Diego Lucio Rapoport (Campodonico) - Profile on Academia.edu (original) (raw)

Papers by Diego Lucio Rapoport (Campodonico)

Torsion Geometry 5-Fold Symmetry, Anholonomic Phases, Klein Bottle Logophysics, Chaos, Resonance: Applications Towards a Novel Paradigm for the Neurosciences and Consciousness

Journal of physics, May 1, 2023

We discuss the torsion geometries as the universal dynamical setting for the five-fold symmetry a... more 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…

Random representations of viscous fluids and thepassive magnetic fields transported on them

viXra, Jun 1, 2011

We reintroduce logophysics based on self-referential torsion fields and the Klein bottle (KB) log... more We reintroduce logophysics based on self-referential torsion fields and the Klein bottle (KB) logic, which unifies the objective and subjective realms. We apply it to biology, particularly allosterics and the genetic code. We reveal several topologies of the genetic code and its bioinformatics codification, in particular the hyper Klein bottle (HKB) surface. We relate it to the Universal Rewrite System, the Code of Nature, and Dirac algebra.We find that the double helix is unnecessary in this setting, and elaborate the ontology of 3D with regards to time, multistable perception, and a topological (lawless) form of Newton's Third Law. We present the key ideas for a logophysical theory for contextual evolution.

viXra, Mar 1, 2007

Two different derivations of the observed vacuum energy density are presented. One is based on a ... more Two different derivations of the observed vacuum energy density are presented. One is based on a class of proper and novel generalizations of the (Anti) de Sitter solutions in terms of a family of radial functions R(r) that provides an explicit formula for the cosmological constant along with a natural explanation of the ultraviolet/infrared ( UV/IR) entanglement required to solve this problem. A nonvanishing value of the vacuum energy density of the order of 10 -123 M 4 P lanck is derived in agreement with the experimental observations. A correct lower estimate of the mass of the observable universe related to the Dirac-Eddington's large number N = 10 80 is also obtained. The presence of the radial function R(r) is instrumental to understand why the cosmological constant is not zero and why it is so tiny. Finally, we rigorously prove why the proper use of Weyl's Geometry within the context of Friedman-Lemaitre-Robertson-Walker cosmological models can account for both the origins and the value of the observed vacuum energy density ( dark energy ). The source of dark energy is just the dilaton-like Jordan-Brans-Dicke scalar field that is required to implement Weyl invariance of the most simple of all possible actions. The full theory involving the dynamics of Weyl's gauge field A µ is very rich and may explain the anomalous Pioneer acceleration and the temporal variations ( over cosmological scales ) of the fundamental constants resulting from the expansion of the Universe. This is consistent with Dirac's old idea of the plausible variation of the physical constants but with the advantage that it is not necessary to invoke extra dimensions.

Stochastic Geometry Approach to the Kinematic Dynamo Equation of Magnetohydrodynamics

Progress in nonlinear differential equations and their applications, 2005

We review the geometry of diffusion processes of differential forms on smooth compact manifolds, ... more We review the geometry of diffusion processes of differential forms on smooth compact manifolds, as a basis for the random representations of the kinematic dynamo equations on these manifolds. We realize these representations in terms of sequences of ordinary (for almost all times) differential equations. We construct the random symplectic geometry and the random Hamiltonian structure for these equations, and derive a new class of Poincaré-Cartan invariants of magnetohydrodynamics. We obtain a random Liouville invariant. We work out in detail the case of R3.

