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In our current day and age, it seems that many people can’t be convinced. Their beliefs can’t be changed, their minds can’t be altered. They are utterly and truly convinced they are right, and nothing can sway them from that conviction. Why does this happen? It turns out that we can prove that if someone holds certain types of beliefs, no amount of contrary evidence can change their mind. Furthermore, in certain cases, contrary data will actually convince them that they are more right, instead of causing them to question their beliefs. In particular, if a person believes in a theory that perfectly explains a situation, like a conspiracy theory, evidence that seems to show something else will actually make them more sure of their conspiracy. 1

This post will be in two parts. In the first, non-technical post, I will discuss the concepts without math. This post should be accessible to everyone, and so if you don't understand, the problem is me, not you. I will be using a Bayesian perspective, but don’t worry if you’re not familiar, I will explain the concepts as we go. It turns out that Bayesian statistics describes how we think, and so we can use it to prove what’s going on, and the concepts are surprisingly simple. In the second part, I will work through the math of the examples, and give a little more depth in introducing Bayesian statistics.

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