Topology of Lyricism

The question. What does it mean for two lines to rhyme, topologically — and does a poet's rhyme scheme leave a persistent-homology fingerprint?

Reading as

Why do two lines rhyme? Here's an attempt to answer it with geometry, on real poems.

Status — Active. 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: CMU Pronouncing Dictionary · Gudhi · Python · LaTeX.

The bet

Phonemes can be placed in a metric space. In that space, a rhyme is a near-collapse of distance — two syllables that should be far apart sit close. A whole poem becomes a point cloud, and a poet's habits — internal rhyme, slant rhyme, end-rhyme — become its shape.

If that shape is a real invariant, a persistence diagram should distinguish Eminem's dense internal rhyme (the stress test) from Dickinson's slant rhyme and Shakespeare's metered end-rhyme — using geometry, not hand-labeled rhyme schemes.

The setup

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

The space

Phonemes from the CMU Pronouncing Dictionary, vectorized so that phonetic similarity is metric distance (slant rhyme = small but non-zero distance).

The cloud

Each syllable (or stressed nucleus) of a poem becomes a point; a poem is a labelled point cloud over the phoneme metric.

The signature

A Vietoris–Rips filtration's persistence diagram. H₀ captures clustering (rhyme groups); the question is whether H₁ — actual loops — separates dense internal rhyme from end-rhyme.

Data & sources

The corpus the pipeline runs on — cited so the work is reproducible.

Eminem Lyrics — All Albums — Thaddeus Segura · Kaggle. The core lyric corpus — Eminem's catalogue is the rhyme-density stress test — vectorized against the CMU Pronouncing Dictionary for the phoneme metric.
Public-domain poetry baselines — Shakespeare · Emily Dickinson · nursery rhymes · public domain (Project Gutenberg &c.). The comparison corpora — Shakespeare's metered end-rhyme, Dickinson's slant rhyme, and nursery rhymes as a low-complexity floor. All public-domain, so the cross-corpus H₁ spectrum (Eminem > Shakespeare > Dickinson > nursery) can be shown openly.

Use: Strictly non-commercial, personal research. The copyrighted lyrics (Eminem) are analysis input only — kept out of version control and never redistributed here; only derived metrics (persistence diagrams, correlations) are reported. The comparison corpora — Shakespeare, Dickinson, nursery rhymes — are public-domain. Honest integrity caveat: the lyric corpus is crowd-transcribed, so transcription noise is real at the individual-line level; claims are therefore reported at corpus scale (scale-free z-scores and subspace shares), not per line. If you know ethical and legal methods for sourcing lyric corpora, I'd genuinely like to hear them — research@backporch.studio.

The method — what actually gets run

Finish the phoneme-vectorization → filtration pipeline (current build).
Run persistence on 2–3 works per author across genres.
Test: does H₁ distinguish Eminem from Dickinson from Shakespeare, or is it all H₀ (clustering only)?
Write the setup section: “what does it mean for two lines to rhyme, topologically?”

Open questions (honestly open)

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

Which metric captures slant rhyme without collapsing everything — phonetic feature distance, edit distance, learned embedding?
Is rhyme a 1-cycle (a loop you can walk) or only clustering (H₀)? The answer decides whether topology buys anything over a distance matrix.
Does author identity live in the diagram, or only genre?

Reading the work rests on

Computational TopologyAlgebraic Foundations for Applied Topology and Data AnalysisMathematical Principles of Topological and Geometric Data AnalysisInformation Theory

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.