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.
The Universe in a Mirror: My Theory of a Self-Defining Reality
For decades, a single, profound question has been the driving force behind my work: How can a universe give rise to beings within it who can, in turn, understand and describe that very universe?
Think about it. The existence of a physicist, a mathematician, or even just a conscious mind capable of introspection, is a paradox. It means the “stuff” of reality—the substrate of the cosmos—must be powerful enough to create a complete and accurate representation of itself. I call this the Principle of Cognitive-Substrate Equivalence, and in my new treatise, “The Self-Defining Universe,” I argue that this simple observation is the key to unlocking a new foundation for all of science.
This principle, however, immediately confronts us with one of the most formidable intellectual barriers ever discovered.
The Great Wall of Self-Reference
In the 20th century, a trio of brilliant minds—Kurt Gödel, Alan Turing, and Alfred Tarski—proved a devastating limitation that applies to all traditional formal systems, from mathematics to computer science. In essence, they showed that any system complex enough to be interesting cannot describe itself in a way that is both complete (capturing all truths about itself) and consistent (containing no contradictions).
This is the Gödel-Turing-Tarski Barrier. It’s like trying to create a perfectly detailed map of a country that also contains a perfect copy of the map itself. That map-within-a-map would need its own map, and so on, into an infinite, impossible regress. This barrier tells us that any hierarchical system—one where the rules are separate from the things the rules operate on—is fundamentally incapable of perfect self-knowledge.
If our universe were such a system, we simply couldn’t exist. The fact that we do exist is proof that the universe operates on a different principle. It must be non-hierarchical.
The Solution: A System That Is Its Own Language
My work resolves this paradox by introducing a new class of formal system I call a Self-Defining System (SDS).
The defining characteristic of an SDS is that it is a perfect, non-hierarchical loop of self-reference. I formalize this with a simple but powerful equation: S = L(S). Here, S is the system itself, and L is a language-creation operator. This equation states that the system is its own language of self-description.
It’s not a computer running a program. It’s a system where the computer and the program are one and the same. It’s not a territory with a map inside it; it’s a territory that is its own map. In the paper, I rigorously prove that the only possible meta-topological structure for such a system is a closed, self-referential loop—what I call the Primordial Loop. This is not a loop in space or time, but a loop of pure definition, where every element is ultimately defined by every other element, with no need for any external foundation.
The Two Engines of Reality: Computation and Transputation
Once you have this Primordial Loop, you can ask: what can it do? My research reveals two fundamentally different modes of operation.
- Computation: This is the process we are all familiar with. It involves executing operations according to a fixed set of rules. This is the domain of the Turing Machine, of classical logic, and of our digital world. On the Primordial Loop, computation describes the behavior of stable sub-systems—patterns that have temporarily settled into a consistent set of rules. This is the source of the predictable, clockwork aspects of our universe that classical physics describes so well.
- Transputation: This is the crucial, new concept I introduce. Transputation is the process by which the system modifies its own fundamental rules. It is the Loop re-wiring itself. It’s not just processing information; it is the act of transforming the processor. Transputation is the engine of creation, evolution, and novelty. It is the source of the universe’s ability to generate new structures, new laws, and new meaning.
Our universe, I propose, is a constant interplay between these two modes. Stable structures emerge and operate according to computational rules, but the underlying transputational capacity allows for genuine creation and change.
Deriving Physics from Pure Logic
This framework would be mere philosophical speculation if it didn’t connect with the world we observe. The most powerful part of my work is demonstrating that the fundamental features of our physical reality are not arbitrary facts but are necessary mathematical theorems that can be derived directly from the topology of the Primordial Loop.
In the paper, I provide formal derivations showing how:
- The Fermion/Boson Distinction, the two fundamental classes of particles, arises from the two ways information can circulate on a self-referential loop. One way is a simple loop (a boson), and the other involves a topological twist, like a Möbius strip (a fermion).
- Spin-1/2, the bizarre and foundational property of all matter particles (like electrons), is a direct consequence of this topological twist. The need to traverse the loop twice to return to the original orientation is the formal origin of spin-1/2.
- Quantization, the fact that energy and other properties exist in discrete packets, is a necessary result of the Loop needing to find stable, self-consistent standing waves to exist without generating destructive interference.
Physics, in this view, is not a set of arbitrary laws imposed on reality. Physics is the set of theorems that describe the most stable ways for a self-defining system to exist.
The Deepest Implications: Consciousness and a Final Theory
This theory extends into the deepest questions of science and existence. It offers a new resolution to the quantum measurement problem, framing it as a process of Dissonance Minimization, where the system naturally settles from an incoherent superposition into the most stable state available.
Most radically, I propose that consciousness is not computation, but transputation. The subjective experience of being aware—of having agency, of introspection, of creativity—is the direct phenomenological experience of the system actively reconfiguring its own informational structure. This explains why consciousness feels like something; it is the feeling of self-creation in action.
“The Self-Defining Universe” puts forward a new foundation for reality—one grounded not in matter or energy, but in the logic of perfect self-reference. It presents a universe that is not a machine, but a single, coherent thought, proving its own existence through the act of thinking. And we, as conscious observers, are the part of that thought that is finally becoming aware of itself.