TY - JOUR A1 - Wood, Danielle A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Turn the beat around: Commentary on "Slow and fast beat sequences are represented differently through space" (De Tommaso & Prpic, 2020, in Attention, Perception, & Psychophysics) JF - Attention, perception, & psychophysics : AP&P ; a journal of the Psychonomic Society, Inc. N2 - There has been increasing interest in the spatial mapping of various perceptual and cognitive magnitudes, such as expanding the spatial-numerical association of response codes (SNARC) effect into domains outside of numerical cognition. Recently, De Tommaso and Prpic (Attention, Perception, & Psychophysics, 82, 2765-2773, 2020) reported in this journal that only fast tempos over 104 beats per minute have spatial associations, with more right-sided associations and faster responses for faster tempos. After discussing the role of perceived loudness and possible response strategies, we propose and recommend methodological improvements for further research. KW - Distance effect KW - Music cognition KW - Pitch KW - magnitude association KW - Semantic KW - congruity effect KW - SMARC KW - Sound recognition KW - Spatial cognition Y1 - 2021 U6 - https://doi.org/10.3758/s13414-021-02247-8 SN - 1943-3921 SN - 1943-393X VL - 83 IS - 4 SP - 1518 EP - 1521 PB - Springer CY - New York ER - TY - JOUR A1 - Shaki, Samuel A1 - Sery, Noa A1 - Fischer, Martin H. T1 - 1 + 2 is more than 2 + 1: Violations of commutativity and identity axioms in mental arithmetic JF - Journal of cognitive psychology N2 - Over the past decade or so, a large number of studies have revealed that conceptual meaning is sensitive to situational context. More recently, similar contextual influences have been documented in the domain of number knowledge. Here we show such context dependency in a length production task. Adult participants saw single digit addition problems of the form n1 + n2 and produced the sum by changing bi-directionally the length of a horizontally extended line, using radially arranged buttons. We found that longer lines were produced when n1 < n2 compared to n1 > n2 and that unit size increased with result size. Thus, the mathematical axioms of commutativity and identity do not seem to hold in mental addition. We discuss implications of these observations for our understanding of cognitive mechanisms involved in mental arithmetic and for situated cognition generally. KW - Operand order effect KW - Situated cognition KW - Mental number line KW - SNARC KW - Operational momentum Y1 - 2015 U6 - https://doi.org/10.1080/20445911.2014.973414 SN - 2044-5911 SN - 2044-592X VL - 27 IS - 4 SP - 471 EP - 477 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Shaki, Samuel A1 - Pinhas, Michal A1 - Fischer, Martin H. T1 - Heuristics and biases in mental arithmetic BT - revisiting and reversing operational momentum JF - Thinking & Reasoning N2 - Mental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum (OM) effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems (e.g., 3+0, 3-0) but reverse OM with non-zero problems (e.g., 2+1, 4-1). In a third experiment, we tested the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving. KW - Heuristics KW - mental arithmetic KW - mental number line KW - operational momentum KW - problem-solving Y1 - 2017 U6 - https://doi.org/10.1080/13546783.2017.1348987 SN - 1354-6783 SN - 1464-0708 VL - 24 IS - 2 SP - 138 EP - 156 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. A1 - Goebel, Silke M. T1 - Direction counts A comparative study of spatially directional counting biases in cultures with different reading directions JF - Journal of experimental child psychology N2 - Western adults associate small numbers with left space and large numbers with right space. Where does this pervasive spatial-numerical association come from? In this study, we first recorded directional counting preferences in adults with different reading experiences (left to right, right to left, mixed, and illiterate) and observed a clear relationship between reading and counting directions. We then recorded directional counting preferences in pre-schoolers and elementary school children from three of these reading cultures (left to right, right to left, and mixed). Culture-specific counting biases existed before reading acquisition in children as young as 3 years and were subsequently modified by early reading experience. Together, our results suggest that both directional counting and scanning activities contribute to number-space associations. KW - Counting KW - Numerical cognition KW - Reading direction KW - Number-space association KW - Mental Number KW - Cross-cultural Y1 - 2012 U6 - https://doi.org/10.1016/j.jecp.2011.12.005 SN - 0022-0965 VL - 112 IS - 2 SP - 275 EP - 281 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Competing Biases in Mental Arithmetic BT - When Division Is More and Multiplication Is Less JF - Frontiers in human neuroscience N2 - Mental arithmetic exhibits various biases. Among those is a tendency to overestimate addition and to underestimate subtraction outcomes. Does such “operational momentum” (OM) also affect multiplication and division? Twenty-six adults produced lines whose lengths corresponded to the correct outcomes of multiplication and division