@unpublished{FischerShaki2015, author = {Fischer, Martin H. and Shaki, Samuel}, title = {Two steps to space for numbers}, series = {Frontiers in psychology}, volume = {6}, journal = {Frontiers in psychology}, publisher = {Frontiers Research Foundation}, address = {Lausanne}, issn = {1664-1078}, doi = {10.3389/fpsyg.2015.00612}, pages = {3}, year = {2015}, language = {en} } @article{MyachykovCangelosiEllisetal.2015, author = {Myachykov, Andriy and Cangelosi, Angelo and Ellis, Rob and Fischer, Martin H.}, title = {The oculomotor resonance effect in spatial-numerical mapping}, series = {Acta psychologica : international journal of psychonomics}, volume = {161}, journal = {Acta psychologica : international journal of psychonomics}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0001-6918}, doi = {10.1016/j.actpsy.2015.09.006}, pages = {162 -- 169}, year = {2015}, abstract = {We investigated automatic Spatial-Numerical Association of Response Codes (SNARC) effect in auditory number processing. Two experiments continually measured spatial characteristics of ocular drift at central fixation during and after auditory number presentation. Consistent with the notion of a spatially oriented mental number line, we found spontaneous magnitude-dependent gaze adjustments, both with and without a concurrent saccadic task. This fixation adjustment (1) had a small-number/left-lateralized bias and (2) it was biphasic as it emerged for a short time around the point of lexical access and it received later robust representation around following number onset. This pattern suggests a two-step mechanism of sensorimotor mapping between numbers and space a first-pass bottom-up activation followed by a top-down and more robust horizontal SNARC Our results inform theories of number processing as well as simulation-based approaches to cognition by identifying the characteristics of an oculomotor resonance phenomenon. (C) 2015 Elsevier B.V. All rights reserved.}, language = {en} } @article{FischerShaki2014, author = {Fischer, Martin H. and Shaki, Samuel}, title = {Spatial associations in numerical cognition-From single digits to arithmetic}, series = {The quarterly journal of experimental psychology}, volume = {67}, journal = {The quarterly journal of experimental psychology}, number = {8}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {1747-0218}, doi = {10.1080/17470218.2014.927515}, pages = {1461 -- 1483}, year = {2014}, abstract = {The literature on spatial associations during number processing is dominated by the SNARC (spatial-numerical association of response codes) effect. We describe spatial biases found for single digits and pairs of numbers, first in the "original" speeded parity task and then extending the scope to encompass different tasks, a range of measures, and various populations. Then we review theoretical accounts before surveying the emerging evidence for similar spatial associations during mental arithmetic. We conclude that the mental number line hypothesis and an embodied approach are useful frameworks for further studies.}, language = {en} } @article{FischerRielloGiordanoetal.2013, author = {Fischer, Martin H. and Riello, Marianna and Giordano, Bruno L. and Rusconi, Elena}, title = {Singing numbers ... in cognitive space - a dual-task study of the link between pitch, space, and numbers}, series = {Topics in cognitive science}, volume = {5}, journal = {Topics in cognitive science}, number = {2}, publisher = {Wiley-Blackwell}, address = {Hoboken}, issn = {1756-8757}, doi = {10.1111/tops.12017}, pages = {354 -- 366}, year = {2013}, abstract = {We assessed the automaticity of spatial-numerical and spatial-musical associations by testing their intentionality and load sensitivity in a dual-task paradigm. In separate sessions, 16 healthy adults performed magnitude and pitch comparisons on sung numbers with variable pitch. Stimuli and response alternatives were identical, but the relevant stimulus attribute (pitch or number) differed between tasks. Concomitant tasks required retention of either color or location information. Results show that spatial associations of both magnitude and pitch are load sensitive and that the spatial association for pitch is more powerful than that for magnitude. These findings argue against the automaticity of spatial mappings in either stimulus dimension.}, language = {en} } @article{FischerShaki2018, author = {Fischer, Martin H. and Shaki, Samuel}, title = {Repeating Numbers Reduces Results: Violations of the Identity Axiom in Mental Arithmetic}, series = {Frontiers in psychology}, volume = {9}, journal = {Frontiers in psychology}, publisher = {Frontiers Research Foundation}, address = {Lausanne}, issn = {1664-1078}, doi = {10.3389/fpsyg.2018.02453}, pages = {9}, year = {2018}, abstract = {Even simple mental arithmetic is fraught with cognitive biases. For example, adding repeated numbers (so-called tie problems, e.g., 2 + 2) not only has a speed and accuracy advantage over adding different numbers (e.g., 1 + 3) but may also lead to under-representation of the result relative to a standard value (Charras et al., 2012, 2014). Does the tie advantage merely reflect easier encoding or retrieval compared to non-ties, or also a distorted result representation? To answer this question, 47 healthy adults performed two tasks, both of which indicated under-representation of tie results: In a result-to-position pointing task (Experiment 1) we measured the spatial mapping of numbers and found a left-bias for tie compared to non-tie problems. In a result-to-line-length production task (Experiment 2) we measured the underlying magnitude representation directly and obtained shorter lines for tie-compared to non-tie problems. These observations suggest that the processing benefit of tie problems comes at the cost of representational reduction of result meaning. This conclusion is discussed in the context of a recent model of arithmetic heuristics and biases.