XXII
BELLWATTLE ON THE HIGHER MATHEMATICS

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?”

She acquiesced.

“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.