Lecture III

This is what occurs above, in the realm of thought schemes, through the nerve-sense system. One would not achieve a relationship to such a process in space if it were not for what one does with one's limbs, with one's whole body, if it were not for inserting oneself into the whole world in accordance with the inward orientation of above-below, right-left, and front-back. When I walk forward, I know that on one hand I place myself in the vertical direction in order to remain upright. I am also aware that in walking I adjust my direction to the back-to-front orientation, and when I swim and use my arms, I orient myself in right and left. I do not understand all this if I apply Descartes’ space scheme, the abstract scheme of the coordinate axes. What gives me the impression of reality in dealing with matters of space is found only when I say to myself: Up in the head, in the nerve system, an illusory image arises of something that occurs deep down in the subconscious. Here, where man cannot reach with his ordinary consciousness, something takes place between his limb system and the universe. The whole of mathematics, of geometry, is brought up out of our limb system of movement. We would not have geometry if we did not place ourselves into the world according to inward orientation. In truth, we geometrize when we lift what occurs in the subconscious into the illusory of the thought scheme. This is the reason why it appears so abstractly independent to us. But his is something that this only come about in recent times. In the age in which mathesis, mathematics, was still felt to be something close to mysticism, the mathematical relationship to all things was also viewed as something human.