Is there a relation between string theory and fractals?

[Melancholyman]

I am currently reading the book "the elgeant universe" by Brigan Greene and an intuition suddenly struck me. According to Brian Green the empirical implications of string theory might not be able to be tested, since the technology for it might be very far away, so the only option is to test the theory theoretically. I am thinking, computers, simulations so forth and so on. What arrested my attention was the picture of the curled up extra spacial dimension, called yuga-kali (or something like that) space. This looked very much like a fractal.

This is far fetched and I haven't thought it through really, but the fact is that nobody has ever seen a string and the postulation of curled up dimensions are just assumptions that can give explanatory power to some of the questions needs answering in string theory. I am thinking, that what if this kaluga space really isn't a space, it is the string itself, and strings should be able to have infinite vibrational pattern which might make them "look" different, and there is an infinite number or mandelbulb that can be produced right? What if, the mandebulb really is a mathematical representation of a string that can alter itself indefinately to get different shapes.

Let's say mandelbulbs are not strings, but they might be good representations of curled up spaces, you can zoom in indefinately right? More dimensions occur the further you zoom in, this I think fits well with the notion of an infinite universe, who says infinity only has to go on macroscopic scales? My intuition is that maybe computer simulation, mandelbulbs, that is fractals and string theory might have something in common.....What are your takes onj this?

[s31415]

Hi,

I am a theoretical phyisicist and I dare to say I know string theory rather well. I am not aware of any serious work in string theory using fractal spaces.

What you saw is probably the depiction of a Calabi-Yau space, or rather a picture of a three-dimensional slice of part of it, the full Calabi-Yau being six-dimensional. In some sense, these spaces are as far as you can be from a fractal. They are smooth (except sometimes at some specific places) and are often even algebraic, that is the solution space to polynomial equations in several variables. To get a picture, in two dimension, this would be for instance ellipses, parabola, hyperbolas and their higher order cousins. Very far from anything fractal. Moreover they have to satisfy very specific conditions for them to have a chance to be compatible with the physics we observe in the world.

Also I would like to point out that even if Brian Greene is gifted as a vulgarizer, he necessarily gives an overly simplistic and distorted picture of string theory. Simply because if you want to describe it accurately, there is no other choice than using concepts from (fairly advanced) mathematics and physics. This is somewhat unfortunate but that's how it is. Therefore, making conjectures about how it could be possible to modify string theory based on his book is not likely to yield a successful proposal.

Best,

Sam

[Melancholyman]

Yeah I actually looked into some of the formulas and it's beyond me. Just a fools intuition Anyways, I have a question, how does a 6 dimensional space look like? Is there anyone than can even imagine or render it in 3D? Shouldn't it be impossible for us as humans with our constitution to perceive such an object?

regards
Erik

[s31415]

It is not possible to visualize directly objects with more than 3 dimension (even some 3 dimensional objects are problematic, like a 3-sphere or a 3-torus). However, it possible to describe them mathematically. The 3-sphere for instance is the set of point at a given distance to the origin of 4-dimensional Euclidean space. The latter is just the set of points labeled by four real coordinates. Once they are described by equation, it is also possible either to cut slices of them or project them on a lower dimensional space. If the latter is 2- or 3-dimensional, it is possible to visualize a "shadow" of the higher dimensional object. This is was the picture of the Calabi-Yau manifold you saw was. Here is a rotating hypercube (4-dimensional cube) projected down in 3 dimensions:
<a href="http://www.youtube.com/v/S_DIQqT455c&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/S_DIQqT455c&rel=1&fs=1&hd=1</a>
While the 3-dimensional "shadow" seems to get deformed, the 4-dimensional cube is rotating rigidly.

The type of fractals called "quaternionic" are also four dimensional objects that have been sliced to obtain 3-dimensional ones.

[weavers]

Intuition and sudden gut feelings are the universes in which we reside, way of talking to us; not in words or languages we can currently comprehend but in mathematical harmonies constructs, in an intuitive waves of an ocean our eyes  cannot see but the primal core of our ears can hear..
The wave is the wave ,the brain of the most intelligent human specie, uses human logic, because up until recently, it doesn't fathom how to access any other logic but that doesn't preclude that there not be others.
 The quantum logics just discovered;  will need more than our brains, to perceive the volume of formulas and stratus that comprise them.
But intuitive waves of thought, intuitive waves of feelings are picked up by the residual remnants of what's left of our primal brain, which was here long before so called modern man evolved. So hold on to your intuition, have faith in it. It is the universes kissing you and instructing you. We don't mean to sound corny by using an over used acronym, but it is the force: the forces of the universe. It travels in waves and touches those lucky enough to be born with an predisposition to be channelers open to them.
The revelations of the force that rides the waves of intuition, leaves little empirical proof behind, but empirical proof does not hinder nor cease our belief in something. Empirical proof did not stop us for hundreds of thousands of years.
Nevertheless, one may argue, the ability to understand something devoid of conscious reasoning is intuition, and according to our brains processors, the protocols of space are often  devoid of empirical conscious reasoning.
Ask yourself this,without letting your human ego opaquing your answer. You like others are here because a string is dragging you here to the new frontier,unable to break free cause you count yourself, one of the new astronauts ,with new eyes that can see into the space of fourth dimensionality of  fractology and all of its exciting and  intriguing self similarities.
Do  you not think, that there are spies from many governments watching the many mathematical geniuses that reside here and their unstoppable addictive quest  to explore and show the marvels of the fractals tiny nano worlds that heretofore were unknowable,unimaginable and unseeable, until now?
The world around us is going to hell in a hand basket, meanwhile here we dedicating ourselves to decode the mysteries of space, because the power of the string theory of intuition is dragging us to learn, create and to be amongst the first and best Architectural Fractologists of the twenty first century,and this power is bigger than all us!

