Let us consider the Man at C&A, where C and A are points on a plane equidistant from central point B. We might ask, reasonably, why C precedes A in this hypothetical space, when it is more usual, much more usual, for A to precede C, but quite frankly this is the least of our worries. Far more problematic is the idea that the Man is at C and A simultaneously. Greater minds than mine have, over the centuries, devised the natural laws by which everything in the known universe is bound, and I would not be exaggerating if I said that these laws simply will not tolerate a man being in two places at once.
We can immediately dispose of the somewhat desperate solution that the Man at point A is a doppelgänger, one who appears identical in every respect to the “original” man at point C, but is not him. To show how facetious this idea is, we need only remark that we are dealing with the Man at C&A, not the Men, and it is the plural Men we would be speaking of if we had the Man at C and another Man at A, no matter how uncannily the latter resembled the former, even down to the precise number of hairs on the head or the disposition of pockmarks on the grisly countenance.
So we must be clear that when we speak of the Man at C&A, we speak of the same Man, absolutely identical in all particulars, at both point C and point A which, if you are paying attention, you will remember are equidistant from point B. Point B, by the way. is unoccupied, by either Man or Woman or Beast of the Field. We posit its existence the better to comprehend the space between C and A, and also because, in its absence, there would be no reason I can think of why we should not call point C point B. But as I say, there are greater minds than mine, and perhaps one of them could devise a compelling reason why B should be ejected from the hypothesis entirely. Until such reasoning is applied, however, we will continue to insert an unoccupied point B between, and equidistant from, the two points at C and A which, as we have seen, are occupied by the Man.
Gosh, this is fun.
We might stumble towards a comprehensive explanation of the Man being at C and A if we introduce the element of Time. Let us imagine we are wearing a cheap wristwatch, and keeping one eye upon it as we consider the Man at C&A. The whole damn thing makes sense if we are able to say that the Man is at C at, say, 10.30 AM, and at A at 2.30 PM. We might want to ask how on earth it takes him four hours to make the simple journey from C to A, passing through B to pick up a sausage roll for sustenance, but we can perhaps account for that by giving him a pair of crutches upon which he must lug himself along, his legs being withered. Such infirmity would fit neatly with the grisly countenance above noted.
The obvious objection to this ostensibly happy solution is that we are thus dealing not with the Man at C&A but with the Man at C then A. We must, then, regrettably, remove the cheap wristwatch and chuck it into a ditch and scratch our head in bewilderment. Think! Think! Aha! A faint glimmer slowly resolves itself into the near certainty a solution can be found if we imagine point C and point A as so close together, almost abutting one another, with only tiny little point B between them, that the Man is straddling them, one foot planted firmly at C and the other at A. He is indubitably the Man at C&A!
But on second thoughts we must knock this proposition down, violently. It has already been shown that the man’s legs are withered and he must rely upon crutches. It is beyond the bounds of sense that such a cripple could stand, steady and upright and resolute, with either foot planted firmly anywhere at all. The best he could do would be to lock the base of one crutch in position at point C and the other at point A, and balance himself, swinging between them. But it can be proved, using geometry or one of the allied disciplines devised by better minds than my own, that he would of necessity be swinging in the air just above point B, the tiny point, you recall, we have jammed between point C and point A for cogent reasons not to be gainsaid. He is therefore the Man at B, or, at best, the Man at B whose crutches are planted at C&A. Even a halfwit, I think, would have to concede that such a fellow is a very different beast to a bona fide Man at C&A.
Increasingly befuddled, we may have to return, reluctantly, to the less than satisfactory doppelgänger theory or, even more reluctantly, suspend the laws of physics. But wait! Could it be that the answer is staring us in the face, or rather glancing at us slantwise, at an unexpected angle? Could it all be a bit of stage trickery mustered up by a conjurer, employing a mirror, perhaps, placed at point B? If we could identify an encrutched variety theatre magician of grisly countenance, we would surely be home and dry. And immediately one springs to mind. Who will ever forget the crippled crutch-bound maestro The Amazing Blinko And His Lovely Assistant Janet? Surely it is The Amazing Blinko who, with the aid of a mirror, or more likely mirrors plural, is the Man who appears to be at both C and A at one and the same time!
We can now go and take a nap, having solved the conundrum. Alas, our nap is troubled by uneasy dreams, and we wake in a cold sweat, an unanswerable question clanging in our head – by what feat of legerdemain did The Amazing Blinko make His Lovely Assistant Janet softly and suddenly vanish away from C&A?