TY - JOUR A1 - Fischer, Martin H. T1 - Why Numbers Are Embodied Concepts JF - Frontiers in Psychology KW - arithmetic KW - numerical cognition KW - number concepts KW - embodied cognition KW - philosophy of science Y1 - 2018 U6 - https://doi.org/10.3389/fpsyg.2017.02347 SN - 1664-1078 VL - 8 SP - 1 EP - 3 PB - Frontiers Research Foundation CY - Lausanne ER - TY - GEN A1 - Fischer, Martin H. T1 - Why Numbers Are Embodied Concepts T2 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 440 KW - arithmetic KW - numerical cognition KW - number concepts KW - embodied cognition KW - philosophy of science Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-412097 IS - 440 ER - TY - JOUR A1 - Fischer, Martin H. A1 - Brugger, Peter T1 - When digits help digits spatial-numerical associations point to finger counting as prime example of embodied cognition JF - Frontiers in psychology N2 - Spatial numerical associations (SNAs) are prevalent yet their origin is poorly understood. We first consider the possible prime role of reading habits in shaping SNAs and list three observations that argue against a prominent influence of this role: (1) directional reading habits for numbers may conflict with those for non-numerical symbols, (2) short-term experimental manipulations can overrule the impact of decades of reading experience, (3) SNAs predate the acquisition of reading. As a promising alternative, we discuss behavioral, neuroscientific, and neuropsychological evidence in support of finger counting as the most likely initial determinant of SNAs. Implications of this "manumerical cognition" stance for the distinction between grounded, embodied, and situated cognition are discussed. KW - embodied cognition KW - finger counting KW - numerical cognition Y1 - 2011 U6 - https://doi.org/10.3389/fpsyg.2011.00260 SN - 1664-1078 VL - 2 PB - Frontiers Research Foundation CY - Lausanne ER - TY - INPR A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Two steps to space for numbers T2 - Frontiers in psychology KW - spatial-nunmerical association KW - SNARC KW - mental number line KW - numerical cognition KW - spatial cognition Y1 - 2015 U6 - https://doi.org/10.3389/fpsyg.2015.00612 SN - 1664-1078 VL - 6 PB - Frontiers Research Foundation CY - Lausanne ER - TY - GEN A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Two steps to space for numbers T2 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 412 KW - spatial-nunmerical association KW - SNARC KW - mental number line KW - numerical cognition KW - spatial cognition Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-406522 IS - 412 ER - TY - JOUR A1 - Miklashevsky, Alex A1 - Lindemann, Oliver A1 - Fischer, Martin H. T1 - The force of numbers BT - Investigating manual signatures of embodied number processing JF - Frontiers in human neuroscience / Frontiers Research Foundation N2 - The study has two objectives: (1) to introduce grip force recording as a new technique for studying embodied numerical processing; and (2) to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line (MNL), A Theory of Magnitude (ATOM) and Embodied Cognition (finger counting-based) account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and unconscious grip force changes related to number magnitude occurred in the left hand already 100-140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research. KW - ATOM KW - embodied cognition KW - finger counting KW - grip force KW - mental number KW - line KW - number processing KW - numerical cognition Y1 - 2021 U6 - https://doi.org/10.3389/fnhum.2020.590508 SN - 1662-5161 VL - 14 PB - Frontiers Media CY - Lausanne ER - TY - THES A1 - Sixtus, Elena T1 - Subtle fingers – tangible numbers: The influence of finger counting experience on mental number representations T1 - Der Einfluss von Fingerzählerfahrung auf mentale Zahlenrepräsentationen N2 - Numbers are omnipresent in daily life. They vary in display format and in their meaning so that it does not seem self-evident that our brains process them more or less easily and flexibly. The present thesis addresses mental number representations in general, and specifically the impact of finger counting on mental number representations. Finger postures that result from finger counting experience are one of many ways to convey numerical information. They are, however, probably the one where the numerical content becomes most tangible. By investigating the role of fingers in adults’ mental number representations the four presented studies also tested the Embodied Cognition hypothesis which predicts that bodily experience (e.g., finger counting) during concept acquisition (e.g., number concepts) stays an immanent part of these concepts. The studies focussed on different aspects of finger counting experience. First, consistency