Our 2007 NKS Summer School started about two weeks ago, and one of my roles there was to show a little of how NKS is done.

In the past, it would have been pretty unrealistic to show this in any kind of live way. But with computer experiments, and especially with Mathematica, that’s changed. And now it’s actually possible to make real discoveries in real time in front of live audiences.

I’ve done a few dozen “live experiments” now (here is an account of one from 2005). My scheme is as follows. Sometime between a few hours and a few minutes before the live experiment, I come up with a topic that I’m pretty sure hasn’t been studied before. Then I make sure to avoid thinking about it until I’m actually in front of the live audience.

Then, once the experiment starts, I have a limited time to discover something. Just by running Mathematica. Preferably with a little help from the audience. And occasionally with a little help from references on the web.

Every live experiment is an adventure. And it seems like almost every time, at around the halfway point, things look bad. We’ve tried lots of things. We’ve opened lots of threads. But nothing’s coming together.

But then, somehow, things almost always manage to come together. And we manage to discover something. That’s often pretty interesting. (There are still papers coming out now based on the live experiment I did at our very first Summer School, back in 2003).

I usually make my first live experiment at each Summer School be a piece of “pure NKS”: an abstract investigation of some simple program out in the computational universe.

This year I decided to take a look at an “old chestnut” that I’d recently been reminded about: a simple program (though it wasn’t thought of that way then) that was actually first investigated all the way back in 1920. Continue reading