The Compression Hypothesis

The Compression Hypothesis

The central claim of this dissertation: meme fitness correlates with compressibility.

Formal Statement

Let $M$ be a meme with information content $I(M)$ bits. Define:

• Compression ratio: $\rho(M) = I(M) / L(M)$ where $L(M)$ is the compressed representation length
• Reconstruction fidelity: $F(M, \hat{M})$ measuring similarity between original and reconstructed meme
• Transmission probability: $P_T(M)$ — probability of successful human-to-human transmission
• Fitness: $W(M) = P_T(M) \cdot F(M, \hat{M}) \cdot R(M)$ where $R$ is replication motivation

Claim: For memes in competition:

$$W(M) \propto \rho(M)^{-1}$$

when controlling for content utility.

Intuition

A meme that can be compressed to fewer bits while maintaining reconstruction fidelity has advantages:

1. Lower cognitive load — Easier to remember
2. Faster transmission — Takes less time to communicate
3. Higher fidelity — Less information lost in compression/decompression
4. More redundancy budget — Can afford error-correction bits

Evidence

Proverbs vs. Explanations

Proverb	Full Explanation	Compression
”A stitch in time saves nine"	"Addressing problems early prevents them from becoming larger problems that require more effort to fix later”	~5x
”Don’t count chickens before they hatch"	"Don’t make plans based on outcomes that haven’t yet occurred, as circumstances may change”	~4x

The proverbs spread; the explanations don’t.

Cross-Cultural Convergence

Many proverbs appear independently across cultures:

• “Strike while the iron is hot” (English)
• “Beat the iron while it’s hot” (German)
• “Forge the iron while it’s hot” (French)

Same compressed representation, same meme. The compression is the message.

Predictions

The hypothesis predicts:

1. Short beats long — Controlling for content, shorter versions spread further
2. Concrete beats abstract — Imagery compresses better than abstraction
3. Rhythm aids memory — Phonetic patterns add error-correction
4. Lossy beats lossless — Some detail loss is acceptable for transmission gain

Open Questions

• What’s the optimal compression for different channel capacities?
• How do we measure “reconstruction fidelity” for ideas?
• Are there ideas that cannot be compressed below a transmission threshold?

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See: Notes on Claims for working research