The Laziness of Reductionist Analyses

In his review of David Luke‘s translation of Thomas Mann’s Tonio Kröger and Other Stories W. H. Auden wrote,

Polar opposites as in appearance they look, the two literary doctrines of Naturalism and Art-for-Art’s-Sake, as propounded by Zola and Mallarmé, are really both expressions of the same megalomania. The aesthete is, at least, frank about this. He says: “Art is the only true religion. Life has no value except as material for a beautiful artistic structure. The artist is the only authentic human being: all the rest, rich and poor alike, are canaille.”

The naturalist is more disingenuous. Officially, he says: “Down with all art that prettifies life. Let us describe human life and nature as they really are.” But his picture of life “as it really is” is a picture of human beings as animals, enslaved to necessity, who can only manifest behavior and are incapable of personal choice or deeds. But if human beings are really as the naturalist describes them, then they cannot be loved or admired. Who can be? Only the naturalist himself for his accurate clinical observations. Like all kinds of behaviorists, he does not apply his dogmas to himself. He does not say: “My books are examples of behavior, conditioned by blind reflexes.” The hidden link between the naturalist and the aesthete is revealed by the total absence in both of any sense of humor. [links added]

An absence of a ‘sense of humor’ it seems, is almost endemic to all reductive, ‘X is nothing-but or merely Y’ style analyses (as in the example of the naturalist above, who suggests that books are nothing but examples of conditioned behavior). They are also depressingly narrow-minded and lacking in imagination.

Wittgenstein once pointed out–in his critique of psychoanalysis–that a facile reduction of this sort was misguided for the most elementary of reasons: when it was over, you simply weren’t talking about the same thing any more. Boil a man down to flesh, blood and bones to show us that that was all he was, and what you’d have left was a bag of just that. You wouldn’t have a man any more.

All too often, reductionist analyses fail to answer the most basic questions about their enterprise: Why is one necessary? How would it be accomplished? What explanatory power or insight do we gain with the new language of description that is now afforded by these ‘nothing-but’ locutions that you provide us? What would we lose in its place? A reduction for reduction’s sake seems extremely unappealing.

This is not to discount the explanatory power that some reductionist analyses have afforded us, especially within the sciences. But even there, occasionally, as the misguided efforts to reduce biological explanations to exclusively physical and chemical ones shows, the seductive allure of the catch-all, explain-all impulse dies hard. That same urge fuels the intemperate extension of the reductive net to catch all manner of fish, be it literature, psychology, or the social sciences.

Auden is right: the reductionist is megalomaniacal and a bore. He fails to see that what makes inquiry interesting is the creation of meaning in rich and diverse forms; he’d rather channel that fundamental impulse into some narrowly circumscribed channel. And Auden is right too, about the lack of a sense of humor. The universe is laughing at you behind your back anyway; why not join in and crack a joke or two yourself?

My Father’s Record Collection

Among the many seeming treasures I left behind in India when I migrated to the US in 1987 was my father’s vinyl record collection. It contained the music I grew up with, played on a turntable, piped through a Phillips amplifier, and then, finally, emitted through a pair of custom-made speakers. The collection was eclectic and diverse, ranging from Amir Khusrow ghazals and qawwalis to Bill Haley and the Comets to Benny Goodman to Ella Fitzgerald to Louis Armstrong to K. L. Saigal to Noor Jehan to Polish jazz to Cuban salsa to Bollywood soundtracks to Manu Dibango to Tchaikovsky to Bach to…I should stop. You get the picture. There was lots of music. (Later, when my brother and I started our additions to this collection, we contributed Thin Lizzy, Uriah Heep, AC/DC, and other cacophonous upstarts. I do not know if my father would have approved but given his taste for rock-n-roll in its formative years, I’m going to wax optimistic and conjecture that he would have at least given these folks a sympathetic listen.)

