Chapter IX (part 8)

Thus in all its relations to the world the animal is quite analogous to the imagined, unreal two-dimensional being living upon a plane. All our world appears to the animal as the plane through which phenomena are passing, moving upon time, or in time. And so we may say that we have established the following: that under certain limitations of the psychic apparatus for receiving the outer world, for the subject possessing this apparatus, the entire aspect and all properties of the world will suffer change. And two subjects, living side by side, but possessing different psychic apparatus, will inhabit different worlds—the properties of the extension of the world will be different for them. And we observed the conditions, not invented for the purpose, not concocted in imagination, but really existing in nature; that is, the psychic conditions governing the lives of animals, under which the world appears as a plane or as a line. That is to say, we have established that the three-dimensional extension of the world depends upon the properties of our psychic apparatus. Or, that the three-dimensionality of the world is not its property, but a property of our receptivity of the world. In other words, the three-dimensionality of the world is a property of its reflection in our consciousness. If all this is so, then it is obvious that we have really proved the dependence of space upon the space-sense . And if we have proved the existence of a space-sense lower in comparison with ours , by this we have proved the possibility of a space-sense higher in comparison with ours . And we shall grant that if in us there develops the fourth unit of reasoning as different from the concept as the concept is different from perception, so simultaneously with it will appear for us in the surrounding world a fourth characteristic which we may designate geometrically as the fourth direction or the fourth perpendicular, because in this characteristic will be included the properties of objects perpendicular to all properties known to us, and not parallel to any of them. In other words, we shall see, or we shall feel ourselves in a space not of three, but of four dimensions; and in the objects surrounding us, and in our own bodies, will appear common p. 111 properties of the fourth dimension which we did not notice before, or which we regarded as individual properties of objects (or their motion), just as animals regard the extension of objects in the third dimension as their motion. And when we shall see or feel ourselves in the world of four dimensions we shall see that the world of three dimensions does not really exist and has never existed: that it was the creation of our own fantasy, a phantom host, an optical illusion, a delusion—anything one pleases excepting only reality. And all this is not an "hypothesis," not a supposition, but exact fact, just such a fact as the existence of infinity. For positivism to insure its existence it was necessary to annihilate infinity somehow, or at least to call it an "hypothesis" which may or may not be true. Infinity however is not an hypothesis, but a fact, and such a fact is the multi-dimensionality of space and all that it implies, namely, the unreality of everything three-dimensional. Footnotes 99:1 In this connection, there have been some interesting observations made upon the blind who are just beginning to see. In the magazine Slepetz (The Blind, 1912) there is a description from direct observation of how those born blind learn to see after the operation which restored their sight. This is how a seventeen-year-old youth, who recovered his sight after the removal of a cataract, describes his impressions. On the third day after the operation he was asked what he saw. He answered that he saw an enormous field of light and misty objects moving upon it. These objects he did not discern.