Thinking Visually

Mapping A second class of problems does not require one to consider spatial or visual information per se, but recruits imagery by establishing a mapping between non-spatial information and spatial representations. There are two situations in which such a mapping would be useful. The first is when a depictive representation would be more concise than a verbal or propositional representation alone. For example, finding a representation that facilitates solution of the problem is the impetus behind setting up and working with 'models' of syllogisms rather than carrying out a purely syntactical calculation. Just as Venn diagrams were developed to facilitate the solution of syllogisms on paper, people may spontaneously adopt depictive representational methods for reasoning problems performed 'in the head'. In these cases, the depictions should have a direct correspondence between spatial and conceptual properties. For example, putting one circle inside another corresponds directly to the idea that members of one class are also members of another class; similarly, having more of a visual dimension correspond to more of a quantity (e.g. increased height for increased intelligence) has such a direct correspondence. Thus, the depiction is useful not only because it is concise, having fewer 'chunks' than would be required in a different format, but because there is a simple and direct way of decoding the depiction. The second situation is when the imagery method of solution involves a simpler algorithm. For example, consider a problem in which one tries to 'exclusive-or' (XOR) together two strings of binary digits. The exclusiveor takes a pair of digits (e.g. 1, 0) and yields a 1 if either the first or the