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Mini-Feature: The Mathematical Outlook
It can't measure it all
Is looking at reality mathematically an accurate representation of how things work?
Not in the sense most people understand it. Math both tells us about reality, and has a reality of its own.
What people mean by math in the deepest, most “pure” sense (2+2=4, or Euclidean geometry) arises from what humans abstract from nature. What’s wild is that we can uncover something so pristine from messy, material things and discover new truths in a whole new realm of thought that exists outside of physical reality. The status of what sort of existence this kind of math has is a mystery that great minds have pondered and even used to point to the existence of the soul and non-material things. But it’s also useful, and was likely arrived at based on practical efforts to cultivate nature and then applied again to such pursuits. Then there is all the dirty sort of “math”—say, statistics for the social sciences—which is based on utilizing and deploying these abstract truths and a very useful but imperfect measuring tool, easily used badly.
Math clearly gives us a deep insight into the truth about reality in the first sense described above. And in terms of application through calculus and all that has come after, we have used it as a tool to unlock much. This should be obvious. But to speak of knowing reality solely through math is absurd. It does not explain itself; it did not spring into our understanding full grown. Its own existence in our understanding comes to us by way of ourselves. In one sense we hold it within us and explore it as a truth that is beyond and outside us; in another sense we use it as a tool we made from what we found in nature. It can help us see reality and is itself a part of reality. But its very existence points to a greater whole.
-Matthew Peterson, founding editor of The American Mind
Math is pretty good for mechanics, although for this reason it breeds a desire to know ever more bizarre and alienating things. What comes after the Large Hadron Collider? Knowledge of how things work is inextricably implicated with how to break things. Knowledge that implies its own totality implies knowledge of how to destroy all.
That said, math is not what most think it is. Math is ultimately about the myriad kinds of relationships that provide fundamental embodied order. The implication here is not so much about how things work as how possibly, or why, they do. Math in this sense promises an encounter with God, although it is Man, not Number, that is made in the image of God.
Above all what math is not is a part which can supplant the whole, a shortcut away from the limitations imposed by responsibility. When it appears to people this way, or is actively (however explicitly) bent by them in that way, math is stripped of its instructive mystery and made an instrument of unteaching. Be careful!
-James Poulos, executive editor of The American Mind
Math is accurate for some things but not others. For instance, math or science can provide an account of the body. Its operations are every day more revealed. But math and science cannot, for example, provide an account for this thing we call "soul". Men of science cannot find the soul and so deny its existence, claiming instead that what we are talking about is instead a function of brain activity. Do you believe that?
Anyway, get right with Zeus before your cord is cut!
-David Bahr, managing editor of The American Mind
It has been suggested that Plato believed music was more than anything a pointer toward the mathematical truths which underlay it: if we experience certain tones in a certain order as artistically beautiful, it is because they are giving us a physical experience of the rational order between numbers. These, and not music itself, are the realest thing. We must seek an unmediated experience of them by looking beyond music to the purely cognitive truths it expresses. Andrew Barker, the great scholar of Greek music, suggests in his anthology of Greek musical texts that this is essentially the import of the Timaeus.
Yet it seems there is something cold about Number in its pure form, at least as abstracted by the Pythagoreans and then, via Plato, made into the hardest and most stable bedrock of being and epistemology. It works well as a theory of the cosmos; as an analysis of Bach, it lacks a certain glow. Yet I suspect that both Plato and Pythagoras, properly understood, were saying something true and really essential, in the original sense, about creation and the math which gives it order.
This has been a little bit lost by our own cultural prejudice for materialism which, no matter how the Neil deGrasse Tysons of the world try to decorate it in wonder and loveliness, always ends up by its very nature bleeding the world dry of color and life. To get the groove of things back, all you have to do is acknowledge that numbers are ideas—you can’t hold “two” in your hand. You can only hold things which instantiate two, like two oranges or two books. Once realize this profound truth—that something purely immaterial is the premise behind all our perceptions of the supposedly physical world and, yet more miraculously, that purely immaterial thing is not arbitrary but makes sense of the cosmos—and equations become more than dry bones. They are in fact living sinews of a breathing organism, that vast reality sprung from the mind in which we live and move and have our being.
-Spencer Klavan, associate editor of The American Mind