Hi Jonathan, congrats, I liked a lot your essay.
I have some questions, I beleive strongly that we cannot create a quantum computer because we don t know the main codes at this planck scale and whjat are the foundamental objects in fact and nor the origin of these codes philosphically speaking. What are your ideas? regards
Sorry for being unresponsive folks...
I've had to deal with complications at home resulting from my Dad's illness and hospitalization. Various tasks required my immediate attention, but now with my father recovering and in rehab, there is more time for responding to comments here - among other things. I'll try to get back to commenters more quickly now.
All the Best,
Jonathan
Thanks for your detailed comment John...
I think you meant 'splaying out' but the rest of the description was apt. It's not quite that simple of course. What condenses out of a matter-energy soup depends on both the properties of energy and the types of particles that are viable. The Mandelbrot Set appears to show that from quantum foam the cosmos needed to form large enough voids of volumetric space (bubbles) to fit particles as large as a proton before baryogenesis could commence. That is; it reveals a specific mechanism that allows fermionic particles to form.
I agree regarding the Physics-Metaphysics thing. Being forced up against a wall to explain things that are too paradoxical for an ordinary material world description to fit, will propose things that are about as odd as anything found in metaphysics, Science Fiction, or magical fantasies. Some of it could be true and one has to ask tough questions of the right expert, and know just how to ask them, to find out. Of course; it took a lot of effort just to get to FFP10 in Australia as a presenter to ask Gerard 't Hooft about evidence validating or disconfirming his CA-based quantum gravity theory. But his answer was worth the effort.
Of course; I was totally floored when the following year at FFP11 in Paris he devoted 4 or 5 new slides to the desirability of obtaining Lorwntz invariance and of the difficulty with doing that in a CA-based theory. So the detailed answer contained a lot of insight into the Physics-Metaphysics balance of his work at the time - but no definite answers on a route to validation or disproof.
All the Best,
Jonathan
Thanks Phil,
These are exciting times for me, and I appreciate the praise. At this point; I have a handful of mathematical conjectures that, if proven, would demonstrate conclusively the Physics relevance of the Mandelbrot Set. One proof involving the discs around the periphery of the Mandelbrot Butterfly is basically a covering problem and it may benefit from your improvements on the Lebesgue measure.
Furthermore; this work is a wholesale and explicit demonstration of the notion that your 'Theory of Theories' idea holds water. One of the posters I got lofted at GR22 (through the kind efforts of Profs. Pullin and Agullo - as I could not attend) focused on the fact that M displays analogies for a large number of theories in quantum and analog gravity at once. My Prespacetime article elaborates on this.
But I see a confluence of work all pointing to a single result as more validating than having one all-encompassing theory - even if that theory was my own work.
All the Best,
Jonathan
I'm glad it gave you the thrill Jim...
If I brought you back to school days and made you put on your thinking cap; mission accomplished. I am a champion of the idea that future Science will make the current crop of ideas appear lame, but I also think that there are some universal principles and dominating ideas that will have their way within any framework that we or future researchers can devise.
It is also true that nature will be as it is, regardless of what ideas we apply to understand it. Perhaps many models can contribute to a full understanding, and most will later be seen as special cases of a more encompassing theory.
I think our level of technological advancement is on a par with our social advancement as a culture. So long as we get or choose leaders who behave like adolescents we are not fit to join the community of space faring cultures visiting other planets. I hope we go anyway, at least as far as Mars, so we can get a taste of the rigors of space and the demands of conquering that journey. We may want to be fully adult, by the time we venture to other stars however.
All the Best,
Jonathan
Thinking about the Planck scale...
We need to imagine everything is maximally uncertain but can't vary by much. Even dimensionality itself is undetermined, and we must consider that it could have zero or infinite dimensions and the exact number is undetermined and emerges via the process of geometrization. I agree with Smolin that, in a sense, time is more fundamental. But it needs to be woven together with space, and then create volumetric packets (bubbles) large enough to allow energy to congeal into particles of matter, before the material universe can come into existence.
I think the properties of higher-d spheres, the Lie groups from E8 to G2, and the Monster group, all figure into the background from which the universe emerges, and influence that emergence, however.
More later,
Jonathan
Thanks for sharing your ideas Jonathan. Indeed we don t know what we have at these planck scales, what are these foundamental mathematical and physical objects in fact. We cannot affirm. Have we 1D strings and a 1D main cosmological field creating our geonetries, topologies, matters, spacetime? or a geometrodynamics and points or in my model spheres ? we don t know. I see the generality of this universe like this, but it is an assumption of course, I must prove and I work about this. I consider like you know an universal sphere in optimisation evolution or a future sphere and I consider a central main cosmological sphere sending and coding finite series of spheres playing between these two constants, the zero absolute and the planck temperature. It is a gravitational coded aether made of these finite series of spheres, I consider that they have the same number than this finite serie cosmological of spheres. Oddly I have calculated, it approachs the dirac large number. The relevance of these series if we apply a specific serie is that the space disappears, so the space, the vacuum disappears and is made of particles coded. Take a central biggest sphere and after we applay 3 snmaller around this central sphere after 5 smaller around the 5 and we continue with the number that I have explained. You see that my model is totally different than the strings or the geonmetrodynamics because I consider particles coded and this aether, and so I don t consider that all comes from Waves, fields, oscillations to create this physicality. Now and I work about this , the relevance at my humble opinion is to formalise mathematically these finite series of spheres, a photon is too a finite serie , coded , they are for me like a fuel permitting the electromagnetism, the life Death and the fact to observe, they are just series coded so in resume like all. Now if we fornalise these series, finite with the Hamilton Ricci flow, the cold and heat, the heat equations, the lie derivatives, the lie groups, the topological spaces and euclidian spaces and the poincare conjecture, so it becomes relevant for the distribution and the rankings of our particles and the sortings, superimposings, synchronisations, we can consider the volumes,surface(even the hopf fibrations can be considered here on surfaces of spheres) , the mass, the densities, the angles, the deformations of spheres, the motions, rotations, senses of rotations, the moments and many others. I have even reached this quantum gravitation with this reasoning and in considering a cold Dark matter encoded in nuclei, more a fith force due to a serie of quantum BHs farer than our nuclear forces. I have respected the newtonian mechanics for this quantum gravitation. Like at our cosmological scale this matter non baryonic balances our electromagnetism and heat with this cold. This superfluid gravitational aether is maybe the key to explain all our unknowns and this gravitational aether creates the luminiferous one simply.
