Abstract
Why do people create extra representations to help them make sense of situations, diagrams, illustrations, instructions and problems? The obvious explanation—external representations save internal memory and computation —is only part of the story. I discuss seven ways external representations enhance cognitive power: they change the cost structure of the inferential landscape ; they provide a structure that can serve as a shareable object of thought ; they create persistent referents; they facilitate re-representation ; they are often a more natural representation of structure than mental representations; they facilitate the computation of more explicit encoding of information ; they enable the construction of arbitrarily complex structure; and they lower the cost of controlling thought—they help coordinate thought. Jointly, these functions allow people to think more powerfully with external representations than without. They allow us to think the previously unthinkable.
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- 1.
Although this argument concerns visual processing, it applies equally well to the physical interactions we can perform on the physical object.
- 2.
Reformulation is not limited to formal problem solving. The statement “Police police police police police” is easier to understand when restated at “Police who are policed by police, also police other police”. Most people would not break out their pens to make sense of that statement, but few of us can make sense of it without saying the sentence out loud several times.
- 3.
To see why music can be both referent and representation (terrain and also map) ask whether there is a difference between hearing sound and hearing sound as music. The sound is the terrain; music is the conceptualizing structure that interprets the sound; it maps it.
- 4.
Vygotsky among others has suggested that we mastered thinking externally, by conforming our behavior to social norms of rational inquiry, and that what we learned to do first on the outside we came to do on the inside. Thus, the reason we can do math in our head is because we can do math in the world. The same applies to thinking internally in auditory images. We think in words internally, using auditory images of sounds, because when we think in public we speak. Thinking internally is simulating what we do externally, though Vygotsky did believe that inner speech of adults would be much compressed and unintelligible to anyone except the thinker (Vygotsky 1986).
- 5.
Hutchins (2001).
- 6.
Entry from Wikipedia on Kim Peek the inspiration for the character in the movie Rain Man: “He reads a book in about an hour, and remembers almost everything he has read (…) His reading technique consists of reading the left page with his left eye and the right page with his right eye and in this way can read two pages at time with a rate of about 8–10 s per page. He can recall the content of some 12,000 books from memory. Wikipedia on Kim Peek. http://en.wikipedia.org/wiki/Kim_Peek Nov 2009.
- 7.
From Marr (1977, p. 38) “One promising candidate for a Type 2 theory is the problem of predicting how a protein will fold. A large number of influences act on a large polypeptide chain as it flaps and flails in a medium. At each moment only a few of the possible interactions will be important, but the importance of those few is decisive. Attempts to construct a simplified theory must ignore some interactions; but if most interactions are crucial at some stage during the folding, a simplified theory will prove inadequate. Interestingly, the most promising studies of protein folding are currently those that take. a brute force approach, setting up a rather detailed model of the amino acids, the geometry associated with their sequence, hydrophobic interactions with the circumambient fluid, random thermal perturbations etc., and letting the whole set of processes run until a stable configuration is achieved (Levitt and Warshel 1975).”
- 8.
In practice, though not in principle, computers fall into this category. When a workplace has been augmented with tools such as wizards, software agents and the like, it is possible to multiply the potency of basic strategies of interaction to the point where such increases qualitatively change what humans can do, what they can make sense of, and so on. Sometimes our best tools are analog, however, and these are the ones that may provide in principle augmentations to human thought.
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Kirsh, D. (2017). Thinking with External Representations. In: Cowley, S., Vallée-Tourangeau, F. (eds) Cognition Beyond the Brain. Springer, Cham. https://doi.org/10.1007/978-3-319-49115-8_4
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