12 · Intuition on the Central Limit Theorem
Chaos, Added Up
I'm interested in using AI to make maths more accessible. This is one experiment in that direction: explaining the central limit theorem through things you can change and watch.
Adding up independent random quantities often gives a distribution close to a bell curve. The essay approaches that from a few different angles, starting with dice and working through to geometry.
A few ways into the same idea
- Counting: add dice and look at how many ways there are to get each sum.
- Blending: draw a distribution and repeatedly combine it with itself.
- The truce: change the jitter and tether in a particle swarm.
- The budget: reshape a distribution while keeping its variance fixed.
- Geometry: rotate a cloud of samples and watch the distribution of its shadow.
How it's put together
It's a single HTML file with canvas experiments, CSS and JavaScript. The experiments are different ways to build intuition around the bell curve; they aren't all proofs of the central limit theorem. There are no dependencies to install, and the copy here opens as a standalone page.