Manifolds

(Attention Conservation Notice: As previously confessed, this three-plus-part series is a grossly distended remake of a more reasonably proportioned essay from 2013.
Some people claim Peli Grietzer's to blame, but I know it's my own damn fault.)

3. Adaptive Manifold Learning

I sometimes feel as if I've never had a single relatable experience. Like, whenever I try to tell a story, it degenerates into a series of explanations and everyone gets this face like they're doing math.

- Sandra Newman on Twitter

With apologies aforethought

Being the product of a body embedded in history, my writing frequently passes through drizzles of autobiographical asides or illustrative anecdotes. But attempting to narrate "personal life" tout court calls on an internal voice I trust considerably less far than I can throw it. I'm not fond of memoir as a genre, I think "creative nonfiction" was just a way for academic-workshop fiction to become more formulaic, and I'm not so crazy about myself either.1

Moreover, my story-as-told-by is even drabber than existence-as-lived-by: my memory maintains a spare-the-rod-and-spoil-the-child bias, and my greatest pleasures have been literally unspeakable. Even after trimming to what's most germane to this topic, reserving other polyps of sad-sackery for use in other cans of dogfood, the prospect remains unappetizing.

The last vivid image I retain from my father's deathbed is his reflexive wince-and-glare as I tried to reassure him. I sometimes see that expression of pained disgust on my brother's face, and I sometimes feel it on my own. Much of this draft seems to beg for the editorial query "Well, boo fucking hoo."

Still, meat was promised, and if you're willing, I guess I am. Take a an oxygenated breath from Charles Kerns's posts now and then, though.

1959 – 1964

(After all, the word "infant" means, literally, "unable to speak," and as my efforts to describe them reveal, experiences of love and art are also intrinsically nonverbal.)

- Art and Intimacy: How the Arts Began by Ellen Dissanayake 1

This here particular scrap of meat was a mistake incurrable only before abortion became legal and prolongable only after doctors could prescribe effective antibiotics. (One of which permanently darkened my teeth, but hey, you win some you lose some.)

My brother might disagree, but I believe our adoptive parents genuinely (if standoffishly) cared for us. Unlike some of my sissy peers, I wasn't shipped to military school or routinely beaten at home: our mother was too clueless for homophobic panic, and our father was basically a tolerant sort. Aided by progressive taxation, they kept us fed, clothed, sheltered, doctored, and schooled; they bought Christmas and birthday presents after consulting our obsessively curated wishlists.

But despite the lengthy and thoroughly conscious labor required to adopt, neither had much feel for parenthood.

Mom came from a large rural family low on sentimentality and high on feuds. In a movie she would have played the vain sister, unwilling to do chores and coming to an instructively unpleasant end after some terrible romantic decisions. In life, after a failed marriage or two, she escaped to the Navy.

Dad's father died or disappeared early on; his "mother" (or possibly his aunt, it's all very Southern Gothic) was a vicious tobaccy-spitting bible-thumping racist; his stepfather was a physically abusive drunk. Dad ran away several times, dropped out of high school, joined a street gang, and finally lied about his age to enlist.

The Navy was good for both of them, but its training didn't include childcare. They were able to hold things together so long as I remained in the company of books and tolerant adults. Once I was forced to associate with other children, my poor brother first and foremost, they (and we) were quickly swept out of their depth.

Kindergarten was so disastrous as to call for public intervention. Nowadays such a disruptive five-year-old might be arrested or drugged or both. Instead, Mrs. Nickerson, the first of many female saviors, diagnosed my severe myopia and suggested an IQ test.

Sit Down Behind things or in front of them, always a goddamn adamant number stands up and shouts, I’m here, I’m here! — Sit down. - Hello: A Journal, February 29–May 3, 1976 by Robert Creeley

The Navy trained my father as an electronics technician and deployed him accordingly: Adak on his own; then, with us, Karamürsel, Bremerhaven, sunny Guantanamo Bay, and, on the edge of the Great Dismal Swamp, Northwest Radio Station. A few years before my birth, Dad was on one of the many teams tracking Sputnik's progress and wondering what the hell the Russians were up to this time.

By scaring the bejezus out of everyone, Sputnik successfully initiated what may have been the least anti-intellectual period in American history. Well done, Commies! In 1964, New York City public schools had just decided to drop IQ testing, but interest continued to run high elsewhere. (And in some sad circles of Hell apparently still does.)

I've never felt like reexamining those early tests, but I take for granted that their makers wouldn't get far comparing five-year-olds on their retention of trivia from AP History or Chemistry. Instead, the "general" aptitude being measured likely coincided with my little pony's forever one-and-only trick.

Besides exaggerating the importance of my signature cognitive strength, such a test would tend to miss my signature cognitive weakness: a near pathological aversion to habituation. Before a single onion is chopped, I'll have veered from sous-chef to Norman Bates; language drills induce increasingly bizarre variations in grammar and vocabulary; any daily exercise regimen will be interrupted by prostration of one sort or another....

To compensate I interject consciousness; what would normally become near-autonomous actions must be continuously re-invented if they're to be kept in place. Hooky phrases fill my noggin with lint and clothe my discourse in flannel, but more "arbitrary" symbols — companions' names, historical dates, distances and measurements, the Java runtime library — simply vanish because I have no way to reconstruct them from scratch.

By Taylorist notions of efficiency, I'm not so much an Optimizing Function as sand in the gears. And so, once again, the Navy got ripped off.

But back in 1964 neither it nor I had an inkling of all this. For myself, the testing and follow-up discussions and tasks simply kept me happier than I'd been for several years. Reasonable arguments! Interesting conversations! With a lady! What sport!

The one frustration in these prized outings, the one game in which I felt the familiar shadow of a trouncing, was mathematics. The abstraction of quantity, OK; addition, multiplication, exponents, sure. But I sat slack-jawed before the Pythagorean theorem, unable to learn the trick no matter how often I requested a replay. Fractions were a mean-spirited practical joke — and the irrationals?

Between intuitive verbal logic and unfathomable geometry was a gulf I couldn't imagine crossing.

[Once we give up] the myth according to which certainty relies only on sequence matching and formal induction, then any work based on the ordered structure of numbers, on the geometric judgment lying at the core of mathematics, can go smoothly. Incompleteness shows that this judgment is elementary (it cannot be further reduced), but it is still a (very) complex judgment. [...] A mathematician understands and communicates to the student what the continuum is by gesture, since behind the gesture both share this ancient act of life experience: the eye saccade, the movement of the hand. [...] What is lacking in formal mechanisms, or in other words their provable incompleteness, is a consequence of this hand gesture which structures space and measures time by using well order. This gesture originates and fixes in action the linguistic construction of mathematics, indeed deduction, and completes its signification.

- Mathematics & the Natural Sciences by Giuseppe Longo & Daniel Bailey

Or, as revealed to a brat more precocious than myself:

Eternity was not an infinitely great quantity that was worn down, but eternity was succession.

Then Joana suddenly understood that the utmost beauty was to be found in succession, that movement explained form — it was so high and pure to cry: movement explains form! — and pain was also to be found in succession because the body was slower than the movement of uninterrupted continuity.

Near to the Wild Heart by Clarice Lispector,
translated by Alison Entrekin

1964 – 1969

And this speech the goddesses first of all spoke to me
The Olympian Muses, daughters of Aegis-bearing Zeus:
"Shepherds of the field, base, shameful things, mere bellies:
We know how to speak many falsehoods which are like verities,
And we know, whenever we wish, how to utter truths."

