[conservatism_IS_compassion]

turns left and walks one mile West,

One mile. Due north, of course . . .

Ooops, you got me good - I made two errors - one in drawing a rectangular grid and coming back to the unit circle, and the prior mistake of proceeding in a straight line when “one mile west" is a circular arc of one radian on the unit circle.

Revised answer: the defined path takes you one mile away from the pole, one mile on the unit circle, and one mile back exactly to the pole. Final answer: zero (but no matter, the direction of that distance, zero tho it be, is still north).

Lots of “gotchas” in there, and I fell for most of them!

[Elsie]

(I tested this puzzle on waitresses first. Out of 5; one actually got it!)

I wonder what GoogleEarth® does at either pole?