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PSYCHISM AND THE FOURTH DIMENSION
Let a straight line be drawn on it. At any point in this straight line, let a perpendicular be drawn. Here the perpendicular, being on the surface of the paper, is also in two-dimensional space. Now let two. other straight lines be drawn, intersecting the first line at a point where the perpendicular meets it. It is. evident, as every geometer can demonstrate, that neither of these lines, nor any other lines through the same point, except that first drawn, will be at right angles to the perpendicular, so long as it remains on the surface of the paper, that is in two-dimensional space, but that the perpendiculars to the intersecting lines at the point of intersection will be represented by a series of lines, all in different directions. But let the first perpendicular be supposed to be raised upright into three dimensional space, representing it by a pencil held upright with its point at the point of intersection; it is evident that it is now perpendicular to all the intersecting lines; and the only conception a two-dimensional being could form of this line, represented by the pencil, would be a straight line going in several directions at once; since it is perpendicular to all the intersecting lines, and he perceives that all their perpendiculars go in different directions.
Suppose a beam of light, coming from a point several feet above the paper, so that its rays are sensibly parallel, for small distances. Suppose it to fall on a suitable reflector at the point of the intersection, so that it may be spread evenly in every direction from that point along the surface of the paper :-a right-angle
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