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

      Dear Jonathan,

      Your very well composed, balanced and clear writing style only benefits your arguments. I found a few very powerful ideas in your essay, expressed in a memorable form. Allow me to quote them: "there are some structures that can be described as mathematical invariants, which arise as unchanging patterns within the core of Mathematics, or enduring features of the mathematical landscape, that are timeless and exist apart from any specific construction of that form." and "That Mathematics is a precursor to Physics is more difficult to prove, than the utility of Math as a descriptive tool for Physics". Even the question you are posing "Why should pure Mathematics shape Physics?" is deep and striking. Your essay does a very good job at reclaiming and shedding new light on the meaning of math. You are using well-chosen examples and you are illustrating your point with the words and thoughts of classics like Mandelbrot and 't Hooft. Congratulations on this great piece!

      Warm regards,

      Cristi

        Wow!

        This is excellent Michel. I will have to read the referenced papers for detail, when there is time, but they look very interesting. I have passed this comment and those papers on to Ed Klingman, as well.

        All the Best,

        Jonathan

        Thank you so much Peter!

        Your comments are gracious. I have bookmarked your presentation, and viewed part of it. The linked experiment looks very interesting. People don't realize the strange power of the Bessel beam (using a conical lens). But one can attain a degree of control over the fringes conventional optics cannot offer.

        All the Best,

        Jonathan

        Thanks very much Marc..

        I am happy that my essay so resonated with you. Over the course of the contest; I have found that many people have dabbled in some of the ideas I explore in my essay, such as the universal path integral you mention. I think it is very cool that by simply comparing notes with the other participants, there is so much to learn.

        All the Best,

        Jonathan

        Your thoughtful remarks are most appreciated Cristi..

        I try to go to the heart of some of the deep concepts that shape this subject, and I am glad that you feel I have succeeded in some measure. I look forward to reading your essay, which I hope will happen before the cutoff time.

        All the Best,

        Jonathan

        Dear Jonathan,

        It is very interesting to read an essay where the dynamical evolving systems that fractals are playing a key role, because they are the closest relative of symmetry breaking. I enjoyed your insightful remarks about the pattern behind patterns, the mathematical invariants and the internal consistency of theory. My main take away from your essay is the idea that we should further study the way that symmetries are conserved and broken; I think that indeed that is a key area of research, if we are aiming for a complete description of nature. You are doing a very good job presenting new arguments for supporting the mathematical universe, arguments that would have much benefited the initial proposal of this principle, I would dare say. Thank you for a very engaging read! I wish you best of luck in the contest and I accompany my wish with a well-deserved rating.

        Warm regards,

        Alma

          Good to rate those who write good essays and also remain here after the contest to engage intellectually. My rating didn't seem to change the score but certainly will neutralize the 1-bombers.

          Regards,

          Akinbo

            Thanks greatly Alma,

            Your comments were gracious. I hope I can return the favor. Contrasting conserved and broken symmetries is a major focus for me, right now, and I also think it will be a focus for Physics down the road.

            All the Best,

            Jonathan

            Thank you my friend..

            I have just had the pleasure to read and rate your essay. Excellent work, and enjoyable discussions, as always.

            Regards,

            Jonathan

            2 months later

            Hi Jonathan,

            Thank you for sharing your essay, in particular for reminding me about fractals, how wonderful they are, and for showing us your butterfly set. Also thanks for responding to the many comments.

            I thought you might find this you tube video TED talk interesting if you haven't already come across it. Michael Hansmeyer talking about building shapes that can not be imagined because they are too complex and at a scale of folding that can't be carried out by human beings. He shows that how to produce these shapes can be thought about quite simply, even though the output itself is unimaginable. It is a very simple process likened to morphogenesis and he mentions breeding of types to produce new designs. He also mentions designing processes rather than shapes in the future. So it seems we are not limited by our imagination. Michael Hansmeyer: Building unimaginable shapes.

            I also posted it on Silvia Wenmackers discussion as she wrote and talked about being unable to imagine the unimaginable. Best wishes, Georgina

              Thanks very much Georgina!

              I'll have to check out the link when I am awake. Hansmeyer's content sounds really cool. But fractals are like that; a simple seed lets one create forms of unimaginable beauty and complexity - and that's how nature works too!

              My gratitude for sharing this, and for your appreciation of my contributions.

              All the Best,

              Jonathan

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