Visualizing thought: Mapping category and continuum

Visualizing thought: Mapping category and continuum Barbara Tversky Teachers College, Columbia University, 525 W. 120 th Street New York, NY 10027 USA James E. Corter Teachers College, Columbia University, 525 W. 120 th Street New York, NY 10027 USA Lixiu Yu Stevens Institute of Technology, Castle Point on Hudson Hoboken, NJ 07030 USA David L. Mason Teachers College, Columbia University, 525 W. 120 th Street New York, NY 10027 USA Jeffrey V. Nickerson Stevens Institute of Technology, Castle Point on Hudson Hoboken, NJ 07030 USA Abstract Abstract thought has roots in the spatial world. Abstractions are expressed in the ways things are arranged in the world as well as the ways people talk and gesture. Mappings to the page should be better when they are congruent, that is, when the abstract concept matches the spatial one. Congruent mappings can be revealed in people’s performance and preferences. Congruence is supported here for visual representations of continuum and category. Congruently mapping a continuous concept, frequency, to a continuous visual variable and mapping a categorical concept, class inclusion, to a categorical visual variable were preferred and lead to better performance than the reverse mappings. Keywords: Diagrammatic reasoning; spatial metaphors; design; networks; information systems Introduction Abstract thought has roots in the spatial world (e. g., Boroditsky, 2002; Lakoff & Johnson, 1980; Shepard, 2001; Talmy, 1983; Tversky, Kugelmass, & Winter, 1991). These abstractions are expressed in the ways people organize space as well as in the ways they speak, gesture, and put things on the page (Tversky, 2011, in press). External visual expressions of thought, from cave paintings to computer bits, go back tens of thousands of years, though expressions of abstract thought have become common only with the widespread use of paper. Visualizations of thought are especially apt for conveying information that is intrinsically spatial, like environments, organisms, and objects, where elements and relations in real space can be mapped onto elements and relations on the page. Yet they are also effective for conveying concepts and relations that are metaphorically spatial, including temporal, social, quantitative, and more, in part because such concepts have “natural” mappings to space (e. g., Landy & Goldstone, 2007; Tversky et al., 1991). These natural mappings seem to come from the ways that we arrange space to suit our needs and the ways that space governs our behavior (Tversky, in press). They are also evident in language, in common expressions and metaphors (e. g., Cooper & Ross, 1975; Lakoff & Johnson, 1980). For example, people, trees, and more grow stronger as they grow taller; taller piles, buildings, and bridges must be stronger than smaller ones. Such associations provide a worldly foundation for the many metaphors associating up with good, strength, and power. By mapping abstract concepts and relations congruently to space and spatial relations, visualizations not only promote comprehension but also inference (cf. Bertin, 1981; Norman, 1993; Zhang, 2000). They allow users to apply highly-practiced skills of spatial reasoning to abstract reasoning (e. g., Tversky, 2001; in press). Despite natural mappings, representing abstract relations graphically is not always straightforward. Several alternative means of visual expression are often available, and, typically, each of these has several possible interpretations. Many common and useful devices, like dots, lines, boxes, and arrows, are ambiguous, with multiple meanings, not unlike related spatial terms like link, frame, field, and relationship, which also have multiple meanings (e. g., Tversky, Zacks, Lee & Heiser, 2002). Arrows, for example, can indicate order, direction, movement, causality, and more (Heiser & Tversky, 2006). Yet, choosing the right representation is essential to fast and clear communication, and to effective reasoning with diagrams. Selecting the right representation for an abstraction does not have to be at the whim of a designer. The Production- Preference-Performance program provides empirical