Hi Vladimir,

I sympathize with the idea that everything (including the vacuum, energy, matter, antimatter, radiation, dark energy and dark matter) should emerge from the interactions of simple units. We have very good examples of complex phenomena resembling particle trajectories or life-like patterns, emerging from interactions of elementary, binary cells arranged in 2-D (Conway) and even 1-D (Wolfram) arrays. Your Kepler packing of magnetic dipole spinning nodes reminds me of Fredkin's theories, e.g. his 3-D Reversible Universal Cellular Automaton model.

The hope of these approaches is to explain the highly complex in terms of the very simple, and I believe that the powerful notion of emergence (in computation) might indeed satisfy this need.

But what I find annoying in cellular automata models, as well as in yours is that you assume (if I understand correctly) an infinite, pre-existing, regular lattice, for the game to start. That's very costly a structure to set up in one shot. Wouldn't it be much cheaper to have the 'ether' structure be built progressively, starting from (almost) nothing? In my experiments with algorithmic causal sets, meant as instances of discrete spacetime, the structure is a directed, unlabeled graph that grows. Depending on the underlying algorithm, some regular, grid-like structure can develop, on top of which localized structures may start playing their interactions; both the 'background' and the actors are produced by the same mechanism.

Also, you attribute some state properties to your nodes, some labels, e.g. spin, in the same way as cellular automata assign a binary state (or ternary, in Fredkin's models) to the grid nodes. Let me just mention that, if one is concerned with (extreme) minimality, there is an alternative approach, that I explore in my essay here: one could try to use stateless, unlabeled nodes, and hope to see everything emerge from the dynamics of the graph growth. Ciao. Tommaso.

Caro Tomasso

Thank you for your interesting remarks. I looked at your paper again and this time I was struck by the similarity of your simulation Fig. 4 lower right to a print illustrating a paper on vortices in the ether by ... Descartes! I had reproduced this illustration as Fig. 22 in my original 2005 Beautiful Universe paper on which my present fqxi paper is based. I definitely do not assign spin states to the nodes! In my model there is an infinite number of possible spin orientations (the nodes are spherically symmetrical and in some cases when the nodes are not rotating they are totally neutral and do not react with their neighbors! The Bloch sphere was just to show how a node may express any quantum state.

I envy you the training and means to simulate your ideas. That would be a very nice way to prove or disprove my and other minimal universal theories. Yes I based my model on a pre-existing crystal-like set of nodes which self-assembles because of induction forces as in Fig. 1 of my original paper. An 'organic' self-generating universe like you propose would be nice too, but my simplistic brain prefers a "nuts and bolts" approach. In the above paper I propose various experiments to prove or disprove the model, and if it is wrong, it is wrong. I also envy you your working in beautiful Pisa where Galileo must have walked and wondered. I will try to study your work more closely.

Ciao Vladimir

    Dear Vladimir,

    thank you for the pointer to the nice pictures by Descartes, which I had not seen before; in fact, the analogy with fig 4 in my essay is only superficial, since the former provides a 'static' snapshot of the vortices, while the latter is a whole spacetime, in which time progresses outwards. But it would be interesting to derive, at least in principle, the causal set for those cartesian vortices, and see how they would look like...

    You are right, the exploration of these models based on the relatively simple interactions of a moltitude of small entities greatly benefits from some simulation, and luckily the software I am using supports such experiments without need of much programming effort (probably less than what you put in your beautiful graphics!).

    As for the stateful (as opposed to stateless) nature of your nodes, I suppose what I meant is that even the fact that a node may or may not be rotating, as you write in your reply, corresponds to a node 'state'. A binary state. You may then consider angles of the rotation axis, in which case the state ranges in a continuous set.

    Dear Vladimir,

    Thank you for your kind remarks on my essay.

    I have not been able to understand from your essay how the Born probability rule emerges from your basic constructs. Maybe you could explain some more through posts here? Thanks.

    For me the emergence of probability follows by noting that there are fundamental reasons why the Schrodinger equation is modified by nonlinear stochastic corrections during the measurement process.

