meaning is not a possibility.

        REMEMBER: the description of the dynamics of a Living Organism REQUIRES Imaginary Numbers because its relational model includes Closed Causal Loops. This is NOT TRUE for Fabricated Mechanisms, which do NOT contain Closed Causal Loops and which, as a result, can be described in terms of dynamics using Real Numbers ONLY–ie. using classical Newtonian mechanics. Similarly, Quantum Physics REQUIRES the use of Imaginary Numbers because it deals with relational modeling that includes the dynamical effects of Closed Causal Loops. This tells us that all natural systems are actually Organisms (whether or not we would consider them to be ‘living’). Quantum Physics is NOT a mechanics. The term ‘Quantum Mechanics’ contains an internal contradiction. Quantum Physics is a science of Organisms, NOT Mechanisms.

      • Gary

        December 25, 2023 at 7:54 pm

        And this all fits beautifully, I think, with Iain’s approach to the differentiation of function between the left and right hemispheres. The approach of the left hemisphere is analytic and mechanistic. The left hemisphere seeks deterministic certainty and this is what the mechanistic formalism provides for it. So it holds onto the fundamental belief that the universe is a physical mechanism which fits well with its materialistic, nominalistic foundation and its focal mode of attention that tends to see the trees, but not the forest. The left hemisphere approach is ‘bottom-up’ starting with the ‘pieces’ and moving toward putting them together to assemble the ‘whole’. This can work under restricted conditions and scales. Which is what it was evolved to do–basically to provide a non-veridical ‘interface’ with reality that enables survival in the context of physical embodiment at the human scales at which the evolved non-veridical sensory interface operates. But, as Donald Hoffman maintains, this is a NON-veridical interface that HIDES the underlying relational reality from us. In the context of human species-specific ‘meta-consciousness’, it is the left hemispheric perspective that dominates through language-encoded thought (ie. egoic ‘self-talk’). This is the ‘approach of the line’–ie. the linearization of externality.

        The Right Hemisphere takes a completely different approach which is fundamentally relational and based on vibrational frequencies that link to the relational reality through interactive resonances and nonverbal communication. It interacts with the world through a holistic, relational approach that links to the ‘big picture’ through a global pattern-seeking view. And it operates through affective connection, through ‘feeling’. As opposed to the tendency of the left hemisphere to see everything as machinery, the right hemisphere links to the rhythms of life and through musicality. This is the approach of the circle which involves relational communicative connection with alterity through affect-based intuition. And the recognition that interaction between self and other occurs through cyclical dynamics in which the perceiving of the other changes the other which in turn changes the perceiver which in turn changes the other, which in turn changes the perceiver… and so on. All interaction is a cyclical ‘coupling’ of connectional influence. This is the magical mystique of the right hemisphere that is not readily articulated but can be felt in a context of attunement.

      • Gary

        December 25, 2023 at 8:44 pm

        So, the implication is that the left hemisphere is not inclined toward direct self-reference in response to paradox but the right hemisphere is all set to deal with ‘re-entry into the form’ as a means of responding to and resolving paradox. When paradox arises, the left hemisphere is ‘stuck’. Its job is to enact the calculus of indications through making ‘distinctions’ via separation. But it is only adequately prepared to do this at the ‘first-order’ level. When we get up to the ‘second-order’ level and paradox becomes possible, then the right hemisphere is called in to resolve incommensurable contradiction and paradox through the introduction of continuous cyclical time via its operation in the frequency domain. With the introduction of continuous time as a primordium of continuity that serves as a mediating foundation of ‘Thirdness’ (in the ‘New List of Categories’ of Charles Sanders Peirce that also includes ‘Firstness’ and ‘Secondness’), paradox can be resolved through circular alternation and converted from an incommensurable bind to a dynamic complementarity. And what was an unresolvable split, or a bound-down polarizing lock-up, is mediated into a generative harmonization. So that, in fact, it is ‘the Medium that is the Message’ as McLuhan insisted. Without the medium there can be no communication, and without real communication (or connecting ‘trans-action’), there can be no living existence.

