Veritasium
June 8, 2026
How Random Systems Create Predictable Patterns
TL;DR
Individual random events appear unpredictable, but when observed collectively, they form predictable statistical patterns like the normal distribution—a principle Louis Bachelier applied to stock market modeling.
Key Takeaways
- 1Individual random walks are impossible to predict, but large collections of random events create predictable normal distributions
- 2The Galton board demonstrates that randomness at the individual level produces order at the aggregate level
- 3Louis Bachelier modeled stock prices as random walks similar to balls falling through a Galton board, with prices spreading over time
- 4The mathematical pattern of random walks mirrors the heat diffusion equation discovered by Joseph Fourier in 1822
- 5More paths exist to reach the center of a distribution than the edges, explaining why outcomes cluster around the mean
Notable Quotes
“each ball follows a random walk as it passes through these pegs, which makes it basically impossible to predict the path of any individual ball, but if I flip this over, what you can see is that all the balls together always create a predictable pattern”
“Bachelier believed a stock price is just like a ball going through a Galton board. Each additional layer of pegs represents a time step.”
“Bachelier realized he had rediscovered the exact equation which describes how heat radiates from regions of high temperature to regions of low temperature.”
Chapters
1. The Galton Board: Random Individuals, Predictable Collective
A Galton board with 6,000 ball bearings demonstrates how individual random paths (50/50 left or right at each peg) collectively create a predictable normal distribution centered around the middle.
2. Why the Middle is Most Likely
The normal distribution forms because there are thousands of different paths leading to the center but only one path to reach the extreme edges, making middle outcomes statistically most probable.
3. Louis Bachelier's Application to Financial Markets
Bachelier modeled stock prices as random walks through a Galton board, where each time step represents one layer of pegs, predicting that future stock prices follow a normal distribution spreading over time.
4. The Connection to Heat Diffusion
Bachelier's probability radiation equation matches Joseph Fourier's 1822 heat diffusion equation, revealing a deep mathematical connection between random processes and physical phenomena.
Key People & Entities
- Louis Bachelier
- Pioneer of mathematical modeling in financial markets; applied random walk theory to stock prices (born 1870)
- Joseph Fourier
- Mathematician who discovered the heat diffusion equation in 1822, which Bachelier's probability equation matched
Glossary
- Galton board
- A triangular apparatus with pegs arranged in rows through which ball bearings fall, each hitting pegs at 50/50 probability of going left or right, demonstrating how random individual paths create predictable distributions
- Random walk
- A path traced by an object making a series of random steps in unpredictable directions, with each step independent of the previous one
- Normal distribution
- A bell-shaped probability distribution that is symmetric around its mean, with most values clustering near the center and fewer values at the extremes
- Radiation of probabilities
- Bachelier's term for the mathematical principle describing how probability distributions spread and diffuse over time, analogous to heat radiation