Jonathan,

Are you familiar with Keenan Crane's GPU code for ray-tracing the Julia set?

https://www.cs.cmu.edu/~kmcrane/Projects/QuaternionJulia/

About inverse ray-tracing, I'm not sure that would work well. You'd have to assume that the ray can penetrate the mesh many times, and that it's only the last (the outermost) penetration which counts. This is inverse of the regular method, where the ray only has to march to the first penetration point. I hope this makes some sense... I'm not a mathematician.

Just for fun, I'd like to mention something about the Julia set: Normally one uses the quaternion magnitude to determine if a point remains within the set. The path followed by the quaternion not only has a magnitude, but also a total length and total displacement. These three properties of a path are all different in value (histogram). However, they all produce the same fractal shape. I would have thought for sure that the shapes would be different, but they're not. Weird.

- Shawn

P.S. Haha! You have The Beauty of Fractals too! Page 61 is my favourite version of the Mandelbrot set!

8 days later

Dear Johnathan

Thank you for your kind comments on my essay. You are correct re the way I have structured it. My overall point is that I think there does need to be cojoining of physical theories with ontological landscapes. A new mathematical-physical-philosophical language formal in its nature that allows us to better categorise but also expose the landscape of what we think we know and what we do not. I look forward to commenting on your paper before the deadline.

Also, I have gotten into Seeger after reading your Bio. In particular the songs 'little boxes' and 'what did you learn at school today' are remarkably profound. So many people live narrow, controlled, social lives, but as they are the vast majority those outsiders who sit on mountains although wise, are lonely and frustrated. Being right or being a fool... how should one live.

    Thanks Jack,

    Little Boxes was actually a collaboration with Malvina Reynolds inspired by the comment of local resident Fred Mercer, an architect, who described the row houses in Levittown as 'ticky tacky.' And yes; we need to build those bridges connecting Physics back to Ontology. Some try to do that, but plenty are content to 'shut up and calculate.' I'd rather find some meaning; thank you.

    All the Best,

    Jonathan

    I don't think the universe is dead yet Shawn...

    But we might be, and just not realize it yet. I tend to be a little less gloomy, although I am told my 'Professor Snape' imitation is spot on. And my 'Boris Karloff' is right up there with the best. But seriously; how about 'all symmetries are broken eventually.' That's a bit closer to the truth.

    Thanks for reading.

    All the Best,

    Jonathan

    I do have Crane's Quaternion Julia program...

    And in addition to "The Beauty of Fractals" I have "The Science of Fractals" "Fractals Everywhere" "The Fractal Geometry of Nature" and a few other Fractal or Chaos Theory related or included books. I like and would recommend "Turbulent Mirror" by Briggs and Peat because it explains a lot of stuff relating to the edge of chaos and what lies beyond its boundaries. Fun stuff.

    More later,

    Jonathan

    A point of interest...

    I mention in my paper that there are 3 types of Misiurewicz point in the Mandelbrot Set. At all Misiurewicz points; the scale factor goes to zero where patterns of repeating forms get smaller and smaller coming to a point, and then exhibit one of 3 behaviors.

    Type 1 are branching points where one path in then splays out into multiple equally spaced (near the center) branches. Type 2 are what I call inflection points, having one path of entry and one path of exit (2 external arguments). Type 3 are terminal points, where repeating forms get smaller and smaller along one thread - and just stop.

    The Mandelbrot Butterfly I discovered about 32 years ago is useful in the study of these points because Type 2 Misiurewicz points are rather innocuous and hard to spot, but they have great importance for understanding formation. The Butterfly figure lets us identify, label (by pre-period), and classify these points which would otherwise remain hidden.

    I am writing something up about this.

    All the Best,

    Jonathan

    Dear Jonathan,

    Please forgive me if I see you first of all an artist who intends "trying to help the human race harmonize with Mother Earth and heal our planet". If only we all were children-like like you. I feel guilty for even blaming Fourier wrong.

    Eckard Blumschein

    Thanks so much Eckard,

    I think that play gets to the heart of learning. No need to feel guilt over your critique of Fourier either, because it's what brains do - one half always putting things together and the other taking them apart.

    Glad for your visit,

    Jonathan

    Jonathan,

    You quickly noted my posting. Hope you get a chance to read it. I am printing out yours, as I plan to do for several. It looks weighty in message so I will do my best on it.

    Later.

    Jim Hoover

    Dear Jonathan Dickau,

    I was about to comment on your essay when I realized that I was not reading your essay, I was reading another of your papers, "Gravitation by condensation." I've now read the essay and have a few remarks.

    You explore a large conceptual realm, and most of what you discuss cannot be proved or disproved, a point you make up front. In this regard you observe that

    "Things requiring proof or explanation by one person may be intuitively obvious to another..."

    I meet somewhat regularly with a physicist who is adept at proof and seems to have no intuition. It seems those who have weak intuition do not value it much. I find your Mandelbrot map an excellent metaphor for math. One can infinitely branch in any direction, but without intuition, it's just turning the crank - only intuition can drive the boat - mere calculation is endless (turning computers loose to calculate endlessly as in Mandelbrot is quite interesting, and hopefully enlightening.) You've certainly become good at making analogies and you seem to have honed your intuition in this regard. Once the data has been generated, our pattern recognition can reduce the dimensionality and discern features and regularities. For example your remark on the interplay of local symmetry and global asymmetry in M is possible only after one has produced the map. One would probably find it difficult to predict from the generating equations, but after seeing it in the data, one can probably identify relevant aspects of the equations. Also quite interesting is structure with pre-period 3 (the delay before repeating) then it repeats every time.

    As we have discussed, I believe that focus on convergence and condensation is potentially extremely valuable.

    You note that "the main difficulty theoretical physicists face in crafting a unifying theory of physics is that in relativity time is flexible, while in QM it is absolute." My essay will deal with this, and I think you might find it interesting.

    I'm encouraged that Foundations of Physics published three papers in November 2019 analyzing the mismatch between relativity and intuition, so the topic is not dead.

    And like you and Rick Lockyer, I suspect 0HCR is telling us something important, but I'm not sure what.

    Best regards and good luck,

    Edwin Eugene Klingman

      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