Fig 2. The wicked-map problem.

(A) An ambitious mountaineer may follow the gradient in Euclidean metric to reach the mountain top (red route from square to triangle). Because the map is plotted in Cartesian coordinates, the route stands perpendicular to the contour lines. (B) If the ambitious mountaineer does not realize that a map given by a wicked hotelier is sheared, the blue route would be chosen, as it is now the one that stands perpendicular to the contour lines in the sheared map. The blue route corresponds to gradient ascent in another metric. Of course, each route on the normal map could be transformed to the sheared map and vice versa, but what looks like naive (Euclidean) gradient ascent in one map may look different in another map.