Even given no, um, deadline on our lives, as long as the writing population is at least maintained you will continue to have more than you can read for 'as long as you shall live.'
Now, if you were to say the visions of us uploading ourselves and being able to split off multiple selves who can all read different things, well then all bets are off. But I'd still envision a relatively small split limit based on resources of power or hardware memory.
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