Thread: Infinite Supersets

  1. #1
    (?<!re)tired Mario F.'s Avatar
    Join Date
    May 2006
    Location
    Ireland
    Posts
    8,446

    Infinite Supersets

    Something has been nagging me about the Universe. Uh-oh!

    If a true random number generator could produce random numbers for an infinite amount of time, isn't it true that this RNG could produce an infinite list of numbers of the same value?

    Or to put it in more common terms; if on an infinite universe there must be an earth where a chimpanzee wrote Macbeth in flawless Esperanto by typing randomly on a keyboard, isn't it true that there will be an infinite number of earths where this happened?
    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

  2. #2
    Unregistered User Yarin's Avatar
    Join Date
    Jul 2007
    Posts
    2,158
    Quote Originally Posted by Mario F. View Post
    If a true random number generator could produce random numbers for an infinite amount of time, isn't it true that this RNG could produce an infinite list of numbers of the same value?
    "Probably" (read: Yes)


    Quote Originally Posted by Mario F. View Post
    Or to put it in more common terms; if on an infinite universe there must be an earth where a chimpanzee wrote Macbeth in flawless Esperanto by typing randomly on a keyboard, isn't it true that there will be an infinite number of earths where this happened?
    Yes, but only if you assume your hypothetical Multiverse allows it. It could just as well ignore repeats, creating only one universe for each unique number produced by the RNG.

  3. #3
    (?<!re)tired Mario F.'s Avatar
    Join Date
    May 2006
    Location
    Ireland
    Posts
    8,446
    Quote Originally Posted by Yarin View Post
    "Probably" (read: Yes)
    Nice what you did there, hehe. You should have left out the Yes.

    Quote Originally Posted by Yarin View Post
    Yes, but only if you assume your hypothetical Multiverse allows it. It could just as well ignore repeats, creating only one universe for each unique number produced by the RNG.
    Seems a little too arbitrary of a choice to me. But in any case, I'm not considering a multiverse. Just a single verse entity. So in our universe, if it was infinite, there would be an infinite number of earths that would have lucky chimps.

    But I want to go back to the RNG because it think it is easier to conceptualize and finally present the kicker that is what has been bothering me about set theory and that I cannot seem to find an explanation in text books...

    So, assuming an infinite RNG will eventually generate an infinite succession of the number 49, that RNG will not generate any other number from then on. However, that same RNG will also eventually generate an infinite succession of the number 2, and of the number 17, and... and infinite number of infinite successions.

    So how can the RNG be described in terms of a superset of all those infinities, if the first infinity will stop all others from ever happening? Or is it instead the case that infinite supersets can only be described in terms of the mathematical formal systems and cannot describe any physical system, like an RNG? And the kicker is, if the last question is positive, doesn't that mean that infinity is purely a mathematical concept and that it doesn't exist in our physical universe?
    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

  4. #4
    Unregistered User Yarin's Avatar
    Join Date
    Jul 2007
    Posts
    2,158
    I read your first post again and realized your RNG sequentially produces scalars. For some reason I assumed it could produce nested sequences. I blame George Cantor.

    Does your RNG produce rationals, reals, or a closed range of integers?

    Are we allowed to describe not just planets, but other RNGs with these numbers?
    Last edited by Yarin; 05-30-2016 at 10:31 PM.

  5. #5
    Lurking whiteflags's Avatar
    Join Date
    Apr 2006
    Location
    United States
    Posts
    9,616
    So how can the RNG be described in terms of a superset of all those infinities, if the first infinity will stop all others from ever happening?
    It's a paradox. If there can only be one RNG generating the same number over and over infinitely, then you can logically believe (instead of a stronger word like prove) that we know the RNG produces other sets part of the super set. I'm not really trained in maths, but this seems similar to the supertask: if you wanted to perform an infinite number of tasks in 10 minutes, spend the first 5 doing the first thing, then 2 1/2 minutes doing the next, and so on. It seems like the number of tasks, or the number of sets in a superset, is a countable infinity.

    Anyway, that's me babbling. I almost deleted it, but it could be important to keep in case I made a mistake somewhere.

