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Learning path · 7 parts

Chance, Chaos & Information

What can be said about a system nobody can predict — from a jittering pollen grain to the bell curve, the limits of forecasting, and the arithmetic of uncertainty itself.

About 1 hour of reading · 14 widgets

Start with Brownian Motion
  1. Physics9 min

    Part 1: Brownian Motion

    How the jittery path of a pollen grain became the mathematical foundation of diffusion, drug delivery, and molecular biology.

  2. Mathematics8 min

    Part 2: The Central Limit Theorem

    The theorem that explains why the bell curve appears everywhere from exam scores to measurement errors.

  3. Mathematics9 min

    Part 3: Bayes' Theorem

    The rule for updating belief in the face of evidence, and why ignoring the base rate makes accurate tests wildly misleading.

  4. Mathematics10 min

    Part 4: Markov Chains

    How a process that remembers only where it is right now can settle into a stable long-run distribution — the idea behind PageRank, MCMC, and text generation.

  5. Mathematics10 min

    Part 5: Chaos and Strange Attractors

    How a rounding error in a weather simulation revealed that deterministic systems can be unpredictable in principle — and why that caps forecasting at about two weeks.

  6. Mathematics10 min

    Part 6: Information Theory

    Shannon entropy counts the yes/no questions you need to pin down an unknown. That count turns out to be the exact limit of lossless compression, and the reason error correction has a price.

  7. Mathematics10 min

    Part 7: Game Theory and the Nash Equilibrium

    How a single fixed-point idea — nobody can improve by changing their mind alone — explains cartels, auctions, arms races, and why cooperation still manages to survive.