Theory of Everything. Is it Fractals or Strings??

emperor_of_localgroup · Oct 29, 2008

After watching last night's Nova, this question should come to many people's minds. If we can explain the shapes of nature, evolutionary process, workings of human body parts, even design antennas, I think we should give Fractals a chance.I have been saying this for many years, life here is not an accident or random occurrence, but it followed a well defined process that can be explained by science. We may someday even find a fractal order in  chaos in microscopic levels. I wonder how long will it take for scientists to theorize orbit of an electron around a nucleus is not a circle or ellipse or cloud but fractals. or de Broglie waves are waves made by fractals... etc.I'm new in fractal business, although years ago I tried to understand and use fractals. I would  appreciate if someone direct me to some online materials on fractals of low to moderate difficulties.   <div class="Discussion_UserSignature"> Earth is Boring </div>

kyle_baron · Oct 30, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>After watching last night's Nova, this question should come to many people's minds. If we can explain the shapes of nature, evolutionary process, workings of human body parts, even design antennas, I think we should give Fractals a chance.I have been saying this for many years, life here is not an accident or random occurrence, but it followed a well defined process that can be explained by science. We may someday even find a fractal order in  chaos in microscopic levels. I wonder how long will it take for scientists to theorize orbit of an electron around a nucleus is not a circle or ellipse or cloud but fractals. or de Broglie waves are waves made by fractals... etc.I'm new in fractal business, although years ago I tried to understand and use fractals. I would  appreciate if someone direct me to some online materials on fractals of low to moderate difficulties.   Posted by emperor_of_localgroup</DIV>This is just a rhetorical question, but aren't fractals similar to strings, in a way they have  symmetry? <div class="Discussion_UserSignature"> </div>

thor06 · Oct 30, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>After watching last night's Nova, this question should come to many people's minds. If we can explain the shapes of nature, evolutionary process, workings of human body parts, even design antennas, I think we should give Fractals a chance.I have been saying this for many years, life here is not an accident or random occurrence, but it followed a well defined process that can be explained by science. We may someday even find a fractal order in  chaos in microscopic levels. I wonder how long will it take for scientists to theorize orbit of an electron around a nucleus is not a circle or ellipse or cloud but fractals. or de Broglie waves are waves made by fractals... etc.I'm new in fractal business, although years ago I tried to understand and use fractals. I would  appreciate if someone direct me to some online materials on fractals of low to moderate difficulties.   Posted by emperor_of_localgroup</DIV>   #$#@$!! I missed it!       Try and catch it later.  NOVA is so good at putting these complicated theories into terms most of us can at least grasp the jist.  Thus I can't comment on your post directly but I do remeber a favorite quote "The Mandlebrot represents nothing less than the thumbprint of God".  So cool.  If you don't already have one get a free Mandlebrot set generator, and start zooming in.        Strings seem to my very lamen brain, to be more of the theory of everything.  The end of the question "what is the smallest piece?".  Yet this also seems to mean we will never be able to observe or test "string theory".  "If an atom is the size of the solar system, a string is a tree on the Earth."     Cool stuff, great topic.  NOVA is good for the curious among us.      <div class="Discussion_UserSignature"> www.watchnasatv.com ONE PERCENT FOR NASA! </div>

a_lost_packet_ · Oct 31, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>.. NOVA is good for the curious among us.      Posted by thor06</DIV>It was a great show.Basically, the gist was the actual application of fractals in solving complex problems, not, necessarily, a treatise on fractals themselves.  Particular care was made to separate the "neato" graphical depiction of fractals from the more serious mathematical application of them.  It was a real treat to see Mandelbrot explain them himself and a bit of the history behind his work.One application using fractals was to attempt some predictive values for a rain forest's capacity to process carbon.  They found some interesting things but, unfortunately, they didn't go far into their methodology which I was disappointed with.

(I also don't remember if they showed any final results from their effort other than the below.)Their premise was that they believed they could take very accurate measurements of one tree and then, using fractals, apply those measurements in making predictive values regarding the entire forest.  That addresses an essential thing concerning fractals - repetition of sets.  No matter how closely portions are examined, they retain their complexity even though they are derived from simple formulas.  It makes handling very complex sets of data much easier.  Computing an entire progression of data of a forest, tree by tree, would probably take several lifetimes. The found some very interesting things including that the fractal set depicted in their measurements of one, single tree were fractally expressed in comparison to the distribution of the population of that same species of tree.  The curves for the comparison of the original set and the derived values were remarkably similar to their actual census observations for a portion of the forest's population.  In essence, they hope(d) to use this simple data from one tree transformed into a fractal set to better understand and provide predictive data for a very, very complex system which might be almost impossible to do otherwise.  The similarity between their specific measurement of one tree, their derived values for the rest of the population based on the generated fractal and the actual observations of the population of a representative sample were very, very similar.  In short, a possible predictive value was the result. (It was implied not stated as proven so I don't know where the study ended up.) Very interesting stuff and a show worth watching.There's lots of information and free generators for fractals out there.  There are also several generators for 3D fractals as well. Those can be pretty amazing looking.  But, the most important thing out of all of it is finding areas where it can be applied which results in knowledge being gained.  They're not just pretty pictures.

