Interactions between abstract actions and apparent distance

Interactions between abstract actions and apparent distance Kathryn Sears (kathryn.sears@richmond.edu) David Landy (dlandy@richmond.edu), Jessica Lesky (jessica.lesky@richmond.edu) Department of Psychology, University of Richmond Richmond, VA 23173 Abstract Perceptions influence the way we act in our environment based upon judgments assessing required efforts to perform an action and the availability and demand for immediate action on an object (Proffitt, 2006B). Social and physical anxiety has been shown to distort perceptions of depth and perceptions of object size (Stefanucci et al., 2008; Canal- Bruland et al., 2010). Relatively little work, however, has explored the potential role of depth perception in abstract reasoning tasks (Landy & Linkenauger, 2010). In Experiment 1, the relationship between depth perception and the order of actions taken to simplify arithmetic expressions was investigated by manipulating apparent distances of arithmetic operations of high and low syntactic precedence. When the high precedence operations appeared to be closer to the participant, expressions were solved more quickly than when low precedence expressions appeared to be closer. Experiment 2 explored the whether the affordance of abstract actions conversely impacted perceived distance by asking participants to make distance judgments to multiplication and addition operations. Experiment 2 found no impact of anxiety about mathematics on perceived distance. However, effects resulting from condition assignment were found to influence perceived distances, as well as solving strategy. We interpret results in terms of attention, which we speculate plays a key role moderating both ordering behavior and perceived distance. Keywords: Perception; Anxiety; Attention Introduction The basic purpose of perception is to guide sensible action. Specifically, perception functions as a tool that informs and guides actions (Proffitt, 2006A). Perception involves consideration of the necessary efforts required to perform an action, which in turn may bias judgments of object size and proximity. For instance, perceived distance of an object is more than simple metric distance. Participants carrying a heavy backpack estimate the slant of hills to be steeper than those not wearing backpacks (Proffitt, 2006B). Likewise, simply intending to act on an object could make it seem closer Witt & Proffitt (2005). Witt & Proffitt (2005) found that athletes playing well reported a softball ball as being bigger than its actual size and therefore closer. Their ability to hit the ball was correlated with their batting average, demonstrating the relationship between perceptions of object size and performance when acting on that object. Perceptual phenomena like these indicate that perception relates the body and goals to the opportunities and costs of acting in the physical environment. Although the connection between concrete physical action capabilities and depth perception is well documented, much less work has explored the relationship between perceived depth and non-concrete behaviors. There is evidence that anxiety also influences perception (Proffitt, 2006A). For instance, participants with a fear of heights judge hills to be steeper than do those who are less afraid (Stefanucci et al, 2008). According to Teachman et al (2008), fear of heights is associated with perceptual biases in judging heights, implying that an individual’s emotional state influences what is seen, perhaps because it affects perceived costs, such as the cost of falling down a steep hill. Anxiety not only distorts perception in the sense that distances appear farther and angles steeper, but also by altering the appearance of an object’s size. Canal-Bruland, Pijpers, & Oudejans (2010) studied the relationship between anxiety and depth perception, while also taking into consideration perceptions of object size. Participants were asked to throw darts at a target from a position on a rock wall. Canal-Bruland, et al. found that the low anxiety group performed better and saw the target as bigger. However, these findings are limited to perceptions related to actions in the physical world. Even less is known about cases in which the action itself is abstract or non-physical. In the case of abstract calculation, since all actions are in principle equally easy to perform, the logic of perceived energetic cost per se does not predict any relationship between depth and intentions to act. However, mathematical rules specify that certain operations are to be performed before other others. Particularly relevant for the studies reported here are the order of precedence rules, which require that multiplications be executed before additions., As a result, some operations demand action before others, making, it possible to vary the relative availability of actions. Furthermore, since the actions do not depend on reach distance, any action lies within the action boundary (Fajen, 2005). Landy & Linkenauger (2010) found a relationship between the availability of computational actions in compound arithmetic expressions and judgments of depth. The study explored judged depth of terms, and indeed found that participants in a forced-choice task preferred to align depth and precedence; furthermore, in a face-vase illusion in which sub-expressions of mathematical equations were superimposed onto a face-vase illusion, when the times sign was over the vases, participants reported seeing the faces less often than when the times sign was over the faces. These perceptual effects can be explained by the