A humble science

Mathematics is the lowest and humblest of all the sciences. It makes slow but steady progress, and it says little to nothing about the questions dearest to the hearts of human beings, but what it says is absolutely certain. What gives it such certainty? It is content to study objects which are wholly abstract, so that the relations between them are absolute, eternal, and necessary. The word abstract implies that they are drawn away from reality. In this way they are lifeless. Rather than exploring strange new worlds with their own vibrant existence, the mathematician is content to study lifeless forms which are absolutely transparent to the mind. Let the brave adventurers go off to study living creatures, the cosmos, and that most mysterious object of all, human pyschology. The mathematician will humbly work at understanding that which is already closer to home than anything can be--that is, close to the mind.

It would be a fatal mistake, then, to view mathematics as a lofty venture, towering over all the other sciences, for that is the opposite of the truth. Mathematics, like anyone who wishes to be great in God's kingdom, must be the servant of all. We happily live in a world which follows certain patterns, often not at all obvious, and the objects we encounter, though they have in some sense a life of their own, can be seen to follow abstract rules which can be studied at the level of theory. In this way the applications of mathematics are abundant, starting with the simplest of all objects (physics) and working our way up even to the most complex and spontaneous (biology, economics).

But it is a slippery slope from application to assimilation. The problem with much modern thought is the way it treats all objects as abstract, lifeless forms. What mathematics so useful and reliable is that it studies objects which have no independent existence and no context. To study living things--and particularly the human mind--in such a way would be (and often is) disastrous. Psychologists have noticed, for example, that searching for universal principles governing human thought by observing only Western, educated, industrialized, rich, democratic people is a flawed idea. Yet in observing that our methods do not lead to what we are searching for, rarely do we ask whether the search itself is misguided.

Why does modern thought push relentlessly toward that which is universal? I suspect the reason is as much moral as scientific. On the one hand, science seeks that which is universal because it gives us a deeper understanding of life as a whole, and that allows us to do the greatest amount of good. On the other hand, we would also find it unfair if our particular context really mattered. The universe should be, above all, fair, even if that implies it is meaningless. History must be random, because otherwise that would imply something special about the way things happen to be. We have concluded, after thoroughly deconstructing the moral pretentions of past generations, that there can be nothing special about our heritage, culture, or anything else passed down to us.

As an aside, I highly suspect this attitude explains why physicists have come up with the idea of a multiverse. If there really is one universe, with exactly one history, that means a practically infinite number of possibilities are shut off forever from all reality. That would mean all of reality is dependent on a particular context--it is no longer held captive by abstract concepts. Such a conclusion is intolerable in our intellectual climate.

The modern reaction against the Judeo-Christian tradition can be explained in these terms. If there is a God, its existence should be explicable in rational, abstract terms that do not depend on context--that is, mathematically. There is a long tradition of such proofs in Western tradition. But that is not what we find in the Bible. What we find there is a God who, though he is supposed to be the creator of all things, has attached himself to a particular people in the Middle East. "I Am Who I Am," God says, affirming his utterly transcendent identity, and then adds soon after, "the God of Abraham, Isaac, and Jacob." How can all of reality find its source in a God so particular? How could one petty group of people out in the middle of nowhere happened to have stumbled onto the source of life and hope for all humanity, and indeed all the universe?

As much as it offends our sensibilities, we ought to be able to understand this. Life is a serious of decisions and commitments, each of which cuts off others which were at one time possible. Once you say a word, it will be forever true that you said it. Once you are married, it will be forever true that you decided to marry. Once you go to your grave, whatever you have done with your life is all that you have done. There is no going back. Indeed, we might perhaps better understand this than our ancestors, since because of the Internet, nearly everything we say in public will be forever recorded somewhere in this vast ocean of data.

Is it really so impossible to believe that God himself would make such commitments, and that those commitments would be the basis of all reality? In fact I myself find it very hard. If at one time in human development it was natural to anthropomorphize God, today it seems difficult to think of God as anything other than an abstract concept.

Theology isn't the only thing at stake. It is not just the living God whom we try to kill with our abstract thinking. It is anything living. We moderns are increasingly detached from our own history, living in the dream that we can transcend history, which was random and arbitrary up to exactly our generation, and then build the future on abstract principles from here on. Naturally, we refuse to believe that this dream came from anywhere other than our own reason.

To be sure, looking at the abstract principles behind living realities is a good thing. It helps us to simplify problems and find solutions agreeable to everyone. It can even help us know better what we observe, so that we can appreciate it all the more. (I find this especially true of music, and I suspect it is true of art. For me, music theory makes great works come to life even more than they already do.)

The problem comes when we confuse abstract principles with true or ultimate reality. That is the path to self-destructive rationalism--it empties the world of all meaning, it jettisons history as a source of knowledge, and it risks degrading civilization itself, which is built on living traditions. No, reality is not a set of equations. It is a living, spontaneous, external universe which imposes its particularity on us. I say this not to denigrate my own field, but merely to put it in its rightful place as a loving servant of the real.