Markov Chains: Only Now Matters
Andrey Markov, working in St. Petersburg at the turn of the twentieth century, was trying to settle a mathematical dispute about whether the law of large numbers applied to dependent events. His solution introduced what we now call Markov chains: sequences where the probability of the next state depends only on the current state, not on any history of how you got there.
The Markov property is sometimes called "memorylessness." The system has no history. Given where you are now, knowing where you've been provides no additional information about where you're going next.
Why this is a powerful abstraction
Most real systems have some history-dependence, but Markov chains are useful approximations for many of them — and they're exactly right for a surprising number. More importantly, the Markov assumption makes systems tractable for analysis. When you can assume memorylessness, the mathematics becomes clean and powerful.
Google's original PageRank algorithm is a Markov chain. A web surfer clicks links at random; the probability of landing on any particular page depends only on the current page, not on the entire browsing history. PageRank computed the long-run probability distribution of this random walk — the stationary distribution — and used it as a measure of importance. Pages where the random surfer is most likely to end up, in equilibrium, are the most important pages.
Weather forecasting uses Markov models. Tomorrow's weather depends primarily on today's weather, not on the weather from six months ago. This isn't perfectly true, but it's accurate enough to make Markov chains useful for short-range forecasting.
The stationary distribution
Every well-behaved Markov chain converges to a stationary distribution — a probability distribution over states that doesn't change once reached. Start the system anywhere and run it long enough; it settles into the stationary distribution.
This convergence property has profound practical implications. In customer behavior modeling, the stationary distribution tells you the long-run proportion of time a customer spends in each state (active, dormant, churned) regardless of where they started. In economics, Markov chains model income mobility — the probability of transitioning between income brackets — and the stationary distribution shows where incomes concentrate in the long run.
Language models and the limits of memorylessness
The simplest language models are Markov chains over words: the probability of the next word depends only on the current word or the last few words. Text generated by these models can be surprisingly coherent at the sentence level and nonsensical over longer stretches — which is exactly what you'd expect from a memoryless model.
Modern large language models use attention mechanisms that condition on the entire preceding context, not just the last state. But many of their failure modes — losing track of a constraint established early in a conversation — look like Markov failures, as if the model is operating on a compressed summary of history rather than the full sequence.
India's credit scoring and memorylessness
India's formal credit system has historically given disproportionate weight to history. A borrower's credit score is heavily influenced by their past behavior, but the past in many cases is an artifact of access rather than character. Someone who never had formal credit doesn't have a "good" history — they have no history, which the system often treats as bad history.
The Markov insight here is useful as a corrective. For many credit decisions, the current state — current income, current employment, current digital transaction patterns — is more predictive than a credit history that may reflect constrained access more than actual risk. UPI transaction histories and GST filings are being incorporated into credit scoring precisely because they are current-state signals that don't require past formal credit participation.
The limit of the assumption
Markov chains fail wherever history matters. A person's health today depends on cumulative lifetime habits, not just yesterday's choices. An organization's culture reflects decades of hiring and management decisions, not just last quarter's. Reputation is inherently non-Markovian — it accumulates. When the Markov assumption is applied where it doesn't hold, the model gives you precise answers to the wrong question.
Quick answers
What is Markov Chains?
Andrei Markov's 1906 model: a system where the next state depends only on the current state, not the full history. Weather models, Google's PageRank, and language models all use this principle.
Where does this concept come from?
The concept originates with Andrey Markov (1906).
