ABSTRACT
Common sense, supplemented or created by our education in Euclidean geometry, leaves us quite certain that parallel lines at sea cannot intersect. Surprise. It is not a Euclidean problem, and the problem is misframed to begin with. Common sense has enough pragmatic truth in it to represent a danger to the unwary. None (or all) of it can be used as a guide without skeptical testing. “You can’t go broke taking a profit.” Is that so? How do you know that? In this case the exact opposite within the Magee method is probably more true. A better formulation is to take losses quickly and profits slowly.
Suppose that in some sort of naval maneuvers an oil tanker is ordered to take a course parallel to that of a destroyer, the course to pass through a specified buoy or marker. Common sense tells us that there can be one and only one course that fills these requirements, since one and only one parallel line can be drawn to a given line passing through a specified point not on the given line. We learned this in school.
