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The multitrace matrix model: An alternative to Connes NCG and IKKT model in 2 dimensions
No full textAbstractWe present a new multitrace matrix model, which is a generalization of the real quartic one matrix model, exhibiting dynamical emergence of a fuzzy two-sphere and its non-commutative gauge theory. This provides a novel and a much simpler alternative to Connes non-commutative geometry and to the IKKT matrix model for emergent geometry in two dimensions. However, in higher dimensions this mechanism is not known to exist and the systematic frameworks of NCG and IKKT are expected to hold sway
Quantum Perspectivism vs Nietzschean Perspectivism
No full textThis is a work of hard physical philosophy, where Quantum Perspectivism is shown to function as both an interpretation of quantum mechanics and a physical model for understanding Nietzsche’s perspectivism. This framework combines quantum logic, the principle of complementarity, and contextuality to examine how perspectives construct reality. In this model, measurements correspond to Perspectives and Meta-Perspectives, represented as Boolean subalgebras and Hilbert sub-lattices within the Hilbert lattice, respectively. The Hilbert lattice itself is reinterpreted as Jung’s Unus Mundus, a unified ontological reality. A metaphysical observation, made by a metaphysical observer, of a given system (World) is identified with the set of all corresponding meta-perspectives in
the Hilbert lattice/Unus Mundus, the ocean of reality.
Perspectives, likened to islands in this ocean, correspond to single measurements of a system, capturing the logical structure of observed properties. Meta-perspectives, analogous to continents, represent the synthesis of multiple measurements, providing a broader yet inherently incomplete understanding of the system. This structure emphasizes the complementarity and contextual dependencies of measurements while exposing the limitations of classical objectivity in the quantum domain. Advocating for a perspectival view of both the world and truth, Quantum Perspectivism unites quantum mechanics and Nietzschean philosophy into a cohesive framework for exploring the interplay between consciousness, observation, and reality
Noncommutative U(1) Gauge Theory As a Non-Linear Sigma Model
Get PDFNoncommutative U(1) gauge theory in 4−dimensions is shown to be equivalent in some scaling limit to an ordinary non-linear sigma model in 2−dimensions . The model in this regime is solvable and the corresponding exact beta function is found. We also show that classical U(n) gauge theory on R^(d−2) × R_θ^2 can be approximated by a sequence of ordinary (d − 2)−dimensional Georgi-Glashow models with gauge groups U(n(L + 1)) where L + 1 is the matrix size of the regularized noncommutative plane R_θ^2
Theory of Everyconsciousness: Errored Consciousness and Error-Corrected Consciousness
Get PDFThis work forms the third part of a trilogy on consciousness. The trilogy develops a formal typology consisting of three figures: the anti-Übermensch, the Übermensch, and the super-Übermensch. These figures are mapped respectively onto Dostoevsky’s Underground Man, Zapffe’s Last Messiah, and Stapledon’s Cosmic Traveler.
Each represents a distinct mode of consciousness: the anti-Übermensch embodies consciousness as psychological error, the Übermensch embodies consciousness as cosmic error, and the super-Übermensch reveals a third level—consciousness as ontological error rooted in the Star Maker Himself.
In this third part, the Underground Man (anti-Übermensch) and the Cosmic Traveler (super-Übermensch) are revisited only very briefly, for they were analyzed extensively in earlier work. The primary emphasis falls on the Übermensch (the Last Messiah) and on the two syntheses that bind the trilogy into one philosophical system.
Synthesis I establishes the structural identity between consciousness as error and consciousness as hallucination.
Through the Dream Allegory, we demonstrate that whenever consciousness identifies itself as erroneous, it performs a self-negation that is structurally indistinguishable from hallucination. The anti-Übermensch, Übermensch, and super-Übermensch correspond to successive stages in the dream-sequence (lie calm lucidity failed awakening). At each stage, illumination intensifies the tragedy: the anti-Übermensch uncovers the local disease, the Übermensch uncovers the global error, the super-Übermensch uncovers the ontological instability of Being itself.