- Theogony by Hesiod, as translated by Shaul Tor
in Mortal and Divine in Early Greek Epistemology

A book is a projection of higher-dimensional structures onto a three-dimensional sheaf of two-dimensional planes. A handily compact thing, but decompressing that projection requires some sense of those higher dimensions.

I spontaneously began to read at age three. Unlike many hyperlexics, I also seem to have been an early talker; like most, however, I was comfortable with a certain level of incomprehension, and that level increased after I learned that the very best people were expected to speed-read.1

Like Mowgli was raised by wolves, like Estella was raised by Miss Havisham, I was raised by books. Being a Dickens character, Miss Havisham stays reliably on model; say what you want about wolfishness, at least it's an ethos. The intention of books en masse is harder to read. Sometimes I'd be convicted for not living up to the instructions laid out by Dennis the Menace 2 or Boy's Life or Robert Heinlein; other times for failing the tests of Hans Christian Andersen or Madeline L'Engle or Lloyd Alexander. And if I was so smart, why wasn't I solving crimes? Or the Four-Color Theorem? Or finding some way to not get beaten up all the time?

Why, the Bible alone provided an inexhaustible spring of fresh accusations. Should all else succeed, I could always be convicted of pride, that most pernicious of weeds.

If Doctor Aquinas had treated me to his Explanation of Everything, I would have made fine priesthood fodder. If I'd been raised Calvinist, I could at least be certain of my fate. As was — well, consider Nietzsche's normative:

The spirit's power to appropriate the foreign stands revealed in its inclination to assimilate the new to the old, to simplify the manifold, and to overlook or repulse whatever is totally contradictory — just as it involuntarily emphasizes certain feature and lines in what is foreign, in every piece of the "external world," retouching and falsifying the whole to suit itself. Its intent in all this is to incorporate new "experiences," to file new things in old files — growth, in a word — or, more precisely, the feeling of growth, the feeling of increased power.

An apparently opposite drive serves this same will: a sudden erupting decision in favor of ignorance, of deliberate exclusion, a shutting of one's windows....

[It is explicitly no coincidence that placed immediately after this are several sections devoted to misogyny.]

- Beyond Good and Evil by Friedrich Nietzsche,
translated Walter Kaufmann

Disgraceful though that sounds, what would the alternative look like? Whatever you choose to call it, "the feeling of growth, the feeling of increased power" would not be prominent features. Presuming the coherence of my authorities, "studying them as if cramming for a test on how to be the most lovable child in the world," I diagnosed incoherence in myself, and prescribed the traditional course of repentance and purgation, followed by inevitable backslide.

Although this art of logic has manifold utility, still, if one is learned only in it, and ignorant of aught else, he is actually retarded, rather than helped to progress in philosophy, since he becomes a victim of verbosity and overconfidence. By itself, logic is practically useless. Only when it is associated with other studies does logic shine, and then by a virtue that is communicated by them. Considerable indulgence should, however, be shown to the young, in whom verbosity should be temporarily tolerated, so that they may thus acquire an abundance of eloquence.

- "Chapter 28. How logic should be employed"
from The Metalogicon of John of Salisbury

When caged with my brother, I bullied him without mercy and he just as mercilessly tormented me. When alone with my mother, she'd ask advice on clothes, finances, and reading,1 which was pleasant if sometimes a bit nervous-making. My father preferred to note my frauds and outrage my primness, although once, after one of Mom's elaborately sadistic jokes pitched my anxiety to the point of boycotting my own seventh-birthday party, he entered our bedroom, removed his belt, and announced, "I know you're smarter than me, but" (a hot roar flooded my ears) — that's not true! —
— how had I broken so much? —

In classrooms, I strove to reach my imagined potential until halted by overreach and collapse, a cycle which helped convince my parents to keep me on the standard academic track rather than pushing graduation forward a few years. (Given how weirdly underaged I looked, this may have been the healthiest course available at the time. When I consider high school, though, I'm tempted to second-guess.) And I remained "bad at math," which is to say better than average but not ridiculously better than average. Not a good look for a Young Scientist, and at odds with my enthusiasm for puzzle collections, One Two Three... Infinity, and Martin Gardner's columns.

From kindergarten through elementary school, fear and loathing occupied waking hours at school, home, and "playing outside" (i.e., evading my peers), and my sleep was broken by guilt-laden nightmares (I fail to save my family from fire, flood, famine, or freezing; I fail to save my family from a volcano; I fail to save my family from The Bomb). Yet life in the lap o' luxury was not complete misery.

In television-free Bremerhaven especially, the dark brown cobblestones and dark green foliage soothed eyes and mind, as did my father's copies of Playboy (watercolor cartoons! ladies with fascinatingly varied interests!). And there were Saturday movie serials, my favorites being the circus melodramas (ladies in tights! horses!), and matinee features, my favorites being the colonialist/wildlife adventures (elephants! but not enough ladies 2). One morning I opened our door and faced a precisely vertical wall of snow stretching far above my head; I was equally awestruck by the orchestra and lit scrims on my class's field trip to the opera house, and by the forest where my Cub Scout troop camped until I was demobbed by mumps, painfully reminding me (and my weary parents) of the strep throat which had curtailed the family's attempt to visit Istanbul.

More reliably, in Germany, in Cuba, and then in Virginia, there was the comfort of books — books were fine; I was a mess but books were fine — from the library, of course, and from our monthly trip to the dump (where with luck I might garner a textbook reeking of garbage-smoke), and within strict limits the twice-yearly-authorized Scholastic sale (soon replaced by careful gaming of the Science Fiction Book Club's loss-leaders, followed in my teens by gaming of the Book of the Month Club and the Quality Paperback Book Club).

Just as reliably but less explicably, there was, serially, one adult friend. By some mechanism which remains mysterious to me, the universe contrived that on each military base there reside one bookish, pleasantly disputatious Navy Wife who would be willing to host a peculiar little boy and converse for hours. Did my parents post a classified ad? Did there just happen to be that many bookish Navy Wives starved for company?

Aside from incidental bits of knowledge, these dates taught me:

1. Social interactions could provide something better than terror, hatred, or intense boredom.
2. Much as dodgeball justified terror and card games justified boredom, books could serve to justify these better interactions.
3. Intelligent, interesting, and trustworthy people were most likely to be female. (I presumed, based on the evidence of author names, that some worthwhile men — or, to be slightly less snotty, men who seemed worth emulating — must exist somewhere, but it wasn't until age seventeen and a brief audience with pixilated Wilson "Bob" Tucker that I encountered one.)

The most ardent and formative of these friendships was the first, with Mrs.— I remember her eyes and her smile (and her relentlessly friendly Siamese cat) but her name I've lost... Mrs. Kubelik? Or am I thinking of Shirley MacLaine? Mrs. K (to give her for the nonce her new misnomer) collected and lent paperbacks of science fiction and pop-science (on which ground we met), and also parapsychology, reincarnation, astrology, and UFOlogy, on which ground we debated.

I took Con, under the unwieldy banner of rationalism, scientific positivism, religious orthodoxy (insofar as the military's deistic Protestantism could sustain such a concept), law-and-order, and patriotic tolerance: Truth, Justice, & the American Way. Although I hadn't checked those terms for completeness and consistency, they carried a full load of conviction, in both senses of the word.

