Chapter VI (part 6)

To the plane being the idea that some phenomena come whence others go, and vice versa, will seem equally absurd. He will tenaciously think that the future is that wherefrom everything comes, and the past is that whereto everything goes and wherefrom nothing returns . He will be totally unable to understand that events may arise from the past just as they do from the future. Thus we see that the plane being will regard the changes of color of the lines lying on the plane very naively. The appearance of different spokes he will regard as the change of color of one and the same line , and the repeated appearance of the same colored spoke he will regard every time as a new appearance of a given color. But nevertheless, having noticed periodicity in the change of the color of the lines upon the surface, having remembered the order of their appearance, and having learned to define the "time" of the appearance of certain spokes in relation to some other more constant phenomenon, the plane being will be in a position to foretell the change of the line from one color to another. Thereupon he will say that he has studied this phenomenon, that he can apply to it "the mathematical method"—can "calculate" it. _____ If we ourselves enter the world of plane beings, then its inhabit-ants will sense the lines limiting the sections of our bodies. These sections will be for them living beings ; they will not know from whence they appear, why they alter, or whither they disappear in such a miraculous manner . So also, the sections of all our inanimate but moving objects will seem independent living beings. If the consciousness of a plane being should suspect our existence, and should come into some sort of communion with our consciousness, then to him we would appear as higher, omniscient, possibly omnipotent, but above all incomprehensible beings of a quite inconceivable category . We could see his world just as it is , and not as it seems to him. We could see the past and the future; could foretell, direct, and even create events. p. 68 We could know the very substance of things—could know what "matter" (the straight line) is, what "motion" (the broken line, the curve, the angle) is. We could see an angle , and we could see a centre . All this would give us an enormous advantage over the two-dimensional being. In all the phenomena of the world of the two-dimensional being we could see considerably more than he sees—or could see quite other things than he. And we could tell him very much that was new, amazing, and unexpected about the phenomena of his world, provided indeed that be could hear us and understand us . First of all we could tell him that what he regards as phenomena—angles and curves, for instance—are properties of higher figures; that other "phenomena" of his world are not phenomena, but only "parts" or "sections" of phenomena; that what he calls "solids" are only sections of solids—and many things besides. We would be able to tell him that on both sides of his plane (i.e., of his space or ether) lies infinite space (which the plane being calls time); and that in this space lie the causes of all his phenomena, and the phenomena themselves, the past as well as the future ones; moreover, we might add that "phenomena" themselves are not something happening and then ceasing to be, but combinations of properties of higher solids. But we should experience considerable difficulty in explaining anything to the plane being; and it would be very difficult for him to understand us. First of all it would be difficult because he would not have the concepts corresponding to our concepts.