@article{WiemersBekkeringLindemann2017, author = {Wiemers, Michael and Bekkering, Harold and Lindemann, Oliver}, title = {Is more always up?}, series = {Journal of cognitive psychology}, volume = {29}, journal = {Journal of cognitive psychology}, number = {5}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {2044-5911}, doi = {10.1080/20445911.2017.1302451}, pages = {642 -- 652}, year = {2017}, abstract = {It has been argued that the association of numbers and vertical space plays a fundamental role for the understanding of numerical concepts. However, convincing evidence for an association of numbers and vertical bimanual responses is still lacking. The present study tests the vertical Spatio-Numerical-Association-of-Response-Codes (SNARC) effect in a number classification task by comparing anatomical hand-based and spatial associations. A mixed effects model of linear spatial-numerical associations revealed no evidence for a vertical but clear support for an anatomical SNARC effect. Only if the task requirements prevented participants from using a number-hand association due to frequently alternating hand-to-button assignments, numbers were associated with the vertical dimension. Taken together, the present findings question the importance of vertical associations for the conceptual understanding of numerical magnitude as hypothesised by some embodied approaches to number cognition and suggest a preference for ego-over geocentric reference frames for the mapping of numbers onto space.}, language = {en} } @article{WiemersBekkeringLindemann2017, author = {Wiemers, Michael and Bekkering, Harold and Lindemann, Oliver}, title = {Two attributes of number meaning}, series = {Experimental Psychology}, volume = {64}, journal = {Experimental Psychology}, number = {4}, publisher = {Hogrefe}, address = {G{\"o}ttingen}, issn = {1618-3169}, doi = {10.1027/1618-3169/a000366}, pages = {253 -- 261}, year = {2017}, abstract = {Many studies demonstrated interactions between number processing and either spatial codes (effects of spatial-numerical associations) or visual size-related codes (size-congruity effect). However, the interrelatedness of these two number couplings is still unclear. The present study examines the simultaneous occurrence of space- and size-numerical congruency effects and their interactions both within and across trials, in a magnitude judgment task physically small or large digits were presented left or right from screen center. The reaction times analysis revealed that space- and size-congruency effects coexisted in parallel and combined additively. Moreover, a selective sequential modulation of the two congruency effects was found. The size-congruency effect was reduced after size incongruent trials. The space-congruency effect, however, was only affected by the previous space congruency. The observed independence of spatial-numerical and within magnitude associations is interpreted as evidence that the two couplings reflect Different attributes of numerical meaning possibly related to orginality and cardinality.}, language = {en} } @article{KayhanHeilKwisthoutetal.2019, author = {Kayhan, Ezgi and Heil, Lieke and Kwisthout, Johan and van Rooij, Iris and Hunnius, Sabine and Bekkering, Harold}, title = {Young children integrate current observations, priors and agent information to predict others' actions}, series = {PLOS ONE / Public Library of Science}, volume = {14}, journal = {PLOS ONE / Public Library of Science}, number = {5}, publisher = {PLOS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0200976}, pages = {16}, year = {2019}, abstract = {From early on in life, children are able to use information from their environment to form predictions about events. For instance, they can use statistical information about a population to predict the sample drawn from that population and infer an agent's preferences from systematic violations of random sampling. We investigated whether and how young children infer an agent's sampling biases. Moreover, we examined whether pupil data of toddlers follow the predictions of a computational model based on the causal Bayesian network formalization of predictive processing. We formalized three hypotheses about how different explanatory variables (i.e., prior probabilities, current observations, and agent characteristics) are used to predict others' actions. We measured pupillary responses as a behavioral marker of 'prediction errors' (i.e., the perceived mismatch between what one's model of an agent predicts and what the agent actually does). Pupillary responses of 24-month-olds, but not 18-month-olds, showed that young children integrated information about current observations, priors and agents to make predictions about agents and their actions. These findings shed light on the mechanisms behind toddlers' inferences about agent-caused events. To our knowledge, this is the first study in which young children's pupillary responses are used as markers of prediction errors, which were qualitatively compared to the predictions by a computational model based on the causal Bayesian network formalization of predictive processing.