Infinity Paradoxes and Orders of Operation
Alright it has been a long time since I’ve gone and tried to outsmart people way smarter than me. I watched this video earlier this week and one of the examples given in it really really bothered me. Please go watch the video at least through the Hotel example and then come back.
For those of you living in that strange realm that prefers reading over videos I will explain it to the best of my abilities.
A man walks into a hotel with infinitely many rooms. This hotel has a sign outside that reads “no vacancies” but when the man speaks with the concierge the concierge says “Sure I can make room.” They concierge asks the person in room one to move to room two, the person in room two to move to room three, and so on. This person then takes the first room that is now vacant. In this way the hotel can keep adding more and more people while simultaneously being full.
Cool great. I could see that but then I think. No. No I can’t see that at all!
I can’t move into a room until it is vacant. A room is not vacant until the person who was using it has moved into the next room. But for each person moving the next room is currently occupied! Person 1 walks to room 2 and asks them if they are ready to go. They say “Well once room 3 is ready I’ll move.”
Problem is room 3 is saying “well once room 4 is ready” and room 5 is saying “well once room 6 is ready”. But nobody will ever be able to finish this system because the next room is always occupied and it can’t become occupied because the room it is moving into can’t be opened until the person in that room moves into the next room in the sequence.
Basically what the paradox is assuming is that Infinity is like superman. Its powers are directly related to what you need to move the plot along. There are 100 rooms if you only have 100 people and 101 rooms if you have 101 people and so on. I believe however that infinity is a range with no end. It does not get smaller or bigger as needed and instead exists as a non moving thing. There is no wiggle room because it exists in all points at once.
So the original model is:
Room 1 –> Room 2 – > Room 3 – > Room 4 – > Room 5 – > Room *. Move new person into room 1.
My model is:
Room 1 – > Room 2 (when empty) – > Room 3 (when empty) – > Room 4 (when empty) – > Room * (when empty). Person cannot move in because the hotel has no vacancies.
My model makes more intuitive sense (to me) because you wouldn’t want to surrender your room until you were certain you had a new room to sit in. Basically the infinite hotel would suffer a population traffic jam. No matter how many rooms you have you equally have that many people and so nothing ever actually moves.
This also does not make the hotel sign both false and true at the same time. It is definitively true. The hotel has infinite rooms and infinite people and under a sensible order of operations this will be true for as long a time as this statement is true (presumably infinity).
So that’s it to me. I feel that the original paradox is approaching the problem incorrectly. The other paradoxes in the episode are so over my head that I won’t discuss them. Thanks for your time!
Did I mention I put my first book up on Amazon? It’s a short story (emphasis on short) and you can read it for free if you have Amazon Prime!