I remember reading about how the proof to Fermat’s Last Theorem was written. Much of the genius of the proof was fluidly moving from one problem domain to other equivalent representations that allows you to continue the work.
Now I’m not going to even pretend that I understand the proof because I have no fucking clue about the details. I understand from the 50,000 foot hand-wavey pantomime level, but not more. (Note to self: work to understand at the 50,000 foot level without the pantomime)
The key is realizing that different problems can be looked at from other directions. Today I ran into a similar problem at work. By similar, I mean absolutely nothing like the complexity of Fermat’s Last Theorem. But from reading bunches from The Art of Electronics I was used to looking at double log graphs. A simple transformation of our problem from a tech problem to something where we can graph the ratio of a couple of parameters on a double log graph and the solution appears to simply pop out.
Sometimes the fun part is to take a step back… turn to the side and observe. Look at the problem from the side and the solution may well be looking back at you waiting for you.