Processing numerosity, length and duration in a three-dimensional Stroop-like task: towards a gradient of processing automaticity?

The existence of a possible continuum of automaticity for numerosity, length and duration processing was tested with a three-dimensional Stroop-like paradigm. Participants had to compare the numerosity, the length or the duration of two successive linear arrays of sequentially flashed dots in which the three dimensions were manipulated independently to create congruent, incongruent or neutral pairs. The results show that numerosity and length both affected duration processing separately and cumulatively, whereas temporal cues did not influence judgements of numerosity or length. Moreover, length and numerosity influenced each other, with numerical cues having a stronger influence on length processing than the reverse. These findings support the idea that, in sequentially presented stimuli, numerosity, length and duration are processed with different levels of automaticity, with numerosity being processed most, and duration least automatically.

[1]  James L. McClelland,et al.  On the control of automatic processes: a parallel distributed processing account of the Stroop effect. , 1990, Psychological review.

[2]  M. Pesenti,et al.  Numerosity-duration interference: a Stroop experiment. , 2006, Acta psychologica.

[3]  Sylvie Droit-Volet,et al.  Time and number discrimination in a bisection task with a sequence of stimuli: a developmental approach. , 2003, Journal of experimental child psychology.

[4]  Simon Grondin,et al.  When to start explicit counting in a time-intervals discrimination task: A critical point in the timing process of humans. , 1999 .

[5]  John Cohen,et al.  A New Phenomenon in Time Judgment , 1953, Nature.

[6]  M. H. Fischer,et al.  Number processing induces spatial performance biases , 2001, Neurology.

[7]  E. Spelke,et al.  Number-Space Mapping in Human Infants , 2010, Psychological science.

[8]  D. Zakay.  Attention allocation policy influences prospective timing , 1998 .

[9]  Giacomo Koch,et al.  Relativistic Compression and Expansion of Experiential Time in the Left and Right Space , 2008, PloS one.

[10]  Valérie Dormal,et al.  Numerosity-length interference: a Stroop experiment. , 2007, Experimental psychology.

[11]  I. Levin,et al.  Interference of time-related and unrelated cues with duration comparisons of young children: analysis of Piaget's formulation of the relation of time and speed. , 1979, Child development.

[12]  Valérie Dormal,et al.  Common and Specific Contributions of the Intraparietal Sulci to Numerosity and Length Processing , 2009, NeuroImage.

[13]  Scott W. Brown.  Attentional resources in timing: Interference effects in concurrent temporal and nontemporal working memory tasks , 1997, Perception & psychophysics.

[14]  Michael Andres,et al.  Dissociation of numerosity and duration processing in the left intraparietal sulcus: A transcranial magnetic stimulation study , 2008, Cortex.

[15]  Ruth Stavy,et al.  How Students Mis/Understand Science and Mathematics: Intuitive Rules (Ways of Knowing in Science Series) , 2000 .

[16]  J. Piaget.  The Child's Conception of Number , 1953 .

[17]  Z. Pylyshyn,et al.  What enumeration studies can show us about spatial attention: evidence for limited capacity preattentive processing. , 1993, Journal of experimental psychology. Human perception and performance.

[18]  R. Church,et al.  Alternative representations of time, number, and rate , 1990, Cognition.

[19]  R. Church,et al.  A mode control model of counting and timing processes. , 1983, Journal of experimental psychology. Animal behavior processes.

[20]  Elizabeth S. Spelke,et al.  Spontaneous mapping of number and space in adults and young children , 2009, Cognition.

[21]  Ewart A. C. Thomas,et al.  Cognitive processing and time perception , 1975 .

[22]  Daniel Casasanto,et al.  Do monkeys think in metaphors? Representations of space and time in monkeys and humans , 2010, Cognition.

[23]  G. Vallar,et al.  The representational space of numerical magnitude: Illusions of length , 2008, Quarterly journal of experimental psychology.

[24]  H. Helson.  The tau effect—an example of psychological relativity. , 1930 .

[25]  R. Block,et al.  Prospective and retrospective duration judgments: A meta-analytic review , 1997, Psychonomic bulletin & review.

[26]  Sylvie Droit-Volet,et al.  Speeding up a master clock common to time, number and length? , 2010, Behavioural Processes.

[27]  H. H. Clark.  SPACE, TIME, SEMANTICS, AND THE CHILD , 1973 .

[28]  Colin M. Macleod,et al.  Training and Stroop-like interference: evidence for a continuum of automaticity. , 1988, Journal of experimental psychology. Learning, memory, and cognition.

[29]  ROBERT S. MOYER,et al.  Time required for Judgements of Numerical Inequality , 1967, Nature.

[30]  Sheng He,et al.  Larger stimuli are judged to last longer. , 2007, Journal of vision.

