Persistent Homology of Perceptual Space

The question. Does perceptual experience have a stable topological signature — and can Husserl's eidetic reduction be read as the act of computing it?

Reading as

If you've ever wondered whether experience itself has a shape, this is that question made computable.

Status — Building. An open, exploratory thread — shared here for the questions and the method, not for results. Findings are kept off the public site until they're earned and vetted. Tools: Gudhi (Python) · LaTeX · Obsidian (phenomenology notes).

The bet

Phenomenology already claims that experience has an invariant structure — the part that survives when you vary everything incidental (Husserl's eidetic reduction). Persistent homology is, formally, a way to read off the invariant structure of a point cloud: the features that survive as you vary the scale.

The bet is that these are the same move, and that TDA turns a famously un-falsifiable phenomenological claim into a computable, refutable one. If perceptual space has persistent features, you can measure them; if it doesn't, the metaphor dies honestly.

The setup

Definitions first — the part that has to be precise before any computation is allowed to mean anything.

The data

A perceptual stimulus space (e.g. a color or tone space, or judged-similarity data) embedded as a point cloud. The first real decision is which space makes the claim sharpest.

The filtration

A Vietoris–Rips (or witness) filtration over that point cloud — the scale parameter is the “varying” in the eidetic variation.

The invariant

The persistence diagram. The conjecture is that its long-lived features are the candidate “eidetic” invariants — structure no incidental variation removes.

The method — what actually gets run

Pin down one perceptual space precisely enough to embed as points.
Build the Rips filtration in Gudhi; compute H₀/H₁ persistence.
Vary stimulus conditions; ask whether the diagram is stable (the eidetic claim) or drifts (the refutation).
Write the setup section first — definitions only, no claims — and let computation earn the rest.

Open questions (honestly open)

These aren't rhetorical. Each is a place the project could still be a metaphor instead of a result.

What is the right perceptual dataset — synthetic, psychophysical similarity judgments, or sensor data standing in for a modality?
Is a persistent H₁ loop phenomenologically meaningful, or just an artifact of the embedding?
Is this “secretly the same object” (an isomorphism) or “related by a map” (a metaphor that still needs the map written down)?

Reading the work rests on

Computational TopologyAlgebraic Foundations for Applied Topology and Data AnalysisMathematical Principles of Topological and Geometric Data AnalysisIntroduction to Topological ManifoldsPhenomenology and QBism

This is an in-progress thread, not a finished claim. If you work near it — TDA, phenomenology, phonetics, the foundations of inference — I'd genuinely like to compare notes: research@backporch.studio.