The Geometrist

Euclid, the ancient Greek father of geometry, had insisted that parallel lines never meet. He was in error. Understandable, of course, and for many centuries the postulate had withstood close examination, but in error nonetheless. Charles Lightfoot, Geometrist Royal to his namesake monarch, had a proof. It was complicated, certainly to the non-adept, but running through it were the two clear, simple lines, inextricably converging, and yet, although he had arrived at his formula some eighteen months earlier, he was not quite ready to publish it. There was a connection, a kind of Northwest Passage to be negotiated first. If it could be done – he was very close – it would not just be parallel lines but the whole Euclidean system that would come unstuck. The Theory of Triangles would change, and then Time, Distance, Mass.

Meanwhile, as somewhere in the back reaches of his mind it continued to draw itself together of its own accord, as such things will, it had become imperative to investigate rumours he had heard, of geometrists and mathematicians in other parts of Europe working in the same direction and perhaps, for all he knew, perilously close to the same realisation: not a great problem in one sense, since a discovery is a discovery whoever makes it, but he had a reputation to consolidate as the youngest and, conceptually, most daring and elegant thinker in the Royal Academy, with the king’s ears – so even Spratt himself had acknowledged – more and more often pricked in his direction. To secure the discovery for his own would make his future.

So far his luck had held. Böhm in Leipzig was too old and too angry and too often drunk to come up with anything now, though in four days’ talking, drinking with him, sniffing around, he had come to think that the man may well have had it almost within his grasp some years ago, but had let it slip through his fingers. And Fiorelli before that, with whom he’d caught up in Perugia, had been all show: intuitive, yes, but his claim to have done it himself was all bluster, an inept attempt to smoke out anyone who had. Now there was Grucicovic in Klausenberg, two weeks’ travel even to get there, but in this he had been lucky again. New friends in Leipzig had written to friends of their own, these had written to others, and although these had not always had the most sympathetic or informed of minds – what could you ask, in the Black Forest? – he had been kindly, respectfully and often generously accommodated, so that only twice had he needed to put up in an inn along the way.

The present company was amongst the most pleasant so far. His host, although rather boorish and preoccupied with land and his dispute with a neighbour over fishing rights, was generous in the extreme – as perhaps he could afford to be, since his rich estate took in the entire valley about him – and so useful and productive had Charles Lightfoot found his short time in the upstairs chamber, with its warm fire and commodious writing desk before the large window and its panoramic views of tall forest and snow-capped mountains, that he had stayed a third and now a fourth day, although given that his hosts themselves had to depart the next for a short period in Szeged, this night would surely have to be his last.

There was, also, the intriguing matter of his hostess, a woman surely too fine for so earthbound a husband, and starved for intellectual company. She had been so swift to grasp his purposes, so stimulating in her questions, so keen to know any and all of what he might have to tell, that he had wondered how she could survive so remote a life. And at first he had thought that it was this and only this – the chance to speak of England, Germany, physics, philosophy – although before the first evening had ended he had gained the firm impression that there was, to her attentions, something more. Indeed, his noticing, and responding as both chivalry and his own nature demanded – a particular, bipolar force and flow of attentions – had become a sort of substructure to his visit. The way, passing a plate unnecessarily and almost unnoticed, her fingers might accidentally touch his own; the way, more than once, her foot had brushed his, or his had been able, with the merest movement, to touch hers beneath the table as the meal progressed; the way their eyes had locked during the most casual of exchanges; the way, on the second morning, déshabillé, she had passed slowly by a window visible from his own, in such a manner as could neither be said to have shown any consciousness of his presence, nor have been witnessed by any but himself.

It was not the first time that this or some such thing had happened on his travels. Indeed such things had occurred, on this trip, with so pleasing and piquant a frequency that, tempting as it might have been to see behind them some particular attractiveness in his own person, he had at last had to admit the likelier possibility that there is something in the air that travellers wear ineluctably about them, of other places, other climates, other knowledges and customs than one’s own, a greater world. But such had been the graceful and subtle eroticism of this lady’s gestures that she had nonetheless inflamed his imagination remarkably.