There were 45RPM EPs and 33RPM LPs; each one of them was carefully stored in its original paper sleeve and then carefully tucked inside a plastic cover. Two giant stacks of the LPs sat on top of the speakers; the EPs were stored in a book-case.  The records, despite some of them having been owed for almost twenty years, did not bear a single scratch or blemish. Indeed, they managed to gleam, black and pristine, almost as if they had just been transported back from the record store. My father was diligent and careful in his handling of his precious vinyl; the record was carefully removed from the sleeve; the middle-finger was placed on the central aperture, the thumb on the rim, the disc was carefully placed on the turntable, which was then started up; the needled stylus was gently–oh, so delicately–placed on the record; and the music began.

My brother and I received extensive instruction in handling the records. There were warnings and demonstrations aplenty. Looking back now, I’m amazed that my father ever trusted us enough to let us use the music system as autonomously as we did. We were clearly well indoctrinated; I realized quite soon I could not bear to watch my friends (or their parents) handle their records, so careless did they seem, so oblivious to the obvious damage being done to those precious grooves.

My father’s record collection provided soundtracks for parties (whether there was dancing or not), quiet evenings at home (my father played classical music or jazz while he organized, sorted and cleaned his old photo slides collection, or did other housekeeping tasks), winter weekend afternoons,  and a host of other occasions. Its contents provided me with a musical education, an early dose of cosmopolitanism, and taught me tolerance for a diversity of musical styles.

It remains one of the greatest unsolved mysteries of our often displaced home that my brother and I do not know where this collection is now. If those records are in someone else’s hands, I hope they are being taken care of, but I’m not optimistic.

Prohibitionists and Their Impoverished Sense of Human Motivation

A few days ago, I wrote a post here on David Brooks’ inane ‘Weed: Been There, Done That‘ Op-Ed. Looking back on it now, what strikes me as most galling about Brooks’ post and other pro-prohibition sentiments that I’ve heard expressed in the past is the shriveled, impoverished, reductive view they have of human character. Their advocacy of prohibition reveals no concern for their fellow humans; it merely highlights their narrowly conceived view of them.

To wit, the (extreme) prohibitionist seems to believe that once someone, any one, is exposed to an intoxicant, a pleasurable one, perhaps offering some palliative relief from daily routine, or diversion, or entertainment, the consumption of that intoxicant will immediately be placed atop their hierarchy of desires. From then on, the user, now an addict, will divert his time, energy, and monetary resources to the pursuit of the intoxicant. Nothing else may compete with its allure.

This–possibly caricatured–description of prohibitionist sentiment highlights its most salient assumption: that pursuit of intoxicatory pleasures will override other goals entertained by the human agent, even if the price to be paid is ill-health or financial ruin.

I hope this sounds ludicrous to you. For humans have many desires that compete for their attention; these are satisfied depending on their standing in our scheme of values, our capacities, and our stations in life. Many are the pleasures we decline because we feel that some competing goal of ours will be compromised. Some of us, admittedly, are unable to adjudicate thus between competing desires and fall prey to a possibly pernicious indulgence repeatedly; but when these compulsions become pathological, we rightly suggest that such folks seek treatment for behavior that appears to self-destructive.

This point is broader, of course. We are all assumed hedonists by the prohibitionist: any experience deemed pleasurable by us will always be pursued by everyone no matter what its cost. Our tastes are alike; our dislikes and likes are alike.

But all too often, we find that experiences found pleasurable by others are not so for us. Many of my friends love scuba diving. I have been assured it’s an otherworldly experience, taking its exponent into a magical realm beneath the waves. I’m sure that’s the case. But I tried it, and I didn’t like it. I felt no desire to pursue that experience; knowing myself and my capacity to panic at inopportune moments, I reckoned I stood a good chance of hurting myself, and hurting others too, if I continued. So, after one dive down to the Great Barrier Reef, I gave it up. There are many other things I’d rather do on my vacations (hiking well above sea level, for instance!) I might have compromised other goals of mine if I had continued to pursue scuba diving. So, to reiterate, I didn’t do it any more. Or there are those, for instance, like mountaineers or F1 drivers, who pursue their pleasures and then give them up because the risks of their pursuits has become too visible and they feel their lives with their families threatened.

These examples can be multiplied endlessly.

