2 of 5
2
Are fractals representative of the geometry of life?
Posted: 19 December 2010 12:23 PM   [ Ignore ]   [ # 16 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  731
Joined  2007-06-20

It seems to me that all these physical examples are only superficially described by fractals.  The interesting point about fractals is that they are infinitely self-similar whereas self-similarity seems to quickly break down in these examples with each magnitude of detail consideration: molecular, atomic, subatomic, zero-sum energy field (per Krauss et al).

 Signature 

PC

Profile
 
 
Posted: 19 December 2010 12:45 PM   [ Ignore ]   [ # 17 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  6159
Joined  2009-02-26
the PC apeman - 19 December 2010 12:23 PM

It seems to me that all these physical examples are only superficially described by fractals.  The interesting point about fractals is that they are infinitely self-similar whereas self-similarity seems to quickly break down in these examples with each magnitude of detail consideration: molecular, atomic, subatomic, zero-sum energy field (per Krauss et al).

I am not sure if that is correct. The current research seems to suggest that fractals (CDT) may well be a fundamental aspect of the universe, even at the Planck level.
See below

kkwan.
Causal Dynamical Triangulation (CDT), invented by Renate Loll and her colleagues is relevant.
From her website on her research

http://www.phys.uu.nl/~loll/Web/research/research.html

 Signature 

Art is the creation of that which evokes an emotional response, leading to thoughts of the noblest kind.
W4U

Profile
 
 
Posted: 19 December 2010 12:50 PM   [ Ignore ]   [ # 18 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  731
Joined  2007-06-20

A diagram of a romanesco-like molecule, atom, and quark would convince me I was wrong.  The problem is these things would also have to be self-similar with everything that is not similar to a romanesco as well.

EDIT: PS. It does not appear that even CDT proposes infinite self-similarity.

[ Edited: 19 December 2010 12:55 PM by the PC apeman ]
 Signature 

PC

Profile
 
 
Posted: 19 December 2010 01:47 PM   [ Ignore ]   [ # 19 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  6159
Joined  2009-02-26
the PC apeman - 19 December 2010 12:50 PM

A diagram of a romanesco-like molecule, atom, and quark would convince me I was wrong.  The problem is these things would also have to be self-similar with everything that is not similar to a romanesco as well.

EDIT: PS. It does not appear that even CDT proposes infinite self-similarity.


From Loll,

The work on Euclidean path integrals was taken one important step further to a nonperturbative formulation, with both Quantum Regge Calculus [6,7] and, more recently, the related Dynamical Triangulations research program [8,9]. These approaches follow a rather straightforward and geometrically appealing route. In order to make the integral over all spaces computable, the curved spaces are represented in a regularized form, namely, by assembling them from elementary building blocks, usually four-dimensional analogues of triangles [10]. Although the individual building blocks are geometrically flat and therefore carry no curvature, gluing them together in all possible ways results in spaces or spacetimes that are locally curved in all possible ways. One then studies by a combination of analytic and numerical methods how a superposition of such geometries behaves in the limit as the size of the individual building blocks shrinks to zero and their number goes to infinity. If everything has been done right, the dependence on the details of the regularization in terms of discrete building blocks will be completely washed out in the process, and a quantum theory of spacetime will emerge.

The examples of the variety that can be obtained from fractal mathematics is proof not all fractal constructs need be similar to others.

[ Edited: 19 December 2010 01:53 PM by Write4U ]
 Signature 

Art is the creation of that which evokes an emotional response, leading to thoughts of the noblest kind.
W4U

Profile
 
 
Posted: 19 December 2010 01:56 PM   [ Ignore ]   [ # 20 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  731
Joined  2007-06-20

That’s a fine example of searching for words that one would expect to appear in a rebuttal of what I wrote but don’t actually address my criticism.

 Signature 

PC

Profile
 
 
Posted: 19 December 2010 02:05 PM   [ Ignore ]   [ # 21 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  6159
Joined  2009-02-26
the PC apeman - 19 December 2010 01:56 PM

That’s a fine example of searching for words that one would expect to appear in a rebuttal of what I wrote but don’t actually address my criticism.

I see your point about the expected continuation of self similarity into infinity. Did Loll not explain question? I emphasized the pertinent paragraph.

But why is it important to know? I may be missing the point. Can you explain the reason for the question?

Below examples of fractal diversity
http://www.miqel.com/fractals_math_patterns/visual_math_fractal_types.html
from:
http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html

[ Edited: 19 December 2010 02:33 PM by Write4U ]
 Signature 

Art is the creation of that which evokes an emotional response, leading to thoughts of the noblest kind.
W4U

Profile
 
 
Posted: 19 December 2010 05:06 PM   [ Ignore ]   [ # 22 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  731
Joined  2007-06-20
Write4U - 19 December 2010 02:05 PM

I see your point about the expected continuation of self similarity into infinity.

