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FQXi FORUM

September 25, 2021

CATEGORY:
Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020)
[back]

TOPIC: What is Beyond Reckoning? by Jonathan J. Dickau [refresh]

TOPIC: What is Beyond Reckoning? by Jonathan J. Dickau [refresh]

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.

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.

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

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.

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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

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

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

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"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

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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

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

Oh Jonathan,

I was cogitating on your observation that transcendental numbers are non-computable (in proofs) and last night there was a mention of Fermat's Last Theorem on a TV Sci-Fi program which made me wonder if Fermat's cryptic note in the margin wasn't referring to a proof of the non-calculable form of his theorem; but that the incalculable identity of the theorem was itself a proof that such mathematical entities as transcendental numbers were non-computable? Mathematics is, after all, an artifact of human intellect. best - jrc

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I was cogitating on your observation that transcendental numbers are non-computable (in proofs) and last night there was a mention of Fermat's Last Theorem on a TV Sci-Fi program which made me wonder if Fermat's cryptic note in the margin wasn't referring to a proof of the non-calculable form of his theorem; but that the incalculable identity of the theorem was itself a proof that such mathematical entities as transcendental numbers were non-computable? Mathematics is, after all, an artifact of human intellect. best - jrc

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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

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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

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"... 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.)

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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.)

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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

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

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.

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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.

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Just a thought...

It is provable that the Misiurewicz point M_{3,1} 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 M_{3,1} 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

It is provable that the Misiurewicz point M

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 M_{3,1} is a 0^{th} order branching point is wrong, and it should be considered a 1^{st} order point instead, because it stands to reason we would designate terminal Misiurewicz points to be of 0-order in branching, while M_{3,1} has one outgoing branch, which makes it 1^{st} 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

I think that my statement that M

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 »

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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 »

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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

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

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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

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I have begun to read your essay Boris...

More about it on your page. It seems you have some interesting ideas. I'm not sure I see it all fitting together seamlessly. But such is the path of progress.

We may well agree that Descartes was ahead of his time, and that some parts of his methodology still have value for today's Science.

All the Best,

Jonathan

More about it on your page. It seems you have some interesting ideas. I'm not sure I see it all fitting together seamlessly. But such is the path of progress.

We may well agree that Descartes was ahead of his time, and that some parts of his methodology still have value for today's Science.

All the Best,

Jonathan

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

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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

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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

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

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

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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

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

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Dear Jonathan,

your essay touches on many interesting themes. You start off with what I've heard described as the 'edge of chaos'---the site of interesting complexity where the strictly and sterilely lawful and the completely unstructured random meet, and where consequently interesting phenomena occur. Wolfram has extensively written about his 'Class 4'-cellular automata, which are capable of showing persistent, nonrepetitive, novel behaviors. It's conjectured that such behavior is necessary for supporting universal computation, for instance, and, as you note, may be what spurred the origin of life, or even supports its persistence.

Furthermore, you investigate the notion of fixed points: where maps, repeatedly applied, leave their objects invariant. There is an interesting connection here: fixed points---or rather, their absence---are at the heart of results like Gödel's theorem, or the undecidability of the halting problem (for which connection, if I am permitted some self promotion, see my own essay). It's not hard to see how they are related to self-reference: a map, placed on a desert island, if detailed enough, will have to contain a copy of itself, and a single (fixed) point where map and territory, so to speak, coincide.

You combine these notions via the fractal geometry of the Mandelbrot set. This, too, has regions of great complexity at the boundary of more 'boring' regions---an edge of chaos---, and whether a point lies within that region is decided by application of a self-referential formula.

It would be interesting, to me, to see this connection explored more in depth. When does self-reference facilitate the emergence of nontrivial complexity, of novel structures that nevertheless do not degenerate into mere chaos?

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your essay touches on many interesting themes. You start off with what I've heard described as the 'edge of chaos'---the site of interesting complexity where the strictly and sterilely lawful and the completely unstructured random meet, and where consequently interesting phenomena occur. Wolfram has extensively written about his 'Class 4'-cellular automata, which are capable of showing persistent, nonrepetitive, novel behaviors. It's conjectured that such behavior is necessary for supporting universal computation, for instance, and, as you note, may be what spurred the origin of life, or even supports its persistence.

Furthermore, you investigate the notion of fixed points: where maps, repeatedly applied, leave their objects invariant. There is an interesting connection here: fixed points---or rather, their absence---are at the heart of results like Gödel's theorem, or the undecidability of the halting problem (for which connection, if I am permitted some self promotion, see my own essay). It's not hard to see how they are related to self-reference: a map, placed on a desert island, if detailed enough, will have to contain a copy of itself, and a single (fixed) point where map and territory, so to speak, coincide.

You combine these notions via the fractal geometry of the Mandelbrot set. This, too, has regions of great complexity at the boundary of more 'boring' regions---an edge of chaos---, and whether a point lies within that region is decided by application of a self-referential formula.

It would be interesting, to me, to see this connection explored more in depth. When does self-reference facilitate the emergence of nontrivial complexity, of novel structures that nevertheless do not degenerate into mere chaos?

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I can see that you read for detail Jochen,

It is a pleasure to hear your expert analysis and to come up not wanting more than I offer. I too like the edge of chaos notion. I tried to bring that out in my overlay showing the alignment of bifurcations with M at the same location I showed condensation happening earlier. Had I more space to write; I'd have devoted some discussion to Susskind's ideas about complexity being maximal at event horizons, but it was one more thing than I could add.

I remember fondly a book by Briggs and Peat "Turbulent Mirror" where they do a very nice job with that idea and also that there is a far shore of the chaotic realm. I don't know if that was their intended meaning, but it seemed strongly implied. In any case the analogy of the band-merging point at M_{3,1} with gravity is strong. The trajectories gather to a point at the gravitational horizon/critical point of condensation, but behind it the degrees of freedom rapidly multiply as the trajectories expand.

