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    (Original post by elsa_89)
    Whilst they are dumbed down they are still better than 99% of what is on television these days. I have not seen the fusion one; I can't seem to see many on iPlayer but I will try to find them or YouTube if you have any to recommend?

    I just watched the 'How long is a piece of string?' one; was rubbish.
    Here's Horizon: Can we Make a Star on Earth?

    I cant find a hd version, shame because the visuals are nice.
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    (Original post by tazarooni89)
    Also, the idea that "If the universe is truly infinite, then a planet which is an exact replica of yours must exist" is, I'm quite sure, utter rubbish. Sure, it's very likely to exist, but that doesn't mean it must exist.
    Nope, it stacks up, as far as Probability Theory goes... In infinitely many trials, anything that can happen, will happen.

    I don't believe the universe is infinite though.
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    (Original post by tazarooni89)
    Also, the idea that "If the universe is truly infinite, then a planet which is an exact replica of yours must exist" is, I'm quite sure, utter rubbish. Sure, it's very likely to exist, but that doesn't mean it must exist.
    If the universe is infinitely big than a 'repeat' planet definitely will exist, and there will be an infinite number of these planets.

    I didn't like this documentary that much though, the host was annoying. Never see any of the other horizon shows before, are they worth watching?

    Edit - Damnit, I was beaten to it!
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    (Original post by Unbounded)
    I thought the same.
    it would be a bit of a kick in the teeth for your unbounded username too..
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    (Original post by SA319)
    it would be a bit of a kick in the teeth for your unbounded username too..
    :mmm:
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    (Original post by v-zero)
    Nope, it stacks up, as far as Probability Theory goes... In infinitely many trials, anything that can happen, will happen.
    (Original post by The Magnificent KoloToure)
    If the universe is infinitely big than a 'repeat' planet definitely will exist, and there will be an infinite number of these planets.
    Think of it this way:
    I have an infinite x-axis/real line, and I define a function f(x) = 0 if x does not equal 1, and f(x) = 1 if x = 1.
    This infinitely long line represents the infinitely large universe, and the point (1,1) represents a planet. But this "planet" is unique, isn't it? x = 1 is a sole, point on an infinite line, with the unique property that f(x) = 1 here.

    Or think of it another way:
    I have an infinite set of real numbers. But the number 2 is unique in the sense that it is the only even prime number. If I count upwards from 2, I will ever find another even prime number, even if I am given an infinite number of attempts to try this out.
    Once again, the number 2 is a sole member of an infinitely large set with a unique property. It has no replica, no matter how far away you look.

    As we can see, an infinitely large set, or amount of space doesn't have to contain infinite amounts of everything. An infinite line of fruit could contain an infinite number of apples, but only one banana. Could the universe not be such that, even though it is infinitely large in terms of space, it contains only finitely many planets?
    If this scenario is so easy to conceive, an is certainly true in the above analogies - what makes it so "impossible"?

    Even if the universe is infinite, for this "replica planet" theory to be correct, we also have to assume that there are infinitely many planets, and that planets are scattered around randomly in the universe, rather than in some orderly manner (neither of which necessarily have to be the case).
    Even with the infinite monkey theorem, we make the assumption that the monkeys are typing randomly, rather than deliberately pressing the same letter each time, for example. And we also assume the monkeys never stop typing - i.e. they use the infinite amount of time they've been given. But in the case of the infinite universe, we have made no corresponding assumptions.

    What do you guys think?
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    (Original post by tazarooni89)
    Think of it this way:
    I have an infinite x-axis/real line, and I define a function f(x) = 0 if x does not equal 1, and f(x) = 1 if x = 1.
    This infinitely long line represents the infinitely large universe, and the point (1,1) represents a planet. But this "planet" is unique, isn't it? x = 1 is a sole, point on an infinite line, with the unique property that f(x) = 1 here.

    Or think of it another way:
    I have an infinite set of real numbers. But the number 2 is unique in the sense that it is the only even prime number. If I count upwards from 2, I will ever find another even prime number, even if I am given an infinite number of attempts to try this out.
    Once again, the number 2 is a sole member of an infinitely large set with a unique property. It has no replica, no matter how far away you look.

