Chapter VI (part 4)

As has been said, the two-dimensional being will regard the straight lines only as immobile matter; irregular lines and curves will seem to him as moving. So far as really moving lines are concerned, that is, lines limiting the cross-sections or planes of contact passing through or moving along the plane, these will be for p. 64 the two-dimensional being something inconceivable and incommensurable . It will be as though there were in them the presence of something independent, depending upon itself only, animated . This effect will proceed from two causes: He can measure the immobile angles and curves, the properties of which the two-dimensional being calls motion, for the reason that they are immobile; moving figures, on the contrary, he cannot measure, because the changes in them will be out of his control. These changes will depend upon the properties of the whole body and its motion, and of that whole body the two-dimensional being will know only one side or section. Not perceiving the existence of this body, and contemplating the motion pertaining to the sides and sections he probably will regard them as living beings . He will affirm that there is something in them which differentiates them from other bodies: vital energy, or even soul. That something will be regarded as inconceivable, and really will be inconceivable to the two-dimensional being, because to him it is the result of an incomprehensible motion of inconceivable solids. If we imagine an immobile circle upon the plane, then for the two-dimensional being it will appear as a moving line with some very strange and to him inconceivable motions. The two-dimensional being will never see that motion. Perhaps he will call such motion molecular motion , i.e., the movement of minutest invisible particles of "matter." Moreover, a circle rotating around an axis passing through its center, for the two-dimensional being will differ in some inconceivable way from the immobile circle. Both will appear to be moving, but moving differently . For the two-dimensional being a circle or a square, rotating around its centre, on, account of its double motion will be an inexplicable and incommensurable phenomenon, like a phenomenon of life for a modern physicist. Therefore, for a two-dimensional being, a straight line will be immobile matter; a broken or a curved line—matter in motion; and a moving line— living matter. The centre of a circle or a square will be inaccessible to the plane being, just as the centre of a sphere or of a cube made of solid matter is inaccessible to us—and for the two-dimensional being even p. 65 the idea of a centre will be incomprehensible, since he possesses no idea of a centre. Having no idea of phenomena proceeding outside of the plane—that is, out of his "space"—the plane being will think of all phenomena as proceeding on his plane as has been stated. And all phenomena which he regards as proceeding on his plane, he will consider as being in causal interdependence one with another : that is, he will think that one phenomenon is the effect of another which has happened right there , and the cause of a third which will happen right on the same plane. If a multi-colored cube passes through the plane, the plane being will perceive the entire cube and its motion as a change in color of lines lying in the plane. Thus, if a blue line replaces a red one, then the plane being will regard the red line as a past event . He will not be in a position to realize the idea that the red line is still existing somewhere. He will say that the line is single, but that it becomes blue as a consequence of certain causes of a physical character. If the cube moves backward so that the red line appears again after the blue one, then for the two-dimensional being this will constitute a new phenomenon . He will say that the line became red again.