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How important/fundamental is self-similarity in cosmic structure?

  1. Jun 3, 2004 #1
    self-similarity is a self-evident feature of structure in general- but how fundamental/deep/important is self-similarity? and how extensive/rigorous is self-similarity: are fractal structures simply a ubiquitous emergent quality of processes/form that pop up here and there- or can the Universe [or vacua] be wholly described as a fractal crystallization of equilibrating/anihilating forms out of some fundamental Chaos/Nothing?

    if the universe can be described as a fractal structure is the hierarchy finite in one or both directions of the scale-axis and fundamentally discrete or could it simply seem discrete but be a true infinite/eternal fractal where planck-bits/ string-bits/ etc are really the vast quantized macro-structures of the "next-level down" in the cosmic hierarchy like galactic filimamentary walled voids [which seem to have a roughly quantized cellular structure http://www.anzwers.org/free/universe/universe.html ] or planck-scale brane-worlds or singularity networks which are woven together into the spin foam/ brane/ quantum superfluid aethyr/ etc/ etc/ etc :yuck: - and is our universe simply an infinitesimal region of a "particle" in the next level out? so could scale extend indefinitely/infinitely both micro and macro with all major structures like particles/stars/galaxies having the same basic cyclical structure? [ as is suggested by http://www.amherst.edu/~rloldershaw/ and http://www.fractaluniverse.org/index.php and of course Mandelbrot himself ]

    and finally- even if some of this is "true" is this all just an anthropocentric aesthetic observation or a deep principle of nature? is it just a modern "turtles all the way down" metaphor- or maybe an infinite fractal set of turtles within turtles makes sense?! :wink: :eek:

    my view: I think self-similarity may exist on an indefinite scale and that planck-scale discreteness is an illusion of some structural quantization of a smaller hierarchy- howevever I think that ultimately calling it a fractal structure is a limited anthro-perception and is just an approximation of the fundamental emergent structure of the universe [and multiverse/metaverse ] and it may have no relevance to cosmological theory- just the poetry of pattern-recognition
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    Last edited: Jun 3, 2004
  2. jcsd
  3. Jun 3, 2004 #2
    "Big fleas have little fleas upon their backs to bite them,
    and little fleas have lesser fleas, and so ad infinitum."
    - J. Swift

    It seems that there might be some truth in the idea of the universe having a large-scale fractal structure. However, I think your second paragraph takes the idea a bit too far! Perhaps a better way to view it is that the universe seems to have structure at all scales - at no point do we see it becoming isotropic.

    But that's no surprise really, just look out the window and ask yourself how many of the things you see don't have some kind of self-similar property. It seems natural to at least suspect that the same might be true on much larger scales.

    Just one word of warning. I've been studying statistical mechanics for just a couple of years now and already I have seen far too many occurences where people claim to see self-similarity (or more generally, some kind of scale free behaviour) but turn out to be wrong because they used insufficient data. You really need heaps of data to get the statistics required to claim that something is self-similar so just be wary next time you are shown an argument which runs more on the lines of 'hey, don't these things look the same' than 'look at all this neat data'.

    But anyway, the question of what causes this structure is still a very interesting one. There are now a lot of people (including myself :biggrin:) trying to determine exactly why it is that fractals are so ubiquitous in nature - we call these theories things like "complexity", "chaos theory" and "self-organised criticality" etc. The idea is that these patterns will emerge in any system with enough degrees of freedom, the underlying physics is to some extent irrelevant.

    Matt
     
  4. Jun 12, 2004 #3
    Add the requirement of nonlocal structures as a minimum requirement for the completeness of a qauntum mechaniclal model you get your similarlty expressed in th emost obvious way. Why, for instance does a developing fetus take a direction of progress that is totally unpredcitable using fundamental postulates of science? Why doesn't the fetus simply turn out to be a bag of soupy bio-organisms? Not only is the formation of a stable form complex organic structures predictable by excluding, or ignoring, chemistry and biological model, pedictable, in the same sense that the sun rise is predcitable because it lways happens, but how do you seems so similar to your parents, or siblings, for instane? Using the mantra "DNA" says nothig satisfying minimum requirements for an answer, of the etiology of form and similarity in form. The family DNA in your nose is the same DNA found in you knee. DNA does not carry a blue print of the facial and other physical characteriscs of organic entities around for reference.

    Where/what/how is the resonant structure of coherence to be found? If the scientific community is ever going to be part of this they had better get some focus on and familiarity with the world of nonlocal force exchange dynamics.
     
  5. Jun 12, 2004 #4
    The fractal structure of spacetime is based on two distinct topologies that are not equivalent if the assumption of conserved symmetry of local motion is made. The self-similarity comes up because the scalar quantity derived from this local motion does not depend on the scale but the balance of the two forces inside the local motion and the distances between two points. In vectors notation: [itex]r_i \times F_i \cdot r_j \times F_j [/itex]. The probability is a result of the random permutation of the vectors.
     
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