Lecture III

It is surprising, very surprising, to discover that ancient mathematics spoke quite differently about the triangle and the square. Modern nebulous mystics describe great mysteries, but there is no great mystery here. It is only what a person would have experienced inwardly in the blood when he walked the outline of a triangle or a square, not to mention the blood experience corresponding to the pentagram. In the blood the whole of geometry becomes qualitative inward experience. We arrive back at a time when one could truly say, as Mephistopheles does in Goethe's Faust, “Blood is a very special fluid.”[^7] This is because, inwardly experienced, the blood absorbs all geometrical forms and makes of them intense inner experiences. Thereby man learns to know himself as well. He learns to know what it means to experience a triangle, a square, a pentagram; he becomes acquainted with the projection of geometry on the blood and its experiences. This was once mysticism. Not only was mathematics, mathesis, closely related to mysticism, it was in fact the external side of movement, of the limbs, while the inward side was the blood experience. For the mystic of bygone times all of mathematics transformed itself out of a sum of spatial formations into what is experienced in the blood, into an intensely mystical rhythmic inner experience.