The Problem: Dedekind’s UNreal UNkind cut.

I see problems with both a strictly mathematicians’ approach AND a strictly particle physicists’ approach. Yes, Michael Atiyah’s “Fine Structure Constant” paper is vague (not detailed enough in places) in many respects both mathematically and physically. *However, everybody is vague in their expositions, because that’s the nature of modeling ideas.* With one side saying: “I don’t understand the mathematics” and the other side saying “I don’t understand the physics” — we have a problem here. It is a good discussion to have, but watch out for saying “I don’t understand it, therefore it is not applicable”.

Sean Carroll says: “Renormalization teaches us …”. To me, this raises a red flag. Renormalization is a mathematical trick used by particle physicists— to say that “things are too complicated” (therefore we will chose a narrow band (a gauge) ) and treat it as 2D Euclidean “thin enough” approximation and ASSUME that the “real number” constants (mixing angles and/or scale factors) gives you precise process information in higher measure spaces (e.g., 3D, Orthogonal, Simplicial, Lie Groups) reminds me of Nima Arkani-Hamed’s very informative lectures but EQUALLY VAGUE (and hand waving via tensors (assuming “real numbers” and Hemitian products as a foundation)) rant on the “problems with” coming up with a theory of quantum gravity.

This is good that the mathematicians and the physicists enjoy dismissing each other, so that comparative science and relational complexity has a wide open lattice to play with. It’s a Dedekind’s unreal unkind cut.