| Say that love and knowledge are linearly independent, forming a basis of ℝ². So then we can think of linear combinations of love and knowledge as points in ℝ². Then, by Carathéodory's Theorem [1], the convex hull [2] of any set of such points may be written as a convex combination [3] of no more than 2+1=3 points. folksinger simply gave us the set {philosopher, asshole, idiot}, from which to generate a convex hull in the plane (in this case, a triangle). If we choose knowledge as the y-axis and love as the x-axis, folksinger argues that the philosopher lies somewhere in quadrant 1, the asshole in quadrant 2, and the idiot in quadrant 4. I guess the question remains as to whether or not this particular embedding of the triangle in the plane really does represent the truth of the matter. :-) (It seems to me he is saying there cannot be evil philosophers, although maybe somebody can think of examples of people who are "full of love" but evil nonetheless.) [1] https://en.wikipedia.org/wiki/Carath%C3%A9odory%27s_theorem_... [2] https://en.wikipedia.org/wiki/Convex_hull [3] https://en.wikipedia.org/wiki/Convex_combination |