and further details of spontaneously used finger configurations were investigated when participants repeatedly produced finger postures according to specific numbers (Study 1). Furthermore, finger counting postures (Study 2), different finger configurations (Study 2 and 4), finger movements (Study 3), and tactile finger perception (Study 4) were investigated regarding their capability to affect number processing. Results indicated that active production of finger counting postures and single finger movements as well as passive perception of tactile stimulation of specific fingers co-activated associated number knowledge and facilitated responses towards corresponding magnitudes and number symbols. Overall, finger counting experience was reflected in specific effects in mental number processing of adult participants. This indicates that finger counting experience is an immanent part of mental number representations. Findings are discussed in the light of a novel model. The MASC (Model of Analogue and Symbolic Codes) combines and extends two established models of number and magnitude processing. Especially a symbolic motor code is introduced as an essential part of the model. It comprises canonical finger postures (i.e., postures that are habitually used to represent numbers) and finger-number associations. The present findings indicate that finger counting functions both as a sensorimotor magnitude and as a symbolic representational format and that it thereby directly mediates between physical and symbolic size. The implications are relevant both for basic research regarding mental number representations and for pedagogic practices regarding the effectiveness of finger counting as a means to acquire a fundamental grasp of numbers. N2 - Zahlen begegnen uns allerorts im täglichen Leben und variieren sowohl in ihrer Darstellungsform als auch in ihrer Bedeutung, sodass es verblüfft, wie unser Hirn sie mehr oder weniger problemlos und flexibel verarbeiten kann. Die mentale Repräsentation von Zahlen im Allgemeinen bzw. die Bedeutung des Fingerzählens für das mentale Zahlenkonzept im Speziellen sind Inhalt der vorliegenden Arbeit. Fingerposen, die sich aus der Fingerzählerfahrung ergeben, sind eine von vielen Arten, numerische Information zu vermitteln – und sie sind vermutlich diejenige, bei der der numerische Inhalt am greifbarsten wird. In den vier vorgestellten Studien wurde untersucht, inwiefern noch bei Erwachsenen deren Zahlenrepräsentationen „in den Fingern“ verankert sind. Die Grundlage bildet der Embodied Cognition-Ansatz, welcher vorhersagt, dass die körperlichen Erfahrungen (z.B. Fingerzählen), durch welche kognitive Konzepte (z.B. Zahlen) erworben wurden, stets Teil dieser kognitiven Konzepte bleiben. Der Schwerpunkt der vorgestellten Studien lag dabei auf unterschiedlichen Aspekten der Fingerzählerfahrung. Zunächst wurde erfasst, wie Personen Zahlen spontan mit ihren Händen zeigten und wie konsistent sie in der Wahl der Fingerkonfigurationen waren (Studie 1). Weiterhin wurde getestet, inwiefern Fingerzählposen (Studie 2), unterschiedliche Fingerkonfigurationen (Studie 2 und 4), Fingerbewegungen (Studie 3) und taktile Fingerwahrnehmung (Studie 4) numerische Konzepte zu primen vermögen. Die berichteten Effekte deuteten darauf hin, dass die Ausführung von Fingerzählposen und Bewegungen einzelner Finger sowie die taktile Stimulation von spezifischen Fingern das entsprechende sensomotorisch verankerte bzw. symbolisch assoziierte Zahlenwissen aktivierte und dadurch Reaktionen auf die entsprechenden Magnituden oder Zahlensymbole erleichterte. Insgesamt zeigten die Ergebnisse aller Studien, dass Fingerzählerfahrung in spezifischen Effekten in der mentalen Zahlenverarbeitung bei Erwachsenen wiederzufinden ist, was dafür spricht, dass sie ein fester Bestandteil von mentalen Zahlenrepräsentationen ist. Die Befunde werden weiterhin insbesondere im Lichte eines neuen Modells betrachtet. Das MASC (Model of Analogue and Symbolic Codes) beruft sich auf zwei etablierte Modelle der Zahlen- und Magnitudenverarbeitung und erweitert diese. Insbesondere ein symbolischer motorischer Code, welcher kanonische Fingerposen (also solche, welche üblicherweise zur Darstellung von Zahlen genutzt werden) und Finger-Zahl-Assoziationen beinhaltet, wird als wichtiger Bestandteil des MASC vorgestellt. Die vorliegenden Befunde weisen darauf hin, dass Fingerzählen sowohl als sensomotorische Magnitude als auch als symbolische Zahlenrepräsentation fungiert und auf diesem Wege direkt zwischen physikalischer und symbolischer Größe vermittelt. Die Ergebnisse und deren Implikationen betreffen sowohl die Grundlagenforschung bezüglich mentaler Zahlenrepräsentation als auch die angewandte Pädagogik bezüglich der Effektivität des Fingerzählens als