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...any important principles than can be got without their aid; and that there are many problems of pure theory, which no one who has once learned to use diagrams will willingly handle in any other way. (=-=Marshall, 1890-=-) The following is a simple and typical example of their use (see Figure 4): The abcissa of the diagram represents the quantity of a commodity that is produced or demanded, and the ordinate, the price...

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...roblems, human beings use both internal representations, stored in their brains, and external representations, recorded on a paper, on a blackboard, or on some other medium. Some investigators (e.g., =-=Pylyshyn, 1973-=-) have argued that all internal representations are propositional, while others (e.g., Anderson, 1978) have argued that there is no operational way in which an internal propositional representation ca...

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...ntations, recorded on a paper, on a blackboard, or on some other medium. Some investigators (e.g., Pylyshyn, 1973) have argued that all internal representations are propositional, while others (e.g., =-=Anderson, 1978-=-) have argued that there is no operational way in which an internal propositional representation can be distinguished from a diagrammatic one. Although our discussion may be relevant to this current c...

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...tudied in elementary physics. The solver might be asked to relate the masses of A and B. Figure 5b shows the artificial “free-body” diagrams that are always recommended for solution of such problems (=-=Halliday & Resnick, 1970-=-, Sears, Zemansky & Young, 1981, Heller & Reif, 1984). There are two diagrams, one for car A and one for car B. F,, is the force on car A due to car B, and F,, is the force on B due to A. These forces...

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...to just these kinds of procedural replacements of declarative knowledge. Information processing schemes for making such replacements are largely based on the formalism of adaptive production systems (=-=Waterman, 1970-=-). An early example of a program capable of converting declarative statements defining a problem into processes is UNDERSTAND (Hayes & Simon, 1974). This idea has subsequently been developed extensive...

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... Representation Mean? 1.1.1 Informational and Computational Efficiency. At the core of our analysis lie the wholly distinct concepts of informational and computational equivalence of representations (=-=Simon, 1978-=-). Two representations are informationally equivalent if all of the information in the one is also inferable from the other, and vice versa. Each could be constructed from the information in the other...

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...ely based on the formalism of adaptive production systems (Waterman, 1970). An early example of a program capable of converting declarative statements defining a problem into processes is UNDERSTAND (=-=Hayes & Simon, 1974-=-). This idea has subsequently been developed extensively by Neves and Anderson (1981) and others. The benefits of more powerful inference rules are, of course, not limited to physics. For example, in ...

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...in the problem-solving process. Failing to use these features is probably part of the reason why some diagrams seem not to help solvers, while others do provide significant help (Paige & Simon, 1966, =-=Larkin, 1983-=-). The advantages of diagrams, in our view, are computational. That is diagrams can be better representations not because they contain more information, but because the indexing of this information ca...