While doing my Mechanics homework set tonight, I thought back to the last problem set and had a revelation.
When I look at a problem and I think, “Gee that’s an integral” it makes me happy (this set). When I look at a problem and I think “Gee that’s a differential equation” it makes me sad (the last set).
Professor Franklin told us something in the Fall Theory class about most physicists: they fall into two categories.
- They see everything as an integral.
- They see everything as a differential equation.
I’m definitely the former.
I used to be an integral guy too. But that was a long time ago. That was when I was in high school - learning about Newtons laws and the equations of motion. I started looking at Ampares law and Gauss law - and they were all presented in the integral form in those days. So I started to think that the whole world was made of integrals.
Then while studying Maxwells equations, I realized that one could have differentials too - and not just integrals. And for a short time I started thinking that maybe differential equations were what the world was all about. A very short while later however, I realized that Maxwells equations could be expresse in two different forms - the differential and the integral form.
Then I started learning about a number of operators - Laplace in particular. They were useful - very useful in the sence that they took the difficult integral and the differential out of differential equations. They were a little bit akin to logarithms that converted multiplications into additions.
But I started realizing that it is not the math - but the physical phenomenon behind the math that is so interesting. Math by itself was never interesting, for what is the use in solving an integration if it is not for understanding the world around me ???
Today, as I stare into my quantum-mechanics book, I look at the momentum operator and the hamiltonian and I ask myself - what am I physicaly looking at ?
….. At this moment, I have no clue. But maybe I shall grow wiser one day.