In "The Character of Physical Law", Feynman expounds what he calls the Babylonian, as opposed to the Euclidean or axiomatic, approach to mathematics and physics. In the latter, the plan is to deduce statements from a set of axioms, whereas the Babylonian approach exploits alternative representations of physical phenomena and the interchangeability which only mathematical reasoning affords.
Different mathematical representations invite different physical interpretations, and the mathematical generalizations implied may lead to theorems whose generality extends beyond the confines of a proof within a given system. (Cf. Form And Mathematics)
The next step is then the guessing of physical equations, which, Feynman argues, facilitates the guessing of new physical laws in a way that common-sense feeling, philosophical principles, or models cannot.
THE FULLER MAP
© Paul Taylor 2001