I\'d like to know how people decide whether to define a method as static. I\'m aware that a method can only be defined as static if it doesn\'t require access to instance fields
Kevin Bourrillion wrote an insightful answer on this topic some time ago (admittedly from a Java perspective, but I think it's applicable to other languages too).
He argues that you should basically only use static methods for pure functions.
A "pure function" is any method which does not modify any state and whose result depends on nothing but the parameters provided to it. So, for example, any function that performs I/O (directly or indirectly) is not a pure function, but Math.sqrt(), of course, is.
I tend to agree. (Although in my own code, traditionally, I've probably used way too many static helper methods all over the place... :-P And this surely has made code that uses those methods harder to test.)