Civilization is building systems that reason about themselves, audit themselves, and govern themselves — without a formal science of what self-referential systems can and cannot do. That gap is not merely academic. It is costing us clarity about AI safety, interpretability, consciousness, and the foundations of physics.… Read More “Toward a New Science of Self-Referential Systems”
This is a browser-based cellular automaton experiment that takes a different approach to the same challenge as the trend-aware experiment: how do you keep a self-tuning CA alive and interesting? Here the key innovation is that the rule parameters are not uniform scalars — they are spatial fields.… Read More “Neural CA: Spatial Parameter Fields and Greatest-Hits Memory”
This is a browser-based cellular automaton in which two cooperating neural agents learn — in real time, from scratch — to keep the simulation alive and interesting. No pre-training, no external data. The neural network trains itself as the simulation runs, and the agents use what they’ve learned to steer the system away from death and toward sustained complex behavior.… Read More “Neural CA: Trend-Aware Agents Learn to Keep a Cellular Automaton Alive”
New to this research? This article is part of the Reflexive Reality formal research program. Brief introduction ↗ · Full research index ↗
Series: Mind, Intelligence, and Sentience — What NEMS Proves · Parts 1–3: The Nature of Self · Actual vs.… Read More “Is the Universe Sentient? What the Formal Proofs Say”
New to this research? This article is part of the Reflexive Reality formal research program — a suite of 93+ machine-checked papers and 17 Lean 4 proof libraries. Brief introduction ↗ · Full research index ↗
Series: Mind, Intelligence, and Sentience — What NEMS Proves (4-part) · All research ↗
This is Part 1 of a four-part series on what NEMS formally proves about mind, intelligence, and sentience.… Read More “The Nature of Self: What NEMS Proves About Self-Models at Every Scale”
New to this research? This article is part of the Reflexive Reality formal research program. Brief introduction ↗ · Full research index ↗
Mind uploading — scanning a brain and running the data on a new substrate — is widely discussed as a path to digital immortality.… Read More “Mind Uploading Won’t Work the Way You Think — Here’s What It Would Actually Require”
New to this research? This article is part of the Reflexive Reality formal research program. Brief introduction ↗ · Full research index ↗
Observers — systems like us that experience, record, and adjudicate reality — are usually treated as evolutionary accidents, products of a long biological contingency that could easily have not happened.… Read More “Why the Universe Must Have Observers: Necessary Adjudicators”
New to this research? This article is part of the Reflexive Reality formal research program. Brief introduction ↗ · Full research index ↗
What if the universe is not a physical system that happens to encode information — but something closer to a distributed error-correcting code, where the distributed record fragments of the universe behave like codewords imposing constraints on each other?… Read More “The Universe as a Semantic Error-Correcting Code”
New to this research? This article is part of the Reflexive Reality formal research program. Brief introduction ↗ · Full research index ↗
Bell’s inequalities prove quantum correlations are real and non-local — two particles, measured far apart, show correlations that no local hidden variable theory can explain.… Read More “Semantic Nonlocality: Correlation Without Signaling, Formally Proved”
New to this research? This article is part of the Reflexive Reality formal research program — a suite of 93+ machine-checked papers and 17 Lean 4 proof libraries. Brief introduction ↗ · Full research index ↗
Series: NEMS on Physics (4-part) · All research ↗
This is Part 1 of a four-part series on what NEMS proves about physics.… Read More “Why the Born Rule Is the Only Possible Probability”
New to this research? This article is part of the Reflexive Reality formal research program. Brief introduction ↗ · Full research index ↗
Series: NEMS on Physics (4-part) · Part 1: Born Rule · Part 2: Standard Model · Part 3: Arrow of Time · Part 4: Exotic Physics
The Standard Model’s gauge group — SU(3)×SU(2)×U(1) with three generations of fermions — has always seemed like a lucky accident.… Read More “Why the Standard Model Gauge Group Is the Only Possible Choice”
New to this research? This article is part of the Reflexive Reality formal research program. Brief introduction ↗ · Full research index ↗
Series: NEMS on Physics (4-part) · Part 1: Born Rule · Part 2: Standard Model · Part 3: Arrow of Time · Part 4: Exotic Physics
The laws of physics are mostly time-symmetric — they work the same forward and backward.… Read More “Where Does Time’s Arrow Come From?”
