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.