Hugh,

I like your idea of a digital simulation model in which you view the implicate cosmos as "a dynamical fluid on the surface of a hypersphere". Good food for thought!

You wrote that the "the explicate world of 'It' arises from the implicate world of 'Bit'. For Bohm, knowledge of the implicate order is acquired by insight. What we perceive is implicate order unfolded as explicate order. If so, it is explicate order, as the contents of our consciousness, that is epistemic (composed of "bits") and the underlying implicate order that is ontic ("it").

Also see my response to your comments to my essay "A Complex Conjugate Bit and It".

Best wishes,

Richard

    Hi Richard,

    > If so, it is explicate order, as the contents of our consciousness, that is epistemic (composed of "bits") and the underlying implicate order that is ontic ("it").

    Rather than a binary epistemic/ontic distinction, I would break these up into three categories: (1) an observer's physical environment, the explicate, (2) an objective, shared reality, the implicate, and (3) the contents of our consciousness.

    My category (2) may be best described by "ontic", but notice that (1) is the only thing we can measure, and what we commonly take for "it". Categories (1) and (2) are closely linked by via a (mathematical) transformation, which I think of as (1) from (2) or "It from Bit".

    To properly account for the phenomenology of consciousness, I see Mind as an architectural layer (in the sense of software architecture) below Matter (i.e. not emergent from Matter as in the conventional view). This is what I call "Us" and is what informs (2). Thus my category (3) would correspond to the epistemic.

    (1) Explicate, It

    from (2) Implicate, Bit, ontic

    from (3) Consciousness, Us, epistemic

    Hugh

    Hi Hugh,

    I found this to be an interesting essay. I'm not really sold on the more mystical overtones at the end, but the idea of a search for systematic effects that might arise from the source code of the Universe is a good one. Maybe such a search is a low-likelihood, high-payoff undertaking, like SETI. Rather than looking for evidence that highpoints on Earth are in some way correlated, it seems more reasonable to me to search for correlations at galactic or super-galactic scales. If the idea that most computational power is given to the places close to observers, then I would expect the CMBR to be quite "crude", and the detail in the planet I live on to be very high.

    Cheers,

    Sundance

      Hi Hugh

      thank you for taking time to answer my questions. I really appreciate it!

      In regard to this:

      > The other *proof* I was looking for is that 4-space is unique among all N-spaces (N>2) in the sense that it has the highest degree of all conceivable symmetries.

      you wrote:

      "I think the hypersphere plays an important organizing role, but there are other structures involved. For example, even though any system of great circles is symmetric (the structure at antipodes are mirror images), the Earth itself is not. In fact highpoints do not ever occur at antipodal points. And the cosmos as a whole does not appear to have a mirror symmetry. So there is another geometric factor that breaks such symmetries."

      I'm afraid I meant it in a different context. Here I meant it precisely just as a Euclidean flat 4-space. 4D houses the highest number of regular polytopes (6), while all higher spaces have only 3. Based on this fact and perhaps some others --I'm looking for them-- I want to find a proof that 4D corresponds to the lowest energy state for a... N-dimensional vibrating structure that seeks to conserve its energy. Here dimensionality is one of the properties of this structure -- i.e. it can dynamically be 'compressed' into higher dimensional state or 'relax' by expanding into a lower-dimensional structure/state.

      I visualize it as a dynamic vibrating wire frame of N-dimensions, N>4. I believe that if one takes such a N-dimensional structure, undisturbed, it will naturally settle by expanding into a 4D configuration, precisely because, topologically, it offers the highest degree of symmetries.

      I wonder if you know where I could find the answer to this :)

      Thanks a lot for all your feedback,

      -Marina

      Hi Sundance,

      > Rather than looking for evidence that highpoints on Earth are in some way correlated, it seems more reasonable to me to search for correlations at galactic or super-galactic scales.

      There was interest in this sort of analysis of the CMB about 5 years ago. Jean-Pierre Luminet and also Jeff Weeks have described techniques and results. They basically look for regions of space that appear to be replicated in more than one direction, suggesting the shape of space is, for example, dodecahedral.