Elevenses : 1970 – 1973

JOHN FREEMAN: Can I take you back to your own childhood? Do you remember the occasion when you first felt consciousness of your own individual self?

CARL JUNG: That was in my eleventh year. There I suddenly, on my way to school, I stepped out of a mist. It was just as if I had been in a mist, walking in a mist, and then I stepped out of it and then I knew, I am. I am what I am. And then I thought, But what have I been before? And then I found that I had been in a mist, not knowing to differentiate myself from things. I was just one thing among many things.

- Face to Face, BBC, 1959

After seven years overseas, in 1970 we left Gitmo and landed stateside. Virginian high spring was so verdant my eyes watered.

One day that summer, doing nothing much, probably while sitting on the porch of our base housing, I felt something happen to me, in me, between me and not-me. My surroundings suddenly (it was quite sudden) snapped into focus and into depth, and I awoke, as if all I'd known until then had been a twilit coma and I'd become fully conscious. There was no other immediate revelation: only the pure sensation itself. And then I started to move and perceive.

Very slowly over the next few years I came to understand that my spirit's nosebleeds and broken toes and assflops weren't exclusively the product of clumsiness — that I'd sometimes been walking into plate-glass windows or funhouse mirrors or at any rate prison walls not strictly of my own making.1

For example, it seemed as if I might not be the only sinner so tainted as to be shunned by the Voice of God. To an alarming extent, what most adults and children professed was faith in hearsay rather than replicated experiment. Even more alarmingly, few of them felt shunned. (Ten years later, the personal touch of Jayzus would become epidemic among my people. We were better off with hearsay.)

Somewhere in there I also began to notice that the demand for truth was asymmetrical: it could be safely made by those in power but not safely reciprocated by the powerless. Which seemed, against my grain, to lend the powerless (my brother, for example; or myself, as I ventured into less approved adolescent waters) some strictly limited moral justification to prevaricate.2

Somewhere in there I also became obsessed with mid-century American depressive celebrity-wits — Oscar Levant, Dorothy Parker, James Thurber...— my introduction to our native species of Romantic Irony.3 "Teacher's Pet," Thurber's clumsy thrash against a riptide of resentful self-loathing, pushed Shock of Recognition into Sublimity of Terror. It didn't cure anything, but it surely counted as a treatment.

Somewhere in there I also learned why reading Playboy interfered with urination.

I entered sixth grade that fall. Because the Chesapeake public school was much larger than overseas base schools, or maybe because my cohort was older, for the first time I made some (three, to be precise) friends my own age. Bullying maintained its accustomed level but at least there was someone with whom to play chess and commiserate.

Also that fall, the local library received Asimov's Guide to Shakespeare, placing me in an awkward position. An Asimov completist, I'd easily downed the big-gulps of his Guide to the Bible as a summit meeting between authoritative voices. But in conversations with teachers, librarians, and Navy Wives, I'd already staked a claim that Asimov was indubitably better than Shakespeare insofar as Shakespeare had small physics and less biochemistry. Asimov's introductory tribute clarified nothing. The Little Leather Library's Tempest and Midsummer Night's Dream had always baffled me. Where was the appeal?

I used King John as the test case (why King John? beats me; I don't think my presumed bastardy played a part), refusing to move past it until I cracked the secret. And after increasingly brake-pumped re-readings, I more or less did. It turns out (stop me if you've heard this already) that patterns of sound and mouth-feel are more than disposable cartons of discovery; as portals they could be revisited, and replenish with fresh discovery.4 Moreover, this seemingly crazy, previously unsuspected reading technique could open other closed volumes, particularly volumes of poetry, and support thrift by extending their lifespans.

Also that fall, Miz Johnson made me good at math. She was the sort of teacher who transforms lives (and I do not fucking want to hear a whisper about Jean Brodie): charismatic, clear-sighted, articulate, and inexhaustible, at least by us. After a few observant weeks, Miz Johnson shifted me and one of my friends to a far back corner of the room, gave us new textbooks which included some basic proofs, and somehow contrived to guide us through high school algebra while simultaneously managing the rest of the sixth-grade class.

In the vocabulary favored by this current narrative, she demonstrated how one might approach mathematics as the exchange and extension of abstract verbal models of social reality. I was enthralled; I was absorbed. I was triumphant.

For example, if one be bird-witted, that is, easily distracted and unable to keep his attention as long as he should, Mathematics provides a remedy; for in them if the mind be caught away but a moment, the demonstration has to be commenced anew.

- The Advancement of Learning by Francis Bacon

Later that year, Miz Johnson improvised an equally powerful lesson in American political science when some kid's remark triggered an account of her path to the front of our classroom: the bribes, threats, and extortionate debts her grandparents and parents faced to retain a bit of land and a restaurant business; the extended family's decades of extended labor, waking when farmers did and reaching bed when bars closed; how their place became favored by the white elite at the cost of shucking and jiving and, when all else failed, a nails-spitting grovel only partly repaid by petty revenge served hot from the kitchen — all to grant her and her siblings a chance to work their asses off with at least a shred of dignity.5

Seventh grade brought a follow-up lesson when one of my three friends announced he could no longer associate with us: accused of acting white, he needed to spend time with his own people. Another one, my fellow algebra student, the smallest and most eccentric of us — when I first watched Rebel Without a Cause, Sal Mineo brought him to mind — vanished between semesters; military school, I heard.

By eighth grade I'd negotiated a truce with base-housing bullies through neighborhood football: although I couldn't pass or receive, and never learned the rules, I made a fearlessly tenacious tackle. Harassment stayed the norm among my academic cohort but paused for a daily bus ride to high school, where I took trig and sub-pre-introductory French. In English class I had my first lesson in writing down to an audience; in social studies, I discussed McCarthyism with my equally-Republican teacher, eventually retaining respect for him but not for the Republicans.

Then my father retired from the Navy and decided to move us to my mother's home town, Braymer, Missouri, population 880, SAAH-LUTE!

Intermission (1970 – 1982, 2019 – 2020)

While the Nightmare of Personal History changes reels, let's all go to the lobby for a chat.

What I'd like to emphasize in my otherwise unremarkable story is its from-the-start separation of mathematics from ontology.

Clearly I was a needy little boy, craving emotional shelter and unable to distinguish it from intellectual certainty, maybe because both were too elusive to enable a contrast. Received notions of "math people" as arrogant icicles would then suggest I took solace from mathematics' irrefragability.

Instead, the prepubescent period in which I was most rigidly rationalistic, positivist, orthodox, and puritanical was the same period in which I was "bad at math," and the period in which I studied math most intently was one of increasing aestheticism, relativism, and depravity. They grew together like, say, the rose and the brier. And that mathematical parallel-track (a little action on the side) terminated as my empirical-pluralism reached full ripeness.

In Ian Hacking's Why Is There Philosophy of Mathematics at All?, his answers include a pair of mathematical pleasures peculiar enough to invite analysis:

1. The pleasurable feeling of certainty when holding an entire mathematical proof in one's mind, preferably one with an unexpected twist or two.
2. The pleasurable feeling of surprise when some uncompromisingly abstract aspect of mathematics is discovered to apply usefully outside its original context.

