Jonathan,

Perhaps I missed it. I see no mention of the chief characteristic of the Mandelbrot set -- self-similarity.

What's interesting about this characteristic is that it emerges from an arbitrary function in the complex plane, to become a completely coherent object at any choice of scale. In other words, the global set looks like any local subset. This being so makes it the most symmetric object in mathematics. Just as a see-saw depends on weight distribution to induce an oscillation, so does symmetry depend on a compensating factor -- time in this case -- equal areas in equal times, as Kepler formulated it for planetary orbits. Nonequilibrium states of asymmetry therefore, are due to a symmetry principle. To know this, however, we have to appeal to a measure space -- and the 2-dimensional measure space of the Mandelbrot set is infinite.

If gravity is subject to self-similarity, then it is fundamental.

My opinion. Though I find your essay well argued and well written, I have to disagree. Let's debate.

All best,

Tom

    Is anyone else experiencing this loss of format? Is it my computer only?

    Thanks greatly Tom, | As it turns out, I could probably argue some of your points using my diagrams with different identifiers. And the FQXi system appears to be turning all carriage returns into the character n; maybe they wanted to replace them with en-dashes, but this formatting glitch is pretty obnoxious. For FFP15; I showed that any of several different constructions lead to the same conclusions. Absolutely; self-similarity should be added to the list. In fact; I used self-similarity as part of my explanation in a recent reply to Christian Corda. | The attached image file illustrates that variations on either side of the Misiurewicz point are self-similar but appear in opposite phase! This makes the gravitational horizon like a mirror in reverse. In the diagram; the Schwarzschild event horizon is seen to correspond with the virtual ground or amplitude null at the summing junction of an inverting feedback amplifier - a common op-amp configuration. But perhaps we can think of the feedback resistor as sitting at the surface and bringing those reverse-phase variations across the BH event horizon. I tried to add a second attachment, arXiv:1610.08518 - but it was too large - and I had to create a text file because it would not let me delete it without losing my message. | Ahh, computers... | All the Best, | JonathanAttachment #1: 1_MandelAmp2.jpgAttachment #2: null.txt

    I can include a link, however... | The paper I unsuccessfully attempted to attach above is [link:arxiv.org/abs/1610.08518]Entanglement area law in superfluid 4He[/link]. | Enjoy! | Jonathan

    Its systemic... that 'n'.

    Jonathan, your identifying an approximate time for the problem is about three hours after the most recent uploading of three essays to the output display.

    I thought on reading your essay that the item about phase reversal on either side of the Misiurewicz point was perhaps the most important thing you addressed. If we look at a naïve model of condensed matter with the Maxwellian identification of c proportion between magnetic and electrostatic intensities in a point charge, then hypothetically we might argue an ontology that boundary conditions of density are by c, c^2, c^3, and c^4. But if phase reversal occurs at those junctures it might resolve the problem of how an electron can have a uniform negative charge and the proton a positive charge without a directional physical rotation, and without counter-rotating torque on vectors. Very similar to the inversion by a simple lens. jrc

    I also wish to announce this... | Just published in Prespacetime is the paper I wrote for last year's Gravity Research Foundation contest for essays on gravitation, entitled "How Simple Can Gravity Be?," which outlines and further discusses some of the ideas presented in my FQXi contest essay. | I am also working on Supplementary Notes for my essay, which specifically address some of the things not understood by my readers, and which provide more background for the ideas presented therein. | All the Best, | Jonathan

    I continue to think on this...

    And I thank you for your excellent thoughts John. A perfect mirror surface is the analogy of a white body, reflecting all light that strikes it, so an inverting mirror is what the black body surface represents. It looks like they fixed the formatting problems, because I didn't see your carriage returns replaced by n in the entry above. Did you know that the words 'think' and 'thank' both stem from the same root word 'tong' - which is a device used for picking things up and turning them over or around for inspection?

    All the Best,

    Jonathan

    Thank-you Jonathan,

    I did not know that. But ironically I spent a dozen years from my early 20's handling 300# blocks of ice and lesser chops with a set of tongs. I preferred a strap handle where others liked a two handle. ("There's no such thing as cold. Cold is the absence of heat.")

