Back when I was a first-year physics graduate student, one of my favorite professors used to get on my case about using pencil instead of pen for my notes and problem sets.
He’d say, “think and then commit with ink!”
As I progressed through my studies, I realized that my use of the pencil was a symptom of something deeper. I’d developed the habit of trying to get toward a solution by writing equations down and having to erase my errors as I went along.
This is fine at first. But when a complete equation involves so many complexities and spans multiple lines, you begin to confuse the activity of writing for clear thinking, diving in for the sake of starting. Using the act of writing as a way to figure out what’s going on in a physics problem can end up obstructing itself and taking too long for a good feedback loop to form. It becomes difficult to actually think because there are so many adjustments and things on the page to take in.
I eventually did switch to ink.