}, language = {en} } @article{ShakiFischer2014, author = {Shaki, Samuel and Fischer, Martin H.}, title = {Random walks on the mental number line}, series = {Experimental brain research}, volume = {232}, journal = {Experimental brain research}, number = {1}, publisher = {Springer}, address = {New York}, issn = {0014-4819}, doi = {10.1007/s00221-013-3718-7}, pages = {43 -- 49}, year = {2014}, language = {en} } @article{ShakiFischer2012, author = {Shaki, Samuel and Fischer, Martin H.}, title = {Multiple spatial mappings in numerical cognition}, series = {Journal of experimental psychology : Human perception and performance}, volume = {38}, journal = {Journal of experimental psychology : Human perception and performance}, number = {3}, publisher = {American Psychological Association}, address = {Washington}, issn = {0096-1523}, doi = {10.1037/a0027562}, pages = {804 -- 809}, year = {2012}, abstract = {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.}, language = {en} } @misc{WinterMatlockShakietal.2015, author = {Winter, Bodo and Matlock, Teenie and Shaki, Samuel and Fischer, Martin H.}, title = {Mental number space in three dimensions}, series = {Neuroscience \& biobehavioral reviews : official journal of the International Behavioral Neuroscience Society}, volume = {57}, journal = {Neuroscience \& biobehavioral reviews : official journal of the International Behavioral Neuroscience Society}, publisher = {Elsevier}, address = {Oxford}, issn = {0149-7634}, doi = {10.1016/j.neubiorev.2015.09.005}, pages = {209 -- 219}, year = {2015}, abstract = {A large number of experimental findings from neuroscience and experimental psychology demonstrated interactions between spatial cognition and numerical cognition. In particular, many researchers posited a horizontal mental number line, where small numbers are thought of as being to the left of larger numbers. This review synthesizes work on the mental association between space and number, indicating the existence of multiple spatial mappings: recent research has found associations between number and vertical space, as well as associations between number and near/far space. We discuss number space in three dimensions with an eye on potential origins of the different number mappings, and how these number mappings fit in with our current knowledge of brain organization and brain-culture interactions. We derive novel predictions and show how this research fits into a general view of cognition as embodied, grounded and situated. (C) 2015 Elsevier Ltd. All rights reserved.}, language = {en} } @article{MioniFischerShaki2021, author = {Mioni, Giovanna and Fischer, Martin H. and Shaki, Samuel}, title = {Heuristics and biases in the mental manipulation of magnitudes}, series = {Quarterly journal of experimental psychology / published in association with Experimental Psychology Society}, volume = {74}, journal = {Quarterly journal of experimental psychology / published in association with Experimental Psychology Society}, number = {3}, publisher = {SAGE Publishing}, address = {Thousand Oaks, CA}, issn = {1747-0218}, doi = {10.1177/1747021820967663}, pages = {536 -- 547}, year = {2021}, abstract = {There is a debate about whether and why we overestimate addition and underestimate subtraction results (Operational Momentum or OM effect). Spatial-attentional accounts of OM compete with a model which postulates that OM reflects a weighted combination of multiple arithmetic heuristics and biases (AHAB). This study addressed this debate with the theoretically diagnostic distinction between zero problems (e.g., 3 + 0, 3 - 0) and non-zero problems (e.g., 2 + 1, 4 - 1) because AHAB, in contrast to all other accounts, uniquely predicts reverse OM for the latter problem type. In two tests (line-length production and time production), participants indeed produced shorter lines and under-estimated time intervals in non-zero additions compared with subtractions. This predicted interaction between operation and problem type extends OM to non-spatial magnitudes and highlights the strength of AHAB regarding different problem types and modalities during the mental manipulation of magnitudes. They also suggest that OM reflects methodological details, whereas reverse OM is the more representative behavioural signature of mental arithmetic.}, language = {en} } @article{ShakiSeryFischer2015, author = {Shaki, Samuel and Sery, Noa and Fischer, Martin H.}, title = {1 + 2 is more than 2 + 1: Violations of commutativity and identity axioms in mental arithmetic}, series = {Journal of cognitive psychology}, volume = {27}, journal = {Journal of cognitive psychology}, number = {4}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {2044-5911}, doi = {10.1080/20445911.2014.973414}, pages = {471 -- 477}, year = {2015}, abstract = {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.}, language = {en} }