    I think Tom's point is interesting also. And its the interplay of symmetry and asymmetry that becomes fascinating, like you spoke about of teaching methods. I am reconciled to my naivete, and know at times I can't help but be a pest. I came too late to the party of what mathematics really is to attempt a comprehensive study, comprehension is my goal. One thing for certain is that symmetry is essential to achieving empirical measurement, but that also is a mathematical requirement more than a physical absolute. Epistemology, I guess. Its the actual math that for me is the unnecessarily complicated, mindless chore unless I can intuitively see a reason for chasing it down. And even then I have a bear of a time remembering the symbolic meaning of function. I think it goes back to working nights in high school and having to cover for my folks when a creditor would call who was my algebra teacher's spouse. But I do enjoy how much enjoyment you all show in the endeavor, and have managed to learn some of real value. And I get a good laugh at my audacity at times trying to figure out what people are talking about. What I like is that Physics is about that which is physical and trying to puzzle what is.

    All the best. jrc

    Thanks greatly John,

    Keep on learning. Keep plugging away. Math is not hard or easy, but it is very demanding of accuracy and precision. Not all Math is so mundane that it is tedious. Keep at it until you get to a better class of problems.

    All the Best,

    Jonathan

    Hi Jonathan,

    Another good essay and interesting thesis. I also read your Gravity paper. Of course all very speculative but speculation is essential to find the way round present barriers to understanding (your; 'Impasse'). John Bell said of QM it would take an 'astonishing leap of imagination.. which would amaze'.

    Actually I do hope you'll get to my essay (and Declan Traill's short code & plot) as after trying many such leaps, amazingly one seems to have worked! And yes, it came from a more complex partial symmetry of momentum on a condensed electron than the imaginary 'spin up/down' Bohr allowed for.

    You identified; 'Condensation is a natural consequence of thermodynamic cooling that also arises in the context of emergent gravity theories'. Yet for Higgs and 'pair production' it seems to relate more to an additional macro spin state in the dark energy or 'sub matter condensate' whatever that is (smaller fractal spins?). I don't think the thermodynamic view has born fruit (or maybe now will), have you seen advances?

    But I vote Yes & No, Gravity is a fundamental effect but as a consequence of the process condensing matter, which just any relative 'motion' seems to do. Then isn't the real question; what is the Mandelbrot set, and matter, 'made of'?

    Very nice job & best of luck.

    Peter

    Respected Prof Jonathan J. Dickau

    ..............Reply.......

    I posted the revised abstract on Jan 2, I was travelling and I posted an earlier essay by mistake. I was in Bhilai for few days then. I know FQXi will not change the essay

    .....May please see... sorry for the error....

    Author Satyavarapu Naga Parameswara Gupta wrote on Jan. 2, 2018 @ 21:58 GMT

    .............Your words.......

    I am sorry to disappoint, Satyavarapu...

    ..............Reply.......

    No disappointment sir, I am trying to understand your nice observations about this model, it is a learning for me....

    .............Your words.......

    There is some value to various ideas featured in this essay, but it is full of basic errors that seem to reflect a fundamental misunderstanding. Perhaps you have under-estimated the depth of the problem, or perhaps you have some misconceptions about what the endeavor of Physics should be. However; if I was sent this paper as a reviewer for any of the journals where I have been a referee, I would have to say it has some flaws too deep to fix. Academic reviewers often use a three strike rule, where once they see 3 major flaws they will stop reading and if they are kind, they will enumerate those errors.

    ..............Reply.......

    I want to learn the basic errors in this model, you will be pointing out....

    .............Your words.......

    I read the whole paper, however. So I'll start with the color vs frequency issue; do you realize that blue has a higher frequency than red? In several places; you appear to be saying the opposite. I think you mean that wavelength increases are a red shift while decreasing wavelengths indicate a blue shift. I agree, by the way, that evidence for blue-shifted galaxies is often ignored, and people have the false impression that everything in the cosmos is red-shifted. ..............Reply.......

    Author Satyavarapu Naga Parameswara Gupta wrote on Jan. 2, 2018 @ 21:58 GMT

    .............Your words.......

    At the 2nd Crisis in Cosmology conference, back in '08; more than one speaker cited blue shift evidence in their talk.

    ..............Reply.......

    Some references please

    .............Your words.......

    I also agree with your basic premise that gravity can be treated as a kind of frequency shifting phenomenon. There have been a handful of serious academic papers about this, and it is an interesting topic to explore. Unfortunately; a much deeper understanding of things like virtual particles and photons, wave-particle duality, energy of motion, deBroglie wavelength, and so on, is required for a factual treatment of this subject. You come up short.