<div class="Discussion_UserSignature"> I put on my robe and wizard hat... </div>

thor06 · Nov 1, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'> Those can be pretty amazing looking.  But, the most important thing out of all of it is finding areas where it can be applied which results in knowledge being gained.  They're not just pretty pictures.

Posted by a_lost_packet_</DIV>Hey ALP,    Thanks for the info, sounds really interesting.  I'll be looking for it in the program guide, it might also be on their site.  The application of fractals is promising, pretty pictures with great potential.

<div class="Discussion_UserSignature"> www.watchnasatv.com ONE PERCENT FOR NASA! </div>

emperor_of_localgroup · Nov 1, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>It was a great show.Basically, the gist was the actual application of fractals in solving complex problems, not, necessarily, a treatise on fractals themselves.  Particular care was made to separate the "neato" graphical depiction of fractals from the more serious mathematical application of them.  It was a real treat to see Mandelbrot explain them himself and a bit of the history behind his work.One application using fractals was to attempt some predictive values for a rain forest's capacity to process carbon.  They found some interesting things but, unfortunately, they didn't go far into their methodology which I was disappointed with.

  (I also don't remember if they showed any final results from their effort other than the below.)  Very interesting stuff and a show worth watching.There's lots of information and free generators for fractals out there.  There are also several generators for 3D fractals as well. Those can be pretty amazing looking.  But, the most important thing out of all of it is finding areas where it can be applied which results in knowledge being gained.  They're not just pretty pictures.

Posted by a_lost_packet_</DIV>Here you go, lost_packet , you understood it much better than I did. Yes, they didn't go into details of their tree experiment.  I once in the 80's  tried to use fractals in my image processing research but got distracted and had to use other techniques. Since then I never looked back at fractals again and now I'm surprised to find fractals have matured so much and found applications in so many other fields.Fractals also use iterative method for final results just like genetic algorithms, which actually mimics evolutionary process, and each iteration produces the 'next  generation'. For this reason I am looking at fractals favorably to give us some answers about nature which are still unknown to us. In the back of my mind I have a weird feeling everything in the universe (including the univ itself) have gone through certain forms of evolutions.   I guess I have to search Amazon for some cheap used books on fractals.I think Baron correctly noticed similarity between fractals and strings, at least certain strings of string theory.   <div class="Discussion_UserSignature"> Earth is Boring </div>

DrRocket · Nov 2, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>After watching last night's Nova, this question should come to many people's minds. If we can explain the shapes of nature, evolutionary process, workings of human body parts, even design antennas, I think we should give Fractals a chance.I have been saying this for many years, life here is not an accident or random occurrence, but it followed a well defined process that can be explained by science. We may someday even find a fractal order in  chaos in microscopic levels. I wonder how long will it take for scientists to theorize orbit of an electron around a nucleus is not a circle or ellipse or cloud but fractals. or de Broglie waves are waves made by fractals... etc.I'm new in fractal business, although years ago I tried to understand and use fractals. I would  appreciate if someone direct me to some online materials on fractals of low to moderate difficulties.   Posted by emperor_of_localgroup</DIV>Fractals already have a chance, but it has virtually nothing to do with any "Theory of Everything".  The word "fractal" comes from a reference to the notion of a fractional topological dimension.  They are not a physical entity, but are topological spaces created by a limiting process in mathematics.There is no reason to believe that electron orbitals are fractal in nature, and if they were the entire structure of quantum mechanics would be in trouble, since it relies heavily on descriptions provided by partial differential equations and fractal structures are extremely irregular and certainly not compatible with differentiable structures.For references you will probably need to look at books by Mandelbrot (who started the field) or Hannes Otto Peitgen's book.  I think you will find that trying to relate that material to elementary particle physics and reconciling it with general relativity will be impossible. <div class="Discussion_UserSignature"> </div>

