Inhibitory Mechanisms in the Processing of Negations: A Neural Reuse Hypothesis

Negation is known to have inhibitory consequences for the information under its scope. However, how it produces such effects remains poorly understood. Recently, it has been proposed that negation processing might be implemented at the neural level by the recruitment of inhibitory and cognitive control mechanisms. On this line, this manuscript offers the hypothesis that negation reuses general-domain mechanisms that subserve inhibition in other non-linguistic cognitive functions. The first two sections describe the inhibitory effects of negation on conceptual representations and its embodied effects, as well as the theoretical foundations for the reuse hypothesis. The next section describes the neurophysiological evidence that linguistic negation interacts with response inhibition, along with the suggestion that both functions share inhibitory mechanisms. Finally, the manuscript concludes that the functional relation between negation and inhibition observed at the mechanistic level could be easily integrated with predominant cognitive models of negation processing.

Categories of Large Numbers in Line Estimation

How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words-thousand, million, billion-to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position and response time are expected near the boundaries between categories. In contrast to previous work (Landy, Silbert, & Goldin, 2013) that suggested only that a minority of college undergraduates employed categorical boundaries, we find that discontinuities near category boundaries occur in most or all participants, but that accurate and inaccurate participants respond in opposite ways to category boundaries. Accurate participants highlight contrasts within a category, whereas inaccurate participants adjust their responses toward category centers.

Mastering algebra retrains the visual system to perceive hierarchical structure in equations

Formal mathematics is a paragon of abstractness. It thus seems natural to assume that the mathematical expert should rely more on symbolic or conceptual processes, and less on perception and action. We argue instead that mathematical proficiency relies on perceptual systems that have been retrained to implement mathematical skills. Specifically, we investigated whether the visual system-in particular, object-based attention-is retrained so that parsing algebraic expressions and evaluating algebraic validity are accomplished by visual processing. Object-based attention occurs when the visual system organizes the world into discrete objects, which then guide the deployment of attention. One classic signature of object-based attention is better perceptual discrimination within, rather than between, visual objects. The current study reports that object-based attention occurs not only for simple shapes but also for symbolic mathematical elements within algebraic expressions-but only among individuals who have mastered the hierarchical syntax of algebra. Moreover, among these individuals, increased object-based attention within algebraic expressions is associated with a better ability to evaluate algebraic validity. These results suggest that, in mastering the rules of algebra, people retrain their visual system to represent and evaluate abstract mathematical structure. We thus argue that algebraic expertise involves the regimentation and reuse of evolutionarily ancient perceptual processes. Our findings implicate the visual system as central to learning and reasoning in mathematics, leading us to favor educational approaches to mathematics and related STEM fields that encourage students to adapt, not abandon, their use of perception.