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Updated: May 24, 2025
"Mary Louise is always on the wrong side. Other schools are not criterions for this ramshackle establishment, anyhow. We have twelve boarders and four day scholars, and how Miss Stearne ever supports the place and herself on her income is an occult problem that the geometries can't solve.
There are so many geometries, so many logics, so many physical and chemical hypotheses, so many classifications, each one of them good for so much and yet not good for everything, that the notion that even the truest formula may be a human device and not a literal transcript has dawned upon us.
If we deny the relation between the body of axiomatic Euclidean geometry and the practically-rigid body of reality, we readily arrive at the following view, which was entertained by that acute and profound thinker, H. Poincare: Euclidean geometry is distinguished above all other imaginable axiomatic geometries by its simplicity.
Toward what solution do these geometries in action, which are plants, progress? I do not know. But there is a fascinating mystery in considering that even as species correspond to certain geological periods and thus group their sympathies, even so to-day they group themselves according to the seasons.
The same publisher told me he thought well of my scheme, and I'm going ahead with it." "Well, don't you kill yourself writing geometries: I should think teaching the youngsters would be a full job." "That's not a job at all, Aunt Sally; that's just fun. And you know I'm not going to do it always. I'm learning things now that I needed to know. I only wish my mind were as sound as my health."
In other words there are alternative metrical geometries which all exist by an equal right so far as the intrinsic theory of space is concerned. Poincaré, the great French mathematician, held that our actual choice among these geometries is guided purely by convention, and that the effect of a change of choice would be simply to alter our expression of the physical laws of nature.
"Rachel," he repeated, his eyes no longer on the old man. "Her name is unchanged...." He opened von Stinnes's silver case and removed a cigarette. He stood gazing at the snow on roofs, on window ledges, on pavements. Crystalline geometries. Houses that made little puzzle pictures against the stagnant curve of the darkening sky.
The drying stalks were woven with endless spider-webs, all white with frost. Peter stood regarding their delicate geometries a moment longer and then reentered his room, not knowing precisely what to do. He could hear Rose walking across the piazza to and from the dining- room, and the clink of tableware.
We read them in one serial order or another, class them in this way or in that, treat one or the other as more fundamental, until our beliefs about them form those bodies of truth known as logics, geometries, or arithmetics, in each and all of which the form and order in which the whole is cast is flagrantly man-made.
But after watching them they lose these false significances. They suggest nothing. They are the amputations of men. Things, playthings men have left behind for the corset and the ice cream ads to wink at. And this is the real secret of their beauty. The night devours their meaning and leaves behind lines; angles, geometries, rhythms and lights.
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