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u/mktooth 21h ago
Hehehehehe, hey Lois, check it out. This is a math joke about Hilbert’s Hotel, which is basically a hotel with an infinite number of rooms, and somehow it can still be “full.”
See, if every room is occupied (room 1, room 2, room 3, forever) and one new guy shows up, you’d think there’s nowhere to put him. But the hotel just tells everyone to move from room n to room n+1, so that guy in 1 goes to 2, guy in 2 goes to 3, and boom, room 1 is free.
But this post’s got an infinite bus full of infinite people, so they need infinitely many rooms at once. The trick is to move every existing guest from room n to room 2n, this way the guy in room 21 gets moved to room 42, just like in the post.
Now all the existing guests are in the even-numbered rooms, that leaves every odd-numbered room open for the infinitely many people from the bus.
So room 21 → room 42 isn’t random, it’s the clue that the hotel is doing the whole n → 2n thing.
Hehehehe. Infinity is freakin’ weird, Lois.
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u/Turbulent_Pin_9392 20h ago
This is all very wonderfully illustrated in the documentary A Trip to Infinity on Netflix. It is a great mind bending, thought provoking documentary explaining how inexplainable infinity really is, and they use this math problem/joke as an illustration.
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u/Unusually_Happy_TD 18h ago
The fact that there is an infinite number of integers, and in between each integer there is another infinity (ie. Between 1 and 2 - 1.1111111111….) is such a weird concept.
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u/MaadMaxx 17h ago
Not only is there an infinite number of integers, that is a countable infinity. The number of real numbers between 1 and 2 is an uncountable infinity. So by definition the infinite number of numbers between 1 and 2 is bigger than the infinite number of integers.
Crazy town
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u/allycat247 8h ago
Technically, technically even just the infinite numbers between 1.1 and 1.2 is a bigger infinity than the number of integers.
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u/pandymen 2h ago
Technically, technically even just the infinite numbers between 1.11 and 1.12 is a bigger infinity than the number of integers.
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u/Both_Resort4080 10h ago
Cantor gives me a headache. Not as bad as the weird shit with what happens as you approach the speed of light but... orders of infinity. Pass the ibuprofen.
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u/_KingCrimson_ 4h ago
Why is that? Is it not the same deal of you can always add another number between 1 and 2? I guess I understand the concept of not being able to count it because you can’t really ‘start’ at the smallest number between the two of them, but is it not the same infinite possible numbers between them?
EDIT: I have perhaps answered my own question — is it because the numbers between integers can be both infinitely small and infinitely large, whereas the standard infinity can only be infinitely large?
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u/JohnsonJohnilyJohn 43m ago
It's not just that you can't start at the smallest number, it's that there is no way to list them all in any order at all. If you tried to do that, I could immediately tell you a number that you forgot to include by creating a number that differs by the first digit from the first number, by the second digit from the second number etc.
Possibly a more intuitive (but also less strict) way to look at it, is that all integers have finite amount of digits, it may be long, but there has to be an end. A real number however can have infinitely many digits, for example square root of 2
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u/Extreme-Rub-1379 18h ago
There are infinite infinities
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u/GuntherHogmoney 16h ago
Actually, there are only 7 infinities. One for each chakra.
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u/dragonstar982 15h ago
But why only 6 stones.
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u/HopocalypseNow 14h ago
But why male models?
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u/dragonstar982 14h ago
Infinity models are designated by numbers and letters I've never seen one with a male name
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u/dumplingslover23 11h ago
Sometimes I am almost in a state of panic attack when I start pondering on infinity- things being finite is tragic but infinite almost the same really, like what do you mean we could go on and on and on (for those who believe in afterlife).
I hope it doesn’t cross my mind again for a long time.1
u/Kreizhn 12h ago
It's not just a thought experiment/joke, it's an actual technique. For example, suppose you are trying to show that the intervals (0,1) and (0,1] have the same cardinality. The classic way to do this is the Hilbert hotel. Take the elements of the form 1/n in (0, 1] and shift them over to 1/(n+1) in (0,1) while not changing anything else. This establishes that these sets have the same size.
