collection / modern mathematics

Week 04 — Probability Information and Emergence

Week 04 — Probability Information and Emergence

Central Question

How can randomness at the microscopic level produce predictable macroscopic mathematics?

The Story

Follow aggregate randomness through limiting laws and diffusion, then ask how uncertainty connects with information and physical equilibrium.

\text{Randomness}\rightarrow\text{Large Numbers}\rightarrow\text{Gaussian Behaviour}\rightarrow\text{Random Walks}\rightarrow\text{Diffusion}\rightarrow\text{Entropy}\rightarrow\text{Information}

Sessions

Connections Beyond This Week

Week 03 — Geometry and Manifolds

Month overview · Exploration Map · Home

Related

Session 01 — What Is Randomness Mathematically?Session 02 — Law of Large Numbers Session 03 — Central Limit Theorem Session 04 — Combinatorics Behind the Gaussian Session 05 — Random Walks Session 06 — From Random Walk to Brownian Motion Session 07 — Brownian Motion and the Heat Equation Session 08 — Markov Chains Session 09 — What Is Entropy?Session 10 — Shannon Information Session 11 — Statistical Mechanics Connection Session 12 — Week 4 Synthesis Week 03 — Geometry and Manifolds Month 01 — From Familiar Mathematics to Modern Mathematics Exploration Map Mathematics Exploration Library

Referenced by

Month 01 — From Familiar Mathematics to Modern Mathematics Week 03 — Geometry and Manifolds Session 01 — What Is Randomness Mathematically?Session 02 — Law of Large Numbers Session 03 — Central Limit Theorem Session 04 — Combinatorics Behind the Gaussian Session 05 — Random Walks Session 06 — From Random Walk to Brownian Motion Session 07 — Brownian Motion and the Heat Equation Session 08 — Markov Chains Session 09 — What Is Entropy?Session 10 — Shannon Information Session 11 — Statistical Mechanics Connection Session 12 — Week 4 Synthesis Probability Mathematics Exploration Library