Torsion Geometry 5-Fold Symmetry, Anholonomic Phases, Klein Bottle Logophysics, Chaos, Resonance: Applications Towards a Novel Paradigm for the Neurosciences and Consciousness
Authors: Rapoport Diego Lucio 
Published: May 2023

Abstract
We discuss the torsion geometries as the universal dynamical setting for the five-fold symmetry and its relation to nonorientable surfaces of selfreference embodying a supradual logophysics, rooted in the Möbius strip and Klein Bottle. We frame the discussion in terms of image-schemas in cognitive semantics and their disruption stemming from supraduality and nonorientability. We present the relation with anholonomic phases, chaos and the brain-mind as an integrated dynamical system. We discuss nonorientability as the characteristic transcendental metapattern of resonant connection, pattern formation and recognition. We present the torsion geometry and nonorientability in psychophysics and the neurosciences. We discuss the homology of the torsion geometry of physical space or spacetime with that of the unconscious modelization by the brain-mind of the kinematics of objects in physical space and in the perception of music, elaborating on the Principle of Complementarity of cognitive psychology due to Shepard. We elaborate on the phenomenological construal of experience, the world as experience. We discuss the supraduality of the liminal states of consciousness and the basis of awareness in memory. We introduce the cognitive psychology foundations of memory on nonorientability and its relations to the short-memory space and its quantumlike nature, and the hyperbolicity of the psychophysics of vision. We discuss the chaotic behaviour of dynamical systems as a manifestation of supraduality as their nonorientability. We propose a basis for the source of consciousness, the Hard Problem, given by the principles of selfreference and hetero-reference which generate the Klein Bottle supradual logophysics. We present the supradual logophysics of neuron cytoskeletal structures, its relation to torsion, resonances, topological and geometrical phases and the microtubule dynamics in terms of nonlinear buckling patterns and nonorientability, and still the torsion geometry of the irreversible thermodynamical processes supporting interactions-at-a-distance. We discuss the primal relation of torsion, nonorientability and memory, particularly arising in the buckling of microtubules. We discuss the primal morphogenesis of the cell as a tensegrity structure, torsion and the indiscernibility of elastodynamics, electromagnetic and gravitational wavefronts as morphogenetic fields. We discuss nonorientability as the metaform pattern of connection and resonance, particularly of interaction-at-a-distance. We apply it to a topological allosteric effect mediated by electromagnetic fields. We discuss the topological chemistry paradigm, particularly of organic chemistry where conformation superposition is crucial, its relation to anaesthetics and its application to the ORC OR theory of Penrose and Hameroff for consciousness as arising from the collapse of the wave function which we relate to the multiconformation in the topological chemistry paradigm. We propose a model of continuous signal processing in digital terms which allows an optimal reconstruction -from digital to continuous-in terms of the Nyquist-Shannon theorem whose constraints on frequencies and bandwidths is naturally interpreted in the terms of the 2:1 harmonics of nonorientability in the Möbius strip or Klein Bottle. We discuss the non-dual logic of the tubulin code and the resonator nature of the neuronal cytoskeleton. We propose that the topological phases appearing in the cytoskeleton may correspond to the topological anholonomity, namely, nonorientability, as was elicited empirically by the Bandyopadhyay group, the existence of anholonomity corresponding to the 360° rotation characteristic of the topological anholonomity, Möbius strip. We propose the Matrix Logic representation of the Klein Bottle logic as the basis for microtubule computations, and discuss the relation to quantum computation, topological entanglement and the topological coherence/decoherence Klein Bottle cycle. We also relate it to holography, the brain’s integration and Velmans’ Reflexive Monism extended by Rapoport. We discuss the multiconformation orientable and nonorientable resonators electronic devices and antennas as classical-quantum realisations of microtubule coherent behaviour. We discuss the relation of life and consciousness and the topological nonorientable embodiment of memory. We introduce the dynamical reduction program for the collapse of the quantum state in terms of the torsion stochastic differential geometry of the quantum geometry of Quantum Mechanics as projective space, and particularly the stochastic extension of the Schroedinger equation to account for the coupling of quantum system and environment, say a measurement apparatus. Thus we identify a realisation of the dynamical reduction program which is based on the torsion geometry, yet supports an agent-free collapse of the quantum state, as an objective albeit random process due to quantum fluctuations. We shall discuss the present supradual logophysics in several aspects such as 1) microtubule structure and dynamics, 2) the orientable and nonorientable conformations of organic molecules, 3) the relation with anaesthetics and the altered states of consciousness and 4) confront them with the tenets of Penrose & Hameroff ORC OR theory for the origin of consciousness, not only the topological chemistry but their choice of a superposition of null torsion as in General Relativity, which renders a trivial selfreferentiality, with the topological chemistry multiconformations which requires non-null torsion. The nontrivial selfreferentiality is both proper to the mind and the torsion geometry, be that on the physical, chemical, perceptual or cognitive domains. All in all, we propose that consciousness is neither based on panpsychism nor the collapse of quantum states, nor exclusively on the control of superposition of conformations of organic chemistry, but rather on the torsion-nonorientable geometry-topology based on the principles of selfreference and hetero-reference, operating in all domains: that of meaning, the mental-anatomical-physiological domain, structural processes of matter energy and in-formation, be that physical, chemical, biological, cognitive and perception. We present a remarkable connection between them. Our approach rather than multidisciplinary will be transdisciplinary, a possibility supported on supraduality - transcending the dual-logic based logophysics-from which the theory will follow in a rather smooth way.