Mittel zur Erreichung eines kompetenten Zahlenverständnisses. KW - numerical cognition KW - finger counting KW - mental number representations KW - Model of Analogue and Symbolic Codes KW - MASC KW - numerische Kognition KW - mentale Zahlenrepräsentation KW - Fingerzählen Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-420115 ER - TY - JOUR A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Repeating Numbers Reduces Results: Violations of the Identity Axiom in Mental Arithmetic JF - Frontiers in psychology N2 - 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. KW - AHAB KW - cognitive bias KW - mental arithmetic KW - numerical cognition KW - operational momentum KW - SNARC KW - tie problems Y1 - 2018 U6 - https://doi.org/10.3389/fpsyg.2018.02453 SN - 1664-1078 VL - 9 PB - Frontiers Research Foundation CY - Lausanne ER - TY - JOUR A1 - Fischer, Martin H. A1 - Hartmann, Matthias T1 - Pushing forward in embodied cognition: may we mouse the mathematical mind? JF - Frontiers in psychology N2 - Freely available software has popularized "mousetracking" to study cognitive processing; this involves the on-line recording of cursor positions while participants move a computer mouse to indicate their choice. Movement trajectories of the cursor can then be reconstructed off-line to assess the efficiency of responding in time and across space. Here we focus on the process of selecting among alternative numerical responses. Several studies have recently measured the mathematical mind with cursor movements while people decided about number magnitude or parity, computed sums or differences, or simply located numbers on a number line. After some general methodological considerations about mouse tracking we discuss several conceptual concerns that become particularly evident when "mousing" the mathematical mind. KW - mousetracking KW - numerical cognition KW - SNARC effect KW - trajectories KW - on-line processing Y1 - 2014 U6 - https://doi.org/10.3389/fpsyg.2014.01315 SN - 1664-1078 VL - 5 PB - Frontiers Research Foundation CY - Lausanne ER - TY - INPR A1 - Kucian, Karin A1 - Plangger, Fabienne A1 - O'Gorman, Ruth A1 - von Aster, Michael G. T1 - Operational momentum effect in children with and without developmental dyscalculia T2 - Frontiers in psychology KW - developmental dyscalculia KW - operational momentum KW - children KW - learning disability KW - numerical cognition KW - mental number line KW - symbolic calculation KW - attention Y1 - 2013 U6 - https://doi.org/10.3389/fpsyg.2013.00847 SN - 1664-1078 VL - 4 IS - 45 PB - Frontiers Research Foundation CY - Lausanne ER - TY - JOUR A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Number concepts: abstract and embodied JF - Philosophical transactions of the Royal Society of London : B, Biological sciences N2 - Numerical knowledge, including number concepts and arithmetic procedures, seems to be a clear-cut case for abstract symbol manipulation. Yet, evidence from perceptual and motor behaviour reveals that natural number knowledge and simple arithmetic also remain closely associated with modal experiences. Following a review of behavioural, animal and neuroscience studies of number processing, we propose a revised understanding of psychological number concepts as grounded in physical constraints, embodied in experience and situated through task-specific intentions. The idea that number concepts occupy a range of positions on the continuum between abstract and modal conceptual knowledge also accounts for systematic heuristics and biases in mental arithmetic, thus inviting psycho-logical approaches to the study of the mathematical mind. KW - embodied cognition KW - mental arithmetic KW - mental number line KW - numerical cognition KW - SNARC effect Y1 - 2018 U6 - https://doi.org/10.1098/rstb.2017.0125 SN - 0962-8436 SN - 1471-2970 VL - 373 IS - 1752 PB - Royal Society CY - London ER - TY - INPR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Newborn chicks need no number tricks. Commentary: Number-space mapping in the newborn chick resembles humans' mental number line T2 - Frontiers in human neuroscienc KW - mental number line KW - innate number sense KW - numerical cognition KW - spatial cognition KW - spatial numerical associations Y1 - 2015 U6 - https://doi.org/10.3389/fnhum.2015.00451 SN - 1662-5161 VL - 9 PB - Frontiers Research Foundation CY - Lausanne ER - TY - GEN A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Newborn chicks need no number tricks BT - Commentary: Number-space mapping in the newborn chick resembles humans' mental number line T2 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe N2 - kein Abstract T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 414 KW - mental number line KW - innate number sense KW - numerical cognition