Echoes of the Sunset club, comprising a number of the papers read, and addresses delivered, before the Sunset club of Chicago, during the past two years

If I examine it with a microscope, I will see a very rugged terrain. If I look at it with a magnifying glass, the terrain will be smoother but still highly uneven. But when I look at it from a standing position, it appears uniformБЂ”it is almost as smooth as a sheet of paper. The rug at eye level corresponds to Mediocristan and the law of large numbers: I am seeing the sum of undulations, and these iron out. This is like Gaussian randomness: the reason my cup of coffee does not jump is that the sum of all of its moving particles becomes smooth. Likewise, you reach certainties by adding up small Gaussian uncertainties: this is the law of large numbers. The Gaussian is not self-similar, and that is why my coffee cup does not jump on my desk. Now, consider a trip up a mountain. No matter how high you go on the surface of the earth, it will remain jagged. This is even true at a height of 30,000 feet. When you are flying above the Alps, you will still see jagged mountains in place of small stones. So some surfaces are not from Mediocristan, and changing the resolution does not make them much smoother. (Note that this effect only disappears when you go up to more extreme heights ...»