Dynamics, Algorithms, and Structured Experience: What Must a Brain Simulation Preserve?

A brain simulation can match every behavior and every brain scan of a person and still leave open whether it preserves what actually matters for shared experience — because "matching outputs" and "running the same computation" are different claims entirely.

This paper is BCOM's attempt to make that gap precise. Its background theory, Kolmogorov Theory (KT), takes experience as a basic fact about physical processes and treats mathematical structure as how that experience is organized — not something computation manufactures from scratch. If that's your starting premise, then the question "does a simulation share the person's experience?" reduces to: does it preserve the same organization the brain realizes? And that turns out to split into two genuinely hard problems, which the paper tackles with a string of small, concrete examples rather than hand-waving.

First: what computation does a physical system actually run? Not every way of summarizing a system's state gives you a valid "next state" prediction. The paper's spring example is the clearest illustration — two masses connected by a spring have a clean, closed description in terms of their center of mass (it just drifts, ignoring the spring entirely), and a different clean closed description in terms of the internal vibration. But an arbitrarily weighted average of the two masses' positions is not closed: two setups can have the same weighted average now and different weighted averages a moment later. So "coarse-graining" a system doesn't automatically give you a real computation running inside it — you have to check that the retained variables actually determine their own future (this is called dynamical closure), and that the physical system genuinely supports the states you're attributing to it, not just that your description happens to fit the data.

Second, harder problem: once you've identified an organization, how do you tell if two systems share it? The paper leans on a mathematician named Yanofsky's distinction between three things that get conflated: a function (input-output behavior), an algorithm (a procedure, up to some notion of sameness), and a program (the actual implementation). Two systems can compute the identical function while running utterly different procedures — the paper's toy example is a four-state counter and a two-state counter that both report the same parity bit forever, yet the four-state machine retains a distinction (which of two "even" phases it's in) that the two-state machine simply cannot express. Matching behavior at an interface doesn't tell you what's happening behind it. Similarly, Fourier-transforming a ring of coupled oscillators turns local, physically-connected sites into "independent" oscillating modes on paper — but that's just a change of coordinates, not evidence that the system is secretly built from separate mode-processors. Sameness of description is cheap; sameness of physically realized organization is not.

The payoff of grinding through this machinery is a sharper diagnosis of the classic thought experiments in philosophy of mind. Searle's Chinese Room and its brain-simulator variant, the "unfolding arg