Power Laws

Zipf's Law

The second most common word appears half as often as the first. The third, a third as often. This isn't a quirk of English — it's a law that shows up in every language, every city, every fortune.

f(r) = C / r^α
// rank r, frequency f
// α ≈ 1 for natural language
// C = freq of rank-1 word

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The Reframe

Zipf's Law means that the most common word in any text is not a quirk of style — it's a mathematical inevitability. Language, wealth, city sizes, and earthquake magnitudes all obey the same curve. Something deep in complexity itself generates this shape.

Frequency vs. Rank — Moby Dick

Top Words — click to highlight on chart