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Frank J. Tipler's Omega Point Theory is the coolest thing I've found in a long time. Maybe ever. It's defended by David Deutsch here, and that's probably as good a starting point as any.
The key discovery in the omega-point theory is that of a class of cosmological models in which, though the universe is finite in both space and time, the memory capacity, the number of possible computational steps and the effective energy supply are all unlimited. This apparent impossibility can happen because of the extreme violence of the final moments of the universe's Big Crunch collapse.In Tipler's theories, intelligent beings (like humans) are not epiphenomenon, but are instead required by the laws of physics. They are required so that the collapsing universe can be "steered" along the correct course to result in an approach to the Omega Point (singularity) in which the universe becomes an infinitely powerful computer.
The stabilization procedures, and the accompanying knowledge-creation processes, will all have to be increasingly rapid until, in the final frenzy, an infinite amount of both occur in a finite time. We know of no reason why the physical resources should not be available to do this, but one might wonder why the inhabitants should bother to go to so much trouble. Why should they continue so carefully to steer the gravitational oscillations during, say, the last second of the universe? If you have only one second left to live, why not just sit back and take it easy at last? But of course, that is a misrepresentation of the situation. It could hardly be a bigger misrepresentation. For these people's minds will be running as computer programs in computers whose physical speed is increasing without limit. Their thoughts will, like ours, be virtual-reality renderings performed by these computers. It is true that at the end of that final second the whole sophisticated mechanism will be destroyed. But we know that the subjective duration of a virtual-reality experience is determined not by the elapsed time, but by the computations that are performed in that time. In an infinite number of computational steps there is time for an infinite number of thoughts - plenty of time for the thinkers to place themselves into any virtual-reality environment they like, and to experience it for however long they like. If they tire of it, they can switch to any other environment, or to any number of other environments they care to design. Subjectively, they will not be at the final stages of their lives but at the very beginning . They will be in no hurry, for subjectively they will live for ever. With one second, or one microsecond, to go, they will still have 'all the time in the world' to do more, experience more, create more - infinitely more - than anyone in the multiverse will ever have done before then.Here's an interview from transhumanism.com. And here's his disinfo page with lots more links.
I think I'll need infinite time to understand all this suff.