Early accidents become permanent advantages. Small differences in timing or circumstance — not quality, not design — determine which outcome locks in and persists. The same starting conditions, run again, would produce a different world.
Trajectory color reflects current proportion — matching the histogram below. Strongly biased marks histories above 90% or below 10%; the Pólya urn can converge to any proportion, so this threshold is a marker, not a boundary.
🎯 The Core Insight
Each history starts identically: one red ball, one blue ball. On each draw, one ball is selected at random — with probability proportional to the current composition of the urn. Its color is noted, it is returned, and one extra ball of the same color is added. This is the reinforcement: whichever color was just drawn becomes slightly more likely to be drawn next.
The first few draws create a slight imbalance. The reinforcement mechanism amplifies it. After enough draws, each history has locked into a stable proportion — shaped by early randomness and cemented by reinforcement. Neither element alone is sufficient: randomness without reinforcement doesn't lock in; reinforcement without early randomness would converge deterministically to 50%.
Try Replay Same Seed: the simulation runs again with the exact same random sequence and produces the exact same set of locked-in worlds. Path dependence is not randomness — it is early randomness amplified into permanence. The same history, replayed, always ends the same way.
📐 What the Math Says
This is the Pólya urn model. Its remarkable property: the final proportion of red is equally likely to be anywhere between 0 and 1. Not clustered around 50% — uniformly distributed across all possibilities. Early chance events don't just nudge the outcome; they determine it across the full range. The distribution of locked-in worlds is flat.
⌨️ QWERTY
Designed in 1873 to prevent typewriter jams. Faster layouts exist. But early adoption locked QWERTY in — billions of keyboards later, the accident persists.
📼 VHS vs. Betamax
Betamax had better picture quality. VHS won because early rental availability gave it a slight lead, which network effects amplified into a total lock-in.
🏙️ Cities
Why is a city where it is? Often: a river crossing, a safe harbor, a colonial fort. Centuries of infrastructure accumulation follow from accidents of geography and history.
💻 Programming Languages
C was written for Unix. Unix spread through universities. Generations of programmers learned C-family syntax. Today's languages still echo 1970s contingencies.