When climbing our attic staircase, I never seem to be facing in the direction I’m going — I always seem to be looking at a wall, instead of up the stairs. I’d always assumed this was because of the tangents to the circle, but having just done some detailed analysis (such are the joys of a week off work), I have discovered it’s just that I (apparently) feel the need to make my feet go lengthways along each step (apart from at the end, when everything returns to normal staircase behaviour).