Collision and the Perspectivity

Extract

Captain W. Burger and Captain A. G. Corbet in their general comment on the meeting of the Technical Committee in London, 16 April 1969, gave a curious and instructive hypothetical example of end-on encounter, a problem in navigation which they and others have found by experiments to have importance and practical difficulties. Their example is set in surface navigation at sea, and especially when using radar in fog. Two ships close with each other (in their example head-on and green-to-green), the two tracks being straight and parallel, and separated (in their example by half a mile). Should both ships stand on? My answer is affirmative, my argument difficult.

If one makes the fruitful assumption that neither ship in this example alters course or speed, and then tries to plot The Edge [ of regression of The (mutual) Line (of bearing)], he discovers that the result is not a non-singular parabola, but rather simply a fixed finite point, i.e. at best a degenerate parabola—yet clearly there can be no finite collision, and collision at infinity is an empty threat. What do plotters of The Edge make of this paradox? Here handbook summaries will not do.