A man is told to make a circle
He makes this:
Where is the man?
In Manhattan, because that is what a "circle" (defined to be the set of points of a certain set distance d away from a given point) looks like when using the taxicab (or Manhattan) metric.
Clearly the man is
in $L^1$ space.
He was asked to draw a circle, namely the set of all points at distance $1$ from a fixed centre.
He's in another distance metric, one where distance is determined by the addition of coordinates, instead of pythagorean theorem.