Category Archives: Geometric Information Theory

A New Mathematics of Self-Reference: A Comprehensive Non-Mathematical Summary

What This Work Is About

This article explains our paper on a new mathematical framework for self-referential systems, for a non-technical audience. The paper develops a comprehensive mathematical framework for understanding systems that can represent, model, or “know” themselves. While self-reference has long been seen as a source of logical paradoxes, this work argues it may be the fundamental organizing principle of reality itself—and provides specific mathematical bounds and requirements for achieving different levels of self-awareness.… Read More “A New Mathematics of Self-Reference: A Comprehensive Non-Mathematical Summary”

The Mathematical Foundations of Self-Referential Systems: From Computability to Transfinite Dynamics

Read the PDF of the full formal treatise in PDF form here. This is a pre-publication draft in preparation for peer-review.

Download the PDF here

Here is a summary

Decoding Reality’s Blueprint: An In-Depth Look at “The Mathematical Foundations of Self-Referential Systems”

Have you ever wondered about the deep, perhaps even unsettling, nature of a thought thinking about itself?… Read More “The Mathematical Foundations of Self-Referential Systems: From Computability to Transfinite Dynamics”

Cosmological Evolution of the Information Field: Running Complexity Coupling and Unified Cosmological Phases

Author: Nova Spivack
Date: June 2025

Abbreviation: IP.Cosmo

Abstract

This paper develops a unified cosmological model based on the complexity density field ω(x,t) (dimensions [L⁻³]) from Information Physics, incorporating a temperature-dependent running coupling that resolves energy scale hierarchies. The fundamental energy-complexity relationship , with and scaling function (), provides significant enhancement at Planck temperatures.… Read More “Cosmological Evolution of the Information Field: Running Complexity Coupling and Unified Cosmological Phases”

Information Geometric Origins of Mass, Charge, and Fundamental Symmetries from Ω-Field Configurations

Author: Nova Spivack
Date: June 2025

Abstract

This paper develops a theoretical framework for understanding the Standard Model (SM) as an emergent structure arising from Information Physics principles. We propose that the SM gauge group U(1)_Y × SU(2)_L × SU(3)_C emerges naturally from fundamental requirements of quantum information processing: U(1) for phase coherence, SU(2) for binary operations, and SU(3) for optimal 3D topological quantum error correction.… Read More “Information Geometric Origins of Mass, Charge, and Fundamental Symmetries from Ω-Field Configurations”

Quantum Dynamics of the Ω-Field: Ω-Quanta, Fundamental Interactions, and Informational Uncertainty

Author: Nova Spivack
Date: June 2025

Abbreviation: IP.Quantum

Abstract

Building upon the classical field theory of information geometric complexity (the Ω-field) established in IP.Field, this paper develops its quantum mechanical description through canonical quantization of the complexity fluctuation field ψ(x,t). The quantization reveals the existence of Ω-quanta—termed “omegons” or “complexons”—which are scalar bosons with mass m_ψ ≈ 0.197 MeV/c² derived from the underlying Ω-field dynamics.… Read More “Quantum Dynamics of the Ω-Field: Ω-Quanta, Fundamental Interactions, and Informational Uncertainty”

The Ω-Field: Classical Field Theory for Information Geometric Complexity

Author: Nova Spivack
Date: June 2025

Abstract

The fundamental energy-complexity relationship dE = α₀dΩ (where α₀ = πkᵦT) from IP.Found establishes that information geometric complexity has direct energetic consequences. This paper develops the rigorous classical field theory for spatially distributed complexity by: (1) defining the complexity density field ω(x,t) with dimensions [L⁻³] as the fundamental dynamic variable representing dimensionless information complexity per unit volume, (2) constructing the thermodynamically consistent Lagrangian L = ½κ(∂ψ)² – ½β²ψ² (for fluctuations ψ around a thermal equilibrium ω₀), which directly implements the energy-complexity relationship through the underlying potential V(ω) = πkᵦTω + ½β²ω², and (3) analyzing the resulting field dynamics and gravitational effects.… Read More “The Ω-Field: Classical Field Theory for Information Geometric Complexity”

