Diego Rapoport

National University of Quilmes | UNQ · Department of Science and Technology

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 suprad...

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, namely the Möbius strip and Klein Bottle. We present the relation with anholonomic phases, chaos and the brain-mind as an integrated dynamical system. We discu...

We present a reflection on the Leonardo Project

This Project is the development of a form of art hitherto unknown. It fuses music, the artistic spatial representations, holography as the physical field for this unification and further integrates the observer as an agent-participating of this fusion. Thus this art surmounts the manifold dualisms, object/subject, physical medium/subject, artistic...

We discuss the contextual information associated with the Klein Bottle Logic (KBL) and its jointly digital and analogical codification of a KBL logophysics which surmounts the Cartesian divides.We introduce the nonorientable surfaces of selfreference, the Moebius strip and the Klein Bottle, as the metaform of morphogenesis, pattern formation and re...

Based on the supradual Klein Bottle logophysics and ontopoiesis we present a critique of the toroidal "Great Unified Musical Quantum" model of consciouness and the Universe as an emergent physicalist reductionism due to Meijer, Jerman, Melkhik & Sbitnev, published in Quantum Biosystems, vol.11, no.1, 1-107, 2020 https://www.iamaq.org/quantumbiosyst...

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 HyperK...

Abstract : 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 Möbius strip and Klein Bottle surfaces, 3) related to the Golden ratio in s...

Abstract : 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 are...

In this second part of a series of articles, we discuss the fusion of analogue and digital decurring from the Klein Bottle, the Inside/Outside image-schema of Cognitive Semantics and its role in the dualistic organization of knowledge, presenting several examples in biology, astrophysics and chemistry. We present the Möbius strips and Klein Bottle...

In this first part of a series of articles we discuss the torsion geometry of biology, physics, cognition and perception. We discuss the relations with the non-linear morphomechanics of organisms and the integration of the body's chiralities. We present the connections with the topology of neural networks as heterarchies and with multi-loci logics...

In this third and last Part of this series, we introduce the Klein Bottle Logic and its digital codification. We present a codification of the four letters of DNA or RNA in terms of the four states of this logic, and further relate it to three subalphabets –introduced by Petoukhov and He-as three primal biochemical distinctions –in the sense of Spe...

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 logo-physics, as a basis for the unification of science and phenomenology, by surmounting the Car...

Title: Surmounting the Cartesian Cut Through Philosophy, Physics, Logic, Cybernetics, and Geometry: Self-reference, Torsion, the Klein Bottle, the Time Operator, Multivalued Logics and Quantum Mechanics Abstract: In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Hei...

We present a unified principle for science that surmounts dualism, in terms of torsion fields and the non-orientable surfaces, notably the Klein Bottle and its logic, the Möbius strip and the projective plane. We apply it to the complex numbers and cosmology, to non-linear systems integrating the issue of hyperbolic divergences with the change of o...

We present a theory that surmounts the Cartesian Cut through self-reference, torsion geometry, multivalued logic, paradox, cybernetics, time-waves, quantum physics, the Moebius and Klein bottle surfaces, philosophy and semiotics. We apply it to visual perception and the problem of brain hemisphere integration for stereoscopic vision and its relatio...

We develop the relation between space-time and state-space quantum geometries with torsion fields (the so-called Riemann-Cartan-Weyl (RCW) geometries), statistical thermodynamics -and particularly the second law of thermodynamics- and their associated Brownian motions. In this setting, the metric conjugate of the trace-torsion oneform is the dr...

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...

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,...

In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (theMoebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds)...

We introduce logophysics at the foundations of biology and stereochemistry, and discuss its bearing in biomembranes and quantum torsion tensegrity structure for cell biology, proposing a unified logophysics paradigm integrating topological chemistry and cell biology. We discuss the relations with the differentiation waves in embryogenesis, and a qu...

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...

We present a conception that surmounts the Cartesian Cut -prevailing in science- basedon a representation of the fusion of the physical 'objective' and the 'subjective' realms.We introduce a mathematical-physics and philosophical theory for the physical realmand its mapping to the cognitive and perceptual realms and a philosophical reflectionon the...

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 a...

In recent years, there are attempts to describe quantization of planetary distance based on time-independent gravitational Schr"odinger equation, including Rubcic & Rubcic's method and also Nottale's Scale Relativity method. Nonetheless, there is no solution yet for time-dependent gravitational Schr"odinger equation (TDGSE). In the present paper, a...

We review the relation between spacetime geometries with trace-torsion fields, the so-called Riemann–Cartan–Weyl (RCW) geometries, and their associated Brownian motions. In this setting, the drift vector field is the metric conjugate of the trace-torsion one-form, and the laplacian defined by the RCW connection is the differential generator of the...

In recent years, there are attempts to describe quantization of planetary distance based on time-independent gravitational Schroedinger equation, including Rubcic & Rubcic's method and also Nottale's Scale Relativity method. Nonetheless, there is no solution yet for time-dependent gravitational Schroedinger equation (TDGSE). In the present paper, a...

We present the space‐time and Hilbert‐state space quantum geometries and their associated Brownian motions. We discuss the problem of the reduction of the wave function associated to these geometries and their Brownian motions. © 2007 American Institute of Physics

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We fi...

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 t...

We give a formulation of continuous-spin (taking values in a smooth compact n-manifold, the one-particle space) infinite particle systems with interactions described by a Gibbsian potential, in terms of stochastic differential geometry. We give invariant constructions for the interaction representation of the random dynamics. In the case of n ≠ 1 (...

