Jonathan,

It's all weird to me! As I said in an exchange with Constantinos Ragazas on Steve Sax's page, I often wonder if mathematicians realize how phenomenal their memory capabilities are. I rely on people like you to gain some insight of what the myriad maths are about, and often find myself completely out of my depth.

Intuitively though, it seems that if the addition operation is short-cutted, a moderating value would be lost, and the butterfly comes out of chrysalis in the round, as one direction lengthens without restraint. I still can't grasp the morphology of quarternions and division algebras that project a 4-D shape, and lost track of where I read a post of yours about 3-D imagining being an approximation. Like many I suppose, I find the images beautiful and can only wonder how that fills space over time.

And of course there is the ever present counter-intuitiveness of QM that over-shadows just how counter-intuitive Relativistic spacetime is itself! I for one greatly appreciate that yours is a genuine kindness in patient explanations of the rudiments of mathematical physics, thank-you. jrc

Thanks for sharing Joe,

I think I am starting to get the gist of what you are saying.

All the Best,

Jonathan

I have considered these questions, Akinbo...

1st - the Mandelbrot's cusp at (.25,0i) is the minimum extent and highest energy represented in the Mandelbrot figure. But the theory would indicate that this translates into a minimum time step. However; for anything to persist longer than the Planck time, in this theory, it must have a non-zero size.

2nd - particles act as probes of the properties of a given space, retaining and conveying information about separability and separation. I would say that once forms exist as self-contained independent units, which can move relative to each other, this defines or helps determine the dimensionality of space as well.

3rd - I think part of the meaning of Math is that it preserves some features of natural law that are persistent, from cosmological era to era, from inception to its demise or the beginning of a new cycle, or from universe to universe in a multiverse scenario (more below).

As for atoms of space, however; that concept speaks mainly to how the fabric of spacetime emerges, and one can't discern individual unit cells after that. If space and time are relativistically indistinguishable; then there is a lower limit of around 10^-13 cm - where particle separability is possible - in which Relativity is defined. And item 2 answers this.

The Cosmology based on the Mandelbrot Set does not tell us whether a cold dark end is the universe's ultimate fate, or whether a new cycle would begin, as I can show you the graphical representation of both scenarios. Likewise; it supports the idea that the universe is singular and allows for the possibility of multiple universes. This suggests these possibilities coexist equivalently.

All the Best,

Jonathan

Hi Jonathan,

You get my high mark, even while I disagree with your view of Tegmark's view.

You and Max both approach your respective frameworks for a unifying physical theory with personal, subjective accounts of your journey through mathematics -- Max's hypothesis is not philosophy, however; he explicitly holds forth a way to refute the physical framework.

That's why I have a hard time getting my mind around a particular mathematical structure, such as the Mandelbrot set (or Julia, or Koch or ...) as fundamental to a unifying theory. (Same goes for Lisi's E_8 symmetry.)

For if we allow the fundamental reality of such structures, we lend more meaning to the calculating machinery that creates them, than to relations between and among the quantities and qualities that dominate our physical experience. The former is static and discrete; the latter is dynamic and continuous.

All best,

Tom

    Thanks Tom,

    This same question was raised by Lorraine on the general discussion page for the contest (Brendan's thread); she asserted that the Mandelbrot Set is 100% boring, and I presented a different view. To me; the static nature of the object belies what's going on beneath the surface (so to speak), where every point on the set is associated with a different flavor of dynamism.

    In fact; we can look at the Julia Set for any one point, and study its properties as a dynamical system. This can get boring too, though it leaves room for variations. But when the entire Mandelbrot spawning these Julias is considered, the evolutive properties of the dynamism become apparent. It is this evolution of dynamism that is my primary area of research and interest in M.

    All the Best,

    Jonathan

    Well, of course I don't think that the Mandelbrot set, or any of the variety of self similar sets are boring. The Mandelbrot set, in fact, has earned its title as the most complex object in mathematics.

    What I mean, is that the initial conditions for any of these structures are arbitrarily chosen and cannot be shown to be generated from any first principle more general than the spatial assumptions that precede them.

    Best,

    Tom

    4 days later

    Dear Jonathan,

    Thank you for your generous comments on my blog. I did not attempt to be on the ridge, there are many snipers! For sure, we will contnue to interact and learn from each other as I experience from many authors at this contest.

    Best.

    Michel

    6 days later

    Jonathan, Sorry I hate this essay. It is entirely too hagiographic, in that it makes mathematics into a Godlike hero. That is entirely unjustified by the facts. What I see is a human illusion that mathematics is effective in physics and a lot of propaganda to justify making mathematics take over the role of GOD. Sorry I am not buying this modern mythology of mathematics as the new GOD.

      4 days later

      Dear Jonathan,

      I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

      All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

      Joe Fisher

        Dear Jonathan,

        Thank you ever so much for the terrific you left about my essay.

        All real things have a real surface. Real light does not have a real surface. Real light does not consist of abstract photons, or abstract plasmons. It is physically impossible to create a real light by means of manipulating an abstract photoelectric effect.

        Proof that real light did not have a real surface was established by the slit test. When the pre-light emission struck the first surface, real light appeared on all of the area of the surface, except of course where the slit, or slits had been cut. The pre-light emission flew through the slit or slits and when they struck the surface behind the slits they had to produce a real light effect that was different than the real light showing on the first surface.

        Joe Fisher

          Dearly Beloved Jonathan,

          I am so excited about your absract,which constitutes a significant commentary on the inseparable coefficiency between Maths and Physics.I am even much more elated with your lucid explanation of the phenomenon in the body of your essay.

