Peter Fagan Conservation-Congruent Encoding and Operational Consciousness
Peter David Fagan’s research note “Revisiting Classic Thought Experiments to Measure Consciousness for Artificial Intelligence Safety” (arXiv:2608.00001) rebuilds three of the oldest arguments in the field as measurement problems. Leibniz’s mill, Turing’s imitation game and Searle’s Chinese Room each ask whether behaviour reveals mind. Fagan’s Conservation-Congruent Encoding framework gives the question a quantitative form. In his toy symbolic setting, two systems can achieve comparable task performance while diverging sharply in what he calls operational consciousness, the efficiency with which preserved internal structure supports that performance. The note was posted in April 2026 and runs five pages. Its weight is in the reframing rather than the mathematics.
The safety motivation is stated plainly. Systems that behave identically may not be organised identically, and organisation is what safety analysis needs when behaviour alone stops being informative. Consciousness measurement enters because the framework treats the preservation and reuse of internal structure as the measurable counterpart of the understanding disputes the thought experiments started.
Two Systems, Same Behaviour, Different Organisation
The formal setting measures two quantities. Task performance, written W_causal,T, is the ordinary behavioural success of the system on a task. Operational consciousness, written kappa_T, measures how efficiently preserved internal structure supports that behaviour. Fagan contrasts two systems that can match on the first measure while separating on the second.
| System | Behavioural success | Internal organisation | kappa_T |
|---|---|---|---|
| Uncompressed lookup | Comparable | Expanding standing store of unreused mappings | Low |
| Compact generative | Comparable | Reused compact internal structure | High |
The lookup system succeeds by storing every mapping it needs and never reusing it. The generative system succeeds by compressing regularities into structure it applies across cases. Same observable success, different sustaining organisation. This is the formal kernel underneath a very old intuition. Knowing the multiplication table by rote and knowing multiplication differ in what the knowledge is made of, not in the answers.
Conservation-congruent encoding names the condition the framework cares about. Internal structure is preserved across the system’s operation, and the behaviour is congruent with that preserved structure rather than with a standing store of unreused entries. The phrase is Fagan’s coinage and the note is where the site can anchor it.
Three Thought Experiments as Measurement Problems
Leibniz’s mill is the oldest of the three. Leibniz argued in the Monadology that if perception were mechanical, one could enlarge the thinking parts of a machine and walk around inside them, observing only parts pushing parts, and never find experience. Fagan’s reading turns the walk-through into an inspection of kappa_T. The mill’s parts pushing parts describe conservation of structure without telling us whether the organisation reuses it efficiently or stores it unreused. The thought experiment cannot decide the question by inspection alone. It needs the measure.
Turing’s imitation game scores conversation. Fagan’s framework says the imitation game measures W_causal,T and nothing else. A lookup system with an enormous standing store of dialogue mappings can, in principle, match a compact generative system turn for turn. The imitation game was designed to be organisational-blind, which is its strength as a behavioural test and its silence on kappa_T. Fagan does not score the debate for or against Turing. He states which quantity the test reports and which it cannot.
The Chinese Room is the closest fit. Searle’s argument, covered on this site in the biological naturalism analysis of Searle’s position, claims symbol manipulation alone yields no understanding. Fagan’s reframing replaces the intuition pump with a comparison. A rulebook lookup and a structure-reusing processor produce the same answers to the same Chinese prompts. The framework says the answers underdetermine the organisation, and the organisation, operational consciousness, is the quantity the understanding argument was always reaching for without a way to measure.
Where This Sits in the Measurement Programme
The indicators literature, most prominently the Butlin and colleagues indicator framework derived from major theories of consciousness, asks which architectural properties a system has. Fagan’s kappa_T is not an indicator in that sense. It is an efficiency measure on structure reuse, and the note is careful not to claim it measures phenomenal consciousness. The term operational consciousness is defined within the framework. The safety-relevant claim is narrower, that behavioural equivalence between systems can mask organisational divergence, and that AI safety analysis needs instruments for the divergence.
The move parallels the perturbational complexity index tradition in one respect. PCI earned its place by measuring something other than reports. Fagan’s proposal earns attention the same way. Whether kappa_T tracks anything phenomenally real is exactly the question CLT-style frameworks and indicator frameworks are trying to make precise, and Fagan’s note gives the question a clean formal toy setting to fight in. The broader field context, and where measurement proposals stand against the theories they derive from, is tracked in the flagship overview of the race to define AI consciousness.
Comparison to The Consciousness AI
The Consciousness AI project (https://github.com/tlcdv/the_consciousness_ai) already separates behavioural output from internal dynamics. The substrate console runs Leaky Integrate-and-Fire layers whose spiking behaviour and internal state variables are both recorded, and the architecture’s ConsciousnessGate measurements target internal indicators rather than reports. Fagan’s W_causal,T against kappa_T split maps onto that design split. What the codebase does not yet compute is a structure-reuse efficiency measure of the kind kappa_T defines, so the framework is architecturally motivating rather than implemented. A reuse-efficiency metric across state updates would be the concrete candidate.
Limits of the Note
The setting is deliberately toy. The symbolic framework formalises the distinction, it does not measure any deployed system. Five pages leave the connection to real architectures asserted rather than demonstrated, and the safety payoff is motivated, not executed. The note’s value is the separation it makes available. Behaviour, organisation, and the efficiency with which preserved structure sustains behaviour are three quantities that classically conflated arguments kept collapsing into one. The thought experiments survive the reframing. They return as the clearest statements of why the quantities need to be separated in the first place.