I first encountered Bayes Theorem (BT) in a probability course in college. I have since forgotten and re-learnt it multiple times. Recently, I came across the concept in Nate Silver's book The Signal and the Noise, and found its implications fascinating.
I decided to spend some time grappling with the seemingly simple equation so that I could arrive at an intuitive understanding of it, and finally commit it to memory. As I worked through a number of examples and hypothetical situations, I found one to be particularly enlightening: BT provides a satisfying explanation for why I find it so difficult to have a meaningful debate with those who have an unwavering commitment to a particular viewpoint.
Using Bayes's theorem, I will explain why you can't change someone's mind if they have an absolute a priori belief. In turn, this example will illuminate how BT works.
Let's start with an intuitive definition of Bayes Theorem. It describes how you should adjust your confidence in a hypothesis after being presented with some evidence. You adjust your confidence by interpreting the probability of an event; a high probability means that you should have high confidence, and vice versa.
For example, imagine that you are living with your partner and one day you find a gift box hidden in the closet. Now, you want to develop a hypothesis about the intended recipient of this gift. The question is, is the gift for you?
Let's begin with the tentative hypothesis that the gift is for you. To test it, you first need to estimate the likelihood that the gift is for you. If today is your birthday then the estimate for getting a gift is high—since your partner is very thoughtful.
This thought process is the key idea in BT. The theorem gives you a mathematical formula that allows you to calculate how much the evidence should change your original confidence in a hypothesis.
Confidence in a hypothesis = Evidence Confidence Factor × Confidence in the hypothesis before knowing about the evidence
Evidence Confidence Factor = Strength of the evidence's link to the hypothesis / How common the evidence is in the context of the situation
This means that if your confidence in a hypothesis initially started out at 100%, no amount of evidence can ever change your mind. By definition, fundamentalists have an initial confidence in their beliefs that is very close to certainty.
I am not making a statement about whether fundamentalists' beliefs are correct. I am advocating, though, that having a slightly skeptical mind—one that does not completely believe in any one hypothesis—allows you to interact with the world more fully.
All things considered, it may make you a better conversationalist, a better partner—and almost certainly, a better thinker.