Reunions And Changing Persons

A couple of weeks ago, in a reunion of sorts, I had lunch with some folks I to went high school with; six of us attended. Out of the attendees, I was meeting three after a gap of thirty-four years. This is the longest interval of time in my life between two meetings with the ‘same person.’ The reason for those quotes should be evident to all of those who have undergone such encounters: very often, our intuitions about the identity of those we meet after such a long time are shaken by the differences between the two stages of their ‘growth’ or ‘evolution’ that we have encountered.  Moreover, in these encounters, we experience something of the puzzling nature of time and memory: Where have all those years gone? Is the past a place? Why do those past events seem so ephemeral? How can the memories of events so distant in time be so much fresher than the memory of yesterday’s events? The chilling thought crosses our mind that perhaps we will experience a similar sensation on our deathbeds, if we are fortunate enough to be lucid to experience them as such–will we experience then, just as now, the curious sensation of two points in time, seemingly separated by an insuperable gap, folding as it were to make contact with each other? Will all that came before seem like a ‘mere dream’?

That afternoon in Palo Alto, as I sat in a backyard patio, enjoying pizza and salad in the company of my high school friends, I was struck by variants of these thoughts. Across the table from me sat my five-year old daughter, on my left sat a classmate from thirty-four years ago. My daughter perplexes me consistently with her ever changing self; she is not the girl she was a year ago; she is not the tantrum throwing toddler from three years ago; she is not the babbling language learner from four years ago; she is not the infant of five years ago; soon, her present self will change, ever so imperceptibly, into its next ‘stage.’ My friend looked a lot like she used to but she sounded different; her accent was modulated, she spoke of college-age daughters. At another end of the table sat another friend; his turban was gone, his hair was a silvery white–his appearance was so radically dissimilar that I put the older self I knew out of mind and concentrated on the one present at the moment. In the case of yet another one of my friends, we had realized that we had hardly known each other in school, hardly ever conversed; yet, here, now that we had met, our new selves liked each other well enough to fall almost instantly into a pattern of behavior that approximated that of old friends; our old selves were the anchoring memory that allowed us to so easily trade in a kind of otherwise inaccessible familiarity.

Here, new relationships were possible, indeed, they were necessary. The older lives offered material for reminiscing; our new selves and lives possibilities for new friendships configured on different grounds.

The Endless Surprises Of Memory

Memory is a truly wondrous thing. A couple of weeks ago, I met an old friend’s younger brother for lunch in midtown Manhattan; we were meeting after over thirty years. We ordered food, grabbed our trays, and headed to a table, our conversation already picking up pace as we did so. We talked about our high school days (his brother and I had been in the same class; the ‘kid’ had been a year junior); I asked about his sister, whose home in Delaware I had visited a few times during my first years in the United States; we laughed uproariously, as all those who reunite seem to do, when recounting tales of days gone by, which now suddenly seem more peculiar, more distinctive, with their ever-increasing vintage; and of course, we talked about my friend, now physically absent, but who loomed larger than life as the reason which had brought our two lives together. In the course of our conversation, I made note of how I  used to walk over to my friends’ home in New Delhi; the section of town I lived in was about a mile or so away, and walking and biking roads offered an easy connection. As I offered up this little recollection, a thought went through my mind; my friend’s house, like all those in planned ‘residential colonies’ in New Delhi, had an alphanumeric address consisting of a ‘block’ letter and a number; it seemed to me I could remember it. (Mine was S-333; the three hundred and thirty-third residential ‘plot’ in ‘S’ Block. Quite obviously, I remembered this address; only a nihilist cannot remember his childhood home’s location.)

This fact, of my being able to remember my friend’s old address, caused me some astonishment; I sought confirmation of this remarkable feat. I asked my friend for some; he supplied it. I had remembered his childhood home’s address–I-1805–clearly and distinctly. I had not thought about this alphanumeric combination for over thirty years now; and yet, somehow, by dint of being placed into a context in which it was relevant, I had been able to summon up its details with little difficulty. Other details came flooding back too, unprompted and unbidden. I felt an older self within me stir; amnesia fell away.

I will freely admit–as an immigrant who lost his parents a very long time ago–to being obsessed with memory and nostalgia and recollection. (I am surprised that I did not do more academic work on memory, given my interests in the philosophy of mind and the conceptual foundations of artificial intelligence; I am unsurprised that I was deeply fascinated by the work my friend John Sutton did in the same field.)  Here again, was another instance of why this particular human capacity captivated me endlessly. And I could not but wonder yet again about the nature of my self, and of the interactions of memory with it: how much remained, ‘locked away,’ in the recesses of my cranial stories, merely awaiting for the right contextual cue to be reinvigorated; are there other discoveries and understandings of myself possible as a result?

