Teaching is a dialogue, and it is through the process of engaging students that we see ideas taken from the abstract and played out in concrete visual form. Students teach us about creativity through their personal responses to the limits we set, thus proving that reason and intuition are not antithetical. Their works give aesthetic visibility to mathematical ideas.
Humans are in delusion by default, and those who conquer their delusion can understand good and evil. Morality is an arbitrary abstract, it is not good or evil and those who provoke morality a righteous act, are still at the sideways of delusion and conquer.
We have come to understand the phenomena of life only as an assemblage of the lifeless. We take the mechanistic abstractions of our technical calculation to be ultimately concrete and "fundamentally real," while our most intimate experiences are labelled "mere appearance" and something having reality only within the closet of the isolated mind. Suppose however we were to invert this whole scheme, reverse the order in which it assigns abstract and concrete. What is central to our experience, then, need not be peripheral to nature. This sunset now, for example, caught within the network of bare winter branches, seems like a moment of benediction in which the whole of nature collaborates. Why should not these colours and these charging banners of light be as much a part of the universe as the atoms and molecules that make them up? If they were only "in my mind," then I and my mind would no longer be a part of nature. Why should the pulse of life toward beauty and value not be a part of things? Following this path, we do not vainly seek to assemble the living out of configurations of dead stuff, but we descend downwards from more complex to simpler grades of the organic. From humans to trees to rocks; from "higher grade" to "lower grade" organisms. In the universe of energy, any individual thing is a pattern of activity within the flux, and thereby an organism at some level.
Music, uniquely among the arts, is both completely abstract and profoundly emotional. It has no power to represent anything particular or external, but it has a unique power to express inner states or feelings. Music can pierce the heart directly; it needs no mediation.
When you see a fish you don't think of its scales, do you? You think of its speed, its floating, flashing body seen through the water. Well, I've tried to express just that. If I made fins and eyes and scales, I would arrest its movement, give a pattern or shape of reality. I want just the flash of its spirits.
Oh, don't pull your hand away from me, I've promised myself that maybe by the end of this impossible narrative I shall understand, oh maybe it will be on Hell's road that I shall be able to find what we need—but don't pull your hand away, even though I now know that the finding has to come on the road of what we are, if I can succeed in not sinking completely into what we are.