KW - spatial cognition KW - spatial numerical associations Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-406425 IS - 414 ER - TY - JOUR A1 - Wiemers, Michael A1 - Bekkering, Harold A1 - Lindemann, Oliver T1 - Is more always up? BT - evidence for a preference of hand-based associations over vertical number mappings JF - Journal of cognitive psychology N2 - 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. KW - SNARC effect KW - embodied numerosity KW - numerical cognition Y1 - 2017 U6 - https://doi.org/10.1080/20445911.2017.1302451 SN - 2044-5911 SN - 2044-592X VL - 29 IS - 5 SP - 642 EP - 652 PB - Routledge, Taylor & Francis Group CY - Abingdon 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 - GEN A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Competing Biases in Mental Arithmetic BT - When Division Is More and Multiplication Is Less 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 312 KW - heuristics and biases KW - mental arithmetic KW - mental number line KW - numerical cognition KW - operational momentum Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-103492 ER - TY - INPR A1 - Fischer, Martin H. A1 - Sixtus, Elena A1 - Göbel, Silke M. T1 - Commentary: A pointer about grasping numbers T2 - Frontiers in psychology KW - numerical cognition KW - embodied cognition KW - gestures KW - numeracy training KW - mathematical cognition Y1 - 2015 U6 - https://doi.org/10.3389/fpsyg.2015.00227 VL - 6 PB - Frontiers Research Foundation CY - Lausanne ER - TY - JOUR A1 - Fischer, Martin H. A1 - Miklashevsky, Alex A. A1 - Shaki, Samuel T1 - Commentary : The Developmental Trajectory of the Operational Momentum Effect JF - Frontiers in Psychology KW - embodied cognition KW - operational momentum KW - SNARC effect KW - mental arithmetic KW - numerical cognition Y1 - 2018 U6 - https://doi.org/10.3389/fpsyg.2018.02259 SN - 1664-1078 N1 - A Commentary on The Developmental Trajectory of the Operational Momentum Effect by Pinheiro-Chagas, P., Didino, D., Haase, V. G., Wood, G., and Knops, A. (2018). Front. Psychol. 9:1062 doi: 10.3389/fpsyg.2018.01062 VL - 9 PB - Frontiers Research Foundation CY - Lausanne ER - TY - GEN A1 - Fischer, Martin H. A1 - Miklashevsky, Alex A. A1 - Shaki, Samuel T1 - Commentary : The Developmental Trajectory of the Operational Momentum Effect T2 - Postprints der Universität Potsdam Humanwissenschaftliche Reihe T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 502 KW - embodied cognition KW - operational momentum KW - SNARC effect KW - mental arithmetic KW - numerical cognition Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-423169 SN - 1866-8364 N1 - A Commentary on The Developmental Trajectory of the Operational Momentum Effect by Pinheiro-Chagas, P., Didino, D., Haase, V. G., Wood, G., and Knops, A. (2018). Front. Psychol. 9:1062 doi: 10.3389/fpsyg.2018.01062 IS - 502 ER - TY - GEN A1 - Fischer, Martin H. A1 - Sixtus, Elena A1 - Göbel, Silke M. T1 - Commentary BT - a pointer about grasping numbers T2 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe N2 - kein Abstract vorhanden T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 420 KW - numerical cognition KW - embodied cognition KW - gestures KW - numeracy training KW - mathematical cognition Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-406260 IS - 420 ER - TY - THES A1 - Reike, Dennis T1 - A look behind perceptual performance in numerical cognition T1 - Ein Blick hinter die perzeptuellen Leistungen numerischer Kognition N2 - Recognizing, understanding, and responding to quantities are considerable skills for human beings. We can easily communicate quantities, and we are extremely efficient in adapting our behavior to numerical related tasks. One usual task is to compare quantities. We also use symbols like digits in numerical-related tasks. To solve tasks including digits, we must to rely on our previously learned internal number representations. This thesis elaborates on the process of number comparison with the use of noisy mental representations of numbers, the interaction of number and size representations and how we use mental number representations strategically. For this, three studies were carried out. In the first study, participants had to decide which of two presented digits was numerically larger. They had to respond with a saccade in the direction of the anticipated answer. Using only a small set of meaningfully interpretable parameters, a variant of random walk models is described that accounts for response time, error rate, and variance of response time for the full matrix of 72 digit pairs. In addition, the used random walk model predicts a numerical distance effect even for error response times and this effect clearly occurs in the observed data. In relation to corresponding