The understanding of human beings as being constantly and relentlessly afflicted by a form of what the ancient Greeks termed akrasia, and thus not worth being granted the freedom to live their lives according to their own, autonomously-arrived-at scale of values, is prohibition’s central incoherence.

Game of Thrones AKA The Widow’s Revenge

I quite enjoy HBO’s Game of Thrones and after accounting for all the sex and violence have often wondered why I find it so entertaining; I’m not inclined toward the fantasy genre under normal circumstances and do not think I had read any of its productions before Game of Thrones. (That has changed; I have now read the first novel of George Martin‘s epic series).

Daniel Mendelsohn provides an answer of sorts, beginning with:

This has a great deal to do with the complex satisfactions of Martin’s novels, whose plots, characterization, and overall tone the series reproduces with remarkable fidelity—and whose mission is, if anything, to question and reformulate certain clichés of the fantasy/adventure genre about gender and power.

And concluding:

Whatever climax it may be leading to, however successfully it realizes its literary ambitions, George R.R. Martin’s magnum opus is a remarkable feminist epic.

Quite correctly, Mendelsohn’s central reason for regarding Game of Thrones as a ‘feminist epic’ is the position it accords to Daenerys Targaryen (and to a lesser extent to Arya Stark). Her struggle for power, wherein she will challenge men for the throne of the Seven Kingdoms is an often dominant plot line. She might be assisted by men, she might take advice from them, but she remains her own boss (and as Ser Jorah Mormont often finds out, she is not shy about letting him know this fact); all too often, she commands and rules them.  She is not shackled and dependent on male sexuality: 

The pubescent Dany…is no innocent: deprived of the attentions of her dead husband, she now and then accepts the ministrations of a teenaged handmaiden.

Mention of her dead husband, the Dothraki chieftain Khal Drogo, serves as a reminder that a crucial component in realizing Martin’s feminist vision in Game of Thrones is Daenerys’ status as a widow.

The widow, of course, is the archetypal weakened and destitute woman: she lacks a male guardian, protector, provider, and lover. She is incomplete in many ways. For instance, she lacks that which will realize her motherhood–her sole raison d’etre–a father for her children. From now on, she can only be a dependent, cast out to the not-so-tender mercies of other men, or the sympathies of her own family. The loss of her husband has marked her out as a singular unfortunate; the more superstitious might regard her as the bearer of misfortune for her husband, and seek to consign her to the margins of our world where she may infect us no more. Those women who know the standing of widows in a society like the Dothraki–and many of ours have approximated theirs in the past and sometimes even in the present–may find any inner resolve crumble when confronted with a fate as terrible as that which befell Khal Drogo. But not Daenerys Targaryen. Her mighty man–it is no coincidence that Martin made him the epitome of rugged, virile strength–is brought to his knees by a witch’s sorcery, but this loss, while tragic, does not detract her from her quest.

It is the refusal to embrace the Dothraki widow’s fate that makes Daenerys the strong woman that she is, and that allows Martin to give his epic a feminist hue.

Bert Williams and the (Funny) Sadness of Clowns

WC Fields described his fellow Ziegfield Follies mate Bert Williams–‘one of the pre-eminent entertainers of the Vaudeville era and one of the most popular comedians for all audiences of his time…the best-selling black recording artist before 1920′–as ‘the funniest man I ever saw and the saddest man I ever knew.’ Williams certainly made no secret of the melancholia in his work; as Jervis Anderson notes in This Was Harlem: A Cultural Portrait 1900-1950 (Farrar, Strauss and Giroux, New York, 1981):

Williams once said that nearly all his songs were based on the idea that he was getting the worst of it….If he had any sunshine in his heart, only his friends and family saw any evidence of it. Onstage, it seldom broke through the overcast of his face, the melancholy of his voice, and the other inclemencies of his style. [pp. 41]

Anderson quotes a critic of the time remarking that:

Williams is the…butt, the abused one. He manifests…a pathetic knowledge that something is wrong somewhere with the eternal scheme of things. [pp. 38]

Funny and sad; how can those afflicted with the wrong kind of humors be humorous? The ‘tears of a clown’ trope tells us that in fact we are quite familiar with this seemingly incongruous blend. We are not unfamiliar with the proximity of laughter and misfortune; it’s only a short journey from snickering at banana peel slips to full-blown schadenfreude. It might even be that our awareness of the grimness partially visible behind the facade put up by the performer makes us laugh just a little harder as a protective measure, a warding off of the black clouds that might roll over us too.

