Discovery

During the past few months, my continued admiration for Richard "master of my universe" Feynman has led me to browse many writings about the man, including a copy of The Beat of a Different Drum that I happened to stumble across, which is a very scientific treatment of his life and work. I was hiding in the tucked away library of the theoretical physics department, where they have very quiet workspace, when I felt the book staring at me from the "returned" rack. I went over and "happened" to read chapter about his life as an undergraduate. The biographies discusses Feynmans senior thesis work, and near the end of the chapter, it is made clear that a substantial part of the heavy lifting in his research was a well known way to manipulate the problem (something about Hamiltonian operators). Essentially, much of the thesis was a reinvention of the wheel. Fortunately, Feynman had come to some other exceptional conclusions that were far from unoriginal, and he was allowed to graduate.

The reason I bring this little tale up is because lately I've found that it's a very healthy exercise to reinvent a few wheels now and then. All the problems of the world that haven't been solved yet are unsolved for a reason: because they're hard. And if you don't practice by inventing a few wheels every now and then, taking on unsolved problems is a fools errand.

Yesterday I was working on a Statistics problem set, and was crossed by the peculiar fact. I was trying to type (8.2)^2, when I mistyped on my calculator, 8.0^2, which gave 64. Of course. Retyping the correct number, I got 67.24. I thought about this for a second, and wondered, hmm, I wonder I could have used my result of 64 and just add whatever accounts for the difference of 3.24...what is it? It can't be 0.2^2. Hmm. 324. That's a square, I'm sure of it. Ha! 1.8^2 = 3.24. Quaint. Why is 8.2^2 = 8.0^2 + 1.8^2? I thought and thought and thought...

Why is 41^2 = 40^2 + 9^2? What an odd triplet. Are there any other adjacent integers where the difference of their squares is the square of an integer? I started brute forcing around a bit, and realized that they were all odd integers, as well. And then....OF COURSE! How could I be so stupid? Pythagorean triplets! 3, 4, 5! Wow, they sure are beautiful. I sat and admired them for a few moments, maybe drawing a triangle of five. And then got back to work.

OK, so my discovery was 15 orders of magnitude less significant than Feynmans, but it (along with a slightly more complicated wheel I reinvented last weekend that I won't go into here, involving graph connectedness and Dijkstras algorithm) was nonetheless an instance where I felt I had discovered something, reduced a data set of events to a underlying theory describing it, and that was one of the best feelings (OK, the feeling was much stronger with the graph problem last weekend, but that's a much longer and more technical story) I've had in a long time, and it's why I bother to study what I do.

It was practice at explaining the universe with a really great reward, and the fact that it was already done was completely irrelevant. So next time you've spotted something strange, don't ask google, work it out! It might turn out to be the trivial result of a basic theorem and obvious to anyone more learned then you and I, but that's not the point. If you can't deduce that, then how are you ever going to be able to explain the universe? And hey, you don't know it's trivial until you've checked!

Oh, and I got posted to 3 Quarks Daily today...!