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Infinite Hotel Paradox
(lemmy.world)
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this post was submitted on 17 Feb 2025
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Thing is, the message has to be passed along either by an intercom or by the person moving to the next room passing it on... Either way or travels at fastest at the speed of light, so you'll have people in the corridors moving to the next room for an infinite amount of time purely from the time it takes to propagate.
Given you're therefore committing to (at least on average) at least one person being without a room for the rest of time, why not just tell the chap in the first room to keep walking until he finds an available room? In terms of overall inconvenience (overall time spent without a room per person), it's the same as the original as both are infinite, but for the average person it goes from the time to walk from one room to the next to 0
But if being without a room is a form of suffering, then wouldbt it make more sense to distribute that suffering equally, so that no one person has to bear an unendurable length of time without a room, instead each person is just momentarily inconvenienced as they shift.
That's without considering the time to pack up your bags etc - ie there's a fixed cost as well as the cost per room moved
To minimise the total societal cost, only one person has to leave their room, and by that (or any) one person not making the sacrifice, the average suffering increases across all of median, mean and mode...
It's the opposite situation from where one person can get huge gains to the detriment of many others - eusocially it makes sense to do what's best for the average person
What you could do is tell each next person to move out in half the time it took the previous person. This way you get an infinite amount of moves done within a finite time limit.