I learned myself once, quite dramatically–literally perhaps–how close together laughter and tears run. A few years ago, I attended a clown workshop taught by the brilliant Matt Chapman of Under the Table Theatre. One of our final exercises was a partnered effort: we paired off with fellow students, sat down next to each other, and then, one of us began laughing while the other one began crying. We were asked to raise the intensity of our laughing and crying from one to ten, and at the ‘ten’ mark, to abruptly switch over to the other: the ‘laugher’ would become the ‘crier’ and vice-versa.  The pair would then wind down from the ‘ten’ to the ‘zero’ mark.

I expected this to be difficult. I didn’t see how was I going to ‘fake’ laughing and crying so hard and how I could switch over from one mode to the other. But it wasn’t. Turns out, when you are laughing really hard, you’re close to crying anyway. (Remember that bit about ‘I laughed so hard I cried’?) And interestingly enough, when you force yourself to laugh, you find yourself overtaken by a great embodied chuckle that further fuels all the guffawing and chortling. The converse held true too: my crying made me genuinely sad and shaken for a while afterwards.

Perhaps William found the laughter of those who appreciated his act infectious; perhaps he found it easy to summon up a chuckle as the outward manifestation of an inner lament.

Perhaps, hopefully, he found his own routines the best palliative for the pain he felt.

Sports, the Distraction from the ‘Main Game’

Sometime ago, I received an email from an Australian friend of mine, who, among other things, wrote:

Been thinking about how you and I love sport, how it really means something to us, how we cheer for our teams and are gutted when they lose. Yet we all know that sport (particularly non-participatory sport) is just another way the bosses keep the people distracted from the main game.

Is it? Well, yes. My friend is right, and he certainly doesn’t need to convince me. After all, here, on this blog, I’ve alluded to ‘the massive narcotizing effect of professional sports’ and waxed critical about the shamateurism and excesses of college football. The puzzle, if there is one, is why folks who consider themselves alive to the political dimensions of the social, economic and cultural phenomena they encounter, who are ever so ready to offer critique and revisionist commentary, so blasé about professional, big-budget, franchise-based sports, all of which are so very distant from the game played in neighborhood parks?  Why are they so ready to believe the patently false premises of college sports?

I do not get off lightly in this charge-sheeting, for despite the critical commentary mentioned above, not only do I watch sport, I write on it, thus possibly diverting myself from more critical political engagement with the pressing issues of our day. (To be more precise, while I watch many sports, I only write on cricket, thus ensuring that here, in my adopted ‘home’, I have consigned myself to being treated as an oddity of sorts.)

My writing on sport, of course, is what enables me to excuse my extensive and expensive investment of time and energy in sports spectating; I reassure myself that I use professional sport as a lens through which to examine topics that are of broader interest to me: nationalism, labor relations, media studies, race relations, xenophobia, technology, ethics, and so on. (My philosophy department at Brooklyn College offers a class on Philosophy of Sport; I still hope to teach it some day.) Some readers of this blog have noticed that my posts often flirt with memoirish inclinations; that tendency is present in my cricket writings too, thus allowing me to explore a life via a recounting of its entanglement with a cultural endeavor. This is certainly of cathartic value to me, and hopefully, will might even be of some value to others, including, most promisingly, my daughter. (Well in the future, obviously; right now, she can’t read.)

Perhaps I apologize too much; sports is leisure, and spectating, along with participating in it, brings us diversion from our weekday preoccupations, surely a much-needed escape valve. And yet, as the word ‘diversion’ indicates, we aren’t too far from the worry expressed by my friend: that we are just being ‘distracted from the main game.’ The least lame rejoinder I can offer to this indictment is that if our gaze is to be diverted to sports at all, then it must always be a critical one, alive at all times to its political ramifications. Anything less than that is to be co-opted, as desired, by the ‘bosses.’