    Or is it instead the case that infinite supersets can only be described in terms of the mathematical formal systems and cannot describe any physical system, like an RNG? And the kicker is, if the last question is positive, doesn't that mean that infinity is purely a mathematical concept and that it doesn't exist in our physical universe?
    It's not the first time math got something useful out of a paradox. To prove that there is an infinity in the universe, you would have to show me something, an ideal curve or ideal circle, for instance. I don't really count the universe as infinite. The observable universe is shrinking all the time. From a pragmatic point of view, the way we handle infinity in terms of limits, as well as being able to understand different kinds of infinity makes it true as long as we can use it, and I would extend this belief to infinite supersets.

    To put it another way - why does everything we know have to be real? I guess my answer is "no," because even thinking about it now, it still doesn't bother me. It is philosophically interesting, though.
    Last edited by whiteflags; 05-30-2016 at 10:49 PM.

  6. #6
    and the hat of copycat stevesmithx's Avatar
    Join Date
    Sep 2007
    Posts
    587
    Quote Originally Posted by Mario F. View Post
    Or to put it in more common terms; if on an infinite universe there must be an earth where a chimpanzee wrote Macbeth in flawless Esperanto by typing randomly on a keyboard, isn't it true that there will be an infinite number of earths where this happened?
    Theoretically yes, but thanks to universe's entropy and drake's equation, we are talking odds of finding a needle in all the known galaxies in the observable universe.
    Not everything that can be counted counts, and not everything that counts can be counted
    - Albert Einstein.


    No programming language is perfect. There is not even a single best language; there are only languages well suited or perhaps poorly suited for particular purposes.
    - Herbert Mayer

  7. #7
    Registered User
    Join Date
    Mar 2011
    Posts
    596
    The concept of a RNG producing an infinite sequence of numbers is interesting in itself.

    I wonder if there is any guarantee that such a RNG must eventually produce an infinite sequence of any definite type, eg, all 49's?

    It's true that for an infinite generation of numbers, there is an ever increasing probability that some finite length sequence might occur. But on the other hand, that probability decreases as the length increases.

    Perhaps the actual probability of an infinite sequence of definite type is the product of the infinitely small and the infinitely large.

    -

  8. #8
    (?<!re)tired Mario F.'s Avatar
    Join Date
    May 2006
    Location
    Ireland
    Posts
    8,446
    Quote Originally Posted by megafiddle View Post
    Perhaps the actual probability of an infinite sequence of definite type is the product of the infinitely small and the infinitely large.
    You got it! And I can't believe I didn't think of the obvious. Was so enthralled in trying to solve the paradox that I didn't question the mathematical mistake of my assumptions. Classical newb mistake.

    That's just it. In laymen terms there is simply an infinitely small probability of generating an infinite large sequence of the same numbers. And this itself an infinite superset. There is a likewise infinitely small probability of generating an infinite sequence of another number, or any number.

    My problem with the whole thing is that I could see the exception, but not the bug. I was reaching a conclusion that seemed to negate the possibility of an infinity in the physical world (assuming an infinite RNG is a possible construct). But this was going against some concepts of infinity in the universe that have already been described, such as Singularities, certain measurements in fluid mechanics, geometric points in a plane, etc. It was bothering me because I was moving towards Aristotles' negation of actual infinities and the constructivist mathematicians that couldn't understand Cantor. I'd hate to be associated with either.

    Whiteflags and stevesmithx posts were already hinting in the right direction. But was so embroidered in the concepts that I failed to realize I was doing a basic mistake. Thanks for that.
    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

  9. #9
    Registered User
    Join Date
    Mar 2011
    Posts
    596
    Glad it helped, but don't give me too much credit; I'm sure I don't know any more about this stuff than you do!

    -

Popular pages Recent additions subscribe to a feed

Similar Threads

  1. Why am I getting an infinite loop?
    By sameertelkar in forum C Programming
    Replies: 14
    Last Post: 01-01-2013, 01:26 PM
  2. Replies: 3
    Last Post: 10-14-2011, 11:33 PM
  3. Infinite Loop
    By ASCII in forum C Programming
    Replies: 10
    Last Post: 09-03-2011, 09:11 AM
  4. infinite loop
    By leahknowles in forum C Programming
    Replies: 2
    Last Post: 03-31-2011, 03:40 PM
  5. help with infinite loop please
    By officedog in forum C Programming
    Replies: 4
    Last Post: 11-05-2008, 02:42 PM

Tags for this Thread