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Hotel Infinity paradox (your brain will hurt, promise)

Discussion in 'Science & Technology' started by qubit, Dec 20, 2011.

  1. pantherx12

    pantherx12 New Member

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    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"


    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.
     
    Last edited: Dec 20, 2011
  2. Benetanegia

    Benetanegia New Member

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    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.
     
  3. Damn_Smooth

    Damn_Smooth New Member

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    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.
     
  4. pantherx12

    pantherx12 New Member

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    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.
     
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  5. Damn_Smooth

    Damn_Smooth New Member

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    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. :laugh:
     
  6. Benetanegia

    Benetanegia New Member

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

    Damn_Smooth New Member

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    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.
     
  8. qubit

    qubit Overclocked quantum bit

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

    Drone

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    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.
     
  10. pantherx12

    pantherx12 New Member

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    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 !
     
  11. Benetanegia

    Benetanegia New Member

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    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.
     
  12. Damn_Smooth

    Damn_Smooth New Member

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    I'll let you know when I get there. :laugh:
     
  13. Fourstaff

    Fourstaff Moderator Staff Member

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    Read up on Cantor's work on cardinal numbers.
     
  14. Drone

    Drone

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    It's 13.7 billion ly
     
  15. dorsetknob

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    Dorset where else eh?
    here is another headfu*K for ya

    whats the square root of infinity
     
  16. pantherx12

    pantherx12 New Member

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    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.
     
  17. theJesus

    theJesus

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

    [​IMG]
     
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  18. pantherx12

    pantherx12 New Member

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  19. Benetanegia

    Benetanegia New Member

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

    Where did you hear that anyway?
     
  20. W1zzard

    W1zzard Administrator Staff Member

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    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
     
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  21. pantherx12

    pantherx12 New Member

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    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 :laugh:


    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 :laugh: 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 :p
     
  22. Drone

    Drone

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    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.
     
    Last edited: Dec 20, 2011
  23. Benetanegia

    Benetanegia New Member

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    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.
     
    Last edited: Dec 20, 2011
  24. Damn_Smooth

    Damn_Smooth New Member

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    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.
     
  25. Drone

    Drone

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    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 ...
     

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