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Mitchell_Porter comments on One possible issue with radically increased lifespan - Less Wrong Discussion
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If your civilization expands at a cubic rate through the universe, you can have one factor of linear growth for population (each couple of 2 has exactly 2 children when they're 20, then stop reproducing) and one factor of quadratic growth for minds (your mind can go as size N squared with time N). This can continue until the accelerating expansion of the universe places any other galaxies beyond our reach, at which point some unimaginably huge superintelligent minds will, billions of years later, have to face some unpleasant problems, assuming physics-as-we-know-it cannot be dodged, worked around, or exploited.
Meanwhile, PARTY ON THE OTHER SIDE OF THE MILKY WAY! WOO!
If dark energy is constant, and if no-one artificially moves more galaxies together, then after 100 billion years, all that's left in our Hubble volume is a merged Andromeda and Milky Way. On a supragalactic scale, the apparent abundance of the universe is somewhat illusory; all those galaxies we can see in the present are set up to fly apart so quickly that no-one gets to be emperor of more than a few of them at once.
It seems no-one has thought through the implications of this for intelligence in the universe. Intelligences may seek to migrate to naturally denser galactic clusters, though they then run the risk of competing with other migrants, depending on the frequency with which they arise in the universe. Intergalactic colonization is either about creating separate super-minds who will eventually pass completely beyond communication, or about trying to send some of the alien galactic mass back to the home galaxy, something which may require burning through the vast majority of the alien galaxy's mass-energy (e.g. to propel a few billion stars back to the home system). There will be periods, lasting billions of years, in which some galaxies are beyond material reach, but visible and thus capable of communicating.
This cosmology of alien paperclip maximizers fighting over a universe of mutually receding galaxies, is not exactly proved by science, but it would be interesting to see it fleshed out.
Also see this timeline of the far future.