1. Proofs

Logical demonstrations were indeed the means by which Miz Johnson transported me to a comfortable home in math, but that comfort was drawn from familiarity rather than novelty. She'd shown how mathematical study could be made to merge with my studies of fictional narrative, poetic form, and discursive rhetoric, all of which required similar reconstitutions of achronological higher-dimensional cognitive structures from chronologically sequenced discourse, and all of which rewarded me with a similarly stabilizing pleasure.

There's an obvious difference, of course. Outside mathematics, even something as seemingly straightforward as a location or a date could become contentious, and god help anyone who claims to establish causality. Subjective certainty is felt across all disciplines, but mathematicians could be unusually confident that anyone willing and able to follow their demonstration would feel the same subjective certainty.

Math doesn't just construct knowledge; it constructs objective knowledge: rational coherence creates objectivity; objectivity leads to new discoveries/inventions, which then provide properly air-dried fodder for rational coherence. And yes, there's something attractively restful about objectivity.

Equally, there's something agitating about construction — it's not all lunch breaks and wolf-whistling, you know. And if anything, what drew me to this newly-understood conception of mathematics was its brush-clearing exposure of the difference between objective knowledge and a conservative ontology of static being:1

This approach will obviously replace, in mathematics and in natural science, the notion of “ontological truth” by knowledge construction, the ultimate result of the human cognitive activity, as well as, thanks to this activity on reality, the notion of construction of objectivity.

- Mathematics & the Natural Sciences by Giuseppe Longo & Daniel Bailey

We call a proposition "true," not because it agrees with a fixed reality beyond all thought and all possibility of thought, but because it is verified in the process of thought and leads to new and fruitful consequences.

- Substance and Function by Ernst Cassirer

Now, it is not because a concept can be defined in set-theory that the concept makes sense. This is most flagrantly demonstrated for the concept of truth, defined by Tarski by means of a pleonasm, typically:

∀x A[x] is true when A[n] is true for any integer n

The truth of A is nothing but A, which is what we called essentialism. One must legitimately doubt a notion that turns out to be so opaque. In place of the academistic interpretation « want of truth », I propose to substitute the more stimulating « truth means nothing » (I didn’t say « is not definable in arithmetic », I really meant « no meaning »). Which does not imply that I was wrong in saying that G is true, since we established it. I only say that, in the same way there is no general notion of beauty, good, etc., there is no « general » definition of truth. What we logicians manipulate under the name « true » is only an empty shell.

- The Blind Spot: Lectures on Logic by Jean-Yves Girard

At the same time, mathematics exposed the gulf between objectivity and experience. Although mathematics made some of its most startling advances by way of working around obstacles to material application, those were momentous interventions rather than day to day practice, and in the most obsessive-compulsive notion of "proofs," they have no place at all. The price of peace was a certain distancing from life.

And since life (rather than logic) was the source of my perplexity, this obvious difference was not entirely to math's advantage. For me, then, the chief pleasure of proof was not that aspect specific to mathematics.

Nor is it always present in mathematics, any more than the intuition of aesthetic structure depends upon having a verbal projection of that structure:

Jena, Feb. 8 1793

Your idea of the dominating power is based on the idea of the whole, on the concept of the unity of the connected parts, the manifold, but how can we recognize this unity? Apparently only through a concept; one must have a concept of the whole under which the manifold is united. [...] Now, Kant is certainly right in saying that the beautiful pleases without a concept. I can have found an object beautiful for quite a while before I am able to articulate the unity of its manifold, and to determine what power dominates it.

- Friedrich Schiller, ‘Kallias or Concerning Beauty: Letters to Gottfried Körner’
translated by Stefan Bird-Pollan,
from Classic and Romantic German Aesthetics, ed. J. M. Bernstein

Just as aesthetic objects and operations must be intuited before they can be analyzed, mathematical objects and operations must be intuited before being established by proof. And, as tediously demonstrated by pre-Miz-Johnson classes, mathematical objects can be (and mostly are) studied proof-free as off-the-shelf tools. Disputatious Greeks found a need to hybridize those tools with logical arguments, but not everyone does. "Calculus for Engineers" will always draw more students than "Category Theory for Philosophers." To quote Hacking citing someone else who isn't Chinese:

China, in ancient times, developed brilliant mathematics, but it chiefly worked on a system of approximations. Proof seems seldom to have reared its head in China, and was seldom esteemed in its own right. Geoffrey Lloyd, who has devoted his mature years to comparative Chinese/European intellectual history, notes that the hierarchical structure of a powerful education system, with the Emperor's civil service as the ultimate court of appeal, had no need of proofs to settle anything.

According to histories of Western mathematics, no intuited hypothesis, theorem, or equation is fully accepted by the discipline until it's been convincingly (objectively) proven. What strikes the reader of such histories, however, is how long the wait for that proof might be. Even after one is provided, skeptics may demand (or the ambitious may publish) clearer, more convincing proofs. And yet during that time the mathematical intuition remains part of "mathematics" and no other discipline, and may be put to use.

And professional surveys show that the proofs prized most by mathematicians were those whose techniques and transitional byproducts became productive in their own right. The best proofs aren't built for contemplative coziness but for leaving.

Which brings us to the second of Hacking's pair, the pleasure of transference — the unexpected applicability of an existing mathematical object in a new context — which he splits into its own sub-pair:

2.1. What Eugene Wigner called "The Unreasonable Effectiveness of Mathematics in the Natural Sciences."

2.2. What David Corfield called "the unreasonable effectiveness of mathematics in mathematics."

2.1. Transfers out of math

"All else being equal," two full-grown hogs are equivalent to two swimming pools. But the equality of these elses depends on hunger, heat, financial need, and so on. If we want a working pretext of arithmetical certainty, we'll need some third entity that can set a ratio with some wiggle room. And so as social groups grow (possibly by force), the lure of easily transported objectivity — arithmetical certainty — urges economies towards money or something like, but even Adam Smith knew that money economies needed constant intervention to maintain the objective fiction. (Ayn Rand was more a "Pi equals 3.0" sort of capitalist.)

Although the neighborhoods-of-Euclidean-space found in Riemann's continuous-manifold might be thought of as a formalization of "wiggle room," formality forbids much wiggling. Almost by definition mathematics consists of only and all "things being (objectively) equal" and anything outside mathematics is almost by definition not precisely equal. Mathematical objects are unambiguous non-conflicting abstractions drawn from the world, mathematics is the unambiguous non-conflicting rhetoric thereof, and so a match (with wiggle room) between mathematics and selected aspects of reality seems no more startling than effective real-life applications of fables, novels, aphorisms, plays, or jokes. The unreasonable correspondence of mathematics to the world is simply the exsanguinated and beetle-cleaned progeny of the unreasonable correspondence of words to the world.

2.2. Transfers within math

Like (in their incalculably better informed ways) Hacking, Winfried Scharlau, Gian-Carlo Rota, Giuseppe Longo, Fernando Zalamea, and Wittgenstein,2 in my doltish, shallow, smash-grab-and-run way I was impressed less by the ontological immortality of mathematical truth, or its commercial applicability, than by its cross-breeding variety-unity. Its entities merge and multiply like skeletonic goats and monkeys, and Pascal was right to condemn mathematics as another sin of the flesh. "Saint Francis didn't run numbers."

I should like to say: mathematics is a MOTLEY of techniques of proof.— And upon this is based its manifold applicability and its importance.

