Lecture I

When we take a closer look we see that not only are they not real in themselves but in fact they have the effect of destroying reality. The question now arises: would it be possible to strengthen our capacity to make these inner mathematical constructions by which we then penetrate the sense-perceptible world? Is it possible that what is first experienced mathematically as pale abstractions can be made stronger? In other words, could the force which we have to use to attain a mathematical knowledge of nature be used more effectively?—with the result not just a mathematical abstraction, but something inwardly, spiritually concrete? In that case, we would not just see a re-created version of the outer world or an abstract mathematical picture, but we would have something formed in an entirely different manner. We would have gained something with the full character of reality, but obtained similarly to the way we obtain mathematical pictures. We would then have before us spiritually a reality that shines out toward us in the same way that the outer sense-perceptible world streams toward us. But we would have this from pictures filled with reality, not from mathematically abstract pictures. We would have lifted ourselves, through strengthening our mathematical capacity, to a higher level, and in doing so we would reveal more of our own inner reality. This we can see as a third step in our attainment of knowledge. The first step would be the familiar grasping of the real outer world. The second step would be the mathematical penetration of the outer world, after we have first learned inwardly to construct the purely mathematical aspect. The third would be the entirely inner experience, like the mathematical experience but with the character of spiritual reality.