I have already been at some pains in a few of these pages to give an idea of the feminine appreciation of mathematics. Undoubtedly it is more practical than that of many an eminent mathematician. For let it at once be understood that the first function of a higher mathematician is to express himself in terms of mathematics, just as an artist expresses himself in the colours he lays upon his canvas, or a musician by the little black and white dots he writes between and through the lines.
“Nobody”—so a scientist once said to me—“nobody seems to understand this. They have never learnt the language we talk in and they fancy that we only fit our place in the universe so long as we are useful. If I were to talk to you now of the things I am doing in my laboratory, using the terms and the technicalities that I use there, you’d probably think I was endeavouring to be scientifically brilliant in my conversation, stringing together all the most exaggerated words to get an effect which you could not understand; whereas, in reality, I should be talking the most ordinary commonplaces which even the boy who cleans out the vessels and the flasks can probably understand. Let a man invent a talking machine, or a calculating machine, and they call him a great scientist. Good heavens! If you knew how the real scientists and the real mathematicians despise him. Why, I’ve seen a mathematician express the soul in himself so absolutely by the solution of an abstruse problem, that he has cried with joy like a child—like an artist when he has finished his masterpiece, a writer when he has ended his book.”
“May I never burst into tears, if ever I write a book,” said I.
“Well—you know what I mean,” said he.
And I suppose I did know. Utility is the prostitution of most things as well as science and mathematics. But that is just where women are more practical mathematicians than men. I have never known a woman set out to express herself in mathematics yet. What is more, I pray God, most fervently, I never shall. She will employ the wildest means of expression in the world, but nothing so wild or incoherent as mathematics.
I try to conceive a woman in a fit of jealousy sitting down to express her emotions through the medium of the binomial theorem—which I must tell you I know to be a method of expanding X and Y, bracketed to the Nth power, to an infinite series of powers—I try to conceive her doing that, but my conception always fails. Far more readily can I see her inviting to tea the creature who is the cause of her jealousy, and evincing the sweetest friendship for her. Now that is expression, if you like, bracketed, moreover, without any necessity for your binomial theorem, to the Nth power, and expanded to an infinite expression of femininity.
To give you just the simplest example of this matter of the practicality of women in mathematics, I must tell you that Cruikshank and I the other evening were recalling our prowess at Euclid; setting each other problems to prove—well, you know the routine of the propositions of Euclid.
In the midst of darning some socks and, having listened to us in silence for at least an hour, Bellwattle looked up.
“Was Euclid mad?” she asked, quite seriously.
There was something in the nature of a ricochet in that question. It touched not only Euclid, for whom we have infinite respect, but also ourselves, for whom we have more.
“The sanest person that ever lived,” said Cruikshank, shortly.
“Then why did he waste his time inventing all that rubbish? What’s the good of it, anyhow?”
I put away my pencil with which from memory I had just been drawing the diagram for the fourth proposition of the second book.
“It develops,” I answered, “the reasoning power in the human animal—a not unworthy or wholly unnecessary purpose.”
She darned a few stitches in silence.
“Has it ever done any good besides that?” she inquired presently.
“Well,” said Cruikshank, “it teaches you, for example, how, without measuring and purely by the light of reason, to construct an equilateral triangle on a given finite straight line.”
Bellwattle laid down her sock with the knob of wood inside it and she looked at both of us as though we were creatures from another world.
“And what in the name of goodness,” said she, “is an equi—whatever-you-call-it triangle?”
Cruikshank went on with his explanation quite cheerily. On this proposition he was so sure of himself that confidence was actually glowing in his face.
“Well,” said he, “you know what a triangle is, don’t you?”
She nodded her head promisingly.
“One of those things they sometimes play in bands.”
The look of confidence dropped heavily from Cruikshank’s face; but I seized the opportunity. She understood. At least she had grasped the shape of it. It mattered not at all that in her mind its functions were to play a tune. She appreciated the shape of it. That served its end.
“You’re quite right,” said I quickly. “They have it in an orchestra. It has three sides to it—hasn’t it?”
She nodded her head vivaciously.
“Yes, and two little curly bits at the top where they tie the string on to hang it up by.”
“My God!” said Cruikshank in despair.
