Code words for this in MIT lectures: "It is intuitively obvious to the most casual observer that . . ." On Fri, Jun 28, 2019 at 9:47 AM rwg <rwg@ma.sdf.org> wrote:

-------- Original Message -------- Subject: Re: [math-fun] ellipsoid from girths: multivariate series reversion Date: 2019-06-28 06:18 From: Fred Lunnon <fred.lunnon@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>

"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