My research primarily concerns a latter-day, post-Einstein extension of Newton's key thesis of his 'System of the World', that the principles of geometry "are obtained from other fields" [physics] and "geometry is founded on mechanical practice." [1687, p. 382] Newton's physics-first thesis was further elaborated and defended by Gauss's differential geometry, which demonstrated by geodesics definitively that we derive geometrical properties from 3-dimensional non-Euclidean surfaces (physical space only), that such geometry is right there on the surface, intrinsic to physics--a surface is thus space itself. Riemann, who studied under Gauss, au…
My research primarily concerns a latter-day, post-Einstein extension of Newton's key thesis of his 'System of the World', that the principles of geometry "are obtained from other fields" [physics] and "geometry is founded on mechanical practice." [1687, p. 382] Newton's physics-first thesis was further elaborated and defended by Gauss's differential geometry, which demonstrated by geodesics definitively that we derive geometrical properties from 3-dimensional non-Euclidean surfaces (physical space only), that such geometry is right there on the surface, intrinsic to physics--a surface is thus space itself. Riemann, who studied under Gauss, augments this empirical geometry to any space at all, such that all rules, properties and axioms of geometry are purely physics-based, not analytic at all. By mid-twentieth-century quantum theory, leading physicists like Julian Schwinger were adamant that "the phenomena themselves should force us to the mathematical schemes that will best explain them," with the emphasis on 'force us'. This naturally revives Newton's closure statement in the Principia, in which "I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not yet assigned a cause to gravity...I DO NOT FEIGN HYPOTHESES. For whatever is not deduced from the phenomena must be called hypothesis," which, Newton held, have "no place in experimental philosophy...it is enough that gravity really exists and acts according to the laws that we have set forth," [1687, p. 943] by which he meant any mathematics not "of" the phenomena is mere 'feigned hypothesis', which drops--our mere models and descriptions aren't enough. This, in essence, is the project I am currently plotting: full-blown physicalization of mathematics. Mathematical ontology neither needed nor wanted.
