Subject: Re: Crucial Role for Lorenz Attractor in Pulsors
Date: Tue, 12 May 1998 20:15:08 -0500
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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
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