Chapter II (part 3)

The thought of past ages has used the conception of a three-dimensional space, and by that means has classified many phenomena and has obtained rules for dealing with matters of great practical utility. The path which opens immediately before us in the future is that of applying the conception of four-dimensional space to the phenomena of nature, and of investigating what can be found out by this new means of apprehension. . . . For development of knowledge it is necessary to separate the self-elements , i.e., the personal elements which we put in everything cognized by us, from that which is cognized , in order that our attention may not be distracted (upon ourselves) from the properties which we, in substance, perceive . Only by getting rid of the self-elements in our receptivity do we put ourselves in a position in which we can propound sensible questions. Only by getting rid of the notion of a circular motion of the sun around the earth (i.e., around us — self-element ) do we prepare our way to study the sun as it really is. But the worst about a self-element is that its presence is never dreamed of till it is got rid of. In order to understand what the self-element in our receptivity means, imagine ourselves to be translated suddenly to another part of the universe, and to find there intelligent beings and to hold conversation with them. If we told them that we came from this world, and were to describe the sun to them, saying that it was a bright, hot body which moved around us, they would reply: " You have told us something about the sun, but you have also told us something about yourselves .". . . Therefore, desiring to tell something about the sun, we shall first of all get rid of the self-element which is introduced into our knowledge of the sun by the movement of the earth, upon which we are, round it. . . . One of our serious pieces of work will be to get rid of the self-elements in the knowledge of the arrangement of objects . The relations of our universe or our space with regard to the wider universe of four-dimensional space are altogether undetermined. The real relationship will require a great deal of study to apprehend, and when apprehended will seem as natural to us as the position of the earth among the other planets seems to us now . . . . I would divide studies of arrangement into two classes: those which p. 27 create the faculty of arrangement, and those which use it and exercise it. Mathematics exercises it, but I do not think it creates it; and unfortunately, in mathematics as it is now often taught, the pupil is launched into a vast system of symbols: the whole use and meaning of symbols (namely, as means to acquire a clear grasp of facts) is lost to him. . . . Of the possible units which will serve for the study of arrangement, I take the cube; and I have found that whenever I took any other unit I got wrong, puzzled, and lost my way. With the cube one does not get along very fast, but everything is perfectly obvious and simple, and builds up into a whole of which every part is evident. . . . Our work then will be this: a study, by means of cubes, of the facts of arrangement; and the process of learning will be an active one of actually putting up the cubes. Thus we will bring our minds into contact with nature. ( A New Era of Thought .) ______ Taking all these things into consideration, we should try to define clearly our understanding of those sides of our receptivity dealt with by Kant. What is space? Taken as object, that is, perceived by our consciousness, space is for us the form of the universe or the form of the matter in the universe. Space possesses an infinite extension in all directions.