Best Regard
PS I have shared your essay on Facebook , friendly
Jonathan. In my essay "Clarification of Physics--", I introduce a new Successful Self Creation system that adds a new level to the epistemic "horizon". It adds another level to the basis of our knowledge and uses it to develop a complete creation process/result. I think you may find it interesting. Also, I would appreciate your comments on the essay. John D Crowell
I finally got around to reading you paper. It makes some illustrative points. The associated logistic map is a measure of the chaos on the reals and this terminiates at the Feigenbaum number. BTW, I thought the Mandelbrot set had z в†' z^2 + c.
The relationship between the reals, complex numbers, quaternions and octonions is subtle. With classical mechanics we have strictly reals, but analysis has behind CM has complex numbers. There is then a sort of covering ПЂ:в„‚ в†' в„ќ where the map is a restriction on this "fibration." With quantum mechanics is more straight forwards. The quantum wave is complex valued and the fibration is from nonabelian groups or Clifford groups for gauge fields onto the complex plane or the phase of a wave function ПЂ: в„Ќ в†' в„‚. Where things get a bit strange is with quantum gravitation, where the spacetime is noncommutative. The similar structure would then be ПЂ:O в†' в„Ќ, where now the base manifold is noncommutative and the fibration is nonassociative.
Cheers LC
Thanks for reading my essay Lawrence...
It is true the Mandelbrot formula can be written z 竊' z^2 + c, and whether you are plotting Mandelbrot or Julia Sets is only a matter of how the c is interpreted. If you choose a single value for every point, what you get is the Julia Set for that point. But if your c is z_0 - the location of the point on the complex plane you are evaluating - then what you get is the Mandelbrot Set.
Thanks for explicating the subtle relationship between the number types. And indeed it appears that there is an explicit relationship to different aspects of Physics. The quantum gravity regime is the most demanding, in this regard. As we approach the Planck scale, or near a BH horizon, we must give consideration to the non-commutative and non-associative components to know what is happening.
This brings some interesting and exciting Maths into play.
All the Best,
Jonathan
That is meant to be...
If you choose a single value of c for calculating every point, and only the z in z^2 c changes, you get the Julia Set for that initial value. But if your c is the same as the location you are iterating (z_0), and changes as you go, this gives you the full Mandelbrot Set. The fun thing is that the Mandelbrot Set is therefore a template for and a table of contents or index of all of the Julia Sets, because each Julia Set seed or initial value delineates the behavior and the character of the form found at that point in the Mandelbrot Set.
More later,
Jonathan
If you read my essay I work with the idea of fractals as outlined by Hossenfelder and Palmer. However, I appeal to a more standard definition of incomputability. The Mandelbrot set in some ways is the mother of all fractals, because the fractal dimension of the boundary is 2 - ε in the limit ε --> 0.
The role of octonions is something I discuss in my essay, but more in the appendix or supplementary material.
I am disappointed in how this is going. I entered this contest because the topic has been of interest to me for years. Yet, my essay is not doing well, and I should simply not enter these contests any more.
LC
Thanks again Lawrence...
We are lucky to have you among the entrants. Your essay is of high quality and relevance. I have been pressed for time, and have not had the chance to review and rate essays yet. But I greatly enjoyed skimming yours, and I expect my assessment will raise your score.
I have to wonder why some decent to fine essays have gotten scores of 2 or 3, but your offering is in the good to excellent range and your score should reflect this. The octonions have been occupying my thoughts a lot lately, and I am contemplating how non-associativity figures into everyday tasks like painting or baking, where cycles are completed in sequence.
More later,
Jonathan
Thank you John,
I'll get there. It sounds interesting. I have some thoughts along the lines you suggest, but I'll have to read your paper in order to find out if we agree.
More later,
Jonathan
Hi, I composed the following on my side:
Hi Jonathan,
Actually that was a general note, However thanks for the kind words.
I too have only read a handful of papers here. I have been pretty hard at work on this. I have not had much time to read papers or communicate with authors. I am now off work, as we are now into "social distancing." So we have to endure this exercise in Camus' existential angst in his novel The Plague with the expectation this will lessen the impact.
Stay safe and away from crowds. This virus seems to take older people down a lot. I am not worried about myself much, but I have some concerns with others. My mother is over 90 and I concerns there.
Cheers LC
Hi to both of you,
About these octonions, let s imagine that we consider 3 main E8 and that we consider these finite series of coded Spheres in my model sent from the central cosmological 3D sphere, it is there that sonething codes and transforms the E in matters, coded. I consider these series where space disappears and with a specific number, the same than our cosmological finite serie of 3D spheres, oddly it approachs the dirac large number. Now so consider one E8 in replacing the points or strings by these series and consider 3 E8 , E8xE8xE8 , one for the vacuum space, one for the photons and one for the cold dark matter, so we have main codes inside the E8 vacuum and the two others are fuels and permit the emergence of matters , geonetries, topologies and properties , electromagnetism and gravitation.
Regards
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
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
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; x5 -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
