The historical sciences - economics, anthropology and history - are viewed rather dismissively by a lot of those who read me. I think that's a mistake. Geology and astronomy used to be historical sciences too, but physics invaded with it's equations and "redeemed" them. Economics has imbibed a mighty dose of mathematics but still has trouble feeling respectable.
One of the things I got from reading Feynman - YMMV - is that science starts with narrative. The story is the primary tool we humans use in explaining the universe and mathematics is one of the ways we keep track of the implications of our stories. That's worked out wonderfully for physics, astronomy, meteorology and some other sciences, but slightly less well - so far - for economics.
One very crucial scientific idea Feynman emphasizes is the necessity for honesty and self criticism. These traits are not especially congenial for human nature, and I think economics has provided a perfect growth medium for these anti-scientific elements, mostly because the incentives for stacking the deck are so great when such huge opportunities for rent extraction exist.
Neils Bohr once remarked that a crucial advantage that physicists had over philosophers was that they had "all written papers that were subsequently proven wrong." Of course this advantage is less clear cut in the age of string theory, when experiment hardly ever has anything to say. A good test of an economists character is to ask when he or she has been wrong and admitted it.