How A Random System Can Actually Be Predictable

Why It Matters

Understanding that market prices follow a normal‑distribution diffusion process lets firms price derivatives and manage risk with mathematically sound models.

Key Takeaways

• Random walks on a Galton board produce a normal distribution.
• Central outcomes have many paths; extremes have few.
• Louis Bachelier modeled stock prices as random walks in 1900.
• Bachelier’s formula mirrors heat diffusion equation discovered by Fourier.
• Probability “radiation” links finance, physics, and statistical mechanics.

Summary

The video uses a Galton board to illustrate how countless random walks generate a predictable bell‑shaped curve.

Each ball’s 50/50 left‑right deflection creates a binomial distribution that converges to a normal distribution; the middle slots have many possible paths, extremes have only one.

Louis Bachelier applied the same mathematics to stock prices, treating each time step as a peg; he independently derived the heat‑diffusion equation later formalized by Fourier, calling it “radiation of probabilities.”

This connection underpins modern quantitative finance, showing that market risk can be modeled with the same statistical tools that describe physical diffusion, guiding pricing, hedging, and risk‑management strategies.

Original Description

The balls in a Galton board fall down randomly. Any time they come to a junction they can take any number of paths and it's almost impossible to accurately predict every ball's trajectory.

However, the system as a whole is predictable.

How can this be? How can random systems actually be predictable?