Saturday, February 13, 2010

BBC Horizon: To Infinity and Beyond

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Aired February 10. 2010 on BBC Two
By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever. But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems.

Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last. And if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you. Older than time, bigger than the universe and stranger than fiction. This is the story of infinity."
(via Atheist Planet)


  1. <span>I don't see how there can be countably many configurations of something the size of the visible universe (or any other volume), that can be used to calculate the average distance to a perfect copy of that volume, unless particle positions and states are discrete. 
    Doesn't quantum theory pretty much blow that possibility out of the water? 
    Elementary particles don't fit in nice discrete areas of space that we can pinpoint and check to see if they are occupy or not (even in theory). So shouldn't the number of possible configurations of a volume itself be infinite, thereby making the average distance between identical volumes of space, infinite? 
    At times the narrator says even the impossible is possible given infinite space, but clearly only that which could theoretically come about in the time given is permitted. No? </span>
    <span>A monkey typing the complete works of Shakespear for example, implies a historic account that has to have taken place before it could feasibly happen. Before the first planets formed, this was impossible. Who knows what might be possible in a universe that is at least 20 billion years old?</span>

    <span>PS: I realize they assume for the sake of the argument that the typing monkey is doing so perfectly at random (that is, unbiased), even though in reality physiology and behaviour would rule out completely the chance of certain sequences ever being produced.

  2. regarding monkeys typing shakespear... if we count that apes evolved from monkeys and we evolved from apes and we still are sort on in monkey regeon of cousins we are sort of monkey that is human ape so monkey writing shakespear is already done :P

  3. I'm also rather skeptical about some of the statements they make.
    I'd say that infinite universe in terms of space and time does not necessarily contain an infinite amount of matter. Therefore even in an infinite (unbounded) universe there is NOT an infinite number of copies of ourselves (or of anything else) because there's not an infinite amount of matter to build those copies from.
    My impression is that throughout the program they explored the mathematical properties of infinity (very interesting indeed) but the thing I was missing in the documentary was a qualified, in-depth comment from cosmologists - how this possibly applies to the universe.

  4. Actually, I think one of the cosmological assumptions at this point is that we're not placed in any special part of the universe and therefore there would have to be matter beyond our visible horizon. The part that peeved me the most was the calculation were he raised 2 to the number of particles in the known universe. As if that accounted for all possible configurations.
    I too would have loved it if they delved more into the cosmological or "real" infinities. They didn't really cover what science had to say about whether space is positively curved (bounded) or not (infinite).

  5. Thanks for the comment.
    My reasoning was that the big bang produced only a finite amount of matter which is now in the process of expanding into infinity.
    Or do you think that without saying it explicitely they went beyond the one (local) big bang of ours and implied an infinite universe as a place where an infinite number of such big bangs occur on different places, infinitely distant from one another?
    Yet another question that came to my mind when watching the program was how the principle of uncertainty and the theory of chaos go together with it all.
    But I know next to nothing about these topics so I can't say anything more about it...

  6. <span>The Big Bang theory doesn't describe a, as you put it, "local" big bang of any sort, but a universal one. More over, you seem to think of the big bang as an explosion in space, from whence our matter exploded outward. Rather it is the expansion of space itself, with any (or no) point being the center of it. 
    Imagine a sheet of graph paper, that is infinite in the plane. Now imagine it enlarging. If you focus on any random point on the paper, it will appear as if the graph is expanding away from that point. But the same observation is true if you look at any other point on the paper. Kind of like a large-scale "zooming" effect. That's the kind of inflation they're talking about, and that's how the Big Bang is different from any ol' explosion.</span>

  7. Thanks for the nice explanation!
    I heard and read quite a lot about the expansion of space before, but now it seems I didn't have the correct mental image of it. Your zooming grid analogy finally cleared it up for me. Thanks :) .
    I think that with this concept in mind, the idea of an ever-expanding infinite universe containing an infinite amount of matter is well possible (unless of course there are other 'technical' reasons that might prevent it).

  8. actually what its saying is to repeat what he did exactly a second time, in a totally unrelated case....

    doesn't have to be shakespear, any large volume of speific text being receated in a totally and absolutely unrelated situation (even by language) would take an infinate amount of subjects in an infinate amound of time to succeed...

    which in my opinion would happen instantly(provided the time to type)...

  9. i really liked that imagery too :D

    but it doesn't help the qeustion, if at some point do these infinate planes(papers) collide?

    because of the implication that there is a specific distance to that other [identical?] plane, that makes me think that the plane may be expanding infinately but the space remains to be the containg space...

    or in other words two infinitys inside an infinity....
    -----------------------(i'm sorry about any spelling...always had a problem with it)

    Btw no ones asked whats infinity divided by zero?

  10. What other planes are you talking about? My example only involves a single plane with no implication of distance to anything else.

  11. <span>Here is how I see it.  This is a very simple way of looking at it...</span>
    <span>Imagine a motorway, which is infinite in length, with an infinite amount of lanes, there are infinite amounts of motorways stacked above and below each other.  </span>
    <span>Now imagine a Russian doll, each layer of the doll has a layer inside itself infinitely, as well as outside infinitely.  They are placed on the surface of the motorway side by side, in all directions infinitely.  </span>
    <span>The known universe we observe is one layer of one doll.  </span>
    <span>I think the question we need to ask is about whether a thing exists or does not exist.  As we know something does not exist from our perspective until we observe or learn about its existence.  Hence, it is likely that nearly everything that can exist, does not exist from our unique perspective.</span>
    <span>So if our unique perspective is 1, and there is an infinite universe then to exist is 1/infinity, so it should also comprehend that non existence is infinity -1/infinity = 1.  </span>
    <span>At least that how I would perceive it.</span>

  12. ok i was very tired when i typed that...

    just don't worry about it >_>