New Scientist fractal universe

[Roger Bagula]

--- In ***@yahoogroups.com
<mailto:science_math_hist%40yahoogroups.com>, "John de Rivaz" <***@...>
wrote:

Is the universe a fractal?

If that is indeed its shape, it could overturn everything we thought
we knew
about cosmology. New Scientist enters the fray

http://www.newscientist.com/contents/issue/2594.html
<http://www.newscientist.com/contents/issue/2594.html>
--
Sincerely, John de Rivaz: http://John.deRivaz.com
<http://John.deRivaz.com> for websites including
Cryonics Europe, Longevity Report, The Venturists, Porthtowan, Alec Harley
Reeves - inventor, Arthur Bowker - potter, de Rivaz genealogy, Nomad
.. and
more

--- End forwarded message ---
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[r***@amherst.edu]

Post by Roger Bagula
Is the universe a fractal?

The scientific evidence for a fractal Universe is overwhelming.
Physicists have largely hoped that fractals would quietly go away like
catastrophe theory, or be relegated to limited domains of science and
nature. The reason for this may be that fractals, chaos and dynamical
systems tend to be highly non-linear, multi-scaled, mathematically
complex and inherently resistant to exact solutions. Alas poor
physicists, so it would appear, is nature.

A new paradigm is on its way and not even the well-organized group of
arrogant and closed-minded "gatekeepers" has the power to stop its
progress. It is purely a matter of time.

Rob
www.amherst.edu/~rloldershaw

[Roger Bagula]

Post by r***@amherst.edu

Post by Roger Bagula
Is the universe a fractal?

A new paradigm is on its way and not even the well-organized group of
arrogant and closed-minded "gatekeepers" has the power to stop its
progress.
Rob
www.amherst.edu/~rloldershaw

Robert Oldershaw,
The faster than light guy from Cambridge says the fractal
people can't be right ( Joao Magueijo) : it has to do with
homogeneousness of the universe: he says on page 137 that:
"If this is true , burn this book, forget about Big Bang cosmology
and start crying convulsively."
Joao Magueijo is definitely not one of the "gatekeepers".

But I go along with the "close-minded" interpretation :
the Weeks -Thurson manifold approach to the cosmic background blackbody
radiation
is the only one I find any real work being done on
by the cosmological physics community.
In these approaches fractal statistics have been rejected.

The most comprehensive paper that I've found on the subject is by
Janna Levin who also wrote a dummied down version as a book.
http://www.amazon.com/How-Universe-Got-Its-Spots/dp/1400032725/ref=pd_bbs_sr_2/104-0029617-0633535?ie=UTF8&s=books&qid=1173628472&sr=8-2

Post by r***@amherst.edu
*How the Universe Got Its Spots: Diary of a Finite Time in a Finite
Space *

The "Soccer ball" dodecahedron manifold was the result.
She used Gaussian statistics in her paper's analysis.

Post by r***@amherst.edu
A very good analysis of the Thurston -Weeks approach in only 97 pages
and it is actually readable to some extent!
http://meghnad.iucaa.ernet.in/~himan/codes/pr.pdf
[PDF]
Topology and the Cosmic Microwave Background
File Format: PDF/Adobe Acrobat - View as HTML
to observe the finite extent of the universe in the cosmic background
radiation. ... Although the Weeks space is the smallest known manifold
it ...

What to someone from fractals likes like a fractal distribution
they are attributing to any but...
I think part of the trouble is that the Russian school of fractal
inflation ( actually chaotic inflation by Linde 1987)
bears very little resemblance to any known actual fractal theory?
Most of the cosmology world seem totally innocent of any exposure to any
of Mandelbrot's work.
( they seem to avoid it like the plague: so other versions of
topological/ geometric fractal manifold theory
is ignorred as well?).
If any one is going to come up with a good cosmic background radiation
theory
from the fractal point of view it has to be a fractalist.
Fractal percolation or fractal Brownian motion seem to be the most
likely approaches.
The WMAP result picture clearly looks like a fractal percolation.
Roger Bagula

[r***@amherst.edu]

Post by Roger Bagula
The WMAP result picture clearly looks like a fractal percolation.

Hi Roger,

The large-scale distribution does look like a fractal distribution,
and also like a high-energy distribution of plasma particles.

But look at nature in a more direct, general way.

The universe is composed of galaxies. These galaxies are composed of
"point-like" stellar objects. These stellar objects are composed of
"point-like" atomic objects. It looks like nature is a *global*
discrete fractal hierarchy.

The Universe is fractal not only *within* one Scale, like the Galactic
Scale; it is also fractal throughout the entire hierarchy of discrete
Scales ( ..., subquantum, atomic, stellar, galactic,
metagalactic, ... ).

Demonstration that the different Scales are highly self-similar and a
derivation of the scaling equations that allow one to compare all
lengths, times and masses of analogues on different Scales, can be
found at www.amherst.edu/~rloldershaw .

When I urge people to consider a new fractal paradigm, I am talking
about something far more radical than just within-Scale fractal
models. Nature is one single unified system with a discrete self-
similar structure. The same geometry and laws of physics should apply
on all fundamental Scales of nature's hierarchy. The incompatability
between QM and GR must be removed because nature tells us that nature
is unified and physics must eventually figure out how to handle that
unity, mathematically. The Self-Similar Cosmological Paradigm already
shows how to handle nature's unity conceptually and empirically.

