Differential Functionalism：Jacobian 如何塑造现象体验的结构

arXiv:2609.09306v2 Announce Type: replace-cross Abstract: This paper investigates the hypothesis that the first-order structure of physical interactions (Jacobians) shapes the structure of phenomenal experience. Two measures of Jacobian structure are introduced: transparency, the effective rank, which counts the independent differences that make a difference; and integrity, the normalised algebraic connectivity, which measures how hard a system is to split. Applied to a series of worked examples, the framework yields correlates of: (1) experiences that overlap without systems merging; (2) the boundaries of a system, which are selected by focus and limited by noise; (3) temporal thickness, the persistence of the past into the present, lengthened by a spread of timescales; (4) spatial structure under convolution, where unity at scale needs long-range connections; (5) the distinction between what is vivid and what is obscure, for errors and attention heads; (6) the incoherence of a randomly initialised network, as a structural model of James's "blooming, buzzing confusion"; (7) distinct versus confused ideas; (8) learning as accumulated experience; and, conjecturally, (9) the contrast between memory as duration in brains and as storage in computer hardware. The measures can be computed at scale in artificial networks and estimated from perturbational data in brains.

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