      If we want to extend the fractal creasing Landscape Test to the cosmological scale we must decide what constitutes a "highpoint". For example, we might use density, or energy. We also have to decide what we want to use as a "center". Using the Earth as a center is convenient but seems overly anthropocentric.

      Nevertheless, about ten years ago I tested a gamma ray burst catalog for evidence of alignment, but found that source positions were not sufficiently resolved to tell anything. The digital elevation data on Earth had much higher resolution and has a natural geometric center so that is what I ended up using for later analysis.

      > If the idea that most computational power is given to the places close to observers, then I would expect the CMBR to be quite "crude", and the detail in the planet I live on to be very high.

      Whether or not it is true in some objective sense, this is true in terms of our state of knowledge. There is a lot of interest now in finding ways to explain CMB anisotropy of various sorts. But the resolution of current CMB data is good enough to find complex creasing patterns, while the detail we have of our planet's terrain is much higher.

      Hugh

      Sorry.. the last sentence should read:

      But the resolution of current CMB data is *not* good enough to find complex creasing patterns, while the detail we have of our planet's terrain is much higher.

      Hi Marina,

      I am not sure that a lower dimension would provide a more relaxed environment for high-D structures (wouldn't they feel "squashed" by the restriction?), but the lower dimensions seem to provide more opportunities for interesting structures to appear. I can think of some links that might give you some ideas for your research. As far as dimensions go, the ones that get the most attention seem to be 4, 8 and 24.

      In my essay, I discuss the 4D case, which corresponds to S3 and the quaternions. One interesting structure in 4 space that comes to mind is the very symmetrical 24-cell which is discussed by Frans Marcelis on several pages. If you are thinking about models for QM, Philip Gibbs has written about how the 24-cell is related to systems of 2-qubits and also systems of 4-qubits.

      The 8D case is related to S7 and the octonions. John Baez discusses 8 dimensions in his Aug 3, 2013 post here, and a related structure here.

      He previously made the case for 24 dimensions here, including an argument related to harmonic oscillators.

      When it comes to a wire frame compressing and expanding, I think of Robert Gray's jitterbug motion between the cuboctahedron and octahedron, but his all takes place in 3D (i.e. does not change dimension). It is worth mentioning that the cuboctahedron has many nice properties and was a favorite of Bucky Fuller. Perhaps you can generalize this motion for the 24-cell, using the Hopf fibration that Frans Marcelis discusses.

      Hugh

      Hugh

      Good to see you're soaring high on the list -- and I suffered a series of 1's :(.

      As usual, you are a source of wonderful info. Thank you! Still, I have my doubts. I have a very strong gut feeling --and I wish I had something more that this-- that 4D is magic. Think about it, why would Universe be 4D? Why not 5? or pick any other number? I am sure that this is because, topologically, it offers the max symmetries. Mathematicians don't get it, because they are mostly dealing with vectors or fields but an nD _object_, which is, essentially a chunk of n-space, has inherent limitations on number of dimensions it lives in and remain... I forget now, unfortunately, but maybe you will remember, there is some kind of limit, something to surface ratio, that reaches infinity already at n=7. There are topological constrains like this that limit the number of 'real' dimensions -- as in reality to actually a rather small number, Of them, 4D is it. There gotta be many good reasons why universe is 4D.

      Thank you for your feedback and good luck in the finals,

      -Marina

      Hi Jonathan,

      Thanks, good to see you in the top 40, as I "rated you highly". (I guess that's the catch phrase in the contest...)

      The process in the last week has been interesting to watch... it gave me the impression of 183 turtles in a bucket, clambering over each other to get to the top.

      But many of my favorites made it, and I think the organizers have at least 20 good essays to choose from.

      Hugh

      Hi Hugh,

      thank you for your reply. I'm afraid I did not explain myself clearly. You wrote: "I am not sure that a lower dimension would provide a more relaxed environment for high-D structures (wouldn't they feel "squashed" by the restriction?)"

