Thought Experiment: The Infinite Hilbert's Hotel
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- เผยแพร่เมื่อ 21 พ.ย. 2022
- 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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Oooh. I love this thought experiment. I struggled to visualize the difference between countable and uncountable infinity until this.
Would there be an infinite number of bran muffins in the continental breakfast?
"Only two things are infinite the universe and human stupidity and I'm not so sure about the first" -Albert Einstein
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
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.
Assuming everyone can pay the full rate for the room, right? How many would like a roommate?
The infinite room hotel will always be short one room for an infinite amount of guests who need rooms
Wrong. There should be one available. Maybe this problem is a play on the meaning of infinite. Regardless it is infuriating for some reason.
but there are infinite rooms so they’re fine
The rooms in the hotel are infinitely countable because for every one who needs a room a room will be provided but only until an infinite number of guests need rooms where the number of guests is uncountable
@@rascallyrabbit717Exactly! Here’s an example. Every robot hotel ever breaks down. There are an infinite number of robot hotels (meaning an infinite number of fires 😖). Each of the hotels has 1 room that is infinitely big fitting an infinite number of guests. However, the robots have to move to the Hilbert Hotel now. Let’s say each robot is named a string of 0s and 1s, but not just any string of 0s and 1s, an infinite string of 0s and 1s. 01110 etc goes in to arrange the rooms, but they can’t all fit. The next comment will show why
So 01110 tried to arrange the rooms. Here’s why they can’t all fit. If you write all the names of all the robots, you’ll have every single possible infinite string of 0s and 1s, right? Wrong. Here’s a list: 01110, 01010, 00000, 11111, 01001. Now, take the character in correspondence to the name’s position and flip it. What do you get? 10100. Continuing on forever, you will have a new name that is different from every other one by at least one character: The one you flipped. And voila. Hilbert’s Hotel has no vacancy. The number of rooms in Hilbert’s Hotel is infinite, sure, but it’s countably infinite. The number of robots is un-countably infinite. People like to think infinity is the end of the number line. Personally, I prefer to think that infinity IS the number line.
Isn't what the hotel manager does when he moves every guest to the room that is twice their room number, changing the cardinality?
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.
wascally wabbit. w(r)ong
This comment bent my lobes infinitely more than the conundrum posited in the video.
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.
They move instantaneously
I stayed here once. Worst. Service. Ever.
Well I'm confused and not surprised by that.
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
Definitely puzzling.
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.
Very true
Math isn’t your strong suit, is it?
'If there are an infinite number of rooms you could never possibly run out because they are infinite'
By that logic the function f(n) = n doesn't exist because there are infinitely many natural numbers which you can't 'run out of'.
'If you ever run out of rooms they are no longer infinite'
Why?
@@thetaomegatheta Because they're infinite.
@@djmoulton1558 And? There are also infinitely many guests.
How does it follow from there being infinitely many rooms that they can't be filled?
I am one of the many who don't understand calculus
To understand 'infinity' one must also ask and honestly answer: 'What exactly is time'?
FOR ME:
'Space' is energy itself. Wherever space is, energy is. Wherever energy is, space is. They are one and the same thing. And for me, the 'gem' photon is the energy unit of this universe that makes up everything in existence in this universe. 'Space' is most probably energy itself in the form of gravitational fields, electrical fields and magnetic fields, varying possibly only in energy modality, energy density and energy frequency.
'Time' is the flow of energy.
'Time' (flow of energy) cannot exist unless 'space' (energy itself) exists. And 'space' (energy itself) that does not flow (no flow of time / energy) is basically useless. An entity cannot even think a thought without a flow of energy. If all the energy in the universe stopped flowing, wouldn't we say that 'time stood still'? Time itself would still exist, it would just not be flowing, (basically 'time' stopped).
But then also, how space and time are linked in what is called 'space time', (energy and it's flow).
* And everything in existence currently appears to be eternally existent energy interacting with itself. There is truly only 1 single 'eternal day', the day of eternally existent ever flowing energy.
So, 'infinity' would be ever flowing energy with no end.
Oh, and no beginning either. Of which consider also this copy and paste from my files:
SPACE IS FINITE AND TIME IS INFINITE:
('Space' being energy itself, 'Time' being the flow of energy):
Consider the following, utilizing modern science and logic and reason:
a. Modern science claims that energy cannot be created nor destroyed, it's one of the foundations of physics. Hence, energy is either truly a finite amount and eternally existent, or modern science is wrong.
First Law Of Thermodynamics: "Energy can neither be created nor destroyed."
b. An 'absolute somethingness' cannot come from 'absolute nothingness', 'absolute nothingness' just being a concept from a conscious entity in 'absolute somethingness'. Hence, an 'absolute somethingness' truly eternally existed throughout all of eternity past, exists today, and will most probably exist throughout all of future eternity. That eternally existent 'absolute somethingness' most probably being energy itself.
c. The universe ALWAYS existed in some form, NEVER had a beginning, will most probably ALWAYS exist in some form, and possibly NEVER have an end. Alpha and Omega, beginning and end, have been replaced by actual reality. No Creator needed.