- Remarks on the Foundations of Mathematics by Ludwig Wittgenstein,
third revised edition

I would like to advance the thesis that the decisive condition for the origin of pure mathematics was the fact that for the first time in the history of mathematics a large number of connections were discovered between seemingly different problem areas and results. Until well into the 18th century, mathematics was comprised of many isolated areas of study, into which some order was slowly introduced with the help of partially developed methods — for example differential equations and the calculus of variations in analysis. The range of application of these methods was easily grasped and apparently somewhat limited. Then connections between the most distant branches of mathematics suddenly appeared. It is obvious that this must have led to a completely new intensity of development and that this development rose to a new level. To that extent I maintain rather the opposite of Struik: Pure mathematics originated in the transcending of special viewpoints.

- "The Origins of Pure Mathematics" by Winfried Scharlau

The back-and-forth between diverse perspectives (conceptual, hypothetical, deductive, experimental), diverse environments (arithmetical, algebraic, topological, geometrical, etc.) and diverse levels of stratification within each environment is one of the fundamental dynamic features of modern mathematics. [...] It was necessary, for example, for obstructions in infinitary systems of linear equations and in classes of integral equations to be confronted in order for the notion of a Hilbert space, one of modern mathematics' most incisive mixtures, to emerge, just as certain singularities in complex variable functions had to be confronted for another paradigmatically modern construction, the notion of Riemann surfaces, to emerge. Similarly, Galois theory — one of the great buttresses of mathematics' development, with remarkable conceptual transfers into the most varied mathematical domains — would be unthinkable had important obstructions between webs of notions associated with algebraic solutions and geometrical invariants not been taken into account. In order to tackle problematics of great complexity — stretched over highly ramified dialectical warps — modern mathematics finds itself obliged to combine multiple mathematical perspectives, instruments and bodies of knowledge.

- Synthetic Philosophy of Contemporary Mathematics by Fernando Zalamea

The mystery as well as the glory of mathematics lie not so much in the fact that abstract theories do turn out to be useful in solving problems, but in that wonder of wonders, in the fact that a theory meant for one type of problem is often the only way of solving problems of entirely different kinds, problems for which the theory was not intended. These coincidences occur so frequently that they must belong to the essence of mathematics.

- "The Concept of Mathematical Truth" by Gian-Carlo Rota

I'd say the histories of literature, of art, of music, of history, and so on exhibit at least as many motivational obstructions and liberating intradisciplinary transfers as the history of mathematics. Still, for me as well (if not as intelligently) as Rota, the pleasure of unexpected transference feels purest (and perhaps most essential) in mathematics, if only because mathematics is made of little else and its transfers tend to be met by relatively short-lived controversy. (Mathematicians save their most lasting rage for squabbles over personal credit. Subjectivity needs to assert itself somehow, I guess.)

But these magical entities gain their ubiquity, flexibility, and stability at the cost of — pretty much everything unmagical? Although the claim that mathematics consists of nothing but tautology is as silly as claiming that a dictionary replaces a library, it's transparently more self-sufficient than other disciplines. For all the impressive fecundity of mathematics' tangle of sturdy dead-oak, a glance over the hedge will show how bare the lawn of excluded middle really is.

---

The lights are dimming and so am I. Back to our seats; I hear his full-frontal scene's coming up.

Contraction : 1973 – 1976

Thus further constraints need to be applied to attempt to separate useful information (to be retained) from noise (to be discarded). This will naturally translate to non-zero reconstruction error.

- "Stacked Denoising Autoencoders" by Pascal Vincent, Hugo Larochelle, Isabelle Lajoie, Yoshua Bengio, Pierre-Antoine Manzagol

Braymer C-4 High School offered no advanced placement classes and no foreign language instruction. (Although librarian Mary Margaret McAllister could've taught French, doing so would have forced the school to raise her salary.) The irresistibly caricaturable math teacher, Russell Clodfelter (affectionately called "Felter" after he forbade us to affectionately call him "Clod"), only rehashed what I'd already learned, but that was enough to fetch us yearly trophies from the state mathematics championship. (Yes, there was such a thing.) The English teacher's favorite works of literature were Mandingo and Gone with the Wind; most of the other teachers were far worse. Aside from one touch-typing course, formal education had come to an end and I was left to my own devices.

Devices were thin on the ground. The bulk of the school library was assembled at the turn of the century, as close to a heyday as Braymer ever got — Artemus Ward and William Dean Howells; Thomson, Cowper, Whittier, and Longfellow — although somehow one paperback of Leonard Cohen's pre-crooner verse had slunk in; I read the sauciest bits aloud to prove that Poetry Is Cool.

The nearest public library was in Chillicothe, population 9500, about forty minutes away, and I relied on my parents' occasional shopping trips to get there. They were usually willing to drop me off for an hour or more, though, the collection was surprisingly ambitious,1 and the person responsible, Ms. DesMarias, became a supportive friend, gifting me with castoffs and lending Finnegans Wake unstamped from a locked cabinet. (Because local book-burners relied on a list last updated in the 1930s, filth-monger James Joyce needed to be kept off shelves where Berger, Pynchon, and Updike were safe.)

My own collection lacked funding. The queue for a grocery store job was years long, and the only farm chore I could handle was slapstick comedy: set the hook in the bale and get yanked off the flatbed; set the hook in the bale and get yanked off the flatbed.... The year before it closed for good, I picked up some cash as a substitute projectionist at my uncle's and aunt's movie theater. (A kid with a tremor maintaining a carbon-arc projector was probably more suspenseful than anything on the screen.) Then I pitched a local history column to the Braymer Bee.2 None of these ventures brought in much.

Walks or cycling offered little escape, since the town was empty of scenery but rife with untrained, unleashed, unfenced dogs. If I wasn't in the back yard with our own unleashed and unfenced dogs, I could sit with Grandma next door while she read her stories (True Confessions) or watched her stories (General Hospital, Beverly Hillbillies, All My Children). On a weekend, I might play chess with a friend at his family farm. Or, and mostly, I could pace my basement bedroom.

In short (ha!) I'd been sentenced to four years in a minimum security prison. And as a prisoner I now had two duties:

1. To survive until I could get out.
2. To resist authority to the furthest extent compatible with my primary duty.

For the first time, then, my ambitions coincided with those of my classmates. Bullying dwindled from a minute-by-minute concern to an occasional issue in gym.

---

I'd tried to keep my musical tastes on the can't-wait-to-grow-up straight-and-narrow — classical, lounge, and show tunes — but Braymer wasn't reached by the necessary radio stations. No matter how I studied Conrad L. Osborne in Chillicothe discards, I couldn't listen to what I couldn't hear, and I needed to hear something other than my chorus of inner hecklers.

The early-1970s rock market welcomed cynicism, petulance, and gossip. Since satire was a traditionally mixed genre with wide allowances for crudity and sketchiness, I wisely advised myself that satirical top-of-the-pops entries made aesthetic sense even if the rest of it was philistine garbage.

After a few months, having already directed my geek gaze away from artifacts as pure virtuosic-thingies-in-a-vacuum and towards a shared outside, I widened it to include more of their implied worlds: jealous songs ethnographically sampled the alien workings and sales of jealousy, boastful songs demonstrated the alien workings of confidence, and so on.

As for having a good beat and being able (or at least eager) to dance to it, I'd always bobbed like a parrot to Gould's Bach and Toscanini's Beethoven, so no issues there.

