@article{MiklashevskyLindemannFischer2021,
  author    = {Miklashevsky, Alex and Lindemann, Oliver and Fischer, Martin H.},
  title     = {The force of numbers},
  series = {Frontiers in human neuroscience / Frontiers Research Foundation},
  volume    = {14},
  journal   = {Frontiers in human neuroscience / Frontiers Research Foundation},
  publisher = {Frontiers Media},
  address   = {Lausanne},
  issn      = {1662-5161},
  doi       = {10.3389/fnhum.2020.590508},
  pages     = {16},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@article{FelisattiLaubrockShakietal.2020,
  author    = {Felisatti, Arianna and Laubrock, Jochen and Shaki, Samuel and Fischer, Martin H.},
  title     = {A biological foundation for spatial-numerical associations},
  series = {Annals of the New York Academy of Sciences},
  volume    = {1477},
  journal   = {Annals of the New York Academy of Sciences},
  number    = {1},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0077-8923},
  doi       = {10.1111/nyas.14418},
  pages     = {44 -- 53},
  year      = {2020},
  abstract  = {"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.},
  language  = {en}
}
@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{BelliFelisattiFischer2021,
  author    = {Belli, Francesco and Felisatti, Arianna and Fischer, Martin H.},
  title     = {"BreaThink"},
  series = {Experimental brain research},
  volume    = {239},
  journal   = {Experimental brain research},
  number    = {8},
  publisher = {Springer},
  address   = {New York},
  issn      = {0014-4819},
  doi       = {10.1007/s00221-021-06147-z},
  pages     = {2489 -- 2499},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@misc{FischerShaki2018,
  author    = {Fischer, Martin H. and Shaki, Samuel},
  title     = {Number concepts: abstract and embodied},
  series = {Philosophical transactions of the Royal Society of London : B, Biological sciences},
  volume    = {373},
  journal   = {Philosophical transactions of the Royal Society of London : B, Biological sciences},
  number    = {1752},
  publisher = {Royal Society},
  address   = {London},
  issn      = {0962-8436},
  doi       = {10.1098/rstb.2017.0125},
  pages     = {8},
  year      = {2018},
  abstract  = {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.},
  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{FischerMiklashevskyShaki2018,
  author    = {Fischer, Martin H. and Miklashevsky, Alex A. and Shaki, Samuel},
  title     = {Commentary : The Developmental Trajectory of the Operational Momentum Effect},
  series = {Frontiers in Psychology},
  volume    = {9},
  journal   = {Frontiers in Psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2018.02259},
  pages     = {3},
  year      = {2018},
  language  = {en}
}
@article{Fischer2018,
  author    = {Fischer, Martin H.},
  title     = {Why Numbers Are Embodied Concepts},
  series = {Frontiers in Psychology},
  volume    = {8},
  journal   = {Frontiers in Psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2017.02347},
  pages     = {1 -- 3},
  year      = {2018},
  language  = {en}
}
@unpublished{FischerSixtusGoebel2015,
  author    = {Fischer, Martin H. and Sixtus, Elena and G{\"o}bel, Silke M.},
  title     = {Commentary: A pointer about grasping numbers},
  series = {Frontiers in psychology},
  volume    = {6},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  doi       = {10.3389/fpsyg.2015.00227},
  pages     = {3},
  year      = {2015},
  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}
}
@unpublished{ShakiFischer2015,
  author    = {Shaki, Samuel and Fischer, Martin H.},
  title     = {Newborn chicks need no number tricks. Commentary: Number-space mapping in the newborn chick resembles humans' mental number line},
  series = {Frontiers in human neuroscienc},
  volume    = {9},
  journal   = {Frontiers in human neuroscienc},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1662-5161},
  doi       = {10.3389/fnhum.2015.00451},
  pages     = {3},
  year      = {2015},
  language  = {en}
}
@article{FischerHartmann2014,
  author    = {Fischer, Martin H. and Hartmann, Matthias},
  title     = {Pushing forward in embodied cognition: may we mouse the mathematical mind?},
  series = {Frontiers in psychology},
  volume    = {5},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2014.01315},
  pages     = {4},
  year      = {2014},
  abstract  = {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.},
  language  = {en}
}
@misc{FischerBrugger2011,
  author    = {Fischer, Martin H. and Brugger, Peter},
  title     = {When digits help digits spatial-numerical associations point to finger counting as prime example of embodied cognition},
  series = {Frontiers in psychology},
  volume    = {2},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2011.00260},
  pages     = {7},
  year      = {2011},
  abstract  = {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.},
  language  = {en}
}
@unpublished{KucianPlanggerO'Gormanetal.2013,
  author    = {Kucian, Karin and Plangger, Fabienne and O'Gorman, Ruth and von Aster, Michael G.},
  title     = {Operational momentum effect in children with and without developmental dyscalculia},
  series = {Frontiers in psychology},
  volume    = {4},
  journal   = {Frontiers in psychology},
  number    = {45},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2013.00847},
  pages     = {3},
  year      = {2013},
  language  = {en}
}
@article{ShakiFischer2017,
  author    = {Shaki, Samuel and Fischer, Martin H.},
  title     = {Competing Biases in Mental Arithmetic},
  series = {Frontiers in human neuroscience},
  volume    = {11},
  journal   = {Frontiers in human neuroscience},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1662-5161},
  doi       = {10.3389/fnhum.2017.00037},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}