I don't really see the connection. Your example is the derivative of a function, and what I am saying is that rearranging 1234 to 3421 doesn't mean anything to

I don't really see the connection. Your example is the derivative of a function, and what I am saying is that rearranging 1234 to 3421 doesn't mean anything to me. Now you have some new number who's only relationship to the old number is that it's one of (432)-1 possible permutations of it. Other than that, what's the significance?