Effective Neural Power and the Phenomenal Vector: Dissipation, Differentiation, and the Locus of Pₙoncalc

Abstract Standard EEG analysis measures neural power — the amplitude of oscillatory activity. We propose that power alone is insufficient to characterise the computational state of a frequency band: a band can produce high amplitude while its spatial pattern across channels becomes disorganised, indicating that computations are occurring but producing no structured output. We introduce Effective Power (Eff = Amp × Sγ), where Sγ is gamma pattern stability measured as the Pearson correlation between the current spatial envelope pattern and a stable baseline reference. The dissociation between Amp and Sγ — amplitude rising while stability falls — we term neural dissipation: energy expenditure without proportional structured output. We test this framework on two EEG datasets requiring cognitive restructuring: probabilistic reversal learning (ds004295, N=22) and anagram insight (Oh et al. 2020, N=30). In reversal learning, gamma shows the characteristic dissociation (dₐmp=+1. 245, dₛtab=−1. 082) and gamma Eff is neutral, while theta/alpha/beta Eff rise significantly (d=+0. 65 to +0. 97). In anagram insight, alpha shows the dominant dissociation (dₛtab=−0. 988, p<0. 001) and alpha Eff falls significantly (d=−0. 640, p=0. 002), while gamma Eff remains neutral in both paradigms. We interpret these results within RDRT (Refusal-Driven Dimensionality Reduction Theory): the band showing the Eff dip identifies the computational level at which the thermodynamic halt occurs and Pₙoncalc (the non-calculable phenomenal residue) is generated. Reversal learning triggers a rule-level halt (gamma) ; insight triggers a conceptual-level halt (alpha). This leads to a theoretical proposal: frequency bands differ not merely in temporal scale but in differentiation power — the number of distinct computational states they can represent. Two pathways to increased differentiation are distinguished: computational (transition to a higher-frequency band) and phenomenal (transition to Pₙoncalc when the computational pathway reaches its boundary). The phenomenal vector Ψ (t) = Eff_δ, Eff_θ, Eff_α, Eff_β, Eff_γ captures both pathways simultaneously. Trajectory analysis reveals that reversal and insight produce geometrically opposite transitions in Ψ-space (angle = 144. 9°), with reversal showing a highly integrated trajectory (inter-band r = 0. 66–0. 95) and insight showing an independent multi-band trajectory (inter-band r = 0. 01–0. 15). These results support a stratified model of Pₙoncalc generation and provide operational criteria for identifying the locus of phenomenal transition in EEG data.