Taleb has a good point about people mistakenly interpreting standard deviation (sigma) as Mean Absolute Deviation (MAD). I like that he gives some conversions (sigma ~= 1.25 * MAD, for Normal distribution).

I think it's rather silly to talk about "retiring" standard deviation, but we can't blame Taleb - the publication itself posed the question "2014: What Scientific Idea is Ready for Retirement?" to various scientific personalities.

What Taleb failed to mention is that, once properly understood, standard deviation has distribution interpretations that can be much more useful than MAD. For example, if the data is approximately normally distributed, then there is approximately a 99.99% probability that the next data observation will be <= 4 * sigma.

Not everything is approximately normally distributed, but a lot of phenomena ARE normally distributed. It's a well known fact that the phenomena which Taleb is most interested in (namely, financial return time-series) are not normally distributed. But I would like to know how Taleb proposes to "retire" volatility (sigma) from financial theory and replace it with MAD? Standard deviation is so central in finance that even the prices of some financial instruments (options) are quoted in terms of standard deviation (e.g. "That put option is currently selling at 30% vol"). How do we rewrite Black-Scholes option pricing theory and Markowitz portfolio theory in terms of MAD and remove all the sigmas everywhere? Surely Taleb has already written that paper for us so that we can retire standard deviation?