Reading the arguments of a learned academic—it could as well have been of an equally learned disputant for the opposition—confidently setting forth proof, which he apparently considered complete and faultless, of the Bible’s restrictions on gay inclusion and affirmation, I am whisked backwards in time 70+ years to a second floor classroom in the northwest corner of Red Oak High School in rural southwest Iowa where Miss Gleneva Klopping used up much effort to teach Geometry to indifferent sophomores (something I learned the hard way later on trying to teach Geometry). One school year in her classroom, however, provided me with enough appreciation and gratitude that, even after so long a time, one grants to a teacher who has had major influence on their life. Miss Klopping passed along to me an appreciation and respect for mathematics as far more than mere calculation, and she inspired high regard for logic—the old-fashioned T form of proof: statements lined up on the left, reasons supporting those statements on the right. I have clear memory of an “Aha!” day when the process became crystal clear and have not forgotten the almost visceral feeling of delight when, after a difficult, many-step proof, I arrived at QED.
Learned professors and bright students, and pastors, too, know that feeling as they expertly negotiate the canon and carefully line up statements and reasons—the latter usually biblical quotations—that culminate in a beautiful QED. I know that comfortable security, for I have so much experience celebrating my arrival at QED in the pulpit or wherever such debates go on. So do many—likely a majority—of those who listen in classrooms and churches, finding welcome relief in such convincing proofs. How wonderfully satisfying it tends to be, having confidence one’s teaching or preaching or writing is producing such influential results!
But as much as I recall Miss Klopping’s delight at a well-honed proof, I recall her sober manner when my proof, so carefully perfected and satisfying, was incomplete, and her quiet, “But you have not adequately proved the proposition. See, here’s where you’re missing a step, and the reason you’ve chosen there does not fit.” My beaming certainties were challenged, my “Aha!” premature. Deflated, I returned to my proof, not at all positive about how to get to a faultless QED, which would come from much hard work, and/or some lucky insight, and/or Miss Klopping’s generous and enlightened assistance.
Paul Kalanithi, the noted brain surgeon and author—himself facing terminal cancer—points us toward another useful mathematical analogy. In a memorable section of his book, after he has learned of the suicide of a colleague and friend following a difficult surgery during which his patient had died, he writes
We had assumed an onerous yoke, that of mortal responsibility. Our patients lives and identities may be in our hands, yet death always wins. Even if you are perfect, the world isn’t. The secret is to know that the deck is stacked, that you will lose, that your hands or judgment will slip, and yet still struggle to win for your patients. You can’t ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving. (When Breath Becomes Air, pp. 114-115)
The asymptote: a line toward which a graphed equation tends but never reaches because the perfection at the hypothetical point where the curve would reach that line is undefined, infinity, and perhaps when we consider the theology with which we work and the canon upon which we depend, our reticence—our finitude—might compel us to be assured that we are on the curve but yet distant from infinite perfection where we imagine only the Holy Trinity to exist. Might we even be able to see that the writers and arrangers of the canon are on that curve approaching the infinite, some drawing very, very close—but are not all human words approximations of infinity?
In fact, an equation might provide two asymptotes or more. Consider a hyperbola: its curve approaches the undefined point in four ways, yet there is one equation, and when we examine the two asymptotes of a hyperbola we see that they intersect at, of all places, the origin (if the equation is in its basic form). Isn’t it interesting to contemplate that persons striving to move toward truth, seemingly far apart, are on the same curve, based on the same equation, moving toward asymptotes that converge in one grand point? And might it not behoove us to take our satisfying QEDs toward some site of joining with others striving toward the same ultimate so that our QEDs linked might help form our understanding of truth?
After all, it just might be true, as a couple of my friends of rather astute mathematical understanding, coupled with deep spirituality, suggested to me as we discussed this asymptotic conjecture, that in heaven we will be able to divide by 0—but not before.
4 thoughts on “Q.E.D.”
Athough I will never have your expertise in math you have made me recall my geometry teacher, Mr. Masters, a man of mysterious origins, possibly a detective in a former life, but an excellent teacher from whom I would have learned a lot had I not been so concerned with girlfriends and sports. He was a fundamentalist Christian and would look askance at my spiritual journey to this point–and my inability to arrive at biblical QED’s much anymore. But I think he would have liked your ability to apply geometry to the issues. Anyway, Jim, you’re a great writer and thinker, and I look forward to reading more.
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Thank God for teachers like Mr. Masters and Miss Klopping. I cared nothing for girls or sports in those days. Studying was my escape from milking cows and grubbing out the barn. I know not a thing about Miss Klopping’s spiritual activity. I appreciate your affirmation. I’ve enjoyed getting back to writing, which is time-consuming enough to make my writing a pleasant relief when it happens.
Your essay made me both smile with delight and think with at least some depth quite seriously. I have a few Q.E.D. stories from my Evangelical upbringing, but my favorite one comes from my earliest days among Quakers. Thank you.