Physical and Ethereal Spaces

The whole field with which the article deals is really one of those places where the exoteric science of our time comes hard upon the threshold of the eternal occult truths and asks to be complemented, to be directed and confirmed by the science of spiritual initiation. The formal mathematics used in the idea of ethereal or negative space - Professor Locher sometimes calls it polar-euclidean space - has long been known to pure mathematicians, but apart from their interest in its beautiful form, they have attached no further importance to it. Its significance lies, however, not in its mere form, but in the fact that its discipline, created by the mathematicians of the nineteenth century, gives insight into a quite new conception of space which exactly corresponds to what has always been described by occultists as the secret of the spatial aspect of the etheric - of life. It was in particular Rudolf Steiner's deed, in this as in many other fields, to make accessible to the modern scientifically inclined mind the ancient truths of occultism, so crucial to the future culture of mankind, and to give his followers the necessary indications towards the further development of the scientific task. It was in this sense that my article in Natura was written, firstly with readers in mind who are familiar with Rudolf Steiner's teaching.