Essay Abstract

Questions arise both in the physical and abstract reality of what is decidable or undecidable, what is computable or uncomputable, and which events are predictable or unpredictable. This is connected, in some measure, with questions in Mathematics of what is solvable conventionally, what can be computed through extended procedures, and what remains entirely beyond solution or computation. But similar questions arise in Physics; in part because indeterminacy at the Planck scale and quantum uncertainty even in large macroscopic systems force us to redefine what is possible to know with absolute or reasonable certainty. So this essay examines how we may find our way through some barriers to knowing or solving and come to grips with the full extent of what is truly beyond reckoning.

Author Bio

Jonathan Dickau considers himself a Renaissance man, with skills and pursuits spanning academic, artistic, and technical endeavors. With an inquisitive mind since childhood; he never grew up. Since winning a Grammy for recording Pete Seeger "At 89," he continues trying to help the human race harmonize with Mother Earth and heal our planet. Jonathan devotes much time to writing and academic studies - especially Physics and Mathematics - and has presented at several international Physics conferences. He is a member of the ISGRG. Jonathan lives in upstate New York, working mainly in Audio production while trying to finish a book.

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Greetings to all!

I welcome your comments and questions. I hope I am able to answer some of them. I will be dividing my time between reading and commenting on others' essays and answering queries that may pop up here. I will try to read a large number of the entries, but I know I will miss quite a few. I will go first to papers that sound interesting to me, but I want to be broad-minded enough to take in the landscape, and thoughtful enough to visit the work of friends or colleagues.

All the Best,

Jonathan

    Hi Johnathan, I have not read every page in detail yet but hope to return to it. I like the unique perspective you bring and that you are considering matters I have not, or in different ways,too. Your"Physics has arguably been more concerned until recently with discerning fixed laws than with understanding how things vary or how variations in general lead to stable conditions, and there is much we have yet to explore. We may have been looking only in a tiny pool on the shore of a great vast ocean." gives hope for physics, that has concentrated on 'the stable shorelines'. I like your calling out time as the ultimate barrier to knowledge, in that there isn't sufficient time ( our lives are short) to find out all that it might be possible to know. I also mention time but in regard to not being able to see all that exists -Now, as it takes time to receive signals.Regards G.

    Thanks for your kind words Georgina...

    I appreciate your taking the time to read my essay. And I'm glad I made you think about some things in new ways. Looking forward to reading yours.

    Best,

    Jonathan

    For what it's worth...

    I am optimistic about this topic and this year's contest. I already see several entries worthy of my attention, and thoughtful participants looking to promote their ideas in a civil forum. I hope we can all have fun doing that, and learn something along the way.

    Best,

    Jonathan

      Thank you for reading my essay, and to have lost some time in reading.

      I read the Zizzi article, that you recommended me: it is interesting.

      I will take some time to read your essay in the coming days.

      Domenico

        "... as we approach the Planck scale we need to use non-associative geometry." Why do string theorists believe in M-theory with 11-dimensional spacetime? My answer is that string theorists fail to realize that Milgrom is the Kepler of contemporary cosmology. I conjecture: String theory with the infinite nature hypothesis leads to M-theory, but string theory with the finite nature hypothesis leads to Wolfram's cosmological automaton with string vibrations confined to 3 copies of the Leech lattice. Google "fredkin milgrom".

        According to Joy Christian, "It should be fairly clear by now that topologically the EPR elements have far deeper structure than has been hitherto appreciated."

        Christian, Joy. "Can Bell's Prescription for Physical Reality Be Considered Complete?" arXiv preprint arXiv:0806.3078 (2008)

        However, Christian does not yet realize that Milgrom's MOND shall change the way physicists understand the foundations of physics. Consider 4 dimensions of spacetime + 1 dimension of number-hook + 3 dimensions of linear momentum + 3 dimensions of angular momentum + 1 dimension of quantum spin for gravitons. If we think of the number-hook as the gravitational energy-density at the 4-dimensional point of spacetime, then we can link the quaternions to general relativity theory. From this we get two fundamental predictions:

        dark-matter-compensation-constant = (3.9±.5) * 10^-5 together with the Riofrio-Sanejouand model to redefine the inflaton field. (See Pipino's 2019 article.)

