“I started putting an error rate on the Gaussian (by having my true distribution draw from two or more Gaussians, each with different parameters) leading to nested distributions almost invariably producing some class of Extremistan. So, to me, the variance of the distribution is , epistemologically, a measure of lack of knowledge about the lack of knowledge of the mean- and the variance of variance is analog to the fourth moment of the distribution, and its kurtosis, which makes such uncertainty easy to express mathematically. This shows that : fat tails= lack of knowledge about the lack of knowledge.”
from The Black Swan by Nassim Taleb
Now that ought to clear up a few things. It basically says we don’t know shit. At least we do not know what we think we know.