Thanks Ed for your insightful remarks...

It is fortuitous that you started off reading the paper summarizing the idea on which the current essay is based. In my talk for FFP15 in Orihuela; I marshaled a whole raft of ideas supporting the idea condensation and gravity are analogous. And indeed; in the survey article by Barcelo, Liberati, and Will; there are almost 100 references to the work of various researchers working in this area.

But since then; I have found it to be a much broader metaphor - possibly explaining the origin of the laws of Physics. This relates to the comment in the essay that we are living in the lowest or densest fraction, where the universe and cosmology is a process of fractional distillation. In this manner; it is possible to see how the physical laws could only turn out one way, when viewed from a reference frame of material form.

I have to break up my reply, so...

More later,

Jonathan

Jonathan and Ed,

when it comes to *decidability*, it is we whom decide. So its not too off topic to address such ideas as condensation being analogous with gravitation. Its nature's way of conserving space! Where it gets interesting is conjuring up an ontology which could quantitatively account for the actual amount of energy that would behave under gravitational condensate parameters, to explain why that fraction of the total would exhibit inelastic (kinetic) properties, and another fraction exhibit inelastic (electric) properties, yet another fraction exhibiting (fluid) magnetic properties, and the last fraction exhibiting (aetherial) gravitational properties. So while we macroscopically associate polarity with angular momentum, at the discrete quantum level the uni-polar characteristic of both electron and proton might be simple fractional portion functions. The ubiquitous Neutron is said to not have a 'charge', but that may be confused with a critically ballanced fractional portion, in proportion. The same amount of energy in a more confined spherical volume would act orthogonally, 'slaying out' laterally force-wise from any of the imaginary 'plumb-lines' in a manifold of n radii.

If metaphysics is such a bad word, then why do diehard Quants treat superposition, entanglement and the other ad hoc descriptive labels as physical truths. If I choose a realistic metaphor, that's my decision. :-) jrc

9 days later

This topic was perfect for you so I am glad to see a great contribution.

The fixed point ideas are excellent. There are iterative processes in the foundations of physics, such as self-reference in computation and quantisation which could be related. You show how fixed points of iterative processes live at the edge of complexity. This is very cool. It is even possible that the Mandlebrot set itself has a direct role in how this works out.

    Jonathan,

    Reading your essay made me a school-boy again, exploring new thinking and checking my smart phone for terms, thus coming out of retirement. You say you expect this paper to be an exciting exploration of what is possible to know, and what is beyond reckoning. I can relate to that, but being an idealist, I believe that eventually, given enhanced cognition and superior tools, our descendants can perhaps decipher all. After all, on the Kardashev scale, our civilization's level of technological advancement is 0.

    I must admit, your argument is quite persuasive, and most likely, we will be in the dustbin of history well before any Type III civilization achievement. But we must stretch ourselves in argument just as I did in reading your excellent essay.

    Your Mandelbrot Set affords a good abstract fractal in the physical and abstract reality forum in which we argue the 3Us. Also important for chaos theory, an element I note in my essay, its edging showing a self-similarity, not perfect because of deformations.

    It is true that we cannot hope to get near the Planck scale, using current type 0 technology, but what about the technology of a Type II or III civilization which our current bone-headed civilization will probably not reach? As Shakespeare might say, "That is the rub."

    But I do agree that the sheer volume of collected LHC data is a barrier to knowledge, especially if we are trying to settle the case between competing theories only. But I think with enhanced cognitive capabilities and quantum computers, we can head in the direction of new Physics you talk about. Tomorrow's computers may help drive more efficient algorithms or methods to sort things - that hunt for a quicker or simpler way to achieve.

    Hope you get a chance to check mine out.

    Jim Hoover

      Hi Jonathan, congrats, I liked a lot your essay.

      I have some questions, I beleive strongly that we cannot create a quantum computer because we don t know the main codes at this planck scale and whjat are the foundamental objects in fact and nor the origin of these codes philosphically speaking. What are your ideas? regards

        Sorry for being unresponsive folks...

        I've had to deal with complications at home resulting from my Dad's illness and hospitalization. Various tasks required my immediate attention, but now with my father recovering and in rehab, there is more time for responding to comments here - among other things. I'll try to get back to commenters more quickly now.

        All the Best,

        Jonathan

        Thanks for your detailed comment John...

        I think you meant 'splaying out' but the rest of the description was apt. It's not quite that simple of course. What condenses out of a matter-energy soup depends on both the properties of energy and the types of particles that are viable. The Mandelbrot Set appears to show that from quantum foam the cosmos needed to form large enough voids of volumetric space (bubbles) to fit particles as large as a proton before baryogenesis could commence. That is; it reveals a specific mechanism that allows fermionic particles to form.

