Fat tails are weird

If you have taken a statistics class it may have included stuff like basic measure theory. Lebesgue measures and integrals and their relations to other means of integration. If your course was math heavy (like mine was) it may have included Carathéodory's extension theorem and even basics of operator theory on Hilbert spaces, Fourier transforms etc. Most of this mathematical tooling would be devoted to a proof of one of the most important theorems on which most of statistics is based - central limit theorem (CLT)

Central limit theorem states that for a broad class of what we in math call random variables (which represent realizations of some experiment which includes randomness), as long as they satisfy certain seemingly basic conditions, their average converges to a random variable of a particular type, one we call normal, or Gaussian. 

The two conditions that these variables need to satisfy are that they are:

  1. Independent
  2. Have finite variance

In human language this means that individual random measurements (experiments) "don't know" anything about each other, and that each one of these measurements "most of the time" sits within a bounded range of values, as in it can actually be pretty much always … Read more...

The Atom of Intelligence

Back in a very distant past, perhaps over 2 billion years ago, a wonderful thing happened: a strand of nucleic acid found itself encapsulated in a little protein bubble, along with a few other ingredients sufficient for it to replicate. This in fact may have happened millions of times before, each time dying out after a few generations. But one such bubble that appeared that day in the primordial sea was going to survive, this was the one which was going to make it and launch an incredible evolutionary process lasting until this day. A process that managed to create incredibly complex beings including you and me. 

As soon as this bubble of life started to replicate, the process "guiding" its evolution "noticed" that there are effectively two aspects of control necessary for survival:

  • Internal control regulating the expression of genetic code and other internal reactions - we call this process metabolism today.
  • External control regulating interaction of the bubble with the surrounding environment - we call the process behavior today.

Initially both control mechanisms were likely only tuned at a generational level, not so much at the level of life of an individual, but clearly an evolutionary pressure to … Read more...