I know I haven’t written on here in a few weeks. I haven’t been on Twitter either. There are a couple of reasons for this. One is that I’ve teamed up with some really cool folks to start a company called Positive Integers (www.positiveintegers.com). We’re in the data analytics space, and already have the fortune of being able to work with a few big customers. Wish us luck. We’re working hard on the projects we have, setting up our office, getting ourselves organized, hiring great people, etc. In the last few weeks, I’ve been focusing a lot on that.
The other reason is that I’ve been spending time on weekends with my older daughter, who just went through her final exams and is now entering the tenth grade. We’ve been working together on preparing for Maths and Physics finals, and then having all kinds of chats about what she could be doing in college. It might seem a tad early to start this conversation. On the other hand, it’s not a bad idea to start mulling things over.
These two forces combined to consume pretty much all my time. But, it’s been great fun. The downside is that it came at the expense of blogging. I guess that’s the way things happen, at times. Having said that, I plan to set aside a couple of hours a week for at least one blog post, and another couple of hours for Twitter ( it’s actually fun to engage with folks on there) going forward. I also plan to blog regularly on our company blog. Let’s see how things play out.
Going through the final exams grind with my daughter reminded me of a fascinating aspect of mathematics education in middle school, which relates to the Pythagoras theorem. Pythagoras was an interesting chap. I’ll save that for another day. But, you probably remember his 2,500 year old theorem which states that the sum of the squares of the sides of a right triangle equals the square of its hypotenuse. This pretty much forms the foundation for areas like trigonometry. The fascinating aspect of Pythagoras theorem is that while it is introduced in middle school (either 8th or 9th grade), the students are not taught the proof of the theorem itself at that time. Rather, the books and teachers tell the students to take the theorem as ‘given’ and motor on. As a matter of fact, the proof for Pythagoras theorem, which is such a fundamental theorem in mathematics, is never taught in school. I’m told that only Maths majors learn to prove the theorem in college, and that too only in some countries.
Do you recall learning the proof? I don’t believe we were ever taught this. Try asking a friend or a colleague. The answer is likely the same. The chances are that very few of us can actually prove the Pythagoras theorem if asked to do so. This is because we never learnt about it. Obviously, it raises the question of why is it that we were not taught this in school? Why are school kids still not being taught the proof for one of the most famous mathematical theorems?
The answer is that the proof for the theorem is apparently considered too complicated to be taught to eighth grade students. So, students are taught to understand this empirically. They’re asked to construct right triangles and physically verify the truth in the theorem by measuring the sides and then by applying the theorem. There’s no “proof” given to them. They’re asked to go along with it. The reason they are asked to ‘blindly’ accept it is because there is a great benefit to knowing and applying the Pythagoras theorem from the eighth grade onward, and because without it, further learning and advancement is not possible in some areas. This is interesting.
It struck me that much of religious and spiritual belief works the same way. We are asked to place faith in a notion (say, the existence of God), the proof for which is complicated and hence unavailable at that time. But trust and belief in the notion is fundamental and critical to moving oneself forward to a state where the proof for the notion may become self evident. Fascinating.
ps: if you’re curious, here’s a simple way to prove the Pythagoras theorem below. cheers.