      Not at all. Let me explain. I'm talking about a dynamic, vibrating structure, for which dimensionality is one of its attributes. Going from higher to a lower dimension does not 'squash' it but *unfolds* it. Take an example of a tesseract. Its surface is 8 cubes. You can stack these 8 cubes in 3D, in effect rearranging the 4-volume into a 3-volume; and the length the edge of this 'dimensionally reduced' object becomes twice as long. That's how, in fact, I understand the expansion of space, i.e. the higher-dimensional structure 'relaxes' into a (n-1) structure, which increases the length of its edges.

      Also, when I spoke about your Landscape Test, I had quantum theory in mind, not the macro world. I am not clear yet --have to reread your essay-- how exactly you apply it to the Earth surface.

      .

      I'm pursuing the answer to the question: Why the universe is 4D? Why not 5, or pick any other number. I strongly believe that there is a good reason for this; and my hunch is that, topologically, 4D offers the maximum number of symmetries => in 4D the structure of space finds its lowest energy state.

      When mathematicians and physicists deal with higher dimensions, the objects they consider are limited mostly to points, vectors and fields consisting of points and vectors. Those are 0 or 1-dimensional objects. But a real object, in real n-space, is essentially a segment of that space. For example, a cloud is a familiar object in 3D and so is a billiard ball. Their densities may differ, but ultimately, both are just segments of space with clearly delineated boundaries. These boundaries is what makes them 'real objects' as opposed to points and vectors -- even when a boundary wraps 'emptiness'.

      Now, regarding 'real objects' in n-D, there is a topological theorem, the details of which I can't recall now, but hope you could remember -- and it says that some important ratio of... surface to.. 'something' -? reaches the limit of infinity already at n=7. This implies that there are not that many 'real spaces' that can contain 'real objects', and 4D is very special.

      Again, there _is_ a clear, logical and unambiguous answer to the question 'Why 4D?' I am looking for it.

      Thank you very much for all your input,

      -Marina

      Hi Hugh

      congratulations on making the cut. I left a post in the end of my thread in your blog above and hope very much that we could continue our discussion about 'Why 4D?'

      Thanks a lot for all your input,

      -Marina

      5 days later

      Hi Marina,

      > That's how, in fact, I understand the expansion of space, i.e. the higher-dimensional structure 'relaxes' into a (n-1) structure, which increases the length of its edges.

      When structures are unfolded in this sense, it seems you would have to pick a place to open it, and thus break any symmetry the original structure had (in addition you are changing vex positions as well as changing angles between edges). If the edge length is not a constant, I am not sure what you are preserving when you come down a dimension (e.g. vertex count, edge count? some edge connectivity?).

      I guess the place to start is to decide what invariants you want to preserve when you change dimensions: this helps make precise the sense in which it is the "same" structure when it changes dimension.

      > Now, regarding 'real objects' in n-D, there is a topological theorem, the details of which I can't recall now, but hope you could remember -- and it says that some important ratio of... surface to.. 'something' -? reaches the limit of infinity already at n=7.

      I do not remember a theorem like that. But you might try a site like http://math.stackexchange.com/ that has a topology section and might have people who can answer that.

      > Again, there _is_ a clear, logical and unambiguous answer to the question 'Why 4D?' I am looking for it.

      Here is something from the wikipedia article on Geometric Topology that may provide a clue:

      "Dimension 4 is special, in that in some respects (topologically), dimension 4 is high-dimensional, while in other respects (differentiably), dimension 4 is low-dimensional; this overlap yields phenomena exceptional to dimension 4, such as exotic differentiable structures on R4. Thus the topological classification of 4-manifolds is in principle easy, and the key questions are: does a topological manifold admit a differentiable structure, and if so, how many? Notably, the smooth case of dimension 4 is the last open case of the generalized Poincaré conjecture; see Gluck twists."

      Hugh

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