Tag Archives: parenting

When Your Child is as Big as You

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.

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Why Have Kids?

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?

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Fields MedalFirst Woman

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 fieldswe 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.

Stating the reason that way doesn’t really explain anything. We have to wonder where this gender difference comes from. Continue reading

Battles Too Small to Fight

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.

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Uninsured by Default

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 notpre-approved.Weirderhow 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 fullpre-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 partrefusing 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?

Another Pen Story of Tough Love

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.

Home No More

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.)

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Physics vs. Finance

على الرغم من الثراء الذي تضفيه الرياضيات على الحياة,,en,يبقى موضوعًا مكروهًا وصعبًا للكثيرين,,en,أشعر أن الصعوبة تنبع من الانفصال المبكر والدائم في كثير من الأحيان بين الرياضيات والواقع,,en,من الصعب أن نتذكر أن المعاملة بالمثل للأعداد الأكبر تكون أصغر,,en,في حين أنه من الممتع معرفة أنه إذا كان لديك المزيد من الأشخاص يشاركون البيتزا,,en,تحصل على شريحة أصغر,,en,اكتشاف متعة,,en,حفظ,,en,ليس كثيرا,,en,الرياضيات,,en,كونه تمثيل رسمي للأنماط في الواقع,,en,لا يضع الكثير من التركيز على جزء التفسير,,en,ومن السهل ضياعها على الكثيرين,,en,لتكرار هذا البيان بدقة رياضية,,en,الرياضيات غنية وصارمة من الناحية النحوية,,en,لكنه ضعيف لغويًا,,en,يمكن بناء الجملة على نفسها,,en,وغالبًا ما تتخلص من فرسانها الدلاليين مثل حصان جامح,,en, 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, يمكن أن تتحول إلى أشكال دلالية مختلفة تبدو مختلفة إلى حد كبير عن بعضها البعض,,en,يستغرق الطالب بضع سنوات لملاحظة تلك الأعداد المركبة,,en,ناقلات الجبر,,en,تنسيق الهندسة,,en,الجبر الخطي وعلم المثلثات كلها أوصاف نحوية مختلفة بشكل أساسي عن الهندسة الإقليدية,,en,أولئك الذين يتفوقون في الرياضيات هم,,en,أنا أفترض,,en,أولئك الذين طوروا وجهات نظرهم الدلالية لكبح جماح الوحش النحوي البري على ما يبدو,,en,يمكن أن توفر الفيزياء أيضًا سياقات دلالية جميلة للشكليات الفارغة للرياضيات المتقدمة,,en,انظر إلى فضاء مينكوفسكي والهندسة الريمانية,,en,وكيف حوّلهم أينشتاين إلى أوصاف لواقعنا المدرك,,en,بالإضافة إلى توفير الدلالات للشكلية الرياضية,,en. 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, يروج العلم أيضًا لوجهة نظر عالمية قائمة على التفكير النقدي والنزاهة العلمية الصارمة,,en,إنه موقف لفحص استنتاجات المرء,,en,الافتراضات والفرضيات بلا رحمة لإقناع النفس بأنه لم يتم التغاضي عن أي شيء,,en,لا يوجد مكان يتجلى فيه هوس الانتقاء أكثر من الفيزياء التجريبية,,en,يبلغ الفيزيائيون عن قياساتهم بمجموعتين من الأخطاء,,en,خطأ إحصائي يمثل حقيقة أنهم قاموا فقط بعدد محدود من الملاحظات,,en,وخطأ منهجي من المفترض أن يفسر عدم الدقة في المنهجية,,en,الافتراضات وما إلى ذلك,,en,قد نجد أنه من المثير للاهتمام أن ننظر إلى النظير من هذه السلامة العلمية في رقبتنا من الغابة,,en,الذي يزين الصرح النحوي لحساب التفاضل والتكامل العشوائي بدلالات الدولار والسنت,,en. 