I strongly doubt the existence of any truly unbounded entity. Even a self-modifying transhuman AI would eventually run out of atoms to convert into computronium, and out of energy to power itself. Even if our Universe was infinite, the AI would be limited by the speed of light.
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.
Wait, so is it bounded or isn't it ? I'm not sure what you mean.
The sequence is unbounded in the sense that any possible intelligence is eventually superseded.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"
There are plenty of planets where biological evolution had not happened, and most likely never will -- take Mercury, for example, or Pluto (yes yes I know it's not technically a planet). As far as we can tell, most of not all exoplanets we have detected so far are lifeless. What leads you to believe that biological evolution is inevitable ?
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
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.
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 "inf...
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