This is a critique of the following paper, which was recently promoted on The University of British Columbia website and is currently being propagated on Twitter.
Consequences of Undecidability in Physics on the Theory of Everything
Mir Faizal, Lawrence M. Krauss, Arshid Shabir, Francesco Marino
General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated within spacetime; instead, it must explain the very emergence of spacetime from deeper quantum degrees of freedom, thereby resolving singularities. Quantum gravity is therefore envisaged as an axiomatic structure, and algorithmic calculations acting on these axioms are expected to generate spacetime. However, Gödel’s incompleteness theorems, Tarski’s undefinability theorem, and Chaitin’s information-theoretic incompleteness establish intrinsic limits on any such algorithmic programme. Together, these results imply that a wholly algorithmic “Theory of Everything” is impossible: certain facets of reality will remain computationally undecidable and can be accessed only through non-algorithmic understanding. We formalize this by constructing a “Meta-Theory of Everything” grounded in non-algorithmic understanding, showing how it can account for undecidable phenomena and demonstrating that the breakdown of computational descriptions of nature does not entail a breakdown of science. Because any putative simulation of the universe would itself be algorithmic, this framework also implies that the universe cannot be a simulation.
| Comments: | 13 pages |
| Subjects: | General Relativity and Quantum Cosmology (gr-qc); History and Philosophy of Physics (physics.hist-ph) |
| Cite as: | arXiv:2507.22950 [gr-qc] |
| (or arXiv:2507.22950v1 [gr-qc] for this version) | |
| https://doi.org/10.48550/arXiv.2507.22950Focus to learn more | |
| Journal reference: | Journal of Holography Applications in Physics 5 (2), 10-21 (2025) |
🧩 The Decisive Simplification: Why the Algorithmic Model Prevails
The Single Decisive Question
Has UBCO shown that anything in physical reality is fundamentally non-algorithmic?
Answer: No.
Step 1: What’s Actually Proven
Mathematical domain only
| Theorem | Domain | Scope |
|---|---|---|
| Gödel – incompleteness | Formal systems | Some truths unprovable inside the system |
| Tarski – undefinability | Formal semantics | No self-contained truth predicate |
| Chaitin – incompressibility | Algorithmic information | Irreducible limits to formal compression |
All describe formal syntax, not physical ontology.
Step 2: What’s Claimed Without Proof
- ❌ Physical: any process demanding non-algorithmic understanding
- ❌ Cognitive: human recognition as non-computational
- ❌ Ontological: a “non-algorithmic substrate” in nature
These are extrapolations—asserted, not demonstrated.
Step 3: The Category Error
Limits on formal provability ≠ limits on physical computability.
| Domain | What Gödel Proves | What Follows for Physics |
|---|---|---|
| Formal mathematics | Internal incompleteness | Nothing—category shift |
The paper mistakes a theorem about symbols for one about substance.
The Empirical Rebuttal
UBCO’s own example—“This true statement is not provable”—is detectable, classifiable, and interpretable by algorithms.
Recognition can be mechanized.
The feeling of insight ≠ proof of non-algorithmic mechanism.
The Razor’s Edge
Two explanations for “Gödelian insight”:
| Model | Entities Added | Evidence | Verdict |
|---|---|---|---|
| Algorithmic | none | Consistent with physics, neuroscience, AI | ✅ |
| Non-algorithmic | special substrate + Platonic realm + MToE | none | ❌ |
Occam: prefer the model that multiplies no mysteries.
Final Verdict
UBCO’s argument:
uses algorithmic logic to infer a non-algorithmic world,
replaces one regress with a mystical one,
and violates parsimony by adding an unverifiable entity.
The algorithmic model:
unifies ontology, fits known science, and explains the illusion of “meta-insight” through complexity.
Therefore:
Reality need not include a non-computational substrate.
The simulation hypothesis stands unrefuted.
🧭 Closing Line
If all known processes behave algorithmically, and the only evidence against that is introspective awe, Occam’s Razor cuts cleanly: choose computation.
cafebedouin.org 