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.
Comment on Infinite Hotel Paradox
1rre@discuss.tchncs.de 4 days ago
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 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
emeralddawn45@discuss.tchncs.de 4 days ago
1rre@discuss.tchncs.de 4 days ago
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
apprehensively_human@lemmy.ca 3 days ago
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.
DragonTypeWyvern@midwest.social 4 days ago
Yes, but, also, logically you can never reach any destination because you can only ever halve the distance therefore everyone is trapped in an infinite loop of suffering.
1rre@discuss.tchncs.de 4 days ago
Theoretically, I guess… But my argument came when introducing the laws of physics into the world of the infinite hotel, but there comes a point where the movement is small enough that the electron orbits are unaffected when the nuclei move therefore there’s functionally no movement.
You’re not a criminal who goes around breaking the laws of physics like the rest of those “mathematician” types are you?
Robust_Mirror@aussie.zone 3 days ago
The rooms are all full by definition. You’re literally telling him to walk until he dies. Just kick him out at that point, hell shooting him on the spot would be more merciful.
But the weird thing about infinite sets is they don’t process over time as we perceive it. Things happen all at once. There’s a classic situation where an infinite tub is filled with an infinite amount of numbered balls, and for every number that goes in, it’s square root is taken out. So when 1 goes in, 1 goes out, when 2 goes in nothing happens, same with 3, when 4 goes in, 2 gets taken out, when 9 goes in, 3 gets taken out.
How many balls are in it at the end?
Intuitively it seems there must be infinite balls, as balls are being taken out at a slower rate than they’re entering. But the actual answer is 0. Because the process happens all at once. So the question becomes, which balls get removed in this process? Well, the numbers that can be squared. Which is every number. If every number can be squared, every number gets removed. So if this infinite process were to play out, there would be no balls left in it.
But if we were to try to physically do this, it’s impossible for it to actually play out. Infinity isn’t a number at the end of a line, it’s the concept of an entire unbound set. That’s why things like the hotel are good to try to explain and visualise the concept, but break down if you try to imagine them as real world places that follow time and physics.
Sotuanduso@lemm.ee 4 days ago
Fun prank.
“How do you know they’re all booked? Maybe someone didn’t show up. Can you go check?”