CHAPTER XIV
"SUPPOSED IMPOSSIBILITIES"
It was only to be expected that the announcement of a lecture with suchan alluring title by such a distinguished scholar and scientist asProfessor 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 MathematicalImpossibilities," were just so many bomb-shells tossed into the middleof the scientific arena. The circle-squarers, the triangle-trisectors,the cube-doublers, the flat-worlders, and all the other would-be workersof miracles plainly impossible in a world of three dimensionsjumped--not incorrectly--to the conclusion that their favouriteimpossibility would be selected for examination, and, perhaps--blissfulthought!--demonstration by one of the foremost thinkers of the day, tothe lasting confusion of the scoffers. Learned pundits of the oldschool, who were firmly convinced that Mathematics had long ago saidtheir last word, and that to talk about "supposed impossibilities" wasblasphemy of the rankest sort, came with note-books and a grimdetermination to explode Franklin Marmion's heresies for good and all.Dreamers of Fourth Dimensional dreams came hoping against hope, for theProfessor was known to be something of a dreamer himself; and added toall these there assembled a distinguished company of ladies andgentlemen who looked upon the lecture as a "function" which their socialpositions made it necessary for them to patronise. The reader's personalfriends and acquaintances, including Prince Oscarovitch and Phadrig,were naturally among the most anxiously interested of the Professor'saudience.
It is almost needless to say that Hoskins van Huysman had donned all hispanoply of scientific war, and had armed himself with what he believedhis keenest weapons; and that Professor Hartley looked with amusedconfidence to a veritable battle royal of wits when the lecture was overand the discussion began. The Prince and Phadrig were keenlyanticipative, and the latter not a little nervous.
A verbatim report of that famous lecture would, of course, be out ofplace in these pages. If Professor Marmion's words of wonder are notalready written in the archives of the Royal Society, no doubt they willbe in the fullness of time when the minds of men shall have becomeprepared to receive them. Here we are mainly concerned with the resultswhich they produced upon his audience. Certain portions may, however, beproperly reproduced here.
When the decorous murmur of applause which greeted the President'sclosing sentences had died away, and Franklin Marmion went to thereading-desk and unfolded his notes, there was a tense silence ofanticipation, and hundreds of pairs of eyes, which had some of thekeenest 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 chosenfor my lecture was not, I hope I need scarcely say, selected with a viewof arousing any but that intelligent curiosity which is alwayscharacteristic of such a distinguished audience as that which I have thehonour of addressing to-night. I chose it after somewhat anxiousconsideration, because I am aware that the bulk of opinion in the worldof science strongly insists upon the finality of the axioms ofmathematics, and therefore it was with no little hesitancy that Iapproached such a subject as this. I am well aware that, in theestimation of most of my learned _confreres_ and fellow-seekers afterscientific truth, to suggest those axioms may not embody final anduniversal truth is, if I may put it so, to lay sacrilegious hands on theArk of the Scientific Covenant."
A low murmur, prelude of the coming storm, ran through the theatre, andProfessor van Huysman permitted himself to snort distinctively, forwhich he was very promptly, though quietly, called to order by hisdaughter, who was sitting in front of the platform between him and LordLeighton. Franklin Marmion paused for a moment and smiled ever sofaintly. Nitocris looked round at the now eager audience a trifleanxiously, for she had a fairly clear idea of the trouble that mightpossibly be ahead. Her father went on as quietly as before:
"Of course, every one here is aware that the great Napoleon once saidthat the word 'impossible' was not French. I need not remind such anaudience as this that more than one distinguished student andinvestigator has suggested that it also may not be scientific."
The murmur broke out again, and Hoskins van Huysman blew his nosesomewhat aggressively. His scientific bile was beginning to rise. Hedisapproved very strongly of the tone which his rival had begun. Itsquiet confidence was somewhat ominous. The lecturer continued withoutthis time noticing the interruption, and proceeded to give a lengthy andlearned but singularly lucid _resume_ of the more recent progress in thehigher mathematics and the deeply interesting speculations to which ithad given rise. This, with certain demonstrations which he made on thegreat black-board beside him, occupied nearly an hour. When he hadfinished there was another murmur, which this time was wholly ofapplause, for this part of the lecture had not only been masterly butentirely orthodox. Then silence fell again, the silence of expectantwaiting, for every one felt that the "Examination" was coming now. Hebegan again in a slightly altered voice.
