Dear Stephen,

You have offered an interesting and attractive written essay. And for me more valuable that you have critical and realistic position, which are close to me. I will reading it more carefully then I will tell you some more certainly. I hope my work ESSAY may deserve your attention because it also call to realism. I think we can have many common points. I hope on your response in my forum.

Sincerely,

George

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    • Post #51

    Dear Stephen,

    I did not yet rated your essay, but now I will quickly do it (on good nine point!) You see as it better for you! (And were from you known the Armenians?)

    All the Best!

    George

    Stephen!

    Thank you for your good attitude. I have some atherantes also; if you see it will reasonable then I will recomended them your work. Kindly let me know.

    Sincerely,

    George

    Dear Stephen

    Just impressed by Penrose

    http://www.ideasroadshow.com/issues/roger-penrose-2013-07-12

    http://www.amazon.com/gp/product/0307278468/ref=as_li_qf_sp_asin_il_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0307278468&linkCode=as2&tag

    Yuri

    I am very keen to bring other people on board with this project. The next steps are even harder than working out the one dimensional model. For example, how does one spin a one dimensional solution into 3-space while maintaining equivalence (I have some ideas)? So any assistance would be welcome.

    So thanks!

    Dear Stephen,

    Your essay is clear, relevant and pleasant to read. The omnet vs asset distinction works well if one considers Wheeler's approach.

    Reading you, I have tried to recognize omnets and assets in my model of quantum observables/measurements

    http://fqxi.org/community/forum/topic/1789

    and it is clear that one cannot identify the dessin/omnet (see for example Fig. 1 (b) and 3 (b)) to its resulting geometry/asset (see for example Fig. 1 (a) and 3 (a). There is no bijection between the omnets and assets, right? In my case there is not bijection. To any simplex (not shown) correspond several unequivalent dessins.

    Good luck,

    Michel

      Hello Michel

      I am working at the moment, so will read your paper and consider your thoughts in that light, tonight, then I will get back to you.

      Hello Michel

      I responded to you on your own page, as a start

      The danger in aligning dessin with omnet is that one may easily forget the distinction between omnets as 'just anything' (what I call possible omnets because the thing we call an omnet, if based on empiricism is not well-founded) and omnets of the actual ontology, being omnets that are well-founded, meaning existing as a consequence of the action of the GPE noumenon upon the possible and actual ontology. Your dessin, if I read you correctly, are models of structures we believe to exist based on empirical studies. They may be a correct description, but would not be well-founded for the Endpoint Rationalist or Endpoint Skeptic.

      I will need to think more on the concept of bijection.

      Thanks for your interest.

      Stephen Anastasi

      Dear Stephen,

      It seems that I am still far from understanding philosophical categories. But it is unimportant here.

      I am preparing a response to your questions and later, if you wish, we can continue our exchange by email.

      I am very glad that you are enthusiastic.

      All the best,

      Michel

      Dear Stephen,

      As you gave a perfect summary of what I did, I don't have much to say.

      You write

      1. "not only does the universe collapse to a single minimally simple omnet, all of mathematics went down the tube with it.",

      The translation of this sentence would be the Belyi theorem (see the step 3 in my Sec. 2 giving the definition of a child's drawing) and the property that the child's drawing D itself is the preimage of the segment [0,1], that is D=f^-1([0,1]), where the Belyi function f corresponding to D is a rational function. All black vertices of D are the roots of the equation f(x)=0, the multiplicity of each root being equal to the degree of the corresponding vertex. Similarly, all white vertices are the roots of the quation f(x)=1. Inside each face, there exits a single pole, that is a root of the equation f(x)=\infty. Besides 0, 1 and \infty, there are no other critical value of f.

      Sorry about the technicalities.

      2. "the thought that a compatibility (i. e., commutativity) diagram of observables has a kind of engine that drives it: a dessin d'enfant (a child's drawing). "

      Yes, exactly. I leave you free to translate it in the GPE language. The point is that you can have many 'engines' for a given compatibility diagram, a kind of redundancy. For your example of the 3-simplex, e.g. the tetrahedron, I just checked that there are 6 distinct dessins/engines, for the 4-simplex, e.g. the 5-cell, there are 13 distinct dessins/engines that can be built with the cartographic group C2+ as the constructor [my equation(1)]. It would be interesting to understant what means this non-bijection in your approach.

      3. Orientabilty: we need an oriented surface like the Riemann sphere, or a torus, not a Möbius strip (that is not oriented). Thus the dessin is more than a graph and corresponds to a permutation group P with two generators, as given in my step 2 of Sec. 2.

      One needs to develop some familiarity with these concepts, then they become natural.

      I anticipate an unexpected and fascinating complementarity between your approach an the one based on Grothendieck's concepts.

      Thank you for your enthusiasm about this work.

      Michel

      Hello Stephan

      Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html)

      said: "It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don't know why that is - it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn't look at all like the way you said it before. I don't know what the reason for this is. I think it is somehow a representation of the simplicity of nature."

      I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.

      The belief that "Nature is simple" is however being expressed differently in my essay "Analogical Engine" linked to http://fqxi.org/community/forum/topic/1865 .

      Specifically though, I said "Planck constant is the Mother of All Dualities" and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism ... and so on.

      Taken two at a time, it can be read as "what quantum is to classical" is similar to (~) "what wave is to particle." You can choose any two from among the multitudes that can be found in our discourses.

      I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!

      Since "Nature is Analogical", we are free to probe nature in so many different ways. And you have touched some corners of it.