But I acceded her the little curly bits. She had grasped the shape of a triangle.
“Well, try and forget the curly bits,” said I. “They have three sides—haven’t they?”
“Like this,” I went on hurriedly, and, dragging out my pencil again, I drew a triangle on a piece of paper.
“That’s it,” said she; “but they don’t meet at the top.”
“Some do,” I replied; “the ones that Euclid made did.”
“Well, go on,” she said, with greater interest. “What’s an equitriangle?”
“An equilateral triangle,” said Cruikshank, now stepping in when I had done all the hard work for him, “is a triangle which has all its sides of equal length. That side,”—he pointed to my drawing—“that side and that side all equal. Now Euclid’ll show you,” he continued, “how to construct an equilateral triangle on a given finite straight line. You needn’t measure anything. You only want a compass to make a couple of circles, and he’ll prove to your reason that all the lines of that triangle are one and the same length as this line you see on the paper now.”
He turned to me.
“Lend me a ha’penny,” said he.
I gave him the only one I had and he set to work to draw the most beautiful circles, though they had but little relation to A as their centre and B as their circumference, which were the letters he had written at each end of his given finite straight line.
“Nevertheless, that’ll do,” said he.
And then, forthwith, he began to prove it to her.
I went out to get myself a cigar in the dining-room, and while there, cutting off the end of it and smiling gently to myself as I did so, I heard the voice of Cruikshank raised in the passion of despair.
“My God! my dear child,” I heard him say. “I proved those two were equal because they both came from the centre of this circle—B.F.G. to the circumference. You don’t remember anything.”
I lit my cigar with a trembling hand. Then I walked to the window of the dining-room and looked out into the garden. There were the tom-tits pecking away at the cocoa-nut shell which Bellwattle had hung up with such infinite trouble; there were the kittens, lapping from a saucer of milk as Bellwattle and their mother had taught them; there were the sweet peas in great walls of colour with the old pieces of red flannel still clinging to the pea-sticks, those same pieces of flannel which Bellwattle had tied to keep off the birds when the shoots were young and green; there was the little robin which Bellwattle fed every afternoon at tea-time; there, in fact, were all the signs of Bellwattle’s beautiful and wonderful and practical utility.
I came back into the other room at the sound of Cruikshank’s voice as he called me.
“She sees it!” he exclaimed in an ecstasy. “She understands it all right. I made it clear, didn’t I, Bellwattle?”
“Oh, quite,” said she. “I understand it now right enough. But I never knew Euclid made instruments for bands.”
Cruikshank tore up his piece of paper and flung it in the grate.
So you see, if she really knew, I’ve no doubt she’d return to question Euclid’s sanity once more. I feel inclined to question it myself, but then that is because I know he did not make instruments for bands. He only expressed himself—that was all.
THE MYSTERY OF THE VOTE
THE MYSTERY OF THE VOTE
THE MYSTERY OF THE VOTE
I never knew how really splendid a possession was this of the vote until the last election. It is no wonder to me now that women throw dignity to the four winds of heaven, leaving it to chance and the grace of God whether it ever blows back to them again. It is no wonder to me that, for the moment, they can forget their glorious heritage in order to obtain this mysterious joy of recording their vote on a little slip of paper in the secrecy of the ballot-box.
As a mystery—and all mysteries are power—it had never appealed to me. As a means of urging the laws of the country in such direction as one was pleased to consider for that country’s good, it did once seem to me to be invaluable. I know by now what a hopeless fallacy that is. But at that time, nursing a political conviction that Home Rule would be good for Ireland as a people, much as I am led to believe food is good to a starving man, or a sense of religion to a drifting woman, I listened to the eloquent appeal of a canvasser for a Unionist candidate.
When he had finished telling me much more than either of us knew about Tariff Reform, and had built such a Navy before my eyes as would have frightened the whole German Government and any single English ratepayer out of their wits, I asked him what the Unionist candidate felt about Home Rule.
“Home Rule?” said he, carefully—“You approve of Home Rule?”
I walked gently and easily into the canvasser’s trap.
