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A line is described by a moving point; a plane by a moving line; a solid by a moving plane. It may, at first sight, seem singular that this conception finds no place in the Euclidian system. But we may regard the omission as a mark of logical purity and rigor.
With my pitiful, earthly, Euclidian understanding, all I know is that there is suffering and that there are none guilty; that cause follows effect, simply and directly; that everything flows and finds its level—but that’s only Euclidian nonsense, I know that, and I can’t consent to live by it!
It is scarcely conceivable that the men and women who have experienced its benefits and its beauty should not demand and have similar buildings in their own home towns. Beyond the oasis of the Community Club House at Camp Sherman stretch the cantonments a Euclidian nightmare of bare boards, black roofs and ditches, making grim vistas of straight lines.
He knew no more than a firefly about rays or about race or sex or ennui or a bar of music or a pang of love or a grain of musk or of phosphorus or conscience or duty or the force of Euclidian geometry or non-Euclidian or heat or light or osmosis or electrolysis or the magnet or ether or vis inertiae or gravitation or cohesion or elasticity or surface tension or capillary attraction or Brownian motion or of some scores, or thousands, or millions of chemical attractions, repulsions or indifferences which were busy within and without him; or, in brief, of Force itself, which, he was credibly informed, bore some dozen definitions in the textbooks, mostly contradictory, and all, as he was assured, beyond his intelligence; but summed up in the dictum of the last and highest science, that Motion seems to be Matter and Matter seems to be Motion, yet "we are probably incapable of discovering" what either is.
With the same light touch, more destructive in its artistic measure than the heaviest-handed brutality of Englishmen or Germans, he went on to upset relative truth itself: "How should I answer the question whether Euclidian Geometry is true? It has no sense! . . . Euclidian Geometry is, and will remain, the most convenient."
"I'll bet there are still some who still believe that, just like there are some people who still think Euclidian geometry must necessarily be true because it can be 'proved' mathematically." Mike nodded. "All Bishop Costin did all he was trying to do was to prove that the axioms of the Christian faith are logically self-consistent.
I have come to the conclusion that, since I can’t understand even that, I can’t expect to understand about God. I acknowledge humbly that I have no faculty for settling such questions, I have a Euclidian earthly mind, and how could I solve problems that are not of this world? And I advise you never to think about it either, my dear Alyosha, especially about God, whether He exists or not.
Scotist, Thomist, Realist, Nominalist, Papist, Calvinist, Molinist, Jansenist, are only pseudonyms. There are no sects in geometry; one does not speak of a Euclidian, an Archimedean. When the truth is evident, it is impossible for parties and factions to arise. Never has there been a dispute as to whether there is daylight at noon.
I believe like a child that suffering will be healed and made up for, that all the humiliating absurdity of human contradictions will vanish like a pitiful mirage, like the despicable fabrication of the impotent and infinitely small Euclidian mind of man, that in the world’s finale, at the moment of eternal harmony, something so precious will come to pass that it will suffice for all hearts, for the comforting of all resentments, for the atonement of all the crimes of humanity, of all the blood they’ve shed; that it will make it not only possible to forgive but to justify all that has happened with men—but though all that may come to pass, I don’t accept it.
Of this latter stage the simple figures of Euclidian plane and solid geometry figures which any child can understand are the appropriate symbols, but for that other more developed state of consciousness less apparent but more important these will not do.
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