I would love to explore the connection you bring up in more depth.

Warm regards,

Jonathan

It is a pleasure to hear your expert analysis and to come up not wanting more than I offer. I too like the edge of chaos notion. I tried to bring that out in my overlay showing the alignment of bifurcations with M at the same location I showed condensation happening earlier. Had I more space to write; I'd have devoted some discussion to Susskind's ideas about complexity being maximal at event horizons, but it was one more thing than I could add.

I remember fondly a book by Briggs and Peat "Turbulent Mirror" where they do a very nice job with that idea and also that there is a far shore of the chaotic realm. I don't know if that was their intended meaning, but it seemed strongly implied. In any case the analogy of the band-merging point at M

I would love to explore the connection you bring up in more depth.

Warm regards,

Jonathan

Hello again folks,

For those who are interested to know more about or do some exploring themselves in the Mandelbrot Butterfly figure and its family of figures, I offer these links to content at Fractalforums.

Jonathan

The Mandelbrot Butterfly is a Spectral Manifold

The Butterfly's inverse is also Spectral

Formula files for Mandelbrot Butterfly family figures on Chaos Pro

I hope this is helpful.

More later,

Jonathan

For those who are interested to know more about or do some exploring themselves in the Mandelbrot Butterfly figure and its family of figures, I offer these links to content at Fractalforums.

Jonathan

The Mandelbrot Butterfly is a Spectral Manifold

The Butterfly's inverse is also Spectral

Formula files for Mandelbrot Butterfly family figures on Chaos Pro

I hope this is helpful.

More later,

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

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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

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Dear Jonathan,

If you could summarize your paper into one sentence, what would it be?

- Shawn

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If you could summarize your paper into one sentence, what would it be?

- Shawn

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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

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

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.

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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.

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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

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

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

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

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

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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

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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

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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

"

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 "

I'm encouraged that

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

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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

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

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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

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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

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

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.

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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.

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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

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

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

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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

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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

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

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

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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

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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

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...

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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

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

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

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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 → 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 π:ℂ → ℝ 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 π: ℍ → ℂ. Where things get a bit strange is with quantum gravitation, where the spacetime is noncommutative. The similar structure would then be π:O → ℍ, where now the base manifold is noncommutative and the fibration is nonassociative.

Cheers LC

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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 π:ℂ → ℝ 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 π: ℍ → ℂ. Where things get a bit strange is with quantum gravitation, where the spacetime is noncommutative. The similar structure would then be π:O → ℍ, where now the base manifold is noncommutative and the fibration is nonassociative.

Cheers LC

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Thanks for reading my essay Lawrence...

It is true the Mandelbrot formula can be written z → 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

It is true the Mandelbrot formula can be written z → 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 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

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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

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Jonathan,

Wanted to let you know that I updated my essay and uploaded it a few minutes ago. Personally I feel that it is greatly improved. I did rate yours on 2/28, giving it the highest rating, feeling it was the best I have read, even now.

Please check mine out again and see if you share my own prejudice. Such honest, No BS, reviews are needed by all of us.

Jim Hoover

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Wanted to let you know that I updated my essay and uploaded it a few minutes ago. Personally I feel that it is greatly improved. I did rate yours on 2/28, giving it the highest rating, feeling it was the best I have read, even now.

Please check mine out again and see if you share my own prejudice. Such honest, No BS, reviews are needed by all of us.

Jim Hoover

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Jonathan,

As usual, well written essay. Personally I still do not have a intuitive feel for the connection to physics, too busy with Octonions to drill down on what others see.

On that note, recently added canvas to my symbolic algebra suite, of course Mandelbrot set presentation is an excellent choice to try it out. As such revisited the Mandelbrot symbolic algebra code I did for you last essay. I should have been more thoughtful by making it more computationally efficient by simplifying the z^2 calculation for complex-Quaternion-Octonion math. Did so for the canvas exercise to put out 4096x3072 pixels without too much of a wait. Color palette from counts quite critical as I am sure you know. Big fun.

The optimizations did bring into focus the fact that doing the iterations in Quaternion algebra and Octonion algebra really does not bring out the non-commutation and non-associative properties of theses Algebras since the iteration is trivially commutative and associative for both.

The 2d pixel location to 4 and 8 dimension mapping for c is interesting, losing the scalar c term yields circles, rotating complex into other dims tears the complex towards the fully circular. Meaningful? Who knows?

On my symbolic algebra software I put the limited functionality source code up on my essay blog last year, i was severely disappointed nobody but you made a peep about it. I had hoped for collaboration and others banging on it for debugging, no such luck. Do you know of anyone that has tried it? It is a wonderful pedagogical tool as someone interested in Octonion algebra would find, can’t really do anything meaningful with paper and pencil.

Rick

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As usual, well written essay. Personally I still do not have a intuitive feel for the connection to physics, too busy with Octonions to drill down on what others see.

On that note, recently added canvas to my symbolic algebra suite, of course Mandelbrot set presentation is an excellent choice to try it out. As such revisited the Mandelbrot symbolic algebra code I did for you last essay. I should have been more thoughtful by making it more computationally efficient by simplifying the z^2 calculation for complex-Quaternion-Octonion math. Did so for the canvas exercise to put out 4096x3072 pixels without too much of a wait. Color palette from counts quite critical as I am sure you know. Big fun.

The optimizations did bring into focus the fact that doing the iterations in Quaternion algebra and Octonion algebra really does not bring out the non-commutation and non-associative properties of theses Algebras since the iteration is trivially commutative and associative for both.

The 2d pixel location to 4 and 8 dimension mapping for c is interesting, losing the scalar c term yields circles, rotating complex into other dims tears the complex towards the fully circular. Meaningful? Who knows?

