Essay Abstract

A conversation with Tevian Dray, on the last day of GR21, brought to light some of the 'elephants in the room' with quantum gravity researchers and highlighted the essential part played by non-associative Maths - in any robust formulation attempting to address those looming concerns. While this is seen as a complication by most researchers; I assert that it is instead a clear road to a solution or family of solutions to long-standing problems in Physics. This lends support to the author's idea that nature employs the totality of all Mathematics - discovered and undiscovered - in its handiwork, such that invariant realities in Math spell out their own importance to Physics, and give rise to the universe we see today. As those same mathematical invariants unfold in the universe over time, they also give rise to processes that make the appearance and evolution of life inevitable.

Author Bio

Jonathan Dickau is an individual with skills and pursuits that span academic, artistic, and technical endeavors. With an inquisitive mind, since an early age; he has never quite grown up. Since winning a Grammy award for recording Pete Seeger "At 89," Jonathan has continued to learn and explored ways he can help the human race to better harmonize with Mother Earth and heal the threats to our planetary biosphere. He lives in upstate New York, working in Audio and Video production, while devoting increasing amounts of time to both writing and academic studies - especially Physics and Mathematics.

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I have not even opened your essay yet. I just noticed you were here. I was a reviewer for a paper you wrote on the cosmological implications of the Mandelbrot set. The idea was intriguing, and I have worked a variation of this up with anti-de Sitter spacetime. I attach what the projection of that is on the spatial part of AdS_3, which is a Poincare disk. So your idea was food for thought, which was one reason I accepted it.

I will read your paper probably later today or tomorrow. I have one up here as well http://fqxi.org/community/forum/topic/2737

LCAttachment #1: Mandelbrot_set_on_AdS.png

    Thanks greatly Lawrence!

    I got to hear several talks on AdS/CFT and holography in the breakout sessions at GR21, and there was quite a lot of food for thought. I am eager to read your paper as well, though I am working through some of the earlier submissions first. I find the AdS Mandelbrot image very intriguing. Presently; I'm working on a follow-up to my GR21 presentation, exploring how a certain Misiurewicz point represents Bose-Einstein condensation and Schwarzschild horizons - a connection recently explored extensively by Gia Dvali and colleagues.

    All the Best,

    Jonathan

    Dear Dickau,

    Good essay on Number Systems....

    Your words .....1." Nature is not limited by our views about what in Math is relevant to physical law, nor is it partial to any specific patterning our Math conventions have introduced. Whether we calculate in Roman or binary is not relevant to how nature generates what we know as Physics.".....

    2. ............ 'Octonionic Inflation avoids some of the problems with conventional Inflation cited by Steinhardt and colleagues [4], and it is a subject of my current research'..............

    But still you are considering inflation models only. That means you are neglecting 60 percent of Galaxies in the universe.... I request you to please revise your model...

    Have look at my essay also...

    Best wishes................

    =snp. gupta

      Thank you Satyavarapu,

      This is decidedly a work in progress, and there will be many revisions made, or variations tried - before the ideas are forged into a finely-tuned theory. I am pleased that some portion of my thesis resonates with you.

      All the Best,

      Jonathan

      Jonathan,

      I too am an advocate for the division algebras. I do not doubt that nature employs these structures in ways that we have yet to even imagine.

      You present several things from a perspective that I had not considered. For example, the problem of non-associativity ... I have been trying to get around this but you essentially argue that it should be embraced as a powerful tool.

      As another example, I was not aware that it was possible to arrive at the same result via different sets of intermediate rules ... but doesn't that basically say that associativity is still true, but you just have to view the whole problem as a single entity?

      I have been wondering how to view SR & GR in terms of quaternions and octonions. Perhaps you have thoughts on this? I understand that the Maxwell Equations can be neatly expressed with quaternions. Therefore, extension to SR should be straight-forward.

      I think we may have a very difficult challenge ahead. I can envision that quaternions and perhaps octonions can revolutionize how math, physics, and engineering are taught and practiced. But, it takes roughly 11 years in the public school system to have the prerequisites just for the Calculus of Real Numbers. With attitudes and constraints being what they are, how can we ever get to the point where these things are widely taught to those who can benefit from them?

      Best Regards and Good Luck,

      Gary Simpson

        Hello Jonatha,;

        Happy to see you on this essay's contest.Always relevant to read your works about maths and physics.

        all the best,and Good luck from Belgium.:)

          Having also not yet downloaded your essay, I fear it might not be as intriguing as your earlier one where you addressed the evolution of children, something that I consider on topic this time.

          Instead you are using teleological language: "nature employs the totality of all Mathematics - discovered and undiscovered - in its handiwork". My view is different. I see mathematics in Cantor's sense endlessly open even to pure phantasm that might not even be always selfconsistent. Cantor agued: "The essence of mathematics is its freedom".

