Surely You Are Joking, Mr. Pathrose

Freud would probably have something to say about it, but for some odd reason a number of my memories about school relate to totally dumb moments, mostly involving my own angelic self. Some have been just outright funny, others embarrassing, but the indelible memories are the ones that have been truly humbling. Simply, incredibly, humbling. Or humiliating. Or both.

While I would readily admit that I was seldom the smartest kid in class, in my own defense I wasn't totally dumb either. (For those that know me today and would argue that point, the total dumbness you witness didn't come till I discovered alcohol in a meaningful way). It is true that angels did not break into spontaneous aria when I walked into class, but the affirmative-action-for-the-stupid recruiting team also didn't have my parents on their A-list. So when Mr. Pathrose in his unique way let it be known that the probability he was trying to teach was not the version I was imbibing, the words remain etched in a corner of my brain. It has taken 22 years but finally I think I am ready to tell all.

To introduce Mr. Pathrose (affectionately known as Patty by all who loved him), try imagining a combination of Hercule Poirot, M. C. Escher, and Professor Calculus. It was well known he built electronic circuits as a mode of relaxation, his form of deep breathing as it were. One thing was clear - Mr. P. had forgotten more mathematics than most of us would ever learn. To give you a sense of how good he was, even Anindya Nandi didn't practice his cricket strokes to imaginary good-length balls from Imran Khan at the back of the class when Patty was in action.

This Mr. Pathrose was the architect of all things math in the last two years of school including many a week he spent teaching us combinatorics and permutatorics (ok, permutations and combinations if you insist). He apparently felt that before graduating high school it was important for people to be able to write things like 7! and that the path to happiness lay in being able to mind your Ps & Cs. Well, ours not to reason why. Ours, as you will see, but to do and cry.

His teaching methodology included frequent examinations euphemistically called "quizzes" to gauge the limited extent to which his tutelage had been imbuing his genius. Most of these quizzes contained 3 - 5 questions with typically the kinds of things you could answer in 10 - 15 minutes, and so naturally by some fuzzy logic, he would give us 5 questions to answer in the first 5 minutes of class and call it a quiz. He would then nonchalantly proceed to spend the rest of the period discussing why Euclidean geometry failed on a sphere - a subject of import to those one assumes destined to draw lines on spheres (one can but hope, since if it doesn't help them, I can only scratch my head as to the point of the exercise).

Anyway, typical quizzes would be of the following variety:

"You are given 24 square tables, but the tables must be used as rectangles, not squares i.e. two together. How many combinations can be made with the 24 tables? (3 points)

What is the maximum number of people that can be made to sit at the tables and under what combination? (4 points)

What is the least number of people that can be made to sit at the tables and under what combination? (3 points)".

Notwithstanding why one would ever put tables together in this rather pointless way or how it actually matters whether there are 2 or 274556 ways to combine these tables, we agonized over such questions for the 5 minutes we were given and then agonized for the remaining 45 minutes of class over just how stupid we had looked with our responses. Disapproval from the master was not a thought one enjoyed, although it was unclear if there was a legitimate way to avoid it.

So anyway this is the Patty we talk about.

Question: "What is the probability that a random 4 digit number is divisible by 7?"

That was it - the question that did me in. The one that has stuck to my brain like a leech on steroids. One that after years of supposedly growing up I have never been able to expel from the little cerebellum I possess. As alluded to earlier, littler though that cerebellum has gotten through constant infusions of alcohol but that question has not been erased from its confines. (My research into this intriguing subject has indicated that said painful memory could be lodged elsewhere - I seem to remember other useless facts like brains have cerebrums and medullas as well. I take clear exception with why some silly biologist would break an already tiny organ into 3 differently named parts, but in the interest of staying on point we shall save that for another day and another diatribe. Regardless though of the number of pieces you might say my brain has, I doubt it should in normal course have allowed the following humiliation to stick on anywhere - since one hopes it is prioritizing what it retains. It is evident the entire organ has shrunk in inverse proportion to age. Hmm or should I say "grown in inverse proportion with age?" Or "shrunk in direct proportion with age"? Heck if I know, go ask Patty.)

In any case, Patty started class that fateful day with this one question. Simple, straightforward and so seemingly innocuous that yours truly looked at it with contempt, shrugged, and wondered if Patty was highly over-rated after all. If the gentleman from the post office who we had introduced in a separate part of this treatise had been around - the one that had politely inquired whether I was from Delhi - he could have confirmed that the attitude I exhibited at this moment was identical to the one he had experienced. You see, no matter how you examined the problem, which angle you saw it from, it seemed like this was so rudimentary that I couldn't believe Patty himself had offered it up as a real problem to brilliant minds like mine. Clearly the shine was off, the man I had revered for so long falling off in one fell swoop from the pedestal I had raised him on. All this build up and one simple quiz question had burst the bubble. I will mix other metaphors as soon as I can remember them.

Answer: "A number is either divisible by 7 or it isn't.
Hence, P(random 4 digit number is divisible by 7) = 1/2"
QED (Quite Easily Done)

I got the quiz back the next day - it had a number, that looked like 0, a clear mistake obviously. He had meant to write 10/10 of course. I continued to read on, expecting some trivial error on his part, driven by the senility of the has-been Math teacher. The short remark that followed stung like a two-by-four into my stomach.

"Surely you are joking Mr. Agrawal. Even by your Quixotic standards, this lacks logic. Just so you know, 14 of every 100 numbers between 1000 and 9999 are divisible by 7. Next time, take your time and don't do it quite so easily."