6. Anthroposophy and Agnosticism

Things become interesting when they are followed mathematically and cross over into the physical, and much could still be contributed to the solution of borderline problems if these theories, which begin to become very real here, were developed. But there is still a terrible lack of understanding for this. For example, I once gave a lecture at a mathematical university society where I tried to introduce these things. I explained that if you have the asymptotes of a hyperbola here and the branches of the hyperbola here, what you have to imagine on the right here, spreading out, you have to imagine on the left here, spreading together, so that a complete reversal takes place. These things gradually lead to a more concrete treatment of space. But today there is little understanding for this. Even pure analysts often show a certain dislike of synthetic geometry. And this newer synthetic geometry is the way to get out of the purely formal mathematical and to the problem where one has to grasp the empirical. As long as one calculates with mere analytical geometry, one does not approach the realms of reality. There one has only developed the end points of the coordinates, the geometric location of the coordinates and so on. If one remains with constructing with the linear and with circles, then one stands in lines within them, but is compelled to take a certain visualization to help. This is what makes synthetic geometry so beneficial for getting out of the formal and showing how to think the mathematical in nature.