In his eloquent article, Breaking the Galilean Spell (worth reading in its entirety), Stuart Kauffman has given me the words to finally be able to articulate the uneasiness I feel about statistical reasoning in an increasingly interconnected world:
…[Can] we make probability statements about the evolution of the biosphere? No. Consider flipping a coin 10,000 times. It will come up heads about 5,000 times with a binomial distribution. But, critically, note that we knew beforehand all the possible outcomes, all heads, all tails, all 2 to the 10,000 possibilities. Thus we knew what statisticians call “the sample space” of the process, so could construct a probability measure.
Can we construct a probability measure for the evolution of the biosphere into its Adjacent Possible? No. We do not know the sample space!
I won’t belabor the point except to say that I view the increasing irrelevance and danger of statistical reasoning as the essential argument of The Black Swan, the fundamental reason why the global financial crisis occurred, and one of the main things we humans need to understand better if we are going to solve the problems facing the world.