Connecting mathematical representation to physical interpretation

Sarita Rosenstock

When we use words and symbols to represent the world, we understand that some features of those representations— such as which font write in or the choice of metres vs. inches—are merely arbitrary or conventional necessities of expression. But how can we tell which aspects of a representation are supposed to have real, physical meaning? While we can often trust our intuitions, many genuine scientific questions revolve around the subtleties of this boundary. In this talk, I introduce concept of a “semantic diagram" as a way to scaffold narrative accounts of how mathematical gadgets represent target systems. Using category theory, the mathematical theory of structure, I demonstrate how semantic diagrams can help us speak more precisely about the core physical content of abstract mathematical descriptions.