We give the realizations by sequences of ordinary (almost everywhere) differential equations of the implicit random exact representations for the Navier-Stokes equations on smooth compact manifolds isometrically immersed in Euclidean spaces (viz. spheres, tori, euclidean spaces, etc.). We construct the random Hamiltonean system structure of the Nav...

We present the random representations for the Navier-Stokes vorticity equations for an incompressible fluid in a smooth manifold with smooth boundary and reflecting boundary conditions for the vorticity. We specialize our constructions to R n-1 × R +. We extend these constructions to give the random representations for the kinematic dynamo problem...

Extending the rules of teleparallelism for the introduction of a metric and a connection with torsion on a smooth manifold, M, we define generalized Brownian motions on M starting with a standard Wiener process. The laplacian operator generating this diffusion is the square of the teleparallelism connection on M, yet it is found to depend on the tr...

Extending our previous work we present implicit representations for the Navier-Stokes equations (NS) for an incompressible fluid in a smooth compact manifold without boundary as well as for the kinematic dynamo equation (KDE, for short) of magnetohydrodynamics. We derive these representations from stochastic differential geometry, unifying gauge th...

WE PRESENT THE RANDOM REPRESENTATIONS FOR THE NAVIER-STOKES VORTICITY EQUATIONS FOR AN INCOMPRESSIBLE FLUID IN A SMOOTH MANIFOLD WITH BOUNDARY AND REFLECTING BOUNDARY CONDITIONS FOR THE VORTICITY. WE SPECIALIZE OUR CONSTRUCTIONS TO R(n-1)xR+. WE EXTEND THESE CONSTRUCTIONS TO GIVE THE RANDOM REPRESENTATIONS FOR THE KINEMATIC DYNAMO PROBLEM OF MAGNET...

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, n, etc.). Our results appear as an extension to smooth manifolds of th...

We integrate in closed implicit form the Navier-Stokes equations for an incompressible fluid and the kinematical dynamo equation, in smooth manifolds and Euclidean space. This integration is carried out by applying Stochastic Differential Geometry, i.e. the gauge-theoretical formulation of Brownian motions. Non-Riemannian geometries with torsion of...

We give a covariant theory of non-linear non-equilibrium thermodynamics in terms of non-Riemannian geometries. We give a gauge potential characterization of irreversibility. We extend our theory to su-persymmetric systems. We present the ergodic structures of the stochastic flows: the Koopman and Perron-Frobenius stochastic semigroups, and the Lyap...

In this article we integrate in closed implicit form the Navier-Stoker equations for an incompressible fluid in a smooth compact manifold without boundary, and in particular, in a compact manifold which is isometrically embedded in Euclidean space, and finally in Euclidean space itself. We further integrate the kinematic dynamo problem of magnetohy...

We integrate in closed form the Navier-Stokes equation for an incompressible fluid in a compact manifold, and in particular, in a compact manifold which is isometrically immersed in Euclidean space. We carry out this integration through the application of the methods of Stochastic Differential Geometry, i.e. the theory of diffusion processes on smo...

We introduce the Riemann-Cartan-Weyl (RCW) space-time geometries of quantum mechanics with the most general trace-torsion non-exact Weyl 1-form, and characterize it in the Clifford bundle. Two electromagnetic potentials appear in the Weyl form, one having a zero field and the other one being the codifferential of a 2-form. We give the derivation of...

We reintroduce the Riemann-Cartan-Weyl (RCW) spacetime geometries of quantum mechanics [Rapoport (1996),Int. J. 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 latt...

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 RC...

We introduce the Riemann-Cartan-Weyl (RCW) space-time geometry of quantum mechanics with exact trace-torsion Weyl one-form. We start by constructing the laplacian operator associated to this geometry, as (twice) the differential generator of spin-0 diffusion processes. We prove that these geometrically determined diffusion processes are time-revers...

We show through its canonical decomposition that a Dirac-Hestenes spinor field (DHSF) creates an effective Riemann-Cartan-Weyl geometry on the Lorentz vacuum. The rotor components of the DHSF creates a geometry with completely skew-symmetric torsion and vanishing curvature. We construct the Weyl transformation by the action of the scalar component...

We construct the Riemann-Cartan geometries with torsion generated by the action of the conformal Weyl group. We study the wave operators associated to these structures, which, in addition to the usual Laplace-Beltrami operator, have a term which is a gradient vector field conjugate to the one-form given by the torsion potential derived from the Wey...

The geometry of Cartan connections and their relation to the theory of spontaneous symmetry breaking is discussed. In S. Sternberg and T. Ungar (Hadronic J. 1 (1978), 33--36) Cartan connections are used to derive equations of motion for classical particles in the presence of external fields. Examined here is the case of a massive chargeless particl...

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 consta...

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...

A geometrical origin of quantum jumps in terms of torsion fields and the propagation of wave-front singularities given by the eikonal equation of geometrical optics, which lies at the basis of Fock's theory of gravitation, is in-troduced. A discussion on the connection between quantum jumps and a global time and space coordinates system is presente...

In this article we integrate in closed form, the Navier- Stokes equation for an incompressible ßuid on a compact manifold which is isometrically immersed in Euclidean space. We carry out this integration through the application of the methods of Stochastic Dif- ferential Geometry, i.e. the theory of diusion processes on smooth manifolds. Thus we st...

We present a geometrization of relativistic quantum mechanics (RQM) in terms of the diffusion processes generated by Cartan-Weyl structures with torsion. We introduce the geometro-stochastic Lyapunov exponents of RQM. The geometry is derived from a mean Cartan scalar curvature extremal principle which yields the coincidence between the quantum pote...