The Spatial Illusion

aware that such subtleties are not attempted by almost the totality of so-called figure draughtsmen, but that is precisely one of the chief reasons why their work is without value. A draughtsman, as I have said before, must so habituate his mind to recessional thinking that he no longer tries to make a curve in perspective look right on the surface of the paper, but that he actually lays, with his pencil, the real curve into its place, or—shall we say ?—follows the appearance of the real curve—it may be, lying horizontally into the paper— with his pencil-point. On one occasion I was looking at a diagram made with a view to explaining the absolute geometry of perspective. The author of the book, a professor of the Paris Polytechnique, had employed the recognized liberty of drawing a three-dimensional diagram without submitting to the laws of perspective, although his treatise was on that very subject. Indeed he put himself, all through the book, to great pains to render the subject as abstract and as difficult of practical application as he very well could. The diagram represented the ground plane and, upright upon it, the plane of the picture. At first glance I realized the spatial convention and said to another person (not an artist) ; £ Why has he made the far side of the picture plane longer than the near side ?' My companion first failed to understand me, then affirmed at once that both sides were equal according to the usual convention of the geometers. Even then I could not see the equality, so much was I under the empire of the three-dimensional spatial illusion I had carefully cultivated for so many years, an illusion that my companion had never troubled about. I was obliged to measure the lines in order to convince myself that they were of the same length. If you are in this way a complete victim of your own spatial illusion you will have little or no need of geometrical construction for establishing perspective ; except in special cases of work too large to be taken in at a glance from a convenient

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