On my symbolic algebra software I put the limited functionality source code up on my essay blog last year, i was severely disappointed nobody but you made a peep about it. I had hoped for collaboration and others banging on it for debugging, no such luck. Do you know of anyone that has tried it? It is a wonderful pedagogical tool as someone interested in Octonion algebra would find, can’t really do anything meaningful with paper and pencil.

Rick

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Hi Jonathan,

I hope you're well, and well upstate! Good essay again, right on the money and far more readable than many. This is certainly a case for Mandelbrot set recursions, which as you may recall I agree reflects all of nature. I found your take interesting for symmetry breaking and also phase transitions. We also agree on the import of reconciling CSL and QM with gravitation, a matter on which my own essay identifies a coherent hypothesis I hope you'll look at. A few points and questions;

1. I like your comment; "*This makes cosmology a bit like a process of fractional distillation, where the entirety of the condensed matter universe is only the denser portion of reality with fixed attributes, the lowest fraction."* In my observational cosmologist role I've found something very similar, and likely cyclic for consistency with the peculiar CMB anisotropies, and with no halting issue.

2. Do you think the reductions of the general quintic equation, by Euler or the simplest form; x^{5} -x + p = 0 can lead to any insights? (I've struggled to see the geometry so far).

3. One thing I have found is that momentum exchange vector addition in a sequence (so complex) of interactions with rotating spheres with random polar axes**does** produce the increasing uncertainty found, and of Chaos theory. That's due to uncertainty of +/-'curl' at the equator and *linear* motion at the poles. Can you rationalise that concept?

4. You rightly define limits, but not quite Dirac's idea of a 'sharp cut off' to maths validity. I've suggested that limit is physically at the lowest (and strongest!) particle 'coupling' scale for EM energy, the electron, or condensed e+/- 'pair'. (My essay identifies useful implications).

5. You rightly identify confirmation bias which I find far more common than most realise, but do you think that removing it and embedding of doctrine might lead to understanding*without* ever larger accelerators?

6. On the same line; Might that also help resolve what you rightly identify as;*"the most vexing problem of all, that we know there is something out there – or in there - waiting to be discovered, but to get the answer would require more waiting time than we have".*

7. But when a good candidate for a coherent set of solutions DOES come along, likely NOT from doctrinal thinking, do you think academics be able to recognise it, or even bother to study it!? From my on experience I suggest not. Do you have a view?

Nice essay Jonathan, certainly down for a top score from me. Well done.

Very Best. Stay safe.

Peter

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I hope you're well, and well upstate! Good essay again, right on the money and far more readable than many. This is certainly a case for Mandelbrot set recursions, which as you may recall I agree reflects all of nature. I found your take interesting for symmetry breaking and also phase transitions. We also agree on the import of reconciling CSL and QM with gravitation, a matter on which my own essay identifies a coherent hypothesis I hope you'll look at. A few points and questions;

1. I like your comment; "

2. Do you think the reductions of the general quintic equation, by Euler or the simplest form; x

3. One thing I have found is that momentum exchange vector addition in a sequence (so complex) of interactions with rotating spheres with random polar axes

4. You rightly define limits, but not quite Dirac's idea of a 'sharp cut off' to maths validity. I've suggested that limit is physically at the lowest (and strongest!) particle 'coupling' scale for EM energy, the electron, or condensed e+/- 'pair'. (My essay identifies useful implications).

5. You rightly identify confirmation bias which I find far more common than most realise, but do you think that removing it and embedding of doctrine might lead to understanding

6. On the same line; Might that also help resolve what you rightly identify as;

7. But when a good candidate for a coherent set of solutions DOES come along, likely NOT from doctrinal thinking, do you think academics be able to recognise it, or even bother to study it!? From my on experience I suggest not. Do you have a view?

Nice essay Jonathan, certainly down for a top score from me. Well done.

Very Best. Stay safe.

Peter

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Hello all...

I am sorry for being absent here. Participating in this contest has been a rewarding distraction from my life, as I nervously awaited news of my father's progress, as he slowly got better. Dad fought valiantly toward the end. But he lost the battle and passed last Wed. the 25th, just 1 day shy of his 88th birthday.

And yes; though he tested negative, he showed the cluster of symptoms characteristic of coronavirus. But since he lost his sense of taste at the end of January, and showed symptoms the first week of Feb.; that would make him one of the first US residents infected. He got better somewhat, then a secondary infection apparently took his life.

But the spread of Covid-19 must have been ongoing before some who later developed the disease showed any symptoms whatever. Pretty scary! I'll come back to comment more here soon, offer some helpful or commemorative items... I have some things to take care of right now though.

All the Best,

Jonathan

I am sorry for being absent here. Participating in this contest has been a rewarding distraction from my life, as I nervously awaited news of my father's progress, as he slowly got better. Dad fought valiantly toward the end. But he lost the battle and passed last Wed. the 25th, just 1 day shy of his 88th birthday.

And yes; though he tested negative, he showed the cluster of symptoms characteristic of coronavirus. But since he lost his sense of taste at the end of January, and showed symptoms the first week of Feb.; that would make him one of the first US residents infected. He got better somewhat, then a secondary infection apparently took his life.

But the spread of Covid-19 must have been ongoing before some who later developed the disease showed any symptoms whatever. Pretty scary! I'll come back to comment more here soon, offer some helpful or commemorative items... I have some things to take care of right now though.

All the Best,

Jonathan

To honor another great soul...

F.D. 'Tony' Smith passed away last December, and he had much to say that inspired me to investigate various areas of Math I would otherwise overlook or fail to understand. Like Steve Dufourny; I came to realize that the properties of spheres in various dimensions have a relation to Physics that is profound. People expect them to be simple but they are not. ...

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F.D. 'Tony' Smith passed away last December, and he had much to say that inspired me to investigate various areas of Math I would otherwise overlook or fail to understand. Like Steve Dufourny; I came to realize that the properties of spheres in various dimensions have a relation to Physics that is profound. People expect them to be simple but they are not. ...