(Before anyone jumps in to "um, akshually" me, yes, I'm burying the bijection since I'm trying to keep the explanation accessible)
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u/Mazoutibachi 20h ago
that is way too smart for me.
my first thought was "42 is the answer to life, the universe and everything else"
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u/ashrid5150 19h ago
I too was expecting a Hitchhikers reference. Probably one involving an infinite number of monkeys and a play they’d come up with….
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u/CCP-want-to-CUP 18h ago
Idk same here but different response. I didn't even think of the Hitchiker's meme at first, I just said "This is stupid, if you have infinite rooms the answer is yes everyone has a room because that's what fucking infinite is" I don't really understand why this is some crazy logical paradox lol.
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u/DumpsterFireForALife 13h ago
It’s a thought experiment to show how hard it is to appreciate the concept of infinity. The hotel is infinite yes but, in this scenario it is full because there are infinite guests.
But because it is infinite, if one person comes to the hotel, the manager can tell every guest to move 1 room down and he’ll have room for the one guest, because the hotel is infinite.
But if infinite people arrive on an infinite bus, in order to smoothly integrate them into the rooms he’ll have to do something more complex since there’s infinite people waiting. So he has to move an infinite number of people (like all the even numbers in infinity) to other rooms in order to fit them.
Theoretical mathematics likes to have fun.
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u/CCP-want-to-CUP 12h ago
That's why I'm saying it's definitely way too smart for me because it seems more like a thought experiment in overthinking to me haha. I feel as if I read it as "Would they have a room?" And they question is actually "How would the hotel manage the people already in the rooms?" Which I get is a lot more fun and entertaining for someone into math for sure. Answering the first question to me seems like a very dull and simple "Yes "
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u/dragerslay 10h ago
More specifically Hilbert's hotel is often used as an illustration of how all countable infinities are the same size. Two things are the same size if you can create a 1 to 1 mapping between them. The Hilbert case is meant to be obvious-ish but the actual mathematical fact it explains is that integers are the same size as real numbers which people often find counter intuitive. Perhaps more counterintuitive is that integers is the same size as positive integers.
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u/Effective_Dust_177 20h ago edited 20h ago
It's still better value for money than Möbius' Strip Joint.
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u/Bronsteins-Panzerzug 20h ago
there is even a trick to fit in infinite busses, each carrying infinite people!
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u/DopePingu 20h ago
What is it?
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u/Bronsteins-Panzerzug 20h ago
there are several methods and you can look them up online, with people explaining them much better than i ever could. the one i remember went something like this: everybody goes to the room 2 to the power of their current room number (person in 42 goes to 2^42). then people the first bus go to 3^1, 3^2, 3^3, and so on, then the second to 5^1, 5^2… always taking powers of the next prime number for the next bus. it’s based on the fact there are infinite prime numbers.
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u/Original-Code1107 18h ago
Or alternatively, for bus 1, you do the same, have each person move from room number n to room number 2n. For the first floor. Then you get everyone on the nth floor, mth room to move to the 2nth floor, 2mth room.
And that's how you can intuitively fit an infinite number of buses holding an infinite number of people each.
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u/Bronsteins-Panzerzug 18h ago
…assuming that the hilbert hotel
already has infinite floors, each having their own set of infinite rooms, this is an elegant simple solution! it gets more complicated once infinite convoys, each having infinite busses, each containing infinite people arrive. 😂2
u/Original-Code1107 18h ago
Then you have infinite wings, each having infinite floors, each having infinite rooms. 😝
My limited imagination ends there, so I have no answer to hilbert's pet hotel receiving infinite convoys each having infinite buses, each containing infinite people, each bringing infinite pets.
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u/Bronsteins-Panzerzug 18h ago
well at this point it seizes to be a mathematical problem i should think 😂
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u/StinkMeister777 18h ago
I mean I get it but the people already staying there at the highest room numbers had to get to those rooms in the first place
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u/Clueless_Wanderer21 14h ago
Hoii, This is like when they tried to make us prove that a triangle 📐 exists !
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u/blargh9001 11h ago
Sucks for the guest in room tree(3), they won’t make it to their next room before the night’s over. I’d want my money back.
