The Small World of English

Summary

The Small World of English Building a word game forced us to solve a measurement problem: how do you rank 40+ ways to associate any given word down to exactly 17 playable choices? We discovered that combining human-curated thesauri, book cataloging systems, and carefully constrained LLM queries creates a navigable network where 76% of random word pairs connect in ≤7 hops—but only when you deprecate superconnectors and balance multiple ranking signals. The resulting network of 1.5 million English terms reveals that nearly any two common words connect in 6-7 hops through chains of meaningful associations. The mean path length of 6.43 hops held true across a million random word pairs—shorter than we’d guessed, and remarkably stable. 1.5M Headwords 100M Relationships <7 Degrees of Separation for 76% of words This is consistent with the small-world structure and near-universal connectivity seen in lexical network research on smaller datasets.1,2 The network’s structure makes intuitive semantic navigation possible—players can feel their way from ‘sugar’ to ‘peace’ because the intermediate steps (sweet → harmony) make sense. sugar → sweet → harmony → peace The Mathematics of Semantic Distance English exhibits network effects remarkably similar to social networks—nearly any random pair of words can reach each other in just a few hops through chains of meaningful associations. This “small world” phenomenon was first measured in word co-occurrence networks,3 and persists even after we deprioritize superconnector words that might otherwise dominate many paths. To probe this, we randomly sampled 1 million word pairs (4 days processing on 32 cores), to get a strong statistical sampling of the connected core of English. How to connect any random 2 words? 1 0.01% 2 0.15% 3 2.07% 4 9.97% 5 21.58% 6 24.15% 7 18.25% 8 11.18% 9 6.19% 10+ 6.45% Hop Distance Between Words This bell curve centered at 5-6 hops creates ideal puzzle parameters. Examples at three distances: ROLLDICE rhyme → ...