The nature of man : approached through the philosophy of Rudolf Steiner

and characterised by Cayley as the whole of geometry, would make it possible to study these etheric forces with mathematical clearness of thought. The late George Adams was able to pioneer these studies particularly in relation to plant forms and metamorphosis. Now the importance of this work for our present purpose is to establish that human cognition can be trained to become inwardly mobile as it has to be in Projective Geometry without losing that clarity of awake consciousness which is the character of mathematical thinking. The etheric forces belong to what George Adams called negative Euclidean space, which arises from the interplay or interweaving of planes as distinct from the points of normal Euclidean space. The primary polarity of space is between the infinitely contracted point and the infinitely expanded plane. Thus positive Euclidean space arises from the relationship between points, negative Euclidean space from the relationship between planes. I can of course only indicate these lines of study on this occasion.

The vegetable kingdom expresses the play of these planar forces working from the periphery. That we can see them in the leaves with our physical eyes is due to the physical substances which are caught up into them as the physical body of the plant. In the plant therefore we have the etheric planar forces from the cosmic periphery in their interplay with the physical forces related to the earth centre. These etheric forces become to some extent individually organised to form what can be called the etheric body of the plant: the word ‘body’ is of course notentirely satisfactory.

In the plant kingdom everything is, so to say, spread out, it grows out into spatial manifestation. When we come to study the animal kingdom another gesture confronts us. A gesture of interiorisation develops. Instead of growing outwards the developing organism turns in on itself and forms a cup-like form. More and more infoldings come about and gradually there arise the wonderfully internally organised bodies of the higher animals. It is not difficult to see that a quite distinct element of form here comes to expression. It pushes inwards, creating inner spaces; what in the plant was still outside now becomes interiorised into the animal. This something then manifests in movement and sensation, in desire and pleasure and pain. Something comes to

6