@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{SixtusLonnemannFischeretal.2019, author = {Sixtus, Elena and Lonnemann, Jan and Fischer, Martin H. and Werner, Karsten}, title = {Mental Number Representations in 2D Space}, series = {Frontiers in Psychology}, volume = {10}, journal = {Frontiers in Psychology}, publisher = {Frontiers Research Foundation}, address = {Lausanne}, issn = {1664-1078}, doi = {10.3389/fpsyg.2019.00172}, pages = {11}, year = {2019}, abstract = {There is evidence both for mental number representations along a horizontal mental number line with larger numbers to the right of smaller numbers (for Western cultures) and a physically grounded, vertical representation where "more is up." Few studies have compared effects in the horizontal and vertical dimension and none so far have combined both dimensions within a single paradigm where numerical magnitude was task-irrelevant and none of the dimensions was primed by a response dimension. We now investigated number representations over both dimensions, building on findings that mental representations of numbers and space co-activate each other. In a Go/No-go experiment, participants were auditorily primed with a relatively small or large number and then visually presented with quasi-randomly distributed distractor symbols and one Arabic target number (in Go trials only). Participants pressed a central button whenever they detected the target number and elsewise refrained from responding. Responses were not more efficient when small numbers were presented to the left and large numbers to the right. However, results indicated that large numbers were associated with upper space more strongly than small numbers. This suggests that in two-dimensional space when no response dimension is given, numbers are conceptually associated with vertical, but not horizontal space.}, language = {en} } @misc{SixtusLonnemannFischeretal.2019, author = {Sixtus, Elena and Lonnemann, Jan and Fischer, Martin H. and Werner, Karsten}, title = {Mental Number Representations in 2D Space}, series = {Postprints der Universit{\"a}t Potsdam Humanwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Humanwissenschaftliche Reihe}, number = {538}, issn = {1866-8364}, doi = {10.25932/publishup-42496}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-424960}, year = {2019}, abstract = {There is evidence both for mental number representations along a horizontal mental number line with larger numbers to the right of smaller numbers (for Western cultures) and a physically grounded, vertical representation where "more is up." Few studies have compared effects in the horizontal and vertical dimension and none so far have combined both dimensions within a single paradigm where numerical magnitude was task-irrelevant and none of the dimensions was primed by a response dimension. We now investigated number representations over both dimensions, building on findings that mental representations of numbers and space co-activate each other. In a Go/No-go experiment, participants were auditorily primed with a relatively small or large number and then visually presented with quasi-randomly distributed distractor symbols and one Arabic target number (in Go trials only). Participants pressed a central button whenever they detected the target number and elsewise refrained from responding. Responses were not more efficient when small numbers were presented to the left and large numbers to the right. However, results indicated that large numbers were associated with upper space more strongly than small numbers. This suggests that in two-dimensional space when no response dimension is given, numbers are conceptually associated with vertical, but not horizontal space.}, 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} } @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} } @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{PinhasShakiFischer2015, author = {Pinhas, Michal and Shaki, Samuel and Fischer, Martin H.}, title = {Addition goes where the big numbers are: evidence for a reversed operational momentum effect}, series = {Psychonomic bulletin \& review : a journal of the Psychonomic Society}, volume = {22}, journal = {Psychonomic bulletin \& review : a journal of the Psychonomic Society}, number = {4}, publisher = {Springer}, address = {New York}, issn = {1069-9384}, doi = {10.3758/s13423-014-0786-z}, pages = {993 -- 1000}, year = {2015}, abstract = {Number processing evokes spatial biases, both when dealing with single digits and in more complex mental calculations. Here we investigated whether these two biases have a common origin, by examining their flexibility. Participants pointed to the locations of arithmetic results on a visually presented line with an inverted, right-to-left number arrangement. We found directionally opposite spatial biases for mental arithmetic and for a parity task administered both before and after the arithmetic task. We discuss implications of this dissociation in our results for the task-dependent cognitive representation of numbers.