emperor_of_localgroup · Nov 4, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>Posted by DrRocket</DIV> There is no reason to believe that electron orbitals are fractal in nature, and if they were the entire structure of quantum mechanics would be in trouble, since it relies heavily on descriptions provided by partial differential equations and fractal structures are extremely irregular and certainly not compatible with differentiable structures. [Dr Rocket]In my opinion, nature  is not differentiable. Only man-made things are differentiable. Differentiability of quantum mechanical micro-structure may due to be over simplification of the structure to satisfy our theoretical needs. You may then ask why then experiments agree with theories?  My guess is experiments may  have been also simplified for the desired results.I understand when fractals first became popular it was mainly for topology and its ability to create incredible patterns. I think string theorists should try to link (or use) fractal math with their theories which may lead to something new.   <div class="Discussion_UserSignature"> Earth is Boring </div>

DrRocket · Nov 4, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>In my opinion, nature  is not differentiable. Only man-made things are differentiable....Posted by emperor_of_localgroup</DIV>Care to back up your opinion with facts and data ?  Unsubstantiated opinions are worthless, or worse.You seem to be rejecting virtually all of known physics.  That is a rather extreme position for one to be taking without a great deal of justification, which you have not supplied. <div class="Discussion_UserSignature"> </div>

emperor_of_localgroup · Nov 5, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>Care to back up your opinion with facts and data ?  Unsubstantiated opinions are worthless, or worse.You seem to be rejecting virtually all of known physics.  That is a rather extreme position for one to be taking without a great deal of justification, which you have not supplied. Posted by DrRocket</DIV>Here I did it again. Doesn't matter how carefully I pick my words, someone would always misinterpret my thought.DrRocket, you are over reacting. I'm not rejecting any of the known physics. I'm just saying the very definition of calculus is based on approximation. Our calculus can give us  answer  which may be 99.9% or even 99.999% correct, I'm arguing on behalf of .001%.Take a simple natural wild field with grasses and shrubs for example, how accurately can one represent it with a continuous differentiable 2d or 3D function? Nature is much more complex than this. Irregularities in nature are enormous. This was the type of  'nature' I had in my mind during my last post. <div class="Discussion_UserSignature"> Earth is Boring </div>

DrRocket · Nov 5, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>Here I did it again. Doesn't matter how carefully I pick my words, someone would always misinterpret my thought.DrRocket, you are over reacting. I'm not rejecting any of the known physics. I'm just saying the very definition of calculus is based on approximation. Our calculus can give us  answer  which may be 99.9% or even 99.999% correct, I'm arguing on behalf of .001%.Take a simple natural wild field with grasses and shrubs for example, how accurately can one represent it with a continuous differentiable 2d or 3D function? Nature is much more complex than this. Irregularities in nature are enormous. This was the type of  'nature' I had in my mind during my last post. Posted by emperor_of_localgroup</DIV>Calculus, as you noted, is indeed based on approximation.  It also allows one to approximate arbitrarily closely and by passing to a limit permits one to arrive at an exact answer in many cases.  The circumference of a circle of diameter 1 is exactly, not approximately, pi.  If you look at natural features closely enough, but still at a macroscopic rather than an atomic level, the features that you see are continuous.  In fact, since there are no absolutely sharp corners or points, I think it fair to say that those features can be described by funtions that are in fact smooth (infinitely differentiable).  So the example that you raised of wild grasses and shrubs should, in principle, admit of descriptions by such functions.  They will not be functions with simple analytical expressions, but they will be smooth.  They will not be functions with power series expansions (analytic or holomorphic).You might be interested to know that given an interval say [a.b] and numbers c<a and b<d it is possible to construct a smooth function f such that f(x) = 1 for x in [a,b] f(x)=0 for x </= c or x>/=d and x between 0 and 1 otherwise.  Such funtions are called b="bump functions" and arise in the theory of Schwartz distributions and in the construction of smooth partitions of unity in the theory of differentiable manifolds.  It is the existence of such functions that allows you to approximate continuous functions arbitrarily closely with smooth functions and I would think to represent your wild grasses and flowers exactly with smooth functions.  This sort of thing also works in higher dimensions.On the other hand analytic functions, which are those most commonly encountered in elementary algebra courses and the functions with which you deal most commonly in introductory calculus classes cannot change rapidly enough to create "bump functions", although they commonly admit of simple representations and always admit at least local representations with power series, hence are approximable with polynomials.  These are the functions of everyday experience.But my point was that the equations of physics are differential equations or partial differential equations and that the functions that describe the physical world are differentiable.  Quantum mechanics relies on partial differential equations.  General relativity treats the universe, space-time, as a differentiable manifold.  Without differentiability, the basic principles of physics cease to make sense.  Those equations and those principles produce predictions of the behavior of nature that agrees with experiment to within the capabilities of our measuring instruments.  Much better than .001% in many cases.  Nature seems to be differentiable.  <div class="Discussion_UserSignature"> </div>