The Most Useful Algebra Lesson Of All

I first encountered algebra in the sixth grade. Numbers disappeared–or at least, were consigned to secondary importance–and letters, mysterious ones like x, y, z, took center stage.  A mathematical expression called the ‘equation’–an incomprehensible sentence underwritten by an esoteric grammar–emerged on my intellectual horizon. (Strictly speaking, my teachers were rigorous enough to call these things ‘linear equations’ but all I could remember was the second word.) The rules for manipulating it, and triumphantly emerging from these machinations with the value of x held high as a trophy for all to see were, as my descriptions above might indicate, utterly incomprehensible to me. I stepped into the water and I immediately floundered, casting about in panic.

Unwilling to seek help outside the confines of my classroom–I did not press my brother, two grades senior to me, or my parents, for assistance with my lessons or my homework, which I was often submitting incomplete and incorrect–I was setting myself up for disaster. The axe fell eventually. In the first of the year’s so-called ‘terminal’ exams–because they were staged at the end of an academic term–I obtained a grand total of sixteen ‘marks’ out of hundred. It was an ‘epic fail,’ long before that term had acquired any currency.

Unfortunately, my fame in this domain of academic achievement did not, and indeed, could not, go unnoticed. My grades were noted on a ‘progress report’ and I was asked to bring it back to school, duly signed by my parents.  When I, hoping to escape the wrath of my father, showed it to my mother, she took one look at my math grade and told me he would sign the report instead. (This transference of responsibilities reflected a traditional division of parental labor when it came to my education; my mother helped me with the ‘humanities,’ my father with the ‘sciences.’)

My ‘interview’ with my father did not go well. He was perplexed by my grade, but even more so by my exam answer-book. I had executed some bizarre, inexplicable mathematical maneuvers, strewing symbols and numbers gaily all over its pages, thus allowing my teacher to grant me a few charity points for visible effort. Most embarrassingly, my father was able to surmise I had cheated, for I could not explain why certain moves had been made by me. (Indeed, I had; I had sent several panicked sideways glances at my neighbor’s answer-book during that fateful exam.) My mother sat close by, watching this interrogation–and my discomfiture–quietly. I could see my father’s visage tautening, his nostrils flaring. A stinging slap that would inflame my cheeks and set my ears ringing was probably headed my way. This was a man who had brooked no incompetence in his subordinates in his days in the air force; he would not stand for this display of stupidity and confusion on my part.

My father finally spoke, “Go get your maths book.” I complied. My father pulled out a notepad and a pen, looked at me, and spoke again, “Algebra is easy if you follow the rules.” I had no idea what those were.

I soon found out. My father explained to me what variables, constants, and coefficients–fractional and whole–were;  he told me I had to “bring all the variables to one side, and all the constants to the other”; I was supposed to “change signs when you change sides”; and so on.  It was not smooth sailing: on one occasion, after I had failed, yet again, to internalize one of my father’s instructions and committed a howler, he, overcome by exasperation, turned to my mother and confessed he would like to throttle me. I quaked and quivered, but he did not make good on that threat. He did though, tell me he would not let me go to sleep till I had mastered the art of solving linear equations.

The night wore on. My mother went to bed. My father and I continued to work through one problem after another. Slowly, algebra became comprehensible; indeed, it made perfect sense, and even began to appear as a little bit of a lark, a sleight of hand, a riddle with a key that could be made to work for you, and not just wizards and magicians. It was entirely plebeian; the masses could partake of its pleasures too.

Finally, my father assigned a set of problems for me to solve and bade me go into the living room to work on them by myself. If I solved them correctly, I could go to bed at last. I got to work; my father began his bedtime ritual of changing clothes and brushing his teeth. A few minutes later, he opened the door of the living room to check on my progress: Was I moving along? I said I was.

Once I thought I was done, I took my work over to my father. For a minute or two, he sat there, looking impassively at my scribbles. Then, he looked up and said, “Good work; go to sleep. You’ve got it.” I complied again.

I never became a mathematician. But I never feared the ‘lazy man’s arithmetic’¹ again.


  1. Legend has it that this is how Einstein’s father explained the heart of algebra to him: ‘you just act as if you know what is.’

A Stutterer and His Cure

In the seventh grade, at the age of eleven, I began to stutter. It began without apparent reason; all too suddenly, I found myself tripping over consonants and unable to begin speaking words that began with vowels. When asked to speak up in class, I found I needed a visible act of physical exertion to get the words rolling; often, I would have to step out from behind my desk with a little skip or hop, an act that never failed to provoke giggles in my classmates and sometimes even my teachers, who would look at me with expressions part amused, part quizzical. I had never stuttered before; I was mortified and humiliated and crushed.

My stuttering was plain for all to see; my audience included my parents. My mother was intelligent and sensitive enough to realize this affliction had a psychological provenance though she could not begin to guess at what it was. Perhaps because I had changed schools the previous year; perhaps because I was still struggling to adjust life as a ‘civilian’ after my father’s retirement from the air force. I had never been particularly gregarious or extroverted, but now, some other barrier to social interaction had arisen from deep within me and laid a formidable roadblock in front of me. I showed no signs of being able to negotiate it.

My mother sought help. She was directed to a child psychologist–reputed to be of sympathetic temperament and disposition–whose offices were located conveniently near by to our home, a mere short bus-ride away. When she told me she planned to take me there for a consultation, I was agreeable. I liked the idea of being ‘treated’ and more to the point, I was curious about what a ‘psychologist’ did. How would she ‘cure’ me? What was the ‘treatment’ like?

