"But that's obvious. No, wait --- is it obvious?" (G. H. Hardy, apocryphally). Is there any trope that reveals insecurity more nakedly and unintentionally? Though Hardy (if it was he --- reference, anybody?) was alert to the trap before tumbling in completely; the anecdote continues with him disappearing to his study to ponder, returning considerably later to announce triumphantly (and to a noticeably shrunken audience) "Yes, it is obvious!", before resuming the lecture (on Number Theory). Those readers remaining awake are invited to consider the parallel with a recent splenetic diatribe in this thread in support of the conjectural obviousness of a certain lemma; then to compare that with a subsequently contributed proof of the lemma itself in approximately one seventh of the same length. Their relative success in illuminating the topic, while harder to quantify, should be easier still to assess; obvious, even? In the outside world of general social intercourse, "Obviously ..." may reliably be interpreted to indicate that the speaker either knows or suspects that the claim introduced is actually false, or at best vacuous; and aims to forestall dissent by implying that only an ignoramus would question it. From a mathematician one expects a diminished tendency to purposeful tergiversation --- that goes with the Asperger's --- so that in a technical setting, a more accurate gloss might run something like the following: "I fervantly hope ... is correct, but have never taken the trouble to establish securely under what constraints; and besides am wary of doing so for fear of discovering instead that, all along, I have been pontificating via my fundament". Compare "It is well-known that ...", etc. Hardly a secure basis for scientific advance one might suppose, however effective such strategies may prove in other areas of human endeavour! Incidentally, pause to recall the "obvious" impossibility of (say) --- Everting a rubbery, phantom sphere without kinking it: https://en.wikipedia.org/wiki/Sphere_eversion Dissecting a unit ball into (five) parts which reassemble into two unit balls: https://en.wikipedia.org/wiki/Banach–Tarski_paradox Electrons that sneak through both slits of a screen only when nobody is looking: https://en.wikipedia.org/wiki/Double-slit_experiment etc. etc. ad infinitum. Personally, I try hard to avoid the word (except ironically, obviously). Along with "simple", with respect to which I more often fail ... Fred Lunnon

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 . . .