fisher-information-unique-riemannian-metric-distributions
IN premise — summaries/2026/08/24/wiki-Manifold_hypothesis.md
Created 2026-08-24T17:11:18+00:00
The Fisher Information Metric provides the unique, natural Riemannian metric on the statistical manifold of probability distributions, grounding information geometry and is mathematically distinct from Euclidean distance
Summary
When measuring how far apart two probability distributions really are, there is one mathematically justified way to do it, and it is fundamentally different from naive straight-line distance in coordinate space. This means any system reasoning over distributions has a principled, non-arbitrary geometry to navigate, rather than being forced to pick a coordinate system and treat it as if it were the natural one.