Aside from any immediate and intermediate gains, the autodidactic approach I'd used — search for an unlocked window or easily jimmied door; enter; make yourself at home; start dropping in on the neighbors — was applicable to other new territories, even if, for political reasons or out of pure cussedness, I didn't always apply it.

And a few months later still, I found discursive models in the Meltzered/Bangsian school of rock-crit, which acknowledged — celebrated, even, in its morose or desperate way — the triune of historical context, tenacious artifact, and fleshly encounter: indissoluble in itself; remixable as fresh context.

---

While pacing through my third year of exile, I had what might be described as an original thought, the first of my life and the most rewarding:3

The time capsule of my high school library established that America's nineteenth-century canon as currently defined differed in almost every respect from the canon chosen by the nineteenth century itself.

And in my limited wandering through the realms of what I'll call for convenience "Modernism" and "1970s New York Times Book Review recommendations," I repeatedly felt a deflation of energy, of risk, of interest in the latter, a diagnosis that even its practitioners sometimes admitted.

Rather than contemporary literature having attained a unique and history-ending exhaustion, what if it was merely the latest in a long sequence of self-inflicted delusions of exhaustion? In the twentieth century, the nineteenth century canon had been sweetened by sources distrusted or inaccessible in their own time: failed or trivial genre exercises; self-published, barely published, or manuscript-only oddities. What would I find if I looked for their contemporary equivalents — not in search of "lively junk" or "mind candy," not with the condescension of Leslie Fiedler's nod to science fiction or Gilbert Seldes's nod to jazz, but instead by granting ambitious practitioners their self-awareness?

Would-be-vocational pride 4 suggested poetry as a starting point, but gathering a critical mass of publications smaller-pressed than APR was impossible from central Missouri. (In fact, I didn't find an opportunity until life placed me and disposable income within walking distance of the Grolier Poetry Book Shop.) Westerns, romances, spy thrillers, and porn were almost as daunting. It seemed more efficient to survey one of the genres I'd read in prepubescence — mysteries and science fiction — since I already had some idea (even if inadequate) of the lay of their lands, both were well represented in the Chillicothe library, and both were widely available in relatively affordable paperbacks.

From mysteries, I remembered a noticeable mid-career shift in my childhood favorite, Ellery Queen, towards — to overstate the case in the way of latter-day superhero comics — maturity, realism, complexity, and relevance.5 That didn't give much to go on, though, and it would be another year before I bought a battered copy of The Long Goodbye (from the same garage sale as a battered copy of The Golden Hits of Leslie Gore; that garage had good taste), and another decade before I first read Patricia Highsmith.

On the other hand, my junior-high transition from science fiction had carried over more than one intriguing oddity — Dangerous Visions and Fun With Your New Head, for example — and its anthologies were easy to find and easy to track leads from.

As it happened, the world science fiction convention was being held in Kansas City later that year. If I could arrange transport, that might make a nice follow-up to the summer session classes I'd gotten permission to take at Mizzou.

Timing was good in another way as well: for sf as well as film, broad distribution of experimental work crested in the mid-1970s, and both New Waves would soon meet breakwaters engineered, in part, by some other MidAmeriCon attendees.

Expansion : 1976 – 1977

When I and another dorm resident pilgrimaged to the Columbia Anarchist League that summer, we found it sharing quarters with a naked woman who avoided conversation and with a member (or possibly the entirety) of the local Communist Party, who jovially assured me that Come the Revolution my sort would be first in front of the firing squad.

I saw both their points, and still do.

---

This is intended to be the origin story of an "image," not a Pooteriad, a Real-Life Top Ten-Zillion, an Apologia Pro Vita Mea, or My Life & Loves. It concerns the development of a survival tactic rather than what I did while surviving. Accordingly I'll knapp the wantons down.

Even if I don't inappropriately-touch on sexual practices, though, I at least need to skirt them. As lawyers and reviewers used to say, they are "essential to the storyline."

When my first lover launched herself at me in reassuringly unambiguous (if inexplicable)1 fashion, I anticipated some sort of relief. But solo training hadn't prepared me for the immersive expanse of that relief: a hitherto unknown knowledge of acceptance, affection, and communication, both verbal and not; an anything-fits-anywhere! security as incontestably Real as a low-hanging ceiling or an unexpected step, and yet not painful. Love served as shelter and shield even from a distance: my final oral surgeries were far less nerve-wracking than earlier installments.

Most unexpectedly, love brought silence. Throughout my life, my skull's been occupied by a 24-hour-theater unspooling and respooling an ever-extended can't-stop-won't-stop shuffle play of blooper reels with commentary — every private or public shame, every slight whether deservedly received by me or unjustly given by me, every mild embarrassment or grievous crime or grevious mispronunciation — sometimes deafening, sometimes subsiding to tinnitus, but always, always ready to intrude. And for the first time, rather than drowning it out or yelling over it, I could walk away.

---

In my senior year, Braymer C-4 dropped even the pretense of education. Mr. Clodfelter tried to prepare me and a few other students for calculus, an effort which proved about as effective as Charlie Chaplin's pre-fight warm-up. Otherwise it was gym and four study halls. I read, or I chatted with Mary Margaret McAllister, or we mocked the white-supremacist propaganda sheet someone had subscribed the library to, or I wrote letters to my lover or to zines, or I searched for a college.

---

My slot for a grocery job had finally come up, providing some financial relief. Even so I could only afford two final-application fees for out-of-state schools. I winnowed the target list to Haverford (as a twofer with Bryn Mawr) and Vassar.

Vassar's alumna decided on a group interview and hosted an afternoon garden party of applicants, most of whom dressed in some indefinably alien fashion, kept their hands steady near the glassware, and (I later came to understand) attended private schools. I suppose she meant to learn which of us would be "a good match," who would best "fit in" at Vassar, and I suppose she did so.

The Haverford alumnus met me at a diner, and then drove us around the neighborhood to extend the conversation. Topics ranged widely, but included a compare-and-contrast between modes of feminist satire in Russ's Female Man and Delany's Triton.

In his congratulatory letter after acceptance, the alum hoped I'd be able to sustain my idealism. In turn I hope that good-hearted man never found out.

---

The summer of '77 was glorious: I'd escaped high school, I'd finalized financial aid for Haverford, and I attended summer sessions in my lover's home city, just a bike ride away from Planned Parenthood. A survey class which included Chekhov and Ibsen was particularly enjoyable, even when its teacher tried to guilt-trip me about intellectuals who deserted their homeland in its hour (or centuries) of need.

In contrast, I don't remember I and my lover worrying much about it. Her parents were academics, mine were military, and so the thought of extended separations was maybe less alien than it would've been to our neighbors. I hadn't yet read enough Burroughs to predict what symptoms might accompany abrupt cessation of a universal anodyne. And neither of us could have imagined the grotesque mash-up of Goodbye Columbus and The Rocky Horror Show at our relationship's terminus. We were far too clever to risk anything so humiliating.

The Philosopher's Calculus, or Stone : 1977 – 1980

Fear of the irrational undoubtedly feeds on our lack of knowledge, but above all on those points of omission, on a certain impatience that keeps us from penetrating to the heart of the operative by confusing learning with the talent for rapidly consuming an "informational content." But to learn is to prepare oneself to learn what one in some way already knows. and to put oneself into such a state where the connection between things reverberates in the connection of the mind. The operation is not at first given as an arrow that links a source to a target, but rather emerges in the places where variables become merged and get tangled up without being policed by parentheses.