Neuroquantology, Nov 14, 2011

We introduce a new paradigm for embryological differentiation with its relations to the genome an... more We introduce a new paradigm for embryological differentiation with its relations to the genome and evolution, in terms of the fusion of logic and physics: logophysics (LGP), associated to the ontology and epistemology of the Klein Bottle (KB). We introduce LGP through the subversion of the fixed dualistic categories of exterior and interior, basis for much of science, in terms of the eversion: turning inside-out of the two dimensional elastic sphere (ovum), which is the actual case. We propose bauplans unfolding from a 6d space in which time waves manifest through torsion fields in real space and in which the eversion is mediated by KBs. We present the torsion geometry, quantum and elastodynamical, of self-referential biology. We apply this to the problem of the physics of embryological differentiation in terms of quantum torsion-elastodynamics waves and the light tensegrity of the cell. We associate it with a topological transformation which extends the proposal by Maxwell and Poynting, founders of electromagnetics, for the interaction of the inanimate and animate worlds. We present a new conception of the world in terms of time waves and the KB, that appears in the natural number system, in cosmology, in vision recognition, in the topographic map of the sensorium, in the periodic table of elements, the genome, etc. We surmount the ancient problem of what life is, providing a LGP basis for both the inanimate and animate realms.

Nonlinear phenomena and complex systems, 2000

Torsion Fields, Propagating Singularities, Nilpotence, Quantum Jumps and the Eikonal Equations

Nucleation and Atmospheric Aerosols, 2010

ABSTRACT We establish a geometrical theory in terms of torsion fields and their singularities of ... more ABSTRACT We establish a geometrical theory in terms of torsion fields and their singularities of quantum jumps and of the propagation of wave‐front singularities described by the eikonal equation of geometrical optics basic to Fock’s theory of gravitation and General Relativity. The latter equations correspond to the wavefront propagation for the Maxwell and Einstein equations. We discuss the genesis of spacetime in terms of these singularities and torsion fields. We introduce the class of solutions of the wave propagation (defined in terms of the metric geometry) and the eikonal equations. The lagrangian functional for quantum jumps defined in terms of the quantum potential is introduced. We give a formula that characterizes the quantum jumps in terms of an extension of the argument principle in complex analysis. We show that the wave propagation in terms of the metric geometry under a change of gauge has a natural expression as a wave propagation in terms of the laplacians associated to a torsion geometry of the Cartan‐Weyl type which has an additional interaction first‐order torsion term. In this geometry there is a differential one‐form trace‐torsion term given by the logarithmic differential of (monochromatic) waves. It is shown that quantum jumps are associated with the Cartan‐Weyl geometry, through a torsion potential given by the logarithmic differential of the composition of an analytic function ‐or alternatively a twice differentiable function‐ with a monochromatic wave function. In particular, if follows that monochromatic wave functions generate torsion. The node sets of monochromatic functions are shown to be the locus for quantum jumps. In the case of the metric being Minkowski or positive‐definite, the generalized laplacians corresponding to this torsion geometry, are generators of Brownian motions in which the torsion describes the drift of the Brownian processes. We show that this torsion potential and its singularities due to the nodes of the monochromatic wave functions, gives rise to an Aharonov‐Bohm effect. We briefly indicate the role of quantum jumps in establishing a global time and space coordinates in semiclassical General Relativity. We indicate some relations between the present approach to the geometry of quantum jumps, and the problem of topographical representation in visual perception, the Klein bottle, quantum physics and holography.

Il Nuovo Cimento A (1965-1970), Apr 1, 1984

A general scheme as been presented for deriving the equations of motion for classical particles i... more A general scheme as been presented for deriving the equations of motion for classical particles in the presence of given external fields. In this paper we illustrate the method for the case of a massive chargeless particle whose spin interacts with the curvature and torsion of a gravitational field. We solve these equations for the case of a constant vector torsion.

Reports on Mathematical Physics, Feb 1, 2002

We derive random implicit representations for the solutions of the classical Navier-Stokes equati... more We derive random implicit representations for the solutions of the classical Navier-Stokes equations for an incompressible viscous fluid. This program is carried out for Riemannian manifolds (without boundary) which are isometrically embedded in a Euclidean space (spheres, tori, I~ n, etc.). Our results appear as an extension to smooth manifolds of the random vortex method of computational fluid dynamics. We derive these representations from gauge-theoretical considerations and the Ito formula for differential forms of stochastic analysis.