problems shown in symbolic format. We found a reliable tendency to over-estimate division outcomes, i.e., reverse OM. We suggest that anchoring on the first operand (a tendency to use this number as a reference for further quantitative reasoning) contributes to cognitive biases in mental arithmetic. KW - heuristics and biases KW - numerical cognition KW - mental arithmetic KW - mental number line KW - operational momentum Y1 - 2017 U6 - https://doi.org/10.3389/fnhum.2017.00037 SN - 1662-5161 VL - 11 PB - Frontiers Research Foundation CY - Lausanne ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Deconstructing spatial-numerical associations JF - Cognition : international journal of cognitive science N2 - Spatial-numerical associations (SNAs) have been studied extensively in the past two decades, always requiring either explicit magnitude processing or explicit spatial-directional processing. This means that the typical finding of an association of small numbers with left or bottom space and of larger numbers with right or top space could be due to these requirements and not the conceptual representation of numbers. The present study compares explicit and implicit magnitude processing in an implicit spatial-directional task and identifies SNAs as artefacts of either explicit magnitude processing or explicit spatial-directional processing; they do not reveal spatial conceptual links. This finding requires revision of current accounts of the relationship between numbers and space. KW - Go/no-go task KW - Implicit association task KW - Numerical cognition KW - SNARC effect Y1 - 2018 U6 - https://doi.org/10.1016/j.cognition.2018.02.022 SN - 0010-0277 SN - 1873-7838 VL - 175 SP - 109 EP - 113 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Your neighbors define your value a study of spatial bias in number comparison JF - Acta psychologica : international journal of psychonomics N2 - Several chronometric biases in numerical cognition have informed our understanding of a mental number line (MNL). Complementing this approach, we investigated spatial performance in a magnitude comparison task. Participants located the larger or smaller number of a pair on a horizontal line representing the interval from 0 to 10. Experiments 1 and 2 used only number pairs one unit apart and found that digits were localized farther to the right with "select larger" instructions than with "select smaller" instructions. However, when numerical distance was varied (Experiment 3), digits were localized away from numerically near neighbors. This repulsion effect reveals context-specific distortions in number representation not previously noticed with chronometric measures. KW - Magnitude comparison KW - Mental number line KW - Numerical cognition KW - Spatial bias Y1 - 2013 U6 - https://doi.org/10.1016/j.actpsy.2013.01.004 SN - 0001-6918 VL - 142 IS - 3 SP - 308 EP - 313 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Multiple spatial mappings in numerical cognition JF - Journal of experimental psychology : Human perception and performance N2 - A recent cross-cultural comparison (Shaki, Fischer, & Petrusic, 2009) suggested that spatially consistent processing habits for words and numbers are a necessary condition for the spatial representation of numbers (Spatial-Numerical Association of Response Codes; SNARC effect). Here we reexamine the SNARC in Israelis who read text from right to left but numbers from left to right. We show that, despite these spatially inconsistent processing habits, a SNARC effect still emerges when the response dimension is spatially orthogonal to the conflicting processing dimension. These results clarify the cognitive conditions for spatial-numerical mappings. KW - mental number line KW - reading habits KW - SNARC Y1 - 2012 U6 - https://doi.org/10.1037/a0027562 SN - 0096-1523 VL - 38 IS - 3 SP - 804 EP - 809 PB - American Psychological Association CY - Washington ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Random walks on the mental number line JF - Experimental brain research KW - Mental number line KW - RNG KW - SNARC KW - Spatial bias KW - Walking Y1 - 2014 U6 - https://doi.org/10.1007/s00221-013-3718-7 SN - 0014-4819 SN - 1432-1106 VL - 232 IS - 1 SP - 43 EP - 49 PB - Springer CY - New York ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Systematic spatial distortion of quantitative estimates JF - Psychological research N2 - Magnitude estimation has been studied since the beginnings of scientific psychology and constitutes a fundamental aspect of human behavior. Yet, it has apparently never been noticed that estimates depend on the spatial arrangement used. We tested 167 adults in three experiments to show that the spatial layout of stimuli and responses systematically distorts number estimation, length production, and weight reproduction performance. The direction of distortion depends on the observer's counting habits, but does not seem to reflect the use of spatially associated number concepts. Our results imply that all quantitative estimates are contaminated by a "spell of space" whenever stimuli or responses are spatially distributed. Y1 - 2020 U6 - https://doi.org/10.1007/s00426-020-01390-5 SN - 0340-0727 SN - 1430-2772 VL - 85 IS - 6 SP - 2177 EP - 2185 PB - Springer CY - Heidelberg ER -