        I agree regarding the Physics-Metaphysics thing. Being forced up against a wall to explain things that are too paradoxical for an ordinary material world description to fit, will propose things that are about as odd as anything found in metaphysics, Science Fiction, or magical fantasies. Some of it could be true and one has to ask tough questions of the right expert, and know just how to ask them, to find out. Of course; it took a lot of effort just to get to FFP10 in Australia as a presenter to ask Gerard 't Hooft about evidence validating or disconfirming his CA-based quantum gravity theory. But his answer was worth the effort.

        Of course; I was totally floored when the following year at FFP11 in Paris he devoted 4 or 5 new slides to the desirability of obtaining Lorwntz invariance and of the difficulty with doing that in a CA-based theory. So the detailed answer contained a lot of insight into the Physics-Metaphysics balance of his work at the time - but no definite answers on a route to validation or disproof.

        All the Best,

        Jonathan

        Thanks Phil,

        These are exciting times for me, and I appreciate the praise. At this point; I have a handful of mathematical conjectures that, if proven, would demonstrate conclusively the Physics relevance of the Mandelbrot Set. One proof involving the discs around the periphery of the Mandelbrot Butterfly is basically a covering problem and it may benefit from your improvements on the Lebesgue measure.

        Furthermore; this work is a wholesale and explicit demonstration of the notion that your 'Theory of Theories' idea holds water. One of the posters I got lofted at GR22 (through the kind efforts of Profs. Pullin and Agullo - as I could not attend) focused on the fact that M displays analogies for a large number of theories in quantum and analog gravity at once. My Prespacetime article elaborates on this.

        But I see a confluence of work all pointing to a single result as more validating than having one all-encompassing theory - even if that theory was my own work.

        All the Best,

        Jonathan

        I'm glad it gave you the thrill Jim...

        If I brought you back to school days and made you put on your thinking cap; mission accomplished. I am a champion of the idea that future Science will make the current crop of ideas appear lame, but I also think that there are some universal principles and dominating ideas that will have their way within any framework that we or future researchers can devise.

        It is also true that nature will be as it is, regardless of what ideas we apply to understand it. Perhaps many models can contribute to a full understanding, and most will later be seen as special cases of a more encompassing theory.

        I think our level of technological advancement is on a par with our social advancement as a culture. So long as we get or choose leaders who behave like adolescents we are not fit to join the community of space faring cultures visiting other planets. I hope we go anyway, at least as far as Mars, so we can get a taste of the rigors of space and the demands of conquering that journey. We may want to be fully adult, by the time we venture to other stars however.

        All the Best,

        Jonathan

        Thinking about the Planck scale...

        We need to imagine everything is maximally uncertain but can't vary by much. Even dimensionality itself is undetermined, and we must consider that it could have zero or infinite dimensions and the exact number is undetermined and emerges via the process of geometrization. I agree with Smolin that, in a sense, time is more fundamental. But it needs to be woven together with space, and then create volumetric packets (bubbles) large enough to allow energy to congeal into particles of matter, before the material universe can come into existence.

        I think the properties of higher-d spheres, the Lie groups from E8 to G2, and the Monster group, all figure into the background from which the universe emerges, and influence that emergence, however.

        More later,

        Jonathan

        Thanks for sharing your ideas Jonathan. Indeed we don t know what we have at these planck scales, what are these foundamental mathematical and physical objects in fact. We cannot affirm. Have we 1D strings and a 1D main cosmological field creating our geonetries, topologies, matters, spacetime? or a geometrodynamics and points or in my model spheres ? we don t know. I see the generality of this universe like this, but it is an assumption of course, I must prove and I work about this. I consider like you know an universal sphere in optimisation evolution or a future sphere and I consider a central main cosmological sphere sending and coding finite series of spheres playing between these two constants, the zero absolute and the planck temperature. It is a gravitational coded aether made of these finite series of spheres, I consider that they have the same number than this finite serie cosmological of spheres. Oddly I have calculated, it approachs the dirac large number. The relevance of these series if we apply a specific serie is that the space disappears, so the space, the vacuum disappears and is made of particles coded. Take a central biggest sphere and after we applay 3 snmaller around this central sphere after 5 smaller around the 5 and we continue with the number that I have explained. You see that my model is totally different than the strings or the geonmetrodynamics because I consider particles coded and this aether, and so I don t consider that all comes from Waves, fields, oscillations to create this physicality. Now and I work about this , the relevance at my humble opinion is to formalise mathematically these finite series of spheres, a photon is too a finite serie , coded , they are for me like a fuel permitting the electromagnetism, the life Death and the fact to observe, they are just series coded so in resume like all. Now if we fornalise these series, finite with the Hamilton Ricci flow, the cold and heat, the heat equations, the lie derivatives, the lie groups, the topological spaces and euclidian spaces and the poincare conjecture, so it becomes relevant for the distribution and the rankings of our particles and the sortings, superimposings, synchronisations, we can consider the volumes,surface(even the hopf fibrations can be considered here on surfaces of spheres) , the mass, the densities, the angles, the deformations of spheres, the motions, rotations, senses of rotations, the moments and many others. I have even reached this quantum gravitation with this reasoning and in considering a cold Dark matter encoded in nuclei, more a fith force due to a serie of quantum BHs farer than our nuclear forces. I have respected the newtonian mechanics for this quantum gravitation. Like at our cosmological scale this matter non baryonic balances our electromagnetism and heat with this cold. This superfluid gravitational aether is maybe the key to explain all our unknowns and this gravitational aether creates the luminiferous one simply.