String theory and the theory of fractal self similarities or lack of similarities,
heretofore and forevermore does not acquiesce to the constraints of  humans brain limitations.
Intuitions are what guided and instructed our primal ancestors : it instructed them which direction to travel in , what foods to eat , and in women, which males were healthy,worthy and wise. The primal women didn't say stop man, i demand empirical proof! They used their intuition as many women do today to instruct them! We owe them so much for their trust and their reliance on their intuition for insight, we owe them so much and  if their intuition was wrong, it would be doubtful you and i would be here to day .
With all due respect, for s31415, the theoretical physicist opinions :,"who is to say what we have to satisfy very specific conditions  for them to have a chance to be compatible with the physics we observe in the world . " if any thing Architectural Fractology teaches us, it is that there are  more worlds variables then there are hairs on your head,and thus the chance for one of them to be compatible with a physics that are existing but to which we are not currently privy to, is plausible !
So Melanchoyman, "just a fools intuition,"patience. ancient ancestors,may they rest in peace,can be considered fools and morons equal to a child. But out of the mouth of a  babes, often comes the truth that will set you free !
So stand up for your intuitions, fight for them if need be, for it is the universes that are  kissing thee! Let them lead thee, surprised you'll be !
Opinions cheerfully expressed, whether in consensus or in disagreement, help understanding and collaboration with one another! Peace be with you .
                                                                                   The fractal forums, the possibilities are infinite!
  

[Melancholyman]

Thank you for that encouraging post, whoever you are. I think I share your conception of the world on many points. It was true enjoyment to read your post. Now I feel better of not being a mathematical genius Just one thing that I think is a flaw with pshysicist ( I have of course great respect) is that the overall conesnsus seems to be that space and time and everything that makes it up is dead, lifeless, and yet somehow we manage to sit down a sunny afternnoon, gaze upon the sunset while Chopin Waltz no.7 in C minor is flowing out of the speakers, could there be anything more alive? It seems strange to presume that complexity at a certain level suddenly creates something that is alive, like us or animals, plants. I think you are very right about women as well, they are what keeps this world from descending straight into hell  I think string theory as I understand it is a beautiful theory, and I cannot help but think that strings are not just "blind force" vibrating in certain patterns creating elementary particles. One problem that is very apparent to me, when reading physics, is that you are always yourself pushing the goal one step further away from yourself. Before string theory, there was quantum mechanics, and as Brian Greene puts it, it cannot account for any explanation of why certain elementary particlas have this or that mass, energy so forth and so on. Now with string theory, voilá! of course the characteristics of elementary particles are due to the vibrational pattern of the string! But then the question arises, why is the string vibrating in that particular manner? If you are to come up with more pshysicist explanations then there will always be one or more questions arising from the conclusions you manage to create. An easy answer is to say, well, of course the string is just another form of life, and it vibrates the way it does because it wants to, thus creating whole of the elegant universe we are living in, but of course it would be childish, insane even to attribute intentionality upon "dead matter". At least the chain of explanation stops lol I think, I said this before on this forum actually, that knowledge is like a fractal, every answer gives rise to one or more questions thus, there will be an infinite number of questions and the number of answers will relative to the amount of questions become zero, beacause the number of questions move ffaster towards infinity (this is a sound mathematical reasoning). Most people would consider this to be the standpoint of a skeptic, why? Look at the Mandelbrot, every branch is a new set of questions, and you can zoom in indefinately and it will give rise to the most astonishing patters, and there is no end to it, doens't this make the fact that there are no answers look beautiful? You can also make the analogy to reality, of course we can never speak about reality and non-reality, how would you know the difference, there is none. Reality is vibrations, the symphony of the universe, this is exactly what string theory says, on a phiilosophical level, and that is what makes the theory so apppealing.

One thing that seems to be true, is that great theories are always simple, elegant and beutiful. Look at the equations for string theory, INSANE, hehe. Now look at the equations for the fractals that we see here on this forum. As simple as can be....

[Kali]

Really good thread... Have lots thing to say about this subject, but no time now. Just wanted to point this about the last posts: I also think that intuition is the key, and that the answer to all has to be as simple as to be understood by many. Maybe the path is complicated, but it should arrive into a surprisingly simple revelation, that will change our vision of the universe dramatically. I think the main problem with science is that it tries so hard to explain what we "normally" percieve, but refuses to explore the ways of internally expanding the perceptions (other than making instruments for measuring), judging all that is not experienced in a "normal" state of conciusness, as "fantasy" or wrongly percieved things.

I will continue later...

Edit: Not really a "problem with science", science is great and I love science... being a science hater is just stupid! What I'm trying to say is that *maybe* using plain science, or our current scientifics methods,  it's near impossible to explain certaings things that *maybe* can lead to the ultimate thruth.

[Melancholyman]

I forgot to thank you s31415 for answering my question about the 4 dimensional object.

Yeah Kali I don't think either that there is a "problem" with science, it's the best way of inquiry we have. I don't want to put it out as a problem either. Maybe what I think is a problem is not science itself as method, but the ontology or metaphysics that many scientists have, I do not think that one should believe in science as purporting the real "states of affairs", but rather as a tooll for inquiry that doesn't pass judgment. And of course it's not scientific inquiry that confer judgment it's the scientists