The mummy and Miss Nitocris
George Chetwynd Griffith (1906)
Country of origin: UK
Available texts by the same author here
Chapter XIV: "Supposed Impossibilities"
It was only to be expected that the announcement of a lecture with such an alluring title by such a distinguished scholar and scientist as Professor Franklin Marmion should fill the theatre of the Royal Society, as the reporters said tritely but truly, "to its utmost capacity."The mere words, "An Examination of Some Supposed Mathematical Impossibilities," were just so many bomb-shells tossed into the middle of the scientific arena. The circle-squarers, the triangle-trisectors, the cube-doublers, the flat-worlders, and all the other would-be workers of miracles plainly impossible in a world of three dimensions jumped—not incorrectly—to the conclusion that their favourite impossibility would be selected for examination, and, perhaps—blissful thought!—demonstration by one of the foremost thinkers of the day, to the lasting confusion of the scoffers. Learned pundits of the old school, who were firmly convinced that Mathematics had long ago said their last word, and that to talk about "supposed impossibilities" was blasphemy of the rankest sort, came with note-books and a grim determination to explode Franklin Marmion's heresies for good and all. Dreamers of Fourth Dimensional dreams came hoping against hope, for the Professor was known to be something of a dreamer himself; and added to all these there assembled a distinguished company of ladies and gentlemen who looked upon the lecture as a "function" which their social positions made it necessary for them to patronise. The reader's personal friends and acquaintances, including Prince Oscarovitch and Phadrig, were naturally among the most anxiously interested of the Professor's audience.
It is almost needless to say that Hoskins van Huysman had donned all his panoply of scientific war, and had armed himself with what he believed his keenest weapons; and that Professor Hartley looked with amused confidence to a veritable battle royal of wits when the lecture was over and the discussion began. The Prince and Phadrig were keenly anticipative, and the latter not a little nervous.
A verbatim report of that famous lecture would, of course, be out of place in these pages. If Professor Marmion's words of wonder are not already written in the archives of the Royal Society, no doubt they will be in the fullness of time when the minds of men shall have become prepared to receive them. Here we are mainly concerned with the results which they produced upon his audience. Certain portions may, however, be properly reproduced here.
When the decorous murmur of applause which greeted the President's closing sentences had died away, and Franklin Marmion went to the reading-desk and unfolded his notes, there was a tense silence of anticipation, and hundreds of pairs of eyes, which had some of the keenest brains in Europe behind them, were converged upon his spare, erect figure and his refined, clear-cut, somewhat sternly-moulded face.
"Mr President, my lords, ladies, and gentlemen," he began, in his quiet, but far-reaching tones. "The somewhat peculiar title which I have chosen for my lecture was not, I hope I need scarcely say, selected with a view of arousing any but that intelligent curiosity which is always characteristic of such a distinguished audience as that which I have the honour of addressing to-night. I chose it after somewhat anxious consideration, because I am aware that the bulk of opinion in the world of science strongly insists upon the finality of the axioms of mathematics, and therefore it was with no little hesitancy that I approached such a subject as this. I am well aware that, in the estimation of most of my learned confrères and fellow-seekers after scientific truth, to suggest those axioms may not embody final and universal truth is, if I may put it so, to lay sacrilegious hands on the Ark of the Scientific Covenant."
A low murmur, prelude of the coming storm, ran through the theatre, and Professor van Huysman permitted himself to snort distinctively, for which he was very promptly, though quietly, called to order by his daughter, who was sitting in front of the platform between him and Lord Leighton. Franklin Marmion paused for a moment and smiled ever so faintly. Nitocris looked round at the now eager audience a trifle anxiously, for she had a fairly clear idea of the trouble that might possibly be ahead. Her father went on as quietly as before:
"Of course, every one here is aware that the great Napoleon once said that the word 'impossible' was not French. I need not remind such an audience as this that more than one distinguished student and investigator has suggested that it also may not be scientific."
The murmur broke out again, and Hoskins van Huysman blew his nose somewhat aggressively. His scientific bile was beginning to rise. He disapproved very strongly of the tone which his rival had begun. Its quiet confidence was somewhat ominous. The lecturer continued without this time noticing the interruption, and proceeded to give a lengthy and learned but singularly lucid resumé of the more recent progress in the higher mathematics and the deeply interesting speculations to which it had given rise. This, with certain demonstrations which he made on the great black-board beside him, occupied nearly an hour. When he had finished there was another murmur, which this time was wholly of applause, for this part of the lecture had not only been masterly but entirely orthodox. Then silence fell again, the silence of expectant waiting, for every one felt that the "Examination" was coming now. He began again in a slightly altered voice.