    Best regards,

    Tejinder

      Dear Tejinder

      Thank you for your interest in my ideas - contained in a remark to your very interesting essay here in fqxi.

      My idea about the origins of Born probability rely on a set of assumptions explained at length in my original 2005 Beautiful Universe paper on which my present fqxi paper is based. There was no space to explain things in detail in the fqxi paper kindly access the pdf of my earlier research through the underlined link above thanks.

      Figures pertaining to probability in my theory (section 2.7) are also attached herein as well. The idea is that the Schrodinger equation describes an actual wave of energy sweeping over a set of "particles" which are the universal nodes of which my model is made. It is like a picture moving on an LED monitor screen - the light in a given LED diode changes with time, but the LED itself stays in place. There is no wave-particle duality in my theory. In the 2D case energy in the form of angular momentum from one node is transferred to two adjoining nodes, and each of them to two others so that across the field of nodes the energy distribution has the form of a normal distribution, the bell curve of the probability function. In an actual 3D lattice each node gives its energy to 9 others. It is a diffusion process. These ideas will only make sense in the context of starting physics from scratch as outlined in my earlier paper.

      Please forgive my rather simplistic ideas that emerged from my stochastic artist's brain - if Nature is more complicated than this I will be unable to understand it!

      Your expert feedback is welcome with thanks

      VladimirAttachment #1: BUFIG29_opt.jpegAttachment #2: BUFIG28_opt.jpeg

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      • Post #16

      I am going to have to spend some time with your essay, but it is one with which it is worth spending some time. I have occasionally read that when you study quantum mechanics you are actually studying music. I have some reservations as to this as the currently held notions of music theory are really out in left field - way out. On the other hand, music is physics. It is its own particular physics with its own unique mathematics, which does not include tempered tuning.

      Thank you for replying to my essay. When I decided to enter this contest, I did not know what to expect but I am finding out that it really is an exciting exchange of ideas.

      I am wondering about that 1954 letter that Einstein wrote to Michelle Besso;

      I consider it quite possible that physics cannot be based on the field concept, i, e., on continuous structures. In that case, nothing remains of my entire castle in the air, gravitation theory [and of] the rest of modern physics.

      Suppose he is right?

      Tom Wagner

        Dear Tom

        Thanks for your very interesting note. Of course at the most basic level everything is related, and more specifically we may think of the physics - i.e. acoustics - of music and even of the musicality of some concepts in physics such as the vibrating strings of String theory. Herschel was a professional musician before turning to astronomy. Further back in time there is Newton's correlating colors with notes and Pythagorus' concepts of number, musical scale and the music of the spheres.

        Your own work on Structural Resonance sounds most interesting and I hope to study more about it in detail when you publish the material. Resonance of course is the basis of the first electronic musical instrument invented by Léon Theremin .

        Einstein was a gifted violinist (but that does not make him a string theorist). Your quoting his letter to Besso where he wonders if his physics would be meaningful if fields are not continuous is most relevant in the context of this contest. His core discovery in general relativity that gravity and acceleration are one would still be a key result in a digital universe, his protest to the contrary notwithstanding. I have tried to show in my in my earlier 2005 Beautiful Universe paper on which my present fqxi paper is based that GR would be greatly simplified in a digital universe, reduced to the 'optics' of refraction in a medium of variable density.

        Best wishes for success in your music and physics! Vladimir

        10 days later

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        • Post #18

        Dear Vladimir,

        I like your ideas, but need to reread them. These spinning tetrahedra also sound closely related to Gingras' magnetic spin ice quasi-particle analogy to Dirac's Magnetic Monople.

        This is a post that I left on my thread @ topic #816:

        "Hi Steve,

        I was at the beach for the last couple of days. It was relaxing to get away. What if the "sphere" is a Buckyball that surrounds the Black Hole "near singularity", and "spinning" tetrahedra (Vladimir Tamari's basic idea - perhaps of red-green-blue-white "color"?) are situated at each of the 60 vertices (of the Carbon-60 Buckyball). This would yield 240 degrees-of-freedom similar to Garrett Lisi's E8 roots, but we would only have 3 dimensions at each of two different scales (the 3-D buckyball scale, and the 3-D tetrahedra scale). I've always liked Buckyballs, and one of the discoverers of Carbon-60, Sir Harry Kroto, lives im my neighborhood.