correct answers error responses were systematically faster. However, different from standard assumptions often made in random walk models, this account required that the distributions of step sizes of the induced random walks be asymmetric to account for this asymmetry between correct and incorrect responses. Furthermore, the presented model provides a well-defined framework to investigate the nature and scale (e.g., linear vs. logarithmic) of the mapping of numerical magnitude onto its internal representation. In comparison of the fits of proposed models with linear and logarithmic mapping, the logarithmic mapping is suggested to be prioritized. Finally, we discuss how our findings can help interpret complex findings (e.g., conflicting speed vs. accuracy trends) in applied studies that use number comparison as a well-established diagnostic tool. Furthermore, a novel oculomotoric effect is reported, namely the saccadic overschoot effect. The participants responded by saccadic eye movements and the amplitude of these saccadic responses decreases with numerical distance. For the second study, an experimental design was developed that allows us to apply the signal detection theory to a task where participants had to decide whether a presented digit was physically smaller or larger. A remaining question is, whether the benefit in (numerical magnitude – physical size) congruent conditions is related to a better perception than in incongruent conditions. Alternatively, the number-size congruency effect is mediated by response biases due to numbers magnitude. The signal detection theory is a perfect tool to distinguish between these two alternatives. It describes two parameters, namely sensitivity and response bias. Changes in the sensitivity are related to the actual task performance due to real differences in perception processes whereas changes in the response bias simply reflect strategic implications as a stronger preparation (activation) of an anticipated answer. Our results clearly demonstrate that the number-size congruency effect cannot be reduced to mere response bias effects, and that genuine sensitivity gains for congruent number-size pairings contribute to the number-size congruency effect. Third, participants had to perform a SNARC task – deciding whether a presented digit was odd or even. Local transition probability of irrelevant attributes (magnitude) was varied while local transition probability of relevant attributes (parity) and global probability occurrence of each stimulus were kept constantly. Participants were quite sensitive in recognizing the underlying local transition probability of irrelevant attributes. A gain in performance was observed for actual repetitions of the irrelevant attribute in relation to changes of the irrelevant attribute in high repetition conditions compared to low repetition conditions. One interpretation of these findings is that information about the irrelevant attribute (magnitude) in the previous trial is used as an informative precue, so that participants can prepare early processing stages in the current trial, with the corresponding benefits and costs typical of standard cueing studies. Finally, the results reported in this thesis are discussed in relation to recent studies in numerical cognition. N2 - Das Erkennen, Verstehen und Verwenden von Mengen sind beachtliche menschliche Fähigkeiten. Die Kommunikation numerischer Information fällt uns leicht, zudem beeinflussen numerische Informationen unser Handeln. Eine typische numerische Aufgabe ist der Mengenvergleich. Um solche Mengen zu beschreiben verwenden wir Ziffern als Symbole zur Bildung von Zahlen. Um Zahlen zu vergleichen, müssen wir auf die zuvor erlernte interne Zahlenrepräsentationen zurückgreifen. In dieser Dissertation werden drei Studien vorgestellt. Diese betrachten den Prozess des Zahlenvergleichs, die Interaktion numerischer und physikalischer Repräsentation und die strategische Nutzung numerischer Repräsentationen. In der ersten Studie sollten Versuchspersonen so schnell wie möglich die größere von zwei präsentierten Zahlen angeben. Sie sollten mit einer Sakkade in Richtung der größeren Zahl antworten. Eine Variante von Random Walk Modellen mit einem sparsamen Set an interpretierbaren Parameter wurde verwendet um die Reaktionszeit, die Fehlerrate und die Varianz der Reaktionszeit zu beschreiben. Auch für Fehlerzeiten sagt dieses Modell einen numerischen Distanzeffekt vorher, der sich in den Daten robust zeigt. Außerdem sind Fehlerzeiten schneller als korrespondierende Reaktionszeiten richtiger Antworten. Diese Asymmetrie lässt sich durch eine schiefe Schrittgrößenverteilung erklären, welche nicht zu den üblichen Standardannahmen von Random Walk Modellen gehört. Das vorgestellte Modell liefert einen definierten