Subject: Re: Crucial Role for Lorenz Attractor in Pulsors Date: Tue, 12 May 1998 20:15:08 -0500 From: vead@uconect.net To: vead@uconect.net this is the dejanews "emailable" version. ------------------------------------------------------------------------------ This message was forwarded to you from Deja News by vead@uconect.net. Deja News, the discussion network, offers free web-based access to more than 50,000 high-quality discussion forums. Come and visit us on the web at http://www.dejanews.com/=zzz_maf/ ------------------------------------------------------------------------------ (beginning of original message) Subject: Crucial Role for Lorenz Attractor in Pulsors From: Vead@q.continuum.net (D. Manchester) Date: 1996/02/26 Newsgroups: sci.fractals Hello, USENETgoers! A Pulsor-News Update (from some of my recent correspondence...me writing) - dave -=-=-=-=-=-=-=-=-=-=-=-=- February 24, 1996 Niantic, CT Hello, All. Here is an encouraging sign for the Pulsor Model's inclusion of nonlinear dynamics and quantum phase-space modeling techniques in a coherent structure. This is an abstract of a preprint, I believe, which I discovered surfing around the UK Universities pages... [ the brackets are mine ] - dcm -=-=-=-=-=-=-=-=-=-=-=-=- "On the shape and dimension of the Lorenz attractor Charles R. Doering(1) and J.D. Gibbon(2). (1) Center for Nonlinear Studies, Mail Stop B258, Los Alamos National Laboratory, NM 87545, USA. (2) Department of Mathematics, Imperial College, London SW7 2BZ, UK. Abstract. It is shown how [the global attractor of the Lorenz equations is contained in a volume bounded by a sphere, a cylinder, the volume between two parabolic sheets, an ellipsoid and a cone.][The first four are absorbing volumes while the interior of the cone is expelling.] By a numerical search over these volumes, it is found that the origin is the most unstable point on the atractor and that an upper bound for the attractor's Lyapunov dimenion is 2.401 when b=8/3, r=28 and sigma=10. " -=-=-=-=-=-=-=-=-=-=-=-=- (Somebody correct me if I am wrong, but...) to me, >"the global attractor of the Lorenz equations" appears to have a _crucial_ role in modeling the structure of the breaking initial symmetry. It is apparently (unless I read it wrong) an operant function that helps determine the precise structure of that Fractal break in symmettry. Hmmm. The Lorenz Attractor would be a good candidate for that error-correction on-MSG function we discussed earlier (see "Pulsor Boundary Regions" postings and contributions to thread on "Re: Does God Play Dice...?") > Further, "is contained in a volume bounded by a sphere, a cylinder, > the volume between two parabolic sheets, an ellipsoid and a cone." Sure sounds like the information circuit I've set forth in the Pulsor model to me. (but that could be just me. I have been known to participate in wishful thinking from time to time...: ) ) Something to think about, anyway... What do You think? Best Regards, dcm. : | (exerpt from cited posting follows...) ========================================================================= "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."- Amendment I to the Constitution of the United States. In God We Trust (C)1996 D.Manchester Vead@q.continuum.net ========================================================================== Excerpt: A pulsor is a stitch in time. Nature is a Cantor Dust of Strange regularity. Euler's identity is a recipe for the fractal folding of Space-Time. Plank's constant reveals an index of this fractal folding with respect to our expanding positively curved Universe, and the probability function describing the Lyapunov-Euler boundary region with our universe's negatively curved (tachyon) counterpart at the center of the pulsor. Leptons, Hadrons, and quarks exists only in the outmost region of a Pulsor, and we call them (leptons and hadrons) Tardyons. The Tachyon universe which is co-incident with our positively curved cosmos has a negative curvature. Our positively curved cosmos exists in the phase space of the outermost portion of a pulsor. The boundary region separating the two is a region of convergence and divergence (of rates of convergence-divergence) , of stretching and folding, of inflation and collapse. The Mandlebrot Set is the reflection of this in our positively curved world. It is the evidence of the fail-safe, informational integrity built into our number system as well as the pulsing cycle of discontinuity we see from our quantum experiments. The Mandlebrot Set is an example of GOD's phase-lock on Thermodynamics for our particular Universe through Plank's Constant. A digression: I used the word "co-incident" above. I do not think as it was used that it would be the same as quantum superposition (qs). It is my current (incomplete! :) ) understanding that qs occurs in the same phase space, and the outer part of a pulsor is a phase space with it's own peculiar rules...those of current QED/QCD, Special and General Relativity... wrt the rules of phase-space of negative curvature. (I mean, I don't _think_ I am talking about quantum superposition here, although that may apply). So "co-incident" as used here means an inter-leaving of phase-spaces of positive and negative curvature, with tardyons extending through the positive, and tachyons extending through ("instending through? ...extension/instension? ugh. that sounds horrible!) the negative. The pattern of that interleaving in Pulsor meta-phase-space is either the Mandlebrot Set, or deeply, directly related to it. Our particular universe in this picture is the one where Plank's constant is what we find it to be here, and it points to a probability function that is discontinuous at those points of the meta-phase-space at which the density of the bands of convergence/divergence between negative and positive curvature approaches infinity. It's like the Mandlebrot set: An infinitely thin line (boundary) separating two regions, one region "inside" i.e. convergent (or oscillating between determinate, sometimes stable values, our cosmos); and divergence, taking off to infinity at increasingly accellerating rates (moving outward from the "more convergent" bands/areas). If GOD used e**ipi+1=0, Euler's equation, in creating the Universe, (and he seems to have, since we can use it ties our math together, the same math we can use to describe nature), then it seems he must also have chosen Plank's Constant for this particular Here/Now. This thought has technological implications, and applications, and I am hereby reserving all rights to any inventions based on this, and all other ideas presented in this message. (a man's got to eat...dcm) To continue, From the Fractal FAQ: "Lyapunov exponents measure the _rate_of_ divergence_ (italics mine) of _nearby_ orbits." If We consider the Universe to be composed of Tardyons and Tachyons: (using plainer words) If We think of the world as two families of bits, one only moving slower than the speed of light, and one moving faster than the speed of light, then the family that moves slower is what scientists call "Tardyons". The ones that move faster than light, "Tachyons", are very subtly interweaved amongst their slower Tardyon brethren-bits. They play a never-ending, transfinite game of tag, yet never touch, passing mass and energy (content) through time and space (channel), over the fence of the Euler-Lyapunov imaginary, transcendental boundary condition in an eternal byplay of IMAGE and MESSAGE, event and image-of-event. This interwoven spindizzy is what the Pulsor model describes. " ...from "Boundary Regions in the Pulsor"...dcm (end of original message) ------------------------------------------------------------------------------ You can view the original message at http://www.dejanews.com/=zzz_maf/getdoc.xp?AN=141152978 or search http://www.dejanews.com/=zzz_maf/ for related messages. We hope to see you soon at Deja News, the discussion network.