Our first meeting with the psychologist went pleasantly enough; my mother and I met her together and provided her with some elementary details on our family, my school life, my friends, my daily activities, and of course, my immediate history preceding the outbreak of stuttering.

This intake meeting out of the way, my sessions with my therapist began. Twice a week, after school, my mother and I traveled by bus to her office, and then, while my mother waited for me, I went into the therapist’s office for an hour. This was a talking cure for talking; so we talked.

It is now almost thirty-five years since those sessions, so I can remember little of them. I do remember my therapist’s gentleness, her curiousness. I think her diagnosis, such as it was, of my stuttering, was that a shy boy had become even more so; that my inability to come out of my shell in my new school, to make friends in my neighborhood, my constant retreat into my books, had driven even my spoken expression back into me, repressed and suppressed it.

In the end, the ‘cure’ was effectuated by the simplest of means; she was a stranger, and she was kind, and she spoke to me, and listened to me and humored me. Those conversations, by themselves, drew me out of my shell and encouraged me to speak. She did not discipline me; she was not harsh; she did not rebuke me or mock me; she listened a great deal. I spoke, I complained, I bemoaned the changes in my life, I spoke of what I felt was missing in my life.

After every session, my mother would ask me how it had gone, and I would always have the same answer: It went well. I grew to like my therapist and looked forward to my bi-weekly  conversations with her.

A few months later, my therapist told my mother I was ‘cured.’ Indeed, I was. I had stopped stuttering; or at least, the most noticeable forms of my affliction were now gone. I do not remember if we did any follow-ups, or if I was upset at having ended the treatment. In any case, soon thereafter, I left home for boarding school. Nothing quite convinced me how valuable my sessions with her had been than my time in boarding school; dealing with its feral residents while suffering from a stutter would have been misery.

Traces of my stutter still survive; when I am angry, stressed out, unhappy, or otherwise not quite psychically comfortable, I notice myself tripping over words, unable again, to begin words with vowels. At those times, the only remedy I can seek is to simply slow down, stop speaking, retreat, and then try again.

I wonder where my therapist is; I never found out her name, never met her again. Here is a belated thank you.

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.

A Long, Hot, Sickened Journey

The worst of the heat might have receded from New York City but that’s not going to deter me from churning out another hot weather-related blog post. On this occasion, about a time when a combination of heat and a mysterious ailment combined to induce in me a misery that has, thankfully, not been rivaled since.

In 1979, I went on a schoolboys trip to a national park, one organized by my school. The trip was everything it was promised to be: though we missed out on spotting a tiger, we saw plenty of wildlife, swam in rivers, went on long hikes, and rounded off each day with a festive campfire. It was a boy’s dream; I loved every minute of it and was saddened by the dawning of its final days. Those entailed a long bus ride back home to New Delhi.

It was April, and the summer had settled in on North India. Daytime temperatures were already reaching into the high nineties (Fahrenheit) and past the hundred mark. The journey back, in a non-airconditioned bus, promised to be a  trying experience. It soon acquired a terrifying new dimension.

For by its commencement, I had become sick. Perhaps a stomach bug of some sort, but though there was pain and churning aplenty in my belly, there were no frequent trips to the bathroom. Instead, I felt weak and nauseous, with a head that spun furiously. I told my companions; little interest or sympathy was forthcoming. I informed the master in charge; he seemed nonplussed. Tired, worn out, and to be honest, a little scared, I withdrew–unmedicated–to a seat by a window, and waited.

Our bus drove on, on roads that were sometimes narrow, sometimes bumpy, sometimes dusty, past field and village and town. As the day progressed, so did the heat and my discomfort.  I kept the window open, hoping for a breeze or two, and sank into a sweat-lined heap at its base. I was sick, sick, sick; a bundle of desperate sensations, hoping for relief in any shape or form.

Toward the middle of the afternoon, we approached a scheduled halt. We would rest and partake of lunch in a park. My illness was now at a crest; I felt close to death, hideously miserable and discombobulated. I staggered out and took a few steps toward a shady spot beneath a tree.

And then, the miracle. I vomited spectacularly, bringing up a torrent of unprocessed material from my last meals. My company scattered, perhaps in fear, perhaps in awe. I swayed; my ability to stay on my feet still seemed in question. But a few seconds later, I felt better. The expulsion had, mysteriously and thankfully, possessed a cleansing quality.

A few minutes later, someone pressed a glass filled with crushed ice and a Coke into my hand. I drank it greedily–the sweetest nectar ever. I still had no appetite, but a cold, sweet drink was welcome.

Home was still several hours away, but for the rest of the drive home, though I still felt weak and exhausted, I was never as sick as I had been earlier in the day. I reached my destination at night, back into the arms of my concerned mother and a bemused father.

I still do not know what had afflicted me that day. And I still continue to hope that I will never, ever, approach the desperate depths of discomfort attained that day via a toxic combination of head-spinning nausea and heat.