I saw an interesting paper tweeted out by Nassim Taleb yesterday:

Working through some of the ideas made for a welcome distraction yesterday afternoon. When I finished up I thought that there was an important idea in the paper that kids could understand even if the math behind the result was beyond them. That result is here:

So, I started today’s Family Math project by explaining this result in a way that hopefully kids can understand:

Next we went to a short program I wrote in Mathematica to explore this result – here’s how I introduced that program to the boys:

Now I had my younger son vary the number of initial trials we had – my program had been picking 20. We looked to see if we picked “n” numbers that the chance that a new selection would be bigger than the maximum of our n numbers was roughly 1/n.

Finally, I had my older son vary the tail parameter of the Pareto distribution. There’s a little surprise that came from my not updating the program correctly – an accidental good experiment / programming lesson for the boys – but eventually we were able to find that our experiment matched Nassim’s result:

It is fun to try to explain results like this to kids. Again, there’s no chance that they can follow the underlying math, but they can certainly see the ideas from the computer experiment.

The overall idea of Nassim’s paper is also an important statistical point for kids (and everyone!) to understand -> what you see and what you don’t see are both important!