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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".
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?
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?
Only if the world isn't granular at some scale.
Posted By: Andrew PalfreymanI feel strangely Bogarted
Posted By: loremanPosted 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.
Posted By: Andrew PalfreymanYou mean me personally?
Posted By: loremanIf you cannot be precise about the location of a particle, how can you be precise about the form of a wave?