Continuity -vs- Discreteness
in [Physics]
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From: Huang on 4 Jan 2010 23:04 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 ? 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.
From: Han de Bruijn on 5 Jan 2010 05:30 On 5 jan, 05:04, 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 ? 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. Continuous and discrete are two ways of looking at the same thing: http://hdebruijn.soo.dto.tudelft.nl/QED/index.htm#ft http://hdebruijn.soo.dto.tudelft.nl/jaar2004/IHXTAK.pdf Han de Bruijn
From: Uncle Al on 5 Jan 2010 19:40 Huang wrote: > > Calculus was extremely successful in modelling natural phenomena. When did it stop being successful? London bridges falling down... > Cellular automata has also been extremely successful in modelling many > of the exact same phenomena. Reference even one instance wherein this is true. > 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. > 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 -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz4.htm
From: Androcles on 5 Jan 2010 23:22 "Uncle Al" <UncleAl0(a)hate.spam.net> wrote in message news:4B43DC04.D0125852(a)hate.spam.net... > idiot Mission accomplished. Bigot.
From: zzbunker on 5 Jan 2010 23:56
On Jan 4, 11:04 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 ? 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. Well, you can, but the problem is that all of the science has already been built around continous brick walls. So the uneducable people still mostly work on Digital Books, Atomic Clock Wristwatches, Light Sticks, and Desktop Publishing, rather than sampling rate problems for the uneducable. And work on Holographic Computing, Laser Disk Libraries, Flat Screen Software Debuggers, XML, USB, HDTV, Home Broadband, External Emulators, Multiplexed Fiber Optics i/o, PGP, and Post Wax Printing Devices, rather than Code Porting for the Fortranners. And work on Self-Replicating Machines and Post 1950 Satellites, rather than tax funds for the AIers. |