Systemic Yoyos: Some Impacts of the Second Dimension20101Yi Lin. Systemic Yoyos: Some Impacts of the Second Dimension. Boca Raton, FL: CRC Press 2009. 408 pp., ISBN: 978‐1‐4200‐8820‐5

Kybernetes, Jun 15, 2010

Springer eBooks, Nov 19, 2013

We present an ontoepistemology based on the self-contained KleinBottle and HyperKleinBottle surfa... more We present an ontoepistemology based on the self-contained KleinBottle and HyperKleinBottle surfaces and their logics; the latter incorporates interrelations and hypercontextualizations within an heterarchy of Otherness. We introduce the associated logophysics, as a basis for the unification of science and phenomenology, by surmounting the Cartesian Cut. Dualism is found to be a projection of the former logic, not an independent primeval ontoepistemology. We present the phenomenology of these logics, with regards to the geometries and topologies of space and time; of thought and language; of semiosis and its geological, cosmological and astronomical signs linked to the Myth of Eternal Return; of perception and cognition; of the common ontopoiesis of life and the inanimate realms, and of biological shape departing from embryological development and its unfolding as body-plans and their anatomy-physiology, and discuss its bearing in evolutionary theory, all which we present as embodiments of this non-dual ontoepistemology. We contrast this paradigm with: 1) the dualism of the theory of autopoiesis and the purported interior/exterior divide, as a general principle, which these logics subvert by self and mutual reentrances of the heterarchies; 2) the dual membrane of cell biology; 3) evolutionary theory associated to the metabolic versus genomic dualism; 4) the mereological fallacies of the neurosciences and the hypercontextuality of metaphors and anthropomorphisms; 5) the dualisms of Newtonian physics, Einstein's relativity and quantum mechanics which are found to be epistemic theories, and the assumption of noncontextualization in physics, chemistry and geology which we show not to be the case; 6) the psychophysics of visual, aural and musical spaces, 7) the anatomy-physiology of the sensorium and the healing reconstitution of integrity; 8) in the division of epistemology and ontology, of language and process, and the top-down and bottom-up systemic, and finally 9) the issue of design related to turning-inside-out of a sphere (the ovum), yet transcending creationism. We present their surmountal through the ontoepistemologies of the Klein and Hyper-Klein Bottles surfaces, of hyper-contextuality and complexity. We discuss teleological causation and design of processes/structures, in particular in paleogeology, physics, chemistry and biology, in terms of the latter ontoepistemologies and of the Golden Mean, generated by time waves and their guidance by the Fibonacci Algorithm. We apply this ontoepistemology to the interpretation of religious texts and discuss the relations with the evolution of science. We discuss the two-dimensionality of biology and the lifeworld, novelty and the time operators. Index 4. Logophysics and the Problem of What is Life .

Constructivist Foundations (Special Issue: 60th Anniversary Meeting of the American Society for Cybernetics, “Living Cybernetics Playing Language”, 2025

This academic paper, "466 OPC on “From Naming to Naming Oneself” by Lou Kauffman" by Diego Lucio ... more This academic paper, "466 OPC on “From Naming to Naming Oneself” by Lou Kauffman" by Diego Lucio Rapoport, explores the concept of signification, particularly the process of naming, through the lens of a supradual logophysics, which transcends traditional dualistic thinking. It proposes the Klein Bottle (KB) and Hyper Klein Bottles (HKB) as topological models for this logophysics, linking them to the physiology and anatomy of perception, cognition, and the material energy domain. The author argues that these non-orientable surfaces and torsion geometry are fundamental to processes like self-reference, hetero-reference, and phenomena like resonance and action-at-a-distance. The paper also applies this supradual framework to understand the limitations of formal systems, citing Gödel's Theorem, the Liar Paradox, and Russell's paradox as examples where a reduction to dual logic leads to paradoxes, suggesting that a supradual understanding, embodied topologically, can offer a different perspective. Ultimately, the text argues that language and cognition operate within a supradual logophysics, even when reduced to dualistic pragmatic applications, impacting fields from physics to social anthropology and cybernetics

Cover image is taken from Neogeometrism book by Florentin Smarandache.

