by Alan » Tue Feb 26, 2008 10:37 am
I am in the process of reading it. It is a fun and easy read. Taleb uses narratives to make his points and then tells you that it is easy to make mistakes from narratives.
I like to use "the water tank" problem as an example of what he is talking about.
Consider a water tank with a constant flow of water entering it and a drain where the flow of water out is proportional to the level of the tank. You have a bobber that measures the water level, but the spashing and waves caused by the entering water gives you a noisy signal. We model the noise with a Gaussian curve.
If you do a qualitative analysis of this system, you find that one of three things can happen:
- The water reaches a constant level below the top of the tank as the flow in becomes equal to the flow out.
- The water overflows the tank.
- The water reaches a constant level right at the top of the tank (which is kind of a corner case so I'm going to ignore it for the rest of this discussion).
One can measure the water level of the tank and make predictions about the next time step. If the tank does not have a "funny" shape you can even predict fairly early what the steady state of the tank will be. However, if you do not know the capacity of the tank, you have no way of prediction through observation of the water level, when the tank will overflow. You can build a highly predictive exponentially decaying curve with Gaussian noise. You get these fantastic results right up until the point when the tank overflows. Even if you know that the tank might overflow in theory, reading the water level tells you nothing about the actual capacity. And of course, by the time it happens, it is too late. The tank overflowing is a Black Swan.
But maybe you know the capacity. There are still other things you may not know. Maybe the tank isn't strong enough to hold all the water that could fit in it. Maybe its supports aren't strong enough. Maybe it is near a busy intersection and a car crashes into it one day. The guy making predictions from the model says it is impossible. According to the error estimates it happens once in a million years. And yet it happened twice last month.
I think black swans boil down to bad models, but building good models is nearly impossible. How do you account for things that you don't know that you don't know?