In 1906, Russian mathematician Andrey Markov introduced a revolutionary concept in probability theory: a system that moves from one state to another where the probability of the next step depends only on the current state, regardless of the history of how the system arrived there. This property—known as memorylessness or the Markov Property—became the foundation for predicting weather patterns, financial stock fluctuations, board game odds, search engine algorithms, and AI language models.
| Today | ☀️ Sunny | ⛅ Cloudy | 🌧️ Rainy |
|---|---|---|---|
| ☀️ Sunny | 60% | 30% | 10% |
| ⛅ Cloudy | 30% | 40% | 30% |
| 🌧️ Rainy | 20% | 40% | 40% |
Run this chain for long enough and it spends about 39% of days sunny, 36% cloudy and 25% rainy (exactly 24/61, 22/61 and 15/61) — whatever the weather on day one.
The thin marks show the long-run shares: 39.3%, 36.1% and 24.6%.
In 1998, Stanford graduate students Larry Page and Sergey Brin revolutionized internet search by inventing PageRank. They modeled the entire World Wide Web as a giant Markov Chain:
By calculating the long-term steady-state probability of where this random surfer spends their time, Google ranked web pages by importance! Pages with many high-quality incoming links had a higher steady-state probability, placing them at the top of search results.
Before modern deep neural networks, early auto-complete and speech recognition engines used Markov Text Generators (n-gram models). By analyzing a large text corpus, the model calculates the probability of the next word given the current word: e.g., after the word "peanut", the word "butter" might have, say, a 70% transition probability in a given body of text.
| If today is 🌧️, then… | ☀️ | ⛅ | 🌧️ |
|---|---|---|---|
| 1 day later | 20% | 40% | 40% |
| 2 days later | 32% | 38% | 30% |
| 3 days later | 37% | 37% | 27% |
| 5 days later | 39% | 36% | 25% |
| 10 days later | 39% | 36% | 25% |
A Markov Chain is a memoryless stochastic process where the next state depends solely on the current state. Regardless of starting conditions, any ergodic Markov chain — one that can reach every state and doesn't cycle in lockstep — converges over time toward a stable steady-state equilibrium distribution. This mathematical property powers search engines (PageRank), predictive auto-complete, financial risk modeling, and weather forecasting.
Action step: Pick a different starting day above and tap "Run 1,000 days" a few times. Notice how the share of sunny, cloudy and rainy days always settles near the same 39 / 36 / 25 split.