Part 7/16:
Remarkably, even with such dependence, the chain's long-term behavior still converges to a predictable distribution—just like the law of large numbers. Markov proved that the independence assumption was not necessary for probability models, directly undermining Nekrasov's argument that societal data reflected free will. His work showed that dependent systems could follow well-defined probabilistic rules.
The Birth of Markov Chains and the Monte Carlo Method
Markov’s breakthrough demonstrated that complex, interdependent systems—like language, nuclear reactions, or climate—could be modeled using Markov chains. These models track the current state and the probabilities of future states without needing memory of the entire past, a property called memorylessness.