The phenomenon of thinking through visual processing
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- In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.
- Martin Gardner "Mathematical Games", in Scientific American (October 1973); also quoted in Roger B. Nelson, Proofs Without Words: Exercises in Visual Thinking (1993), "Introduction", p. v
- When visualization tools act as a catalyst to early visual thinking about a relatively unexplored problem, neither the semantics nor the pragmatics of map signs is a dominant factor. On the other hand, syntactics (or how the sign-vehicles, through variation in the visual variables used to construct them, relate logically to one another) are of critical importance.
- Alan MacEachren, How Maps Work: Representation, Visualization, and Design (1995) p. 368
- Visual thinking is often driven more strongly by the conceptual knowledge we use to organize our images than by the contents of the images themselves. Chess masters are known for their remarkable memory for the pieces on a chessboard. But it's not because people with photographic memories become chess masters. The masters are no better than beginners when remembering a board of randomly arranged pieces. Their memory captures meaningful relations among the pieces, such as threats and defenses, not just their distribution in space.
- Steven Pinker, How the Mind Works (1997) p. 295