    As we can see, an infinitely large set, or amount of space doesn't have to contain infinite amounts of everything. An infinite line of fruit could contain an infinite number of apples, but only one banana. Could the universe not be such that, even though it is infinitely large in terms of space, it contains only finitely many planets?
    If this scenario is so easy to conceive, an is certainly true in the above analogies - what makes it so "impossible"?

    Even if the universe is infinite, for this "replica planet" theory to be correct, we also have to assume that there are infinitely many planets, and that planets are scattered around randomly in the universe, rather than in some orderly manner (neither of which necessarily have to be the case).
    Even with the infinite monkey theorem, we make the assumption that the monkeys are typing randomly, rather than deliberately pressing the same letter each time, for example. And we also assume the monkeys never stop typing - i.e. they use the infinite amount of time they've been given. But in the case of the infinite universe, we have made no corresponding assumptions.

    What do you guys think?
    Your logic here is flawed. Everything we see is an arrangement of particles, these particles are not unique, they are such that all particles of that type are identical. In an infinite universe it is certain that any possible arrangement of partciles must appear infinitely many times, given that the particles themselves are infinitely many.

    In other words, you make this sound like a deterministic problem, when it is in fact a probabilistic problem.
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    (Original post by v-zero)
    Your logic here is flawed. Everything we see is an arrangement of particles, these particles are not unique, they are such that all particles of that type are identical. In an infinite universe it is certain that any possible arrangement of partciles must appear infinitely many times, given that the particles themselves are infinite.
    But how do we know that there are infinitely many of these particles?
    How do we know that they are scattered around randomly, rather than in an orderly manner?

    Another analogy:
    the number 1/6, also written as 0.16666... is infinitely long in its decimal form. But we can be certain that the digit "1" appears only once.
    The reason for this is that the infinitely many digits are arranged according to a pattern, rather than randomly.

    My point is that in order for this replica planet theory to be true, we have to make two further assumptions
    1] There are infinitely many planets
    2] They are not arranged according to a certain pattern.
    Only when we make these two assumptions does the theory hold true. We cannot simply base the entire theory on the assumption that the universe is infinite.


    In other words, you make this sound like a deterministic problem, when it is in fact a probabilistic problem.
    But it can ony be a probabilistic problem if we assume that planets are randomly distributed.

    If I have a pack of cards, probability theory tells us I have a 1/2 chance of picking a red card. Fair enough, but it relies on the assumption that I don't search the pack and deliberately pick a black card. It assumes that I choose my card randomly (which I don't necessarily have to do).
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    (Original post by tazarooni89)
    But how do we know that there are infinitely many of these particles?
    How do we know that they are scattered around randomly, rather than in an orderly manner?

    Another analogy:
    the number 1/6, also written as 0.16666... is infinitely long in its decimal form. But we can be certain that the digit "1" appears only once.
    The reason for this is that the infinitely many digits are arranged according to a pattern, rather than randomly.

    My point is that in order for this replica planet theory to be true, we have to make two further assumptions
    1] There are infinitely many planets
    2] They are not arranged according to a certain pattern.
    Only when we make these two assumptions does the theory hold true. We cannot simply base the entire theory on the assumption that the universe is infinite.
    We only need there to be infinitely many particles, after that it is just a question of probabilities. Quantum Mechanics takes care of that, and makes sure that particles don't get all orderly.
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    (Original post by v-zero)
    We only need there to be infinitely many particles
    Ok, so we're agreeing on one thing: It is not enough for the universe to be infinite in spatial size (since we also need an infinite number of particles).

    The thing in bold is the point I was originally making.

    after that it is just a question of probabilities. Quantum Mechanics takes care of that, and makes sure that particles don't get all orderly.
    Quantum Mechanics takes care of it, how, exactly?
    Quantum Theory does introduce elements of randomness into the positions and momenta of certain particles, but how can it guarantee completely random distribution of them?
    (And further, how do we know that Quantum Theory is accurate anyway?)
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    (Original post by tazarooni89)
    Ok, so we're agreeing on one thing: It is not enough for the universe to be infinite in spatial size (since we also need an infinite number of particles).

    The thing in bold is the point I was originally making.



    Quantum Mechanics takes care of it, how, exactly?
    Quantum Theory does introduce elements of randomness into the positions and momenta of certain particles, but how can it guarantee completely random distribution of them?
    (And further, how do we know that Quantum Theory is accurate anyway?)
    It is enough, since there is no such thing as empty space. Sorry.

