Thread by @SciBry

Buried in Ted Chiang’s new book “Exhalation” is this amazing gem.

Imagine you begin a game of snooker by breaking REALLY hard, so the balls bounce around forever.

If you know everything about the balls, the cue and the table, how many collisions in a row can you predict?

The simple answer is “infinity”. You know the initial conditions and the equations of motion, so you should be able to predict every collision and trajectory until the end of time.

But this is totally wrong.

The answer was worked out by Sir Michael Berry in a 1978 paper entitled “Regular and Irregular Motion”. It’s a fascinating 105-page journey through physics, astronomy and topology.

Especially where he smears a cat out onto a torus.

But I digress

If you invoke quantum mechanics and Heisenberg’s uncertainty principle, it’s impossible to predict more than 15 collisions.

But incredibly, the real number is even smaller than that.

The answer is 9 collisions is the most it’s possible to predict. What happens after that?

After 9 collisions, your simple calculations fall apart because you need to start taking into account the gravitational attraction on the billiard balls of the people standing in the room!

If you wanted to predict >9 collisions, the calculation spirals out of control. Before too long, you need to take into account the gravity of atoms on the other side of the Universe.

Even a simple tabletop calculation is utterly intractable, because of the rest of the Universe.

Here’s the extract showing the calculation, from Berry’s paper:

And if you want to read the full paper, it’s at …chaelberryphysics.files.wordpress.com/2013/07/berry0…