ABSTRACT
Mathematics is a great tool, but the ultimate governing language of science is language. Physics relates natural realities to mathematical idealizations. Gottfried Wilhelm Leibniz took note of the apparent correspondence between the mental and physical realms—in particular, between mathematics and the physical sciences—which he took to be an act of God, a divinely "pre-established harmony." While mathematics is logically self-contained as a conceptual system, its development as a human creation is informed by categories and relationships gleaned from physical reality. The correspondence between mathematics and physical reality is satisfying for psychological reasons as well as for the competence it affords. Just as novel experience, heretofore unexpressed, sometimes gives rise to new language, newly discovered aspects of physical reality—which do not yet correspond to known math—sometimes suggest or require future developments in mathematics. Yet physical space is a phenomenal fact, whereas mathematical spaces are conceptual artifacts. Their very advantage is that—unlike real space—they are malleable products of definition.
