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  1. Heh. Why is it always "crutches"? Also sometimes "cartoons." When it's a drawing that they understand, it's a serious "diagram," but when they don't get it, it's a stupid crutch cartoon. And they also misunderstand its function. They act as if WE need and are relying on the drawings and are deriving our opinions from them. The reality is that we are presenting them as visual aids so that people with low visualizing skills can grasp what we can visualize without the drawings. So, there is some truth that the images are crutches, not for us, but for Bob, who, despite our offe
    1 point
  2. The original problem was walk a mile south walk a mile west (was it east -- no matter) walk a mile north. The east-west walk is less than the length of line of latitude reached by the southword leg so that the return trip is along a different line of longitude. Let me give an example. The coordinates of the north geographic pole are (90, lon) where lon can be any angle between 0 and 360. The north geographic pole and the south geographic pole are the only two points on the earth sphere that do not have unique coordinate. Now let me widen the problem out Start at a point, walk to
    1 point