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The use of diagrammatic reasoning in teaching economics for the digital economy
Published in James Juniper, The Economic Philosophy of the Internet of Things, 2018
This kind of diagram, which first appeared in the work of physicists such as Roland Penrose and Richard Feyneman, represents an alternative approach to that of commutative diagrams for articulating concepts in category theory. Although string diagrams had their origins in Feyneman’s work on quantum electrodynamics and Roland Penrose’s teaching of tensor calculus, these deployments were primarily heuristic. The work of Joyal and Street, from the Australian School of Category Theory, has established that string diagrams are planar diagrams that possess all the formal properties and the rigour of symbolic algebra (see Theorem 1.5 from Joyal and Street, 1988, and Theorem 1.2 from Joyal and Street, 1991, which establish coherence for planar monoidal categories). For this reason, string diagrams are now being used to represent much of the underlying mathematical structure of category theory, but in a far more abbreviated form than can be achieved by resorting to the usual kind of “diagram-chasing” to establish commutative properties (Curien, 2008; Marsden, 2014).
Diagrammatic User Interfaces
Published in Vincent G. Duffy, Advances in Applied Human Modeling and Simulation, 2012
I argue, therefore, that an appropriate diagrammatic user interface can go a long way toward explaining system actions and providing a deeper understanding of how a system works. A diagrammatic user interface employs a diagram of some kind to aid in system understanding. By diagram, I am referring to a graphical representation of how the objects in a domain of discourse are interrelated to one another. Unlike a linguistic or verbal description, a diagram is a type of information graphic that “preserves explicitly the information about topological and geometric relations among the components of the problem” (Larkin and Simon, 1987). That is to say, a diagram indexes information by location on a 2-D plane—3-D diagrams are also possible, but not yet commonplace. As such, related pieces of information can be grouped together on a plane, and interconnections between related elements can be made explicit through lines and other notational elements. Furnished with such a description, the user is better able to cope with technological complexity
Application of shape grammar to vernacular houses: a brief case study of Unconventional Villages in the contemporary context
Published in Journal of Asian Architecture and Building Engineering, 2023
Jiang Wang, Sheng Zhang, Wei Fan
SG is mainly used to express and convey the design intent through diagramming. In the specific application, the diagrams can be subdivided into shape, semantic, and description diagrams. Shape diagrams reproduce the object’s shape characteristics, aiding researchers in visually reasoning shape during the rule reasoning process (Rivollier et al. 2010). These diagrams usually maintain relatively fixed proportions and scales for traceability. Semantic diagrams abstract the object’s shape, obscuring precise “size” details and deleting unnecessary shape information. They present the relationship between shapes in a concise form. Dual diagrams and bubble diagrams (Xie and Ding 2021) fall under this category. Moreover, the description diagrams are a new representation after computer-intervention, representing the graphic information through programming and coding and then converting the digital information into specific shapes with the help of visualization tools. For example, Koning and Eizenberg (1981) constructed a comprehensive SG based on a corpus of 11 Prairie Houses and reproduced the generative reasoning process of Prairie Houses through shape iconography (Figure 4-1). Gholami, Soheili, and Manesh (2021), in the study of vernacular houses in Ekbatan, abstracted the functional shape of the floor plan and illustrated practical information and correlations using basic color blocks (Figure 4-2a). Bubble diagrams were also employed to present logical relationships better (Figure 4-2b). Herbert, Sanders, and Mills (1994) used shape diagrams to demonstrate the regular reasoning process of the layout of the Ndebele house in Africa. Descriptive diagrams were then used to illustrate the algorithm related to the shape diagram (Figure 4-3).