From ‘Filling the Sky’ to ‘Sharing the Earth’

In On the Town: One Hundred Years of Spectacle in Times Square (Random House, New York, 2006), Marshall Berman, in the chapter ‘The Street Splits and Twists’, which, among other things, describes the complicated relationship between women and Times Square, notes in his commentary on Ethel Merman:

Gypsy is one of the most grueling of American plays. It’s amazing how many of the greatest American plays ran on Broadway in a single decade–Death of a Salesman, A Streetcar Named Desire, Long Day’s Journey into Night–heartrending ordeals everyone. Gypsy is the one great ordeal with a happy ending. Its climax, where Gypsy offers to take care of Rose and her mother lets her, is a rare utopian moment when we can actually see tragedy metamorphose into comedy. Our history doesn’t offer many moments like this. Imagine, if we could see King Lear settle into a retirement cottage in Cordelia‘s kingdom; or see Captain Ahab at the very last minute turn the ship around and return to Nantucket, where he could get drunk, try on new clothes, and tell tall tales; or see the Red Army refuse to fire on the people and join in the jubilation of the Prague Spring. Alas, we can’t see any of these things. But Laurents and Sondheim and Merman have brought us a stirring vision of how somebody who used to fill the sky can learn to share the earth. [pp. 159-160; links added]

‘Fill the sky’ and ‘share the earth’; few learn to do that gracefully. The most famous instances of failures to do so are drawn from unsurprising domains like sports. The sports star attains a peak state, one of acute physical and mental co-ordination, performs at the highest levels possible, gains the greatest accolades and laurels, and then, goals attained, suddenly finds himself bereft of inspiration or motivation. Retirement appears as a grim period of enforced lassitude and eventual decrepitude, a time in which the erstwhile star of the heavens, now rudely deposited on humble lower ground, can gaze back wistfully at more exhilarating times. And so thus, the painful ‘comebacks’, which cause former fans and well-wishers so much angst, but which seem to assuage, momentarily at least, our ageing star, before the unfamiliar mediocrity of this new phase of life becomes unbearable and forces a reluctant retreat.

And there are the moon astronauts. Spare a thought for Buzz Aldrin. He graduated third in his class at West Point in 1951, flew in the Korean war, shot down two opponents in aircombat,  earned a Doctor of Science degree in astronautics from MIT for a thesis titled “Line-of-sight guidance techniques for manned orbital rendezvous”, joined the astronaut corps, flew aboard the Gemini 12 mission, and then, finally on Apollo 11, became the second man to walk on the moon. When he returned to earth, having realized, perhaps, multiple summum bonums in the physical and mental domains, a crash landing was almost inevitable: it came in the shape of struggles with depression, alcoholism, and marital infidelity.

‘Filling the sky’ is hard indeed; ‘sharing the earth’ might be even harder once it’s done.

David Brooks Smoked Weed So You Didn’t Have To

David Brooks put down his bong a long time ago:

For a little while in my teenage years, my friends and I smoked marijuana. It was fun. I have some fond memories of us all being silly together. I think those moments of uninhibited frolic deepened our friendships. But then we all sort of moved away from it….

This was not a decision made lightly:

We didn’t give it up for the obvious health reasons….I think we gave it up, first, because we each had had a few embarrassing incidents. Stoned people do stupid things….most of us developed higher pleasures….I think we had a vague sense that smoking weed was not exactly something you were proud of yourself for. It’s not something people admire…. So, like the vast majority of people who try drugs, we aged out. We left marijuana behind.

