Departure question
Read signals from chancePort 4 of 11Travel from dice and insurance to data, noise, and learning algorithms—measuring uncertainty and turning it into decisions.
This voyage is an editorial path for understanding, not a claim of direct historical influence or sole invention.
"The current state contains the information needed for the distribution of the next state." Markov formalized the theory in 1906 and in 1913 analyzed vowel–consonant transitions in Pushkin. Not every chain converges. A finite irreducible, aperiodic chain converges to a unique stationary distribution regardless of its starting state. This structure appears in PageRank, speech recognition, and reinforcement learning.
→ Next | Sunny | Cloudy | Rainy |
|---|---|---|---|
Sunny | 0.7 | 0.2 | 0.1 |
Cloudy | 0.3 | 0.4 | 0.3 |
Rainy | 0.2 | 0.3 | 0.5 |
Stationary distribution (convergence) | 0.46 | 0.28 | 0.26 |
Repeated multiplication by the transition matrix reaches the same stationary distribution ≈ (0.46, 0.28, 0.26) regardless of the starting state — the ergodic theorem. PageRank performs exactly this calculation.
A stochastic process where the next state depends only on the present. Foundation of PageRank, GPT, speech recognition.
Ports in time
Follow the scenes to see problems, notation, standards of proof, and applications changing across different times and places.
Andrey Markov analyzed sequences of vowels and consonants in Pushkin’s Eugene Onegin, demonstrating a probability model with dependence only on the current state.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearWork at Los Alamos introduced Markov chain Monte Carlo, making it possible to draw samples from distributions too difficult to handle directly.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearGoogle’s random-surfer model treated hyperlinks as transition probabilities, using a Markov chain to rank pages across the web.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearToken prediction, reinforcement learning, MCMC Bayesian inference, and analysis of how thoroughly a deck of cards has been shuffled.
Curated sources and problems. Bring one discovery back from OEIS, Project Euler, MathOverflow, or arXiv.
No concept belongs to one person
These are not inventor credits. They are different ports: opening a problem, sharpening a language, or carrying it into another world.
Number lenses
These numbers are editorial lenses for the voyage, not required prerequisites.
Travel from dice and insurance to data, noise, and learning algorithms—measuring uncertainty and turning it into decisions.
Open the number voyage
Travel from dice and insurance to data, noise, and learning algorithms—measuring uncertainty and turning it into decisions.
Open the number voyage
Travel from dice and insurance to data, noise, and learning algorithms—measuring uncertainty and turning it into decisions.
Open the number voyage
Concept genealogy
Concepts arriving from before
Current port
Markov Chains
Concepts opened from here
Only direct editorial links are shown; this is not a complete learning order or historical influence line.
