Hotel Infinity paradox (your brain will hurt, promise)

[pantherx12]

Right. And the wiki mentions this

These cases demonstrate the 'paradox', by which we mean not that it is contradictory, but rather that a counter-intuitive result is provably true:

The only head fucky thing about this hotel is that the person even thought about it in the first instance.


I thought it's common knowledge that infinity functions in this way, a demonstration like this is pointless.


Is this not the kind of thing people had discussions/arguments about as children when people used to say things like " I double dare you times infinite" and some other kid says " infinity + 1"

Maybe before you go making assumptions you should read what I wrote. I said most, not all. Rooms take up space, I don't know how you think there can be an unoccupied room every time someone walks in. I don't know where you're getting this magically gets extra rooms from either, the rooms were already there.

Your shitting me right?

By it's very definition a place with infinite amount of rooms would take up an infinite amount of space.

The only way to achieve that would be with a hotel that expanded as necessary, it doesn't even need to be magical the infinite amount of people could be building the hotel as more people come in.

If an infinite amount of rooms were already pre-existing then the place would have to be magical in order to exist, I.E not actually taking up any space at all.

 

[Benetanegia]

I don't know how you think there can be an unoccupied room every time someone walks in. I don't know where you're getting this magically gets extra rooms from either, the rooms were already there.

Yes and no. That's the paradox of infinity itself.

Now regarding the OP:

The paradox of the hotel is silly. If there's any problem at all when the bus arrives, there's absolutely no way the infinite hotel would have been filled. So since the paradox establishes that the hotel is already filled with an infinte amount of people, we can safely assume that the infinte amount of people from the bus will get to their room in the exact same way the other amount of infinte people did before.

Of course another way to look at it is that the infinite hotel can never be full, because you can not fill infinite with any finite number, and that's what the paradox in the video is proposing.

This is where panther is 100% right.

 

[Damn_Smooth]

The only head fucky thing about this hotel is that the person even thought about it in the first instance.


I thought it's common knowledge that infinity functions in this way, a demonstration like this is pointless.


Is this not the kind of thing people had discussions/arguments about as children when people used to say things like " I double dare you times infinite" and some other kid says " infinity + 1"

Maybe I was just a weird kid, also went through the " am I real" sort of questions in my head very young too.




Your shitting me right?

By it's very definition a place with infinite amount of rooms would take up an infinite amount of space.

The only way to achieve that would be with a hotel that expanded as necessary, it doesn't even need to be magical the infinite amount of people could be building the hotel as more people come in.

So you're actually treating this as if it existed? I thought it was rather self explanatory that it could never actually exist and that it was just something to think about.

 

[pantherx12]

So you're actually treating this as if it existed? I thought it was rather self explanatory that it could never actually exist and that it was just something to think about.

The Universe = The Hotel.

Infinite amount of space =/= Infinite amount of rooms


Hell even humans are technically infinite ( until we all die out anyway)

Our numbers are ever increasing without limit ( if we expand to areas outside of this planet)


It seems you've not thought about infinity all to much*, where as I've wasted many a sleepless night already ha ha

Like I said, I spent my childhood going through this sort of thing : ]


* This is not designed to be an insult in anyway, infinity is a pretty pointless albeit very interesting subject.

People not wasting their time on it is probably a good thing.

 

[Damn_Smooth]

The Universe = The Hotel.

Infinite amount of space =/= Infinite amount of rooms


Hell even humans are technically infinite ( until we all die out anyway)

Our numbers are ever increasing without limit ( if we expand to areas outside of this planet)

I would die before I walked to the other end of the universe. I'm not even sure if a human could walk around the earth in a lifetime. Assuming that there was no water in the way.

Yes, you could spend forever thinking about infinity.

 

[Benetanegia]

I would die before I walked to the other end of the universe.

Unless you were travelling as close as posible to the speed of light. To be precise at v = c - 1/infinity.