}, language = {en} } @article{KrauseBekkeringPrattetal.2017, author = {Krause, Florian and Bekkering, Harold and Pratt, Jay and Lindemann, Oliver}, title = {Interaction between numbers and size during visual search}, series = {Psychological research : an international journal of perception, attention, memory, and action}, volume = {81}, journal = {Psychological research : an international journal of perception, attention, memory, and action}, publisher = {Springer}, address = {Heidelberg}, issn = {0340-0727}, doi = {10.1007/s00426-016-0771-4}, pages = {664 -- 677}, year = {2017}, abstract = {The current study investigates an interaction between numbers and physical size (i.e. size congruity) in visual search. In three experiments, participants had to detect a physically large (or small) target item among physically small (or large) distractors in a search task comprising single-digit numbers. The relative numerical size of the digits was varied, such that the target item was either among the numerically large or small numbers in the search display and the relation between numerical and physical size was either congruent or incongruent. Perceptual differences of the stimuli were controlled by a condition in which participants had to search for a differently coloured target item with the same physical size and by the usage of LCD-style numbers that were matched in visual similarity by shape transformations. The results of all three experiments consistently revealed that detecting a physically large target item is significantly faster when the numerical size of the target item is large as well (congruent), compared to when it is small (incongruent). This novel finding of a size congruity effect in visual search demonstrates an interaction between numerical and physical size in an experimental setting beyond typically used binary comparison tasks, and provides important new evidence for the notion of shared cognitive codes for numbers and sensorimotor magnitudes. Theoretical consequences for recent models on attention, magnitude representation and their interactions are discussed.}, language = {en} } @misc{KrauseBekkeringPrattetal.2016, author = {Krause, Florian and Bekkering, Harold and Pratt, Jay and Lindemann, Oliver}, title = {Interaction between numbers and size during visual search}, series = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe}, number = {623}, issn = {1866-8364}, doi = {10.25932/publishup-43544}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-435442}, pages = {664 -- 677}, year = {2016}, abstract = {The current study investigates an interaction between numbers and physical size (i.e. size congruity) in visual search. In three experiments, participants had to detect a physically large (or small) target item among physically small (or large) distractors in a search task comprising single-digit numbers. The relative numerical size of the digits was varied, such that the target item was either among the numerically large or small numbers in the search display and the relation between numerical and physical size was either congruent or incongruent. Perceptual differences of the stimuli were controlled by a condition in which participants had to search for a differently coloured target item with the same physical size and by the usage of LCD-style numbers that were matched in visual similarity by shape transformations. The results of all three experiments consistently revealed that detecting a physically large target item is significantly faster when the numerical size of the target item is large as well (congruent), compared to when it is small (incongruent). This novel finding of a size congruity effect in visual search demonstrates an interaction between numerical and physical size in an experimental setting beyond typically used binary comparison tasks, and provides important new evidence for the notion of shared cognitive codes for numbers and sensorimotor magnitudes. Theoretical consequences for recent models on attention, magnitude representation and their interactions are discussed.}, language = {en} } @article{StapelHunniusBekkeringetal.2015, author = {Stapel, Janny C. and Hunnius, Sabine and Bekkering, Harold and Lindemann, Oliver}, title = {The development of numerosity estimation: Evidence for a linear number representation early in life}, 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 = {10.1080/20445911.2014.995668}, pages = {400 -- 412}, year = {2015}, abstract = {Several studies investigating the development of approximate number representations used the number-to-position task and reported evidence for a shift from a logarithmic to a linear representation of numerical magnitude with increasing age. However, this interpretation as well as the number-to-position method itself has been questioned recently. The current study tested 5- and 8-year-old children on a newly established numerosity production task to examine developmental changes in number representations and to test the idea of a representational shift. Modelling of the children's numerical estimations revealed that responses of the 8-year-old children approximate a simple positive linear relation between estimated and actual numbers. Interestingly, however, the estimations of the 5-year-old children were best described by a bilinear model reflecting a relatively accurate linear representation of small numbers and no apparent magnitude knowledge for large numbers. Taken together, our findings provide no support for a shift of mental representations from a logarithmic to a linear metric but rather suggest that the range of number words which are appropriately conceptualised and represented by linear analogue magnitude codes expands during development.