      Best,

      Than Tin

        Dear Stephen -

        I agree with your approach - you rigorously re-evaluate our fundamental assumptions, and force the reader to do so - and I like your coining of new terminology so as to avoid 'putting the new wine into old bottles' as one might say.

        As someone wrote on my page - 'The Universe doesn't explain itself, it presents itself to us.' And you take this all the way and define a non-anthropocentric model, which is a bold and unique undertaking.

        I'd be curious to see how you'd apply this imaginary universe to my paradigm, where the Cosmos is described in terms of the correlation existing between Inorganic, Organic, and Sensory-cognitive phenomena.

        I'll certainly re-read your paper - it's a little difficult to absorb all at once - and hope you have time to look at mine soon.

        I also wish you all the best in the competition -

        John

        Hi Stephen,

        to let you know I have replied to your questions on my essay thread.

        Hope to read your essay soon

        I have not understood the relation without Causal Dynamical Triangulations. Can you day more about it. carlo

        Thank you Carlo

        As is pretty obvious, the Harmony Set as shown is a one-space interpretation. Simply, because this model has to be a proper world model (for reasons shown) it remains for the investigator to find how the system gives us our world, as opposed to 'a' world.

        After a long, long period of thought (which of course doesn't make me right) I tried to interpret the system by maintaining equivalence (under the GPE) and distributing the values into three dimensions, assuming that the formulas of mathematics applied to this distribution as much as it does in our present models (this is not strictly allowable for the endpoint rationalist because first one must show how Pi comes to be, but I have no really big concerns there for the moment).

        Doing this redistribution is allowable because of Kant's argument about our never being able to say that a particular world model is reality, meaning 'the' world model (I know this seems to be the antithesis of Kant, but it has the opposite effect for an endpoint rationalist--I can explain in more detail if needed). All models that add up to the values of the Harmony Set are valid.

        Doing this redistribution brings the number i into existence, as the square root of a negative pointing vector, which, combined with the exponential nature of the Harmony Set suggests a possible connection to Schrodinger's equation, and hence Feynman's Path Integral, but in a summation form (as in CDT). The redistribution however, provides an almost flat universe in all but the center, in a region that might be around the Planck scale (one would have to show equivalence between the scale of the Harmony Set and that of the real world, but there are ways to work with this). This flat system applied to the real part of the solution. The imaginary part could be doing anything -- I don't know how to work with this second part in this very different context. While the real part suggests that space is essentially flat except locally, I'm looking for an interpretation that implies more interesting structure.

        One way to achieve this is to begin the development probabilistically. That is, consider the boundaries to be point like structures, and ask oneself where the next point must go, given the boundary condition of maintaining equivalence. In two dimensions, one gets into bothers quite early. In three dimensions placing the first four points is easy, and, with the digraph connections they produce first a line, then a triangle (implied 2-space, not embedded in higher spaces) then a tetragon, and all forms are equivalent under the GPE (e.g. any interaction can be swapped with any other and the same form results). The form of CDT has it that triangles are 'glued' together along their lines, but in the Harmony Set these lines are necessarily glued, because they are ontologically dependent, so if this is a valid world model one might expect CDT to be an expectation. The difference of course is that CDT, if I understand it correctly, assumes a much larger world model initially, where mine brings the world into existence a step at a time (literally).

        To continue adding points and their interactions starts to get more challenging after this. Equivalence can be maintained by assuming extra spacelike dimensions, but doing so leads to another tetragon in 4-space, then another set of these in 5-space and so on. I don't know what to do with these, but this seems to be a bit like CDT's idea of 4-simplices. Another way is to simply add the point to the outside of the initial tetragon, which under equivalence might go in any of four places, but, in the absence of an oriented space, all four places are the same place (meaning the same form arises). The same applies as one adds the next three points. My concern here, as endpoint rationalist, is that I'm not completely convinced of this approach because the bi-vectors have to be 'stretched' to make it fit. But such stretching seems to be the same form as CDT's simplices, as best I can tell.

        Lastly, one interesting thing for me is that CDT hits a wall when it aims to reduce its length scales to zero. They can't do it, and I don't think they should be able to do it, if the tenets of my armchair universe stand (which, under endpoint skepticism leading to endpoint rationalism, they ought, which is a stronger argument than that of empiricism).

        Of course, there is a long way to go with this development. I need someone with a strong knowledge in philosophy (metaphysics), mathematics and physics to talk to about it, but, as this is so far away from present science, finding such a person is likely to be difficult.

        Thank you for your question. Feel free to ask other questions.

        Stephen Anastasi

        Stephen,

        This "ontology" does not even mention any substance? There is an infinite number of truth systems that may describe the universe from a specific point of view. Each truth system requires at least one rule of impossibility that defines it along with the mother of all impossibility, the rule of non-contradiction, required for the system to be internally consistent or "logical". I think, that all points of view require two or more impossibilities while the universe could require two rule of impossibility, that of the non-contradiction and the rule of existence. This is because beyond the question of the logical consistency, there is the question of "existence" and substance. So, the universe needs this other rule, either of impossibility or one boundary rule on the possibilities of existence. This last one would give direction to the whole thing; evolution, time, future ...

        [12] is missing. I have Lowe's possibilities of metaphysics... I did not give him good reviews...

        Marcel,

          Hi, Stephen,

          Wow, what an impressive, well-written and literate essay! I wrote more details after your comments and questions on my essay, "It from Bit from It from Bit..." This seems a good way of tying feedback and nonlinearity into the picture. Also, as I noted there, I'm looking forward to your book when it becomes available.

          Best wishes,

          Bill McHarris