Thanks for the chance to air my views,
Rob
www.amherst.edu/~rloldershaw

[Roger Bagula]

I downloaded a picture of the recent WMAP probe results picture off the web
( it's pretty widely distributed).
I get a fractal dimension of 1.7308302850966197 ( Sqrt[3] to four places)
using Paul Bourke's older version of FDC ( box dimension)
on a 50 per cent black and white threshold calculation.
It's posted at:
http://tech.groups.yahoo.com/group/Active_Mathematica/files/
Basic Mathematica part is the regression and graph:
Ar = {{0, 11.5188}, {-0.693147, 10.5414}, {-1.38629, 9.55584},
{-2.99573, 6.52062},
{-3.61092, 5.34711}, {-4.02535, 4.61512}, {-4.31749, 4.09434}, {-4.54329,
3.73767}, {-4.72739, 3.4012}, {-4.8828, 3.17805}, {-5.01728, 2.99573},
{-5.71043, 2.07944}}
y[x_] = Fit[Ar, {1, x}, x]
Plot[y[x], {x, -6, 0}]
1.7308302850966197/Sqrt[3]

I know that this simple analysis doesn't "prove" anything,
but to me it is a strong indication that an soccer ball
group ( E8 special group ) is probably entirely wrong.
It is more likely a an E6 tetrahedral manifold with this dimension.
Think of a random 3d Sierpinski tetrahedron or something like that.
It would explain the large central void that is observable in the picture.

There is a rule in science called Occam's razor: ( pretty much)
the simplest model is best.

No polemic is necessary.

[r***@amherst.edu]

On Mar 11, 1:13 pm, Roger Bagula <***@sbcglobal.net> wrote:



Let's give other readers 24 hours to think about these ideas, rather
than instantly "covering them up with a follow-up". Would that be
possible?


The large-scale distribution does look like a fractal distribution,
and also like a high-energy distribution of plasma particles.


But look at nature in a more direct, general way.


The universe is composed of galaxies. These galaxies are composed of
"point-like" stellar objects. These stellar objects are composed of
"point-like" atomic objects. It looks like nature is a *global*
discrete fractal hierarchy.


The Universe is fractal not only *within* one Scale, like the
Galactic
Scale; it is also fractal throughout the entire hierarchy of discrete
Scales ( ..., subquantum, atomic, stellar, galactic,
metagalactic, ... ).


Demonstration that the different Scales are highly self-similar and a
derivation of the scaling equations that allow one to compare all
lengths, times and masses of analogues on different Scales, can be
found at www.amherst.edu/~rloldershaw .


When I urge people to consider a new fractal paradigm, I am talking
about something far more radical than just within-Scale fractal
models. Nature is one single unified system with a discrete self-
similar structure. The same geometry and laws of physics should apply
on all fundamental Scales of nature's hierarchy. The incompatability
between QM and GR must be removed because nature tells us that nature
is unified and physics must eventually figure out how to handle that
unity, mathematically. The Self-Similar Cosmological Paradigm already
shows how to handle nature's unity conceptually and empirically.


Thanks for the chance to air my views,
Rob
www.amherst.edu/~rloldershaw

[Roger Bagula]

Post by r***@amherst.edu
Let's give other readers 24 hours to think about these ideas, rather
than instantly "covering them up with a follow-up". Would that be
possible?
Rob
www.amherst.edu/~rloldershaw

There is some stuff in reply in sci.nonlinear
you might be interested in.
The fellow there has given me trouble in the past for innocent posts.
Roger

[r***@amherst.edu]

Post by Roger Bagula
There is some stuff in reply in sci.nonlinear
you might be interested in.
The fellow there has given me trouble in the past for innocent posts.
Roger- Hide quoted text -

Thanks for the help Roger. I'll take a look.

You might be interested in my 3/13 post to the thread "Scale
Invariance, Conformal Invariance and General Relativity" on the
sci.physics.foundations newsgroup.

Rob

[Craig Markwardt]

Post by Roger Bagula
I downloaded a picture of the recent WMAP probe results picture off the web
( it's pretty widely distributed).
I get a fractal dimension of 1.7308302850966197 ( Sqrt[3] to four places)
using Paul Bourke's older version of FDC ( box dimension)
on a 50 per cent black and white threshold calculation.

You probably need a baseline comparison. In other words, would
simulated gaussian noise with the same power spectrum as the CMB give
the same fractal dimension results?

CM

[Roger Bagula]

Post by Craig Markwardt
You probably need a baseline comparison. In other words, would
simulated gaussian noise with the same power spectrum as the CMB give
the same fractal dimension results?
CM

Craig Markwardt,
Wendelin Werner ( recent fields medalist) has done work on
a very similar type of problem
and there are graphics at:
http://www.math.u-psud.fr/~werner/
http://www.math.u-psud.fr/%7Ewerner/pub.html
The area of study is called Brownian islands.
http://swiss.csail.mit.edu/~rauch/islands/

So I'm actually able to answer you for the 2d case
from a Mandelbrot published article on the Internet:
http://www.edge.org/3rd_culture/mandelbrot04/mandelbrot04_index.html

Post by Craig Markwardt
Empirical measurement yielded 1.3336 and on this basis, my 1982 book,
/The Fractal Geometry of Nature, /conjectured that the value of 4/3 is
exact. Mathematician friends chided me: had I told them before
publishing, they could have quickly provided a fully rigorous proof of
my conjecture. They were wildly overoptimistic, and a proof turned out
to be extraordinarily elusive. A colleague provided a numerical
approximation that fitted 4/3 to about 15 decimal places, but an
actual proof took 18 years and the joining of contributions of three
very different scientists. It was an enormous sensation in the year 2000.

It was this proof that got Wendelin Werner the Fields Medal
more than anything.