2. The Position of Anthroposophy among the Sciences

On looking back to the way in which we came to know in early childhood the structure of space—by walking and standing upright, by orientating ourselves to right and left, by learning to gauge the depth-dimension, by connecting all this with the abstractly perceived space of geometry (which the child learns to know from inner experience)—we realise the serious and important consequences that follow if we cannot look back to the living origin, within our own being, of space—of our conception and perception of space—but simply accept it in its already transformed shape, independent of ourselves. For example, in recent times we have come to regard this space (with its three dimensions) in such a way that we have gone on to postulate a fourth and higher dimensions. These spaces and their geometries are widely known to-day. Anyone who has once learnt to know the living structure of space finds it most interesting to follow such an extension of mathematical operations (applicable to three dimensions) and to arrive at a fourth dimension that cannot be visualised, and so on. These operations are logical (in the mathematical sense) and quite correct. But anyone who knows the genesis of our idea of space, as I have described it, will detect something quite special here. We could take a pendulum, for example, and watch it oscillate. Watching it purely externally, we might expect it to swing further and further out. But it does not. When it has reached a definite point, it swings back again to the opposite side. If we know the relation between the forces involved, we know that the pendulum oscillates and cannot go further because of the relation between the forces.