2. The Position of Anthroposophy among the Sciences

In respect to space, one learns to know (to some extent) such an interplay of forces in the constitution of our soul. Then one views these things differently. From the logical, mathematical standpoint one can certainly keep step with those who extend their calculations from three-dimensional to four-dimensional space. But there one must make a halt. One cannot pass on into an indefinite fourth dimension; one must turn back at a certain point, and the fourth dimension becomes simply the third with a minus sign before it. One returns through the third dimension. The mistake made in these geometrics of more than three dimensions is in going on abstractly from the second to the third, from the third to the fourth dimension, and so on. But what we have here, if I may express it in a comparison, is not simple progression but oscillation. Our perception of space must return into itself. By taking the third dimension negatively, we really annihilate it. The fourth dimension is the negative third and annihilates the third, making space two-dimensional. And in like manner we can find a quite real progression, even though, logically, mathematically, algebraically, these things can be carried further and further. When we think in accordance with reality, we must turn back at the fourth, fifth and sixth dimensions to the space that is simply given us. With the sixth dimension, we have abolished space and reach the point.