- Figuring Space (Les enjeux du mobile) by Gilles Châtelet

Have I no weapon-word for thee — some message brief and fierce?
(Have I fought out and done indeed the battle?) Is there no shot left,
For all thy affectations, lisps, scorns, manifold silliness?
Nor for myself — my own rebellious self in thee?

- "To the Pending Year" by Walt Whitman

The next few years were the most intellectually transformative, emotionally mercurial, and socially toxic of my existence, which I suppose is only to be expected when an eighteen-year-old autodidact is removed from years of rural seclusion (but not the gentlemanly sort) and deposited in two of America's finest colleges and near one of America's largest cities.

In that despised and now inconceivable final phase of public support for education, financial aid flowed but first-gen student advising did not. Ten years after I graduated, I discovered that my fellow students considered collaborative reverse-engineering of textbook-and-chalkboard proofs as essential for mathematics as language drills were for French or German classes. If I'd known, maybe I wouldn't have squandered so many opportunities.

On the other hand, who am I kidding? I was a stubborn cuss, and my introduction to the mores of prep-schooled young men — the differences money made and the differences it didn't — had started me on the cynical foot, a stance reinforced when Haverford's presidency passed from two-fisted activist Jack Coleman to dispiriting English toad Robert Bocking Stevens. Told what could be gained from a study group, I'd have said, "Who wants to hang out with math majors? It's bad enough I have to hang out with myself."

As was, I envisioned "college" as that phase of life in which massive blunders incur relatively minor penalties, and I behaved accordingly.

The result was the Great Work advertised by my self-assigned Yeats-and-Joyce-centered curriculum (pursued alongside a full externally-assigned course load): mortared and pestled; flamed and boiled in shit; buried to ferment; seasoned to taste. The most practiced of my little loves once confided on our way out of bed that she'd described me to her mother, a research psychologist, as "probably psychotic," and what shocked me about that was the idea of anyone disclosing their own life to their own parents.

If only to warn young people against the dangers of unsupervised reading, I suppose I should mention the precipitant of my greatest tumble, after which I saw only a choice of downhill slides: an all-out unrequited amour fou, an experience never to be repeated and best avoided in the first place. It's not that the Tudor poets and Baudelaire and Dowson and Yeats and the Confessionals and so on made the idea sound exactly desirable; more, I think, that there are only so many times you can rehearse a part before you put on the show.

Let's keep the rest on ice; there's way too much here for one meal. As a placeholder, though, and because COVID-19 isolation's got me nervy, and because I'm sick to death of writing without any identifiable human beings other than "I" and "me," and most people skip Acknowledgments anyway so no harm done, I'd like to cite some names. Bless this bed that I lie on.

• The initial name's a bit misleading, since Hilda Rooney was 100% Cuban (Wagnerian parents; an Irish-American ex-husband). Her freshman seminar, on African-Christian syncretism in Latin American fiction, appealed to me as a sequel to my Missouri summer-session class on West African empires. In turn, she was intrigued by my and my father's long-ago daytrip to Haiti from Guantanamo. Sharing a tendency to get high on the fumes of X-treme negative capability, we quickly hit it off, and she became my closest friend among the faculty, hosting dinner (a heavenly goat stew) or inviting me to parties several times a year.

  After college, I disappointed her by ignoring the possibility of graduate school — she'd somehow imagined my monolingual sunstroked carcass conducting anthropological field studies — and we lost touch.

  A dozen years later, when web search engines began to appear, hers was the first name I entered. I've tried again every year since then and never found results outside one digitization of an old Haverford course catalog.

• After deciding (to my own surprise) not to accompany mathematics with orthodox analytic philosophy (a breakfast of Spam and watered-down Spam), I barreled to the opposite extreme: Historical Introduction to Philosophy as taught by Paul Desjardins, a Platonist Catholic pert near busting with eudaimonia, and so exemplary of Haverford's approach as to approach caricature. (This overview of the Philosophy department in 1976 includes a photo of Paul in rumpled action, and this comment at J. E. H. Smith's site describes his and Rosemarie's home, proof-by-existence of the Good Life.)

  I found his go-to examples of basic human impulses — rape; shitting in public — a bit alienating, and he didn't fuss much with inclusiveness: in the midst of a dithyramb honoring athletics, he took care to except weightlifting because "it makes the mind slower," while a blush raised on the one weightlifter in our class. (I felt sorry for the guy until later that year I heard him trying to take offense at a WASP joke.) And I believed Desjardins when he (and Gangadean afterwards) said it would've been helpful for me to meet the department's representative pessimist-skeptic, Tink Thompson.

  Still, yes, he did sort of change my life.

• M'sieu' Gérard Defaux gave the only grade, good or bad, I ever enjoyed receiving:

  A+ pour la beauté de tes idées
  C- pour la grammaire et le vocabulaire
  = B

  And his was the only class whose final exam led me to request a meeting. When I entered his office he seemed atypically grim, but brightened up considerable when I asked for the source of the anti-poetical yet completely gorgeous prose translation exercise. (Answer: the opening of Madame Bovary.) He seemed sincere in regretting that I didn't continue French studies — « Gérard a toujours gardé pour les « gens curieux » — ces Ulysse inquiets et touche-à-tout condamnés par une certaine tradition chrétienne et par les livres de Rabelais lui-même — une sympathie profonde » — but one of my scholarships had a GPA requirement and mathematics represented risk enough.

• Across the long, noisy bottoming out of my sophomore year, my most reliably stable supports were Denbigh Hall neighbors Connie Coontz, Roz Cummins, and Sally Seggerman: all of them witty, sane, and generous to a fault. (I was the fault.)

  And I should add, I wasn't their main project, or even a special focal point! That's just how darn nice they all were.

  (My closest male friendship came to too gruesome an end to risk reconnection. Perhaps a shared ambition to mutter "Usurper" wasn't an ideal foundation on which to build.)

• Like Desjardins, logician-Aristotelian-Buddhist Ashok Gangadean was a legendarily inspiring teacher. Unlike Desjardins, Gangadean eventually (fifteen years after I was his student) began publishing, but he proved such a dreadful writer that I can't bear to give a link. Testimonials assure me he's still bringing enlightenment incarnate.

  This interview from 2000 may convey some of his charm and intelligence, and some of what he confirmed or encouraged in me, and where I was unable to follow.

• After sludging through the purgatorial semi-set concrete of calculus, I was rewarded with a series of classes taught by Dale Husemoller. Invariably arriving a variable number of minutes after official start time, Mr. Husemoller, more rumpled even than Desjardins, would stride directly from hallway to top-far-left blackboard and begin chalking a proof with the confidence of a quick-sketch artist gazing at a sitter, simultaneously translating into human speech with frequent exclamations of suspense or astonishment: "But look!" "Oh no!" "But that means!"

  Husemoller was far too distanced a personality (or I was far too mathematically unambitious) to support any illusion of friendship, but he so blatantly resided in mathematics, roaming a lushly self-sufficient world of comforts and novelties, that his willingness to exhibit material presence was in itself inspiring.

  It was my misfortune to take a leave of absence one year before Husemoller left for his own sabbatical, landing me with far too much of the worse-than-nothing Mr. T in my final years. But I understand: he had somewhere else to be.

