Is Physics Made of Information?

Most "information-first" physics isn't actually about algorithmic information — and the one theory that is uses it to explain not what exists, but what persists.

The word "information" is doing a lot of different work in modern physics. Wheeler's "it from bit," black-hole entropy, holographic bounds, quantum reconstructions — these all invoke information, but they mean Shannon entropy, thermodynamic entropy, or operational distinguishability. That's ensemble-level stuff: properties of probability distributions over many possible states. Kolmogorov complexity (K-complexity) is something sharper and different: it's the length of the shortest program that generates a single specific object. This paper maps the whole landscape, shows that most information-first physics never touches K-complexity, and then locates Kolmogorov Theory (KT) precisely within the small minority that does.

The AIT (algorithmic information theory) branch — Zurek's physical entropy, Gell-Mann and Lloyd's effective complexity, Schmidhuber's algorithmic universes, Tegmark's low-information cosmos, Müller's observer-state reconstruction — all use K-complexity as their core currency. KT inherits from all of them: the algorithmic prior, the focus on individual objects rather than ensembles, the split between a globally short description and locally rich experience. But it asks a different question. The others ask which structures are simple or expected. KT asks how a bounded structure holds itself together against perturbation. The answer is regulation-as-compression: a pattern persists to the degree it maintains mutual algorithmic information (MAI) with its own future, and a regulator that keeps a pattern alive must, with high probability, contain a model of the world it's tracking. This is an algorithmic, single-sequence version of the classical Conant-Ashby good-regulator theorem.

The deeper move is ontological, and it runs backward from every information-first program. Wheeler says bits are fundamental; KT says information is derived. Reality, in KT's picture, is a static mathematical tiling — a timeless block structure with no intrinsic causality. Time and computation emerge only when that tiling admits a time-like foliation, a slicing direction along which one slice determines the next. Information appears one level further up still: it's what bounded agents produce when they compress the slices they inhabit. The hierarchy runs mathematics (plus experience) → computation → information → physics → agents. This means KT is simultaneously the most thoroughly algorithmic program in the survey and the one most committed to information not being the fundamental stuff of reality. Using description length as a tool is not the same as positing it as an ontology.

What makes this more than philosophy is that the dynamical layer generates testable commitments. If a regulator sustains a compression gap — makes its environment's readout more compressible than it would be without regulation — then the MAI between regulator and world must be correspondingly large. Ablate the regulator, and readout complexity should rise measurably. The same MAI signatures should appear across substrates (cells, organisms, artificial agents), because the criteria are defined on descriptions, not on any particular physical medium. These are the threads KT follows into the "Pattern, Persist!" line (WP0161/WP0162), which this paper is designed to accompany as a standalone map of the intellectual terrain.