New to this research? This article is part of the Reflexive Reality formal research program. Brief introduction ↗ · Full research index ↗
Series: NEMS on Physics (4-part) · Parts 1–3: Born Rule · Standard Model · Arrow of Time · Part 4: Exotic Physics
Science fiction loves exotic physics: time travel, wormholes, black-hole computers that solve undecidable problems, quantum entanglement as a telephone.… Read More “Black Holes, Time Travel, and the Limits of Exotic Physics”
Over the past several years I have been building a substantial formal research program — machine-verified, mathematically precise, and published with permanent DOIs on Zenodo. Today I am making the full index available at novaspivack.com/research. This post is an introduction to what the program covers and why I think it matters.… Read More “Introducing My Formal Research Program: From the Foundations of Reality to the Structure of Mind”
A machine-checked theorem proves that any closed physical universe rich enough to contain computation cannot internally contain a complete algorithmic account of its own record-truth. This is not about the limits of human knowledge. It is a theorem about the architecture of reality.… Read More “Physical Incompleteness: The Universe Cannot Contain a Complete Account of Itself”
A machine-checked theorem proves that no parametric self-model — no matter how rich, how large, or how powerful — can represent its own diagonal. The blind spot is not a resource limitation. It is structural. And it holds with no computability assumption, no arithmetic, no cardinality.… Read More “Representational Incompleteness: Why No Self-Model Can Capture Its Own Diagonal”
Gödel’s incompleteness, Turing’s halting undecidability, Kleene’s recursion theorem, Tarski’s truth undefinability, and Löb’s reflection theorem are five of the most celebrated results in 20th-century logic and computation. A new machine-checked theorem proves they are all instances of one master fixed-point framework.… Read More “One Theorem Behind Gödel, Turing, Kleene, Tarski, and Löb”
A machine-checked theorem proves that no sufficiently expressive reflexive system — no formal logic, no computer, no physical universe, no mind — can internally exhaust its own realized semantics. Physical incompleteness, representational incompleteness, and the classical barriers of Gödel, Turing, Kleene, Tarski, and Löb are all corollaries of one result.… Read More “Closure Without Exhaustion: Why Every System That Models Itself Has an Irreducible Remainder”
A new paper — backed by 422 machine-checked theorems and zero gaps — proves that a system can be completely governed by fixed laws and still never admit a final explanation. The implications reach from physics to biology to organizations to AI.… Read More “The End of Final Theories: How Fixed Laws Produce Inexhaustible Explanation”
This is the sixth essay in a series. The first, The Twist Move, describes the operation itself across mathematics, biology, physics, and business. The second, The Twist and the Ground of Being, argues that the consciousness twist is real, that the substrate must support it, and that this tells us something fundamental about the nature of reality.… Read More “The Theorem Behind the Twist – Lawvere’s Fixed-Point”
This is the second essay in a series. The first, The Twist Move, describes the operation itself across mathematics, biology, physics, and business. The second, The Twist and the Ground of Being, argues that the consciousness twist is real, that the substrate must support it, and that this tells us something fundamental about the nature of reality.… Read More “The Twist and the Ground of Being”
This article summarizes my book on The Self-Defining Universe, which focuses on how the universe can exist without an external runner – a fully self-contained universe that “runs itself.”
NOTE: This book is part 2 – following on my more general book on the Mathematical Foundations of Self-Referential Systems.… Read More “The Self-Defining Universe”
This article is about a new kind of simple computational rule (“LACE rules” running on LACE, the Link Automata Computing Engine platform) which, when applied locally on a grid of cells, demonstrates fascinating emergent “artificial life” behavior.