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Hello dear Jonathan,

Ulla tells you Hello too , I live in Finland now I have immigrated and we live together.

I thank you a lot to tell my name, I am honored. I work a lot and study a lot of maths to formalise correctly this Theory of Spherisation, an optimisation evolution of the Universal sphere or future Sphere with quantum and cosmological spheres.

I have found this...

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Ulla tells you Hello too , I live in Finland now I have immigrated and we live together.

I thank you a lot to tell my name, I am honored. I work a lot and study a lot of maths to formalise correctly this Theory of Spherisation, an optimisation evolution of the Universal sphere or future Sphere with quantum and cosmological spheres.

I have found this...

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I am happy for you and for Ulla...

A lot of Cosmology relates to the properties of spheres. But a lot of scientists like to put things in square grids. Maybe that is why the pieces don't quite fit.

All the Best,

Jonathan

A lot of Cosmology relates to the properties of spheres. But a lot of scientists like to put things in square grids. Maybe that is why the pieces don't quite fit.

All the Best,

Jonathan

Hi Jonathan,

Thank you very much, it is very nice.

Yes lol indeed , a lot of scientists now have created prisons of thoughts forgetting the simplicity of this universe generally speaking, for me these spheres are the choice of this universe and this geometry is totally different than the others and is the perfect equilibrium of forces and can create all geometries and topologies when we consider these geonetrical algebras and 3D finite series of spheres where space disappears , one coded for the vacuum space and two main fuels, photons and cold DM. Maybe the scientists must understand this general universal simplicity and work on complex details differently.

Regards

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Thank you very much, it is very nice.

Yes lol indeed , a lot of scientists now have created prisons of thoughts forgetting the simplicity of this universe generally speaking, for me these spheres are the choice of this universe and this geometry is totally different than the others and is the perfect equilibrium of forces and can create all geometries and topologies when we consider these geonetrical algebras and 3D finite series of spheres where space disappears , one coded for the vacuum space and two main fuels, photons and cold DM. Maybe the scientists must understand this general universal simplicity and work on complex details differently.

Regards

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Jonathan,

Math! - Its so long ago, that it now resides only in my ‘imaginary’ brain cells.

‘Your paper is to be an exciting exploration of bouncing between what is ‘possible to know’ and ‘what is beyond reckoning’. ‘.

Perhaps the (interesting) Mandelbrot Set and Planck scale are guides specifically for mathematicians. You are seeking converges or...

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Math! - Its so long ago, that it now resides only in my ‘imaginary’ brain cells.

‘Your paper is to be an exciting exploration of bouncing between what is ‘possible to know’ and ‘what is beyond reckoning’. ‘.

Perhaps the (interesting) Mandelbrot Set and Planck scale are guides specifically for mathematicians. You are seeking converges or...

view entire post

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I try to find the good general way for the formalisation of my general theory and these 3D spheres, I search the good mathematical Tools to superimpose ,it could be very relevant to work in complementarity, alone it is not easy, John Baez, Susskind , Witten, Hooft and Connes more Penrose could come on this platform, together with their skillings in maths, we can create a real revolutionary work at my humble opinion, I know the maths but they are better than me. The complementarity is essential it seems.

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wordy essay (your usually are). But I gave you a 9 for content. Had it been more succinct you would have gotten a 10

Your points are well taken.

Andrew

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Your points are well taken.

Andrew

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I am back on the forum...

And I have started to rate essays. I'm starting with some of the earlier submissions and those I already read once, but I expect to get a broad sampling of essays read before the deadline. I like to choose some from near the bottom, and some from near the top of the ratings spectrum. I don't feel like I can be fair reading only the work of pros or that of friends, and so on. So I will deliberately seek out some outliers.

But I will largely focus on those essays that spark my interest in some way. I like to read the abstracts first, and then read things where my knowledge and opinions overlap, but I will also go for papers that offer something completely different from what I have learned or understood before. FQXi contests tend to offer a lot of that variety. So I will try to get as many essays read in the remaining time as possible, and rate those I can form an honest opinion about.

All the Best,

Jonathan

And I have started to rate essays. I'm starting with some of the earlier submissions and those I already read once, but I expect to get a broad sampling of essays read before the deadline. I like to choose some from near the bottom, and some from near the top of the ratings spectrum. I don't feel like I can be fair reading only the work of pros or that of friends, and so on. So I will deliberately seek out some outliers.

But I will largely focus on those essays that spark my interest in some way. I like to read the abstracts first, and then read things where my knowledge and opinions overlap, but I will also go for papers that offer something completely different from what I have learned or understood before. FQXi contests tend to offer a lot of that variety. So I will try to get as many essays read in the remaining time as possible, and rate those I can form an honest opinion about.

All the Best,

Jonathan

Hi Jonathan,

Your paper was quite interesting. I had no idea about the connections between the Mandelbrot set and Physics. There is a lot I don't understand about it, but it just makes me want to read a lot more about it.

There was one thing you said I could use a little clarification on: 'that which converges or condenses into congruent forms.' What do you mean by congruent forms and what is converging to them?

Do you think the lack of focus on non-linear dynamics is because of difficulty, or possibly something else?

You mentioned the Heisenberg Uncertainty principle, and it made me wonder if we could ever stumble across a mathematical structure to describe the behavior of waves without the limitations of the uncertainty principle. (A little tangential).

One thing you said in your concluding remark struck a chord in me, even if I don't fully understand the full implications. That " the reality in both Math and Physics is that what is relevant or real arose from a larger spectrum of what is possible". It makes me wonder on the limitations of what is possible.

Best regards,

Ernesto

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Your paper was quite interesting. I had no idea about the connections between the Mandelbrot set and Physics. There is a lot I don't understand about it, but it just makes me want to read a lot more about it.