          Dearest Jonathan,

          As usual, you wrote a remarkable and interesting Essay. In particular, based on our previous conversations, I am not surprised by your using the fascinating Mandelbrot Set as a fundamental ingredient of this nice Essay. I also appreciated your stressing the importance of the remarkable formula r = 1, which represents, among other things, the foundations of trigonometry.

          Summarizing, this is an excellent Essay deserving the highest score. Thanks for sharing it and good luck in the Contest.

          Cheers, Ch.

            Thank you Domenico...

            I am glad my comment was useful or helpful. I look forward to further interaction.

            Best,

            Jonathan

            Thanks for the thoughtful comments David...

            I find value in the work of Joy Christian as well. People do not appreciate the subtle features of higher-dimensional spheres. I draw your attention to the work of Nikodem Poplawski, who is using the Einstein-Cartan model to derive results similar to what DGP gravity suggests (see Pourhasan, Afshordi, and Mann). As it turns out; Christian has recently written papers with Fred Diether exploring Einstein-Cartan via Sciama and Kibble, to derive a modified Hehl-Datta equation.

            I used to imagine that the only way mainstream folks would consider Joy Christian's work valid would be if he came up with a full-blown Quantum Gravity theory to explain the context. But I think a large class of models with a higher-d origin are in the bulk compatible with Christian's work. I cite a few of the papers relevant to this discussion in my essay. Thanks for reading it.

            All the Best,

            Jonathan

            Thanks for the high praise Christian,

            Coming from you, it means a lot, because I know you are demanding about proper technical rigor. I am glad my hard work on this essay was appreciated Sir.

            All the Best,

            Jonathan

            Glad to hear from you again, Jonathan,

            "r=1 also defines a unit sphere"

            given that there exists no universal reference of scale for either time or space, that deceptively simple statement is key to rationalizing a proportional base volume in theoretical criteria that can be then scaled to the standards of empirical measure chosen (I like cgs). best as always jrc

            Thanks so much John!

            Yes it's true. I have been using r = 1 in my lectures as a talking point for more than 20 years, and it never grows old. People's eyes light up when they see that such a simple mathematical statement can lead to a host of generalizations.

            All the Best,

            Jonathan

            Just a thought...

            It is provable that the Misiurewicz point M3,1 is a repeater, so long as you use the exact algebraic value derived in the endnotes of my essay. However; no numerical value, even the 600 digit result I provide, will remain stable or repeat indefinitely. This is because M3,1 is a repelling point, which means that any point in its local neighborhood displaced from that spot is divergent. So it is not possible to enter a numerical value in that neighborhood that will repeat indefinitely.

            Therefore we have a known property that is not provable or decidable through numerical calculation, because its exact value is a transcendental number. I just thought this fact was curious enough to be worthy of mention.

            All the Best,

            Jonathan

            Erratum:

            I think that my statement that M3,1 is a 0th order branching point is wrong, and it should be considered a 1st order point instead, because it stands to reason we would designate terminal Misiurewicz points to be of 0-order in branching, while M3,1 has one outgoing branch, which makes it 1st order instead. I was not able to find this information in the literature during a quick review, but I will research this further.

            In the meanwhile; I think this correction should stand.

            All the Best,

            Jonathan

            Dear Jonathan J. Dickau, I was impressed with your statement, "Questions arise both in the physical and abstract reality of what is decidable or undecidable, what is computable or uncomputable, and which events are predictable or unpredictable." So I argue that it is necessary to distinguish geometric space from physical space. Geometric space is an abstraction of physical space. Physical space moves relative to itself, because according to Descartes it is matter. Arguing in this way, I showed that the probability density of states in an atom depends on Lorentz abbreviations: length, time, mass, etc. I believe that this is the unifying principle of modern physics, which will reduce the level of unsolvability, uncomputability and unpredictability in it.