          I nonetheless agree: It is doesn't matter whether or not something is already discovered. Where is the borderline in physics between fabricated Platonism and discovered strictly logical common sense? My criterion is non-arbitrariness.

            Thanks Gary,

            You are right about associativity still working for the system as a whole. The octonions, for example, are alternative (where associative and anti-associative terms alternate), so they obey a weaker form of the associative rule. The next periodicity is 8, so things get more complicated there. Rick Lockyer points to 16 flavors of octonion multiplication, which he and I think pertains to different areas of physics, much as the individual flavors of String Theory have their greatest utility for a certain portion of the energetic and interaction landscape, but become intractable in other regimes.

            I think the problem is starting with the real numbers, to a degree. My nephew had trouble in Math because he had a hard time taking the concept of numbers that just sit there on faith. But in more advanced Maths, numerical quantities are more chimeric. So he could have been seeing something his teachers didn't, but was forced to conform anyway. Recent papers by Hyun Seok Yang on Emergent Spacetime claim to show that if spacetime is non-commutative at the microscale, then spacetime must also be emergent. If his proof is true, then my premise for this essay also holds water.

            Warm Regards,

            Jonathan

            Dear Jonathan.

            Please excuse me for I have no intention of disparaging in any way any part of your essay.

            I merely wish to point out that "Everything should be made as simple as possible, but not simpler. Albert Einstein (1879 - 1955) Physicist & Nobel Laureate."

            Only nature could produce a reality so simple, a single cell amoeba could deal with it.

            The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

            Joe Fisher, Realist

              Thank you Eckard,

              From where I sit, there is very little difference between the Platonist's view and the discovered strict logic of common sense - if they are bumping into the same hidden structure. Most of what Maths describe arises from an exploratory testing of what is strictly logical. It makes sense to me that certain patterns emerge, where what is logical in the real world and what is logical in some purely abstract frameworks agree perfectly.

              I think some folks do dwell on invented abstractions too much. Sure the Kac-Moody algebras capture many of the salient properties of the natural hyper-complex types Quaternion and Octonion, but I think the latter are fundamental - in terms of non-arbitrariness - since they arise in a simple construction from the spheres. One can fabricate spaces of the Calabi-Yau type which fit well the requirements of String Theory, but I question whether nature works like that, and therefore the naturalness of such fabrication. I like better the idea of Baez and Huerta; that Stings inherit their power from the strength of the natural algebras.

              All the Best,

              Jonathan

              Happy to hear you chime in Steve..

              I'm glad too, that I can help inform people that the properties of higher-order spheres matters to Physics in the real world - even if that connection might not be apparent on the surface.

              All the Best,

              Jonathan

              Thanks Joe,

              It is good to have a realist among us, and I agree that we should keep things simple - but only as simple as things really are.

              All the Best,

              Jonathan

              That was meant to be..

              As Baez and Huerta suggest; "Strings inherit their power from the strength of the natural algebras."

              Sorry for the misspelling. But maybe Sting Theory makes as much sense; yes?

              Regards,

              Jonathan

              You are welcome Jonathan,

              I am less parano lol ,I like now these geometreical algenbras.I beleive strongly Jonathan that my 3D quant and cosm sphères could be superimposed with an infinite higher oder considering thisn uniquenss.If max tegmark is right about multiverse that I consider like multispheres.So we have an interesting superimposing.Now if my theory of spherisation is correct, and if I am right about these BHs, quant BHs, spherons particles of gravitation, cold dark matter and my equation, so you can see this standard model encircled by this gravitational sphere.See that the spherical volumes are essential for the proportions.The gravitational aether so fromthe central cosm BH so implies the gravitational aether, this spherte seems tending to infinity and still more when I consider the multiverse of Mr Tegmark.The sphères so are sumperimposed due to these BHs implying gravitational aethers.A little if I sad that oour gravitational aether due to our milky way and its supermassive BH was connected with this infinite gravitational sphere.So you can understand why l is not constant because proportional with the correlated BH where these particles come from.Now if we parallelize these 2D sphères due to maths and that we superimpose my 3D sphères and these encodings of photons and spherons in nuclei,which are gravitational due to this serie of BHs towards the singularity.That becomes relevant if we consider multiverse.We have so a play of laws foreach universe with its own gravitational aether,a gravit sphere.See that in our universal sphere so we have c,h,G,alpha and this and that but not for others due to thie volume of the central sphere of each universe implying its own gravitational aether and coded,informations.Now if my équations are correct,we can play with all these laws.Lie,; Cifford,hopf,banach,hilbert,euler,maxwell, lagrangen;hamilton,feynman,einstein, newton, tesla,dirac,.....HELP US :)

              Ps insert these 3D sphères quant and cosm in these 2D parallelizations......

