Chapter VI (part 8)

Suppose now the spiral to be still and the film to move vertically upward, the whole spiral will be represented in the film in the consecutive positions of the point of intersection. FIG I FIG II If instead of one spiral we take a complicated construction consisting of spirals, inclined and straight lines, broken and curved lines, and if the film move vertically upward we shall have an entire universe of moving points the movements of which will appear to the plane being as original. The plane being will explain these movements as depending one upon another, and indeed he will never happen to think that these movements are fictitious and are dependent upon the spirals and other lines lying outside his space. 1 Returning to the plane being and his perception of the world, and analyzing his relations to the three-dimensional world, we see that for the two-dimensional or plane being it will be very difficult to understand all the complexity of the phenomena of our world, as it appears to us. He (the plane being) is accustomed to perceive the world as being too simple. Taking into consideration the sections of figures instead of the figures themselves, the plane being will compare them in relation to their length and their greater or lesser curvature, i.e., their for him more or less rapid motion. The differences between the objects of our world, as they exist for us he would not understand. The functions of the objects of our world would be completely mysterious to his mind—incomprehensible, "supernatural." p. 71 Let us imagine that a coin, and a candle the diameter of which is equal to that of the coin, are on the plane upon which the two-dimensional being lives. To the plane being they will seem two equal circles, i.e., two moving, and absolutely identical lines; he will never discover any difference between them. The functions of the coin and of the candle in our world—these are for him absolutely a terra incognita . If we try to imagine what an enormous evolution the plane being must pass through in order to understand the function of the coin and of the candle and the difference between these functions, we shall understand the nature of the division between the plane world and the world of three dimensions, and the complete impossibility of even imagining, on the plane, anything at all like the three-dimensional world, with its manifoldness of function. The properties of the phenomena of the plane world will be extremely monotonous; they will differ by the order of their appearance, their duration, and their periodicity. Solids, and the things of this world will be flat and uniform, like shadows , i.e., like the shadows of quite different solids, which seem to us uniform. Even if the plane being could come in contact with our consciousness, he would never be in a position to understand all the manifoldness and richness the phenomena of our world and the variety of function of the things of that world. Plane beings would not be in a position to master our most ordinary concepts. It would be extremely difficult for them to understand that phenomena, identical for them , are in reality different; and on the other hand, that phenomena quite separate for them are in reality parts of one great phenomenon, and even of one object or one being. This last will be one of the most difficult things for the plane being to understand. If we imagine our plane being to be inhabiting a horizontal plane, intersecting the top of a tree, and parallel to the surface of the earth, then for such a being each of the various sections of the branches will appear as a quite separate phenomenon or object. The idea of the tree and its branches will never occur to him. Generally speaking, the understanding of the most fundamental and simple things of our world will be infinitely long and difficult p. 72 to the plane being. He would have to entirely reconstruct his concepts of space and time. This would be the first step. Unless it is taken, nothing is accomplished.