CONCEPT
The Markov Chain
A mathematical structure in which the future depends only on the present—each state’s probability conditioned solely on the state immediately preceding it—the structure
Andrey Markov forged in 1906 to win a mathematical argument about free will, and the structure that, extended to sequences of words and tokens, underlies every language model ever built.
The Markov chain is a controlled act of forgetting. It says: to predict what comes next, you need to know only where you are now. Everything that led to the present state—the full trailing history of how the system arrived—is irrelevant once the present state is known. This disciplined amnesia is what makes the mathematics tractable and what makes the chain so widely useful: it captures a genuine class of real-world processes while remaining computable.
Andrey Markov built the structure in 1906 to demonstrate that the law of large numbers applies to dependent events as well as independent ones—a proof aimed at defeating a colleague who had inferred free will from the stability of social statistics. The weapon he built for that fight became the first formal model of language: when he applied his chains to the letter sequences of Pushkin’s
Eugene