I doubt it.

Did Loll not explain question? I emphasized the pertinent paragraph.

But why is it important to know? I may be missing the point. Can you explain the reason for the question?

What question?  I haven’t asked any questions.

Below examples of fractal diversity
http://www.miqel.com/fractals_math_patterns/visual_math_fractal_types.html
from:
http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html

I am already aware that different formulas and starting values yield different fractal sets.  It doesn’t address my initial criticism.  Zooming into the romanesco is, I presume, operating within only one set.  And this diversity would also be unhelpful in addressing my later aside about things macroscopically dissimilar to a romanesco.  There would be counterexamples of those things that happen to be very similar molecularly or atomically.

 Signature 

PC

Profile
 
 
Posted: 19 December 2010 05:30 PM   [ Ignore ]   [ # 23 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  6159
Joined  2009-02-26
the PC apeman - 19 December 2010 05:06 PM
Write4U - 19 December 2010 02:05 PM

I see your point about the expected continuation of self similarity into infinity.

I doubt it.

Did Loll not explain question? I emphasized the pertinent paragraph.

But why is it important to know? I may be missing the point. Can you explain the reason for the question?

What question?  I haven’t asked any questions.

Below examples of fractal diversity
http://www.miqel.com/fractals_math_patterns/visual_math_fractal_types.html
from:
http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html

I am already aware that different formulas and starting values yield different fractal sets.  It doesn’t address my initial criticism.  Zooming into the romanesco is, I presume, operating within only one set.  And this diversity would also be unhelpful in addressing my later aside about things macroscopically dissimilar to a romanesco.  There would be counterexamples of those things that happen to be very similar molecularly or atomically.

Your infinity criticism implies that you attach an importance to it. My question was for clarification of the importance of the need for infinite iteration. Theoretically it is possible to arrive at a zero state (infinity), practically we are restricted by computing powers.
But pointing out random irregularities in a vegetable does not invalidate the mathematics which caused the similarities. Moreover, external forces (collisions, mergings) may well be instrumental in creating new fractal patterns. Fractals are not things, they are a mathematical explanation for the apparent similarities in many forms of universal evolutionary expression. Much as 2+2=4 to explain the addition function of mathematics in the universe. Does addition function need to be reducible into infinity or is the event horizon sufficiently small (or large)?
As I understand Loll, fractals work at any level, thus any counter examples on the molecular or atomic scale would also be subject to fractal geometry. Loll seems to think that CDT works at quantum (Planck) level. She proposes that the very curvature of space/time at Planck level is fractal in nature. If we can get there Loll believes it might lead to TOE.

[ Edited: 19 December 2010 06:11 PM by Write4U ]
 Signature 

Art is the creation of that which evokes an emotional response, leading to thoughts of the noblest kind.
W4U

Profile
 
 
Posted: 19 December 2010 06:26 PM   [ Ignore ]   [ # 24 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  731
Joined  2007-06-20

This looks too much like a rabbit hole for my tastes.  I still you have your “A tachyon is a metaphysical particle” fiasco in mind.

 Signature 

PC

Profile
 
 
Posted: 19 December 2010 06:34 PM   [ Ignore ]   [ # 25 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  6159
Joined  2009-02-26
the PC apeman - 19 December 2010 06:26 PM

This looks too much like a rabbit hole for my tastes.  I still you have your “A tachyon is a metaphysical particle” fiasco in mind.

http://nextbigfuture.com/2009/03/theory-of-space-time-with-quantum-scale.html

Please allow me to grow intellectually, without automatic rejection of anything I may posit.

EDIT
From Wiki

A tachyon (pronounced /ˈtæki.ɒn/; Greek: ταχύς, takhus, “swift” + English: -on “elementary particle”) is a hypothetical subatomic particle that moves faster than light. In the language of special relativity, a tachyon is a particle with space-like four-momentum and imaginary proper time. A tachyon is constrained to the space-like portion of the energy-momentum graph. Therefore, it cannot slow down to subluminal speeds.

Ok, so I called it metaphysical. No big deal.

[ Edited: 19 December 2010 06:46 PM by Write4U ]
 Signature 

Art is the creation of that which evokes an emotional response, leading to thoughts of the noblest kind.
W4U

Profile
 
 
Posted: 19 December 2010 08:08 PM   [ Ignore ]   [ # 26 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  4400
Joined  2010-08-15
Write4U - 19 December 2010 12:02 PM

Do we think fractally?

Perhaps with a bit of the holographic tossed in?

 Signature 

We need each other, to keep ourselves honest

Profile
 
 
Posted: 19 December 2010 08:15 PM   [ Ignore ]   [ # 27 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  4400
Joined  2010-08-15
the PC apeman - 19 December 2010 12:23 PM

It seems to me that all these physical examples are only superficially described by fractals.  The interesting point about fractals is that they are infinitely self-similar whereas self-similarity seems to quickly break down in these examples with each magnitude of detail consideration: molecular, atomic, subatomic, zero-sum energy field (per Krauss et al).