“You don’t denationalise a country,” said I, “because you conquer it. You can’t cut the soul out of Ireland any more than you can wash a nigger white. You can only boycott it. You can only paint a nigger. But boycotting won’t starve the soul of any nation. If it can’t get food for itself from the nation’s stores, it will still live, feeding from the country-side on the wild herb of endurance. But there is that which you can do. You can boycott it.”
“And you think that Home Rule will encourage the development of the Irish people?” said he.
I admitted that the idea had occurred to me.
“Well, Mr. —— is quite of your way of thinking,” he replied.
“He would support it with his vote in the House?” said I.
“Most assuredly!” he declared.
“I shall vote for Mr. ——,” said I.
And so I should, had I not gone to one of his meetings in the Town Hall. He, too, spoke eloquently about Tariff Reform and a Navy that would keep our country what it was; but in the midst of it, a cockney voice endeavoured to heckle him from the back of the hall.
“’Ow about ’Ome Rule?” shouted the voice.
The Unionist candidate had been heckled before.
“How about it?” he asked sharply, like the crack of a pistol.
“Are you going to let the Roman Catholics get the ’old in Ireland?”
“And make them a menace to England, too—do you think it’s likely?” replied the candidate.
I walked away. “The vote,” said I to myself, “the vote is only a catchpenny title for a popular game. It would be much better to gamble than vote. You might get something for your money if you backed the right man with a shilling; but you get nothing for backing him with your vote. In future,” said I, “I shall bet.”
Yet only a little while afterwards I was to learn what a glorious thing the vote is.
In my village there is an amiable labourer with that cast of countenance upon which, as on the possessions of his great country, the sun never sets. And with it all, he has that placidity of manner, that evenness of gait which suggest that he is always going to or coming from a service at his chapel.
No one would ever dream of consulting him upon anything, though, indeed, I once did ask him the name of a certain plant.
“There be some as call it the Deadly shade,” said he, “and some as call it the Nightly shade, but I don’t know rightly which it be.”
When later on, for my own foolish amusement, I said I had heard it was called the Deadly shade, he replied in precisely the same fashion. I tried him once more, by saying that I had looked up a book on the subject and found it to be the Nightly shade. Again he replied, word for word, as before.
At last, a few weeks later, I came to him and said—
“You know we were all wrong about that plant. I find at South Kensington Museum that the proper name for it is the Deadly Nightshade.”
And what do you think he replied? “There be some,” said he, “as call it the Deadly shade, and some as call it the Nightly shade, but I don’t know rightly which it be.”
Now that man’s wife had no respect for him, and truly I’m not surprised. I found out, too, that he knew it—it would not, of course, be a difficult fact to ascertain—and I felt sorry for him.
And then one day—the day before the polling in our village—all my pity for him was ended. I met him on the road, carrying home his bag of tools.
“Well,” said I, “are you going to vote to-morrow?”
His face broadened with a beaming smile.
“I am that,” said he.
“Who are you going to vote for?” I asked.
A cunning look crept into his little twinkling eyes, and he said—
I admitted that there was that to it and asked him to tell me.
He shook his head.
“I keeps that to myself,” said he. “We’re not supposed to tell who we vote for. All they votes is counted secret.”
“Do you mean to say you don’t tell anybody?” I asked.
“No,” he replied—“I don’t tell none.”
“But you tell your wife,” said I.
He shook his head again, and his smile was broader and his eyes more cunning than ever.
“Surely she wants to know,” I exclaimed.
“Ah—she may want to know, but that ain’t my tellin’ her—is it?”
Then I suddenly realised what a glorious weapon he possessed. A weapon which, when everything else—even intelligence—failed, would make him master in his own house.
“That must give you a splendid sense of importance in your own home,” said I—“Don’t they think you’re a fine fellow?”
“P’raps they do.”
“And all because you’ve got the mystery of a vote.”
“I can’t think of no other reason,” said he.
So whenever the question of giving women the vote is raised, I can think, too, of no other reason for their wanting it. A woman will bow her head before a mystery when all sense of worship has left her. It is this which gives her so much respect for the priesthood; it is this perhaps which gives her her desire for the vote.
There is a yard by the river-side in London—opposite Lambeth or somewhere thereabouts, I think it must be—where you may come so close in touch with Romance as will set your fancy afire and transport you thousands of miles away upon the far-off seas of the Orient.
