Reinvent the wheel (your own wheel)

In recent weeks, I spent time for implementing the surface Green’s function method from the paper,

M. P. Lopez Sancho, J. M. Lopez Sancho, and J, Rubio
Highly convergent schemes for the calculation of bulk and surface Green functions
I. Phys. F: Met. Phys. 15 (1985) 851-858

This is a quite well-known method in the field, which many people already use. I am also aware of a few codes having this scheme of implementation. But in this post, I don’t intend to talk about this particular method.

I want to talk more about the style of research, my case, specifically. Personally, I enjoy really a lot writing down lines of a code, which I missed a bit in recent years as my work life became busier. Since when I was a graduate student, I have often experienced that my understand on theoretical methods becomes much deeper by deriving everything in my own way and writing down a code. Now, I am strongly convinced that writing down a code is probably one of the best ways to deeply understand theoretical methods. Even if it may seem obvious by reading papers, I often encounter numorous errors, including technical as well as conceptual ones, while writing down a code. Looking back after making the code, then I realize that I did not really understand before.

So, I like deriving every equation in my own way and writing a code that implements the idea in general setups. And the best part is, when I use it for the solution that only my code can answer. A tricky part is to make the right balance between method development and science ideas.

It is often said in our soceity that reinventing the wheel is unnecessary. I agree that one doesn’t have to develop “everything”. But I see the huge benefit of remaking one’s own wheel, at least part of it; it may seem like a lot of work in the beginning, but by experience, you see that it doesn’t take too long either to have one’s unique method. Surely, one can benefit a lot from the tool made by oneself, which is a fun part.

In business and industry, we often see multiple rivalry companies, and all the others, except for the very first one, were the “followers” in the beginning. But the existence of the first company did not discourage them. Instead, they all thought “I can do better”. That’s what really pushed the field and how the innovations were made. I suppose we don’t always need to do entirely new things. Instead, one can simply “do well” and develop skills step by step, so that one is ready to catch the Eureka moment and not miss the opportunity.