        In case of a rotating Black Hole, the Buckyball symmetry may not be stable enough, and two nested Buckyballs may transform into their homotopic cousin, a lattice-like near-torus (similar to a lattice-like Tokamak) with spinning tetrahedra at each of 120 vertices. This would yield the 480 degrees-of-freedom of a Supersymmetric model similar to Lisi's.

        I need to reread Vladimir's essay, and think more on these ideas."

        Have Fun!

        Dr. Cosmic Ray

        Thank you Dr. Cosmic Ray nice to hear from you. I need to rest my eyes for a while after successful cataract surgery. Will answer your interesting points in a week or so. For a full description of my ideas (with buckyballs included) please read my earlier 2005 Beautiful Universe paper on which my present fqxi paper is based. Lisi's E8 far too complex than need be. A few years ago I emailed Dr. Kroto asking whether a buckyball constructed of dipole "rods" has a weak spot due to Brouwer's theorem (it says a vector field on a sphere always has a vortex) but no answer. More later.

        Cheers Vladimir

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          • Post #20

          Hi Vladimir,

          You asked "whether a buckyball constructed of dipole "rods" has a weak spot due to Brouwer's theorem".

          My guess is that IF the buckyball has a weak spot due to Brouwer's theorem, then this weak spot would be part of a hexagon. Clearly, the pentagons have the wrong symmetry for this type of instability, but if a Buckyball is orientated similarly to Figure 2 of The Nature of Dimensions, then it might have a weak spot (and this weak spot might be partially responsible for inducing a triality of generations). If a sphere collapses due to this instability, then the natural new shape would be toroidal. Two nested Buckyballs are homotopic to a torus, so I anticipate that this new toroidal "lattice" should have the equivalent of 120 Carbon sites (although this "lattice" is comprised of the very fabric of Spacetime near the Black Hole "singularity", and not actual Carbon atoms - the same concept as Subir Sachdev's graphene analogy [Reference 12 of the above linked paper] to the Holographic Principle). If we place a spinning tetrahedron at each of those 120 sites, then we may have as many as 480 degrees of freedom on the surface of our torus (plus the frame degrees of freedom), which may be related to an E8xE8*~SO(32) TOE of order 496.

          I especially like the pentagon symmetries of the Buckyball (and my TOE), because these pentagon/pentagram symmetries lead to the possible application of the Golden Ratio, as experimentally determined by Coldea et al [Reference 6 of the above linked paper], and as pictorially represented by the appendix figure in my essay.

          Have Fun & may your eyes continue to heal!

          Dr. Cosmic Ray

          Thank you Ray for your response and wishes. If Brouwer's theorem (also called the hairy-ball theorem because you cannot comb a hairy ball without leaving a vortex) causes a weak joint to exit in polihedra, this may well be the cause of decay in subatomic particles.

          I will have to re-read your essay and your answers soon. I think we both have the right faith that polyhedral arrangements are the key to the construction of matter. Just to clear one point- in my essays I show a figure of a tetrahedron with what appears like rotation vectors. Such a tetrahedron would be made up of two dipoles on opposite sides their vertices making up the shape. The rotation arrows are to show how such a configuration resulted from a homogeneous field of parallel dipoles involving slight twisting of all lattice points all over the universe (weak linkage but all lattice nodes are involved).

          Indeed nested polyhedra are what would make up particles, whether they are C60 or others. This was the conviction of Buckminster Fuller and of Kenneth Snelson. I think these models should work in and of themselves, not grafted onto existing theories such as the Standard Model, GR , SR and QM (as Lisis's E8 does). I tried to show in a rudimentary and mostly qualitative fashion that such a reconstruction of physics is possible. I am having fun indeed!

