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

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 offer two 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 effect that no other model of area perception would predict. These results not only confirm 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.