We have no choice but to use mathematical analogies in even our most subtle thoughts about moral and spiritual issues since mathematics, by definition, is the proper way in this universe to describe paths. We move over paths even in the events of our innermost lives, we develop over paths. Our current moral talk and thought assumes a Euclidean space for our moral lives, including our innermost selves and our relationships to others. At the same time, mathematicians and scientists and engineers have moved on to far more sophisticated geometries for the description of not only exotic sorts of stars and black-holes but also spinning components in machines.
With all the self-justifying talk of moral theologians and philosophers and literary men about the differences between physical objects and moral natures, I find it hard to believe we live in a world where it’s appropriate to describe the moral lives of men and beasts with simpler words and concepts than those which are necessary for physical objects. Surely, we can enrich our understandings and discussions of our own lives by using a richer set of words and concepts. Surely, the more abstract concepts corresponding to paths which can be found in more modern geometries can help us to speak more truly of our lives and our societies than the simpler concepts which correspond to simple paths and journeys over the surface of the earth.
Don’t we spin and twist, often discovering that a simple event in our lives or a change in attitude leaves us in a state that might be labeled orthogonal to our societies or families? Don’t we often feel ourselves relatively unchanged as our surroundings change around us, generating forces on us which might well be analogous to the so-called ‘fictitious forces’ of physics which are, in one sense at least, generated by nonlinear changes in coordinates though no ‘true’ forces be involved?
Call me proud in my human nature, but I simply find it hard to believe that my insides can be described by analogies to simpler concepts than what is necessary to describe the forces on a spinning disc in my computer. I find it still harder to believe that my relationships to others, including those who are long dead, can be described by those simpler concepts.
My personal situation is making it difficult to put in as much time as I’d like in exploring the mathematics and physics which might give clues as to the true nature of the created being which is our human stuff and of which we are part. Yet, I’m plowing through, slowly, trying to learn as much as I can about concepts appropriate to more abstract sorts of paths, more abstract states of being, concepts which can be used to analyze seeming messes to determine what the true invariant relationships are. I know not what the end result might be, but I hope to at least inspire others to move on in this effort to expand the horizons of human reason, to borrow an image from Pope Benedict XVI.
In the end, a human being is far more than a star, far more than a spinning disc in a computer. My problem with those in literary and other human sciences is that they so strongly prefer inherited language and concepts which imply we’re triangles in Flatland rather than being — potentially — encapsulations of all of complex Creation described by such ideas as those of General Relativity and quantum mechanics, transfinite set theory and abstract algebra. The moral nature of a creature struck with wonder by the glories of God’s Creation, the mind of a creature capable of exploring those wonders, are at least as complex as what they can appreciate, as least as complex as what they can understand — however incomplete that understanding might be.
To complete the title of this entry:
If we have to use mathematical analogies in describing our moral and spiritual and intellectual journeys, shouldn’t we using the best available mathematics rather than ancient stuff?
To be sure, that ancient stuff is still true, but it’s so small a part of the truths of modern empirical knowledge.