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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?

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    $\begingroup$ "merely as a visual supplement of the underlying ideas" - my internal representation of many ideas is visual. In considering scientific progress, I suspect it may be difficult to disentangle the effect of explicit graphical schemes from both written information (which allows multiple people to converse about particular concept) and from life experience (since this experience is capable of impressing visual information). It may be easier to find studies which consider the effect of graphics in the reproduction of scientific knowledge, rather than in its initial production. $\endgroup$
    – Steve
    Feb 4 at 15:14
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    $\begingroup$ @Steve Right, I agree that it might be difficult to disentangle these concepts. I do think, however, it might be worthwhile to try to focus on graphical representations. They seem like an understudied phenomenon in the history and philosophy of science. I'm not entirely sure what you mean by the last sentence - could you elaborate on how you think graphics play a role in the reproduction of scientific knowledge, rather than in its initial production? Do you mean that they harbor important didactic properties? $\endgroup$
    – Max Muller
    Feb 5 at 13:05
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    $\begingroup$ Well, if we hold that some scientific knowledge or insight about a phenomenon is generated by our visual or tactile senses, and if some of this is found difficult to reduce to words, then a good graphical representation of those impressions will help to reproduce the knowledge. Because reproduction happens repeatedly under different circumstances, it is easier to study the benefit of individual factors - such as the presence of absence of a graphical representation. For example, an educator can try and talk about circuits with and without a circuit diagram. (1/2) $\endgroup$
    – Steve
    Feb 5 at 14:55
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    $\begingroup$ With the initial production of the knowledge however, the process tends to be haphazard and not clearly characterised. Feynman invented his (fairly abstract) diagrams to teach his own understanding - which bear no correspondence to how he learned. The diagrams may have helped to reproduce more practitioners, and advance science in that way, but it's not clear they make anyone's knowledge any deeper than Feynman's already was. Unless by chance, there's no reason the diagrams should contain more insight than what Feynman already had, and what he intended to teach. (2/2) $\endgroup$
    – Steve
    Feb 5 at 14:57
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    $\begingroup$ Your question is written as if under an assumption that diagrams were always a help to scientific advancement. Would it also be within the scope of what you are looking for, to hear about cases where diagrams have been a hindrance? :) $\endgroup$
    – terry-s
    Feb 10 at 1:51

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