Well, that’s not too bad. You did some weed, as did your friends; you went on to ‘higher pleasures’ (no pun intended, right? Right?). No one seemed to have been harmed; heck, some of you became columnists for The New York Times. There’s no stories of stoned assaults on significant others, overdoses, or even bouts of violent retching or hangovers induced by marijuana. The narrative arc of this little bildungsroman that Brooks has deigned to share with us is disappointingly slight and bland: young men indulge in lower pleasures, then move on to higher ones–some opera, some good food, some ballet, perhaps?–the salaried life  and a comfortable middle-class existence. (Some might have been fortunate enough to become one-percenters.) It’s not a particularly enlightening  one, and one might be mystified by why a highly-paid writer for the nation’s most prominent newspaper thought this was a story worth sharing with his readers.

Well, apparently, the dangers seen on this scenic road to enlightenment were enough for Brooks to want to warn off everyone from ever traveling on it. Whatever the lessons learned on it, one of them didn’t include enough respect for individual self-determination or choices or the consideration of the possibility that others–like Brooks and his cohort–might possess the capacity for arriving at a host of idiosyncratic decisions about how their lives should be lived. Humans are interesting; they just aren’t interesting enough to be left to their own devices.

So:

I don’t have any problem with somebody who gets high from time to time, but I guess, on the whole, I think being stoned is not a particularly uplifting form of pleasure and should be discouraged more than encouraged.

How so discouraged? Apparently, by keeping marijuana illegal, and continuing an expensive, racist ‘war on drugs‘, a moral, economic and legal catastrophe whose full cost has still not been reckoned with:

Laws profoundly mold culture, so what sort of community do we want our laws to nurture? What sort of individuals and behaviors do our governments want to encourage? I’d say that in healthy societies government….subtly encourages the highest pleasures, like enjoying the arts or being in nature, and discourages lesser pleasures, like being stoned.

Funnily enough, I hadn’t thought that illegality amounted to ‘subtle discouragement.’ And interestingly enough, another lesson that Brooks learned while aging out–a peculiar one given his avowed insistence that laws do not change behavior as much as social norms, expectations and customs do–is that we cannot rely on them to adequately discourage marijuana use. This isn’t the moral I would have derived from Brooks’ little tale of how his youthful indulgence in marijuana waned, where its continued illegality had nothing to do with his decision to stop consuming. Instead, Brooks, along with his other friends, managed to figure out, miraculously enough, that marijuana didn’t fit into the life he wanted.

And so Brooks made his choice. But the freedom to arrive at such decisions on their own is not one he can trust the members of this society with, Perhaps his cohort was a moral and rational singularity in a universe of blindly hedonistic, amoral original sinners who need protection from themselves. Thus, leaving to them the choice of how to live their lives is in fact, inhibiting them from self-realization:

In legalizing weed, citizens of Colorado are….nurturing a moral ecology in which it is a bit harder to be the sort of person most of us want to be.

Mostly, columnists reveal their internal incoherence of thought in their corpus of writings. It takes a rare talent to so do so as comprehensively as Brooks does in the space of just some seven hundred words.

The Terror of the Formerly Utterly Incomprehensible

Yesterday’s post detailing my rough introduction to calculus in high school reminded me of another encounter with a forbiddingly formidable mathematical entity, one that in later times served as an acute reminder of how even the utterly incomprehensible can come to acquire an air of familiarity.

One reason for the rough ride I experienced in my physics class in the eleventh grade was that I had transitioned to studying a more advanced science and mathematics curriculum after my ninth and tenth grades. In those, I had been assigned to a ‘Arts and Humanities stream’; the science and mathematics I had studied were pitched at a more elementary level compared to those assigned to the ‘Science stream’. Not content with my placement, and overcome by the surrounding familial and social pressure to pursue a more ‘applied’ and ‘practical’ course of study, I switched schools and curricula. Unsurprisingly, this meant I had some catching up to do, which I intended to get started on in the break between my tenth and eleventh grades. My brother, who was about to graduate high school and move on to university, helpfully handed me his textbooks and study guides, throwing in the singularly unhelpful warning that I was about to be swamped.

Armed with this grim prognostication, I began what I hoped would be a rewarding period of autodidactic endeavor, one that would equip me with not just the requisite curricular background by the time regular classes began in the new academic year, but also some confidence.

