The problem with your example is that ‘not-S’ is not an event, it’s a huge set of events. It’s like talking about the integer 452 and the ‘integer’ not-452.
The simplest beliefs about the events within that set can be extremely simple. For example, if S is described by the bits 1001001, the beliefs corresponding to non-S would be, “the first bit is 0′, or “the second bit is 1”, or, “the third bit is 1″, and so forth.
The problem with your example is that ‘not-S’ is not an event, it’s a huge set of events. It’s like talking about the integer 452 and the ‘integer’ not-452.
The simplest beliefs about the events within that set can be extremely simple. For example, if S is described by the bits 1001001, the beliefs corresponding to non-S would be, “the first bit is 0′, or “the second bit is 1”, or, “the third bit is 1″, and so forth.
Events aka hypotheses are sets of programs.
Sorry, you’re right, I was totally confused by your (and cousin_it’s) choice of words.
Wow, that was by far my worst comment on Less Wrong. That was really, really dumb.
It’s OK, the post itself was pretty stupid and I guess it was infectious. Here’s my attempt to fix things.