STUDY A · SYNTHETIC SPEECH COMMUNITIES
How fast can a society agree on a word?
N agents, no vocabulary, no coordination. Two meet at random; the speaker utters a word from its inventory (inventing one if empty); on failure the hearer memorizes it, on success both collapse their inventories to the winning word. That is the entire model — the minimal naming game of Baronchelli et al. (2006).
From these three rules, global consensus self-organizes: the lexicon balloons, peaks, and then collapses onto a single shared word in a sharp transition. We measured time-to-consensus for N = 10…400, five seeds each, and fit the scaling law.
Result — consensus time scales as t ∝ N1.40 (R² = 0.994), within reach of the published N3/2 law. A statistical law of language, recovered from 60 lines of code.
METHODS · STUDY A
Populations N ∈ {10, 20, 50, 100, 200, 400}; seeds 1000·s + N for s = 1…5. Speaker and hearer drawn uniformly without replacement per interaction. Convergence = all agents hold exactly one identical word (checked every 50 interactions). Exponent from OLS on ln t̄ ~ ln N. The hero console shows the N=100, seed-42 trace: distinct words in circulation (red) and rolling success rate over the last 200 interactions (blue), consensus at t = 4,550.