Riemann-Cartan-Weyl quantum geometry, I: Laplacians and supersymmetric systems

International Journal of Theoretical Physics, Feb 1, 1996

In this first article of a series dealing with the geometry of quantum mechanics, we introduce th... more In this first article of a series dealing with the geometry of quantum mechanics, we introduce the Riemann-Cartan-Weyl (RCW) geometries of quantum mechanics for spin-0 systems as well as for systems of nonzero spin. The central structure is given by a family of Laplacian (or D'Alembertian) operators on forms of arbitrary degree associated to the RCW geometries. We show that

viXra, Nov 1, 2007

We present the unification of Riemann-Cartan-Weyl (RCW) space-time geometries and random generali... more We present the unification of Riemann-Cartan-Weyl (RCW) space-time geometries and random generalized Brownian motions. These are metric compatible connections (albeit the metric can be trivially euclidean) which have a propagating trace-torsion 1-form, whose metric conjugate describes the average motion interaction term. Thus, the universality of torsion fields is proved through the universality of Brownian motions. We extend this approach to give a random symplectic theory on phase-space. We present as a case study of this approach, the invariant Navier-Stokes equations for viscous fluids, and the kinematic dynamo equation of magnetohydrodynamics. We give analytical random representations for these equations. We discuss briefly the relation between them and the Reynolds approach to turbulence. We discuss the role of the Cartan classical development method and the random extension of it as the method to generate these generalized Brownian motions, as well as the key to construct finite-dimensional almost everywhere smooth approximations of the random representations of these equations, the random symplectic theory, and the random Poincaré-Cartan invariants associated to it. We discuss the role of autoparallels of the RCW connections as providing polygonal smooth almost everywhere realizations of the random representations.

Neuroquantology, Dec 1, 2011

We reintroduce the Klein Bottle (KB) logophysics at the foundations of the unification of quantum... more We reintroduce the Klein Bottle (KB) logophysics at the foundations of the unification of quantum geometry, cell biology, embryology and evolution, to extend it to the genetic code and allosteric recognition. We find that the genetic code has three possible fractal topologies: two different families of KBs embedded in HyperKBs, or still a 2-torus, depending which pair of three subalphabets for the genetic "letters" is chosen; this does not require the double helix. We complete the genetic codification of embryological differentiation introduced in an accompanying article. We discuss the Hadamard-KB representation of this codification and discuss its robustness and that of embryological development with respect to environmental noise. We discuss this KB codification of the 64 codons with its isomorphic representation in terms of the Dirac Algebra (DA) of Quantum Mechanics, in the Nilpotent Universal Computational Rewrite System (NUCRS), a self-referential syntax that generates much of mathematics and the fundamental symmetries of physics. We show that the double helix can be obtained from the duplication of the KB associated with the bistable perception of the tetrahedron representation of the four genetic letters. The DA and its double tetrahedron codification in NUCRS is found to be associated with a pair of superposed KBs, yielding the double 3D (space and momentum) space of physics, and the double helix of DNA, which thus appears related to a pair of KBs, being the case that only one is necessary to construct the genome. We show that the depth-time variable of visual perception materializes as space Thus, the DA is derivable from two KBs, and the purported dualism of physics as presented in NUCRS, is rendered to be based in the non-dualistic KBL. We discuss the relations with a theory of evolutions, and between biological periodicities and the KB of the Mendeleev table (Boeyens). We present relations between metacognition and the HyperKlein Bottle, and evolution in terms of time waves defining in toto the different structures. We present rudiments of the ontoepistemology of the Hyper KB Logic, its relations with the anthropic principles and the universal physical constants, which are found to be contextual.

