My cadence was the reverse of Hardy, and slower by an order of magnitude. First, a question was asked, then after an objection, and admittedly a few hours of analysis, finally an assertion was made. In truth, Fred... I had trouble understanding your email (especially the part about Asperger's--Is [math-fun] a forum for studying medical diagnoses?). However, I think you may be getting at the idea that words like "Obvious" and also "Clearly" have limited usefulness in maths writing because they are subjective rather than objective. Adam came up with a nice insight that the proof would turn out better, for once, by the tactic of thinking inside a box (lol). However, the lemma at the finish is really non-obvious (to me). In case-by-case analysis of nested convex bodies, a quarter ellipse inside its bounding box shows relatively no pathology, but what is the elementary-most proof of the arclength inequality in this case? I don't know. The other idiomatic phrase is "splitting hairs". In this era of high-precision science, this phrase seems to have lost its negative connotation. The problem is so extreme that it sometimes seems like we don't have any experts left with experience at the synthetic task of putting the hairs back together. So, should we change perspective, and look at another related question? A week ago, I got into a bit of a spat with Brooks Pate about whether or not centrifugal distortion exists in nature. His argument was that--in his lab--he can essentially freeze the molecules, and when he does so, the rotational spectra show no signs of centrifugal distortion. This is good news relative to our current discussion, because (if we also set aside spin variables) the rotational Hamiltonian will reduce to the shape of an ellipsoid, and the parameter extraction looks for the semi-axis lengths. Then we can ask another difficult inversive question: Given a set of sufficiently nice rotational spectra, what are the different ways for extracting the (a,b,c) parameters? Is the only option just to use SPFIT? Cheers --Brad On Fri, Jun 28, 2019 at 8:20 AM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Those readers remaining awake are invited to consider the parallel with a recent . . .