Yesterday's considerations led us to conclude that at one boundary of cognition we must come to a halt within phenomena and then permeate them with what the phenomena call forth within our consciousness, with concepts, ideas, and so forth. It became apparent that the realm in which these ideas are most pure and pellucid is that of mathematics and analytical mechanics. Our considerations then climaxed in showing how reflection reveals that everything present in the soul as mathematics, as analytical mechanics, actually rests upon Inspiration. Then we were able to indicate how the impulses proceeding from Inspiration are diffused throughout the ancient Indian Vedanta: the same spirit from which we now draw only mathematics and analytical mechanics was once the source of the delicate spirituality of the Vedanta. We were able to show how Goethe, in establishing his mode of phenomenology, always strives to find the archetypal phenomenon while remaining within the phenomena themselves and that his search for the archetypal phenomenon that underlies complex phenomena is, inwardly, the same as the mathematician's search for the axiom underlying complex mathematical constructs. Goethe, therefore, who himself admitted that he had no conventional mathematical training, nevertheless sensed the essence of mathematics so clearly that he demanded a method for the determination of archetypal phenomena rigorous enough to satisfy a mathematician. It is just this that the Western mind finds so attractive in the Vedanta: that in its inner organization, in its progression from one contemplation to the next, it reveals the same inner necessity as mathematics and analytical mechanics. That such connections are not uncovered by academic studies of the Vedanta is simply a consequence of there being so few people today with a universal education. Those who engage in pursuits that then lead them into Oriental philosophy have too little comprehension — and, as I have said, Goethe did have this — of the true inner structure of mathematics. They thus never grasp this philosophy's vital nerve. At the one pole, then, the pole of matter, we have been able to indicate the attitude we must assume initially if we do not wish to continue weaving a Penelope's web like the worldview woven by recent science but rather to come to grips with something that rests upon a firm foundation, that bears its center of gravity within itself.