Dear Aldo Filomeno,

While many essays speak of Grothendieck's 'dessin d'enfants', or the Langlands program, or the Monster group, etc. in hopes that these will answer some questions, you address probably the most significant mathematics of the last 60 years, gauge theory – and you properly put it in its place.

As no other general field of math has had the impact on physics as has...

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Dear Aldo Filomeno,

While many essays speak of Grothendieck's 'dessin d'enfants', or the Langlands program, or the Monster group, etc. in hopes that these will answer some questions, you address probably the most significant mathematics of the last 60 years, gauge theory – and you properly put it in its place.

As no other general field of math has had the impact on physics as has gauge theory, I'd say you have your priorities right. Also, you rightly include "(and vice versa)" when you note the relation of symmetry principles for every continuous global symmetry of the Lagrangians to which corresponds a conservation law.

It seems to me that if one had to classify these entities, the conservation laws would be ontological facts, while the symmetry principles would be epistemological effervescences.

The really amazing thing, to me, is that none of the basic symmetries are exact, from iso-spin to SUSY. You mention 'astonishing success' such as the prediction of the Omega minus. But have there really been that many such? Perhaps I'm jaded, but when it comes to trying various hierarchical layouts of the known particles, just how hard was it to notice "one seems to be missing here"?

I very much enjoyed your "Elegant but contingent…" analysis of gauge symmetry. I particularly liked that (B) assumes "a language full of non-actualized possibilities, and that the mathematics constituting our best physical theories is only one of the infinite possible mathematical descriptions of the regularities of the world."

My essay begins by 'extracting' regularities from measurement data to find a 'best' [in a max entropy sense] feature vector that represents the measured properties. Your analysis of the strong force leads again to the particular final choice being made among an extremely vast space of possibilities.

[I have suggested another possibility in The Chromodynamics War in which SU(3) is based on structure, not color. You might enjoy some of the ideas in this 'hard sci-fi' novel.]

It is not insignificant that the gauge fields are put in 'by hand' to a large extent.

But, to return to your "Elegant but contingent…", I have made the same argument against the Bell's basic model: it is 'Elegant but contingent' in the sense that it is contingent on a constant field, which leads to a null experimental result, and hence begins with a contradiction. There is much more to the story which is presented in my essay . I invite you to read it and would welcome feedback.

Thanks again for your very well written and quite on-target essay.

My best regards,

Edwin Eugene Klingman

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