You may talk in disbelieving tones of wishing-rings, of seven-leagued boots and magic carpets, counting them as fairy tales, food only for the minds of children; but they are after all only the poetic materialisation of those same subtle things in life which give wings to our own imagination, or bring to eyes tired with reality the gentle sleep of a day dream.
Nearly every one must know the place I write of. It is where they break up into logs the timber of those ships which have had their day—the ships that have ridden fearless and safe through a thousand storms, that have set forth so hopefully into the dim horizon of the unknown and evaded to the last the grim, grasping fingers of the hungry sea.
And there you will see their death masks, those silent figureheads which, for so many nights and so many days with untiring, ever-watchful eyes have faced the mystery of the deep waters unafraid. There is something pathetic—there is something majestic, too—about those expressionless faces. They seem so wooden and so foolish when first you look at them; but as your fancy sets its wings, as your ears become attuned to the inwardness that can be found in all things, however material, you will catch the sound of dim, faint voices that have a thousand tales of the sea to tell, a thousand yarns to spin, a thousand adventures to relate.
Nothing is silent in this world. There is only deafness.
It has always appealed to me as the most noble of human conceptions, that burial of the Viking lord. The grandeur of it is its simplicity. There is a fine spectacular element in it, too, but never a trace of bombast. The modern polished oak coffin with its gaudy brass fittings, the super-ornate hearse, the prancing black stallions, the butchery of a thousand graceful flowers—all this is bombast if you wish. It no more speaks of death than speaks the fat figure of Britannia on the top of the highest circus car of England. Funerals to-day have lost all the grandeur of simplicity. But that riding forth in a burning ship, stretched out with folded hands upon the deck his feet had paced so oft; riding forth towards that far horizon which his eyes had ever scanned, there is a generous nobility in that form of burial. You can imagine no haggling with an undertaker over the funeral about this. Here was no cutting down of the prices, saving a little on the coffin here, there a little on the hearse.
No—this was the Viking’s own ship—the most priceless possession that he had. Can you not see it plainly, with sails set, speeding forth upon its last voyage—the last voyage for both of them? And then, as the lapping, leaping flames catch hold upon the bellied canvas, I can see her settling down in the swinging cradle of the waves. I can see the dense column of smoke mingling with and veiling the tongues of orange flame, until she becomes like a little Altar set out upon a vast sea, offering up its sacrifice of a human soul to the ever-implacable gods.
Now every time you burn a ship’s log you attend a Viking’s burial. In those flames of green and gold, of orange, purple and blue, there is to be found, if you will use but the eyes for it, all the romance, all the spirit and colour of that majestic human sacrifice—the burial of a Viking lord. As you sit through the long evenings, while the rain is beating in sudden, whipping gusts upon the streaming window pane and the drops fall spitting and hissing down the chimney into the fire below, then the burning of a ship’s log is company enough for any one. With every spurt of flame as the tar oozes out from the sodden wood, and the water, still clinging in the tenacious timber, bubbles and boils, you can distinguish but faintly the stirring voice of Romance telling of thrilling enterprise and of great adventure. There are few sailors can spin a yarn so much to your liking. Never was there a pirate ship so fleet or so bold; there were never escapes so miraculous, or battles so stern, as you can see when in those long-drawn evenings you sit alone in the unlighted parlour and watch a ship’s log burning on the fire.
Pay no heed to them when they tell you the green flames come from copper, the blue from lead, the pale purple from potassium. The chemist’s laboratory has its own romance, but it shares nothing in common with the high seas of imagination upon which you are riding now. Let the green flames come from copper! They are the emeralds, the treasure of the Orient to you. Let the blue flames come from lead, the pale purple from potassium! In your eyes as you sit there in that darkened room, with the flame-light flickering upon the ceiling and the shadows creeping near to listen to it all, they are the blue sash around the waist, the purple ’kerchief about the head of the bravest and the most bloodthirsty pirate that ever stepped.
At all times a fire is a companion. Yet set but a ship’s log upon the flames and I warrant you will lose yourself and all about you; lose yourself until the last light flickers, the last red ember falls, and the good ship that has borne you so safely over a thousand seas sinks down into the grey ashes of majestic burial.