# Interaction generates non-normality

When there are multiple agents, reacting to each other’s behaviors, the overall behavior will not be normally distributed. This is true even if the behavior of each of the individual agents is normal.

The interactions which generate non-normalities in children’s games repeat themselves in real world systems – natural, social, economic, financial. Where there is interaction, there is non-normality. – Randomness, Fat Tails and Ergodicity – A Keynesian Perspective on Knightian Uncertainty

An extension — another way to conceive of interaction is correlation. Correlated random variables effectively “interact” with one another. If this doesn’t make sense, consider the extreme opposite — two perfectly uncorrelated random variables clearly do not “interact” in any way.

So an equivalent statement would be that correlation generates non-normality.

It turns out that, in the real world, variables are rarely i.i.d. That is to say, variables in a system are rarely independent of one another. They frequently interact and are hence dependent. This dependency generates fat tails.

Fat tails are therefore common, much more common that they would be if these interactions did not occur - Tails should not be unexpected, for they are the rule. As the world becomes increasingly integrated – financially, economically, socially – interactions among the moving parts may make for potentially fatter tails. Catastrophe risk may be on the rise.

This is closely related to the idea that Fat tails preclude ergodicity