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cousin_it comments on Shock Level 5: Big Worlds and Modal Realism - Less Wrong
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I'm talking about our universe. Don't try to confuse me.
What makes you think so? Pure shock value?
I'm willing to (provisionally) believe in MWI, but not Tegmark's ensemble. You haven't provided any actual evidence why the latter is true, and chocolate bars indicate that it's almost certainly false. Here's the cousin_it scale of science-worthiness:
This is true.
This works.
This sounds true.
This sounds neat.
From the looks of things, you have yet to rise above level 4.
No. That's just one small part of the evidence, far from sufficient and I would say far from necessary. By itself, these ideas would cause me to say "so much the worse for chaotic inflation theory" which is, as far as I know, not terribly well confirmed (or more to the point, not terribly clear in its proper interpretation).
If I understand it correctly, chaotic inflation theory implies a multitude of universes with differing but stable physical laws, not a multitude of universes that evolved just like ours but will soon begin turning chocolate bars into hamsters.
If arbitrarily large universes exist, then there would be people with arbitrarily large computers running every possible program. From that you would get worlds in which chocolate bars turn into hamsters.
Question: Tegmark, in one of his multiverse papers, suggests that ordering measure by complexity seems to be an explanation for finding ourselves in a simple universe as well as a possible to answer to the question 'how much relative existence do these structures get?' My intuition says rather strongly that this is almost assuredly correct. Do you know of any other sane ways of assigning measure to 'structures' or 'computations' other than complexity?
Could you elaborate? It seems to me that because there exists a much greater number of complex computations than there are simple computations, we should expect to find ourselves in a complex one. But this, obviously, does not seem to be the case.
Meanwhile, a newly-minted hamster scurries down the candy aisle in a vacant supermarket.
If we run each universe-program with probability 2 to the power of minus L, where L is the length of the program in bits, and additionally assume that a valid program can't be a prefix of another valid program, then the total probability sums to 1 or less (by Kraft's inequality). In this setup shorter programs carry most of the probability weight despite being vastly outnumbered by longer ones. I think the same holds for most other probability distributions over programs that you can imagine.
Doesn't follow at all. A large variety of physical laws and universe sizes doesn't imply arbitrarily large computers. It's quite possible that sentient life that can build computers exists only in universes with parameters very much like ours, and our particular universe seems to have hard physical limits on the size of computers before they collapse into black holes or whatever.
Who said anything about sentient life? Arbitrarily numerous computers should simply emerge, within this universe though not this Hubble volume, and should run every computation.
There's no upper limit on the size of a computer in our universe. Black holes are only a problem if you assume a very dense computer.
Moreover, it isn't that hard to construct hypothetical rules for a universe that could easily have arbitrarily large Turing machines. For example, simply using the rules of Conway's Game of Life.
If you make the computer sparse, other limits come into play: all matter decays in finite time, and the speed of light is finite.
Assuming the existence of a Game of Life universe is begging the question.
The discussion above was in the context of arbitrarily large universes existing. The point is that one can construct very simple universes which allow arbitrarily large simulation. You only need one such universe for the argument to go through.