ALICE +
BIT
THE
WHITE
------
RABBIT
Shortly before school dismissal, Mrs. Malone, my sixth grade teacher, chalks something wondrous on the blackboard:
ALICE +
BIT
THE
WHITE
------
RABBIT
It’s a cryptarithm! I know this! I’d encountered sums like
SEND + MORE = MONEY in library books.
The goal is to assign a digit to each letter so the equation holds. Distinct
letters are distinct digits, and leading zeroes are usually forbidden.
This one looks tougher than other cryptarithms I’d seen, and indeed, Mrs. Malone has no idea how to solve it. A friend had mentioned it to her. So it was certainly not homework; rather, she hopes we’ll grow curiouser and curiouser and take a crack at it ourselves.
Oddly, I worry whether 0 is legal. (I forget why. Maybe a digit was mistakenly defined as "1 to 9" and I blindly followed?) My errant belief leads me to doubt a solution exists because of the digits column. I overlook that there are ten distinct letters so the puzzle only makes sense if 0 is allowed.
I later show the puzzle to Mum, who promptly solves it. She instantly deduces E = 0 with no qualms, and uses bounds to argue that R = 1 and W = 9. The tens column means C + H + T is 10 or 20, and since 0, 1, 9 are accounted for, they are either 2, 3, 5 or 5, 7, 8 in some order. Adding the carry of this sum to I + I + T also yields 10 or 20, which whittles away more possible assignments. A few more flourishes flush out the answer.
The next morning, the puzzle remains perched at the front of the classroom, staring defiantly at us. But I know all its secrets.
Mrs. Malone enquires if anyone found the solution. I raise my hand, conceitedly noting my arm alone is aloft. She calls upon me to tell the whole class. O frabjous day! My chance to shine. I’m to share the ingenious tricks that make a molehill out of an apparent mountain. I bet they’ll get a kick out of this! I stride to the front of the room, and as I begin explaining why E = 0, Mrs. Malone interrupts me.
It turns out she just wants the digits. I concede I don’t know the substitutions by heart, but before I can add that it only takes a moment to find them, she unceremoniously boots me off the stage. I wordlessly slink back into my chair.
Why are those decade-old events indelibly seared on my neurons? They must have elicited strong emotional responses at the time.
Today, I’m most disturbed by the mathematical ineptitude of the person entrusted with my schooling in an "Opportunity Class" that let me in because I was good at taking tests. Though to her credit, she introduced this delightful gem to us in the first place, and made no attempt to hide her inability to tackle it.
While solutions are important, the methods to reach them are more important. ("Give a man a fish…"; I could also drop many a journey-versus-destination adage here.) In detective stories, catching the baddie is satisfying, but we enjoy them mostly for the cat-and-mouse game leading to the denouement. By itself, "the butler did it" has little value.
What did she hope to glean from the numbers? She could check they add up, but how would she know the solution is unique? How would she solve similar problems? How would she know if I were lying if I had claimed no solution existed? Some of these questions relate to the idea of mathematical proofs. Did she even know what they were?
Why was my teacher so keen to shut me up? What did she think I was going to do? A song and dance? If only she had kept her own mouth shut for a few seconds, I would have proved that the answer must be 67820 + 483 + 350 + 95830 = 164483. I didn’t remember this; I figured it out just now, because it’s easier and almost as fast.
There is a widespread notion that STEM is plugging numbers into formulas and the word "creative" should be reserved for non-STEM fields. My experiences illustrate that these are pernicious myths perpetuated by the establishment; the system; the Man. In truth, it is Scientists who light candles in the dark (and Technologists who upgrade those candles to efficient and affordable LEDs); it is Engineers who reveal the face of God; it is Mathematicians who look on Beauty bare, a beauty sublimely pure, and capable of a stern perfection such as only the greatest art can show.
Enough proselytizing for now. There’s more to my story: noticing someone’s shortcomings seems insufficiently traumatic to scar one’s memory. (At least I hope so, for the sake of those who interact with me!) Thus we look further afield.
The subjects of the Milgram experiments felt unease when an authority figure issued orders that conflicted with their conscience. This resonates with me, but the Asch conformity experiments fit better. While I did feel reluctant to obey, my brain has spun my old memory so that I now perceive it as a triumph over a feeling akin to loneliness. Nobody else had raised their hand. Nobody spoke of the puzzle again. Was I the only one who cared? Then so be it! I refuse to conform.
To use terms from Asch’s reports, I was "independent", and not one who "yielded" because I overcame self-doubt and a desire to be normative. Though I prefer Henley’s words: my head was bloody, but unbowed.
Another memory comes to mind:
A couple of years after Alice bit the White Rabbit, I’m in a different school. The next step in a production line of the education factory.
I’m sitting at a table with two students whose grades are the envy of the entire year. It’s the perfect opportunity to share the secret to solving quadratic equations, which I had learned recently. Surely these academic rock stars would appreciate the elegant technique that is almost indistinguishable from magic. Surely they’d enjoy being a god amongst men, with the power to solve equations that dumbfound mere mortals.
Instead, after I demonstrate how to complete the square, the guy who tops every class he takes (except for mathematics; I topped that one) mockingly smirks: "Why would we want to know that?"
I’m stunned into silence, even though I know a good answer for him: "Because you’ll have a head start when they teach it to us within a year or so" (by which time one needs new superpowers to stand out). Despite their intelligence and strong work ethic, even these two view mathematics as plugging numbers in formulas to get high marks.
This is a valuable skill, but they could easily have so much more. I hope my schoolmates change their attitudes one day. Nonetheless, it’s not my problem.
A couple of years later, I learn the secret to defeat cubic equations. I keep it to myself.
Despite the absence of a clueless authority figure, I vividly recollect this episode, suggesting the emotions studied in the Asch conformity experiments are most responsible for the formation of both of the above memories.
So if you’re a student wondering: "Is it just me, or does mathematics possess an unearthly beauty?", the answer might be: yes, mathematics is beautiful, and yes, it is just you who sees it.
Hang in there. It gets better, especially after you find your tribe. Until then, never give the normies an inch. By this, I mean you should stay true to yourself; not openly rebel! It’s risky to antagonize anyone in positions of authority; to bite the hand that feeds you. Suffer fools gladly, particularly those with power over you.
Bide your time should you wish to pen a jeremiad like this one. (No longer do academic grades hold sway over me. If anything, the tables have turned, and I’m the one dishing them out. It is others who must suffer me.)
Lastly, the Asch experiments are a warning to everyone, whether or not you’re a fan of mathematics. Beware of groupthink. I must heed this advice more myself, as past failures to do so have made me poorer, literally and figuratively. While it could be that you really are wrong and everyone else really is right, let the data change your mind, and not that nagging, unsettling, dark feeling that springs from a natural human desire to go along with the rest.