String Diagram
A string diagram is a graphical notation for 2-categories and bicategories in which objects are drawn as regions, 1-morphisms as lines, and 2-morphisms as nodes. Developed by Roger Penrose for tensor calculus and later formalized by Joyal and Street, string diagrams make the structural content of 2-categorical equations visually obvious. The interchange law — that horizontal and vertical composition commute — becomes the statement that nodes can slide past each other along wires. In quantum field theory, string diagrams represent Feynman diagrams; in control theory, they represent signal-flow graphs; in computer science, they represent data-flow diagrams. The unification is not metaphorical. The same graphical syntax describes all three because all three are instances of 2-categorical structure.
String diagrams prove that the right notation is not a convenience but a revelation — what was hidden in the algebra becomes obvious in the picture.