    Quantum Theory implies that sub-atomic particles cannot be described as being in one place at a time, but will rather fulfill a probability distribution of where they're most likely to turn up - until somebody goes an observes them of course, but then they're interfering and it's no longer valid to say anything much about them...

    Of course we cannot say how accurate Quantum Theory is, but we can say it's the best we've got in that area, and makes brilliant predictions fitting with empirical data.
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    (Original post by DeanK22)
    He was Russian and it was completely ridiculous. I literally cannot believe someone would be prepared to pubicly announce they think there is a largest natural number - it is just literally absurd to do mathematics working on that assumption*.

    I can only imagine he was doing it for a laugh but it wasn't very funny.

    * I imagine you can do OK for a while but you certainly wouldn't be able to do "proper" analysis for instance and you would ofcourse either have to come up with a new system of numbers entirely or just do away with ZFC and miss out on things [like uncountability of the reals to name something glaringly obvious].
    Let x = ...9999.0
    Now, what happens if you add 1 to it?

    I think this is what he was talking about.
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    (Original post by v-zero)
    It is enough, since there is no such thing as empty space. Sorry.
    What do you mean, "no such thing as empty space"? What is in between the electrons in an atom?
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    (Original post by tazarooni89)
    What do you mean, "no such thing as empty space"? What is in between the electrons in an atom?
    Particles popping in and out of existence... http://en.wikipedia.org/wiki/Zero-point_energy
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    (Original post by v-zero)
    Particles popping in and out of existence... http://en.wikipedia.org/wiki/Zero-point_energy
    So what happens when a particle pops out of existence? What does it leave behind?

    (As a side note - I don't really see what the wikipedia article you've linked me to has got to do with what you're telling me )
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    (Original post by tazarooni89)
    So what happens when a particle pops out of existence? What does it leave behind?

    (As a side note - I don't really see what the wikipedia article you've linked me to has got to do with what you're telling me )
    Another particle immediately takes its place. In any case, all of the spacial vaccuum is teeming with these particles, and hence infinite space must imply infinite particles.

    Maybe this page helps more: http://en.wikipedia.org/wiki/Zero-point_field

    The two things are quie equivalent, ZPE is just more interesting to me.
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    (Original post by Sk1lLz)
    Let x = ...9999.0
    Now, what happens if you add 1 to it?

    I think this is what he was talking about.
    I don't think it was.
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    (Original post by DeanK22)
    He was Russian and it was completely ridiculous. I literally cannot believe someone would be prepared to pubicly announce they think there is a largest natural number - it is just literally absurd to do mathematics working on that assumption*.

    I can only imagine he was doing it for a laugh but it wasn't very funny.

    * I imagine you can do OK for a while but you certainly wouldn't be able to do "proper" analysis for instance and you would ofcourse either have to come up with a new system of numbers entirely or just do away with ZFC and miss out on things [like uncountability of the reals to name something glaringly obvious].
    Measure theory commonly assumes an extended real line. The topology's a *****, however.
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    (Original post by DeanK22)
    He was Russian and it was completely ridiculous. I literally cannot believe someone would be prepared to pubicly announce they think there is a largest natural number - it is just literally absurd to do mathematics working on that assumption*.

    I can only imagine he was doing it for a laugh but it wasn't very funny.

    * I imagine you can do OK for a while but you certainly wouldn't be able to do "proper" analysis for instance and you would ofcourse either have to come up with a new system of numbers entirely or just do away with ZFC and miss out on things [like uncountability of the reals to name something glaringly obvious].
    :eek:
    typo of the century right there :p:
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    (Original post by v-zero)
    Your logic here is flawed. Everything we see is an arrangement of particles, these particles are not unique, they are such that all particles of that type are identical. In an infinite universe it is certain that any possible arrangement of partciles must appear infinitely many times, given that the particles themselves are infinitely many.

    In other words, you make this sound like a deterministic problem, when it is in fact a probabilistic problem.
    Do you listen to radio lab?

    I'm no physicist, but I'm basing what I said on a show they did on this very topic, hosted by a Maths and Science lecturer from Columbia.
 
 
 
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