Is math erotic?

As the universities die, real education may have a renaissance.

The most shining moment of my education as a physics major at U.C. Santa Barbara came in the final lecture of an upper-division course on electricity and magnetism. We had learned the facts early in the semester, and could do the problem sets. Then the instructor, Nobel laureate Bob Schrieffer, seemed to take us backwards. He spent a few lectures plumbing the depths of “the wave equation” that can be used to describe all phenomena with periodic motions or variations, from water waves to sound waves. It also describes the patterns that appear when you walk past two fences and their visual elements of light and darkness superimpose — called a “moireé pattern.” (My dad, a physics professor at Berkeley, liked to point these out to me as we walked past fenced tennis courts toward the swimming pool at the Claremont Hotel, where he would do beautiful dives off the high dive.)

The next several lectures seemed totally unrelated. They were about magnetism, with field patterns and lines of force and whatnot.

Professor Schrieffer hinted that some big reveal was coming, but I was loosing patience. I couldn’t see the coherence of these disparate things. In the final lecture, without announcing where we were headed or giving anything away, he worked the blackboard furiously. Chalk dust floated in the air, and found its way onto his clothes in random smears. About one minute before the end of this last class, he turned and grinned triumphantly. There on the blackboard was something that I “knew” and recognized from early in the course, as something to be accepted and memorized. But it now appeared as a revelation, something of incomparable beauty and wonder: Maxwell’s Equations. They show the fundamental unity of electrical and magnetic phenomena. We had arrived at them beginning from water waves. I was stunned.

Don’t ask me to explain any of this now. It made sense at the time.

The purely mental activity of doing mathematics can be a mode of access to something that transcends the human mind. That this should be the case would seem to indicate that there is a deep resonance between mind and cosmos. Almost as if … cosmos participates in mind?

Jacob Tawney writes that there are “some things from mathematics that you should experience.” What an odd and arresting way to open a book about math. It is not the sort of exhortation we are used to hearing from the STEM-winders-and-grinders who push math for the sake of economic competitiveness, critical thinking skills, or other ends extrinsic to math itself. For Tawney, there is something beautiful and important to be experienced. He comes to us not as an “educator” in the dreary, institutional sense of that word, but as an evangelist.

His book Another Sort of Mathematics arrives at a time when it has become necessary to rethink education altogether. David McGrogan at News From Uncibal writes about “the coming competence apocalypse.” The likely atrophy of our mental faculties from outsourcing mental tasks to AI will only accelerate the long-running collapse of competence that McGrogan details. Meanwhile, John Carter at Postcards from Barsoom likens the state of the university to that of the monasteries in late-medieval England, where, he writes, “religious vows were more theoretical than daily realities for many monks. Does anyone truly think that Harvard professors take Veritas at all seriously?”

Scholarly careerism, declining curricular standards, the replication crisis, a demented ideological monoculture, administrative bloat ... a steady accumulation of chronic cultural entropy has built up inside the organizational tissue of the academy, rendering universities less effective, less trustworthy, less affordable, and less useful than ever before in history.

The function universities have long played is less one of educating than of credentialing. Carter gives us good reason to think the credentialing function of universities is about to collapse, due to AI. But he finds new possibilities, or rather old possibilities, emerging from the wreckage: liberal education in the original sense, as a leisure activity (“scholar” is from schole, leisure) for its own sake; for the love of truth. Unburdened of its current gatekeeping role in the political economy of managerialism and bullshit jobs, and no longer serving as a legitimation operation for unpopular political projects (producing “the Science” that must be “followed”), the successor to the modern university will be something subterranean rather than publicity-seeking, disconnected from power and money, a place where people with the most searching minds gather to pursue truth for the love of it.

Read the rest at First Things. Then come back to Archedelia for the postscript below, which is too nerdy for a real publication.

POSTSCRIPT

I haven’t re-read the whole of Heidegger’s essay for this occasion, but what I took away from it when I read it twenty years ago cuts in a direction nearly opposite of the one I am taking here. He doesn’t land on the theological-tending idea that “cosmos participates in mind,” but rather on the idea that in trying to apprehend the world through mathematics (an activity of mind), we are engaged in “a projection of thingness which, as it were, skips over the things.” You have to introduce idealizations such as the frictionless surface, the point mass, the perfect vacuum, and the perfectly elastic collision to make the word intellectually tractable, to the point that you can do math on it. For Heidegger this is a falsification, an anthropocentric game. But I’m not sure what force this critique of mathematical physics can carry for him, ultimately. In Being and Time, he says the most original way things in the world “show up” for us, prior to theoretical posits and abstractions, is under the sign of use, or “readiness to hand” (Zuhandenheit). You come to know a hammer not by gazing at it (“theory” comes from the Greek theorein, to gaze at disinterestedly) but from using it. This applies not just to tools and artefacts, but to all things, via their affordances. And this pragmatism is not merely epistemic, but ontological. Yet somehow for Heidegger, this insistence on use as the ground of apprehension/being (an agent-centered ontology) escapes the imputation of subjectivism that he pins on mathematical physics.

Putting that aside, action implies some good to be achieved. For the Platonist, goods in this everyday sense are intelligible as good only via their participation in “the good.” This remains a bit obscure to me. A Platonist more confident than I might want to say that Heidegger re-introduces the good via action. So his rejection of math as a mode of access to the world, replacing it with readiness-to-hand, doesn’t actually do away with the idea of cosmos, understood as good and beautiful order. An order that is good would seem to imply a benevolent creator.