From: Robert L. Oldershaw on 30 Jun 2010 23:53 On Jun 30, 8:53 pm, Robert Higgins <robert_higgins...(a)hotmail.com> wrote: > Pity your understanding is poor, and the quality of > your ideas inferior. ----------------------------------------------- But if you steadfastly aviod my website, how would you know? 'When the next great awakening arrives in this world, you will know it by this sign, that all the dunces are in confederacy against it.' (apol. to R. Feynman and J. Swift) RLO www.amherst.edu/~rloldershaw
From: Robert L. Oldershaw on 30 Jun 2010 23:58 On Jun 30, 10:00 pm, Huang <huangxienc...(a)yahoo.com> wrote: > > Excuse me sir but I did not say that fractals have a lower bound. I > said that NATURE has a lower bound. And if you are making the claim > that the universe is a fractal then you might want to think about the > very bascic questions which naturally arise when one floats the > premise that the universe is a fractal. > > Aside from the mathematics involved, there are some straightforward > philosophical questions which are simple to state but difficult to > answer, and Im not hearing any answers (from you) to the issues I > raised. ------------------------------------------------------- Nature has no lower bound, nor any upper bound. Nature is an infinitely infinite discrete hierarchy of self-similar systems. Any respectable natural philosopher can see that. 'When the next great awakening arrives in this world, you will know it by this sign, that all the dunces are in confederacy against it.' (apol. to R. Feynman and J. Swift) RLO www.amherst.edu/~rloldershaw
From: Huang on 1 Jul 2010 00:18 On Jun 30, 10:58 pm, "Robert L. Oldershaw" <rlolders...(a)amherst.edu> wrote: > On Jun 30, 10:00 pm, Huang <huangxienc...(a)yahoo.com> wrote: > > > Excuse me sir but I did not say that fractals have a lower bound. I > > said that NATURE has a lower bound. And if you are making the claim > > that the universe is a fractal then you might want to think about the > > very bascic questions which naturally arise when one floats the > > premise that the universe is a fractal. > > > Aside from the mathematics involved, there are some straightforward > > philosophical questions which are simple to state but difficult to > > answer, and Im not hearing any answers (from you) to the issues I > > raised. > > ------------------------------------------------------- > > Nature has no lower bound, nor any upper bound. > > Nature is an infinitely infinite discrete hierarchy of self-similar > systems. > > Any respectable natural philosopher can see that. > > 'When the next great awakening arrives in this world, you will know it > by this sign, that all the dunces are in confederacy against > it.' (apol. to R. Feynman and J. Swift) > > RLOwww.amherst.edu/~rloldershaw Please think for a second about one other very "minor" issue which bears directly on your thesis. The issue of sensitive dependence on initial conditions. Please explain to me how on earth you can ever expect to sufficiently isolate _any_ experiement from minute perturbations which are caused by an observer, because it is proveable that mathematical models which exhibit chaos are inextricably linked to this notion. Because such perturbations caused by the mere presence of an observer or instrument may affect the sensitive dependence of initial conditions in a dynamical system, it does seem a bit hopeless to say that chaos occurs in nature even if you observed it, because there is no way to discern if you yourself might have caused it merely by being present to witness it. Such perturbations can be small, very small. You might even call them "minor", were it not for the fact that there is presently no engineerable answer. I'd love to see that instrumentation, and no I dont think that spooky distant action stuff will be any type of bailout for this either. Im not saying that you are wrong because I cannot prove one way or the other, but would you agree that ANY manifold whether abstract or tangible may be regarded trivially as a fractal at iteration n=1 ??
From: BURT on 1 Jul 2010 00:54 On Jun 30, 9:18 pm, Huang <huangxienc...(a)yahoo.com> wrote: > On Jun 30, 10:58 pm, "Robert L. Oldershaw" <rlolders...(a)amherst.edu> > wrote: > > > > > > > On Jun 30, 10:00 pm, Huang <huangxienc...(a)yahoo.com> wrote: > > > > Excuse me sir but I did not say that fractals have a lower bound. I > > > said that NATURE has a lower bound. And if you are making the claim > > > that the universe is a fractal then you might want to think about the > > > very bascic questions which naturally arise when one floats the > > > premise that the universe is a fractal. > > > > Aside from the mathematics involved, there are some straightforward > > > philosophical questions which are simple to state but difficult to > > > answer, and Im not hearing any answers (from you) to the issues I > > > raised. > > > ------------------------------------------------------- > > > Nature has no lower bound, nor any upper bound. > > > Nature is an infinitely infinite discrete hierarchy of self-similar > > systems. > > > Any respectable natural philosopher can see that. > > > 'When the next great awakening arrives in this world, you will know it > > by this sign, that all the dunces are in confederacy against > > it.' (apol. to R. Feynman and J. Swift) > > > RLOwww.amherst.edu/~rloldershaw > > Please think for a second about one other very "minor" issue which > bears directly on your thesis. The issue of sensitive dependence on > initial conditions. > > Please explain to me how on earth you can ever expect to sufficiently > isolate _any_ experiement from minute perturbations which are caused > by an observer, because it is proveable that mathematical models which > exhibit chaos are inextricably linked to this notion. > > Because such perturbations caused by the mere presence of an observer > or instrument may affect the sensitive dependence of initial > conditions in a dynamical system, it does seem a bit hopeless to say > that chaos occurs in nature even if you observed it, because there is > no way to discern if you yourself might have caused it merely by being > present to witness it. > > Such perturbations can be small, very small. You might even call them > "minor", were it not for the fact that there is presently no > engineerable answer. > > I'd love to see that instrumentation, and no I dont think that spooky > distant action stuff will be any type of bailout for this either. > > Im not saying that you are wrong because I cannot prove one way or the > other, but would you agree that ANY manifold whether abstract or > tangible may be regarded trivially as a fractal at iteration n=1 ??- Hide quoted text - > > - Show quoted text - If things always move forward in space the idea of time always going forward is a perfect match. Mitch Raemsch
From: Robert L. Oldershaw on 1 Jul 2010 12:28
On Jul 1, 12:18 am, Huang <huangxienc...(a)yahoo.com> wrote: ----------------------------------------- (1) I agree that any system in nature is a nonlinear dynamical system that can exhibit deterministic chaos and its sesnitive dependence on initial conditions, etc. This limits the prefection of our observations, especially as you go to ever-smaller Scales. Think quantum coherence/ decoherence, for example. Is this any reason to say we cannot observe/know anthing? Hardly! Atmospheric physics is a classic of NLDS. Much can be observed, studied, and understood. Complete predictability - forget it. Don't merely focus on what you cannot know. What you can know is more important. Also we can observe large-scale systems like stars and galaxies virtually without disturbing them. (2) Consider carefully: Nature is an infinite hierarchy. The infinite hierarchy is divided into discrete Scales. The Scales are completely equivalent except for discrete differences in mass, length, time scales. There is one unified physics for one unified cosmos. Forget your Platonic mathematics and look at nature. Observe a subatomic particle, observe a neutron star, observe a typical spiral galaxy. Then compare their size, mass and spin properties. Repeat for atoms and stars. Getting a picture yet? RLO www.amherst.edu/~rloldershaw |