Lecture I

The second of the three to which I have referred is again a thing we do before we come to outer Nature. I mean Geometry,—all that is known by means of pure Geometry. What a cube or an octahedron is, and the relations of their angles,—all these are things which we determine without looking into outer Nature. We spin and weave them out of ourselves. We may make outer drawings on them, but this is only to serve mental convenience, not to say inertia. Whatever we may illustrate by outer drawings, we might equally well imagine purely in the mind. Indeed it is very good for us to imagine more of these things purely in the mind, using the crutches of outer illustration rather less. Thus, what we have to say concerning geometrical form is derived from a realm which, to begin with, is quite away from outer Nature. We know what we have to say about a cube without first having had to read it in a cube of rock-salt. Yet in the latter we must find it. So we ourselves do something quite apart from Nature and then apply it to the latter.