}, language = {en} } @article{WiemersBekkeringLindemann2014, author = {Wiemers, Michael and Bekkering, Harold and Lindemann, Oliver}, title = {Spatial interferences in mental arithmetic: Evidence from the motion-arithmetic compatibility effect}, 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 = {10.1080/17470218.2014.889180}, pages = {1557 -- 1570}, year = {2014}, abstract = {Recent research on spatial number representations suggests that the number space is not necessarily horizontally organized and might also be affected by acquired associations between magnitude and sensory experiences in vertical space. Evidence for this claim is, however, controversial. The present study now aims to compare vertical and horizontal spatial associations in mental arithmetic. In Experiment 1, participants solved addition and subtraction problems and indicated the result verbally while moving their outstretched right arm continuously left-, right-, up-, or downwards. The analysis of the problem-solving performances revealed a motion-arithmetic compatibility effect for spatial actions along both the horizontal and the vertical axes. Performances in additions was impaired while making downward compared to upward movements as well as when moving left compared to right and vice versa in subtractions. In Experiment 2, instead of being instructed to perform active body movements, participants calculated while the problems moved in one of the four relative directions on the screen. For visual motions, only the motion-arithmetic compatibility effect for the vertical dimension could be replicated. Taken together, our findings provide first evidence for an impact of spatial processing on mental arithmetic. Moreover, the stronger effect of the vertical dimension supports the idea that mental calculations operate on representations of numerical magnitude that are grounded in a vertically organized mental number space.}, language = {en} } @article{KrauseLindemannTonietal.2014, author = {Krause, Florian and Lindemann, Oliver and Toni, Ivan and Bekkering, Harold}, title = {Different brains process Numbers differently: Structural bases of individual differences in spatial and nonspatial number representations}, series = {Journal of cognitive neuroscience}, volume = {26}, journal = {Journal of cognitive neuroscience}, number = {4}, publisher = {MIT Press}, address = {Cambridge}, issn = {0898-929X}, doi = {10.1162/jocn_a_00518}, pages = {768 -- 776}, year = {2014}, abstract = {A dominant hypothesis on how the brain processes numerical size proposes a spatial representation of numbers as positions on a "mental number line." An alternative hypothesis considers numbers as elements of a generalized representation of sensorimotor-related magnitude, which is not obligatorily spatial. Here we show that individuals' relative use of spatial and nonspatial representations has a cerebral counterpart in the structural organization of the posterior parietal cortex. Interindividual variability in the linkage between numbers and spatial responses (faster left responses to small numbers and right responses to large numbers; spatial-numerical association of response codes effect) correlated with variations in gray matter volume around the right precuneus. Conversely, differences in the disposition to link numbers to force production (faster soft responses to small numbers and hard responses to large numbers) were related to gray matter volume in the left angular gyrus. This finding suggests that numerical cognition relies on multiple mental representations of analogue magnitude using different neural implementations that are linked to individual traits.}, language = {en} } @article{KrauseBekkeringLindemann2013, author = {Krause, Florian and Bekkering, Harold and Lindemann, Oliver}, title = {A feeling for numbers shared metric for symbolic and tactile numerosities}, series = {Frontiers in psychology}, volume = {4}, journal = {Frontiers in psychology}, number = {3}, publisher = {Frontiers Research Foundation}, address = {Lausanne}, issn = {1664-1078}, doi = {10.3389/fpsyg.2013.00007}, pages = {8}, year = {2013}, abstract = {Evidence for an approximate analog system of numbers has been provided by the finding that the comparison of two numerals takes longer and is more error-prone if the semantic distance between the numbers becomes smaller (so-called numerical distance effect). Recent embodied theories suggest that analog number representations are based on previous sensory experiences and constitute therefore a common magnitude metric shared by multiple domains. Here we demonstrate the existence of a cross-modal semantic distance effect between symbolic and tactile numerosities. Participants received tactile stimulations of different amounts of fingers while reading Arabic digits and indicated verbally whether the amount of stimulated fingers was different from the simultaneously presented digit or not. The larger the semantic distance was between the two numerosities, the faster and more accurate participants made their judgments. This cross-modal numerosity distance effect suggests a direct connection between tactile sensations and the concept of numerical magnitude. A second experiment replicated the interaction between symbolic and tactile numerosities and showed that this effect is not modulated by the participants' finger counting habits. Taken together, our data provide novel evidence for a shared metric for symbolic and tactile numerosities as an instance of an embodied representation of numbers.}, language = {en} }