How the Totality of Mathematics Shapes Physics by Jonathan J. Dickau

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

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

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

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