        Best Regard

        9 days later

        Jonathan. In my essay "Clarification of Physics--", I introduce a new Successful Self Creation system that adds a new level to the epistemic "horizon". It adds another level to the basis of our knowledge and uses it to develop a complete creation process/result. I think you may find it interesting. Also, I would appreciate your comments on the essay. John D Crowell

          I finally got around to reading you paper. It makes some illustrative points. The associated logistic map is a measure of the chaos on the reals and this terminiates at the Feigenbaum number. BTW, I thought the Mandelbrot set had z в†' z^2 + c.

          The relationship between the reals, complex numbers, quaternions and octonions is subtle. With classical mechanics we have strictly reals, but analysis has behind CM has complex numbers. There is then a sort of covering ПЂ:в„‚ в†' в„ќ where the map is a restriction on this "fibration." With quantum mechanics is more straight forwards. The quantum wave is complex valued and the fibration is from nonabelian groups or Clifford groups for gauge fields onto the complex plane or the phase of a wave function ПЂ: в„Ќ в†' в„‚. Where things get a bit strange is with quantum gravitation, where the spacetime is noncommutative. The similar structure would then be ПЂ:O в†' в„Ќ, where now the base manifold is noncommutative and the fibration is nonassociative.

          Cheers LC

            Thanks for reading my essay Lawrence...

            It is true the Mandelbrot formula can be written z 竊' z^2 + c, and whether you are plotting Mandelbrot or Julia Sets is only a matter of how the c is interpreted. If you choose a single value for every point, what you get is the Julia Set for that point. But if your c is z_0 - the location of the point on the complex plane you are evaluating - then what you get is the Mandelbrot Set.

            Thanks for explicating the subtle relationship between the number types. And indeed it appears that there is an explicit relationship to different aspects of Physics. The quantum gravity regime is the most demanding, in this regard. As we approach the Planck scale, or near a BH horizon, we must give consideration to the non-commutative and non-associative components to know what is happening.

            This brings some interesting and exciting Maths into play.

            All the Best,

            Jonathan

            That is meant to be...

            If you choose a single value of c for calculating every point, and only the z in z^2 c changes, you get the Julia Set for that initial value. But if your c is the same as the location you are iterating (z_0), and changes as you go, this gives you the full Mandelbrot Set. The fun thing is that the Mandelbrot Set is therefore a template for and a table of contents or index of all of the Julia Sets, because each Julia Set seed or initial value delineates the behavior and the character of the form found at that point in the Mandelbrot Set.

            More later,

            Jonathan

            If you read my essay I work with the idea of fractals as outlined by Hossenfelder and Palmer. However, I appeal to a more standard definition of incomputability. The Mandelbrot set in some ways is the mother of all fractals, because the fractal dimension of the boundary is 2 - ε in the limit ε --> 0.

            The role of octonions is something I discuss in my essay, but more in the appendix or supplementary material.

            I am disappointed in how this is going. I entered this contest because the topic has been of interest to me for years. Yet, my essay is not doing well, and I should simply not enter these contests any more.

            LC

            Thanks again Lawrence...

            We are lucky to have you among the entrants. Your essay is of high quality and relevance. I have been pressed for time, and have not had the chance to review and rate essays yet. But I greatly enjoyed skimming yours, and I expect my assessment will raise your score.

            I have to wonder why some decent to fine essays have gotten scores of 2 or 3, but your offering is in the good to excellent range and your score should reflect this. The octonions have been occupying my thoughts a lot lately, and I am contemplating how non-associativity figures into everyday tasks like painting or baking, where cycles are completed in sequence.

            More later,

            Jonathan

            Thank you John,

            I'll get there. It sounds interesting. I have some thoughts along the lines you suggest, but I'll have to read your paper in order to find out if we agree.

            More later,

            Jonathan

            Hi, I composed the following on my side:

            Hi Jonathan,

            Actually that was a general note, However thanks for the kind words.

            I too have only read a handful of papers here. I have been pretty hard at work on this. I have not had much time to read papers or communicate with authors. I am now off work, as we are now into "social distancing." So we have to endure this exercise in Camus' existential angst in his novel The Plague with the expectation this will lessen the impact.

            Stay safe and away from crowds. This virus seems to take older people down a lot. I am not worried about myself much, but I have some concerns with others. My mother is over 90 and I concerns there.

            Cheers LC