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, من النوع الذي ينتهي في التقارير السنوية ويولد مكافآت الأداء,,en,قد يقول المرء حتى أن له تأثير عميق على الاقتصاد العالمي ككل,,en,نظرا لهذا التأثير,,en,كيف نقوم بتعيين مستويات الأخطاء والثقة لنتائجنا,,en,لتوضيح ذلك بمثال,,en,عندما يقوم نظام التداول بالإبلاغ عن ربح / خسارة الصفقة على أنها,,en,سبعة ملايين,,en,فعلا,,en,أو هو,,en,الأخير,,en,يحمل قيمة أكبر للمؤسسة المالية ويجب أن تكافأ أكثر من الأولى,,en,نحن على علم بذلك,,en,نحن نقدر الأخطاء من حيث تقلبات وحساسيات العوائد ونطبق احتياطيات الربح / الخسارة,,en,لكن كيف نتعامل مع الأخطاء المنهجية الأخرى,,en,كيف نقيس تأثير افتراضاتنا على سيولة السوق,,en,تناسق المعلومات إلخ.,,en,وتعيين قيم الدولار للأخطاء الناتجة,,en. 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? إذا كنا حريصين على نشر الخطأ لهذا,,en,ربما الأزمة المالية,,en,ما كان ليحدث,,en,على الرغم من أن علماء الرياضيات,,en,خالية من مثل هذه الشكوك الذاتية الحرجة مثل علماء الفيزياء,,en,على وجه التحديد بسبب الانفصال التام بين سحرهم النحوي وسياقاته الدلالية,,en,هناك البعض ممن يأخذون صحة افتراضاتهم على محمل الجد تقريبًا,,en,أتذكر أستاذي الذي علمنا الاستقراء الرياضي,,en,بعد إثبات بعض النظرية البسيطة باستخدامه على السبورة,,en,نعم كان ذلك قبل عصر السبورات,,en,سألنا عما إذا كان قد أثبت ذلك,,en,نحن قلنا,,en,بالتأكيد,,en,لقد فعل ذلك أمامنا مباشرة,,en,ثم قال,,en,"آه,,en,ولكن يجب أن تسألوا أنفسكم ما إذا كان الاستقراء الرياضي صحيحًا ". إذا كنت أفكر فيه على أنه عالم رياضيات عظيم,,en, 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, ربما يكون ذلك فقط بسبب الهوى الرومانسي المشترك الذي يمجد معلمينا السابقين,,en,لكنني متأكد تمامًا من أن الاعتراف بالمغالطة المحتملة في تمجدي هو نتيجة مباشرة للبذور التي زرعها ببيانه,,en,ربما يكون أستاذي قد أخذ هذا الشك الذاتي بعيداً,,en,ربما ليس من الصحي أو العملي التشكيك في خلفية عقلانيتنا ومنطقنا,,en,الأهم من ذلك هو ضمان سلامة النتائج التي نصل إليها,,en,باستخدام الآلات النحوية الهائلة الموجودة تحت تصرفنا,,en,الطريقة الوحيدة للحفاظ على موقف من الشك الذاتي الصحي وما يترتب على ذلك من فحوصات العقل هي حماية العلاقة بين أنماط الواقع والشكليات في الرياضيات,,en,وذلك,,en. 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, ستكون الطريقة الصحيحة لتطوير حب الرياضيات أيضًا,,en,الرياضيات والأنماط,,en,يحب معظم الأطفال الأنماط,,en,الرياضيات مجرد أنماط,,en,هكذا هي الحياة,,en,رياضيات,,en,وبالتالي,,en,هي مجرد طريقة رسمية لوصف الحياة,,en,أو على الأقل الأنماط التي نواجهها في الحياة,,en,إذا كانت العلاقة بين الحياة,,en,يمكن الحفاظ على الأنماط والرياضيات,,en,يترتب على ذلك أن يحب الأطفال الرياضيات,,en,ويجب أن يولد حب الرياضيات قدرة تحليلية,,en,أو ما يمكن أن أسميه القدرة الرياضية,,en,لفهم وفعل معظم الأشياء بشكل جيد,,en,لقد كتبت عن اتصال,,en,ثلاثة أشياء قبل بضع جمل,,en,أعلم أنه يجب أن تكون اللغة الإنجليزية سيئة لأنني أرى ثلاثة رؤوس لمثلث ثم اتصال واحد لا معنى له,,en,ربما يضع الكاتب الجيد الأمر بشكل أفضل بشكل غريزي,,en,كاتب رياضي مثلي سيدرك هذه الكلمة,,en.