I think I see what you’re saying… but does it need to be mathematically perfect… to be counted as a fractal?

And then, there’s this . . .

New view reveals how DNA fits into cell
Posted 23 November 2009


dna-globule-big.jpg

Applying the method to human cells, the researchers found that the genome has a highly organized structure. Small pieces of DNA fold into globs, and those globs fold into larger globs and so on. The researchers report that this “globule of globules of globules” is fractal, meaning it is organized in such a way that it has the same pattern no matter how far you zoom in. This fractal shape is “super-dense, but has no knots,” says Lieberman-Aiden. . . “

 Signature 

We need each other, to keep ourselves honest

Profile
 
 
Posted: 19 December 2010 08:24 PM   [ Ignore ]   [ # 28 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  4400
Joined  2010-08-15

Oh and then there was this, what I had intended to post before getting side-tracked.
I was going to offer it as another example of fractal, but I’m thinking Apeman wouldn’t agree,
still at least the woo of fractals is in here somewhere

Rise in Oxygen Drove Evolution of Animal Life 550 Million Years Ago

ScienceDaily (Dec. 18, 2010) — Researchers funded by the Biotechnology and Biological Sciences Research Council (BBSRC) at the University of Oxford have uncovered a clue that may help to explain why the earliest evidence of complex multicellular animal life appears around 550 million years ago, when atmospheric oxygen levels on the planet rose sharply from 3% to their modern day level of 21%.

The team, led by Professor Chris Schofield, has found that humans share a method of sensing oxygen with the world’s simplest known living animal—Trichoplax adhaerens—suggesting the method has been around since the first animals emerged around 550 million years ago.

Trichoplax adhaerens is a tiny seawater organism that lacks any organs and has only five types of cells, giving it the appearance of an amoeba. By analysing how Trichoplax reacts to a lack of oxygen, Oxford researcher Dr Christoph Loenarz found that it uses the same mechanism as humans—in fact, when the key enzyme from Trichoplax was put it in a human cell, it worked just as well as the human enzyme usually would.

 Signature 

We need each other, to keep ourselves honest

Profile
 
 
Posted: 19 December 2010 09:43 PM   [ Ignore ]   [ # 29 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  6159
Joined  2009-02-26
citizenschallenge.pm - 19 December 2010 08:08 PM
Write4U - 19 December 2010 12:02 PM

Do we think fractally?

Perhaps with a bit of the holographic tossed in?

That would not be contradictory. I read somewhere that you can take a part of a hologram and reconstruct the whole from it. Fractal geometrics may well be the method by which that is accomplished.

 Signature 

Art is the creation of that which evokes an emotional response, leading to thoughts of the noblest kind.
W4U

Profile
 
 
Posted: 19 December 2010 09:51 PM   [ Ignore ]   [ # 30 ]
Sr. Member
Avatar
RankRankRankRankRankRankRankRankRankRank
Total Posts:  6159
Joined  2009-02-26
citizenschallenge.pm - 19 December 2010 08:24 PM

Oh and then there was this, what I had intended to post before getting side-tracked.
I was going to offer it as another example of fractal, but I’m thinking Apeman wouldn’t agree,
still at least the woo of fractals is in here somewhere

Rise in Oxygen Drove Evolution of Animal Life 550 Million Years Ago

ScienceDaily (Dec. 18, 2010) — Researchers funded by the Biotechnology and Biological Sciences Research Council (BBSRC) at the University of Oxford have uncovered a clue that may help to explain why the earliest evidence of complex multicellular animal life appears around 550 million years ago, when atmospheric oxygen levels on the planet rose sharply from 3% to their modern day level of 21%.

The team, led by Professor Chris Schofield, has found that humans share a method of sensing oxygen with the world’s simplest known living animal—Trichoplax adhaerens—suggesting the method has been around since the first animals emerged around 550 million years ago.

Trichoplax adhaerens is a tiny seawater organism that lacks any organs and has only five types of cells, giving it the appearance of an amoeba. By analysing how Trichoplax reacts to a lack of oxygen, Oxford researcher Dr Christoph Loenarz found that it uses the same mechanism as humans—in fact, when the key enzyme from Trichoplax was put it in a human cell, it worked just as well as the human enzyme usually would.

The fractal fern structure can also be found in some of the earliest life in the ocean. Apparently, this early attempt of iteration of a single cell was not sufficiently sophisticated yet. The species was at a genetic dead end and was replaced with the chromosomal method (itself also fractal in nature).

[ Edited: 19 December 2010 09:53 PM by Write4U ]
 Signature 

Art is the creation of that which evokes an emotional response, leading to thoughts of the noblest kind.
W4U

Profile
 
 
   
2 of 5
2