Sometimes we may want to formally talk about objects that actually exist in the world, using mathematical language. One way to try to do this is by recording some sequence of observations about the world, and then applying Solomonoff induction. The hope would then be: if you apply Solomonoff induction to the sequence of things you’ve seen so far, it will correctly predict whatever you next see. In this post I’ll describe a problem with applying this approach to anything particularly important.
(Apologies: this post will probably be incomprehensible.)
In my post on Indirect Normativity, I describe the definition of a very complicated utility function U. A U-maximizer has a very interesting task: it is supposed to optimize a utility function that is completely opaque, and it is supposed to care about worlds (alternatively, assign worlds prior probabilities) according to a metric which is too complicated to understand! A U-maximizer may be able to understand the implications of the definition after amassing a great deal of computational power, or by understanding the process that generated the definition, but at first it would have no idea what U was. And if you are a U-maximizer, and you don’t know anything about what U is, you might as well behave randomly. This is problematic for two reasons: Continue reading