IndisputableMonolith.Aesthetics.BerlyneInvertedU
The BerlyneInvertedU module defines the pleasure function as one minus the normalized J-cost, supplying the mathematical core for an inverted-U aesthetic response in Recognition Science. Researchers modeling subjective pleasure via information cost would cite these definitions when linking J-cost to Berlyne's classic curve. The module consists of targeted definitions and short lemmas that establish the peak location, symmetry, and acceptance-band properties without further derivation.
claimThe Berlyne pleasure function is $P(x) = 1 - J(x)/J_0$, where $J(x) = (x + x^{-1})/2 - 1$ is the J-cost and $J_0$ its normalizing maximum. Related results establish $P(1) = 1$, symmetry $P(x) = P(1/x)$, and the acceptance-band ratio exceeding unity.
background
Recognition Science expresses all quantities in native units with $c=1$, $h-bar = phi^{-5}$, and the fundamental time quantum $tau_0 = 1$ tick supplied by the Constants module. The Cost module defines the J-cost via the functional equation $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$, which measures deviation from self-similarity. This aesthetics module applies that cost directly to subjective pleasure by taking its normalized complement, thereby reproducing the inverted-U shape central to Berlyne's empirical findings.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the pleasure function that realizes Berlyne's inverted-U curve inside the Recognition Science framework, directly connecting the J-cost to aesthetic response. It feeds the aesthetics domain by providing the core object whose properties (maximum at unity, symmetry, acceptance-band ratio) are used in downstream certification lemmas. The construction sits at the interface between the forcing chain's J-uniqueness and observable psychological structure.
scope and limits
- Does not derive the inverted-U shape from the T0-T8 forcing chain.
- Does not include empirical fitting to psychological datasets.
- Does not extend the model to multi-dimensional or temporal stimuli.
- Does not address normalization constants beyond the J-cost maximum.