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“The struggle itself towards the heights is enough to fill a man’s heart. One must imagine Sisyphus happy.”
He will struggle to ask the infinite staff of the infinite hotel to move infinite occupants into another set of infinite rooms. After all:
It is also possible to accommodate a countably infinite number of new guests: just move the person occupying room 1 to room 2, the guest occupying room 2 to room 4, and, in general, the guest occupying room n to room 2n (2 times n), and all the odd-numbered rooms (which are countably infinite) will be free for the new guests.
Even if Sisyphus is infinite and the boulder is infinite, they can be accommodated within an infinite space.
Hilbert’s paradox is a veridical paradox: it leads to a counter-intuitive result that is provably true. The statements “there is a guest to every room” and “no more guests can be accommodated” are not equivalent when there are infinitely many rooms.
This struggle will, according to Camus, provide some meagre happiness to offset the fact he’s stuck in a stupid, made up, unrealistic trolley problem; one which serves only to trap people within consequentialist moral thought as if that is the only ingredient for a moral decision, ignoring all other bases for moral decisions.
Sadly, the Hilbert Hotel is slated for demolition which is why it’s on Sisyphus’ path. After that whole “everyone moves to double their room number” debacle, Hilbert had to process a fraction of the infinite guests’ refunds because they didn’t feel like changing rooms to one several million hallways down. And a percentage of infinite guests refunds is still infinite, so Hilbert is in infinite debt now.
Theseus, meanwhile, has been trying to justify buying a new ship for ages but his crew is adamant about right to repair, so he’s looking for an easy exit.
Infinite guest = infinite money, infinite refunds would be fine, and infinite money would still be left over.
Even if Sisyphus is infinite and the boulder is infinite, they can be accommodated within an infinite space.
But not if they’re uncountably infinite.
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One must at least imagine Sisyphus happy, even under such circumstances
He might be happy, when his boulder gets to sink the reconstructed Ship of Theseus and he is finally rid of the thing that made him unhappy.
One must imagine the intimate number of people the bolder would kill if it smashed into it, and the ship can always be rebuilt, but is he happy, maybe if he pushes the bolder through an infinite amount of rooms killing an infinite amount of people.