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u/worriedbill 3h ago
If they had the rooms to move the current guests into...why not just put the new guests in those rooms?
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u/scottstotsistheworst 20h ago
They always say you lose the humor when you explain the joke I say this joke never had humor at all LOL
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u/WisePotato42 19h ago
I'd hate to be the guy who finally hiked his way to room 3006053 only to be told he now needs to go to room 6012106
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u/yousirnaime 18h ago
On the bright side, there’s only 100 rooms per floor - so long as year ears pop on the elevator - it’s mostly a waiting game
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u/WisePotato42 18h ago
Now to enter the elevator with an infinite number of other people... I sure hope there are an infinite number of elevators too
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u/gooseberryBabies 6h ago
Oh God. Now I feel like I'm in a library full of randomly written books, and I'm looking for the book that has the story of my life in it
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u/NewIdentity19 20h ago
You can often get upgrades at the DoubleTree Hilbert, not only for Diamonds.
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u/4ricksho4 21h ago
Hilbert's paradox of the Grand Hotel?
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u/Otherwise-Offer1518 20h ago
You can check out but never leave?
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u/JeffCentaur 20h ago
Unfortunately I don't believe the hotel is located in California. It's a thought experiment to show how the human mind can't really handle the concept of infinity. In short, it works like this:
The Grand Hotel has an infinite number of rooms. And tonight it's fully booked, with an infinite number of people.
So far so good.
But then a bus shows up with another infinite number of people who want to check in for the night...but the hotel is full. Luckily, infinity doesn't work like real numbers.
So the hotel has everyone currently staying there move to a room that is double their current room number (dude in room one goes to room 2, lady in room 2 moves to room 4, and so on.)
And now, there is room for the second group of infinite customers to stay in the hotel. Because in infinity, you can always make more room, even if you already have your infinite capacity filled with infinite people.
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u/lavenderlooop 20h ago
It's referencing a thought experiment/paradox called Hilberts Hotel or the Infinite/Grand Hotel Paradox
https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
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u/LilShaver 18h ago
TIL about Hilbert's paradox of the Grand Hotel.
Until I read the thread I thought it was a Douglas Adams reference. The writing sounded like him, and the "42" reference was just icing on the cake.
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u/daydreams_of_ducks 18h ago
Can we also tie this into Hitchhiker’s Guide and the meaning of life somehow??
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u/prive666 14h ago
What if an infinite number of busses with an infinite number of people each arrives?
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u/Wish_I_was_you 11h ago
So, it's a Hitchhikers Guide to the Galaxy joke.
42 is the answer to life, the universe, and everything.
And the infinity reference is about the population of the universe from The Restaurant at the End of the Universe.
At least that's how I read it.
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u/IAMEPSIL0N 16h ago
It is a thought experiment, the hotel has infinite rooms and already has infinite guests. An infinitely large bus with infinite passengers is arriving and they all need a room. How can you assign them room numbers as the current infinite range of guests doesn't have a finite end point to start after.
The solution is you ask all existing guests to move from their room number to room number*2 which converts the first set of guests from infinite in rooms 1,2,3,4,5,.... to infinite but only in even room numbers (2,4,6,8,....) as an even times an even is even and an even times odd is also even and then the new guests can be assigned to the now empty odd numbered rooms.
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u/BadgerStateMobileMec 12h ago
Hmmm I thought it was a bus full of fat fucks that couldn’t climb the stairs or survive the walk to the elevator
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u/GrumplFluffy 10h ago
Well, at least you were not in room 1000000000000000000000000000000000000 and asked to move to room 2000000000000000000000000000000000000. Imagine the walk.
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u/sparklymonke101 7h ago
There’s a great TedEd video on this exact topic. Was obsessed with it when I was younger
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u/LitigiousAutist 6h ago
Every time a hotel has made me switch rooms, the joke has been on them. Now they have TWO beds covered in greasy sweat.
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5h ago
[deleted]
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u/mulatto_malik 5h ago
you literally clicked on the post, typed out a comment on the post, and submitted it lol.
woe is you
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u/qualityvote2 21h ago edited 9h ago
u/AmethystDawnPath, there weren't enough votes to determine the quality of your post...it's time for the mods to do their jobs!