# Non linearities and the Black Swan

The book Black Swan by Nassim Nicholas Taleb is an interesting book about probability outside of the traditional Gaussian framework and how paradigm changing often arise.  The highlight of the book is its philosophy of the black swan, and its unknown unknown.  The book also includes discussion of behavioral economics and tries to discredit Gaussian statistics.  The book is interesting but rambles somewhat.  Further, Taleb writes in a condescending manner disparaging other intellectuals and experts.  Although Taleb does make some good points but the negative tone does become tiresome.

The Turkey Problem

The crux of the book can be understood by looking at the following series.  This series represents the weight of the turkey over 30 days.

Assume you are a turkey, what would you predict would happen to your weight over then next 15 days. Using ordinary least squares, one would predict that the turkey would continue to grow at 1/4 pound per day. Let us see what happened in reality.

We see that a “black swan” event has a occurred; one that was outside the paradigm one would establish based on past data. We see that on day number 41, the turkey is slaughtered. This is a huge paradigm shift from the point of view of the turkey. One can see that relying on past data to predict the future will be highly inaccurate in the presences of these black swans.

Other Non-linearities

Let us look at another seemingly linerar series.

How would you predict the series would continue into the future?  Using linear extrapolation techniques, one would predict the series would increase linearly ad infinitum. However, let us examine the true data generating process.

We can see that the data come from a sine function.

The key insight of Taleb’s book is that these non-linearities, paradigm shifts and black swans occur all the time. Further, they are responsible for most of the innovatiations and important events in history. Thus, ignoring black swans can be perilious. Taleb’s message is one of humility.  It is exceedingly difficult to predict the future.  A sure thing is rarely ever such.  Thus, we should view expert opinion with some skepticism and embrace–rather than reject–uncertainty.