  • Gary

    December 25, 2023 at 8:52 pm

    “A deep principle of complementarity underlies life, brain, mind and society. Thinking in terms of contrarieties is very easy, but in complex coordinated systems, sharp dichotomies and contrarieties will have to be replaced by far more subtle and sophisticated complementarities.” J Scott Kelso

  • Gary

    December 26, 2023 at 6:40 pm

    These ideas connect to the work of the late Francisco Varela and Humberto Maturana on the concept of autopoiesis and its connection to self-reference and closed causal loops…. The paper by Varela on the ‘Calculus of Self-Reference’ was mentioned and referenced previously. The latest issue of the Journal of Consciousness Studies has a collection of fascinating and important papers related to ‘the Legacy of Francisco Varela’ and these are definitely worth careful review. There is a fundamental valuable connection to the difference between the function of the two cerebral hemispheres, Robert Rosen’s ‘Life Itself’, and Varela’s ‘Calculus of Self-Reference’ related to what I am calling the ‘Ouroboric Principle of Continuous Self-Reference’ upon which the categorical differentiation between living organisms and fabricated mechanisms is founded.

  • Niels Hoffmann

    January 21, 2024 at 9:54 pm

    Hi Gary, seek and you shall find, and the truth will set you free. What is this truth? Truth is about order, not chaos theory. I feel it is very important for mankind to see things from the right perspective. What happened with backpropagation in our discussions?

    Since there is a lot of confusion about what computers and computation is about. I have offered to lead a learning session on the members Zoom account. If you stay the distance, I will promise a liberating understanding of the issue of the hemisphere differences. And a better understanding of the true power of computers and computation. LH is like Force vs RH Power. Like the Line and the Ring of decision making the Lord of the rings.

    It takes attention to accept a change of mind is needed. I took the trouble to read Rosen’s book about life. Yes, he did say it wasn’t possible, but within current mathematics. The top scientists of the day are talking about what is called P=NP-complete as something subtle we have overlooked. Yes, you are right, they do work together in this world to make something good and beautiful but in terms of intelligence the RH is supreme. If we want to see an increase in what the LH calls consciousness which incidentally is not fundamental. The transformation will save mankind to be able to converse with ETs and their most likely higher intelligence. I know how hard it is to shed our habitual way of thinking. In other words, the more we get used to hear the voice of the Holy Spirit the better our ways of thinking. None of this contradicts Iain’s hypothesis, wouldn’t you like to join with me and our brothers in creating a better world of freedom, Brother Niels.

  • Niels Hoffmann

    January 21, 2024 at 9:58 pm

    I forgot to say, we will do it together learning together instead of a talking to. teaching is learning. But the goal has to be clear.

  • Gary

    January 22, 2024 at 1:37 am

    Looking forward to your presentation, Neils. It appears that we operate at a mediated boundary between chaos and order. Too much chaotic drive and organismic life is precluded by excess energy, instability, and a ‘run-away’ toward heat death. Too much order and organic functionality is limited by inadequate adaptability and a run-down toward ‘cold death.’

  • Niels Hoffmann

    February 7, 2024 at 5:06 pm

    Your Brain Operates at the Edge of Chaos.<div>


    You really are brilliant at finding impossible ideas.

    Iain has clearly defined the difference of the two thought systems.

    LH is sequential processing and RH is propper intelligent processing, the Sacred.

    What is propper intelligent emergent processing, from order to order to order…?

    It is the Right Hemisphere: The New Math of Life.

    It negates the LH fear of complexity. The RH is noncomplex complexity.

    It sounds Miraculous; indeed, it is as it is in Nature!

    It takes attention as we need to increase awareness to a certain level where a need for RH cognition can be recognised?

    I notice my writing over a year ago has been removed from the members area. I am still waiting for Ian’s response as he showed an interest in it, ca 14 month ago!

    The invitation is to Iain as well. I accept Iain’s work as exceptional, empirically.

    But this is an opportunity for understanding the ART of creating Algorithms.

    Niels Bohr to David Bohm:” Quantum Mechanics is not a theory it’s an Algorithm.

    When the QM algorithm is expanded by the RH algorithms, we have solved the major problem of paradoxes in physics and science as well as systemic problems.

    Roger Penrose sees this as something subtle we have overlooked.

    A group between 7 and 10 partipants

    With love,

    Brother Nelson.


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