CALLIOPE · BCOM

This position paper argues that the claim "consciousness is not computation" rests on a linguistic confusion rather than a substantive philosophical or scientific insight. Drawing on a formal definition of computation as coarse-grained dynamical isomorphism between physical systems — developed within the Kolmogorov Theory (KT) program and the dynamical-systems framework of Wolpert and Korbel — the work demonstrates that computation, properly understood, is not confined to silicon symbol-shuffling but encompasses all physical dynamics, including the oscillatory activity of biological neural systems. Under the physical Church–Turing–Deutsch thesis and the digital physics hypothesis, every physically realizable process is Turing-computable, rendering the biology-versus-computation dichotomy incoherent: to deny that consciousness is computational is, on this account, equivalent to denying that it is physical. The paper further shows that neural oscillations are best understood as the natural coarse-graining at which the brain's compressive modeling machinery becomes visible, not as an alternative to computation. The productive question, reframed within the KT framework, is not whether consciousness involves computation but what kind — specifically, what compressive world-modeling, objective evaluation, and counterfactual planning structures characterize conscious systems.

The word "computation" is doing three different jobs in the consciousness debate, and conflating them makes the whole argument collapse.

Peter Godfrey-Smith's claim — that consciousness depends on biological substrate and therefore isn't "mere computation" — sounds like a substantive philosophical position. This paper argues it's actually a terminological accident. The target is the folk meaning of computation: silicon chips shuffling discrete symbols, substrate-free and abstract. But that's not what computation means mathematically. The paper's central move is to replace that folk definition with a precise one: system A computes system B if there exist coarse-grainings of both (simplified, zoomed-out views) whose dynamics are isomorphic — structurally identical as dynamical systems. No silicon required. No symbols. Just matching behavior at some scale.

This definition has an immediate and somewhat surprising consequence: it's symmetric. If a computer simulates the ocean, the ocean equally "computes" the computer at the relevant scale. More importantly, under the physical Church–Turing–Deutsch thesis — the well-supported conjecture that every physically realizable process is simulable by a universal Turing machine — computation and physical dynamics are not analogous, they're identical. Every dynamical system computes; every computation is a physical dynamics. So "consciousness is not computation" becomes "consciousness is not physical dynamics," which no neuroscientist would sign up for.

The paper then handles the intuition that neural oscillations feel different from "real" computation. It flips this around: oscillations are computation, specifically the natural coarse-graining at which the brain's compressive modeling machinery becomes legible. Alpha rhythms and gamma bursts aren't alternatives to computation — they're the macroscopic signatures of billions of discrete spike events, already an emergent coarse-graining of something maximally digital. The paper also dispatches the objection from continuous mathematics: real numbers are constructed through formal procedures (Dedekind cuts, Cauchy sequences), every step of which is an effective computation, and the Curry–Howard correspondence makes this explicit — proofs are programs.

What the paper actually wants to argue, once the terminological fog clears, is that the productive question is what kind of computation characterizes conscious systems. Within the Kolmogorov Theory framework, the answer involves three specific structures: a compressive world model (internal dynamics that share algorithmic information with the environment), a non-trivial objective function (caring about some states over others), and counterfactual planning (simulating alternatives before acting). This is what separates a bee from a weathervane — not biology versus computation, but the type of computation instantiated. Godfrey-Smith is right that substrate matters, the paper concedes, but only because substrate constrains which computations are physically realizable and at what speed — not because biology escapes the computational description entirely.