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    I can't see a thread about this.
    This documentary was on recently on BBC Two and I thought it was very good, even for layman that have have little interest in the subject.

    I liked the implication of a monkey writing Shakespeare . The German (I think) mathematician who absolutely rejects infinity was interesting too: you count to the largest number and return to zero. The little children in between are funny as always in their responses. And then Graham's number :eek:
    Check it out.

    http://bbc.co.uk/i/qszch/
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    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].
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    I liked it, what I seen of it.

    The whole concept of infinity... It's kind of splits into the domains of physics, mathematics and philosophy, does it not? I'm pretty sure it's a nightmare for the first category, too...

    I've never heard anyone pronounce googolplex before, though "Googolplex to the power of googolplex!"
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    (Original post by DeanK22)
    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 thought the same.
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    How weird and until now i was under the impression that to even reach the speed of light you need an infinite amount of energy not to mention all the other laws of physics as well based on infinite.
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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*.
    He said that if you assume there to be as such thing as the largest natural number, then you shouldn't have "all those paradoxes". What paradoxes was he referring to?
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    (Original post by ibysaiyan)
    How weird and until now i was under the impression that to even reach the speed of light you need an infinite amount of energy not to mention all the other laws of physics as well based on infinite.

    but once an object has mass, it cannot reach the speed of light.
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    (Original post by I4talent)
    He said that if you assume there to be as such thing as the largest natural number, then you shouldn't have "all those paradoxes". What paradoxes was he referring to?
    There are many. In the programme they gave the example of the even numbers having the same 'size' inifinty as all the counting numbers, despite only consisting of half of them. Similarly there are as many primes as natural numbers, despite primes occurring very sparsely.

    Edit: think i misunderstood what you asked... what did you ask? paradoxes if infinity doesn't exist?
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    (Original post by The-Wi$e-One)
    but once an object has mass, it cannot reach the speed of light.
    Dont photons have zero rest mass?
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    (Original post by silent ninja)
    There are many. In the programme they gave the example of the even numbers having the same 'size' inifinty as all the counting numbers, despite only consisting of half of them. Similarly there are as many primes as natural numbers, despite primes occurring very sparsely.
    That isn't a paradox. In a sense both are purely logical from basic definitions of counting i.e. bijection between sets. They do not lead to inconsistency.
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    (Original post by silent ninja)
    I can't see a thread about this.
    This documentary was on recently on BBC Two and I thought it was very good, even for layman that have have little interest in the subject.

    I liked the implication of a monkey writing Shakespeare . The German (I think) mathematician who absolutely rejects infinity was interesting too: you count to the largest number and return to zero. The little children in between are funny as always in their responses. And then Graham's number :eek:
    Check it out.

    http://bbc.co.uk/i/qszch/
    He blatently wrote a program in C to count to infinity, then it wrapped round after 4294967295 and he's therefore theorised that the universe must be a signed long int.
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    (Original post by ibysaiyan)
    Dont photons have zero rest mass?
    correct. but we cant make a space shuttle out of photons
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    (Original post by Mad Vlad)
    He blatently wrote a program in C to count to infinity, then it wrapped round after 4294967295 and he's therefore theorised that the universe must be a signed long int.
    very good vlad +ve repped.
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    (Original post by Simplicity)
    That isn't a paradox. In a sense both are purely logical from basic definitions of counting i.e. bijection between sets. They do not lead to inconsistency.
    That is a paradox, it's simply the maths that allows us to understand it.
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    (Original post by silent ninja)
    That is a paradox, it's simply the maths that allows us to understand it.
    A paradox would be say like the largest set, as then you can take the power set of it causing a contradiction. But, no what you mean is counter intuitive. The point is the maths that cantor has done is perfectly valid.

    Please, paradox is when something leads to a contradictions, not that its strange.
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    (Original post by The-Wi$e-One)
    very good vlad +ve repped.
    :awesome: Thanks!
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    (Original post by Simplicity)
    A paradox would be say like the largest set, as then you can take the power set of it causing a contradiction. But, no what you mean is counter intuitive. The point is the maths that cantor has done is perfectly valid.

    Please, paradox is when something leads to a contradictions, not that its strange.
    I think you miss the point. We're not talking about mathematical contradictions. I'm using the word paradox as it is used in everyday language, because that is how it is used in the programme: a situation or statement which seems impossible or is difficult to understand because it contains two opposite facts or characteristics

    Fact 1: list is half the length of the other
    Fact 2: they are the same size

    This is pedantic. Move on.
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    (Original post by silent ninja)
    I think you miss the point. We're not talking about mathematical contradictions. I'm using the word paradox as it is used in everyday language, because that is how it is used in the programme: a situation or statement which seems impossible or is difficult to understand because it contains two opposite facts or characteristics

    Fact 1: list is half the length of the other
    Fact 2: they are the same size

    This is pedantic. Move on.
    Hmm, okay. Yeah, I guess to the laymen it would seem strange.

    But, I reject Fact 1. But, that could be because I have spent a ton of hours thinking about it so lol even numbers to me are the same size as any countable infinite set.

    P.S. Sorry, but yeah fact 1 isn't true. I guess to a laymen it would seem that way, but lol bijections.
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    (Original post by Simplicity)
    Hmm, okay. Yeah, I guess to the laymen it would seem strange.

    But, I reject Fact 1. But, that could be because I have spent a ton of hours thinking about it so lol even numbers to me are the same size as any countable infinite set.

    P.S. Sorry, but yeah fact 1 isn't true. I guess to a laymen it would seem that way, but lol bijections.
    Yeah obviously it's not true because Fact 1 is not really a fact at all, but in non-mathematician speak it's a paradox.

    Going back to the programme, they could've distinguised a little more between the physics aspect and the maths. If you assume the universe is infinite (which is a massive assumption), then the monkey writing Shakespeare is inevitable. I dont know anything about Physics, but what was all that red-shift stuff we learned at school? Doesn't that show it's finite and expanding? Then there's the theory that space is curved. I dont buy the inflation theory they spoke about, sounds like nonsense, but reality is weirder than fiction so who knows!
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    I get the general impression that the physics videos on Horizon are edited to make them "sexy" while the maths ones are edited to portray a kind of mystery and insanity.

    Worst of all, the physics videos actually show some physics or try and explain something; I am not saying it is a lecture and sometimes the things are too advanced but at least every 10 minutes there is a short explanation of something that is put into laymen's terms. The only "explanation" on the video was Cameron explaining remarkably well why the two sets have the same cardanility and then when the interviewer asks the question "How?" the shot is over without explanation!
 
 
 
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