When someone tells you it was a 10 sigma event, meaning it is 10 standard deviations and it is Gaussian; unless the information came from God, you can reject the Gaussian distribution for that domain. We show the derivations.

This is extracted from my book.

Let us take the idea of the last chapter [the intransigent minority’s disproportional influence] one step further, get a bit more technical, and generalize. It will debunk some of the fallacies we hear in psychology, “evolutionary theory”, game theory, behavioral economics, neuroscience, and similar fields not subjected to proper logical (and mathematical) rigor, in spite of the occasional semi-complicated equations. For instance we will see why behavioral economics will *necessarily* fail us even if its results were true at the individual level and why use of brain science to explain behavior has been no more than great marketing for scientific papers.

Consider the following as a rule. Whenever you have nonlinearity, the average doesn’t matter anymore. Hence:

*The more nonlinearity in the response, the less informational the average.*

For instance, your benefit from drinking water would be linear if ten glasses of water were ten times as good as one single glass. If that is not the case, then *necessarily* the average water consumption matters less than something else that we will call “unevenness”, or volatility, or inequality in consumption. Say your average daily consumption needs to be one liter a day and I gave you ten liters one day and none for the remaining nine days, for an average of one liter a day. Odds are you won’t survive. You want your quantity of water to be as evenly distributed as possible. Within the day, you do not need to consume the same amount water every minute, but at the scale of the day, you want maximal evenness.

The effect of the nonlinearity in the response on the average –and the informational value of such an average –is something I’ve explained in some depth in *Antifragile*, as it was the theme of the book, so I will just assume a summary here is sufficient. From an informational standpoint, someone who tells you “We will supply you with 0ne liter of water liter day *on average*” is not conveying much information at all; there needs to be a second dimension, the variations around such an average. You are quite certain that you will die of thirst if his average comes from a cluster of a hundred liters every hundred days.

Note that an average and a sum are mathematically the same thing up to a simple division by a constant, so the fallacy of the average translate into the fallacy of summing, or aggregating, or looking at collective that has many components from the properties of a single unit.