There was one thing you said I could use a little clarification on: 'that which converges or condenses into congruent forms.' What do you mean by congruent forms and what is converging to them?

Do you think the lack of focus on non-linear dynamics is because of difficulty, or possibly something else?

You mentioned the Heisenberg Uncertainty principle, and it made me wonder if we could ever stumble across a mathematical structure to describe the behavior of waves without the limitations of the uncertainty principle. (A little tangential).

One thing you said in your concluding remark struck a chord in me, even if I don't fully understand the full implications. That " the reality in both Math and Physics is that what is relevant or real arose from a larger spectrum of what is possible". It makes me wonder on the limitations of what is possible.

Best regards,

Ernesto

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Thank you Ernesto,

I like to think of congruency in terms of self-agreement and one might talk about things that hang together well. I've heard of congruency relating to where a person's thoughts, feelings, and actions are in agreement, and I am extending this idea to forms in general. In theories of process; one regards all stable forms as a process that is in agreement with itself.

People are unreasonably put off by non-linear terms. In some cases, that is where the fun stuff is happening. Just as in painting or baking; the order of terms and the directionality of elements within a process become relevant. As soon as you tell some people they need to use a certain ordering instead of applying the commutative and associative rules; they give up.

On uncertainty; the octonions relation to the projective geometry (the geometry of perspective) gives a tantalizing answer to your query. There is a lot to explain with that, however. More is possible than exists in human philosophy... Food for another essay and then some.

More later,

Jonathan

I like to think of congruency in terms of self-agreement and one might talk about things that hang together well. I've heard of congruency relating to where a person's thoughts, feelings, and actions are in agreement, and I am extending this idea to forms in general. In theories of process; one regards all stable forms as a process that is in agreement with itself.

People are unreasonably put off by non-linear terms. In some cases, that is where the fun stuff is happening. Just as in painting or baking; the order of terms and the directionality of elements within a process become relevant. As soon as you tell some people they need to use a certain ordering instead of applying the commutative and associative rules; they give up.

On uncertainty; the octonions relation to the projective geometry (the geometry of perspective) gives a tantalizing answer to your query. There is a lot to explain with that, however. More is possible than exists in human philosophy... Food for another essay and then some.

More later,

Jonathan

Hi again Jonathan,

I posted a copy of this to my page, not knowing if you get it there.

Thanks for reading my paper. I don’t know why you called it a revised version as it was never revised.

An ideal response for me would be of someone willing to read and discuss the whole model. That type of analysis could be worth some money to me. You mentioned finding misses and flubs,...

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I posted a copy of this to my page, not knowing if you get it there.

Thanks for reading my paper. I don’t know why you called it a revised version as it was never revised.

An ideal response for me would be of someone willing to read and discuss the whole model. That type of analysis could be worth some money to me. You mentioned finding misses and flubs,...

view entire post

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For what it is worth...

I did consider a re-write but I thought this paper was nicely polished already. So instead I wrote a few more papers - what I might have said if... - and then submitted them for publication in Prespacetime. I still have one more on the "Unit Cell of Quantum Gravity" that would have been a nice addition to this field. But it isn't finished yet. The essay I did upload was ready in plenty of time, though I might have given a little more time to a grant proposal instead.

The Covid-19 pandemic has hit me hard, though my health has been good. When my father passed on Mar. 25, everything stopped for a while, or continued in spurts, but now I can begin some steady progress toward reading the remaining essays. I may also post links to more related content, create a video or two highlighting the work featured in my essay, and so on. I will let you all know here.

More later,

Jonathan

I did consider a re-write but I thought this paper was nicely polished already. So instead I wrote a few more papers - what I might have said if... - and then submitted them for publication in Prespacetime. I still have one more on the "Unit Cell of Quantum Gravity" that would have been a nice addition to this field. But it isn't finished yet. The essay I did upload was ready in plenty of time, though I might have given a little more time to a grant proposal instead.

The Covid-19 pandemic has hit me hard, though my health has been good. When my father passed on Mar. 25, everything stopped for a while, or continued in spurts, but now I can begin some steady progress toward reading the remaining essays. I may also post links to more related content, create a video or two highlighting the work featured in my essay, and so on. I will let you all know here.

More later,

Jonathan

Jonathan,

Hope you have time to recheck my update before the deadline: https://fqxi.org/community/forum/topic/3396

Jim Hoover.

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Hope you have time to recheck my update before the deadline: https://fqxi.org/community/forum/topic/3396

Jim Hoover.

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Thanks, for taking another look. Your comments are always incisive. Hard crowd this year. Your score, so far, doesn't accurately represent a superior effort. From personal experience, Much more ambushing this year.

Jim

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Jim

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Dear Jonathan Dickau,

Yesterday you commented my “essay” (Concentration and tessellation in quantized space). At first I couldn’t understand your comment (What is “Loll” and “Ambjorn”? And what is “causal dynamical triangulations or energetic causal sets”?).

But an hour ago I tried Google and I am really surprised. I never had heard of the work of Renate Loll and Jan Ambjørn. I suppose I have a lot to read now… ;-))

Anyway, I am really thankful that you wrote that comment. I didn’t know that there are other physicists who are involved in the same type of research as I have always done.

With kind regards, Sydney

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Yesterday you commented my “essay” (Concentration and tessellation in quantized space). At first I couldn’t understand your comment (What is “Loll” and “Ambjorn”? And what is “causal dynamical triangulations or energetic causal sets”?).

But an hour ago I tried Google and I am really surprised. I never had heard of the work of Renate Loll and Jan Ambjørn. I suppose I have a lot to read now… ;-))

Anyway, I am really thankful that you wrote that comment. I didn’t know that there are other physicists who are involved in the same type of research as I have always done.