            I invite you to discuss my essay, in which I show the successes of the new Cartesian generalization of modern physics, based on the identity of space and matter of Descartes: "The transformation of uncertainty into certainty. The relationship of the Lorentz factor with the probability density of states. And more from a new Cartesian generalization of modern physics. by Dizhechko Boris Semyonovich »

              It interesting your essay. A good essay.

              You use a simple formula to study a simple condensation (simple to obtain using a computer), then you can use the results on this set to obtain general results for condensation.

              I think that each condensation phenomenon, with a general use of critical exponent, that come out from a statistical mechanics study of simple system (for example Ising model), and experimentally tested, to obtain same results (condensation of cluster from short range interaction); then, I have a problem: in a Mandelbrot set there is not a interaction from points, in a lattice, so that a statistical analysis is not possible; it could be possible using different initial points, and consider a swarm of moving points, but there is not interaction (so that the statistical phase transition is improbable); but it is possible that I am wrong.

              I understand that the Mandelbrot set is interesting because of the dynamics is unpredictable a priori, but a Conway's Game of Life (a hypothesis) or the Ising model (a classic analysis), with many different interacting patterns have the semplicity and the statistical complexity of a physical system.

              I tkink that it is possible to use the chaos theory to reduce the dimension of a space dynamics (for example Hausdorff dimension for chaotic system), but almost every differential (or discrete) dynamics system reduce the dimension of the space.

              Domenico

                Thank you for your enlightened feedback...

                Your comments really make me think Domenico. I know there are ways to resolve the Mandelbrot Set from a chaotic initial value, that jumps all over the complex plane and eventually resolves into the Mandelbrot Set we know. You can set the graininess of what is going on behind the screen, in that case, so that what emerges is an averaged value for the outcome of nearby points. And I know there has been some research into fuzzy Mandelbrots, where exact trajectories are uncertain.

                What you seem to be looking for is a procedure like the inverse of the distance estimation method used in ray-tracing, ray marching, and ray forcing algorithms. In that case, we are looking from the outside shooting at the body of the Set from a distance, and bouncing off the repeller sets that surround it. This is used extensively for higher-d fractals. It would indeed be interesting to see if the Mandelbrot outline could be obtained shooting from the inside instead, where if you hit a repeller edge or surface you know you have gone to far.

                Thanks again,

                Jonathan

                Thank you Dizhechko...

                I invite you also to read my essay for more detail, and to discuss the relative merits and faults of my approach. I will definitely get around to reading yours soon, and I appreciate the heads up about what is in your paper. Descartes had a lot to offer, and reviving a Cartesian approach might be the shake-up Physics needs. We will discuss this more later.

                Best,

                Jonathan

                Dear Jonathan J. Dickau.

                In the time of Descartes, they did not think that speed had a limit. Now that we are confident that the speed of light is the highest speed and nothing can move faster than it, we should consider how space, which is matter, resists its movement relative to itself. Therefore, the physics arising from this should be called new Cartesian. I will read your essay again to comment on it from the point of view of a new Cartesian generalization of modern physics, which is based on the identity of Descartes's physical space and matter, in order to bring our views on physics closer.

                However, I noticed this: "This is because M3,1 is a repelling point, which means that any point in its local neighborhood displaced from that spot is divergent. So it is not possible to enter a numerical value in that neighborhood that will repeat indefinitely. " A similar situation arises when I gave the opposite meaning to the Heisenberg uncertainty principle, which has now become the principle of definiteness of points in physical space. According to the new principle, an infinitely large momentum is needed to separate a point from other points.

                Boris Dizhechko