"Give me a lever long enough and I will move the Earth," said Archimedes.
True ... but you won't move it very far, and you sure won't do it very fast! As with some areas of mathematics or logic programming, you can get something for (almost) nothing --- but only if you're willing to wait (almost) forever to get it.
But on the brighter side, if you're patient enough then you can win, and win big. Which brings to mind a lovely extended essay that I first saw a few decades ago by Freeman J. Dyson: Time Without End: Physics and Biology in an Open Universe (in Rev. Mod. Phys., v.51, n.3, July 1979). Dyson takes simple but plausible models of the cosmos and the laws of nature, and then extrapolates them --- far beyond their known realms of validity, as he himself admits, but hey, that's ok. It's a "take your best shot" approach to looking deep into the future, and he does it brilliantly.
Dyson's bottom-line conclusions? To put infinite space into a nutshell: even if the universe is open and expands into an ever-colder ever-thinner soup, nonetheless life and mind and communication can go on forever --- though at an ever-slower pace.
The mainspring of thought winds down, but the gears never come to a stop. It's like the harmonic series 1/1 + 1/2 + 1/3 + 1/4 + 1/5 + ... . Given enough time there's no upper bound to the total accumulation. Mind is like that. (Maybe!)
And as Freeman Dyson concludes, this is a profoundly optimistic vision: "... a universe growing without limit in richness and complexity, a universe of life surviving forever and making itself known to its neighbors across unimaginable gulfs of space and time."