My mom used to say that when your child is as big as you, you have to treat them with respect. What she actually said was that you had to address them using a respectful form of “you,” which doesn’t make any sense in English, but may work in Hindi or French. It worked poetically well in Malayalam. I was reminded of this maternal pearl of wisdom recently when I was watching a movie with my son.
At some point in their life, most parents of teenage children would have asked a question very similar to the one Cypher asked in Matrix, “Why, oh, why didn’t I take the blue pill?” Did I really have to have these kids? Don’t get me wrong, I have no particular beef with my children, they are both very nice kids. Besides, I am not at all a demanding parent, which makes everything work out quite nicely. But this general question still remains: Why do people feel the need to have children?
Just read the news that Prof Maryam Mirzakhani won the prestigious Fields medal (the equivalent of Nobel prize in Mathematics). She is the first woman to ever win the prize. First of all, congratulations to her. Coming from an Iranian background, being a woman, I’m sure it must have been hard for her.
Women seem to have difficulties in quantitative fields — we see this everywhere. The general belief is that compared to men, women are more creative and intuitive, but less analytical. They take in the world as a whole. Theirs is a romantic understanding, concentrating on the immediate appearance and values of the objects around them. This mode of understanding is to be contrasted with the analytic, classical understanding of men, who seem to mentally divide things in smaller, manageable chunks and drill down to the underlying forms to come to grip with world around them. In giving this description, I’m trying to paraphrase what Richard Pirsig said in the opening chapters of Zen and the Art of Motorcycle Maintenance. The analytic mode of understanding lends itself better to quantitative fields like mathematics, and hence the paucity of brilliance among female mathematicians.
A few years ago, I had significant income from online advertising because of my networked business model that worked extremely well at that time. At one point the ad serving company decided to cancel my account because some sites in my network violated their terms and conditions. They told me that they couldn’t pay me for the last two months because they had already refunded the money to the advertisers who were outraged at my T & C violations. Mind you, it was a small fortune. But a couple of months later, they decided to reinstate me. The first thing they did after reactivating my account was to pay me my outstanding balance — the money they had “refunded” to their disgruntled advertisers. I, of course, was quite gruntled about the outcome. But the joy didn’t last; they banned me again a month later.
Long time ago, I had a run-in with an insurance company. It was after my first trip back home from the US. During my four years in the sanitized and relatively virus-free conditions of upstate New York, my natural third-world immunity had deteriorated significantly, and I came back from India with a bad respiratory infection, which had stopped responding to the antibiotics my doctor uncle had prescribed me. So I went to the emergency room at the Tompkins County Hospital in Ithaca, where they determined that I had pneumonia. The medical bill came up to over $450, and had multiple parts to it, like the X-Ray, radiologist’s fees, physician’s fees, ER fee, pharmacy etc. For payment, I handed them my student insurance card and went home.
A couple of weeks later, the hospital called me to tell me that the insurance had refused to pay one out of the many bills and that I still owed them about $80. I found it weird and ask them to try again, and went back to my PhD and whatnot. Then the insurance company told me that they were refusing because the procedure was not “pre-approved.” Weirder — how could one part of the same ER visit have different reimbursement criteria? Anyway, I proceeded to ignore the bill, which soon got handed over to some collection agency who started making harassing calls to me.
The whole thing went on for a few months before I decided enough was enough. Luckily, my university had a free legal service. So I went and met Mike Matterson (or some such name) at the legal office. He listened to my plight sympathetically, and advised me that it was pointless fighting some small battles in which you would lose even if you won. But he called the insurance company and proceeded thus, “Hello, this is Mike Matterson, attorney at law, calling on behalf of Manoj Thulasidas. I would like to make a few enquiries.” True, he had to rehearse my name a few times, but he made the whole opening salvo sound impressive. At least, I was impressed with this courtroom drama unfolding before my very eyes. But nothing really happened and I went back to my Danby Road apartment determined to stretch the payment a few more weeks if possible.
But four days later, I get this letter from the insurance company stating that they had decided to pay the bill in full — pre-approved or not. I realized that a call from a lawyer meant something to the company. It meant trouble, and they didn’t want to fight a small battle either. I wondered if this was a standard practice on their part — refusing a legitimate reimbursement if the amount is too small for the policy holder to wage a legal war.
