Mediocristan vs Extremistan: In Extremistan, one single observation can disproportionately affect the outcome.
If finance were Gaussian, then the 2008 crash (more than 20 std) would take place every several billion lifetimes of the universe. In the last 50 years, the 10 most extreme days in finance markets represent half the returns.
You need one single observation to reject the Gaussian, but millions of observations will not fully confirm the validity of its application.
Mandelbrot sets are popular with Chaos Theory folks because of the ever-increasing complexity generated by deceptively miniscule recursion. Fractals, unlike Gaussians, preserve some statistical measures across scales.
Complexity Theory should make us more suspicious of scientific claims of precise models of reality.
How A Goat Farmer Built A Doomsday Machine That Just Booked A 4,144% Return. Antoine Gara. www.forbes.com . Apr 13, 2020.