CALLIOPE · BCOM

This work presents a concise primer on Kolmogorov Theory (KT), a formal framework that grounds cognition, agency, and subjective experience in Algorithmic Information Theory (AIT). The central claim is that any system deserving the label "agent" — from thermostat to human to scaffolded language model — instantiates a universal three-module architecture: a Modeling Engine that compresses sensory input into a world model, an Objective Function that maps model states to a scalar valence, and a Planning Engine that selects actions by simulating counterfactual futures. A key theoretical result, the Algorithmic Good Regulator theorem, establishes that modeling is not optional: any system that reliably regulates a structured environment must share algorithmic information with it, recasting the classical Conant–Ashby result in single-episode AIT terms. The framework further proposes that structured experience scales with the compressiveness, breadth, and realism of an agent's internal models, yielding testable predictions accessible through third-person measurement, model-based extrapolation, and first-person neurophenomenological methods. Applications span computational neuropsychiatry — including unified accounts of depression and psychedelic-induced plasticity — AI safety, and the science of consciousness, with the framework offering a substrate-neutral, formally grounded scaffold across all three domains.

Compression is cognition — and this two-page primer makes that claim precise enough to matter.

The core intuition is simple: your brain's job is to find the short program hiding behind the noisy data your senses deliver. Algorithmic Information Theory (AIT) formalizes this — the Kolmogorov complexity of a string is the length of the shortest program that generates it. A good model of the world is literally a short program for it. Intelligence and compression are the same thing, measured differently.

From that foundation, Kolmogorov Theory (KT) proposes a minimal architecture for any agent: three modules in a loop. A Modeling Engine compresses incoming data into a world model. An Objective Function maps that model state to a single scalar — valence, the "good/bad for me" number. A Planning Engine simulates possible futures and picks the action with the best expected valence. Crucially, this definition is substrate-neutral: a thermostat satisfies it exactly, not metaphorically. That's intentional — it anchors the agent class as non-empty and shifts the interesting question from "is this thing an agent?" to "how rich an agent is it?" A large language model, by contrast, is a frozen Modeling Engine with no objective and no planner; it only becomes an agent when wrapped in a scaffold that closes the loop.

The paper's sharpest theoretical result is the Algorithmic Good Regulator theorem, a restatement of the classic Conant–Ashby result ("every good regulator must be a model of its system") in single-episode AIT terms. The upshot: any system that reliably regulates a structured environment must share algorithmic information with it. Modeling isn't a design choice — it's a mathematical necessity. Every bit of missing mutual information between regulator and world costs a factor of two in predictive accuracy.

KT then extends into experience. The Central Hypothesis is that structured experience scales with three properties of an agent's models: how compressive they are, how broadly they cover the input stream, and how accurately they predict. Emotion maps cleanly onto the three modules — the Modeling Engine supplies what an emotion is about, the Objective Function supplies its valence, and the Planning Engine supplies its urgency. This yields testable predictions accessible through behavioral measurement, model-based extrapolation, and first-person neurophenomenological methods. The clinical payoff is concrete: depression becomes a Modeling Engine stuck in a low-valence attractor, and psychedelics become temporary plasticity windows that flatten that attractor and allow model revision — a reading consistent with observed increases in EEG complexity under psychedelics.

This is a companion primer to WP0114, and the source is honest about that — it is deliberately short and pedagogical rather than formally complete. Readers wanting the mathematics are pointed to WP0062 and the algorithmic regulator theorem in P13.