Another incident taught me that it might well be. A family friend of ours passed away a few years ago. His widow knew that he, being the prudent and caring soul he was, had some life insurance policies, but could not find the papers. So she called the two major insurance companies here and made inquiries using his national identification number. Both companies expressed their condolences to the widow, but regretted that the late husband had no policy with them. Never heard of him, in fact. A few days later, while going through his papers, she found the policies with the same two companies. She called again, and the reply was, “Oh yeah, of course. Sorry, it was an oversight.” If it was just one company, it might have been an oversight. Is it again part of the corporate policy to discourage policy payouts if at all possible? Uninsured until proven otherwise?
If you have had similar experiences with insurance companies, why not leave your story as a comment below?
Once a favorite uncle of mine gave me a pen. This uncle was a soldier in the Indian Army at that time. Soldiers used to come home for a couple of months every year or so, and give gifts to everybody in the extended family. There was a sense of entitlement about the whole thing, and it never occurred to the gift takers that they could perhaps give something back as well. During the past couple of decades, things changed. The gift takers would flock around the rich “Gulf Malayalees” (Keralite migrant workers in the Middle-East) thereby severely diminishing the social standing of the poor soldiers.
Anyway, this pen that I got from my uncle was a handsome matte-gold specimen of a brand called Crest, possibly smuggled over the Chinese border at the foothills of the Himalayas and procured by my uncle. I was pretty proud of this prized possession of mine, as I guess I have been of all my possessions in later years. But the pen didn’t last that long — it got stolen by an older boy with whom I had to share a desk during a test in the summer of 1977.
I was devastated by the loss. More than that, I was terrified of letting my mother know for I knew that she wasn’t going to take kindly to it. I guess I should have been more careful and kept the pen on my person at all times. Sure enough, my mom was livid with anger at the loss of this gift from her brother. A proponent of tough love, she told me to go find the pen, and not to return without it. Now, that was a dangerous move. What my mom didn’t appreciate was that I took most directives literally. I still do. It was already late in the evening when I set out on my hopeless errant, and it was unlikely that I would have returned at all since I wasn’t supposed to, not without the pen.
My dad got home a couple of hours later, and was shocked at the turn of events. He certainly didn’t believe in tough love, far from it. Or perhaps he had a sense of my literal disposition, having been a victim of it earlier. Anyway, he came looking for me and found me wandering aimlessly around my locked up school some ten kilometer from home.
Parenting is a balancing act. You have to exercise tough love, lest your child should not be prepared for the harsh world later on in life. You have to show love and affection as well so that your child may feel emotionally secure. You have to provide for your your child without being overindulgent, or you would end up spoiling them. You have to give them freedom and space to grow, but you shouldn’t become detached and uncaring. Tuning your behavior to the right pitch on so many dimensions is what makes parenting a difficult art to master. What makes it really scary is the fact that you get only one shot at it. If you get it wrong, the ripples of your errors may last a lot longer than you can imagine. Once when I got upset with him, my son (far wiser than his six years then) told me that I had to be careful, for he would be treating his children the way I treated him. But then, we already know this, don’t we?
My mother did prepare me for an unforgiving real world, and my father nurtured enough kindness in me. The combination is perhaps not too bad. But we all would like to do better than our parents. In my case, I use a simple trick to modulate my behavior to and treatment of my children. I try to picture myself at the receiving end of the said treatment. If I should feel uncared for or unfairly treated, the behavior needs fine-tuning.
This trick does not work all the time because it usually comes after the fact. We first act in response to a situation, before we have time to do a rational cost benefit analysis. There must be another way of doing it right. May be it is just a question of developing a lot of patience and kindness. You know, there are times when I wish I could ask my father.
I have been called a lot of unflattering things in my life. One of the earlier ones of that series was that I was hard-hearted, which I countered by pointing out that I was perhaps harder on myself than anybody else. Thankfully, my accuser concurred. One of the recent epithets in the same vein is that I’m cold and calculated, and I use my head to think rather than my heart; I believe it is a fair assessment. Then again, using my head is the only way I know how to think (which, of course, is exactly the sort of cynical comments that earned me the said assessment.)
