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Thinking with Diagrams

Edited by Alan F. Blackwell
Dordrecht: Kluwer Academic Publishers
Cloth: 0-792-36944-0

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Reviewed by
Suchi Patel
Operational Research and Systems Group, Warwick Business School, University of Warwick, UK.

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Diagrammatic representations range from maps, line graphs and bar charts to engineering blueprints and architects' sketches. Their definition encompasses any type of abstract pictorial representation and thus does not include photographs and videos. Research into diagrammatic representations is long established. In the latter half of the twentieth century much of this research has concentrated on how we construct diagrams to resemble systems or problems and how we use these diagrams to give us a greater understanding of these systems.

The main reason for the renewed interest in such matters is progress in computer systems. With the advance of this technology, increasing numbers of studies have considered how machines may represent information in diagrammatic form and how they can reason using the resulting diagrams. Some studies concentrated on issues relating to comprehension and reasoning; exploring the construction of diagrams and considering how both humans and computers can comprehend, communicate and reason by using them. Other studies have looked at the differences between diagrammatic and linguistic representations of the same situation; how people respond to these and how effective each type of representation is in conveying information.

Thinking with Diagrams (like previous books in the area of diagrammatic representation) comprises a number of investigations into cognition and logic across a set of applications ranging from the teaching of ideas to the development of architectural sketches. The book starts with a concise introduction, illustrating the suspicions that various people have entertained about the actual value of diagrams. Arguments for the necessity of diagrammatic research are then developed. There is then a brief overview of the subject matter to be found in the subsequent chapters.

The first paper, entitled The Graphic-Linguistic Distinction considers the properties of linguistic and graphical representations and examines where the boundary between the two lies. It illustrates the relevant distinctions by giving clear and appropriate examples and formulating hypotheses. The hypotheses explain the differing nature of the two representational types in terms of seven key ideas:

  1. Digital versus Analogue
  2. Sequential versus Two Dimensional
  3. Relation Symbols and Object Symbols
  4. Homomorphism
  5. Content Specificity
  6. Intrinsic and Extrinsic Constraints
  7. Projection of Nomic Constraints

Overall, the paper provides a good overview of this issue in terms of the dichotomies set up. It is left up to the reader to decide which of the ideas, if any, s/he considers relevant.

The aim of the second paper, entitled Aligning Logical and Psychological Perspectives on Diagrammatic Reasoning, is to establish a conceptual framework for explaining the efficacy of diagrammatic representations for diverse users in varied tasks (p. 29). The authors identify a requirement that such a framework should fulfil: being able to provide a basis for predicting and comparing diagrammatic performances with analogous performances using differing representation systems for example sentential ones (p. 29). The paper defines the efficacy of a representational system in terms of computational efficacy (low complexity of inference) and expressive efficacy (semantic properties such as consistency).

The authors identify three areas which their proposed framework should focus on: constraints on representations and their domains, direct interpretation of representing relations and the availability of constraints (p. 30). The paper then explicitly looks at these areas in more detail and explores past examples such as Euler's circles and the Helly constraint for convex regions in two dimensions. Section 7 then describes the theoretical framework, by logically and psychologically defining what is considered to be an effective Diagrammatic Representation system. The next section analyses Tile diagrams to see how they fare under this framework and to illustrate how the proposed framework may be implemented in deciding the efficacy of a diagrammatic representation. The rest of the paper identifies ways of extending both the logical approach and the psychological theory behind the framework. The conclusion is well-balanced and identifies the key limitations of the study.

The next paper, entitled Diagrammatic Reasoning: An Artificial Intelligence Perspective, examines the use of diagrammatic representation in automated problem solving. The review explains how artificial intelligence (AI) systems that have claimed some degree of diagrammatic reasoning capability have tended to operate within the two problem domains of geometric theorem proving and discovery, and reasoning about physical systems (p. 63). The paper identifies contrasting features of these two domains with respect to how well defined the problems generally are. It explores the concepts of concretisation, knowledge indexing, and inference by inspection and transformation to convey how important diagrams are to humans.