 

[Damn_Smooth]

Unless you were travelling as close as posible to the speed of light. To be precise at v = c - 1/infinity.

Even at light speed. I have about 50-60 years left if I'm lucky. I wouldn't make it across the universe in that short of time.

 

[qubit]

What I don't understand is the concept of adding an infinite amount of people to an already infinite amount of people. It's like multiplying infinity by two, you get infinity regardless.

Yes you do, that's why it's weird. I've a slight headache...

 

[Drone]

To be nitpicky: Infinity is not a number.

Yes in maths infinity is a set. And one set can be wider than other. Actually maths doesn't have a single conception for infinity.

 

[pantherx12]

Unless you were travelling as close as posible to the speed of light. To be precise at v = c - 1/infinity.

He still wouldn't even get close though XD

From here the end of the observable universe is about 45 billion light-years away or something crazy.


And there's still more beyond that !

 

[Benetanegia]

Even at light speed. I have about 50-60 years left if I'm lucky. I wouldn't make it across the universe in that short of time.

Time dilation. Yes universe is (almost) infinite, so even at speed of light it would take you an (almost) infinite amount of time, based on any frame of reference other than yourself. For you it would only be 50 years, or only 1, who knows, depends on how close to c you could travel and how much your time was dilated.

 

[Damn_Smooth]

Time dilation. Yes universe is (almost) infinite, so even at speed of light it would take you an (almost) infinite amount of time, based on any frame of reference other than yourself. For you it would only be 50 years, or only 1, who knows, depends on how close to c you could travel and how much your time was dilated.

I'll let you know when I get there.

 

[Fourstaff]

Read up on Cantor's work on cardinal numbers.

 

[Drone]

From here the end of the observable universe is about 45 billion light-years away or something crazy.

It's 13.7 billion ly

 

[dorsetknob]

here is another headfu*K for ya

whats the square root of infinity

 

[pantherx12]

Time dilation. Yes universe is (almost) infinite, so even at speed of light it would take you an (almost) infinite amount of time, based on any frame of reference other than yourself. For you it would only be 50 years, or only 1, who knows, depends on how close to c you could travel and how much your time was dilated.

Isn't the general consensus that if a person were to travel at light speed their time would be experienced as per normal how ever an observer not travelling at light speed would be experiencing time 7* times faster than the person at light speed?


* May of got number wrong

I tell you what I really wish I didn't have difficulties with words, I'm not sure if what I wrote just then will make any sense to anyone else lol.

So to put it simply.

If I travelled at light speed for one year I'd of aged 1 year but all my friends back on earth would of aged 7 years.

 

[theJesus]

Everybody, all your answers are right here, in this guy's head:

 

[pantherx12]

It's 13.7 billion ly

Only because the light we get is ancient so it would seem closer where as it is actually around 45 billion light years away : ]

( since the universe is expanding)

http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN

 

[Benetanegia]

Isn't the general consensus that if a person were to travel at light speed their time would be experienced as per normal how ever an observer not travelling at light speed would be experiencing time 7* times faster than the person at light speed?


* May of got number wrong

I tell you what I really wish I didn't have difficulties with words, I'm not sure if what I wrote just then will make any sense to anyone else lol.

So to put it simply.

If I travelled at light speed for one year I'd of aged 1 year but all my friends back on earth would of aged 7 years.

No, time dilation approaches infinity as v gets close to c.

Where did you hear that anyway?

 

[W1zzard]

infinity is an abstract concept and does not exist in the physical universe, so linking infinity and physical things leads to paradoxes because the underlying assumption is wrong (that something physical an be infinite)

it doesn't stop you from doing math with it of course

 

[pantherx12]

No, time dilation approaches infinity as v gets close to c.

Where did you hear that anyway?

TBH man I'm not entirely certain, it was quite some time ago when I was still at school and expecting to get a career in the field of science.

Then I got kicked out of school


Since then a lot of stuff has kind of dissolved away in my mind, it's not that I'm no longer interested it's just a whole lot easier to study when amongst peers, and all to easy to procrastinate when your by yourself.


