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

 

                                                                      Louis Pasteur 

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 discuss the theoretical criticism of Bayesianism.

The Bayesian model of how a human being’s thinking evolves can be broken down into a few basic components. 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, and as I try to judge how true—and therefore how useful—a picture of the world this new hypothesis may give me, I look for ways of testing it that will show decisively whether it and the model of reality it is based on really work. I am trying to determine whether this hypothesis will help me to understand, anticipate, and respond effectively to events in my world.

 

                                                          Dr. Edward Jenner testing his smallpox vaccine 

When I encounter a test situation that fits within the range of events that the hypothesis is supposed to be able to explain and make predictions about, I tend to become more convinced the hypothesis is a true one if it enables me to make accurate predictions. (And I tend to be more likely to discard the hypothesis if the predictions it leads me to make keep failing to be realized.) I am especially more inclined to accept the hypothesis and the model of reality it is based on if it enables me to make reliable predictions about the outcomes of these test situations and if all my other theories and models are silent or inaccurate when it comes to explaining my observations of these same test situations.

 

In short, I tend to believe a new idea more and more if it fits the things I’m seeing. This is especially true when none of my old ideas seem to fit the events I’m seeing at all. Bayes’ Theorem merely tries to express this simple truth mathematically. 

 

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 practices. 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 become 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 biases in an individual mind struggle to become the idea system that the individual follows. The difference is that the individual usually does not settle heated internal debates by blinding his right eye with his left hand. That is, we usually choose to set aside unresolvable internal disputes 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 a given society and one of its  neighbouring societies that is perceived as being the carrier of the threatening new ideas. 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 gives in and learns the new ways. The most extreme alternative, one tribe’s complete, genocidal extermination of the other, is only rarely the final outcome.