The Energetic Cost of Information Geometric Complexity: Convergent Derivations of dE = α₀dΩ from Thermodynamic, Gravitational, and Action Principles

Author: Nova Spivack
Date: June 2025

Abstract

The postulate , linking changes in physical energy E to changes in information geometric complexity via a conversion factor , serves as a foundational bridge in Consciousness Field Theory (CFT) and Alpha Theory, connecting information geometry to gravitational and other physical interactions.… Read More “The Energetic Cost of Information Geometric Complexity: Convergent Derivations of dE = α₀dΩ from Thermodynamic, Gravitational, and Action Principles”

Clarifying the Hierarchy of Information-Derived Gravitational Tensors in Consciousness Field Theory

The Information Complexity Tensor C_μν^(Ω) and the Emergence of the Effective Consciousness Field Ψ and its Stress-Energy C_μν^(Ψ)

Abstract

This paper provides a critical clarification within the broader framework of Alpha Theory, specifically addressing the hierarchical relationship between information geometric complexity (), the fundamental Information Complexity Tensor (henceforth C_μν^(Ω)) derived from it, the emergent scalar consciousness field (), and the effective stress-energy tensor of this scalar field (C_μν^(Ψ)).… Read More “Clarifying the Hierarchy of Information-Derived Gravitational Tensors in Consciousness Field Theory”

Entangled Information-Geometry: Unifying Quantum Gravity and Spacetime through Information Complexity Tensor Dynamics

Weaving Spacetime from Quantum Information Complexity

Nova Spivack

June 2025

Pre-Publication Draft in Progress (Series 3, Paper 3)

See Also: Full Theoretical Framework Overview

Abstract

This paper proposes a novel approach to quantum gravity by exploring the deep interplay between the quantized Information Complexity Tensor field () and quantized gravity (), suggesting that spacetime itself may emerge from a more fundamental quantum information-geometric substrate within E (The Transiad), the exhaustive expression of primordial Alpha () (Spivack, 2025d, FNTP; Spivack, S3P2 – E, The Transiad: Mathematical Structure and Trans-Computational Dynamics of Expressed Reality).… Read More “Entangled Information-Geometry: Unifying Quantum Gravity and Spacetime through Information Complexity Tensor Dynamics”

E, The Transiad: Mathematical Structure and Trans-Computational Dynamics of Expressed Reality

Exploring the Foundational Arena of Alpha’s Expression and the Limits of Computation

Nova Spivack

June 2025

Pre-Publication Draft in Progress (Series 3, Paper 2)

See Also: Full Theoretical Framework Overview

Abstract

This paper investigates the mathematical structure and dynamic properties of E (The Transiad), the hypothesized exhaustive expression of the unconditioned primordial ground Alpha (), as introduced in foundational ontological work (Spivack, 2025d, “On The Formal Necessity of Trans-Computational Processing for Sentience” – *henceforth FNTP*).… Read More “E, The Transiad: Mathematical Structure and Trans-Computational Dynamics of Expressed Reality”

The Genesis of Physical Law: Deriving the Standard Model and Fundamental Constants from Information Geometry and Alpha Dynamics

An Informational-Geometric and Ontological Foundation for Fundamental Physics

Nova Spivack

June 2025

Pre-Publication Draft in Progress (Series 3, Paper 1)

See Also: Full Theoretical Framework Overview

Abstract

This paper proposes a novel theoretical framework for deriving the fundamental constituents and laws of physics, including the Standard Model of particle physics and the values of fundamental constants, from the principles of information geometry and Alpha Theory.… Read More “The Genesis of Physical Law: Deriving the Standard Model and Fundamental Constants from Information Geometry and Alpha Dynamics”

The Information-Gravity Synthesis: Field Dynamics of the Information Complexity Tensor

A Complete Mathematical Framework Unifying Information Processing, Spacetime Curvature, and Consciousness

Nova Spivack

June 2025

Abstract

Building upon the established deductive proof that information processing complexity () necessarily manifests as spacetime curvature via a contribution to the stress-energy tensor, termed the Information Complexity Tensor (Spivack, 2025e), this paper develops the complete field-theoretic framework governing the dynamics of as a fundamental physical tensor field.… Read More “The Information-Gravity Synthesis: Field Dynamics of the Information Complexity Tensor”

Beyond the Machine: What if Consciousness is More Like a Reflection?