For readers familiar with the Game of Life (GOL), this is a next-level class of cellular automata that utilizes neighborhood topology — the state of the grid is a function of both cell states and their connectivity (links).… Read More “Introducing LACE – A New Kind of Cellular Automata”
This article explains my paper on the
Mathematics of 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”
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”
This paper explores whether the complexity density field ω(x,t) of Information Physics could play a cosmological role — driving inflation, contributing to dark energy, and providing a unified framework for the cosmic history. The model belongs to the broad class of quintessence models with a running coupling.… Read More “Cosmological Evolution of the Information Field: Running Complexity Coupling and Unified Cosmological Phases”
This paper explores whether the gauge group structure of the Standard Model — U(1)Y × SU(2)L × SU(3)C — can be understood as the inevitable consequence of quantum information processing requirements, rather than as an empirical fact to be postulated.… Read More “Information Geometric Origins of Mass, Charge, and Fundamental Symmetries from Ω-Field Configurations”
This paper canonically quantizes the complexity fluctuation field ψ(x,t) developed in IP.Field, treating it as a standard massive scalar quantum field. The result — termed Ω-quanta or “omegons” — are scalar bosons whose mass is set by the free parameters κ and β² of the classical theory.… Read More “Quantum Dynamics of the Ω-Field: Ω-Quanta, Fundamental Interactions, and Informational Uncertainty”
Given a conjectured energy-complexity relationship dE = πkBT dΩ (developed in IP.Found), this paper constructs the simplest classical field theory for a spatially distributed information geometric complexity density ω(x,t). The fluctuation field around thermal equilibrium satisfies standard massive Klein-Gordon dynamics, with all predictions expressed in terms of two free parameters.… Read More “The Ω-Field: Classical Field Theory for Information Geometric Complexity”
This paper develops theoretical support for a conjectured relationship between physical energy and information geometric complexity, dE = α₀dΩ, motivating the form α₀ = πkBT through three independent lines of reasoning: an extension of Landauer’s erasure principle to geometric complexity, a derivation from black hole thermodynamics, and an action principle consistency check.… Read More “The Energetic Cost of Information Geometric Complexity: Convergent Derivations of dE = α₀dΩ from Thermodynamic, Gravitational, and Action Principles”
This paper develops the classical field theory for the Information Complexity Tensor Cμν — a tensor field sourced by information geometric complexity Ω — and its dynamics as a physical tensor field. The central hypothesis is that Ω sources gravity not just through the scalar stress-energy of the ω-field (IP.Field)… Read More “The Information-Gravity Synthesis: Field Dynamics of the Information Complexity Tensor”
This paper develops the hypothesis that information processing complexity Ω — the integral of squared Riemann curvature of a system’s Fisher information manifold — contributes a novel stress-energy term to Einstein’s field equations, over and above the ordinary heat dissipation already accounted for by Landauer’s principle.… Read More “Information Processing Complexity as Spacetime Curvature: A Formal Derivation and Physical Unification”
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)”
Status note (April 2026): The papers in this series on Information Physics have been substantially revised and clarified, but still contain conjectures and speculative explorations. The NEMS formal research program — the machine-checked suite of 93 papers and 17 Lean 4 libraries — is a separate, more rigorous program described at novaspivack.com/research… Read More “From Information Physics to Alpha Theory”
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”
Geometric Information Theory applies differential geometry to the parameter spaces of information processing systems — neural networks, biological brains, and self-referential systems. This paper presents the mathematical framework, its computational predictions (well-grounded), its biological hypotheses (medium confidence), and its consciousness applications (highly speculative).… Read More “Toward a Geometric Theory of Information Processing: Mathematical Foundations, Computational Applications, and Empirical Predictions”
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”