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Comment by danbruc | Hacker News Reader

No, there is no reordering wave, it happens all in parallel. Everyone steps out of his room at the same time, everyone walks to his new room, whether it is n + 1, n + k, 2n, or whatever, and everyone steps into his new room at the same time. So it is not what you probably imagined, that the person steps out of room 1, knocks on the door of room two, tells the person in there to move to room three, and so on.

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Distributed synchronisation is lost upon mathematicians.

There’s no requirement for it to be instantaneous. It could be, buy it could also be sequential. The thought experiment works fine either way.

Why assume that the hotel's hallway is strait? Maybe it has an infinite number of rooms all around a circular lobby, a lobby that grows in diameter/circumference every time someone books a room. The message from the desk (in the middle of the lobby) then hits every room at the same time. No waves. Just instant simultaneous movement in every room.

As soon as the hotel has taken in even a small infinity of patrons, this layout is not possible - a circle must have a finite circumference (and if we did try to generalize our definition of circle it would result also in an infinite radius).

Maybe a hypersphere with finite bounds but infinite dimensions? My geometry is fairly poor but I think this is what is called, for reasons not directly related to the hotel paradox, a Hilbert sphere.

And how is everyone supposed to know when to leave their room and where to go?

There is a screen in each room that shows you a message when to move where. Or you get a call from the receptionist, but not an individual call but one broadcasted to all rooms, announcing the formula for your new room number. Make up whatever you want, its a thought experiment.

It's a very unique universe that quite a bit different that ours - It would require an infinite amount of energy to communicate that call leading to infinite entropy. Given that the moves happen instantaneously, the first guest to arrive would instantly cause the heat-death of this universe.

They all hear an announcement at the same time via the hotel’s speaker system. (And we’re already ignoring so many laws of physics that the speed of light is the least of our problems.)

In a universe with an infinite speed of light, can there even be any kind of waves? Do physical waves not also propagate instantly?

What kind of waves? I guess you could at least have a light source that periodically gets brighter and dimmer and a detector at the other end of the universe would detect the brightness oscillation and it would not really make any difference whether the light propagates with an finite or infinite speed besides of course the propagation time.

> What kind of waves?

Any wave! Including sound waves.

> I guess you could at least have a light source that periodically gets brighter and dimmer

Would it even be possible to make a timer that periodically gets brighter and dimmer in a world with an infinite speed of light? Would the crystal oscillators in CPUs still work?

I believe that some processes (like nuclear decay) stop happening when there's an infinite speed of light. I guess my overall question is: does time still exist in a world with an infinite speed of light?

Can you explain how all of that would follow? Naively, if we take the limit of c to infinity, aren’t we simply back to Newtonian physics? Why wouldn’t a pendulum work, for example?

The laws of physics get chucked out the window the moment you say "infinitely many rooms".

They always leave their room after 24hrs and go to the room next door?

I know we’re already assuming a hotel with infinite rooms but doesn’t this break causality by assuming FTL information propagation?

Just make each room half the size of the preceding one and you can fit all the rooms in twice the length of the first room. Also solves the problem that, when moving from room n to 2n, the guy in room one has only to walk to next room while the poor guy in room Graham's number has quite a journey ahead of him. Please address complaints about narrow rooms that can not even fit a single proton to the manager.

We consider different universes with different properties to our own in mathematics, and indeed in physics, all the time.

Oh, I’m not arguing that the thought experiment is wrong. Just extending it in the direction of “reasons this doesn’t work in the real world”

Where would you even find the fuel for the infinitely-long bus! Mathematicians must be idiots.

I don't see an issue if you want the communication to not be instantaneous. The only requirements i see are that it has to be faster than the guests, so that everyone's room is empty when they get there.

Alternately, the rooms can simply be renumbered with no guest motion.

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