"What I have just been saying was necessary to my subject as far as itwent, but for all that it was chiefly introductory to what I am nowgoing to bring to your notice. But this is a matter rather forillustration and discussion than for mere disquisition. Therefore, tosave your time as much as possible, I will proceed at once to theillustration, and then we will have the discussion."
Professor van Huysman snorted again, even as a war-horse that snuffs thefray. This time Franklin Marmion seemed to recognise the impliedchallenge, for he looked round the crowded theatre with a curious smile,which seemed to say: "Yes, gentlemen, I see that some of you are gettingready for a tussle. I am in hopes of being able to oblige you."
"Now," he continued, "it is generally conceded that an ounce of practiceis worth a good many pounds of precept, so I will get to the practice. Ineed hardly remind you that ever since mathematics became an exactscience, three problems have been recognised as impossible ofsolution--trisecting the triangle, squaring the circle, and doubling thecube. I have now the pleasure of announcing that I have had the greatgood fortune to discover certain formulae which, so far, at least, as Ican see, make the solution of those problems not only possible, butcomparatively easy--to those who know how to use them."
As he said this, Franklin Marmion looked directly at Hoskins vanHuysman. He was the challenger now, and there was a glint in his eyesand a smile on his lips which showed that he meant business. TheAmerican writhed, and had it not been for Brenda's gently but firmlyrestraining hand, he might have jumped to his feet and precipitatedmatters in a somewhat embarrassing fashion. The chairman looked up atthe lecturer with elevated eyelids which had a note of interrogationunder each of them, and then there came that sound of shifting in seatsand breathing in many low keys which denotes that an audience has beenwound up to a very tense pitch of expectation. If a smaller man had saidsuch words to such hearers some one would have laughed, and then wouldhave burst forth a storm of derision. But the keenest critic had neverfound Franklin Marmion wrong yet, and he had far too great a reputationto permit himself to say in such a place that which he did not seriouslymean. So the hum died down as he went to the black-board, and Nitocrislooked at Merrill with something like fear in her eyes.
"If he does that," whispered Phadrig to the Prince in Russian, "thestory that Pent-Ah and Neb-Anat told will be true--which the High Godsforbid!"
"As the trisection of the triangle is, perhaps, the simplest of thethree problems," said the lecturer, with almost judicial calmness, "wewill, if you please, begin with that. I hope that gentlemen who havebrought note-books with them will be kind enough to follow mycalculations and check any error that I may make."
But a good threescore note-books, pencils, and stylographic pens wereout already, and hundreds of eyes were eagerly fastening their gaze onthe black-board, their owners desperately anxious to detect the firs
tslip in the demonstration. The demonstrator drew an isosceles trianglerapidly, and without speaking filled the remainder of the board withformulae. The almost breathless silence was broken only by the click ofthe 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 inthe most commonplace voice:
"Now, gentlemen, if, as I hope, you have found my working correct, I maydraw the two lines which will trisect the triangle."
He drew them, and then, as calmly as though he had done nothing morethan cross the much-trodden _pons asinorum_, he told two attendants totake the board down and put it in front of the platform; then, whilethey were lifting another on to the easel, he said:
"As those who have followed me would no doubt like a little time torevise the figures, I will go on with the next problem, which will beour old friend, or enemy, the squaring of the circle."
The second board was filled with diagrams and formulae as rapidly as thefirst.
"There is the demonstration, gentlemen," he said, as the attendantsplaced it beside the other in full view of everybody. "Now, as time isshortening, I will get on with the third problem."
The chalk began to click again, and the pens and pencils scratched on tothe accompaniment of murmurs and whispers and occasional grunts andsnorts of incredulity. By a master-stroke of strategy Franklin Marmionhad, in placing the three demonstrations of the long-supposed impossiblebefore them in quick succession, kept the learned, but now utterlybewildered mathematicians so busy that they literally had not time tobegin "the trouble" which Brenda was now actually dreading. Her father'sface, bent down over his note-book, was getting more terrible to lookupon every moment. The mere fact that he had not uttered a sound sincethe demonstrations had begun was sufficiently ominous, for it meant thathe was puzzled--perhaps even beaten--and if that was so, she dreaded toeven imagine what might happen. On the other hand, Nitocris felt herspirits rising as she looked round and saw the many learned headsbending and shaking over the note-books, each owner of them working athigh pressure to win the honour of first finding the error which allfirmly believed must exist, and which none of them could detect.
