Thought Experiment: The Infinite Hilbert's Hotel

At the Hilbert’s Hotel, there’s always room for one more. This though experiment demonstrates some of the strange properties of infinity.

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[missprizm]

Oooh. I love this thought experiment. I struggled to visualize the difference between countable and uncountable infinity until this.

[TerrySlaven-zdum]

Would there be an infinite number of bran muffins in the continental breakfast?

[beckyburtis]

"Only two things are infinite the universe and human stupidity and I'm not so sure about the first" -Albert Einstein

[xavierowino]

Something is missing from this whole hotel story. With infinite rooms which infinite guests can't want to take, the hotel owner must be f*g rich

[PDogB]

Assuming everyone can pay the full rate for the room, right? How many would like a roommate?

[kadenvanciel]

Little do they realize that there are three solutions to the infinite number of groups each of infinitely many people problem, and that a later problem can show that there are different types of infinity being greater than others as Georg Cantor speculated.

[JDKempton]

Well I'm confused and not surprised by that.

[djmoulton]

This is nonsense. If there are an infinite number of rooms you could never possibly run out because they are infinite. Even if you had an infinite number of guests you could never run out of rooms because they are also infinite. If you ever run out of rooms they are no longer infinite and you have failed your own problem's parameters.

[rascallyrabbit]

The infinite room hotel will always be short one room for an infinite amount of guests who need rooms

[anthonyd]

Wouldn't the infinity plus oneth guest have to walk an infinite distance to get to the infinity plus oneth room? I hope this guest has an infinite lifespan.

[mee]

Isn't what the hotel manager does when he moves every guest to the room that is twice their room number, changing the cardinality?

[midaztouch]

I stayed here once. Worst. Service. Ever.

[kodiakbear]

Hotel. Broca's area, or the Broca area is a region in the frontal lobe of the dominant hemisphere, usually the left, of the brain with functions linked to speech production. 2/8/2021 and I lived again. Broca's aphasia (non-fluent aphasia) Mike Caputo, Year 1 Stroke Recovery, Up Up Up - Aphasia with attitude, Broca's Aphasia, Right-side Weakness, Mark's 22 years-old Stroke: Broca's Aphasia.

[dannymac]

You can’t have an infinite number of anything. You can have infinitely many things, but not an infinite number of things. Wish those trying to explain infinity would keep this in mind. It’s *CRUCIAL* to truly understanding the very concept at the heart of the video.

Honestly, NOVA should take this video down until it can be edited, re-shot, etc…

[imdarrel]

Worst hotel to stay. Or, since there are an infinite amount of rooms, you put the new ones at the end where the person before would go. Makes no since to keep moving people down the line when the rooms are already there. It's infinity, the rooms are there regardless of how many people show up and who goes into them. Aint nothin but a tardis

[mascadadelpantion]

I am one of the many who don't understand calculus

[chaosordeal]

Assume we have two infinities and then we add one to one of them. That's dumb and that's all this "hotel paradox" is -- dumb. There is ONE size of infinity.

[charlesbrightman]

To understand 'infinity' one must also ask and honestly answer: 'What exactly is time'?

[charlesbrightman]

A TRUE THOUGHT EXPERIMENT: (copy and paste from my files):

Question: Where do thoughts actually come from?

For example: Modern science claims that we have billions of brain cells with trillions of brain cell connections. How exactly does the energy signal 'know' where and when to start, what path to take, and where and when to stop to form a single coherent thought?

An analogy I utilize is to spread a brain out like a map. Brain cells are represented by towns and cities, brain cell interconnections are represented by roads and highways, and the energy signal is represented by a vehicle traveling between one or more towns and/or cities. A coherent thought is a coherent trip.

How exactly does the vehicle 'know' where and when to start, what path to take, and where and when to stop to form a single coherent trip? A higher intelligence has to tell it those things. But, that is a coherent 'trip' (thought) in and of itself.

So, how exactly does our brain think a thought before it consciously thinks that thought? And if thoughts can be thought without consciously thinking thoughts, then what do we need to consciously think thoughts for? Just to consciously think thoughts that are already thought? What then of 'freewill' if we don't even consciously think our own thoughts?

And then to further that situation, modern science claims that many different energy signals are starting at various places in the brain, take various pathways, and stop at different places, just to form a single coherent thought. (With the analogy, many vehicles are starting at various places on the map, taking various routes, and stopping at various places, all together forming a single coherent 'trip'.) And somehow it's all coordinated and can happen very quickly and very often.

So, where do thoughts actually come from? Who and/or what is thinking the thoughts before I consciously think those thoughts? Do "I" even have freewill to even think these thoughts "I" am thinking about thoughts and type these thoughts to you here on this internet?

Modern science also claims we have at least 3 brains: The early or reptilian brain, the mid brain, and the later more developed brain. So, are early parts of the brain thinking thoughts before the later parts of the brain consciously think those thoughts? If reptiles can think thoughts, then couldn't the early part of our brain think thoughts, and somehow pass those thoughts on to later more developed parts of later brains? Is our 'inner self' really just our reptilian brain thinking the thoughts that we think we are thinking? Are we all just later more evolved reptiles? Who don't even consciously think our own thoughts?

If not, then how exactly does the brain think thoughts? Where exactly do thoughts originally come from so our brain can consciously think those thoughts?

So "I" am thinking about thoughts, if it is even "I" thinking the thoughts that "I" believe "I" am thinking about thoughts. Or so "I" currently think, here again, if it is even "I" doing the thinking. "My" thinking is imploding as "I" think about thoughts. But then again, is it even 'me' that is imploding? I will have to think about it some more. Poof, I'm gone.

Is just energy interacting with itself the lowest form of sub-consciousness? Is it even consciousness itself?

[accutronitisthend]

Know it, there is always one more room...