Judgments of spatial extent are fundamentally illusory: ‘Additive-area’ provides the best explanation

Abstract

How do we represent extent in our spatial world? Recent work has shown that even the simplest spatial judgments estimates of 2D area present challenges to our visual system. Indeed, area judgments are best accounted for by`additive area' (the sum of objects' dimensions) rather than`true area' (i.e., a pixel count). But is`additive area' itself the right explanation or might other models better explain the results? Here, we oer three direct and novel demonstrations that`additive area' explains area judgments. First, using stimuli that are simultaneously equated for number and all other confounding dimensions, we show that area judgments are nevertheless explained by`additive area'. Next, we show how`scaling' models of area fail to explain even basic illusions of area. By contrasting squares with diamonds (i.e., the same squares, but rotated), we show a robust tendency to perceive the diamonds as having more area an eect that no other model of area perception would predict. These results not only conrm the fundamental role of`additive area' in judgments of spatial extent, but they highlight the importance of accounting for this dimension in studies of other features (e.g., density, number) in visual perception.

A Ubiquitous Illusion of Volume: Are Impressions of 3D Volume Captured by an “Additive Heuristic”?

“…This experiment borrows a design from studies on “additive area,” in which observers were shown stimuli that consisted of two set of shapes (Yousif et al., 2020; Yousif & Keil, 2019). The two sets of shapes varied in either total additive volume (AV) (while mathematical volume was equated) or total mathematical volume (MV) (while additive volume was held constant).…”

“…If perceived volume is veridical, we should expect that observers indicate that a set with more “mathematical volume” has more volume—but they should be unable to discriminate sets which vary only in “additive volume.” However, if perceived volume is captured solely by “additive volume” (as has been shown for 2D area judgments; e.g., Yousif & Keil, 2019; Yousif et al., 2020), observers should indicate that a set with more “additive volume” has more volume, but that sets varying in “mathematical volume” are indistinguishable. Finally, the results may be mixed: Observers may use both “additive volume” and “mathematical volume” to make volume judgments—or they may use “additive volume” under some, but not all circumstances.…”

“…However, according to the “additive area” view, your visual system may perceive these two as being approximately equal (because their “additive areas” both sum to 8). Across many different paradigms, using many different shapes and procedures, variance in “additive area” predicts human area judgments better than variance in true, mathematical area—even to the extent that observers are unable to discriminate differences in true, mathematical area as large as 30% when “additive area” is equated (Yousif et al., 2020; Yousif & Keil, 2019).…”

“…These illusions of area might arise from a failure to properly perceive or integrate multiple spatial dimensions (Carbon, 2016; see also Yousif et al., 2020). If true, 3D volume perception should reveal the same failure.…”

“…To do so, we had observers complete a volume judgment task on 3D printed stimuli. We created sets of 3D printed cubes and spheres that varied in “additive volume” (while “mathematical volume” was equated) or “mathematical volume” (while “additive volume” was equated; see Yousif & Keil, 2019, Yousif et al., 2020 for additional examples of this design).…”