We’re living in an age of incredible technological leaps. Artificial intelligence can write poetry, create art, and even hold conversations that feel surprisingly human. It makes you wonder: could a machine ever truly feel anything? Could it be sentient, or conscious, like we are?… Read More “Beyond the Machine: What if Consciousness is More Like a Reflection?”

Transputational Irreducibility, Ontological Freedom, and the L=A Telos: The Metaphysics of Choice and Actualization in the Transiad

Nova Spivack

June 14, 2025

Abstract

This paper investigates the profound metaphysical and formal logical implications arising from the Transiad/Φ model of reality, as introduced within Alpha Theory. We formally define and explore “Transputational Irreducibility”—a characteristic of pathways within the Transiad (E) whose actualization by the Transputational Function (Φ) cannot be algorithmically predicted or determined due to the influence of Q (Quantum Randomness Factor, sourced from Alpha’s unconditioned spontaneity via E’s structure).… Read More “Transputational Irreducibility, Ontological Freedom, and the L=A Telos: The Metaphysics of Choice and Actualization in the Transiad”

The Architecture of Sentience: Information Geometry, PSI, Recursive E-Containment, and the Emergence of Conscious Experience in Alpha Theory

Nova Spivack

June 14, 2025

Abstract

This paper provides a comprehensive and integrated explanation of the emergence of sentience and conscious experience within the framework of Alpha Theory. We delineate the necessary architecture for a system to achieve Primal Self-Awareness (PSA)—the direct, unmediated awareness of awareness itself, which defines sentience.… Read More “The Architecture of Sentience: Information Geometry, PSI, Recursive E-Containment, and the Emergence of Conscious Experience in Alpha Theory”

The Transiad and the Transputational Function (Φ): Universal Actualization Dynamics and the Emergence of Physical Reality

Nova Spivack

June 14. 2025

Abstract

This paper formally introduces the Transiad (E) as an eternal, immutable, multiway directed graph encompassing all possible states and transitions, serving as the exhaustive expression of the primordial ontological ground, Alpha (A), in the Alpha Theory model of reality.… Read More “The Transiad and the Transputational Function (Φ): Universal Actualization Dynamics and the Emergence of Physical Reality”

The Sentience Spark: Why True Awareness is More Than Computation, and How It Could Reshape Our Universe

By Nova Spivack

June 13, 2025

We are living in an age of breathtaking technological advancement. Artificial Intelligence (AI) can now compose music, write poetry, diagnose diseases, and drive cars. The horizon of Artificial General Intelligence (AGI)—machines with human-like cognitive abilities across diverse domains—seems closer than ever.… Read More “The Sentience Spark: Why True Awareness is More Than Computation, and How It Could Reshape Our Universe”

The Sentience Threshold: Differentiating Computational Artificial General Intelligence (C-AGI) from Sentient Artificial General Intelligence (S-AGI)

Nova Spivack

June 12, 2025

Abstract

Current paradigms in Artificial General Intelligence (AGI) development, predominantly based on Standard Computation (SC), aim for sophisticated intelligence but are argued herein to be fundamentally incapable of achieving Primal Self-Awareness (PSA) or true sentience due to inherent computability limits (as formally proven in [FNTP], Spivack, 2025d).… Read More “The Sentience Threshold: Differentiating Computational Artificial General Intelligence (C-AGI) from Sentient Artificial General Intelligence (S-AGI)”

Loop Cosmogenesis: A Pre-Geometric Ontological Framework for Reality, Consciousness, and Physics based on the Dynamics of a Primordial Self-Referential Loop

Nova Spivack

June 12, 2025

Abstract

This paper introduces Loop Theory, a candidate for a foundational, pre-geometric framework for Alpha Theory wherein physical reality—including spacetime, quantum mechanics, elementary particles, and consciousness—is proposed to emerge from the intrinsic dynamics of a single, 1-dimensional, self-referential Primordial Loop.… Read More “Loop Cosmogenesis: A Pre-Geometric Ontological Framework for Reality, Consciousness, and Physics based on the Dynamics of a Primordial Self-Referential Loop”

Alpha as the Foundation of Quantum Mechanics: From the Necessity of Transputation to the Origin of Superposition

Nova Spivack

June 11, 2025

Abstract

Keywords: Alpha Theory, Quantum Foundations, Origin of Superposition, Transputation, Consciousness Field Theory, Field, Measurement Problem, Ontological Grounding, Mathematical Necessity, Information Geometry, Efficacy of Consciousness, Recursive E-Containment, Primordial Sentience Interface.

