## LESSWRONGLW

My reasoning is this:

Consider the domain of bit streams - to avoid having to deal with infinity, let's take some large but finite length, say a trillion bits. Then there are 2^trillion possible bit streams. Now restrict our attention to just those that begin with a particular ordered pattern, say the text of Hamlet, and choose one of those at random. (We can run this experiment on a real computer by taking a copy of said text and appending enough random noise to bring the file size up to a trillion bits.) What can we say about the result?

Well, almost all b... (read more)

That in turn means that in our domain of programs a trillion bits long, exponentially more programs contain the compact subroutine than the literal print statement.

Are you sure this is right? There's exponentially many different print statements. Do you have an argument why they should have low combined weight?

1Will_Newsome9yThat all makes sense and you put it more clearly than I've seen before, but I dispute the implication that finding that our local universe is the result of a compact generator implies very much about the large-scale structure of an ensemble universe. For example imagine pockets of local universes that look all nice and neat from the inside yet are completely alien to aliens in a far-off universe pocket---"far off" being determined by the Turing languages for their respective universal priors, say. For a slightly more elegant variation on the idea I made the same argument here [http://lesswrong.com/lw/6wy/why_no_uniform_weightings_for_ensemble_universes/4l7y] . Such an ensemble might be "uniform" and even devoid of any information content ---see Standish's Theory of Nothing---yet could look very rich from the inside. Does your reasoning eliminate this possibility in a way that I'm not seeing? Edit: I was assuming you mean "ensemble" when you say "universe" but you might not have actually been implying this seemingly much stronger claim?