| Non-experts tend to think that everything that is
| a function of position has to be a potential, but
| it's just not true. . . . J Denker
This may be misleading. Any continuous, scalar function of position can be
subjected to the gradient operator and generate a vector function of position.
The original scalar is then a genuine potential function for the vector.
It is the converse that is not true: i.e., there are vector functions of
position which are not the gradients of scalar functions. Only vector
functions whose curls are zero can be generated as the gradient of a scalar
function.
| I cobbled up an improved scheme for systematically
| portraying non-potentials, i.e. things that have a
| slope but no well-defined height - J Denker
If the potential function does not exist, then neither does its gradient
("slope"). The gradient ("slope") of a non-existent function is the Cheshire
cat's disembodied smile. : )