Sorry for off topic post But I felt a simple " I don't know" didn't really suffice because I thought I knew.


I think being up for 24 hours isn't helping me remember though so I'll sleep on it, perhaps ask my dad if he has ever heard of the same figures he might be able to point me in the right direction or tell me I'm thinking of something entirely different

 

[Drone]

Only because the light we get is ancient so it would seem closer where as it is actually around 45 billion light years away : ]

( since the universe is expanding)

http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN

Yes right. The 13.7 b ly is a static radius, beyond that it can get up to 47 billion light years and more. Due to accelerated expansion of space-time and the finiteness of speed of light what we see isn't actually the present events. That's why there are terms comoving distance and proper distance.

http://universe-review.ca/F02-cosmicbg.htm

In that article they say that radius of the universe is 10^28 cm, and that universe has 10^11 galaxies, 10^21 stars, 10^78 atoms, 10^88 photons.


p.s. Many scientists wonder why speed of light is 3e8 m/s and not infinity. If particle can have zero mass why it can't have infinite velocity. Or 3e8 is some kind of "infinity" for speed.

 

[Benetanegia]

p.s. Many scientists wonder why speed of light is 3e8 km/s and not infinity. If particle can have zero mass why it can't have infinite velocity. Or 3e8 is some kind of "infinity" for speed.

That's true for every universal constant I think.

Personally I've always considered that our universe is "moving" or "falling" along 1 or various temporal dimensions. Something like a 2 dimension plane falling flat in the 3rd dimension if you get what I mean.

So since "time" is accelerating at a very fast rate, nothing can reach infinite speed and instead can only travel at a set speed. Mathematically it's like an infinity minus infinity, or infinity divided by infinity situation.

EDIT: Another explanation. Our universe (the one that is apparent to us) is the n-th dimensional equivalent of an "sphere". Just like gravity is (almost) constant throughout the surface of Earth, speed of light is constant within the surface of our "spherical" universe.

What I mean when I say spherical universe is not literally a sphere, but that such as a sphere in a 3d cartesian coordinate system is defined as:

x^2+y^2+z^2= r^2, where r is the radius

for our universe it would be:

x1^2+x2^2+...+xn^2 = r^2, where n is the number of dimensions that the universe really has and r is a constant yet to be discovered.

Now to complicate things even more, I don't think the universe would be an sphere (remember what I really mean by sphere), but some kind of elipsoid. Same concept, various constants.

 

[Damn_Smooth]

TBH man I'm not entirely certain, it was quite some time ago when I was still at school and expecting to get a career in the field of science.

Then I got kicked out of school


Since then a lot of stuff has kind of dissolved away in my mind, it's not that I'm no longer interested it's just a whole lot easier to study when amongst peers, and all to easy to procrastinate when your by yourself.


Sorry for off topic post But I felt a simple " I don't know" didn't really suffice because I thought I knew.


I think being up for 24 hours isn't helping me remember though so I'll sleep on it, perhaps ask my dad if he has ever heard of the same figures he might be able to point me in the right direction or tell me I'm thinking of something entirely different

I think that you are talking about gravity's effect on time where people on earth age faster than people in space. I have heard that, but I am far from an expert on this shit.

 

[Drone]

So since "time" is accelerating at a very fast rate, nothing can reach infinite speed and instead can only travel at a set speed. Mathematically it's like an infinity minus infinity, or infinity divided by infinity situation.

Yes and it's strange because all we see isn't just changing in time but also in space. Like Sagan said if we had a magic camera that could take "immediate" shots (with infinite velocity) then we could see the real events (ears on photo would appear later than nose).

Even tho the "speed of gravity" seems to be infinite/immediate otherwise if gravity propogated with slower speed every galaxy would fall part.

http://metaresearch.org/cosmology/speed_of_gravity.asp

But some say it's just too fast (maybe x10^10 or more faster than speed of light) but finite. Go figure ...