Despite the richness that mathematics imparts to life, it remains a hated and difficult subject to many. I feel that the difficulty stems from the early and often permanent disconnect between math and reality. It is hard to memorize that the reciprocals of bigger numbers are smaller, while it is fun to figure out that if you had more people sharing a pizza, you get a smaller slice. Figuring out is fun, memorizing — not so much. Mathematics, being a formal representation of the patterns in reality, doesn’t put too much emphasis on the figuring out part, and it is plain lost on many. To repeat that statement with mathematical precision — math is syntactically rich and rigorous, but semantically weak. Syntax can build on itself, and often shake off its semantic riders like an unruly horse. Worse, it can metamorphose into different semantic forms that look vastly different from one another. It takes a student a few years to notice that complex numbers, vector algebra, coordinate geometry, linear algebra and trigonometry are all essentially different syntactical descriptions of Euclidean geometry. Those who excel in mathematics are, I presume, the ones who have developed their own semantic perspectives to rein in the seemingly wild syntactical beast.
Physics also can provide beautiful semantic contexts to the empty formalisms of advanced mathematics. Look at Minkowski space and Riemannian geometry, for instance, and how Einstein turned them into descriptions of our perceived reality. In addition to providing semantics to mathematical formalism, science also promotes a worldview based on critical thinking and a ferociously scrupulous scientific integrity. It is an attitude of examining one’s conclusions, assumptions and hypotheses mercilessly to convince oneself that nothing has been overlooked. Nowhere is this nitpicking obsession more evident than in experimental physics. Physicists report their measurements with two sets of errors — a statistical error representing the fact that they have made only a finite number of observations, and a systematic error that is supposed to account for the inaccuracies in methodology, assumptions etc.
We may find it interesting to look at the counterpart of this scientific integrity in our neck of the woods — quantitative finance, which decorates the syntactical edifice of stochastic calculus with dollar-and-cents semantics, of a kind that ends up in annual reports and generates performance bonuses. One might even say that it has a profound impact on the global economy as a whole. Given this impact, how do we assign errors and confidence levels to our results? To illustrate it with an example, when a trading system reports the P/L of a trade as, say, seven million, is it $7,000,000 +/- $5,000,000 or is it $7,000, 000 +/- $5000? The latter, clearly, holds more value for the financial institution and should be rewarded more than the former. We are aware of it. We estimate the errors in terms of the volatility and sensitivities of the returns and apply P/L reserves. But how do we handle other systematic errors? How do we measure the impact of our assumptions on market liquidity, information symmetry etc., and assign dollar values to the resulting errors? If we had been scrupulous about error propagations of this, perhaps the financial crisis of 2008 would not have come about.
Although mathematicians are, in general, free of such critical self-doubts as physicists — precisely because of a total disconnect between their syntactical wizardry and its semantic contexts, in my opinion — there are some who take the validity of their assumptions almost too seriously. I remember this professor of mine who taught us mathematical induction. After proving some minor theorem using it on the blackboard (yes it was before the era of whiteboards), he asked us whether he had proved it. We said, sure, he had done it right front of us. He then said, “Ah, but you should ask yourselves if mathematical induction is right.” If I think of him as a great mathematician, it is perhaps only because of the common romantic fancy of ours that glorifies our past teachers. But I am fairly certain that the recognition of the possible fallacy in my glorification is a direct result of the seeds he planted with his statement.
My professor may have taken this self-doubt business too far; it is perhaps not healthy or practical to question the very backdrop of our rationality and logic. What is more important is to ensure the sanity of the results we arrive at, employing the formidable syntactical machinery at our disposal. The only way to maintain an attitude of healthy self-doubt and the consequent sanity checks is to jealously guard the connection between the patterns of reality and the formalisms in mathematics. And that, in my opinion, would be the right way to develop a love for math as well.
Most kids love patterns. Math is just patterns. So is life. Math, therefore, is merely a formal way of describing life, or at least the patterns we encounter in life. If the connection between life, patterns and math can be maintained, it follows that kids should love math. And love of math should generate an analytic ability (or what I would call a mathematical ability) to understand and do most things well. For instance, I wrote of a connection “between” three things a couple of sentences ago. I know that it has to be bad English because I see three vertices of a triangle and then one connection doesn’t make sense. A good writer would probably put it better instinctively. A mathematical writer like me would realize that the word “between” is good enough in this context — the subliminal jar on your sense of grammar that it creates can be compensated for or ignored in casual writing. I wouldn’t leave it standing in a book or a published column (except this one because I want to highlight it.)
