It is sad that Taleb does not see the value in the standard deviation; standard deviation is far more natural, and more useful, than MAD.
For example, if X has a standard deviation of s, and Y has a standard deviation of t, then the standard deviation of X + Y is sqrt(s^2 + t^2). There is a geometry of statistics, and the standard deviation is the fundamental measure of length.
To retire the standard deviation is to ignore the wonderful geometry inherent in statistics. Covariance is one of the most important concepts in statistics, and it is a shame to hide it from those who use statistics.
Additionally, I will mention that we do not need normal distributions to make special the idea of standard deviations. In fact, it is the geometry of probability - the fact that independent random variables have standard deviations which "point" in orthogonal directions - which causes the normal distribution to be the resulting distribution of the central limit theorem.
For example, if X has a standard deviation of s, and Y has a standard deviation of t, then the standard deviation of X + Y is sqrt(s^2 + t^2). There is a geometry of statistics, and the standard deviation is the fundamental measure of length.
To retire the standard deviation is to ignore the wonderful geometry inherent in statistics. Covariance is one of the most important concepts in statistics, and it is a shame to hide it from those who use statistics.
Additionally, I will mention that we do not need normal distributions to make special the idea of standard deviations. In fact, it is the geometry of probability - the fact that independent random variables have standard deviations which "point" in orthogonal directions - which causes the normal distribution to be the resulting distribution of the central limit theorem.