Continuity -vs- Discreteness
in [Physics]
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From: Huang on 6 Jan 2010 01:15 On Jan 5, 6:40 pm, Uncle Al <Uncle...(a)hate.spam.net> wrote: > Huang wrote: > > > Calculus was extremely successful in modelling natural phenomena. > > When did it stop being successful? London bridges falling down... Who designed the Tacoma narrows bridge ? Sure was'nt Newton. That thing oscillated worse than your zipper. > > Cellular automata has also been extremely successful in modelling many > > of the exact same phenomena. > > Reference even one instance wherein this is true. Wolfram. A New Kind of Science. > > Suppose for a moment that any natural phenomena can be modelled with > > equal accuracy using either Calculus or Cellular Automata. Can we say > > that discrete and continuous methods are then equivalent ? > > Calculus is discretized. Look for the little "dx" on each box. And the limit is ......discrete ? > > If > > different models produce the same numeric results and both models > > accomplish the same thing, then we should be able to say that it is > > indeterminate whether the natural world is best modelled using one or > > the other. > > > We might even be able to say that the discrete universe is equivalent > > to the continuous universe in the same sense that relative motions are > > equivalent. > > idiot Of course I am. So what. At least I have a tool that works. You have a unified universe and a broken tool to understand it, and supposedly I'm the idiot. ROFLMAO.
From: nuny on 6 Jan 2010 02:21 On Jan 4, 8:04 pm, Huang <huangxienc...(a)yahoo.com> wrote: > Calculus was extremely successful in modelling natural phenomena. > > Cellular automata has also been extremely successful in modelling many > of the exact same phenomena. > > Suppose for a moment that any natural phenomena can be modelled with > equal accuracy using either Calculus or Cellular Automata. Can we say > that discrete and continuous methods are then equivalent ? In what sense are cellular automata continuous? Mark L. Fergerson
From: FredJeffries on 6 Jan 2010 12:25 On Jan 4, 8:04 pm, Huang <huangxienc...(a)yahoo.com> wrote: > > We might even be able to say that the discrete universe is equivalent > to the continuous universe in the same sense that relative motions are > equivalent. http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/
From: Huang on 6 Jan 2010 21:58 On Jan 6, 1:21 am, "n...(a)bid.nes" <alien8...(a)gmail.com> wrote: > On Jan 4, 8:04 pm, Huang <huangxienc...(a)yahoo.com> wrote: > > > Calculus was extremely successful in modelling natural phenomena. > > > Cellular automata has also been extremely successful in modelling many > > of the exact same phenomena. > > > Suppose for a moment that any natural phenomena can be modelled with > > equal accuracy using either Calculus or Cellular Automata. Can we say > > that discrete and continuous methods are then equivalent ? > > In what sense are cellular automata continuous? > > Mark L. Fergerson CA is discrete. Calculus is based on continuity. What I am saying is that if you can model some "natural event A" using calculus, and you can also model the same "natural event A" using cellular automata, and suppose that both models return the same exact results to an arbitrary accuracy THEN you cannot presume that "natural event A" is continuous or discrete, it is indeterminate whether it is one or the other. They are equivalent in the same sense that relative velocities are equivalent under GR. You wont find anyone applying equivalence like that in orthodox mathematics, but it is perfectly reasonable for a physicist to do so. In fact, if more work were done in this area I "think" that it may be mathematically proveable that such an equivalence might be demonstrable for any physical model. If Einstein, Newton and Wolfram could have a baby together.......that is what the child would say.
From: Huang on 6 Jan 2010 22:16
On Jan 6, 11:25 am, FredJeffries <fredjeffr...(a)gmail.com> wrote: > On Jan 4, 8:04 pm, Huang <huangxienc...(a)yahoo.com> wrote: > > > > > We might even be able to say that the discrete universe is equivalent > > to the continuous universe in the same sense that relative motions are > > equivalent. > > http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-... I believe that many of the results of calculus can be replicated using discrete methods. In fact, I suspect that they all can. Lets suppose you could construct two bodies of formal mathematical models. Calculus on the one hand, and a whole collection of discrete models on the other hand which model the exact same things. Suppose for a moment that these two bodies of knowledge are at our disposal. We might like to show that there are some broad relationships between these two collections of things. To my knowledge....this has not been done. I dont think that it has even been explored to any great extent, if at all. So what the hell are you people waiting for ? Lazy sods ? I explain all of these insights and you just sit on your fat asses ? Must I do everything myself ? |