Over away from Dane Axe Edge sends down the Dove, gathers the Manifold and lets it slip through complexity; the hills in their turns tantalise and instruct, then the learning dissolves. There's no holding it all. - A Furnace, by Roy Fisher

Graduation : 1980 – 1982

No more education was possible for either man. Such as they were, they had got to stand the chances of the world they lived in; and when Adams started back to Cambridge to take up again the humble tasks of schoolmaster and editor he was harnessed to his cart. Education, systematic or accidental, had done its worst. Henceforth, he went on, submissive.

The Education of Henry Adams: a Study of Twentieth-Century Multiplicity

As my dropout year drew to its close, I took inventory:

• I'd been assaulted, home-invaded, threatened, and catcalled, but never raped, shot, stabbed, concussed, or fractured.
• I'd gone hungry for weeks and done some lasting damage to my innards, but never approached actual starvation.
• I'd taken too much of anything free and blacked out numerous times (it's hard to keep count when you're unconscious), but never stopped breathing or entered an extended coma, although I gather a "Street Hassle" discussion took place over my body after it met cocaine.
• I'd proffered my unprofitables widely and on too little pretext, but I hadn't contracted any (diagnosable) diseases or instigated any pregnancies, and I'd lost surprisingly few friends, considering.
• I'd lived with roaches, fleas, mice, freezing cold, steaming heat, and constant noise, but was never bitten by bedbugs or rats, and never lost access to water and power.
• I'd been hassled by cops — in Rizzo's Philadelphia, everyone was hassled but Rizzo — but never clubbed or jailed.
• I'd dressed unbecomingly, covered my arms with scratches, hammered my sconce, walked barefoot in the snow (so refreshing after the dog-shit-and-vomit stank of the locust tree fruits and the vinegar-and-smoldering-tire rot of my shoes), and generally made a spectacle of myself, but (forewarned by a tall stack of autobiographical poetry and prose) always fast-talked my way out of "seeking professional help."

This was as soft as a hardscrabble bohemian life was ever going to get. And I had not found the experience productive; it was not conducive to inspiration. All I'd achieved was that list of unpleasantries.

There was no way around it. Insofar as I had anything to offer existence (and we'll set that question aside for the nonce), I'd need a steady income.

---

Entry to the allegedly non-capitalist sanctuary of tenured Academe was barred by its Customs department: I considered grades and required classes cruel mockeries of education, and had resolved never to become a perpetrator.

Thanks to my tremor and lack of sustain, physical labor was out, as were (due to different uncorrectable flaws) most of the worthwhile jobs open to mouthy intellectuals. (Nowadays I guess I might find hire as the concern troll equivalent of an agent provocateur, but that sounds even less attractive than grifting throwaway money from a venture capitalist.)

I was rarely picked for retail positions, and when I won one, I'd be fired within the month. Having been cursed with a rubber, stage-ready face that exaggerates any fleeting emotion, I couldn't hide contempt and hostility well enough to keep any other sort of service job, either.

It would have to be some sort of clerical position, then, and I'd need a degree to paper over my too-evident defects. Petite bourgeoisie or bust!

And to obtain that degree, I'd need to clean up my act for the sake of the kiddies, stop flinging my Sad-Harpo-Marx seduction technique at all and sundry, buckle down more and under less.

But before and beyond all that, I needed then — as I needed later, as I need now — to invent some — "justification" is too presumptuous a word — some motivation which could be reconciled with my life as stubbornly lived: one which has always compulsively extracted, deformed, misapplied, modified, inverted, ripped, and generally not-left-the-fuck-alone abstract verbal models which then, in their own right, tend to go all Frankenstein's monster on my sorry ass.

---

Before the fiction grew threadbare, announcing myself as poet was meant to signal harmless redundancy. If asked to elaborate, I'd declare an ambition to be a minor poet — not a prophet, not a School-of-Me founder — with a job at the Post Office 1 and an apartment which could host friends. A downscale Eddie FitzGerald rather than a shitkickin' Al Tennyson.

Later, stripped of laurel and intimates, I sought guidance in others from that narrow intersection of people I admired and people I felt akin to: the exceptionists, the easily ignored; those who pursued eccentric interests or contributed to essential goals in oddly irrelevant ways; amusements or annoyances to more important names.

But I anticipate. Returning to 1980:

I'm only of use as a persuasively dissenting voice, but I must never be so persuasive as to dominate.2 If I couldn't talk I had nothing to contribute, but left unmuzzled I was a menace to the community. Well! A short leash, then, and a fenced yard for exercise. Try to avoid battlegrounds which might incur meaningful casualties. Reserve untrammeled discourse for nearest-and-dearests, preferably — as I decided not long afterward, post facto, based on new evidence, per SOP — preferably within the safe all-accepting bounds of a monogamous sexual relationship, where static build-ups and short circuits could be grounded by bed.

I didn't necessarily want to be worthless, but if that was the price of pointlessness, so be it.

---

The advent of this story's shaggy "Rosebud" dogsled, the "image", wasn't memorable. As previously admitted, it's been a cheap sturdy utilitarian thing for daily use, like my father's CPO mug, not a major purchase or knock-me-down Damascan reveal.

I know for certain that by the fall of 1980 I was keeping it within reach: an easily graspable and transportable geometric reminder of the insufficiency of logical discourse, and geometric hint as to how that insufficiency might be addressed and deployed, and then subjected to reminder. A surveying tool for local maxima.

---

I re-entered college and lightened my course load.

With fewer sins to confess, there was less impetus to poeticize, and I diverted attention to my role as lyricist and lead vocalist in my friends' rock band. (I was lead vocalist because I had the least semblance of talent and the most brazen disregard for public humiliation. It was a very traditional rock band.)

Early in 1981 I wrote a song paying homage to my new lover. In honor of those of her friends and family who quite reasonably doubted my worth as boyfriend material, I also drew imagery from those exemplars of disappointing promise, Orson Welles and John Barth. That referential weave kept the lyrics memorable, and on long walks the happy yowl of its third verse still sometimes sets my pace:

After she hits the end of the funhouse or gets lost in the road,
The mirrors will be dusted and the ditches will be mowed.
Oh, but anything worthwhile must be empty, base, and vain!
Extremities are foolish. Even fools get paid.

Publishing the dissertation : 1989 – 2020

There must be no cessation Of motion, or of the noise of motion, The renewal of noise And manifold continuation; And, most, of the motion of thought And its restless iteration, In the place of the solitaires, Which is to be a place of perpetual undulation. - "The Place of the Solitaires" by Wallace Stevens

Eight years later the naysayers were proven right. In our last meeting, my newly-ex cheerfully remarked, "I feel like it's been years since I did my own thinking" (a hot roar flooded my ears) — that's not true! —
— how had I broken so much? —

Predictably enough, I fell apart — substance-abused, fecklessly self-harmed, shucked my duties, composed formal verse, rock-n-rolled all night (well, occasionally past midnight, anyway), re-entered social media (now including a new medium), made some friends, and received far more comfort than I gave.

But this new cycle of breakdown and crawl-from-the-wreckage didn't weaken my faith or smash the icon of my "image." It merely persuaded me to modify some expectations and some habits. (Massless sheets don't provide much warmth but they layer well.)

One of the latter modifications brought us together here today.

Hi. How are you?