Cognitive Scaffold

Preparing your thinking workspace

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MENTAL MODEL · M5665

Heaps' Law

Heaps' Law
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Updated 2026-08-05

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INTRODUCTION

English translation pending.

CORE DEFINITION

Formulated by Harold Stanley Heaps in his 1978 book on information retrieval, the law states that vocabulary size grows with text length according to a power function whose exponent typically lies between 0.4 and 0.6 for natural language. It is closely related to Herdan's law and follows from the Zipfian distribution of word frequencies. The key constraint is that the relation is statistical and corpus-dependent, since the exponent varies with language, genre and text type, so it predicts averages rather than the count in any single document.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

- Plan vocabulary: Estimate how large a lexicon a corpus of a given size will require. - Budget learning: Expect new concepts per page to fall as you read on, and plan effort accordingly. - Stop sensibly: Use the flattening curve to decide when more reading yields too few new terms.

anchor

Anchor fast decisions

Because word frequencies follow a Zipfian distribution, a few words recur constantly while a long tail of words appears rarely. As a text lengthens, the chance that the next word has never been seen before declines in proportion to a power of the length and never reaches zero. Vocabulary therefore grows sublinearly, producing a curve that keeps rising but with diminishing returns.

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Heaps's_lawZH · Explicit
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