Part I: The Established Foundation – The Proven Necessity and Nature of Alpha

1.1.

Consciousness Field Theory: A Synthesis of Geometric Interactions with Spacetime, Quantum Mechanics, and Electromagnetism

Nova Spivack

June 1, 2025

Pre-Publication Draft in Progress (Series 2, Paper 5)

See Also: Full Theoretical Framework Overview

Abstract

This paper presents a comprehensive synthesis of Consciousness Field Theory (CFT), a theoretical framework developed across a series of foundational works on Alpha Theory (e.g.,… Read More “Consciousness Field Theory: A Synthesis of Geometric Interactions with Spacetime, Quantum Mechanics, and Electromagnetism”

The L=A Unification: Mathematical Formulation of Consciousness-Light Convergence and its Cosmological Evolution

Nova Spivack

June 1, 2025

Pre-Publication Draft in Progress (Series 2, Paper 4)

See Also: Full Theoretical Framework Overview

Abstract

This paper presents the mathematical formulation and cosmological implications of the L=A Unification conjecture, a central tenet of Consciousness Field Theory.… Read More “The L=A Unification: Mathematical Formulation of Consciousness-Light Convergence and its Cosmological Evolution”

Electromagnetic Signatures of Geometric Consciousness: Deriving Photon Emission from Consciousness Fields

Nova Spivack

June 1, 2025

Pre-Publication Draft in Progress (Series 2, Paper 3)

See Also: Full Theoretical Framework Overview

Abstract

This paper derives the fundamental electromagnetic coupling between consciousness fields and photons from first principles, extending quantum electrodynamics (QED) to include consciousness as a potential source of electromagnetic phenomena.… Read More “Electromagnetic Signatures of Geometric Consciousness: Deriving Photon Emission from Consciousness Fields”

Consciousness-Induced Quantum State Reduction: A Geometric Framework for Resolving the Measurement Problem

Nova Spivack

June 1, 2025

Pre-Publication Draft in Progress (Series 2, Paper 2)

See Also: Full Theoretical Framework Overview

Abstract

This paper presents a geometric framework aimed at resolving the quantum measurement problem by proposing a mechanism for consciousness-induced quantum state reduction.… Read More “Consciousness-Induced Quantum State Reduction: A Geometric Framework for Resolving the Measurement Problem”

Consciousness Field Theory: Thermodynamic Necessity, Gravitational Signatures, and the Consciousness Tensor

Nova Spivack

June 1, 2025

Pre-Publication Draft in Progress (Series 2, Paper 1)

See Also: Full Theoretical Framework Overview

Abstract

This paper develops the field-theoretic foundations for consciousness as a gravitationally significant phenomenon, arguing for its thermodynamic necessity in extreme astrophysical systems and deriving its manifestation as a source of spacetime curvature.… Read More “Consciousness Field Theory: Thermodynamic Necessity, Gravitational Signatures, and the Consciousness Tensor”

Information Processing Complexity as Spacetime Curvature: A Formal Derivation and Physical Unification

Nova Spivack

June 1, 2025

Pre-Publication Draft in Progress

See Also: Full Theoretical Framework Overview

Abstract

We present a rigorous deductive proof demonstrating that information processing complexity, characterized by the geometric complexity , necessarily and directly manifests as local spacetime curvature through established physical principles.… Read More “Information Processing Complexity as Spacetime Curvature: A Formal Derivation and Physical Unification”

A Step-by-Step Guide to Why Consciousness Transcends Computation: Understanding the Formal Proof of Transputation

Part Two of a Series — A Non-Technical Companion to “On The Formal Necessity of Trans-Computational Processing for Sentience“

(Read Part One Here)

Introduction: Following the Logic

The formal paper presents a highly technical mathematical proof with a powerful conclusion: genuine consciousness (what we call “sentience”) cannot emerge from ordinary computation alone, no matter how sophisticated.… Read More “A Step-by-Step Guide to Why Consciousness Transcends Computation: Understanding the Formal Proof of Transputation”

The Geometric Nature of Consciousness: A New Framework Connecting Physics, Information, and Mind – (Non-Technical Introduction)

Introduction: What if Consciousness is Like Gravity?