[31]  D. Kahneman,et al.  Tests of the automaticity of reading: dilution of Stroop effects by color-irrelevant stimuli. , 1983, Journal of experimental psychology. Human perception and performance.

[32]  The Child's Conception of Time. Le Developpement de la Notion du Temps Chez l 'Enfant , 1971 .

[33]  Avishai Henik,et al.  Automatic and intentional processing of numerical information , 1992 .

[34]  J. Dalrymple-Alford,et al.  Timing ability and numerical competence in rats. , 1998, Journal of experimental psychology. Animal behavior processes.

[35]  R. Shaw,et al.  Precocious Thoughts on Number: The Long and the Short of It. , 1972 .

[36]  S. Dehaene.  Varieties of numerical abilities , 1992, Cognition.

[37]  E. Erdfelder.  Experimental Psychology: A successful transition , 2007 .

[38]  Stanislas Dehaene,et al.  Primed numbers : Exploring the modularity of numerical representations with masked and unmasked semantic priming , 1999 .

[39]  C. Caltagirone,et al.  Perceiving numbers alters time perception , 2008, Neuroscience Letters.

[40]  E. L. Kaufman,et al.  The discrimination of visual number. , 1949, The American journal of psychology.

[41]  Olivier Houdeé,et al.  Negative priming effect after inhibition of number/length interference in a Piaget-like task , 2001 .

[42]  D. Algom,et al.  The perception of number from the separability of the stimulus: The Stroop effect revisited , 1996, Memory & cognition.

[43]  M. Goldberg,et al.  Space and attention in parietal cortex. , 1999, Annual review of neuroscience.

[44]  V. Walsh,et al.  The parietal cortex and the representation of time, space, number and other magnitudes , 2009, Philosophical Transactions of the Royal Society B: Biological Sciences.

[45]  Sylvie Droit-Volet,et al.  Time, Number and Length: Similarities and Differences in Discrimination in Adults and Children , 2008, Quarterly journal of experimental psychology.

[46]  W Fias,et al.  Irrelevant digits affect feature-based attention depending on the overlap of neural circuits. , 2001, Brain research. Cognitive brain research.

[47]  Philippe Pinel,et al.  Tuning Curves for Approximate Numerosity in the Human Intraparietal Sulcus , 2004, Neuron.

[48]  G. Lakoff,et al.  Metaphors We Live By , 1980 .

[49]  Michael Andres,et al.  Contribution of the right intraparietal sulcus to numerosity and length processing: An fMRI-guided TMS study , 2012, Cortex.

[50]  A. Henik,et al.  Is three greater than five: The relation between physical and semantic size in comparison tasks , 1982, Memory & cognition.

[51]  J. Piaget,et al.  The Child's Conception of Number , 1953 .

[52]  Carmen M. Atkinson,et al.  Event-related potentials to Stroop and reverse Stroop stimuli. , 2003, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[53]  H. Heinze,et al.  On the interaction of numerical and size information in digit comparison: a behavioral and event-related potential study , 1998, Neuropsychologia.

[54]  Avishai Henik,et al.  Count me in! On the automaticity of numerosity processing. , 2010, Journal of experimental psychology. Learning, memory, and cognition.

[55]  J. Duncan,et al.  Beyond the search surface: visual search and attentional engagement. , 1992, Journal of experimental psychology. Human perception and performance.

[56]  Stanislas Dehaene,et al.  Development of Elementary Numerical Abilities: A Neuronal Model , 1993, Journal of Cognitive Neuroscience.

[57]  Vincent Walsh.  A theory of magnitude: common cortical metrics of time, space and quantity , 2003, Trends in Cognitive Sciences.

[58]  F N Dyer,et al.  The Stroop phenomenon and its use in the stlldy of perceptual, cognitive, and response processes , 1973, Memory & cognition.

[59]  F. Moore.  Cognitive development and the acquisition of language , 1973 .

[60]  L. Boroditsky,et al.  Time in the mind: Using space to think about time , 2008, Cognition.

[61]  O. Houdé.  Numerical development: From the infant to the child. Wynn's (1992) paradigm in 2- and 3-year olds☆ , 1997 .

[62]  Valérie Dormal,et al.  A common right fronto‐parietal network for numerosity and duration processing: An fMRI study , 2012, Human brain mapping.

[63]  Anja Ischebeck,et al.  On the relative speed account of number-size interference in comparative judgments of numerals. , 2003, Journal of experimental psychology. Human perception and performance.

[64]  Derek Besner,et al.  The stroop effect and the myth of automaticity , 1997, Psychonomic bulletin & review.

[65]  Daniel Casasanto,et al.  Space and Time in the Child's Mind: Evidence for a Cross-Dimensional Asymmetry , 2010, Cogn. Sci..