When he had finished his third demonstration, Franklin Marmion, withoutinterrupting the hard thinking that was going on, took a chair by theside of the President, poured out a glass of water, and waited forresults.
"Marmion, what is this white magic that you have been springing uponus?" whispered the presiding genius of the learned assembly, looking upfrom several sheets of paper which he had been rapidly covering withformulae. "These things are impossible, you know--unless, of course, youhave got a good deal farther than any of us. And yet the calculationsare correct as far as I can follow them, and no one else seems to havehit on any error yet. I must confess, though, that these progressives ofyours are too deep for me. I can follow them, and yet I can't. At acertain point they seem to elude me, and yet the calculations arerigidly right. It's almost enough to make one think you had done whatCayley once told us in this room some one might do some day."
"My Lord," replied Franklin Marmion, almost inaudibly, "I began myaddress by remarking, as you will remember, that perhaps, after all, theword 'impossible' might not be scientific."
Their eyes met, and the President, than whose there was no greater namein the higher realm of learning, saw something in Marmion's which sent alittle chill through him, and that something told him that he was in thepresence of a superior being.
"Dear me!" he murmured, looking down at his papers again, "the age ofmiracles 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 whichseemed 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 somewhatconstrained voice:
"Ladies and gentlemen, Professor Marmion has shown us some very strangedemonstrations which have certainly amply justified the title which heselected. A good many gentlemen, and some ladies as well, I am glad tosee, have followed his calculations very carefully. I have done the samemyself, but I am bound to confess that I have not been able to find anyerror. I think I shall be right in saying that no one will be morepleased than the learned and--er--gifted lecturer to hear that some oneelse has been able to do so."
Franklin Marmion bowed his assent, and a faint smile flickered acrosshis clean-shaven lips. The next instant Professor van Huysman was on hislegs, note-book in one hand and stylo in the other. All the fresh colourhad gone out of his face; his eyes were burning, and his lips weretwitching 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 thelecturer's demonstrations of which I will take permission to call thepossibility of the impossible; in other words, that a contradiction interms can be true and false at one and the same time. That, my Lord, andladies, and gentlemen," he went on, raising his voice almost to ashout, "is still, and, I hope, in the interests of true science, and notadroit jugglery with figures and formulae, will ever remain, anotherimpossibility. Professor Marmion has apparently trisected the triangle,squared the circle, and doubled the cube. It may be that he haspersuaded some present that he really has done so; but, again, in theinterests of science, I desire to protest against the way in which thesedemonstrations have been sprung upon us. Calculations which he hasdoubtless taken months to elaborate, he has asked us to test in a fewminutes. For myself, I decline to accept them as true, and I hope thatothers will do the same until we have had time to satisfy ourselves thatthe hitherto impossible has been made possible."
He sat down, breathing hard and white with anger and excitement, andthen the trouble began. The trisectors, the circle-squarers, and thecube-doublers, had seen their long-flouted theories proved todemonstration by one of the most learned and responsible men of sciencein the world, and one of their most sarcastic and hitherto successfulflouters had been compelled to confess that he could find no flaw in thecalculations of this mathematical Daniel so unexpectedly come tojudgment. They did not understand his proofs, but that was no reason whythey should reject them, and so they rose as one man in support of theirchampion to demand that Professor van Huysman should withdraw hisimputations of jugglery. He sat still, and shook his head. He was toodisgusted and bewildered to do or say anything more until he had made asearching analysis of these diabolical formulae.
But there were others who wanted to have their say in defence ofscientific orthodoxy, and they had it--and the rest was a chaos ofintellectual conflict until, at the end of nearly an hour, thePresident, 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 thewhole night before them, and that all that Professor Marmion had saidand done would be published in the scientific papers; further, that sucha controversy would perhaps be more profitably conducted in print thanby word of mouth. Such a course would give every one ample leisure towork out the problems in the light of the new demonstrations, and alsogive a much better prospect of reaching a logical, and therefore just,conclusion than a discussion in which haste, and possibly pre-conceivedopinions, 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, afterthe usual votes of thanks and acknowledgments, the distinguished companydispersed--amused, mystified, gratified, bewildered, and exasperated:but, saving only four of its members, with no idea of the effect whichthat evening's proceedings were destined to have upon the fate ofEurope, perhaps of the whole human race.
The Mummy and Miss Nitocris: A Phantasy of the Fourth Dimension Page 15