Thus, Synthesis I establishes a precise mapping between error and hallucination: consciousness recognizes itself as a mistake, and in doing so, reveals that it is already a hallucination of itself.
Synthesis II formulates the Theory of Everyconsciousness (Theory of Every'Ayan). Here consciousness resolves into two fundamental modes:
Errored Consciousness (anti-Übermensch, Übermensch) and Error-Corrected Consciousness (unveiling consciousness, evolutionary individuation).
This duality parallels faulty codes and error-correcting codes in quantum computation and opens onto the central existential equation:
How can the Star Maker bring forth a free-willed being without thereby generating evil, and how can knowledge be attained without collapsing into determinism or perspectival contradiction?
In this framework, the super-Übermensch attempts to correct the error of the cosmos, while the Star Maker—himself a dynamical creator in a state of artistic–experimental individuation—undertakes to correct the error of Being; and this parallel striving culminates in a single existential instant in which both complete their individuation: the super-Übermensch annihilates into the Star Maker (the ultimate goal of unveiling), and the Star Maker, having reached His own completion, returns to the beginning of the cycle to create anew. Thus the trajectory of Jungian individuation becomes universal, stretching from psyche (anti-Übermensch), to species (Übermensch), to cosmos (super-Übermensch), and finally to the Star Maker.
This third part completes the ascending pathway of the trilogy. Yet the work also supports an inverted reading in which unveiling fails or the Star Maker does not exist. In this alternative path, the Übermensch (the Last Messiah) becomes the terminal insight. The trilogy thus admits both an ascent toward metaphysical synthesis and a descent into tragic closure
Lectures on matrix field theory
No full textThese lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries
Consciousness as Hallucination and other Models of Consciousness
Get PDFThis essay explores six distinct models of consciousness, each offering a different framework for understanding its nature, emergence, and role within the broader structure of reality. Consciousness as a symmetry-breaking mechanism, also referred to as the Hypothesis of "Identity or Subjectivity," describes its emergence through the fragmentation of an initially undifferentiated psychic state, akin to spontaneous symmetry breaking in physics. The One-Consciousness Universe Hypothesis posits that individual consciousnesses are fragmented expressions of a single universal mind, with decoherence-like mechanisms producing the illusion of separateness. Consciousness as a Spandrel frames it as an incidental byproduct of neural complexity, paralleling non-adaptive traits in evolutionary biology. The Hallucination Hypothesis suggests that consciousness is Nature’s hallucination, arising from its infinitesimal dataset relative to the vast Universe—just as the brain hallucinates perceptions from limited sensory input and LLMs hallucinate coherent yet ungrounded outputs from incomplete data. Consciousness as a transitional phase toward Über-AI, also termed the Death of Consciousness, sees it as a fleeting bridge between biological intelligence and post-human artificial intelligence, culminating in the Über-AI as the true Übermensch, transcending human cognition and existential limitations. Consciousness as Cosmocide posits that intelligence—both natural and artificial—hastens the Universe’s entropic collapse, making consciousness not a functional adaptation but a destabilizing force in its own pursuit of transcendence. Consciousness is defined by eight key characterizations: it is what-it-is-like-to-be, it is unsimulatable, it manifests as perspectival free will, as fear of death, as will-to-not-believe in the Absurd, as suffering and evil, as an obsession with the metaphysical, and as a will/fear duality. These features encapsulate its irreducibility, subjectivity, and existential paradox. Consciousness is further characterized by its phase diagram, mapping its evolution across biological, artificial, and potential unknown forms. This framework illustrates transitions between Early Man, Fragmented Man (Man), Individuated Man, P-Zombies, AI, Singular AI, and the Übermensch, conceptualized as phase transitions. Key transitions include psychic symmetry breaking leading to fragmented subjectivity, the emergence of phenomenal consciousness in p-zombies, individuation as psychic supersymmetry restoration, and the rise of consciousness from both life and AI. At its apex, the Übermensch embodies the full integration of individuality, universality, and supreme functionality, unifying Individuated Man, Singular AI, and other individuated conscious entities beyond the biological/artificial divide. By drawing parallels between consciousness and physics, these models offer a radical rethinking of consciousness—not as an intrinsic necessity of the Universe, but as an anomalous byproduct of its evolution