"What I have just been saying was necessary to my subject as far as it went, but for all that it was chiefly introductory to what I am now going to bring to your notice. But this is a matter rather for illustration and discussion than for mere disquisition. Therefore, to save your time as much as possible, I will proceed at once to the illustration, and then we will have the discussion."
Professor van Huysman snorted again, even as a war-horse that snuffs the fray. This time Franklin Marmion seemed to recognise the implied challenge, for he looked round the crowded theatre with a curious smile, which seemed to say: "Yes, gentlemen, I see that some of you are getting ready for a tussle. I am in hopes of being able to oblige you."
"Now," he continued, "it is generally conceded that an ounce of practice is worth a good many pounds of precept, so I will get to the practice. I need hardly remind you that ever since mathematics became an exact science, three problems have been recognised as impossible of solution—trisecting the triangle, squaring the circle, and doubling the cube. I have now the pleasure of announcing that I have had the great good fortune to discover certain formulæ which, so far, at least, as I can see, make the solution of those problems not only possible, but comparatively easy—to those who know how to use them."
As he said this, Franklin Marmion looked directly at Hoskins van Huysman. He was the challenger now, and there was a glint in his eyes and a smile on his lips which showed that he meant business. The American writhed, and had it not been for Brenda's gently but firmly restraining hand, he might have jumped to his feet and precipitated matters in a somewhat embarrassing fashion. The chairman looked up at the lecturer with elevated eyelids which had a note of interrogation under each of them, and then there came that sound of shifting in seats and breathing in many low keys which denotes that an audience has been wound up to a very tense pitch of expectation. If a smaller man had said such words to such hearers some one would have laughed, and then would have burst forth a storm of derision. But the keenest critic had never found Franklin Marmion wrong yet, and he had far too great a reputation to permit himself to say in such a place that which he did not seriously mean. So the hum died down as he went to the black-board, and Nitocris looked at Merrill with something like fear in her eyes.
"If he does that," whispered Phadrig to the Prince in Russian, "the story that Pent-Ah and Neb-Anat told will be true—which the High Gods forbid!"
"As the trisection of the triangle is, perhaps, the simplest of the three problems," said the lecturer, with almost judicial calmness, "we will, if you please, begin with that. I hope that gentlemen who have brought note-books with them will be kind enough to follow my calculations and check any error that I may make."
But a good threescore note-books, pencils, and stylographic pens were out already, and hundreds of eyes were eagerly fastening their gaze on the black-board, their owners desperately anxious to detect the first slip in the demonstration. The demonstrator drew an isosceles triangle rapidly, and without speaking filled the remainder of the board with formulæ. The almost breathless silence was broken only by the click of the chalk on the board and the scratching of pencils and pens on paper. When he had finished he ran through the calculations aloud, and said in the most commonplace voice:
"Now, gentlemen, if, as I hope, you have found my working correct, I may draw the two lines which will trisect the triangle."
He drew them, and then, as calmly as though he had done nothing more than cross the much-trodden pons asinorum, he told two attendants to take the board down and put it in front of the platform; then, while they were lifting another on to the easel, he said:
"As those who have followed me would no doubt like a little time to revise the figures, I will go on with the next problem, which will be our old friend, or enemy, the squaring of the circle."
The second board was filled with diagrams and formulæ as rapidly as the first.
"There is the demonstration, gentlemen," he said, as the attendants placed it beside the other in full view of everybody. "Now, as time is shortening, I will get on with the third problem."
The chalk began to click again, and the pens and pencils scratched on to the accompaniment of murmurs and whispers and occasional grunts and snorts of incredulity. By a master-stroke of strategy Franklin Marmion had, in placing the three demonstrations of the long-supposed impossible before them in quick succession, kept the learned, but now utterly bewildered mathematicians so busy that they literally had not time to begin "the trouble" which Brenda was now actually dreading. Her father's face, bent down over his note-book, was getting more terrible to look upon every moment. The mere fact that he had not uttered a sound since the demonstrations had begun was sufficiently ominous, for it meant that he was puzzled—perhaps even beaten—and if that was so, she dreaded to even imagine what might happen. On the other hand, Nitocris felt her spirits rising as she looked round and saw the many learned heads bending and shaking over the note-books, each owner of them working at high pressure to win the honour of first finding the error which all firmly believed must exist, and which none of them could detect.
When he had finished his third demonstration, Franklin Marmion, without interrupting the hard thinking that was going on, took a chair by the side of the President, poured out a glass of water, and waited for results.
