Читать книгу The Kernel and the Husk: Letters on Spiritual Christianity онлайн

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It is the same with Geometry. The whole of what we call “Euclid” is based upon a most aerial effort of the Imagination. We have to imagine lines without thickness, straightness that does not deviate the billionth part of an inch from perfect evenness, perfectly symmetrical circles, and—climax of audacity!—points that have “no parts and no magnitude!” Obviously these things have no existence except in the dreams of Imagination; yet Euclid’s severe reasoning applies to none but these things. If you step from your ideal triangle in Dreamland into your material triangle in chalk-land, you step from absolute truth into statements that are not absolutely true. The angles at the base of your chalk isosceles triangle are not exactly equal, if you measure them with sufficient accuracy. In a word the whole of Geometry is an appeal to the Imagination in which the geometer says to us, “I know that my propositions are not exactly true except with respect to invisible, ideal, and imaginary figures, planes, and solids. These ideas, therefore, you must endeavour to imagine. In order to relieve the strain on your imagination, I will place before you material and visible figures about which my reasoning will be approximately true. From these I must ask you to try to rise upward to the imagination of their archetypes, the immaterial realities.”