But the average of the function is as follows. Take the square of every payoff, 1^2+2^2+3^2+4^2+5^2+6^2 divided by 6, that is the average square payoff, and you get 15.67. So, since squaring is a convex function, the average of a square payoff is higher than the square of the average payoff. The difference, here between 15.67 and 12.25 is what I call the hidden benefit of antifragility —here 28 percent “edge”. The conflation problem mistaking a property of a function of something for the function of the property of something leads to severe misunderstanding of the process.

The hidden benefit of antifragility is that you can guess worse than random and still end up outperforming. Here lies the power of optionality —your function of something is very convex, so you can be wrong and still do fine —the more uncertainty , the better.The hidden harm of fragility is that you need to be much, much better than random in your prediction and knowing where you are going, just to offset the negative effect.The property is called Jensen’s inequality and I use a variant of it. This is what the common discourse on innovation is missing. If you ignore Jensen’s inequality, you are missing a chunk of makes the nonlinear world go round. And it is the fact that such idea s missing totally from the discourse. Sorry.

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