The next chapter entitled, Cognitive Approaches to Understanding Diagrammatic Representations, explores the relationship between two different parts of a representational system: (1) internal to the mind (cognition), and (2) external visual media that presents the diagram. It studies how the two aspects can be present to differing extents and illustrates this by using the examples of a weather map, the carbon cycle and elastic collisions. The idea that comes across is that different people will understand different things from certain representations (depending on their knowledge base) while other representations will have less cognitive dependency such that most people who see them will understand everything. The paper also shows that if there is too much visual material, the diagram becomes harder to understand and remember. It also explains how diagrams can be broken up into a few basic parts: symbols, expressions and operators. These parts enable the formation of a huge variety of diagrams consisting of similar components but these diagrams are arguably more diverse than propositional representations. The paper concludes by listing the main points that have been established in the text and this provides a good summary reference.

The next paper, Cognitive Factors in Programming with Diagrams, deals with the scope of visual programming languages (VPLs) from the perspective of the psychology of programming. The paper starts by explaining the reasons why VPLs were introduced and the role they play within software development. The paper goes on to outline some specific methods that have been developed for considering the psychology of programming. Then it goes on to review previous studies in two sections entitled "empirical studies of notations" and "cognitive dimensions of notations". The previous empirical studies of diagrammatic notations used in programming are considered at great length. The examples given include flowcharts and algorithms. The paper explains how these categories of diagrams are not constrained by limitations of physical shape or the restrictions that prose suffers and therefore give greater freedom. It also summarises research reported by Scanlan on the comparison of structured flowcharts and textual "pseudo-code". This research concludes that structured flowchart representations for an algorithm are better understood in terms of comprehension time and response accuracy. The paper then presents a partial list of cognitive dimensions for notations with an explanatory discussion for each dimension and concludes with general paragraph dealing with the trade-offs between these dimensions.

The last sections of the paper consider some future research directions arising from current understanding of the cognitive factors involved in the use of VPLs. These sections again review the relevant literature. The authors indicate that there is potential for more research addressing basic questions arising from previous empirical research in the areas of metaphor and representations, the role of reusable components, programming languages for children, paradigm and comprehension, paradigm and design, multiple representations, scalability and the software lifecycle. Several of these areas are common concerns in other types of programming languages and methodologies.

The penultimate paper (entitled Learning to Think and Communicate with Diagrams: 14 Questions to Consider) focuses on the application of AI techniques that can support the process of learning to think and communicate with diagrams. It tries to convey the issues involved in developing diagrams that are useful for education and the trade-offs that may arise in this process. Three broad areas are considered in detail: (1) whether diagrams make certain things easier, (2) generalisation and transfer of diagrammatic skills once learnt, and (3) possible problems associated with learning too much at the same time. Under these headings, a number of more specific questions are then posed. These are then answered using previously published literature and logical reasoning. All the specific questions serve to add to the in depth understanding of a broad area. For example, for category (3) the two main questions are "How can we partition the cognitive load in a sensible way?" and "Should this experience be avoided?" These questions are then explored further using many sub-questions. The paper concludes by identifying some further issues that are emerging in the context of AI research in sections entitled "sense making through diagrammatic representations", "the self explanation effect and diagrams", "diagrams and educational discourse", and "Sensori-motor experience and diagrammatic reasoning."

The last paper concentrates on a specific application of diagrams and is entitled, Thinking with Diagrams and Architectural Design. The discussion starts by conveying the different uses of diagrams; problem solving, thinking, communication, exploration and development. The paper then goes on to describe the graphical indicators employed in architectural diagrams. Previously published work is summarised, explaining the key concepts that have emerged for this type of diagram, such the convention that all shapes and relationships are considered the same. The paper also explores how architects use bubble diagrams to examine relationships among sizes, adjacencies and approximate shapes. The paper focuses mainly on application and no formal conclusion is presented.

Overall, I feel the book comprehensively outlines the key motivations for research in the field of diagrammatic representations. The book is fairly concise and readable. However, it might have benefited from a concluding chapter in which the common themes of the individual chapters were drawn together.

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© Copyright Journal of Artificial Societies and Social Simulation, 2003