Hyperbolic Space & other dimensions

Discussion in 'The Science Forum' started by Dashing_Chap, Dec 30, 2010.

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  1. I haven't got a clue about either but I'm fascinated, can anyone explain this in a simple fashion? There's the famous concept of flatlanders living on a curved piece of paper but trying to imagine curved space in 3D is a bit more technical.

    I've found some great videos on Youtube regarding dimensions, I'm still in the process of watching them:










    Further details here:

    Dimensions Home

    Does anyone know about Hyperbolic space? This I suppose has something in common with religion too as God is supposed to exist outside of time and space AKA in another dimension.

    DC
     
  2. Thanks for that DC, great stuff I am still trippin. :) Here's Carl Sagan, a reliable old stalwart, on the subject ....


    and Michio Kaku on 'hyper space' revelant at 5 mins 40 secs into the vid ........

     
  3. A pleasure, it's always fascinated me that there might be other unseen places which we don't have the senses to perceive. That Carl Sagan vid is a good one. Here's a good vid where they use flatlanders on a piece of paper and then cut the paper, loop it round into a Mobius curve and use it as an example of how space can be curved but the flatlanders are unable to see it.



    DC
     
  4. Nothing to do with religion. It is all just to do with the amount of mass in a space. Too little mass, and space is hyperbolic (each point is a "saddle point") - too much mass and space is closed (spherical). Just enough, as Goldilocks would have it, and you have flat space. Okay, as we are already in 3 dimensions, we need to imagine it in 4 which is hard. The best example of a hypersphere (4 spatial dimension sphere) passing through 3D space would be you see a tiny sphere which grows and then shrinks. But that doesn't help you to imagine living on one.

    If the universe is hyperbolic (ignoring the dark energy issue), the expansion rate will slow but never stop - it reaches a limit > 0. In a flat universe, the expansion rate will slow to 0 (mass balanced). In a spherical universe, it will reverse and you get a "Big Crunch" or something similar.
     
  5. Please give up some time to watch this... ignore Dawkins, just listen to what Krauss has to say.

     
  6. Okay - that's fairly standard modern cosmology - what were you expecting me to get from it?

    Krauss didn't mention symmetry breaking wrt vacuum energy - it may have been one of the slides he left out. He didn't mention the contribution of inflation to the flat universe supposition.

    There were a couple of simplifications - the hydrogen atoms in our bodies probably haven't been in a star. The "our Galaxy" of his 100 billion year future will probably be an amorphous clump of at least the Local Group if not more, rather than the Milky Way of today (yes, we are gravitationally bound, possibly even to the Shapely Supercluster).

    And the bugger used my analogy ...
     
  7. I just mull over this stuff and add bits to my more accurate and complete theory for everything…. you will claim that I nicked the ideas from you so forget it…I’m not daft.

    This morning I discovered that Douglas Hofstadter had stole my colony of ants analogy for the human free will… but because I am a random manifestation of molecules pointlessly going nowhere, something inside made me decide not to choose what I thought was right. So I will be doing nothing about it very soon…. :)
     
  8. Huh? I watched this because you suggested there was something important in there. There was little that wasn't in Frank Levin's 2007 "Calibrating the Cosmos" - which (unless I'm even brainier than even I think I am) is an undergraduate level text.

    Okay, once he had glossed over the fact that we have known for decades that the universe is very, very close to flat and stated that it is flat, he made the assumption that flat = 0 energy (probable but not rigorously proven) and therefore (unknowable) that there is no God.

    You clearly didn't get the humour in my suggestion that he stole my Goldilocks analogy (in precise context, I'll point out) for a 2009 talk from a 2011 posting on what, to professional physicists, is an obscure bulletin board.

    Aunt Hillary? Serves you right for not reading (or not understanding) Godel, Escher and Bach before, then. Oh, and that 'pointlessness' is your personal choice (see what I did there!) The universe, physics, quantum mechanics, even the posited divine creator you disbelieve in - none of these impose it on you.
     
  9. As a cluster of molecules in my head were chatting among themselves I overheard one say that Krauss was not the first to spot erotic curves in the cosmos…A well known peeping tom with a telescope in UK once referred to the ‘Bell end nebular’ but the term never found it’s way into text books for some reason… or was it the Bar bell nebular?…Oh well.

    In fact Krauss has little to do other than present ideas from across science that have already been worked upon by others… a kind of Technical Sales Exec on big bucks. As a lay person I was fairly impressed and always willing (with permission from one of the ants) to embrace any theories that do not require a kick start from some divine creator otherwise it’s back to the dribbling board….

    The fiction of Hofstadter may serve a purpose for some but thankfully I can enjoy the contrapuntal genius of Bach without any misconceptions of it’s meaning. This is the way things are, not the way we want them to be.
     
  10. I haven't looked at the videos (no time), but if one of them doesn't cover it, the Poincare disc is one way to get to grips with hyperbolic geometry

    An easy introduction to the subject is Mlodinow's Euclid's Window - virtually no equations.