I've been thinking about the question from Edge that I blogged about below: What do you believe is true even though you can't prove it? I have been thinking about several possible answers, but I think that I have the most interesting things to say about this one.
I believe, but can't prove, that much human intellectual activity is the accidental product of our large brains and has no evolutionary or other purpose. Whenever I read another "evolutionary biologist" speculating about the adaptive purpose of our innate attraction to music, I think, who says it has any purpose at all? I don't think it does. Modern religious thinkers have made much of the "god-shaped hole" in our psyches, that is, the great desire many people have to believe in higher powers; I think this is probably just an evolutionary accident. Belief in conspiracy theories, I suspect, is just our useful ability to search for and recognize patterns run amok.
It is a commonplace notion that we only use our whole intellectual capacity on rare occasions. On those occasions, the full size of our brains may make the difference between life and death. The rest of the time a lot of our neurons are just noodling around.