ZenGalacticore · Nov 24, 2008

I saw that NOVA episode, it was very informative and entertaining. Fractals and the Mandlebrot set will definitely help us to understand the natural world better than we do, and much more. I was especially interested in its applications in art and design.I have to agree with Doc Rocket on its meaning for a theory of everything. However, I do have faith in string theory. <div class="Discussion_UserSignature"> ZenGalacticore </div>

why06 · Nov 24, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'> I would  appreciate if someone direct me to some online materials on fractals of low to moderate difficulties.   Posted by emperor_of_localgroup</DIV>Here's a good book on fractals: "Chaos" by: James GleickIt's a very well-known book for an introduction into Fractals and the math is not hard at all to understand   Thought I would Include and image of the most famous fractal. It is infinitely complex.  <img src="http://sitelife.space.com/ver1.0/Content/images/store/0/0/d0727f8f-305f-4b3a-b07d-988b369b66de.Medium.jpg" alt="" width="449" height="339" /> <div class="Discussion_UserSignature"> <div>________________________________________ </div><div><ul><li>your move...</li></ul></div> </div>

DrRocket · Nov 25, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>I saw that NOVA episode, it was very informative and entertaining. Fractals and the Mandlebrot set will definitely help us to understand the natural world better than we do, and much more. I was especially interested in its applications in art and design.I have to agree with Doc Rocket on its meaning for a theory of everything. However, I do have faith in string theory. Posted by ZenGalacticore</DIV>Peitgen's book ought to be pretty good.  I have not read it, but I met Peitgen years ago (he was chasing differential equations then) and he is a real mathematician.  http://www.alibris.com/booksearch?qwork=604836&matches=69&wquery=The+Beauty+of+Fractals&cm_sp=works*listing*title <div class="Discussion_UserSignature"> </div>

jdweston · Dec 18, 2008

It was recomended to me to post this over here. T’was the night before EverythingBy Daniel Weston T’was the night before, (as if night mattered) and all through the universe, not a fermion was stirring, not a quark or it’s inverse.Everything was nothing yet in a moment later, the size of a dot, something - an energy radiator.Then a phase transition, caused a cosmic inflation, that grew exponentially towards, quark-gluon plasmatiation.An excess of quarks as it cooled In the first seconds, by the time down to a billion K, an annihilation dance beckons.Time not to rest still way too hot, just not as hot as before, particle energies drop, now the physics we can’t ignore.379,000 light years later the electrons and then nuclei combine, Still 11,000 plus degrees C, now into atoms it finally sublimes. Then slowly gravitationally attracted, to nearby each others and more, two, four, eight, a million, soon sextillions and decillions galore. Then speckles and sparkles, like first falling snow, gives a depth to space, and a pattern to the glow. When out on the edge, a shutter, and chatter, from the swirls and the collapses, out-shed matter. When, what to the deep and the deeper should show, But a star that lasts more then a fleeting you know. With a force super lively and light way too bright, They shine, fade, expand, and explode with the might. More and more the elements by orbital came, And they spun in layers, and periodic by name! "Take Hydrogen first! and now Helium! too, make Lithium and Carbon to name just a few!Now, Nitrogen!, Now Oxygen! Now Beryllium and Boron!, Now more and more and more they flew on!To the column of the group and rows of little balls, Now fusion away! Fusion away! Fusion away all!"And then, in a twinkling of stars, and a swill of dust danced, Galactic arms twist to a center, that disappeared into blackness.Pulled towards the hole, with one last drift around, Down the chimney the light went with only a slight sound. Gravity wins or does it really a few great minds must ponder, Does something leak out and fatten the warp, they now all wonder.Space-time bends and it twists, but does it break or falter. Can we ever know just one everything equation or another. With all this and that when you add all the parts, the mass not enough to hold the whole thing should fall apart.The numbers not-exact but checked time and time again by the add-ers, There’s only one answer (maybe), it's full of Dark matter! Will it grow forever, until it’s runs out and lapses, Just can’t stay the same, must at least relapses!But what is the mass balance and how will we know, whether times runs forever, or someday backwards to no. We measured the shift rates and much to our surprise, not only just away they all flew but still accelerating, we weren't very wise.So we heard it exclaim, I go ‘perpetually out of sight, "Happy forever to all, and to all a very slowly dimming night!" ---30—

