Start reading a book and every word is new; keep reading and new words come slower and slower — the vocabulary grows, but sublinearly, as a fractional power of the words read. Twice the text is nowhere near twice the words. Language runs out of new things to say faster than you’d think. Slide the reading and watch the vocabulary bend.
Heaps’ law: the number of distinct words V grows as V ≈ K·N^β with β < 1 (typically 0.4–0.6), so vocabulary rises but with diminishing returns — the curve is concave, flattening as common words repeat. The instrument walks a real text word by word, adding each first-seen word to the vocabulary. A fail-loud self-check throws unless V grows (more text → more words) yet SUBLINEARLY: V(N) < 2·V(N/2) — doubling the text less than doubles the vocabulary, the signature of Heaps.
Measured on one short text, so the exponent β is only indicative; Heaps is an empirical companion to Zipf (they are mathematically linked). The word-by-word vocabulary count and the sublinear-growth check are exact for this text.