M. C. Escher’s painting Ascending and Descending illustrates a non-conservative vector field, impossibly made…. In reality, the height above the ground is a scalar potential field [the scalar (single number attached to a point) being the height above the ground]. If one returns to the same horizontal place, one has gone up exactly as much as one goes down.
So that’s that picture related to
Conservative vector field
s obey the product rule:
(and the conservative scalar field
is also the output of a derivative operation…just a different dimensionality)