DrRocket · Dec 18, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>It was recomended to me to post this over here. T’was the night before EverythingBy Daniel WestonT’was the night before, (as if night mattered) and all through the universe,not a fermion was stirring, not a quark or it’s inverse.Everything was nothing yet in a moment later,the size of a dot, something - an energy radiator.Then a phase transition, caused a cosmic inflation,that grew exponentially towards, quark-gluon plasmatiation.An excess of quarks as it cooled In the first seconds,by the time down to a billion K, an annihilation dance beckons.Time not to rest still way too hot, just not as hot as before,particle energies drop, now the physics we can’t ignore.379,000 light years laterthe electrons and then nuclei combine,Still 11,000 plus degrees C, now into atoms it finally sublimes.Then slowly gravitationally attracted, to nearby each others and more,two, four, eight, a million,soon sextillions and decillions galore.Then speckles and sparkles,like first falling snow,gives a depth to space, and a pattern to the glow.When out on the edge,a shutter, and chatter,from the swirls and the collapses, out-shed matter.When, what to the deep and the deeper should show,But a star that lasts more then a fleeting you know.With a force super lively and light way too bright,They shine, fade, expand, and explode with the might.More and more the elements by orbital came,And they spun in layers, and periodic by name!"Take Hydrogen first! and now Helium! too, make Lithium and Carbon to name just a few!Now, Nitrogen!, Now Oxygen! Now Beryllium and Boron!,Now more and more and more they flew on!To the column of the group and rows of little balls,Now fusion away! Fusion away! Fusion away all!"And then, in a twinkling of stars, and a swill of dust danced,Galactic arms twist to a center, that disappeared into blackness.Pulled towards the hole, with one last drift around,Down the chimney the light went with only a slight sound.Gravity wins or does it really a few great minds must ponder,Does something leak out and fatten the warp, they now all wonder.Space-time bends and it twists, but does it break or falter.Can we ever know just one everything equation or another.With all this and that when you add all the parts,the mass not enough to hold the whole thing should fall apart.The numbers not-exact but checked time and time again by the add-ers,There’s only one answer (maybe), it's full of Dark matter!Will it grow forever, until it’s runs out and lapses,Just can’t stay the same, must at least relapses!But what is the mass balance and how will we know,whether times runs forever, or someday backwards to no.We measured the shift rates and much to our surprise,not only just away they all flew but still accelerating, we weren't very wise.So we heard it exclaim,I go ‘perpetually out of sight,"Happy forever to all, and to all a very slowly dimming night!"---30—  Posted by jdweston</DIV>That's cute but you have now made this same post in 3 different threads and that is not cute. <div class="Discussion_UserSignature"> </div>

jdweston · Dec 18, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>That's cute but you have now made this same post in 3 different threads and that is not cute. Posted by DrRocket</DIV> Very sorry I was unsure where it should go and am spenting all my free time  reading all the interesting posts in all the groups.

DrRocket · Dec 18, 2008

Replying to: <DIV CLASS='Discussion_PostQuote'>Very sorry I was unsure where it should go and am spenting all my free time  reading all the interesting posts in all the groups. Posted by jdweston</DIV>Not a big problem.  Welcome to the forumSince you made the posts, you have the power to delete any "extras" with the controls at the bottom of the window.  If it were me I would keep one and delete the others. <div class="Discussion_UserSignature"> </div>

GraemeH · Mar 11, 2010

One of the great things about insomnia is that it gives you plenty of time to think ... or maybe I am mixing up cause and effect here

Anyways, last night I was thinking about fractal geometry and its application to cosmology in general. Searching through SDC brought up this thread and searching the internet, I came across this very interesting article:

http://www.newscientist.com/article/mg2 ... ?full=true

It turns out that fractal quantum mechanics is a current line of scientific investigation.

Theory of Everything. Is it Fractals or Strings??

emperor_of_localgroup

Guest

kyle_baron

Guest

thor06

Guest

a_lost_packet_

Guest

thor06

Guest

emperor_of_localgroup

Guest

DrRocket

Guest

emperor_of_localgroup

Guest

DrRocket

Guest

emperor_of_localgroup

Guest

DrRocket

Guest

ZenGalacticore

Guest

why06

Guest

DrRocket

Guest

jdweston

Guest

DrRocket

Guest

jdweston

Guest

DrRocket

Guest

GraemeH

Guest

Similar threads

TRENDING THREADS

Latest posts

Share this page