Chapter VI (part 5)

For the being living on a plane, everything above and below (if the plane be horizontal), and on the right or left (if the plane be vertical) will be existing in time, in the past and in the future: that which in reality is located outside of the plane will be regarded as non-existent, either as that which is already past, i.e., as something which has disappeared, ceased to be, will never return; or as in the future, i.e., as not existent, not manifested, as a thing in potentiality. ______ Let us imagine that a wheel with the spokes painted different colors is rotating through the plane upon which the plane being lives. To such a being all the motion of the wheel will appear as a variation of the color of the line of intersection of the wheel and the plane. The plane being will call this variation of the color of the line a phenomenon, and observing these phenomena he will notice in them a certain succession. He will know that the black line is followed by the white one, the white by the blue, the blue by the red, and so on. If simultaneously with the appearance of the white line some other phenomenon occurs—say the ringing of a p. 66 bell—the two-dimensional being will say that the white line is the cause of that ringing. The change of the color of the lines, in the opinion of the two-dimensional being, will depend on causes lying right in his plane. Any pre-supposition of the possibility of the existence of causes lying outside of the plane he will characterize as fantastic and entirely unscientific. It will seem so to him because he will never be in a position to represent the wheel to himself, i.e., the parts of the wheel on both sides of the plane. After a rough study of the color of the lines, and knowing the order of their sequence, the plane being, perceiving one of them, say the blue one, will think that the black and the white ones have already passed, i.e., disappeared, ceased to exist, gone into the past ; and that those lines which have not as yet appeared—the yellow, the green, and so on, and the new white and black ones still to come—do not yet exist, but lie in the future. Therefore, though not conceiving the form of his universe, and regarding it as infinite in all directions, the plane being will nevertheless involuntarily think of the past as situated somewhere at one side of all , and of the future as somewhere at the other side of this totality. In such manner will the plane being conceive of the idea of time . We see that this idea arises because the two-dimensional being senses only two out of three dimensions of space; the third dimension he senses only after its effects become manifest upon the plane, and therefore he regards it as something different from the first two dimensions of space, calling it time. ______ Now let us imagine that through the plane upon which the two-dimensional being lives, two wheels with multi-colored spokes are rotating and are rotating in opposite directions. The spokes of one wheel come from above and go below; the spokes of the other come from below and go above. The plane being will never notice it . He will never notice that where for one line (which he sees) there lies the past, for another line there lies the future. This thought will never even come into his head, because he will conceive of the past and the future very confusedly, regarding them as concepts, not as actual facts. But at the same time he will be firmly convinced that the past goes in one direction , and the future in another. Therefore p. 67 it will seem to him a wild absurdity that on one side something past and something future can lie together, and on another side—and also beside these two—something future and something past .