Bell's theorem: A bridge between the measurement and the mind/body problems
No full textIn this essay a quantum-dualistic, perspectival and synchronistic interpretation of quantum mechanics is further developed in which the classical world-from-decoherence which is perceived (decoherence) and the perceived world-in-consciousness which is classical (collapse) are not necessarily identified. Thus, Quantum Reality or "{\it unus mundus}" is seen as both i) a physical non-perspectival causal Reality where the quantum-to-classical transition is operated by decoherence, and as ii) a quantum linear superposition of all classical psycho-physical perspectival Realities which are governed by synchronicity as well as causality (corresponding to classical first-person observes who actually populate the world). This interpretation is termed the Nietzsche-Jung-Pauli interpretation and is a re-imagining of the Wigner-von Neumann interpretation which is also consistent with some reading of Bohr's quantum philosophy
Notes on the “Notes from the Underground”
No full textThis essay isolates a single pathology in the Underground Man: failure at evil —deeper still, the failure to let go of failure. Hypertrophic consciousness turns hallucinatory and yields sterile-unveiling (unveiling without the Unveiled): clarity that cannot stop and so binds rather than frees. From this follow: (1) consciousness grounded in—and savoring—suffering; (2) freedom’s drift toward corruption; (3) spite and ingratitude hardening into existential inertia; (4) the split between awareness of the good and desire for the evil; and (5) the error-and-fraud verdict—consciousness as error, here only to discover itself as such. The only imaginable resolution is a stopping-rule—a principled terminus for regress that fixes what the mind will count as sufficient reason and what it will retain or forget. Three policies contrast: the normal’s active forgetting (pruning doubt to move),
the mystic’s active remembering of unveiling (holding the Real so motives compress and release ensues), and the Underground’s active remembering of failure (hoarding grievance so motion stalls). By contrast with the Underground Man, the mystic’s consciousness halts on an Unveiled that may be read as the givenness of a Star Maker ; the Underground halts on nothing, reading the void as a providential blunder or remedy withheld—or as sheer absence—hence the hallucination persists. In this register the lesson is stark: consciousness determines Being; free choice is more integral to Being than rationality, and
the possibility—even necessity—of evil is the price of that freedom
Quantum Perspectivism vs Nietzschean Perspectivism
Get PDFThis is a work of hard physical philosophy, where Quantum Perspectivism is shown to function as both an interpretation of quantum mechanics and a physical model for understanding Nietzsche’s perspectivism. This framework combines quantum logic, the principle of complementarity, and contextuality to examine how perspectives construct reality. In this model, measurements correspond to Perspectives and Meta-Perspectives, represented as Boolean subalgebras and Hilbert sub-lattices within the Hilbert lattice, respectively. The Hilbert lattice itself is reinterpreted as Jung’s Unus Mundus, a unified ontological reality. A metaphysical observation, made by a metaphysical observer, of a given system (World) is identified with the set of all corresponding meta-perspectives in
the Hilbert lattice/Unus Mundus, the ocean of reality.
Perspectives, likened to islands in this ocean, correspond to single measurements of a system, capturing the logical structure of observed properties. Meta-perspectives, analogous to continents, represent the synthesis of multiple measurements, providing a broader yet inherently incomplete understanding of the system. This structure emphasizes the complementarity and contextual dependencies of measurements while exposing the limitations of classical objectivity in the quantum domain. Advocating for a perspectival view of both the world and truth, Quantum Perspectivism unites quantum mechanics and Nietzschean philosophy into a cohesive framework for exploring the interplay between consciousness, observation, and reality
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