Dear Edward McKinnon,
First of all I have liked your lucid account of the co-evolution and path-breaking (Laplace and Cauchy) history of MP. En Passant wrote here a short essay about "qualities could admit of quantitative representations, an essential step in developing the mathematical relations and laws needed in physics". I also fully agree that language is the new ingredient needed by QM and fully recognized by Bohr. Finally, my experience as an engineer and a mathematical physicist is just like the Dirac quote "A great deal of my work is just playing with equations and seeing what they give" most of the time I use the magic found by clever mathematicians, ask the computer to pursue the play and try to use my "human ingenuity", "not the objective existence of mathematical forms" to improve on the existing knowledge.
To develop further what you are saying about QM and language, a better understanding of human cognition seems to me essential. In this direction, I recently found (following Grothendieck) that the language of permutations is a needed ingredient for further progress. This is explained in my essay: a free group with only two letters, a permutation group (two permutations), a corresponding Riemann topology, a point-line incidence geometry, an algebraic curve over the rationals "objects so simple that a child learns them while playing" (say Grothendieck).
Thank you for a very pleasant and relevant essay.
Michel
