INTERACTIVE FIGURE 14The wall and the gradient — how far ahead of commitment is the future readable?
distance before commitment 4 steps out
Both curves are measured, normalized as readability relative to base rate (1× = no information). Chess (rust): can the network's state predict which endgame program this game will enter? Zero lift beyond eight plies, then a step of +0.13 at the door — a wall, and arguably correct calibration: between near-equal players the destination genuinely isn't determined earlier. Language (green): can kernel neighbors predict the token a continuation will settle on? 5.5× base one token out, decaying smoothly, still 2.6× base sixteen tokens out — a gradient with a long tail, partly because single-author text telegraphs its destinations topically where adversarial games hide theirs. Same question, opposite epistemic structures — and for language, upcoming content is substantially readable before emission, by nothing fancier than nearest neighbors.