Gödel in the Machine
Why Incompleteness Doesn’t Apply to Physics.
The recent claim that the universe cannot be a computer simulation strikes at the heart of one of modern physics’s most powerful meta-assumptions: the Deutsch–Church–Turing (DCT) thesis, which holds that every physically realizable process can, in principle, be simulated by a universal computing device. This is not merely a claim about our current computational tools, but a statement about the nature of reality itself. If the laws of physics are algorithmic, the universe is simulable. If not, computation is only an approximation of being.
1. What the DCT Thesis Asserts
The DCT thesis extends the Church–Turing thesis from logic into physics. It states:
Every finitely realizable physical system can be perfectly simulated by a universal computing device operating by finite means.
Under this view, all evolution of state—every quantum event, every interaction, every emergent phenomenon—is ultimately computable. Physical law corresponds to an algorithm. This assumption underpins not only simulation hypotheses but also digital physics, computational cosmology, and much of theoretical AI alignment research.
2. The Non-Algorithmic Challenge
The new paper (Faizal et al., 2025) claims that reality is non-algorithmic. It draws an analogy from Gödel’s incompleteness theorems: in any consistent formal system, there exist true propositions that cannot be proven within that system. The authors transpose this logic into physics:
If the universe were algorithmic, every physical truth would be derivable from its computational rules.
Gödelian incompleteness shows that no consistent formal system is complete.
Therefore, there must exist physical truths that cannot be computed by any finite algorithm.
Hence, the universe transcends computation.
This directly contradicts the DCT thesis. If some truths about the world are non-computable, then no universal computing device—no matter how powerful—can perfectly simulate reality.
3. Ontological vs. Epistemic Non-Computability
It is crucial to distinguish two senses of non-computability:
Epistemic: Humans cannot compute or predict everything due to limited knowledge or resources. (Compatible with DCT.)
Ontological: Some physical processes in themselves have no computable description, even in principle. (Contradicts DCT.)
The Faizal argument appears to assert the latter—that non-algorithmicity is baked into the structure of reality itself. If true, this would mean that computation cannot exhaust ontology. The universe is not a program running on cosmic hardware; it is a generative process that exceeds the formal limits of algorithmic reasoning.
4. The Stakes for Physics and Philosophy
Rejecting the DCT thesis would have profound implications:
Digital physics collapses. Models like Wolfram’s cellular automaton universe or Lloyd’s quantum computer universe would be strictly false, not merely incomplete.
Strong simulation hypotheses fail. If reality includes non-computable dynamics, no higher-level civilization could run a perfect simulation of us.
AGI limits emerge. No machine bound by algorithmic law could fully model or predict reality—only approximate it.
Physics reopens to metaphysics. A non-algorithmic universe invites reexamination of emergence, continuity, and causation beyond computation.
5. The Counterpoint: DCT as a Boundary, Not a Fact
The DCT thesis was never a theorem—it was a boundary condition, an assumption of closure. It defines a cosmos that can, in principle, be rendered as finite information evolving under computable rules. To refute it, one must show a physically real process that provably exceeds Turing computability—a natural hypercomputer.
No such demonstration yet exists. Invoking Gödel’s incompleteness in physics is powerful metaphorically but not formally. Gödel’s results apply to symbolic systems; physical law may not be symbolically representable in the same way. Until a clear mapping between mathematical undecidability and physical non-computability is shown, the DCT thesis stands—not as proven truth, but as the best available approximation.
6. Beyond the Binary
The deeper insight here is not that one side must be right, but that the computability of reality may itself be conditional. It may hold locally within domains of decohered structure, yet fail globally at boundaries of emergence—consciousness, quantum measurement, cosmogenesis. The universe may be partially computable: a simulation engine embedded within a non-algorithmic substrate.
This reconciles both intuitions: the success of computational physics and the persistent residue of uncomputable truth.
In summary: The claim that the universe is non-algorithmic, if substantiated, would overturn the Deutsch–Church–Turing thesis and with it the metaphysics of digital physics. But until a physically grounded instance of non-computability is shown, the DCT thesis remains the default metaphysical assumption of science—a boundary condition, not a law. The true challenge is to identify where computation ceases to be an adequate model of reality and to understand what, if anything, lies beyond its limits.