}, 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{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{MiklashevskyFischerLindemann2022, author = {Miklashevsky, Alex and Fischer, Martin H. and Lindemann, Oliver}, title = {Spatial-numerical associations without a motor response? Grip force says 'Yes'}, series = {Acta Psychologica}, volume = {231}, journal = {Acta Psychologica}, publisher = {Elsevier}, address = {Amsterdam}, issn = {1873-6297}, doi = {10.1016/j.actpsy.2022.103791}, pages = {1 -- 17}, year = {2022}, abstract = {In numerical processing, the functional role of Spatial-Numerical Associations (SNAs, such as the association of smaller numbers with left space and larger numbers with right space, the Mental Number Line hypothesis) is debated. Most studies demonstrate SNAs with lateralized responses, and there is little evidence that SNAs appear when no response is required. We recorded passive holding grip forces in no-go trials during number processing. In Experiment 1, participants performed a surface numerical decision task ("Is it a number or a letter?"). In Experiment 2, we used a deeper semantic task ("Is this number larger or smaller than five?"). Despite instruction to keep their grip force constant, participants' spontaneous grip force changed in both experiments: Smaller numbers led to larger force increase in the left than in the right hand in the numerical decision task (500-700 ms after stimulus onset). In the semantic task, smaller numbers again led to larger force increase in the left hand, and larger numbers increased the right-hand holding force. This effect appeared earlier (180 ms) and lasted longer (until 580 ms after stimulus onset). This is the first demonstration of SNAs with passive holding force. Our result suggests that (1) explicit motor response is not a prerequisite for SNAs to appear, and (2) the timing and strength of SNAs are task-dependent. (216 words).}, language = {en} } @misc{MiklashevskyFischerLindemann2022, author = {Miklashevsky, Alex and Fischer, Martin H. and Lindemann, Oliver}, title = {Spatial-numerical associations without a motor response? Grip force says 'Yes'}, series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe}, journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe}, number = {810}, issn = {1866-8364}, doi = {10.25932/publishup-57832}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-578324}, pages = {12}, year = {2022}, abstract = {In numerical processing, the functional role of Spatial-Numerical Associations (SNAs, such as the association of smaller numbers with left space and larger numbers with right space, the Mental Number Line hypothesis) is debated. Most studies demonstrate SNAs with lateralized responses, and there is little evidence that SNAs appear when no response is required. We recorded passive holding grip forces in no-go trials during number processing. In Experiment 1, participants performed a surface numerical decision task ("Is it a number or a letter?"). In Experiment 2, we used a deeper semantic task ("Is this number larger or smaller than five?"). Despite instruction to keep their grip force constant, participants' spontaneous grip force changed in both experiments: Smaller numbers led to larger force increase in the left than in the right hand in the numerical decision task (500-700 ms after stimulus onset). In the semantic task, smaller numbers again led to larger force increase in the left hand, and larger numbers increased the right-hand holding force. This effect appeared earlier (180 ms) and lasted longer (until 580 ms after stimulus onset). This is the first demonstration of SNAs with passive holding force. Our result suggests that (1) explicit motor response is not a prerequisite for SNAs to appear, and (2) the timing and strength of SNAs are task-dependent. (216 words).}, language = {en} } @misc{FischerWinterFelisattietal.2021, author = {Fischer, Martin and Winter, Bodo and Felisatti, Arianna and Myachykov, Andriy and Jeglinski-Mende, Melinda A. and Shaki, Samuel}, title = {More Instructions Make Fewer Subtractions}, series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe}, volume = {12}, journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {1866-8364}, doi = {10.25932/publishup-55008}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-550086}, pages = {1 -- 3}, year = {2021}, abstract = {Research on problem solving offers insights into how humans process task-related information and which strategies they use (Newell and Simon, 1972; {\"O}llinger 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 N{\´u}{\~n}ez, 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.}, language = {en} } @article{FischerWinterFelisattietal.2021, author = {Fischer, Martin and Winter, Bodo and Felisatti, Arianna and Myachykov, Andriy and Jeglinski-Mende, Melinda A. and Shaki, Samuel}, title = {More Instructions Make Fewer Subtractions}, series = {Frontiers in Psychology}, volume = {12}, journal = {Frontiers in Psychology}, publisher = {Frontiers Media SA}, address = {Lausanne, Schweiz}, issn = {1664-1078}, doi = {10.3389/fpsyg.2021.720616}, pages = {1 -- 3}, year = {2021}, abstract = {Research on problem solving offers insights into how humans process task-related information and which strategies they use (Newell and Simon, 1972; {\"O}llinger 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 N{\´u}{\~n}ez, 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.}, 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{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} } @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} } @misc{FischerShaki2015, author = {Fischer, Martin H. and Shaki, Samuel}, title = {Two steps to space for numbers}, series = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe}, number = {412}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-406522}, pages = {3}, year = {2015}, 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} } @misc{FelisattiLaubrockShakietal.2020, author = {Felisatti, Arianna and Laubrock, Jochen and Shaki, Samuel and Fischer, Martin H.}, title = {Commentary}, series = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe}, number = {620}, issn = {1866-8364}, doi = {10.25932/publishup-46041}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-460413}, pages = {6}, year = {2020}, language = {en} } @article{FelisattiLaubrockShakietal.2020, author = {Felisatti, Arianna and Laubrock, Jochen and Shaki, Samuel and Fischer, Martin H.}, title = {Commentary}, series = {Frontiers in Human Neuroscience}, volume = {14}, journal = {Frontiers in Human Neuroscience}, publisher = {Frontiers Research Foundation}, address = {Lausanne}, issn = {1662-5161}, doi = {10.3389/fnhum.2020.00099}, pages = {4}, year = {2020}, language = {en} }