              Von Neumann d tell us that the ponts of equilibrium are possible when the respect is mutual and sincereand when we eat all at the same table.We must save this planet Jonathan with this liberation of funds of this world bank for our solar system and the well of all.

              I am not crazy it is God who said me this lol let's reach these points of equilibrium ,after all the sphere is the perfect equilibrium between forces :)they turn so they are.I am not difficult you know Jonathan I have nothing, two small dogs,alone without familly,without money,without nothing.Just a simple theory of spherisation with quant and cosm 3D sphères Inside this sphere.I am jus a simple nursery man for plants and flowers even if people have killed 12000 fuchsias aged of 3 years in belgium iomplyin,g a bankrupcy.I have said me that I will stop the horticulture and production due to this evil act of these bad persons of belgium.But In fact after some years of disaters,I have not said my last words if God permits me ....Nothing Jonathan,I will go at new York if I must.I am almready reincarnated on an other planet, I am already died you know.So this explains that.Take my friend Jedi of The Sphere and don't forget ,we fight the unconsciousness :) universally, altruistically and spherically yours

              Dr Spock Jonathan, we must create this united states of the SPHERE USS ENTERPRISE ....liberation of funds......evolution spherisation......We are travellers from Stars....We are Jedis of the SPHERE lol let's spherisize this solar system .....

              I read your paper. Clearly you have gotten bitten by the octonion issue. Take a look at Baez' paper "The Octonions". This will give you the basic preliminaries on the structure of octonions, the Fano plane, tables, Hopf fibration and group theoretic realizations. There is area to explore here, and in particular how this leads to a general eigenvalued system with the Freudenthal triplet, or J^3(O)

              Cheers LC

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              • Post #19

              Jonathan, thank you for an enjoyable and enlightening read. I'd like to take your provocative opening sentence seriously and see where it leads. If we had to formalize the operations of arithmetic for Roman numerals, we might develop a set of rules and conditions for letter incrementing/decrementing, substitution, and so on. Even something as basic as multiplication might be so onerous it could only be feasibly done by machine. Then algebra and higher-order functions are needed, and the sets of rules and conditions become still more astronomically complex. To say nothing of what would be required when we need calculus, diff eq's, complex numbers, and so on. We wouldn't even be able to solve for X, because X is already taken by a number! (That's an attempt at humor.) In our bizarro-Roman world, we'd recognize that the math required to calculate the trajectory of a cannonball actually does work, and we might therefore be tempted to say that this math describes how the world functions, that the rules and conditions we've discovered dictate how the particles of the universe behave -- although in reality, calculations with Arabic or binary numerals would be equally effective, only much simpler.

              Perhaps we're in a version of this Roman mathematical nightmare today. In our world, there could be a completely undiscovered mathematics that is equally effective at doing for us what higher algebras can do, only in a simpler and more holistic or fundamental manner. In other words the complexity of our higher maths might emerge from the lower maths, in the same way that the vast complexity of the rules and conditions for solving a Roman-numerals differential equation would emerge from the rules and conditions for doing arithmetic in that system. I don't believe we're in a position yet to rule that out.

              Of course no one knows what this ultimate fundamental mathematics might be. But the higher maths remind me of the pre-Copernican epicycles, which were useful for human calculations even though they are demonstrably not features of nature. The added entities of our higher maths may only *seem* necessary for our calculations because we don't have the tools to perform the same operations any other way. Applying Occam's razor, we should demand evidence that these maths really are features of the world (and not just useful/predictive to humans), evidence that is commensurate with their complexity, while at the same time looking for a fundamental mathematics. A deeper math could make our higher maths not only unnecessary, it may also lead to discoveries about the evolution mechanisms of life/intentionality/consciousness and so on -- in the way that Copernicus' model led to discoveries about gravitation, which might have been impossible had we insisted on sticking with the Ptolemaic system.

              Thanks again for the stimulating essay -- I wish I'd had the opportunity to think about these questions for the Trick or Truth contest, which I sat out. Best of luck!

              Karl Coryat

                A cogent argument, Jonathan, but somehow I can't see that Math makes the emergence of the universe and life inevitable. Math certainly helps the dynamics of life be more understandable through modelling and such (which I have done), especially if you are conversant in math, and maybe that's my problem. I can see that nature, for example, wings, flower petals and leave, are mathematically expressed origami-style in their patterns of development. I too worked in an octal system of computers years ago, the Univac 1100, but I can't see that math tells the universe what to create beyond certain mathematical laws of entropy and Dr. England's theory, which I use as an example.

                I am impressed with your presentation, though.

                Jim Hoover