          Keep on flourishing.

          Lloyd Tamarapreye Okoko.

          Jonathan,

          Time grows short, so I am revisiting essays I've read to assure I've rated them. I find that I had questions which leads me to your Mandelbrot algorithm: http://www.fractaldesign.net/FractalAlgorithm.aspxrated. I find that the imaginary number discussion and orbits represented on a Cartesian plane are similar to machinations of Euler's Identity that I use. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345.

          Jim

          Hi Jonathan,

          It is a pleasure to meet you in FQXi Essay Contest. Once again, you made an excellent work through a very interesting and enjoyable Essay. Here are some comments:

          1) Your idea that Nature has been shaped by all of the applicable Maths since the beginning of time is intriguing. In this way Nature seems a unique sentient being.

          2) I am fascinated by fractals. I see that you were a pioneer of fractal cosmology. Is it a coincidence that your original work on this issue is dated 1987, i.e. the same year that Luciano Pietronero and his team attempted to to model the distribution of galaxies with a fractal pattern?

          3) I am pleasured to know that you entertained a proposition similar to Tegmark's MUH long before his framing of it. Congrats, this must be popularized.

          4) I did not know Gibbs' statement that "the laws of physics are a universal behaviour to be found in the class of all possible mathematical systems." I completely agree with Phil. Now, I am going to read his Essay.

          5) It is not a coincidence that you have found that the concepts and entities most central or fundamental to Math also have the greatest relevance to Physics.

          6) Gerard 't Hooft's answer "We don't need atoms of space or whatever, because the laws of nature do the calculating for us" is intriguing and I agree with your interpretation that this means the laws of nature are inherently mathematical.

          Finally, I find your Essay extremely intriguing. Thus, I am going to give you a deserved highest score.

          I hope you will have a chance to read my Essay.

          I wish you best luck in the Contest.

          Cheers, Ch.

            Thank you Christian,

            Your comments and appreciation are gracious. I first started your paper a day or two ago, but have not finished reading and digesting yet. I do expect to read it and rate you before the deadline.

            All the Best,

            Jonathan

            Thank you Lloyd,

            I appreciate your taking the time to read and comment, and also your gracious remarks. I am glad my essay and its message have pleased you, and I look forward to reading yours.

            All the Best,

            Jonathan

            Thanks Joe,

            I'm glad we can find some small area of agreement.

            Regards,

            Jonathan

            I'm sorry too Harry..

            But it appears you are judging me by what I didn't write. Perhaps if this contest had a more spiritual slant, asking how Math might shape or be shaped by the nature of the Divine, I would have written something to your liking. I did ponder some questions relating to that matter, in my writing, some years ago. I do not reject God or a belief in God, but I think that even an all-powerful deity would need some amazingly reliable and dependable tools - to create a universe like the one we observe. This is what I think Math provides.

            All the Best,

            Jonathan

            Dear Jonathan,

            How are you? I noticed a valuable post from you on Foster's blog about this contest

            "Did you grasp (Sylvain) that Ed Klingman is using Dirac's criterion Sylvain, instead of Pauli's? If you accept Dirac's formula, it naturally follows that Pauli's criterion in QM has a restricted codomain - which is only reasonable if the Physics of the experimental setup demand it. This is what Edwin Klingman calls into question, and changes the outcome if all other logical steps are the same."

            Do you mean in the context of Dirac equations?

            If so my paper below may be helpful in the sense that it connects Dirac matrices (i.e. two-qubit operators) to the CPT group and the E8 Weyl group. The work was inspired by Socolovsky's paper in Ref. [1] of the paper.

            http://xxx.lanl.gov/pdf/0906.1063.pdf (Int.J.Theor.Phys.49:1044-1054,2010 ).

            The issue of Bell's theorem is not discussed in the paper although it is implicit through the entangled matrices generating W(E_8). This work had further ramifications as here

            http://xxx.lanl.gov/abs/1002.4287 (Physica Scripta 147 (2012) 014025)

            It may well be that one can gain much by putting Bell's question in a wider group theoretical frame. But this is part of my present "dessin d'enfant" frame, as you already now. Philosophically, more maths is needed than just Bell's too qualitative arguments and his reference to Bohm's classical (space-time) interpretation.

            Best wishes,

            Michel

              Jonathan,

              It was clear the subject was right up your street and you did it good justice in the space available. I'm clearly of the opinion the major 'missing pieces' you identify can be found in the hierarchical structures of fractals, Mandelbrot and also Fibonacci. We must somehow perhaps popularise the concept of phenomena below the 'EM scale' limit of the Planck length.

              I've identified that even the simple rules of brackets in arithmetic form such a structure, extending and repeating indefinitely - in my essay, which I hope you get to. I'm very glad I got to yours, my score should give you a deserved boost. After the contest I hope you may also look at this recent (9min but very dense) video identifying some of the solutions which arise from fractal dynamics.

              http://youtu.be/KPsCp_S4cUs.

              This new paper on the 'twists within twists' of light confirms that concept.)

              Accelerated rotation with orbital angular momentum modes

              Very well done and best of luck in the run in.

              Peter

                Dear Jonathan,

                One again in this contest, you build upon your fascination with the Mandelbrot set! I have to thank you: it is through the reference in your essay that I got acquainted with Philip Gibbs' "Theory of Theories". Like you, I find fascinating the idea that something like an averaged path integral of mathematical structures could converge to yield something like our physical reality. As you put it, "things are shaped by the totality of math"... intriguing!

                Let us keep exploring the mysterious interface between mathematical and physical existence! All the best,

                Marc