"Marmion, what is this white magic that you have been springing upon us?" whispered the presiding genius of the learned assembly, looking up from several sheets of paper which he had been rapidly covering with formulæ. "These things are impossible, you know—unless, of course, you have got a good deal farther than any of us. And yet the calculations are correct as far as I can follow them, and no one else seems to have hit on any error yet. I must confess, though, that these progressives of yours are too deep for me. I can follow them, and yet I can't. At a certain point they seem to elude me, and yet the calculations are rigidly right. It's almost enough to make one think you had done what Cayley once told us in this room some one might do some day."
"My Lord," replied Franklin Marmion, almost inaudibly, "I began my address by remarking, as you will remember, that perhaps, after all, the word 'impossible' might not be scientific."
Their eyes met, and the President, than whose there was no greater name in the higher realm of learning, saw something in Marmion's which sent a little chill through him, and that something told him that he was in the presence of a superior being.
"Dear me!" he murmured, looking down at his papers again, "the age of miracles is not past, after all—in fact, it is only just beginning."
"It is re-beginning, my Lord—for us," came the reply, in a voice which seemed to come from very far away.
The President did not reply. As a matter of fact, he had no reply ready, and he had something else to do. He rose, and said in a somewhat constrained voice:
"Ladies and gentlemen, Professor Marmion has shown us some very strange demonstrations which have certainly amply justified the title which he selected. A good many gentlemen, and some ladies as well, I am glad to see, have followed his calculations very carefully. I have done the same myself, but I am bound to confess that I have not been able to find any error. I think I shall be right in saying that no one will be more pleased than the learned and—er—gifted lecturer to hear that some one else has been able to do so."
Franklin Marmion bowed his assent, and a faint smile flickered across his clean-shaven lips. The next instant Professor van Huysman was on his legs, note-book in one hand and stylo in the other. All the fresh colour had gone out of his face; his eyes were burning, and his lips were twitching with uncontrollable excitement.
"My Lord," he began, in a voice that even Brenda hardly recognised, "like yourself, I have been unable to find any actual error in the lecturer's demonstrations of which I will take permission to call the possibility of the impossible; in other words, that a contradiction in terms can be true and false at one and the same time. That, my Lord, and ladies, and gentlemen," he went on, raising his voice almost to a shout, "is still, and, I hope, in the interests of true science, and not adroit jugglery with figures and formulæ, will ever remain, another impossibility. Professor Marmion has apparently trisected the triangle, squared the circle, and doubled the cube. It may be that he has persuaded some present that he really has done so; but, again, in the interests of science, I desire to protest against the way in which these demonstrations have been sprung upon us. Calculations which he has doubtless taken months to elaborate, he has asked us to test in a few minutes. For myself, I decline to accept them as true, and I hope that others will do the same until we have had time to satisfy ourselves that the hitherto impossible has been made possible."
He sat down, breathing hard and white with anger and excitement, and then the trouble began. The trisectors, the circle-squarers, and the cube-doublers, had seen their long-flouted theories proved to demonstration by one of the most learned and responsible men of science in the world, and one of their most sarcastic and hitherto successful flouters had been compelled to confess that he could find no flaw in the calculations of this mathematical Daniel so unexpectedly come to judgment. They did not understand his proofs, but that was no reason why they should reject them, and so they rose as one man in support of their champion to demand that Professor van Huysman should withdraw his imputations of jugglery. He sat still, and shook his head. He was too disgusted and bewildered to do or say anything more until he had made a searching analysis of these diabolical formulæ.
But there were others who wanted to have their say in defence of scientific orthodoxy, and they had it—and the rest was a chaos of intellectual conflict until, at the end of nearly an hour, the President, who now saw with clearer eyes than any of the disputants, rose and put an end to the discussion by remarking that they had not the whole night before them, and that all that Professor Marmion had said and done would be published in the scientific papers; further, that such a controversy would perhaps be more profitably conducted in print than by word of mouth. Such a course would give every one ample leisure to work out the problems in the light of the new demonstrations, and also give a much better prospect of reaching a logical, and therefore just, conclusion than a discussion in which haste, and possibly pre-conceived opinions, from the influence of which no human being was really free, could possibly promise.
This, of course, put an end to the matter for the time being, and, after the usual votes of thanks and acknowledgments, the distinguished company dispersed—amused, mystified, gratified, bewildered, and exasperated: but, saving only four of its members, with no idea of the effect which that evening's proceedings were destined to have upon the fate of Europe, perhaps of the whole human race.