A number of diagrammatic formulations have played an important role in the advancement of science. Some embody representations of physical phenomena, while others model mathematical or logical ideas in graphical form.
One example that belongs to both classes are the Feynman diagrams. They are pictorial representations of the mathematical expressions that describe the behavior governing the interactions of subatomic particles. In addition to helping understand certain aspects of quantum chromodynamics conceptually, they also serve as an important calculating tool in this area of physics.
Another example, which is aimed more at serving mostly as graphically representing a mathematical modelling language, are the Petri Nets. They describe distributed systems and offer a way through which computer scientists can capture the essence of business processes.
Other instances of these graphical notations in different scientific areas include Bond graphs, circuit diagrams, block diagrams, ZX/ZW calculus, graphical linear algebra, commutative diagrams, and knot diagrams. A presentations in which a number of these diagram types are described and analysed as a whole can be found here.
Despite having found this presentation, so far I have not been able to find many sources that describe the role of graphical languages in the advancement of the sciences. I did retrieve the following article entitled 'The "Physics" of Notation: Toward a Scientific Basis for Constructing Visual Notations in Software Engineering' by Daniel Moody (2009). However, this article is more about making good design choices for the effective communication of scientific diagrams.
What I'm more interested in, is what role these different diagrams have played in the advancement of their respective scientific fields. I wonder how they have contributed to a deeper understanding of physical phenomena and mathematical ideas. So instead of treating them merely as a visual supplement of the underlying ideas, I'm curious as to how these representations actually allowed researchers to make advancements in their respective research areas. I wonder how they allowed to do so both in the different, isolated fields, as well as in 'science' as an integrated whole.
Question: do you know of any references that delve into the role of diagrams in the advancement of the sciences?