Amateur Astronomer (credit: Wikimedia Commons) 

Chapter 7 –  The Second Attack on Bayesianism and a Response to It

The Bayesian way of explaining how we think about, test, and then adopt a new model of reality has been given a number of mathematical formulations. They look complicated, but they really aren’t that hard. I have chosen one of the more intuitive ones below to use in my discussion of the theoretical criticism of Bayesianism.

The Bayesian model of how a human being’s way of thinking evolves can be broken down into a few basic parts. When I, as a typical human, am examining a new way of explaining what I see going on in the world, I am considering a new hypothesis. As I try to judge how true and useful a picture of the world this new hypothesis may give me, I look for ways of testing it that will show me decisively whether this new model of reality helps me to get good results, i.e. whether or not the model works. I am trying to decide whether this hypothesis/model will help me to understand events in my world and then respond to them effectively.

When I encounter a situation that will let me test the hypothesis, and then I do the test, I tend to lean more toward believing that the hypothesis is true if it enables me to make accurate predictions. I tend to lean more toward discarding the hypothesis if the predictions it leads me to keep failing to turn out right. I am especially more inclined to accept the hypothesis and the model of reality it is based on if all my other theories and models are silent or inaccurate when it comes to explaining these test situations. 

In short, I tend to believe a new idea more and more if it fits the things I’m seeing. Bayes’ Theorem merely tries to express this simple truth in a Math formula. 

It is worth noting again that this same process can occur in a whole nation when increasing numbers of citizens become convinced that a new way of doing things is more effective than the status-quo ways. Popular ideas that really work get followers. In other words, both individuals and whole societies really do learn, grow, and change by the Bayesian model.

In the case of a whole society, the clusters of ideas an individual sorts through and shapes into a larger idea system are like clusters of citizens forming factions within society, each faction arguing for the way of thinking it favours. The leaders of each faction search for reasoning and evidence to support their positions in ways that are closely analogous to the ways in which the various ideas in an individual mind struggle to become the ones that the individual will use to handle life. The difference is that a normal individual does not settle his internal debates by blinding his right eye with his left hand. That is, we usually choose to set aside unresolvable internal debates rather than letting them make us crazy. Societies, on the other hand, have revolutions or wars.

In societies, factions sometimes work out their differences, reach consensus, and move on without violence. But sometimes, as noted in the previous chapter, they seem to have to fight it out. Then violence settles the matter—whether between factions within a society or between societies. But Bayesian calculations are always in play in the minds of the participants, and these same calculations almost always eventually dictate the outcome: one side wins and the other side gives in and accepts the new way. The most extreme alternative, one tribe’s total, genocidal extermination of the other, is only rarely the final outcome.

But let’s get back to the so-called flaw in the formula for Bayesian decision making.

Suppose I am considering a new way of explaining how some part of the world around me works. The new way is usually called a hypothesis. Then, suppose I decide to do some research, and then I find some new evidence that definitely relates to the matter I’m studying. What kind of process is going on in my mind as I try to decide whether this new bit of evidence is making me more likely to believe the new hypothesis or less likely to do so? This thoughtful time of curiosity and investigation, for Bayesians, is at the core of how human knowledge forms and grows.