* Some people for some reason (social conditioning/brainwashing/wishful thinking) believe in future eternity without end but do not accept eternity past with no beginning.
d. And for me, 'space' is energy itself. Wherever space is, energy is. Wherever energy is, space is. They are one and the same thing. 'Space' is most probably gravitational energy fields, electrical energy fields and magnetic energy fields, varying possibly only in energy modality, energy density and energy frequency. 'Time' is the flow of energy. Hence 'spacetime' being 'energy and it's flow'. 'Spacetime' had no beginning and will possibly have no end.
* There is really only 1 single truly eternal day that had no beginning and will never ever end. The 'day' of truly eternally existent ever flowing energy.
Time is a human invention to mark the passage of time. Time in physics is using that idea to describe something that doesn’t physically exist.
@@bngr_bngr Well then, 'speed' must not actually exist nor even the 'speed of light' must not actually exist except for as concepts alone. Consider this copy and paste from my files:
And for those who claim 'space' and 'time' do not actually exist except for as concepts, then:
Consider the 'speed of light':
a. 'Speed' is distance divided by time.
b. 'Distance' is two points in space with space between those two points.
c. If 'space' and/or 'time' did not exist in actual existent reality, except for as concepts, then 'speed' could not exist in actual existent reality, except for as a concept.
d. If 'speed' exists in actual existent reality, then 'space' and 'time' both have to have some sort of actual existent reality.
e. Likewise, 'light' which is currently considered as 'em' also has to have an actual existent reality, in addition to being a concept, for 'light' to exist in actual existent reality, in addition to being a concept.
f. So, if the 'speed of light' actually exists in existent reality, then 'space', 'time', 'speed' and 'light' ('em'), all also have to actually exist in existent reality, otherwise, the 'speed of light' could not actually exist in existent reality, other than just as a concept, (which would put a major kink in a lot of physics formulas).
Nice interesting
Mathematicians what do they know?
Know it, there is always one more room...
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.
There are two "dozens," "small dozens" and "large dozens." Nope, "dozen" is twelve, every time, and there simply cannot be more than one size of infinity.
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?
Another thought experiment: (and yet another copy and paste from my files):
Consider the following:
a. I am a human as defined by humans.
b. I am an energy based quarkelectronian as modern science claims that all matter is made up of quarks, electrons and interacting energy and I am made up of matter and interacting energy.
c. I am a being of 'light', 'if' my current theory of everything is correct whereby the 'gem' photon is the energy unit of this universe that makes up everything in this universe, including space, time and numbers. (Currently dependent upon the results of my gravity test).
d. "I" do not even actually exist but eternally existent space time exists as me, currently in the forms as above.
* I exist and yet "I" simultaneously do not exist, dependent upon perspective. But yet, do "I" not truly exist in absolute truth reality as only eternally existent space time exists as all things in absolute truth reality?
* "I" can mentally change between perspectives thereby experiencing existence from those various perspectives. "My" mind continues to expand, but is it truly 'my' mind that is expanding or is it eternally existent space time's mind that is expanding? In absolute truth reality, it would seem to be the later.
you raise some valid philosophical questions about the nature of self ("I") and freewill, the two being of course inextricable. But the part about three brains is pop-psychology, not "modern science." see esp. Richard C. Lewontin and Stephen Jay Gould
@@isaiah5217 Well, consider this comment from another TH-camr to me just today on a video concerning 'consciousness':
With human consciousness, according to Penrose, Microtubules in the prefrontal cortex undergo collective wave function collapse every 25msecs. He says this is possible because they are arranged in a way that can lead to supersymmetry (and in pyrimidal neurons of the limbic system). So imagine this, the microtubules have many funcitons, but in neurons it is basically the highway for neurotransmitters. So 40 times a second, the highway becomes "aware" of things like dopamine, oxytocin, serotonin, etc as they collectively pass by.
So roughly, there are 3 layers to the brain. The Cortex (executive function, newest evolutionarily), the limbic (emotional brain) and the autonomic (the automatic brain, oldest evolutionarily). Wave function collapse in the cortex or, the awareness of "feelings" in the cortex is far different from the awareness of feelings in the amygdala (the limbic system), probably based on the amount of power neurotransmitters have over the function of the neurons in their jurisdiciton. The cortex especially the ventromedial prefrontal cortex allows us subdue the emotional brain and think outside of our emotions. So the brain as a whole allows us to think from the inside of our emotions, interrogate them, determine if their approriate, pick from experiences on how to promote one emotion over the other, etc.
* While I and others talk about humans having 3 brains, sure, it's 3 parts of the same single brain, but is it truly? People that have NDE's, and part of their brain stops functioning, do other parts of their brain (or even earlier 'brains' via evolution) keep functioning and hence the individual has an NDE?
@@isaiah5217 See: th-cam.com/video/TfouEFuB-co/w-d-xo.html&lc=Ugwv4HDX0DT1FUQ8HRF4AaABAg.9ijWrcW4uqA9ikCd5SVTG5
think way too much daydream a future
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…
That cork screw sign is demonic