Math and Patterns

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” جيد بما فيه الكفاية في هذا السياق,,en,يمكن تعويض الجرة اللاشعورية على إحساسك بالقواعد أو تجاهلها في الكتابة غير الرسمية,,en,لن أتركه واقفًا في كتاب أو عمود منشور,,en,ما عدا هذا لأنني أريد إبرازه.,,en,وجهة نظري هي أن حبي للرياضيات هو الذي يتيح لي القيام بعدد كبير من الأشياء بشكل جيد إلى حد ما,,en,ككاتب,,en,لقد عملت بشكل جيد,,en,لكنني أعزو نجاحي إلى قدرة رياضية معينة بدلاً من الموهبة الأدبية,,en,لن أبدأ كتابًا بشيء مثل,,en,كانت من افضل الاوقات,,en,كانت أسوأ الأوقات.,,en,كجملة افتتاحية,,en,بكل قواعد الكتابة الرياضية التي صاغتها لنفسي,,en,هذا فقط لا يصلح,,en,ومع ذلك ، نعلم جميعًا أن افتتاح ديكنز,,en — 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, عدم اتباع أي قواعد خاصة بي,,en,ربما يكون الأفضل في الأدب الإنجليزي,,en,من المحتمل أن أطهو شيئًا مشابهًا يومًا ما لأنني أرى كيف يلخص الكتاب,,en,ويسلط الضوء على التفاوت بين من يملكون ومن لا يملكون انعكاسًا في الشخصيات الرئيسية المتباينة وما إلى ذلك,,en,أرى كيف يعمل ويمكن أن أستوعبه في كتاب الطبخ الخاص بي,,en,إذا كان بإمكاني معرفة كيف,,en,وعملية الاستيعاب رياضية بطبيعتها,,en,خاصة عندما يكون جهدًا واعًا,,en,يمكن أن تساعدك الأساليب المبنية على القواعد الغامضة المماثلة في أن تكون فنانًا ذكيًا بشكل معقول,,en,موظف,,en,مدير أو أي شيء تضع أنظارك عليه,,en,وهذا هو السبب الذي جعلني أتفاخر مرة أمام زوجتي أنني أستطيع تعلم الموسيقى الكلاسيكية الهندية على الرغم من حقيقة أنني عملي,,en,لذا فإن حب الرياضيات أمر جيد على الأرجح,,en, 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, على الرغم من عيوبه الواضحة مقابل المشجعين,,en,لكني لم أتطرق بعد إلى موضوعي المركزي,,en,كيف نشجع وننمي بنشاط حب الرياضيات بين الجيل القادم,,en,أنا لا أتحدث عن جعل الناس بارعين في الرياضيات,,en,أنا لست مهتمًا بتقنيات التدريس في حد ذاتها,,en,أعتقد أن سنغافورة تقوم بعمل جيد بالفعل مع ذلك,,en,ولكن لجعل الناس يحبون الرياضيات بنفس الطريقة التي يحبونها,,en,تتطلب موسيقاهم أو سياراتهم أو السجائر أو كرة القدم قدرًا أكبر من الخيال,,en,أعتقد أنه يمكننا تحقيق ذلك من خلال الحفاظ على الأنماط الأساسية في المقدمة,,en,لذا بدلاً من إخبار أطفالي بذلك,,en,أكبر من,,en,أصغر من,,en,أقول لهم,,en,لقد طلبت بيتزا واحدة لبعض الأطفال,,en,هل تعتقد أن كل منا سيحصل على المزيد إذا شاركه أربعة أطفال أو ستة أطفال,,en. 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?”

من المثال السابق على المسافات والدرجات الجغرافية,,en,أتخيل أن ابنتي ستكتشف يومًا ما أن كل درجة,,en,أو حوالي 100 كيلومتر,,en,تصحيح بواسطة,,en,يعني أربع دقائق من إرهاق السفر,,en,قد تتساءل لماذا,,en,يظهر بالدرجات والدقائق والثواني,,en,وتعلم شيئًا عن أساس نظام الأرقام وما إلى ذلك,,en,تؤدي الرياضيات حقًا إلى منظور أكثر ثراءً للحياة,,en,كل ما يتطلبه الأمر من جانبنا ربما يكون فقط لمشاركة متعة الاستمتاع بهذا الثراء,,en,هذا أملي,,en,حب الرياضيات,,en,إذا كنت تحب الرياضيات,,en,أنت مهووس,,en,مع خيارات الأسهم في مستقبلك,,en,ولكن لا يوجد مشجعون,,en,لذا فإن جعل الطفل يحب الرياضيات هو هدية مشكوك فيها,,en,هل نقدم لهم معروفًا حقًا,,en,طلب مني أحد أصدقائي المرموقين النظر في الأمر,,en,ليس فقط لإثارة اهتمام طفلين بالرياضيات,,en, 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.