Advances in Applied Clifford Algebras, Jun 1, 1998

We introduce the Riemann-Cartan-Weyl (RCW) space-time geometries 1Riemann-Cartan-Weyl Geometries,... more We introduce the Riemann-Cartan-Weyl (RCW) space-time geometries 1Riemann-Cartan-Weyl Geometries, Quantum Diffusions and .

International Journal of Theoretical Physics, Oct 1, 1997

We reintroduce the Riemann-Cartan-Weyl (RCW) spacetime geometries of quantum mechanics [Rapoport ... more We reintroduce the Riemann-Cartan-Weyl (RCW) spacetime geometries of quantum mechanics [Rapoport (1996), int. Z Theor. Phys. 35(2)] in two novel ways: first, through the covariant formulation of the Fokker-Planck operator of the quantum motions defined by these geometries, and second, by stochastic extension of Cartan's development method. The latter is a gauge-theoretic formulation of nonlinear diffusions in spacetime in terms of the stochastic differential geometry associated to the RCW geometries with Weyi torsion. The Weyl torsion plays the fundamental role of describing the first moment (incorporating also the fluctuations due to the second moment) of the stochastic diffusion processes. In this article we present the most general expression of the Weyi torsion one-form given in terms of its de Rham decomposition into the exact component associated with the 0-spin field ~ and two electromagnetic potentials, one the codifferential of a 2-form and the other a harmonic 1-form. We thus give an original description of the Maxwell theory and its relation to torsion. We associate these electromagnetic potentials with the irreversibility of the diffusions. In an Appendix, we give a self-contained presentation of the theory of diffusions on manifolds and the stochastic calculi as a basis for the Cartan stochastic copying method.

Torsion Geometry 5-Fold Symmetry, Anholonomic Phases, Klein Bottle Logophysics, Chaos, Resonance: Applications Towards a Novel Paradigm for the Neurosciences and Consciousness

Journal of physics, May 1, 2023

Random representations of viscous fluids and thepassive magnetic fields transported on them

viXra, Jun 1, 2011

viXra, Mar 1, 2007

Stochastic Geometry Approach to the Kinematic Dynamo Equation of Magnetohydrodynamics

Progress in nonlinear differential equations and their applications, 2005

Neuroquantology, Nov 14, 2011

Nonlinear phenomena and complex systems, 2000

Torsion Fields, Propagating Singularities, Nilpotence, Quantum Jumps and the Eikonal Equations

Nucleation and Atmospheric Aerosols, 2010

Il Nuovo Cimento A (1965-1970), Apr 1, 1984

Reports on Mathematical Physics, Feb 1, 2002

Systemic Yoyos: Some Impacts of the Second Dimension20101Yi Lin. Systemic Yoyos: Some Impacts of the Second Dimension. Boca Raton, FL: CRC Press 2009. 408 pp., ISBN: 978‐1‐4200‐8820‐5

Kybernetes, Jun 15, 2010

Springer eBooks, Nov 19, 2013

Constructivist Foundations (Special Issue: 60th Anniversary Meeting of the American Society for Cybernetics, “Living Cybernetics Playing Language”, 2025

Cover image is taken from Neogeometrism book by Florentin Smarandache.

