--:-- There's also the theory of Solominoff induction. I'm going to mangle the description, but it says if you want to find a theory that explains why something is happening, and now a theory here is something that's encoded as a binary string, then the correct theory is actually going to be a probability-weighted theory that takes into account all the possible theories, but weighs them based on their complexity. So the simpler ones are more likely to be true, and the more complex ones are less likely to be true, and you sum them all together, and that's how you figure out the correct probability distribution function for your explanation. That's similar to Bayesianism, isn't it? In both cases, they're assuming that you can enumerate all the possible theories, but you can't because that's the creativity coming in. It's very rare in science to have more than one viable theory. In physics, we mentioned Newtonian theory of gravity and there was general relativity. That's one of the rare occasions where you actually have these two competing theories. It's almost unknown to have three competing theories. What confuses people is that induction and Bayesianism work really well for finite, constrained spaces that are already known. They're not good for new explanations. Bayesianism is, I got new information. I used it to weight the previous probability predictions that I had. Now I've changed my probability based on the new data. So I believe that something different is going to happen. For example, I don't know if you remember the Monty Hall show. Monty Hall calls you up and there's three doors and there's treasure behind one of them and then two of them don't have anything. And you pick which door it's going to be, door number one, two or three. Then he opens one of the other two doors and shows you there's nothing behind it. Now do you want to change your vote? The understanding of naive probability says, no, I wouldn't change my vote. Why should it matter that one of the ones he showed me doesn't have something? The probability should not have changed. But Bayesianism says, you've got new information, you should revise your guess and you should switch the other door. And the easier way to say that is imagine there were 100 doors and then you picked one at random. Then he opens 98 of the remaining 99 and shows you there's nothing. Now do you switch? And of course you'd want to switch because what are the odds that you picked one of the 100 in the first place? Now your odds are 99 out of 100. And people discover this and say, of course, now I'm a smart Bayesian. I can update my priors based on new information. That's what smart people do, and therefore I'm a Bayesian. But it in no way helps you discover new knowledge or new explanations. That's the uncontroversial use of Bayesianism, which is a very powerful tool. It's used in medicine of trying to figure out which of these medicines might be more effective than others. So there are whole areas of mathematics, like Bayesianism, which can be applied in science without controversy at all. It's where we say that Bayesianism is the way in which we can generate new explanations, or the way in which we can judge one explanation against another. In fact, the way in which we generate new explanations is creativity, and the way in which we judge one explanation against another is either experimental refutation or straightforward criticism of realizing that one of those explanations is just a bad explanation.
