In 1960 the physicist Eugene Wigner published an essay whose title became a genre: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” His puzzle was simple to state and has never been resolved. Mathematics is a game played with symbols, developed largely for its own internal beauty.… Read More “The Unreasonable Effectiveness of AI”
Category Archives: Physics
The Fish Who Could Not Imagine Air
Imagine a fish physicist. She is brilliant. Over centuries her tradition has built a physics of astonishing power: pressure, buoyancy, viscosity, the propagation of waves, the beautiful nonlinearities of turbulence. It predicts everything she can measure. It has no loose ends worth losing sleep over.… Read More “The Fish Who Could Not Imagine Air”
Toward a New Science of Self-Referential Systems
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”
Neural CA: Spatial Parameter Fields and Greatest-Hits Memory
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”
Neural CA: Trend-Aware Agents Learn to Keep a Cellular Automaton Alive
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”
The End of Final Theories: How Fixed Laws Produce Inexhaustible Explanation
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”
The Theorem Behind the Twist – Lawvere’s Fixed-Point
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”
The Twist and the Ground of Being
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”
The Self-Defining Universe
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”
Introducing LACE – A New Kind of Cellular Automata
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”
A New Mathematics of Self-Reference: A Comprehensive Non-Mathematical Summary
What This Work Is About
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”
The Mathematical Foundations of Self-Referential Systems: From Computability to Transfinite Dynamics
This article explains my paper on the
Mathematics of Self-Referential Systems.
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”
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”