Chapter II (part 1)

p. 23 CHAPTER II A new view of the Kantian problem. The books of Hinton. The "space-sense" and its evolution. A system for the development of a sense of the fourth dimension by exercises with colored cubes. The geometrical conception of space. Three perpendiculars—why three? Can everything existing be measured by three perpendiculars? The indices of existence. Reality of ideas. Insufficient evidence of the existence of matter and motion. Matter and motion are only logical concepts, like "good" and "evil." AS already stated, Kant propounded the problem, but gave no solution of it, nor did he point the way to a solution. And not one of the known commentators, interpreters, followers or adversaries of Kant has found a solution, or the way to it. I find the first flashes of a right understanding of the Kantian problem, and the first suggestions in regard to a possible way toward its solution, in the attempts at a new treatment of the problem of space and time, involving the concept of the "fourth dimension" and higher dimensions in general. An interesting synopsis of many things developed in this direction is that of C. H. Hinton, author of the books, A New Era of Thought , and The Fourth Dimension . Hinton notes, among other things, that in commenting upon Kantian ideas, only their negative side is usually insisted upon, namely, the fact that we can cognize things in a sensuous way, in terms of space and time only, is regarded as an obstacle , hindering us from seeing what things in themselves really are, preventing the possibility of cognizing them as they are, imposing upon them that which is not inherent in them, shutting them off from us. But [says Hinton] if we take Kant's statement simply as it is—not seeing in the spatial conception a hindrance to right receptivity—that we apprehend things by means of space —then it is equally allowable to consider our space sense not as a negative condition, hindering our perception of the world, but as a positive means by which the mind grasps its experiences, i.e., by which we cognize the world. p. 24 There is, in so many books in which the subject is treated, a certain air of despondency—as if this space apprehension were a kind of veil which shut us off from nature. But there is no need to adopt this feeling. The first postulate of this book is a full recognition of the fact that it is by means of space that we apprehend what is. Space is the instrument of the mind. Very often a statement which seems to be most deep and abstruse and hard to grasp, is simply the form into which deep thinkers have thrown a very simple and practical observation. And for the present let us look on Kant's great doctrine of space from a practical point of view, and it comes to this—it is important to develop the space sense, for it is the means by which we think about real things. Now according to Kant [Hinton goes on to say] the space sense, or the intuition of space, is the most fundamental power of the mind. But I do not find anywhere a systematic and thorough-going education of the space sense. It is left to be organized by accident. Yet the special development of the space sense makes us acquainted with a whole series of new conceptions. Fichte, Schelling, Hegel, have developed certain tendencies and have written remarkable books, but the true successors of Kant are Gauss and Lobachevsky. For if our intuition of space is the means whereby we apprehend, then it follows that there may be different kinds of intuitions of space. Who can tell what the absolute space intuition is? This intuition of space must be colored, so to speak, by the conditions (of psychical activity) of the being which uses it.