Riemann-Cartan-Weyl quantum geometry, I: Laplacians and supersymmetric systems

International Journal of Theoretical Physics, Feb 1, 1996

viXra, Nov 1, 2007

Neuroquantology, Dec 1, 2011

Advances in Applied Clifford Algebras, Jun 1, 1998

International Journal of Theoretical Physics, Oct 1, 1997

The present book discusses, among other things, various quantization phenomena found in Astrophys... more The present book discusses, among other things, various quantization phenomena found in Astrophysics and some related issues including Brownian Motion. With recent discoveries of exoplanets in our galaxy and beyond, this Astrophysics quantization issue has attracted numerous discussions in the past few years. Most chapters in this book come from published papers in various peer-reviewed journals, and they cover different methods to describe quantization, including Weyl geometry, Supersymmetry, generalized Schrödinger, and Cartan torsion method. In some chapters Navier-Stokes equations are also discussed, because it is likely that this theory will remain relevant in Astrophysics and Cosmology While much of the arguments presented in this book are theoretical, nonetheless we recommend further observation in order to verify or refute the propositions described herein. It is of our hope that this volume could open a new chapter in our knowledge on the formation and structure of Astrophysical systems. The present book is also intended for young physicist and math fellows who perhaps will find the arguments described here are at least worth pondering.

The present book covers a wide-range of issues from alternative hadron models to their likely imp... more The present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of lowenergy reaction (coldfusion) phenomena.

There is beginning for anything; we used to hear that phrase. The same wisdom word applies to us ... more There is beginning for anything; we used to hear that phrase. The same wisdom word applies to us too. What began in 2005 as a short email on some ideas related to interpretation of the Wave Mechanics results in a number of papers and books up to now. Some of these papers can be found in Progress in Physics or elsewhere.

George Spencer-Brown, Fifty Years of the Laws of Form, 2020

We elaborate on the Klein Bottle supradual logophysics in relation to semiosis, perception and co... more We elaborate on the Klein Bottle supradual logophysics in relation to semiosis, perception and cognition, and consciousness, and in particular with the Laws of Form by Spencer-Brown. Meaning -and feeling- which is wholly absent in the attempts to produce a theory for consciousness receive primacy in this setting, and related to the Klein and HyperKlein Bottle extensions of selreference and heteroreference. We discuss their bearing in relation with linguistics and the generation of culture.We discuss their fundamental relevance to Peirce's triad, placing Feeling and its supraduality at the basis of this logophysics, rather than procuring Quantum Mechanics as the basic setting which also is connected to the Klein bottle logophysics. We propose this logophysics as the basic principle of an ecological psyche, first introduced by JJ Gibson. We discuss Goethe's theory of colours in terms of this supradual logophysics. We propose a supradual monism and apply it to cognitive mappings retaking Shepard's work in terms of symmetry Lie groups and projective spaces, the former basic to Klein's Erlanger Program and basic to theoretical physics. We relate this to non-orientability as the basis for pattern formation and recognition, and the cognitive map, and the embeddedness in Euclidean space rather than projectivity as the ultimate foundation for modeling. We discuss this topological theory in relation to Heidegger's phenomenology as founded in topology, and the supradual sociology of Berger and Luckmann

We present 1) a novel unified conception of science, cognition and phenomenology in terms of the ... more We present 1) a novel unified conception of science, cognition and phenomenology in terms of the Klein Bottle logophysics, 2) as a supradual creative agency based on self and hetero-reference and multistate logic associated to the non-orientable topologies of the Moebius strip and Klein Bottle surfaces, 3) the Golden ratio in several areas of biology (particularly genomics), cognition, perception, physics and music, and the multiple biochemical codes of life ; 4) semiosis and topological folding in the génesis of life ; 5) the torsion geometries and non-orientable topologies, and apply them to 6) human-bodyplan, neurosciences, music cognition, structure and processes of thinking, particularly Quantum Mechanics, creativity and the logics of the psyche; 7) a universal principle of self-organization and the genesis of life, the π-related visual cortex and holography; 8) as an harmonic principle in the brain's pattern formation, pattern recognition and morphogenesis, and the topological paradigm to neuroscience; 9) higher-order cybernetics, ontopoiesis and autopoiesis in Systems Biology,the psyche's bi-logic; 10) a rebuttal of Dr. Liu et all's PLOS article claiming the appearance of Phi in genomes as accidental, in terms of the supradual ontopoiesis hereby presented and by reviewing several codes of life discovered by Pérez, which elicit their unity already starting at the level of the periodic table of elements and Life compounds atomic mass; and 11) the Golden mean in the rituals of whales.