Chapter VII (part 4)

Along with Hinton, I postulated that our space itself bears within it the relations which permit us to establish its relations to higher space, and on the foundation of this postulate I built a whole series of analogies which somewhat clarified for us the problems of space and time and their mutual co-relations, but which, as was said, did not explain anything concerning the principal question of the causes of the three-dimensionality of space . The method of analogies is, generally speaking, a rather tormenting thing. With it, you walk in a vicious circle. It helps you to elucidate certain things, and the relations of certain things, but in substance it never gives a direct answer to anything. After many and long attempts to analyze complex problems by the aid of the method of analogies, you feel the uselessness of all your efforts; you feel that you are walking alongside of a wall. Thereupon you begin to experience simply a hatred and aversion for analogies, and you find it necessary to search in the direct way which leads where you need to go. The problem of higher dimensions has usually been analyzed by the method of analogies, and only very lately has science begun to elaborate that direct method which will be shown later on. If we desire to go straight, without deviating, we shall keep p. 79 strictly up to the fundamental propositions of Kant. But if we formulate Hinton's above-mentioned thought from the point of view of these propositions, it will be as follows: We bear within ourselves the conditions of our space, and therefore within ourselves we shall find the conditions which will permit us to establish correlations between our space and higher space . In other words, we shall find the conditions of the three-dimensionality of the world in our psyche, in our receptive apparatus— and shall find exactly there the conditions of the possibility of the higher dimensional world . Propounding the problem in this way, we put ourselves upon the direct path, and we shall receive an answer to our question, what is space and its three-dimensionality? How may we approach the solution of this problem? Plainly, by studying our consciousness and its properties. We shall free ourselves from all analogies, and shall enter upon the correct and direct path toward the solution of the fundamental question about the objectivity or subjectivity of space, if we shall decide to study the psychical forms by which we perceive the world, and to discover if there does not exist a correspondence between them and the three-dimensionality of the world—that is, if the three-dimensional extension of space, with its properties, does not result from properties of the psyche which are known to us. Footnotes 75:1 Roberto Bonola, "Non-Euclidian Geometry." The Open Court Publishing Co., Chicago, 1912, pp. 92, 93.