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  1.  
    Posted By: Andrew PalfreymanYou need an infinite number of oscillators to do "everything". Because Fourier is right.
    Only if the world isn't granular at some scale. Real "things" don't involve infinite series or infinitesimals of any kind. Hence my reference to Zeno and that silly wabbit. Six or eight terms in a Fourier decomposition should be enough for anyone, especially after they have been exposed to hiphop "music".
  2.  
    Point taken. In which case, up to this agreed-upon resolution, my suggestion and yours are identical. Well, nearly. There are some details I noted.
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      CommentAuthoralsetalokin
    • CommentTimeJul 29th 2013 edited
     
    Which, by the way, brings up another interesting point. The calculus involves these imaginary infinitesimals and infinite series and other miracles of symbol manipulation, and we are successful in modeling the world with it. How come? Are the approximations of calculus simply of such high resolution that the granularity of the world is encountered before the richness of infinite series is exhausted?
  3.  
    Well, if you model "the world" as a DFT, then I think the highest frequency component required to stay honest enough will be around the Planck frequency.
  4.  
    Well sure. How many octaves above Middle C is that, again?
  5.  
    More than you can afford!!
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  7.  
    • CommentAuthorloreman
    • CommentTimeJul 29th 2013
     
    Posted By: alsetalokinWhich, by the way, brings up another interesting point. The calculus involves these imaginary infinitesimals and infinite series and other miracles of symbol manipulation, and we are successful in modeling the world with it. How come? Are the approximations of calculus simply of such high resolution that the granularity of the world is encountered before the richness of infinite series is exhausted?


    There's those fuzzy outlines again. In order for Zeno's arrow not to move, you have to be able to distinguish where it's not moving to.
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      CommentAuthorAngus
    • CommentTimeJul 29th 2013
     
    Posted By: alsetalokinWhich, by the way, brings up another interesting point. The calculus involves these imaginary infinitesimals and infinite series and other miracles of symbol manipulation, and we are successful in modeling the world with it. How come? Are the approximations of calculus simply of such high resolution that the granularity of the world is encountered before the richness of infinite series is exhausted?


    Whoops - I tripped on the assumptions you swept under the rug. How did you get to this point from

    Only if the world isn't granular at some scale.
  8.  
    I feel strangely Bogarted
  9.  
    Wait a minute... I have no idea, just yet, whether the world is granular or not. I'm just trying to explore the implications of either case, to see if we encounter any inconsistencies which would falsify one or the other position. Like the calculus of infinitesimals, if Heisenberg and QM predict either a strict chunky granularity at the Planck scale or an irresolvable fuzzyness at a certain limiting level of precision. The calculus would appear to be able to model turtles, all the way down, even if there is actually a smallest turtle, and that would be inconsistent with the view that math is discovered rather than invented, I think.
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      CommentAuthoralsetalokin
    • CommentTimeJul 30th 2013 edited
     
    Posted By: Andrew PalfreymanI feel strangely Bogarted

    That's because you take your tea in cups. Take it in bowls, instead, and you'll feel immediately.... different.

    http://www.youtube.com/watch?v=pSgGCOHuO1U
  10.  
    Posted By: loreman
    Posted By: alsetalokinWhich, by the way, brings up another interesting point. The calculus involves these imaginary infinitesimals and infinite series and other miracles of symbol manipulation, and we are successful in modeling the world with it. How come? Are the approximations of calculus simply of such high resolution that the granularity of the world is encountered before the richness of infinite series is exhausted?


    There's those fuzzy outlines again. In order for Zeno's arrow not to move, you have to be able to distinguish where it's not moving to.


    Would a dollar a year be an acceptable retainer? I may need an attorney some day, and I think you could argue a stone into sand.
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      CommentAuthorAngus
    • CommentTimeJul 30th 2013
     
    Nobody knows if space, time, or strawberry ice cream are ultimately granular. The uncertainty principle does NOT predict either granularity or fuzziness. It says that if you know one thing to a small degree of slack, there is another thing that you can only know to within a large degree of slack. You can adjust the slack on each as much as you like.

    With enough terms you can make a series arbitrarily close to an integral so the granularity issue is a red herring. There has been quite a debate over the appropriateness of differential and integral calculus and analytic functions to model the real world irrespective of granularity because many relationships are nonlinear.


    The dynamic effects of nonlinearities (i.e.chaos) is just as rich a field to argue over pointlessly as are the putative granularity of everything. Howcome nobody does?
  11.  
    tee hee
    https://www.youtube.com/watch?v=y1B12ecW3rU

    Fave version is George Melley's, which have on vinyl
    • CommentAuthorloreman
    • CommentTimeJul 30th 2013
     
    If you cannot be precise about the location of a particle, how can you be precise about the form of a wave?
  12.  
    You mean me personally?
    • CommentAuthorloreman
    • CommentTimeJul 30th 2013
     
    Posted By: Andrew PalfreymanYou mean me personally?


    It's hard to tell
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      CommentAuthorAngus
    • CommentTimeJul 30th 2013
     
    Posted By: loremanIf you cannot be precise about the location of a particle, how can you be precise about the form of a wave?


    You can't.