Rahmen um die Art und Skalierung (z.B. linear vs. logarithmisch) numerischer Repräsentationen zu untersuchen, wobei die Ergebnisse klar für eine logarithmische Skalierung sprechen. Abschließend wird ein Ausblick gegeben, wie dieses Modell helfen kann, komplexe Befunde (z.B. Geschwindigkeit vs. Genauigkeit) in Studien zu erklären, die Zahlenvergleiche als etabliertes Werkzeug verwenden. Außerdem beschreiben wir einen neuen okulomotorischen Effekt, den sakkadischen Overschoot Effekt. Für die zweite Studie wurde ein experimentelles Design entwickelt, das es ermöglicht die Signalentdeckungstheorie zu verwenden. Hierbei sollten Versuchspersonen die physikalische Größe von Ziffern beurteilen. Eine offene Frage ist, ob der Leistungsgewinn in (numerisch - physikalisch) kongruenten Bedingungen auf eine verbesserte Wahrnehmung oder auf einen numerisch induzierten Antwortbias zurückzuführen ist. Die Signalentdeckungstheorie ist das perfekte Werkzeug um zwischen diesen beiden Erklärungen zu unterscheiden. Dabei werden zwei Parameter beschrieben, die Sensitivität und der Antwortbias. Unsere Ergebnisse demonstrieren, dass der Zahlen-Größen Effekt nicht auf einen einfachen Antwortbias zurückzuführen ist. Vielmehr tragen wahre Sensitivitätsgewinne in kongruenten Bedingungen zur Entstehung des Zahlen-Größen Effekts bei. In der dritten Studie sollten die Versuchspersonen eine SNARC Aufgabe durchführen, wobei sie angeben sollten ob eine präsentierte Zahl gerade oder ungerade ist. Die lokale Wiederholungswahrscheinlichkeit des irrelevanten Attributes (Magnitude) wurde zwischen Versuchspersonen variiert. Die Versuchspersonen waren sensitiv für diese Wiederholungswahrscheinlichkeiten. Ein Leistungsgewinn zeigte sich bei tatsächlichen Wiederholungen des irrelevanten Attributes in der Bedingung mit hoher Wiederholungswahrscheinlichkeit des irrelevanten Attributes. Eine mögliche Interpretation ist, dass Informationen aus dem Vortrial als eine Art Hinweis betrachtet werden, so dass die Versuchspersonen im aktuellen Trial frühe Prozessstufen vorbereiten können, was zu entsprechenden Gewinnen und Kosten führt. Die in dieser Dissertation berichteten Ergebnisse werden abschließend diskutiert und in Relation zu aktuellen Studien im Bereich der numerischen Kognition gesetzt. KW - numerical cognition KW - mental number representation KW - numerische Kognition KW - mentale Zahlenrepräsentation Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-407821 ER - TY - JOUR A1 - Felisatti, Arianna A1 - Laubrock, Jochen A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - A biological foundation for spatial–numerical associations BT - the brain's asymmetric frequency tuning JF - Annals of the New York Academy of Sciences N2 - "Left" and "right" coordinates control our spatial behavior and even influence abstract thoughts. For number concepts, horizontal spatial-numerical associations (SNAs) have been widely documented: we associate few with left and many with right. Importantly, increments are universally coded on the right side even in preverbal humans and nonhuman animals, thus questioning the fundamental role of directional cultural habits, such as reading or finger counting. Here, we propose a biological, nonnumerical mechanism for the origin of SNAs on the basis of asymmetric tuning of animal brains for different spatial frequencies (SFs). The resulting selective visual processing predicts both universal SNAs and their context-dependence. We support our proposal by analyzing the stimuli used to document SNAs in newborns for their SF content. As predicted, the SFs contained in visual patterns with few versus many elements preferentially engage right versus left brain hemispheres, respectively, thus predicting left-versus rightward behavioral biases. Our "brain's asymmetric frequency tuning" hypothesis explains the perceptual origin of horizontal SNAs for nonsymbolic visual numerosities and might be extensible to the auditory domain. KW - hemispheric asymmetry KW - numerical cognition KW - SNARC effect KW - spatial KW - frequency tuning KW - spatial-numerical associations KW - spatial vision Y1 - 2020 U6 - https://doi.org/10.1111/nyas.14418 SN - 0077-8923 SN - 1749-6632 VL - 1477 IS - 1 SP - 44 EP - 53 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Belli, Francesco A1 - Felisatti, Arianna A1 - Fischer, Martin H. T1 - "BreaThink" BT - breathing affects production and perception of quantities JF - Experimental brain research N2 - 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. KW - breathing KW - embodied cognition KW - interoception KW - numerical cognition KW - situated cognition Y1 - 2021 U6 - https://doi.org/10.1007/s00221-021-06147-z SN - 0014-4819 SN - 1432-1106 VL - 239 IS - 8 SP - 2489 EP - 2499 PB - Springer CY - New York ER -