In Search of Certainty

Chapter 8. The Equilibrium of Knowing: Or how not to disagree with yourself

“Of all the principles that can be proposed for this purpose, I think there is none more general, more exact, or easier to apply than that we have used in this work; it consists of making the sum of the squares of the errors a minimum. By this method, a kind of equilibrium is established among the errors which, since it prevents the extremes from dominating, is appropriate for revealing the state of the system which most nearly approaches the truth.”

Adrien-Marie Legendre, 1805

Statistics is the name given to that mathematical discipline which concerns itself with characterizing measurements. It determines what we can know about what we have seen. Ludwig Boltzmann made impressive use of probability and statistics at a time when the ideas were still controversial. His analyses of the thermodynamic systems of the industrial revolution practically inferred the existence of atoms, before they were even observed. There is power in theoretical reasoning, provided it is based on a sound grasp of reality. Max Born later showed something similar was possible for the new quantum theory, an even stranger predictive framework. Today it is widely believed, in science, that we cannot really understand observational data without an understanding of the most basic concepts in statistics. Now, this applies to computers too.

The future is an unpredictable phenomenon. No matter what we might hope, it is not deterministic. We ...