Before I would begin systematic study, of course, I would take a peek at what lay ahead. And there, I was confronted by a terrifying, mysterious new entity, one that seemed so beyond my intellectual capacity that I almost resolved there and then to give up my dream of studying the sciences in high school. Perhaps I was meant, as I had originally intended, to study what seemed like the considerably friendlier humanities subjects. What had frightened me so?

Something called the ‘parallelogram law of vector addition.’ It appeared early in my physics textbook, in the second chapter, shortly after the one devoted to something called ‘dimensional analysis.’ While I knew what the geometrical figure termed a ‘parallelogram’ was, I did not know what a vector was, and I did not understand–could not begin to fathom!–what the former had to do with the ‘addition’ of the latter, especially as they seemed to be, from what I could make out, things with arrows, and were described by letters with, you guessed it, arrows above them. This was all black magic; perhaps there were mysterious potions and incantations handed out to initiates in order to enable their understanding of the dark arts of physics. So I retreated in panic; it took some mustering up of an elusive inner resolve to approach those books again.

Months later, deep into my eleventh grade, and having moved on well beyond the parallelogram law of vector addition, I was able to look back on my initial exposure to it with a complex mixture of mortification, relief and euphoria. I had not imagined that something so seemingly esoteric and inaccessible could ever be incorporated into my corpus of academic knowledge, into the grab bag of things known and grappled with. The knowledge of that transition from utter incomprehension to familiarity stood me in good stead on many occasions later; indeed, I would say I still rely on it when confronted with a seemingly insuperable intellectual task.

The Abiding ‘Mystery’ of Calculus

I first encountered calculus in the eleventh grade. A mysterious symbol had made an appearance in my physics text–in the section on dynamics–as we studied displacement, velocity and acceleration. What was this ds/dt thing anyway? I had, at that point in time, never studied calculus of any variety; to suddenly encounter a derivative was to be confronted with mystery of the highest kind. I asked for explanation and clarification; I received less than satisfactory obfuscation in response. Something about ‘instantaneous rate of change’, whatever that was.

A few months later, having encountered differential calculus in the mathematics syllabus, I was considerably, if not totally, edified. Functions, curves, graphs, tangents; somehow, I was able to partially relate the material we had studied in the physics class to this mathematical paraphernalia. And then, a little later, in the twelfth grade, having encountered integral calculus and then differential equations, other pieces of the puzzle fell into place as the relationship between mathematical apparatus, the models they comprised, and the physical world became a little clearer.

But as the story of my introduction to calculus–an abrupt exposure to its application and formalism in dynamical analysis–shows, calculus had an initial air of mystery that took some shaking. It had been suddenly introduced as a mathematical tool to enable grappling with a problem of physical mechanics, but the formal insights that lay at its core–especially the concept of a limit–were decidedly unfamiliar. More to the point, its use seemed utterly gratuitous; I could not see how my understanding of the physical details of velocity and acceleration had been improved in any way. And even when I did study differential calculus, I felt as if I became an expert manipulator of its many recipes and techniques well before I understood what my activity entailed. Syntactical manipulation, the transformation of one set of mathematical symbols into another according to a well-specified algorithmic procedure, was easy enough; understanding what those meant, and how they underwrote our understanding of the world of becoming and change, was a different matter.

We were science students in high school, ostensibly preparing ourselves for careers in engineering, medicine, and perhaps even basic research in the physical sciences; calculus was one of our most important tools. But we remained befuddled by its place in the conceptual apparatus of our studies for a very long time. This should be, and was then, a matter of some perplexity, especially when I consider how enlightened I felt when I better understood its place in making a changing world comprehensible.

Years on, when I became embroiled in debates over curricula in computer science undergraduate education, it occurred to me little had changed; many students remained perplexed by calculus’ importance in their education, by its most foundational presumptions and applications.Nothing quite exercises pedagogues like mathematics education, and in their catalog of perplexities, the failure to properly contextualize calculus should rank especially high. I’m almost tempted to describe it as a civilizational failure, so convinced am I of the judgment of any extraterrestrial visitors when confronted with this peculiar combination of indispensability and incomprehensibility in our epistemic scheme of things.