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Squark comments on Welcome to Less Wrong! (July 2012) - Less Wrong
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In an infinite universe, the speed-of-light limit is not a problem. Surely it limits the speed of computing but any computation can be performed eventually. Of course you might argue that our universe it asymptotically de Sitter. This is true, but it also probably metastable and can collapse into a universe with other properties. In http://arxiv.org/abs/1105.3796 the authors present the following line of reasoning: there must be a way to perform an infinite sequence of measurements since otherwise the probabilities of quantum mechanics would be meaningless. In a similar vein I speculate it must be possible to perform an infinite number of computation (or even all possible computations). The authors then go on to explore cosmological explanation of how that might be feasible.
The sequence is unbounded in the sense that any possible intelligence is eventually superseded. The Asymptote is something akin to infinity. The Asymptote is "like an intelligence but not quite" in the same way infinity is "like a number but not quite"
Good point. Indeed it seems that life formation is a rare event. So I'm not sure whether there really is a "Law of Evolution" or we're just seeing the anthropic principle at work. It would be interesting to understand how to distinguish these scenarios
Does this hold in a universe that is also expanding (like ours)? Such a scenario makes the 'infinite' property largely moot given that any point within has an 'observable universe' that is not infinite. That would seem to rule out computations of anything more complicated than what can be represented within the Hubble volume.
Yes, this was exactly my point regarding the universe being asymptotically de Sitter. The problem is that the universe is not merely expanding, it's expanding with acceleration. But there are possible solutions to this like escaping to an asymptotic region with a non-positive cosmological constant via false vacuum collapse.
wedrifid already replied better than I could; but I'd still like to add that "eventually" is a long time. For example, if the algorithm that you are computing is NP-complete, then you won't be able to grow your hardware quickly enough to make any practical difference. In addition, if our universe is not eternal (which it most likely is not), then it makes no sense to talk about an "infinite series of computations".
Sorry, but I literally have no idea what this means. I don't think that infinity is "like a number but not quite" at all, so the analogy doesn't work for me.
Well, so far, we have observed one instance of "evolution", and thousands of instances of "no evolution". I'd say the evidence is against the "Law of Evolution" so far...
For algorithms with exponential complexity, you will have to wait for exponential time, yes. But eternity is enough time for everything. I think the universe is eternal. Even an asymptotically de Sitter region is eternal (but useless since it reaches thermodynamic equilibrium), however the universe contains other asymptotic regions. See http://arxiv.org/abs/1105.3796
A more formal definition is given in my comment http://lesswrong.com/lw/do9/welcome_to_less_wrong_july_2012/8kt7 . Less formally, infinity is "like a number but not quite" because many predicates into which a number can be meaningfully plugged in, also work for infinity. For example:
infinity > 5 infinity + 7 = infinity infinity + infinity = infinity infinity * 2 = infinity
However not all such expressions make sense:
infinity - infinity = ? infinity * 0 = ?
Formally, adding infinity to the field of real numbers doesn't yield a field (or even a ring).
There is clearly at least one Great Filter somewhere between life creation (probably there is one exactly there) and appearance of civilization with moderately supermodern technology: it follows from Fermi's paradox. However it feels as though there is a small number of such Great Filters with nearly inevitable evolution between them. The real question is what is the expected number of instances of passing these Filters within the volume of a cosmological horizon. If this number is greater than 1 then the universe is more pro-evolution than what is anticipated from the anthropic principle alone. Fermi's paradox puts an upper bound on this number, but I think this bound is much greater than 1