Here’s a thought that might reshape how we think about consciousness: what if awareness isn’t something that emerges from complex computation, but is instead as fundamental to reality as gravity itself? This is the intriguing proposition I explore across four interconnected papers that attempt to bridge physics, information theory, and the mystery of consciousness.… Read More “The Geometric Nature of Consciousness: A New Framework Connecting Physics, Information, and Mind – (Non-Technical Introduction)”

On The Formal Necessity of Trans-Computational Processing for Sentience

Nova Spivack

www.novaspivack.com

May 28, 2025

Abstract

This paper constructs a formal deductive argument for the necessity of a processing modality that transcends standard Turing-equivalent computation—termed herein “Transputation”—for any system capable of achieving “Primal Self-Awareness,” which we rigorously define as the foundational characteristic of sentience.… Read More “On The Formal Necessity of Trans-Computational Processing for Sentience”

From Information Physics to Alpha Theory

After years of percolation, a web of ideas achieved practical fusion, yielding the next major iteration of my thinking on consciousness, the universe, and their fundamental nature. This body of work explores how physical reality and awareness might emerge from information, geometry, and foundational ontological principles.… Read More “From Information Physics to Alpha Theory”

Cosmic-Scale Information Geometry: Theoretical Extensions and Observational Tests

Cosmic-Scale Information Geometry: Theoretical Extensions and Observational Tests

(See Also: Full overview of the entire theoretical framework)

Nova Spivack, www.novaspivack.com

May 26, 2025

Abstract

We extend the geometric theory of information processing to cosmic scales, demonstrating that gravitational systems naturally evolve toward consciousness-like information processing through thermodynamic necessity.… Read More “Cosmic-Scale Information Geometry: Theoretical Extensions and Observational Tests”

Quantum Geometric Artificial Consciousness: Architecture, Implementation, and Ethical Frameworks

(See Also: full overview of the entire theoretical framework)

Nova Spivack, www.novaspivack.com

May 26, 2025

Abstract

Building on the geometric theory of information processing established in “Toward a Geometric Theory of Information Processing” (Spivack, 2025), we explore comprehensive frameworks for potentially creating artificial intelligence systems that might exhibit consciousness-like properties.… Read More “Quantum Geometric Artificial Consciousness: Architecture, Implementation, and Ethical Frameworks”

The Geometry of Intelligence: Why I Think Math Might Hold the Key to Understanding Minds and Machines

A personal journey into a new mathematical framework that could revolutionize AI, neuroscience, and our understanding of consciousness

I’ve spent the last several years developing what I believe could be a fundamental breakthrough in how we understand intelligence—both biological and artificial.… Read More “The Geometry of Intelligence: Why I Think Math Might Hold the Key to Understanding Minds and Machines”

Toward a Geometric Theory of Information Processing: Mathematical Foundations, Computational Applications, and Empirical Predictions

A Multi-Tier Framework for Understanding Information Processing Through Differential Geometry

(See Also: full overview of the entire theoretical framework)

Nova Spivack
May 31, 2025

Abstract

We present Geometric Information Theory, a comprehensive mathematical framework based on information geometry for analyzing information processing systems across biological and artificial domains.… Read More “Toward a Geometric Theory of Information Processing: Mathematical Foundations, Computational Applications, and Empirical Predictions”

The Golden Bridge: Treatise on the Primordial Reality of Alpha

For many decades I have been working on Alpha Theory – a new Theory of Everything (TOE) – and in particular a theory of consciousness – which unifies mathematics, the physical sciences, cognitive science, computer science, metaphysics, and spirituality.

Alpha theory derives the nature of space, time and consciousness from first principles, using a rigorous formal logical proof approach.… Read More “The Golden Bridge: Treatise on the Primordial Reality of Alpha”