Distance in depth: A comparison of explicit and implicit numerical distances in the horizontal and radial dimensions

: Numbers are a constant presence in our daily lives: A brain devoid of the ability to process numbers would not be functional in its external environment. Comparing numerical magnitudes is a fundamental ability that requires the processing of numerical distances. From magnitude comparison tasks, a comparison distance effect (DE) emerges: It describes better performance when comparing numerically distant rather than close numbers. Unlike other signatures of number processing, the comparison DE has been assessed only implicitly, with numerical distance as nonsalient task property. Different assessments permit identification of different cognitive processes underlying a specific effect. To investigate whether explicit and implicit assessment of the comparison DE influences numerical cognition differently, we introduced the distance classification task, involving explicit classification of numbers as close or far from a reference. N = 93 healthy adults classified numbers either by magnitude or by numerical distance. To investigate associations between numerical and physical distance, response buttons were positioned horizontally (Experiment 1) or radially (Experiment 2). In both experiments, there was an advantage for both the closest and farthest numbers with respect to the reference during distance classification, but not during magnitude classification. In Experiment 2, numerically close/far numbers were classified faster with the close/far response button, respectively, suggesting radial correspondence between physical and representational distances. These findings provide new theoretical and methodological insights into the mental representation of numbers. (PsycInfo Database Record (c) 2024 APA, all rights reserved)

More Instructions Make Fewer Subtractions

Research on problem solving offers insights into how humans process task-related information and which strategies they use (Newell and Simon, 1972; Öllinger et al., 2014). Problem solving can be defined as the search for possible changes in one's mind (Kahneman, 2003). In a recent study, Adams et al. (2021) assessed whether the predominant problem solving strategy when making changes involves adding or subtracting elements. In order to do this, they used several examples of simple problems, such as editing text or making visual patterns symmetrical, either in naturalistic settings or on-line. The essence of the authors' findings is a strong preference to add rather than subtract elements across a diverse range of problems, including the stabilizing of artifacts, creating symmetrical patterns, or editing texts. More specifically, they succeeded in demonstrating that “participants were less likely to identify advantageous subtractive changes when the task did not (vs. did) cue them to consider subtraction, when they had only one opportunity (vs. several) to recognize the shortcomings of an additive search strategy or when they were under a higher (vs. lower) cognitive load” (Adams et al., 2021, p. 258). Addition and subtraction are generally defined as de-contextualized mathematical operations using abstract symbols (Russell, 1903/1938). Nevertheless, understanding of both symbols and operations is informed by everyday activities, such as making or breaking objects (Lakoff and Núñez, 2000; Fischer and Shaki, 2018). The universal attribution of “addition bias” or “subtraction neglect” to problem solving activities is perhaps a convenient shorthand but it overlooks influential framing effects beyond those already acknowledged in the report and the accompanying commentary (Meyvis and Yoon, 2021). Most importantly, while Adams et al.'s study addresses an important issue, their very method of verbally instructing participants, together with lack of control over several known biases, might render their findings less than conclusive. Below, we discuss our concerns that emerged from the identified biases, namely those regarding the instructions and the experimental materials. Moreover, we refer to research from mathematical cognition that provides new insights into Adams et al.'s findings

“BreaThink”: breathing affects production and perception of quantities

Cognition is shaped by signals from outside and within the body. Following recent evidence of interoceptive signals modulating higher-level cognition, we examined whether breathing changes the production and perception of quantities. In Experiment 1, 22 adults verbally produced on average larger random numbers after inhaling than after exhaling. In Experiment 2, 24 further adults estimated the numerosity of dot patterns that were briefly shown after either inhaling or exhaling. Again, we obtained on average larger responses following inhalation than exhalation. These converging results extend models of situated cognition according to which higher-level cognition is sensitive to transient interoceptive states

Distance in Depth: A comparison of explicit and implicit numerical distances in the horizontal and radial dimensions.

Numbers are a constant presence in our daily lives: A brain devoid of the ability to process numbers would not be functional in its external environment. Comparing numerical magnitudes is a fundamental ability that requires the processing of numerical distances. From magnitude comparison tasks, a comparison distance effect (DE) emerges: It describes better performance when comparing numerically distant rather than close numbers. Unlike other signatures of number processing, the comparison DE has been assessed only implicitly, with numerical distance as non-salient task property. Different assessments permit identification of different cognitive processes underlying a specific effect. To investigate whether explicit and implicit assessment of the comparison DE influence numerical cognition differently, we introduced the Distance classification task, involving explicit classification of numbers as close or far from a reference. N=93 healthy adults classified numbers either by magnitude or by numerical distance. To investigate associations between numerical and physical distance, response buttons were positioned horizontally (Experiment 1) or radially (Experiment 2). In both experiments, there was an advantage for both the closest and farthest numbers with respect to the reference during distance classification, but not during magnitude classification. In Experiment 2, numerically close/far numbers were classified faster with the close/far response button, respectively, suggesting radial correspondence between physical and representational distances. These findings provide new theoretical and methodological insights into the mental representation of numbers

Effects of attentional shifts along the vertical axis on number processing: an eye-tracking study with optokinetic stimulation

Previous studies suggest that associations between numbers and space are mediated by shifts of visuospatial attention along the horizontal axis. In this study, we investigated the effect of vertical shifts of overt attention, induced by optokinetic stimulation (OKS) and monitored through eye-tracking, in two tasks requiring explicit (number comparison) or implicit (parity judgment) processing of number magnitude. Participants were exposed to black-and-white stripes (OKS) that moved vertically (upward or downward) or remained static (control condition). During the OKS, participants were asked to verbally classify auditory one-digit numbers as larger/smaller than 5 (comparison task; Exp. 1) or as odd/even (parity task; Exp. 2). OKS modulated response times in both experiments. In Exp.1, downward attentional displacement increased the Magnitude effect (slower responses for large numbers) and reduced the Distance effect (slower responses for numbers close to the reference). In Exp.2, we observed a parity by magnitude interaction that was amplified by downward OKS. Moreover, eye tracking analyses revealed an influence of number processing on eye movements both in Exp. 1, with eye gaze shifting downwards during the processing of numbers 1-2 as compared to 8-9; and in Exp. 2, with leftward shifts after large even numbers (6,8) and rightward shifts after large odd numbers (7,9). These results provide evidence of bidirectional links between number and space and extend them to the vertical dimension. Moreover, they document the influence of visuo-spatial attention on processing of numerical magnitude, numerical distance and parity. Together, our findings are in line with grounded and embodied accounts of numerical cognition