Chaos from Zero

How mathematics describes the world, and where it stops predicting it

The eclipse of 12 August 2026 was in the astronomers' tables before anyone who watched it was born. Nobody could have told them, a month earlier, whether the sky would be clear. Both forecasts use the same kind of mathematics. This book is about why one works for millennia and the other for about a week — and why that difference, called chaos, is something everyone who reads a forecast should understand.

It starts from school arithmetic. Every idea is developed step by step, with questions to answer before you read on, and every number that you could not work out in your head was computed by a short Python program printed in the book, which you can run yourself.

What is inside

1. The clockwork. Models, rules applied step by step, feedback, and motion.
2. Where prediction breaks. One line of algebra that does everything; the butterfly effect measured; a number for chaos; the road from order to chaos and Feigenbaum's constant.
3. The shapes of chaos. The Lorenz attractor, strange attractors, fractals, the Mandelbrot set.
4. Chaos in the world. Pendulums and planets, weather and climate, living systems and markets, and chaos inside the computer.
5. Living with chaos. Controlling chaos, and a field guide to judging any prediction.

Run the laboratory

With uv installed, from the repository's code/ directory: uv sync, then uv run python ch01/falling_stone.py.