Consciousness as Structured Probability: A Physical Framework for the Hard Problem

Consciousness can be placed on a graded physical scale rather than treated as an all-or-nothing binary. A Consciousness Index, ranging from 0 to 100, is defined using the Consciousness Potential Phi from an existing framework. The index rises linearly through known sub-human biological systems, with human waking consciousness near 40 to 50. Empirical tests across two dementia EEG cohorts (n=266, with one excluded) and a macaque ECoG dataset (n=2) confirm predicted sleep-stage ordering and replicate two of four brain-connectivity components in dementia. However, the scalar Phi shows no advantage over standard band-power measures for classification. The hard problem of why any physical structure yields subjective experience remains unsolved, but the framework provides a measurable scale with falsifiable predictions.

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Abstract

The hard problem of consciousness, why physical processes give rise to subjective experience, is often framed as binary. This paper proposes a reformulation: replacing the binary question with a graded physical scalar. Conditional on the Consciousness Potential Phi of the companion framework being a substrate measure, we define a Consciousness Index C(Phi) = Phi / (Phi + Phi_ref) on a 0 to 100 display scale. The index is zero at Phi = 0, rises approximately linearly through the range of all known sub-human biological systems, and approaches unity asymptotically. Three structural tiers emerge at regime-boundary thresholds in the four-component product structure of Phi; human waking consciousness anchors near 40 to 50 on the display scale. The framework is empirically tested across three independent dementia EEG cohorts (n = 266; one, figshare 5450293, is excluded as anomalous, so the surviving cross-cohort AD direction rests on the remaining two) and, in the companion empirical paper, a within-subject macaque ECoG dataset with three pharmacologically distinct anesthetics (n = 2 monkeys). On a single identical pipeline across all cohorts, the framework's surviving empirical content is directional: the predicted sleep-stage ordering (wake highest, deep NREM lowest) is confirmed within subjects, and two of the AD components replicate cross-cohort in direction, I_A (reduced) and the organizational term 1 - H_norm (increased). The remaining components do not generalize: the second structural component (whether operationalized as persistence-memory or spectral complexity) does not replicate across cohorts, and the recursive feedback index I_R follows an inverted-U with AD severity only within a single cohort, not as a cross-cohort law. The scalar Phi shows no discriminative advantage over band power on the contrasts benchmarked head-to-head (sleep, anesthesia), and does not separate the dementia cohorts; its empirical content is directional and mechanistic, not that of a superior classifier. A methodological refinement adopted across the framework series redefines I_R as returning mutual information (the normalized spectral radius rho(W) is its linear sub-critical estimator, superseding a saturating reachability ratio), and retires the persistence-based memory channel in favor of a substrate-neutral spectral-complexity component. The framework's position on the hard problem is explicit: the hard problem in its strongest sense (why any physical structure is accompanied by subjective experience at all) is preserved as a separate question, neither solved nor pre-judged. What the framework provides is a measurable physical scale on which that question can be located precisely: a lower bound, an asymptotic ceiling, a graded interior, and falsifiable predictions tested across independent dementia cohorts (three assembled, one excluded as anomalous) and a cross-anesthetic within-subject design. The scope is physics; the explanatory gap is preserved.