Lecture IV

This conception could change into a different one only when men lost their awareness that everything quantitative—including mathematics—is originally experienced by man in direct connection with the universe. It changed when the point was reached where the quantitative was severed from what man experiences. We can determine this moment of separation precisely. It occurred when all concepts of space that included man himself were replaced by the schematic view of space that is customary today, according to which, from an arbitrary starting point, the three coordinates are drawn. The kind of mathematics prevalent today, by means of which man wants to dominate the so-called phenomena of nature, arose in this form only after it had been separated from the human element. Expressing it more graphically, I would say in a former age man perceived mathematics as something that he experienced within himself together with his god or gods, whereby the god ordered the world. It came as no surprise therefore to discover this mathematical order in the world. In contrast to this, to impose an arbitrary space outline or some other mathematical formula on natural phenomena—even if such abstract mathematical concepts can be identified with significant aspects in these so-called natural phenomena—is a procedure that cannot be firmly related to human experiences. Hence, it cannot be really understood and is at most simply assumed to be a fact. Therefore in reality it cannot be an object of any perception. The most that can be said of such an imposition of mathematics on natural phenomena is that what has first been mathematically thought out is then found to fit the phenomena of nature. But why this is so can no longer be discovered within this particular world perception.