Galton Board - Order from Chaos

Each ball makes random left/right choices at each peg → bell curve emerges!

Controls

Parameters

Rows of pegs 12

Left bias (%) 50

Speed 1.0x

Statistics

Total balls 0

Mean bin -

Std deviation -

Theoretical σ -

The Math

P(k) = C(n,k) · p^k · (1-p)^n-k
Binomial → Normal as n → ∞

Each ball makes n independent 50/50 choices. This is exactly the Central Limit Theorem!

"I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the Law of Frequency of Error."

— Francis Galton, 1889

Francis Galton (1874)

Polymath Francis Galton invented the "quincunx" (Latin for "five-twelfths") to demonstrate probability visually. He first showed it at the Royal Institution on February 27, 1874. Galton was Darwin's half-cousin and pioneered statistics, fingerprints, and (controversially) eugenics.

Central Limit Theorem

The board demonstrates why the normal distribution is everywhere! Add up many independent random variables → you get a bell curve. Stock prices, heights, IQ scores, measurement errors—all follow this law. It's one of the most important theorems in statistics!

Pascal's Triangle Connection

The number of paths to each bin matches Pascal's triangle! The kth bin has C(n,k) paths leading to it. This connects combinatorics, probability, and the binomial distribution in one beautiful visual device.

Regression to the Mean

Galton discovered "regression" using this device! Extreme values (edge bins) are rare—most outcomes cluster around the middle. Tall parents have shorter children on average; this isn't genes failing, it's statistics at work. The mean is a powerful attractor.

The Galton Board