Thanks for Radium suppositories! What if humans have long left the Milky Way galaxy and aliens visit us then?
If out descendants become intergalactic spacefarers, then we probably won't ever all leave.
and aliens visit us then?
Those aliens will probably be our descendants. They'll just have to look up the information in their archives. It's not like keeping raw information is going to become so expensive, we have to delete it.
That assumes a future where humans colonize the stars and spread life through the universe. What's more likely for humanity is a future more like the matrix, except instead of being enslaved, we place ourselves there willingly. It seems to me the focus of most of our technology has been to figure out how to poke and prod our pleasure sensors to maximum effect. Forget the stars, we're going to invent our own personal paradises on Earth and just stay here.
https://en.wikipedia.org/wiki/The_Library_of_Babel
Perhaps by then, some very clever entity will have figured out a quantum computer implementation of The Library of Babel. It won't actually store all possible books, but it could be used to very quickly search the space by generating all remotely coherent possible books.
What's more likely for humanity is a future more like the matrix, except instead of being enslaved, we place ourselves there willingly.
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