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

  • 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.