Love of Math

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, ولكن كجهد تعليمي عام في الدولة,,en,بمجرد أن تصبح ظاهرة عامة,,en,قد يتمتع الطلاب المبتكرون في الرياضيات بنفس مستوى القبول الاجتماعي والشعبية التي يتمتع بها,,en,الرياضيين ونجوم موسيقى الروك,,en,تفكير حكيم,,en,يمكن,,en,كنت دائمًا من بين الأشخاص الذين يحبون الرياضيات,,en,أتذكر أيام دراستي الثانوية حيث كان أحد أصدقائي يقوم بعملية الضرب والقسمة الطويلة أثناء تجارب الفيزياء,,en,بينما كنت أتعاون مع صديق آخر للبحث عن اللوغاريتمات ومحاولة التغلب على المتأنق الأول,,en,الذي فاز دائمًا تقريبًا,,en,لا يهم حقًا من فاز,,en,إن مجرد حقيقة أننا سنستخدم ألعابًا كهذه كمراهقين ربما تنذر بمستقبل أقل من المشجعين,,en,كما اتضح,,en,نشأ رجل المضاعفة الطويلة ليصبح مصرفيًا ذا مكانة عالية في الشرق الأوسط,,en. 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, بلا شك بفضل مواهبه لا من المشجعين,,en,نوع الرياضيات phelic,,en,عندما انتقلت إلى IIT,,en,وصلت هذه المهارة الرياضية إلى مستوى جديد تمامًا,,en,حتى بين المهووسين العامين الذين تخللوا هواء IIT,,en,أتذكر اثنين من الرجال الذين برزوا,,en,كان يوجد,,en,الملتوية,,en,الذي كان له أيضًا شرف مشكوك فيه بتقديمي إلى Kingfisher الخاص بي,,en,ألم,,en,من شأنه أن يتألم جدا,,en,من الواضح يار,,en,عندما كنا,,en,المهوسون الصغرى,,en,فشل في متابعة خطه الخاص من الألعاب البهلوانية الرياضية بسهولة,,en,كان كل منا يحب الرياضيات,,en,من أين أتى,,en,وكيف يمكنني أن أجعلها في العالم أداة تعليمية عامة,,en,إن نقل رياضيات الحب إلى طفل واحد ليس بالأمر الصعب,,en,أنت فقط تجعلها ممتعة,,en,في ذلك اليوم عندما كنت أقود سيارتي مع ابنتي,,en,وصفت بعض الشكل,,en, 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 (في الواقع النتوء على جبين جدتها,,en,نصف الكرة,,en,أخبرتها أنه كان في الواقع نصف الكرة الأرضية,,en,ثم أوضحت لها أننا ذاهبون إلى نصف الكرة الجنوبي,,en,نيوزيلاندا,,en,لقضاء إجازتنا في اليوم التالي,,en,على الجانب الآخر من الكرة الأرضية مقارنة بأوروبا,,en,ولهذا كان الصيف هناك,,en,وأخيرا,,en,أخبرتها أن سنغافورة كانت على خط الاستواء,,en,ابنتي تحب تصحيح الناس,,en,هكذا قالت,,en,لم يكن كذلك,,en,أخبرتها أننا على وشك,,en,درجات شمال خط الاستواء,,en,آمل أن أكون على حق,,en,ورأيت افتتاحي,,en,سألتها ما هو محيط الدائرة,,en,وأخبرتها أن نصف قطر الأرض يبلغ حوالي 6000 كيلومتر,,en,واكتشفنا أننا كنا على بعد حوالي 80 كيلومترًا شمال خط الاستواء,,en,التي كانت لا شيء مقارنة بالدائرة العظيمة التي تبلغ مساحتها 36000 كم حول الأرض,,en) 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. ثم توصلنا إلى أننا صنعنا ملف,,en,تقريب على قيمة pi,,en,لذلك كان الرقم الصحيح حوالي 84 كم,,en,كان بإمكاني أن أخبرها أننا صنعنا أخرى,,en,التقريب على نصف القطر,,en,سيكون الرقم أقرب إلى 90 كم,,en,كان من الممتع لها أن تعمل على هذه الأشياء,,en,أتخيل أن حبها للرياضيات قد ازداد قليلاً,,en,ديلان 231,,cy,في دفاعنا,,en,كانت الأزمة المالية بمثابة منجم ذهب حقيقي لكتاب الأعمدة مثلي,,en,نشرت ما لا يقل عن خمس مقالات حول هذا الموضوع,,en,بما في ذلك أسبابه,,en,الدروس المستفادة,,en,الأكثر استنكارًا للذات على الإطلاق,,en,تجاوزاتنا,,en,التي ساهمت في ذلك,,en,النظر إلى الوراء في كتاباتي هذه,,en,أشعر وكأنني قد أكون غير عادل تجاهنا بعض الشيء,,en,لقد حاولت أن أخفف من حدة اتهاماتي بالبخل,,en,وربما الانحطاط,,en 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