I saw a fascinating tweet from Nassim Taleb last night:

It reminded me of this lecture Taleb posted a few years ago (particularly the part starting around 8:45):

So, after seeing the tweet last night I decided to take a shot at sharing some of Taleb’s ideas with my kids. The obvious problem is that the details are pretty advanced. The point I thought I could communicate, though, was the idea of (to borrow Taleb’s terms) Mediocrastan vs. Extemistan – the worlds where one observation shouldn’t change things that much vs one in which one observation can change your world view completely. After talking through those ideas, I thought it would be fun to show the boys how different some probability distributions from Mediocrastan and Extemistan look.

We started by talking about distributions that stay close to the mean (like height) and ones where one observation can be far from the mean (like wealth or damage from volcanic eruptions).

Now we took a close look at a bunch of random draws from a normal distribution. The idea here (and in the following two videos) is a high level introduction to the “probabilistic veil” concept from Taleb’s tweet:

Next we moved to the Cauchy distribution. I was hoping that the kids would be able to see that the draws from this distribution were so different from the draws from the normal distribution that they could say with some certainty that these draws here definitely did not come from the normal distribution. It was fun to hear they take some guesses at the max and mins as I increased the number of data points.

Finally, we looked at the class of stable distributions. I didn’t try to describe these distributions in any detail, but rather just said that there was a parameter that we could vary between 1 and 2. Here the goal was to see if we could say if a distribution looked like a normal distribution or the Cauchy distribution. We were also able to see that varying the parameter changed the distribution, but that it would be pretty difficult to tell from the data if the distribution came from the parameter being 1.2 or 1.5 – this is one of the points in the Taleb video lecture from above.

I’m reasonably happy with how this discussion went today – these are pretty advanced ideas to be sharing with kids. Fortunately Mathematica makes it somewhat easy to see how different the various distributions look. Hopefully this conversation helps the boys get a little peek at the ideas of probability distributions and also helps them understand that the process of going from data to a probability distribution can be extremely difficult (even with millions of data points).