My point is that it is my love for math that lets me do a large number of things fairly well. As a writer, for instance, I have done rather well. But I attribute my success to a certain mathematical ability rather than literary talent. I would never start a book with something like, “It was the best of times, it was the worst of times.” As an opening sentence, by all the mathematical rules of writing I have formulated for myself, this one just doesn’t measure up. Yet we all know that Dickens’s opening, following no rules of mine, is perhaps the best in English literature. I will probably cook up something similar someday because I see how it summarizes the book, and highlights the disparity between the haves and the have-nots mirrored in the contrasting lead characters and so on. In other words, I see how it works and may assimilate it into my cookbook of rules (if I can ever figure out how), and the process of assimilation is mathematical in nature, especially when it is a conscious effort. Similar fuzzy rule-based approaches can help you be a reasonably clever artist, employee, manager or anything that you set your sights on, which is why I once bragged to my wife that I could learn Indian classical music despite the fact that I am practically tone-deaf.
So loving math is a probably a good thing, in spite of its apparent disadvantage vis-a-vis cheerleaders. But I am yet to address my central theme — how do we actively encourage and develop a love for math among the next generation? I am not talking about making people good at math; I’m not concerned with teaching techniques per se. I think Singapore already does a good job with that. But to get people to like math the same way they like, say, their music or cars or cigarettes or football takes a bit more imagination. I think we can accomplish it by keeping the underlying patterns on the foreground. So instead of telling my children that 1/4 is bigger than 1/6 because 4 is smaller than 6, I say to them, “You order one pizza for some kids. Do you think each will get more if we had four kids or six kids sharing it?”
From my earlier example on geographic distances and degrees, I fancy my daughter will one day figure out that each degree (or about 100km — corrected by 5% and 6%) means four minutes of jet lag. She might even wonder why 60 appears in degrees and minutes and seconds, and learn something about number system basis and so on. Mathematics really does lead to a richer perspective on life. All it takes on our part is perhaps only to share the pleasure of enjoying this richness. At least, that’s my hope.
If you love math, you are a geek — with stock options in your future, but no cheerleaders. So getting a child to love mathematics is a questionable gift — are we really doing them a favor? Recently, a highly placed friend of mine asked me to look into it — not merely as getting a couple of kids interested in math, but as a general educational effort in the country. Once it becomes a general phenomenon, math whizkids might enjoy the same level of social acceptance and popularity as, say, athletes and rock stars. Wishful thinking? May be…
I was always among people who liked math. I remember my high school days where one of my friends would do the long multiplication and division during physics experiments, while I would team up with another friend to look up logarithms and try to beat the first dude, who almost always won. It didn’t really matter who won; the mere fact that we would device games like that as teenagers perhaps portended a cheerleader-less future. As it turned out, the long-multiplication guy grew up to be a highly placed banker in the Middle East, no doubt thanks to his talents not of the cheerleader-phobic, math-phelic kind.
When I moved to IIT, this mathematical geekiness reached a whole new level. Even among the general geekiness that permeated the IIT air, I remember a couple of guys who stood out. There was “Devious” who also had the dubious honor of introducing me to my virgin Kingfisher, and “Pain” would drawl a very pained “Obviously Yaar!” when we, the lesser geeks, failed to readily follow a his particular line of mathematical acrobatics.
All of us had a love for math. But, where did it come from? And how in the world would I make it a general educational tool? Imparting the love math to one kid is not too difficult; you just make it fun. The other day when I was driving around with my daughter, she described some shape (actually the bump on her grandmother’s forehead) as half-a-ball. I told her that it was actually a hemisphere. Then I highlighted to her that we were going to the southern hemisphere (New Zealand) for our vacation the next day, on the other side of the globe compared to Europe, which was why it was summer there. And finally, I told her Singapore was on the equator. My daughter likes to correct people, so she said, no, it wasn’t. I told her that we were about 0.8 degrees to the north of the equator (I hope I was right), and saw my opening. I asked her what the circumference of a circle was, and told her that the radius of the earth was about 6000km, and worked out that we were about 80km to the north of the equator, which was nothing compared to 36,000km great circle around the earth. Then we worked out that we made a 5% approximation on the value of pi, so the correct number was about 84km. I could have told her we made another 6% approximation on the radius, the number would be more like 90km. It was fun for her to work out these things. I fancy her love for math has been augmented a bit.
Photo by Dylan231