With kind regards, Sydney

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Jonathan,

I read your essay and gave you a decent score. The Mandelbrot set in principle contains an infinite amount of information. This is even though it is generated by the rather simple iteration of s --> z(z + 1). Points that converge to 0 are marked as black and those points after so many iterations come close or within some distance are color coded. There are some rather spectacular videos of the Mandelbrot set out there.

The Mandelbrot set has these branches on it that have spirals with 3, 5, 8, 13 etc numbers of petals coming off. This is a Fibonacci sequence. The Fibonacci sequence is of course identified with a number φ = (1 + √5)/2 My essay does invoke the idea of fractal geometry in the formation of unital sets. These sets are p-adic. For the Fibonacci sequence we can look at this in a mod(8) system and this gives the primes 2, 3, 5 and we can then reduce this system to these p-adic rings. I choose 8 because that is the sequence for Bott periodicity. Lurking behind this are Cantor sets and fractal geometry.

I attach a picture I took recently of a flower that has Fibonacci structure.

Cheers LC

attachments: fibonacci_flowering.jpg

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I read your essay and gave you a decent score. The Mandelbrot set in principle contains an infinite amount of information. This is even though it is generated by the rather simple iteration of s --> z(z + 1). Points that converge to 0 are marked as black and those points after so many iterations come close or within some distance are color coded. There are some rather spectacular videos of the Mandelbrot set out there.

The Mandelbrot set has these branches on it that have spirals with 3, 5, 8, 13 etc numbers of petals coming off. This is a Fibonacci sequence. The Fibonacci sequence is of course identified with a number φ = (1 + √5)/2 My essay does invoke the idea of fractal geometry in the formation of unital sets. These sets are p-adic. For the Fibonacci sequence we can look at this in a mod(8) system and this gives the primes 2, 3, 5 and we can then reduce this system to these p-adic rings. I choose 8 because that is the sequence for Bott periodicity. Lurking behind this are Cantor sets and fractal geometry.

I attach a picture I took recently of a flower that has Fibonacci structure.

Cheers LC

attachments: fibonacci_flowering.jpg

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Dear Jonathan Dickau,

I have read your essay with a big smile. Personally I admire explanations about abstract subjects that are supported by a “tangible” concept to transform the arguments like clothes that express the personality of a person. Your essay describes ideas that can easily be extended to a number of articles on FQXi’s website. For example, the discussion about the origin of consciousness is futile if we accept that reality is a fractal or has dominant properties that create a fractal-like structure.

I will read your essay again within a couple of days because there is more to rethink than I can grasp if I read it only once.

With kind regards, Sydney

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I have read your essay with a big smile. Personally I admire explanations about abstract subjects that are supported by a “tangible” concept to transform the arguments like clothes that express the personality of a person. Your essay describes ideas that can easily be extended to a number of articles on FQXi’s website. For example, the discussion about the origin of consciousness is futile if we accept that reality is a fractal or has dominant properties that create a fractal-like structure.

I will read your essay again within a couple of days because there is more to rethink than I can grasp if I read it only once.

With kind regards, Sydney

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Dear Jonathan,

Glad to read your work again.

I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

While the discussion lasted, I wrote an article: “Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus”, due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 “Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability”.

I hope that my modest results of work will provide you with information for thought.

Warm Regards, `

Vladimir

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Glad to read your work again.

I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

While the discussion lasted, I wrote an article: “Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus”, due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 “Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability”.

I hope that my modest results of work will provide you with information for thought.

Warm Regards, `

Vladimir

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I am glad you enjoyed it Vladimir...

I have in the past greatly enjoyed reading your papers. It seems like we have a fair amount of common ground in our theoretical landscape. There is not total agreement, but there is certainly a lot on which we can and do agree.

I have replied to the coronavirus insights back on your page. I think we should evxplore every avenue that might provide relief or lead to a cure. We must be cautious not to do harm, but be emboldened by the severity or urgency of the situation to do more than otherwise we might.

All the Best,

Jonathan

I have in the past greatly enjoyed reading your papers. It seems like we have a fair amount of common ground in our theoretical landscape. There is not total agreement, but there is certainly a lot on which we can and do agree.

I have replied to the coronavirus insights back on your page. I think we should evxplore every avenue that might provide relief or lead to a cure. We must be cautious not to do harm, but be emboldened by the severity or urgency of the situation to do more than otherwise we might.

All the Best,

Jonathan

For the benefit of my readers....

One of the BEST sources of information on Covid-19 I have seen anywhere is the ongoing analysis by mathematician Chris King. You can find his Covid page on Dhushara dot com or follow the link below.

The Covid-19 / SARS-CoV-2 Papers

I hope people find this site and info helpful. Please pass it along if you do.

Regards,

Jonathan

One of the BEST sources of information on Covid-19 I have seen anywhere is the ongoing analysis by mathematician Chris King. You can find his Covid page on Dhushara dot com or follow the link below.

The Covid-19 / SARS-CoV-2 Papers

I hope people find this site and info helpful. Please pass it along if you do.

Regards,

Jonathan

Jonathan,

Here is the Mandelbrot update we talked about via email.

Get canvas for node.js from GitHub or node, be sure to download to a new folder. Move content of download to the node_module subfolder your scripting files go into downloaded from my fqxi essay last year blog.

Replace node_moduleNUMBERS.js with new NUMBERS.js from attached.

A script that will generate a jpeg for the Mandelbrot set is also in the attached, move mpixlog.js to your executable script file folder. If you run this script it will regenerate mpixlog.jpeg. You might want to look at it and/or rename it prior to running script

Rick

attachments: mandelbrot_updates.zip

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Here is the Mandelbrot update we talked about via email.

Get canvas for node.js from GitHub or node, be sure to download to a new folder. Move content of download to the node_module subfolder your scripting files go into downloaded from my fqxi essay last year blog.

Replace node_moduleNUMBERS.js with new NUMBERS.js from attached.