    ..............Reply.......

    May please see my paper on Nucleosynthesis

    https://vaksdynamicuniversemodel.blogspot.com/p/10-feb-201-6-all-my-published-papers.html

    .............Your words.......

    I think you got lucky, because I already rated this paper a few days ago, and I was likely more generous than I would be today. Even with some of the deficiencies; it would not be so bad except for the exaggerated claims. But the fact you make such bold promises without a firm basis is offensive.

    ..............Reply.......

    Thank you very much, I am sorry for the mistake done in a hurried way.... I did not intend the post wrong paper...

    I did not rate your essay yet, I did not give less than 10 to any one or I refrain rating that essay...

    Hope you will read the posting on Jan 2nd.

    Hope you will point out some more mistakes... So that I will correct my self...

    Thank you for the valuable time you spent on my paper and work...

    Thank you for the blessings...

    Best Reards

    =snp

    Jonathan Dickau

    I forgot to ask what you mean by 'pedigree', as you said on my page. (English is not my normal language.)

    Regards from ____________ John-Erik Persson

      Oh.. I understand..

      I was saying that the good Dr. Herr Einstein himself had written about some of the things you conjecture years ago. Even though the model was set aside since the Michelson-Morley experiment claimed to be a disproof; many esteemed scientists considered similar notions, at one time.

      All the Best,

      Jonathan

      Jonathan Dikau

      Thanks for clearifications.

      I have proved why Michelson and Morley's tests and stellar aberration cannot give any indications regarding the ether wind. You can see this also at my blog page at:

      http://www.naturalphilosophy.org/site/

      Regards from _______________ John-Erik Persson

      Jonathan Dickau

      I agree to the statement that gravity is fundamental. However, gravity is a property of the ether and the ether is even more fundamental.

      Your reference to Osheroff is important. An important hindrance to making discoveries is the illusion that we already know.

      Einstein added mistakes to an already confused situation. He realized that when he was older. One mistake was to assume clocks without errors.

      Thanks for many links.

      Unfortunately I am not qualified to give an opinion regarding Mandelbrot's fractals in relation to physics.

      Best regards ___________ John-Erik Persson

      Hi Jonathan:

      Your statement is intriguing - "And yet, there is a debate among scientists as to whether gravity is a fundamental force of the universe or not. "

      Stretching your logic further, my research shows that anti-gravity is fundamental reality that explains 96% of the missing universe from the current mainstream theories. I would like to draw your attention to the missing fundamental physics governing - "What causes a photon to accelerate to the speed of light?" I would like to invite you to look into my paper - "What is Fundamental - Is C the Speed of Light". that describes the fundamental physics of antigravity missing from the widely-accepted mainstream physics and cosmology theories resolving their current inconsistencies and paradoxes. The missing physics depicts a spontaneous relativistic mass creation/dilation photon model that explains the yet unknown dark energy, inner workings of quantum mechanics, and bridges the gaps among relativity and Maxwell's theories. The model also provides field equations governing the spontaneous wave-particle complimentarity or mass-energy equivalence. The key significance or contribution of the proposed work is to enhance fundamental understanding of C, commonly known as the speed of light, and Cosmological Constant, commonly known as the dark energy.

      The paper not only provides comparisons against existing empirical observations but also forwards testable predictions for future falsification of the proposed model.

      I would like to invite you to read my paper and appreciate any feedback comments.

      Best Regards

      Avtar Singh

        Dear Jonathan

        What an intriguing, thought-provoking essay! I really liked it. Asymmetry ought to be an important factor and should be investigated thoroughly, especially since nonlinear systems can generate it rather easily. I also appreciate your use of the Mandelbrot Set as an alternate to standard group theory. I have posted a more extensive reply after your comments on my own essay, so I won't repeat those ideas here.

        Keep up the good work.

        Best wishes,

        Bill

          I greatly appreciate your respect of this work Bill!..

          I am so glad that this essay has earned your approval, and also that my work with Mr. Seeger was also enjoyed. One tries first to get it right, to set out things exactly as they need to be, and to nuance every phrase or transition. Only then can we wonder about whether our message was communicated or is worthy of recognition. Your apt message was elegantly well said sir, so I will take your approval as high praise.

          All the Best,

          Jonathan

          I'm happy to see you here Avtar!

          I have downloaded your essay and started reading.

          Warm Regards,

          Jonathan