So in any case it was that on the last night, she having retired early in anticipation of the next day’s travel, he was impelled to an uncharacteristic boldness. With firm assurances of a proper farewell the next morning, he left his already somewhat inebriated host deep in conversation with his estate manager and quietly climbed the stairs toward his own bedchamber, on the way encountering her maid descending with a large pitcher, to all appearances for more hot water for a bath. It was at this point that an idea had occurred to him, outrageous, pointless, but perhaps, being so pointless, also harmless enough, if only it could be carried off. A gesture, a thought, a gift of sight and silence exchanged between two who, in the circumstances, could exchange nothing more: the last of their gallantries, a coup de grâce.

Instead of moving, as he should have, directly to the further staircase and ascending to his own room, he took the short corridor beyond, toward her chamber. As he neared her door – it could only be that one – he heard, the once, a gentle sluicing of water. But no voices. She, if indeed it was she, was alone, as by all his hasty calculations she must have been. She had only two maidservants. One, doubling this evening at the table owing to a kitchen girl’s indisposition, had only a very short time before, as he was leaving, been sent for more cheese and port wine, and could scarcely by this have returned from the kitchen. And the other it was whom he had just seen descending for more water.

The prospect – a glance, a word, nothing else – excited and compelled him profoundly. His heart pounded almost audibly and he experienced, on the threshold, a brief moment of breathlessness. If she were not alone, or if she rejected, repelled him, what could he say? An error, certainly, complete absent-mindedness, a total losing of his way. And he would of course tender his profoundest, confused apologies. He was sure – such was this compulsion, this urgent necessity – that, embarrassing as such an eventuality might be, he could somehow talk his way through it.

But that was not necessary. He opened the door, alarmed even as he did so at his own boldness; and, as if his sudden fantasy had raced before him to arrange the encounter with miraculous precision, she looked up at him from the broad tub, expressing, in a flicker of her eyes that seemed at once a flicker of the flesh also, only the slightest, most rapidly suppressed surprise, and making no attempt whatsoever to cover her nakedness. A long, open stare, as if in the eyes alone there could be all congress, all union, as indeed all that long night in his own bed it would feel as if there had almost been – as if, too, they both knew that this was all that was possible within the albeit exquisite limits of the moment.

He woke, the next morning, far later than he had planned, to find the house almost deserted, one maidservant only in attendance, a note from his host expressing his deep regret (and a smiling aside about layabeds) and wishing him the safest of travel. It was almost ten by the time he himself was ready to set out in the small carriage graciously provided to convey him to a nearby town and the coach for the next stage of his journey, and some twenty minutes later, about the ascend, through dark trees, the low pass out of the valley – the mountain shadow still upon it, the long grass still lank with the night’s precipitation – when, checking on an impulse his leather writing case, he discovered that, most uncharacteristically and unaccountably, he had left behind him his notebook with its precious formula.

He turned back in considerable annoyance. By the time he again entered the grounds of the grand chateau, however, its turrets gleaming, its manicured lawns glistening a deep emerald in the now-full sun, its broad white wings spread out in welcome, he was only grateful for the last and unexpected glimpse. No one answered his knock. It appeared the one servant had removed herself beyond earshot, or taken advantage of her mistress’s absence to go somewhere else entirely. Having no other option he tried other doors and, finding one of them unlatched, let himself in, making his way quickly and directly to the room he had just vacated, fully expecting to find the notebook where he imagined he must have left it, on the small bedside table, or accidentally obscured by the linen of the still unmade bed.

It was not there. Alarmed, he searched the room, to no avail. Sure, however, that no one could have taken it, he could now only imagine that this morning’s maid had found it and already carried it downstairs. Certain, on reflection, that this must be the case, and that he had but to descend the two flights to the front door to find it awaiting his inevitable return – thinking, too, that if this were not so, that if he had to take all day to find it, then that is how it would have to be – he began to make his way back along the passage.

It can only have been the sheer absence of sound, or the irresistible memory of hand-sluiced water, that prompted him to pause at the foot of the first stairway, then turn once more in the direction he had taken so boldly the evening before. There must at least be some trace of her – some handkerchief or shawl, perhaps, or ribbon, or her scent in disordered bedclothes.

The door was slightly ajar. He pushed it – more quickly, perhaps, than he might have done, expecting emptiness, or the maid cleaning, the disarray of departure. Anything, that is, but the very thing he had been looking for. The formula, or rather the notebook, containing it, wide open beside the long, so nearly perfect parallel of her thighs.

© David Brooks
Black Sea, Allen and Unwin, 1997