A script that will generate a jpeg for the Mandelbrot set is also in the attached, move mpixlog.js to your executable script file folder. If you run this script it will regenerate mpixlog.jpeg. You might want to look at it and/or rename it prior to running script

Rick

attachments: mandelbrot_updates.zip

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I guess the windows file folder separator gets dropped. NUMBERS.js in subfolder node_module

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Dear Jonathan

I thank you for your comments on my page.

You are right, I said everything in the presentation of my essay, the rest is just an application.

This kind of “information indigestion” will probably be useful and there will be something left in head of everyone’s to think about.

I could arrange the same “information indigestion” with elementary particles, but I chose the solar system so that I could visualize what each spectral line of an atom is in reality, where their analogues exist, instead of abstractions of quantum mechanics. And then it will be clear that the whole Universe functions according to unified quantum laws.

Gerard't Hooft

is a man of genius person, so he himself admits that he does not understand what people tell him about their theories and why they say it.

But he has keywords that can change the whole of science, how Maxwell changed science by creating his own equations, presenting his rotors in the form of simple cogwheel models.

Gerard't Hooft says:

"We conclude that the most general model will be described as a set of simple periodic cogwheel models with varying periodicities."

We need to ask him a question about the number of teeth in his gears. It is possible that he himself will think of the fact that there should be 137 pieces.

This will be a “shot from a cannon to top of a mountain to turn the potential energy of snow into an avalanche."

All the Best,

Vladimir

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I thank you for your comments on my page.

You are right, I said everything in the presentation of my essay, the rest is just an application.

This kind of “information indigestion” will probably be useful and there will be something left in head of everyone’s to think about.

I could arrange the same “information indigestion” with elementary particles, but I chose the solar system so that I could visualize what each spectral line of an atom is in reality, where their analogues exist, instead of abstractions of quantum mechanics. And then it will be clear that the whole Universe functions according to unified quantum laws.

Gerard't Hooft

is a man of genius person, so he himself admits that he does not understand what people tell him about their theories and why they say it.

But he has keywords that can change the whole of science, how Maxwell changed science by creating his own equations, presenting his rotors in the form of simple cogwheel models.

Gerard't Hooft says:

"We conclude that the most general model will be described as a set of simple periodic cogwheel models with varying periodicities."

We need to ask him a question about the number of teeth in his gears. It is possible that he himself will think of the fact that there should be 137 pieces.

This will be a “shot from a cannon to top of a mountain to turn the potential energy of snow into an avalanche."

All the Best,

Vladimir

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Jonathan,

attachments: 1_Plateau.jpg

Great picture, I need to try to describe it in my leisure time according to my fractal structure formulas.

Vladimir

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attachments: 1_Plateau.jpg

Great picture, I need to try to describe it in my leisure time according to my fractal structure formulas.

Vladimir

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Jonathan,

Thanks for the COVID-19 hyperlink. Yours is one of the superior essays I mentioned to the FQXi administrators that has been under attack. Good luck and regards.

Jim

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Thanks for the COVID-19 hyperlink. Yours is one of the superior essays I mentioned to the FQXi administrators that has been under attack. Good luck and regards.

Jim

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Thank you Jim,

I'll keep plugging away, reading one after another, until day's end. I think some authors rate essays based only on whether the author appears to agree with their views as expressed in the abstract - without attempting to learn whether there are good arguments for that view in the essay itself. I know that I would have been fooled by the summary in the abstract of several papers, because the author turned my head around with skillful debate. That's what it is all about, in my view.

What I don't like are critical ratings without any critique about what was disliked. I'd like to know both strengths and weaknesses in my writing or approach. I guess people who say nothing fear reprisals or are just cowards.

Good luck also to you,

Jonathan

I'll keep plugging away, reading one after another, until day's end. I think some authors rate essays based only on whether the author appears to agree with their views as expressed in the abstract - without attempting to learn whether there are good arguments for that view in the essay itself. I know that I would have been fooled by the summary in the abstract of several papers, because the author turned my head around with skillful debate. That's what it is all about, in my view.

What I don't like are critical ratings without any critique about what was disliked. I'd like to know both strengths and weaknesses in my writing or approach. I guess people who say nothing fear reprisals or are just cowards.

Good luck also to you,

Jonathan

Dear Jonathan Dickau

Thank you very much you read my essay and put some comments on it. Your essay is very interesting and it is amazing you can combine chaos theory with QM and Relativity. I think all these theories are intertwined. The next few days I will read again your essay which merits a lot attention

I wish best luck in this contest

Basileios Grispos

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Thank you very much you read my essay and put some comments on it. Your essay is very interesting and it is amazing you can combine chaos theory with QM and Relativity. I think all these theories are intertwined. The next few days I will read again your essay which merits a lot attention

I wish best luck in this contest

Basileios Grispos

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Dear Jonathan,

Interesting essay. I like the analysis of the limitations imposed to our knowledge. I enjoyed your discussion of the Mandelbrot fractal, and the interesting discussion around the Misiurewicz point. You have an interesting visual style of approaching nature, and use it to make analogies and connections between various domains in interesting ways. Good luck in the contest!

Cheers,

Cristi

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Interesting essay. I like the analysis of the limitations imposed to our knowledge. I enjoyed your discussion of the Mandelbrot fractal, and the interesting discussion around the Misiurewicz point. You have an interesting visual style of approaching nature, and use it to make analogies and connections between various domains in interesting ways. Good luck in the contest!

Cheers,

Cristi

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For what it is worth...

I am not the person who has been low-balling you. If I have left a comment with praise you got a good score, and if I left comments with moderate criticism, you got a decent score from me. I gave out no ratings below 5 and I gave my very first rating of 10, this year.

I gave out more than a few 9s, and a lot of 6, 7, or 8 ratings, this year. But I do not believe in punitive or retaliatory scoring. I use a points system based on a checklist of my own design. I reward for quality and proper rigor. Confusing or confused essays get a lower score.

