This paper examines whether the first‑order physical interactions—gradients or Jacobians—determine the structure of phenomenal experience. The investigation takes place in an idealized neural‑network world called Gradland, where physics are known and functions are largely differentiable. Two Jacobian‑structure metrics are introduced: effective rank and cohesion, both derived from Kirchhoff complexity.
A series of examples supports the hypothesis: experience can last hundreds of milliseconds; the contrast between vivid and obscure perception is explained by cohesion; texture perception corresponds to local gradient variations; the buzzing confusion of newborns appears as a high‑cohesion, low‑effective‑rank state; distinct versus confused ideas map to differences in effective rank; learning manifests as a gradual increase in effective rank; and rich, dense experience emerges from high effective rank combined with moderate cohesion.
Review: By linking precise mathematical descriptors to subjective experience, the study offers a quantifiable framework that could enrich both cognitive science and artificial intelligence research.