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.)
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