If you need to retaliate, or find a scapegoat, please look elsewhere for your detractors. I have been getting hit by people giving me low ratings and making no comments. Please don't imagine that I would treat others that way.

Regards,

Jonathan

I am not the person who has been low-balling you. If I have left a comment with praise you got a good score, and if I left comments with moderate criticism, you got a decent score from me. I gave out no ratings below 5 and I gave my very first rating of 10, this year.

I gave out more than a few 9s, and a lot of 6, 7, or 8 ratings, this year. But I do not believe in punitive or retaliatory scoring. I use a points system based on a checklist of my own design. I reward for quality and proper rigor. Confusing or confused essays get a lower score.

If you need to retaliate, or find a scapegoat, please look elsewhere for your detractors. I have been getting hit by people giving me low ratings and making no comments. Please don't imagine that I would treat others that way.

Regards,

Jonathan

Thanks to all!

I appreciate the positive attention from my supportive readers and visitors, and the unspoken criticism of my detractors is also noted. In a contest about the presence of uncertainty or unknowability in the universe; I guess some measure of that in the identity of those who choose to hit and run is warranted.

I hope everyone who came to my essay got something of value. I'm sorry that, with the death of my Dad in the middle of the contest, I did not have more time to read and comment on other essays. The Covid-19 pandemic took a toll on me personally. I hope that it has spared and will spare most of you.

Warm Regards,

Jonathan

I appreciate the positive attention from my supportive readers and visitors, and the unspoken criticism of my detractors is also noted. In a contest about the presence of uncertainty or unknowability in the universe; I guess some measure of that in the identity of those who choose to hit and run is warranted.

I hope everyone who came to my essay got something of value. I'm sorry that, with the death of my Dad in the middle of the contest, I did not have more time to read and comment on other essays. The Covid-19 pandemic took a toll on me personally. I hope that it has spared and will spare most of you.

Warm Regards,

Jonathan

I'm sorry to hear about your Dad. I hope you're relatively well.

- Shawn

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- Shawn

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I miss him every day...

And I keep wondering if there was something more I could/should have done, or been more cautious with my Dad. It all happened so fast. At the point he was infected; they had just figured out it was human to human transmissible but figured the outbreak was unlikely to spread beyond the far East.

I am healthy and well. Probably got it myself and had a complete recovery back in January. Nobody suspected that it had spread all over Europe by then, and my partner sings in a group where someone had just returned from Italy with a cough, but thought she was over the flu.

So while they were debating whether it could spread, people played beer pong in Ishgl (in Tyrolia in the Austrian Alps), and a bunch of rich people who thought they were immortal spread it all over the continent. So much for containment to the far East. One heck of a wild ride.

All the Best,

Jonathan

And I keep wondering if there was something more I could/should have done, or been more cautious with my Dad. It all happened so fast. At the point he was infected; they had just figured out it was human to human transmissible but figured the outbreak was unlikely to spread beyond the far East.

I am healthy and well. Probably got it myself and had a complete recovery back in January. Nobody suspected that it had spread all over Europe by then, and my partner sings in a group where someone had just returned from Italy with a cough, but thought she was over the flu.

So while they were debating whether it could spread, people played beer pong in Ishgl (in Tyrolia in the Austrian Alps), and a bunch of rich people who thought they were immortal spread it all over the continent. So much for containment to the far East. One heck of a wild ride.

All the Best,

Jonathan

Yeah, there was a cricket game at the local park the other day. I hope none of them were infected.

- Shawn

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- Shawn

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I want to again thank everyone...

I am pleased that people appreciated my work enough to put me at the low end of the high-ranked papers. It is a privilege to be able to share my ideas on this forum with like-minded people. The fact that FQXi participants tend to be open-minded is a bonus. But I hope my quality of work warranted your positive attention, that it provided ample food for thought, and that it will continue to appreciate in value thereby.

All the Best,

Jonathan

I am pleased that people appreciated my work enough to put me at the low end of the high-ranked papers. It is a privilege to be able to share my ideas on this forum with like-minded people. The fact that FQXi participants tend to be open-minded is a bonus. But I hope my quality of work warranted your positive attention, that it provided ample food for thought, and that it will continue to appreciate in value thereby.

All the Best,

Jonathan

You deserve a high rating; your essay is robust for being so short.

- Shawn

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- Shawn

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Thanks Shawn,

I try to squeeze a lot in, pare down the slop, add in a few more details... until there is no more time or space to allot. What good is having a wealth of knowledge if you can't share it? A lot of what I write about is elementary or basic-level stuff on advanced topics, that has been ignored or misrepresented.

If people re-visit some of the things they know, or think they know, from a new angle - something different pops out. I guess I am hoping that if enough true scholars read my work, its value will be obvious, and they will wonder why it has been ignored instead of why a crazy idea is being embraced.

It's pretty radical. But the recent work of Giulio Tiozzo and others conclusively proves there is an enormous potential untapped.

All the Best,

Jonathan

I try to squeeze a lot in, pare down the slop, add in a few more details... until there is no more time or space to allot. What good is having a wealth of knowledge if you can't share it? A lot of what I write about is elementary or basic-level stuff on advanced topics, that has been ignored or misrepresented.

If people re-visit some of the things they know, or think they know, from a new angle - something different pops out. I guess I am hoping that if enough true scholars read my work, its value will be obvious, and they will wonder why it has been ignored instead of why a crazy idea is being embraced.

It's pretty radical. But the recent work of Giulio Tiozzo and others conclusively proves there is an enormous potential untapped.

All the Best,

Jonathan

Due to frustration with others unable to follow my perspectives about space gravity etc, I have taken your advice and e-mailed to Carlo Rovelli with a new 'problem of Doppler' paper that you might find interesting.

I could send it to you if I had your e-mail . mine is pshrodr8@aol.com

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I could send it to you if I had your e-mail . mine is pshrodr8@aol.com

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