          Vladimir

          6 days later

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          • Post #22

          Ray, you are going to laugh,It's the Toe fashion ahahahah no but frankly all people has a toe in fact,you are ok with me I am persuaded it's comic in fact.but it's well it's cool to see all that, a toe hihih the war of toes but of course only one is correct ...extradimensions hihih a toe , and the toe of the day is the the theory of polyhedrisation , tomorrow it will be the theory of really everything, and after the next day, the theory of truly everything. hihihi My spherization is 3D is so far but so far ....me and my rationalities ,I am so far.

          Best Regards thinkers

          Steve

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          • Post #23

          Hi all,

          But it's cool to see all these similarities, I am happy that people makes similarities of my spheres and spherization in 3D ...I repeat in 3D...Sill one in 3D....in fact many of these extrapolations are falses, but it's cool.

          Regards

          Steve

          Vladimir,

          I enjoyed reading your essay. You raise many fascinating points about the fundamental nature of reality. Your node idea is very interesting. I like how you draw connections with cellular automata and qubits.

          Best wishes,

          Paul

            Thank you Paul. The idea that my spherically-symmetric node could be a qubit was not too clear to me in my in my earlier 2005 Beautiful Universe (BU) paper on which my present fqxi paper is based. With new understanding I superposed a Bloch Sphere onto a node in the figure in my present fqxi paper and somehow it all seems to clicks together- if so then in theory all of physics must somehow be reduced to the interactions between a local field of nodes. The (BU) theory needs a lot of work of course - I wish it can be simulated. I can imagine the interactions as linkage made up of 'slippery'spherical gears. Slippery because if they are directly linked like mechanical gears a small local motion must instantly activate all nodes in the universe. OK Steve you have your spheres physics in that form :)

            Best wishes

            Vladimir

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            • Post #26

            Vladimir,

            Very nice! Our research shares a common approach. In relation to your eight distinct states of spin rotation, I think you might be interested in my result contained in this preprint, sidebar 1, figure S1.1 in which the closed, congruent (mod 12) Sophie Germain prime sequence shows correspondence between the least separated primes (11, 23) and (1559, 1583); (479, 491) and (7103, 7151). Reversing the polarities of these four points gives eight states.

            Good luck in the essay contest. I hope you find time to read my entry.

            Best,

            Tom

              Dear Tom

              After looking at your fqxi paper and the preprint I must admit to feeling really unqualified to comment on your work, but will read your paper again - your expertise in number theory and sundry other topic is beyond the range of what I have studied. Over the years I would concentrate on learning whatever happens to be the next item necessary for my research and have obviously lots of gaps in my self-education.

              While sincerely admiring the range of your work, I have to disagree that we have a common approach insofar as the physics itself is concerned. I have not claimed to have eight states of spin rotation - the nodes are spherically symmetrical and can rotate at any solid angle, hence the Bloch sphere representation. An eight-fold symmetry can be obtained however if one considers just the 3D geometry of the node location in the universal lattice.

              Good luck to you too and thanks.

              Vladimir

              Vladimir

              An excellent and interesting paper, which I thought I'd commented on earlier but seemingly not, and have just re-read. It confirmed the reasons why I 'bookmarked' it, as I very much agreed with most of your background sections, and there are some close parallels, but then also the odd major divergence, in your beautiful model. Well done and thanks for the interesting view. I'll try to catch up with your papers.

              I hope you'll read mine if you haven't or perhaps we've already communicated there? I believe I may show you a few options to the directions you've gone which you may appreciate considering (if you haven't) as they seem to open the way to falsifiable solutions. You may also enjoy a short 'logical conclusions' paper with photographic evidence!

              There are a number of consistent essays looking very strong and 'real', currently led by Edwin, which you seem to also be very close to (Ragaza, Parry, Spoljaric, Castel, Wittelman etc etc -see strings).

              Best wishes

              Peter

              PS. loved the drawings too.

                Ooops, that was 'Mittleman!', plus Dan Bendict. I'd expect you may like them all. Do give me feedback on mine (if you haven't!) Too many essays and ageing brain cells!

                Peter

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                • Post #30

                :) it's interesting all that.they turn thus they are .....proportional furthermore with the volumes and their rotations....interesting these similarities , interesting.

                Steve