Conceptual Metaphor and Graphical Convention Influence the Interpretation of Line Graphs

Multimodality matters in numerical communication

“…English speakers talk and write about numbers as "rising, " and they also often gesture upwards when using such language (Winter et al, 2013). This mapping between numbers and vertical space can also be found in graphs, where the y-axis typically represents higher values with higher vertical locations (see, e.g., Woodin et al, 2022). Size-based mappings of quantity are similarly expressed in language, sign, gesture, and graphs: both language and gesture can represent numerical concepts in terms of spatial extent (e.g., "tiny number" or pinching the fingers together), and data visualizations can represent magnitudes in terms of area, such as in the case of pie charts and bar charts, for which area is the primary perceptual cue for quantity (Skau and Kosara, 2016;Kosara, 2019a).…”

“…Size-based mappings of quantity are similarly expressed in language, sign, gesture, and graphs: both language and gesture can represent numerical concepts in terms of spatial extent (e.g., “tiny number” or pinching the fingers together), and data visualizations can represent magnitudes in terms of area, such as in the case of pie charts and bar charts, for which area is the primary perceptual cue for quantity ( Skau and Kosara, 2016 ; Kosara, 2019a ). When data visualizations violate these shared cognitive mappings between space and quantity, they are less likely to be understood (e.g., Pandey et al, 2015 ; Woodin et al, 2022 ). From this we can form the prediction, so far untested, that verticality-based encodings of quantity in graphs and gesture should benefit from language that uses vertical expressions for quantity, while size-based encodings in graphs and gesture should benefit from size-based language.…”

“…The fact that graphs are not always understood correctly without explicit instruction demonstrates the importance of these graphical conventions. Graphs in Cartesian coordinates, for instance, use distance from the origin to represent numerical values—thus using distance iconically —but people must learn the graphical convention that numerical values increase upward and rightward, not downward and leftward ( Woodin et al, 2022 ). Even richly iconic graphs can thus include symbolic elements.…”

The role of perceptual and action effector strength of graphs and bases of mathematical metaphors in the metaphorical processing of mathematical concepts

“…The description of mathematical concepts such as a function through graphs in a Cartesian plane or in a three-dimensional Cartesian coordinate system is one category of mathematical metaphors that a highly abstract mathematical concept can be grounded in concrete concepts through the sensory-motor system. A recent work has suggested that not only mathematical concepts but also ordinary concepts can be processed in terms of embodied graphs ( Woodin et al, 2022 ). Transforming abstract mathematical concepts and problems into visual representations is a common strategy in mathematics.…”

Visualization for Villainy

“…3), aspect ratios, and area encodings. Woodin et al [78] explore the deceptive potential of inverted axes in the context of metaphor. McNutt et al [54] describe a wide family of errors that can be forced upon users from across the visualization pipeline, to cause what they term visualization mirages.…”