Memory Without Storage, Learning Without a Learner

What if memory, learning, and decision-making aren't properties of systems at all?

Recent experiments have shown that single-celled organisms with no nervous system appear to learn. Stentor coeruleus, a trumpet-shaped ciliate, reduces its response to repeated mechanical taps — the classic signature of habituation. Researchers are asking how cells without brains manage something so complex.

This paper proposes a different question: what if the complexity is not in the cell but in the observation?

We define three measures — memory, learning, and decision — as performance characteristics of an observer's predictive model, not as properties of the observed system. Memory is detected when the observer's model goes stale (the system moved and stayed moved). Learning is detected when the observer's predictions improve over time (the system becomes less surprising). Decision is detected when the observer's prediction suddenly fails (something unexpected happened). All three are derived from a single rolling prediction applied to observable emissions.

We apply these measures identically across four computational substrates that share nothing in common: 256 elementary cellular automata, 18 Game of Life (GoL) patterns, 10 Gray-Scott reaction-diffusion regimes, and 6 sorting algorithm variants — 287 systems in total. The same categorical structure emerges in every substrate. The observer constructs "memory," "learning," and "decisions" from a bubble sort running fewer than ten lines of fully visible, deterministic code.

Key results

A partial differential equation habituates. A Gray-Scott reaction-diffusion system subjected to repeated identical perturbations produces a declining response profile that qualitatively matches published habituation data from Stentor. The same PDE produces habituation, sensitisation, or no learning depending solely on the observer's choice of tap frequency. The cognitive attribution is determined by the experimental protocol, not by the system.

Less access, more intelligence. Restricting the observer's access to emission features increases apparent learning. The observer who watches a single informative channel sees more "learning" than the observer who watches everything — because additional channels dilute the signal. What the observer infers depends on which emissions it tracks, when it probes, and how it models the data.

Two independent memory measures agree. A prediction-based measure (model obsolescence) and a classical statistical measure (Cohen's d) rank systems consistently across all substrates (ρ= 0.75), confirming that both capture the same underlying phenomenon: persistent regime change visible in the emission stream.

Cross-substrate convergence. Systems from all four substrates occupy the same region of the M/L/D space — Gray-Scott pattern-forming regimes, sorting algorithms, GoL methuselahs, and Class 4 cellular automata are grouped together by an observer who knows nothing about what it is watching.

What this means

The cognitive vocabulary — memory, learning, decision, intelligence — attaches to emission profiles, not to substrates. An observer with incomplete access to any system's dynamics will inevitably construct these categories from the structure of its own prediction failures. The framework is falsifiable, quantitative, and makes specific predictions distinguishable from the standard cognitive vocabulary.

A companion paper, "Why Observers Construct Intelligence", develops the conceptual implications: why the observer's three categories are co-present rather than sequential, why goals are derived rather than measured, and why the loop closes recursively — the observer constructing M/L/D from a system's emissions is itself a system whose emissions another observer would decompose the same way.

March2026: Main paper: Memory Without Storage, Learning Without a Learner: Observer Inference Across Four Computational Substrates

March2026: Memory Without Storage, Learning Without a Learner: Link to Python scripts for generating results used in this paper.

March2026: Memory Without Storage, Learning Without a Learner: The Hopfield Correspondence. Application and Results for this 5th substrate

March2026: Dissolving the Boltzmann Brain Circularity: Time, Memory, and the Thermodynamic Laws from a Distinguishability Axiom. Discourse on Wolpert, Rovelli, and Scharnhorst recent paper on the dynamics of the universe's entropy as a time-symmetric Markov process.

April2026: Why Observers Construct Intelligence: Cognitive Categories as Prediction Failure. Observer inference, cognitive categories, prediction failure, memory, learning, intelligence, Hidden Markov Model, free energy principle, habituation, protocol dependence