Mental Number Lines

The mental association of numbers with space is familiar: at school children are taught to associate numbers with positions on a visually presented line. Yet the nature of mental number lines, their role in our thinking, and even their origin are not obvious and hold some surprises. Moreover, when cognitive scientists talk of a mental number line they are often not talking about any representation we acquire at school. My aim is to get clearer about mental number lines given the evidence to date; in particular, I shall try to show how innate and cultural factors interact to determine the nature and role of mental number lines in very basic numerical thinking. For this we first need to take a look at our basic number representations.

[1]  Richard B. Ivry,et al.  Activating response codes by stimuli in the neglected visual field. , 1995 .

[2]  S. Scott,et al.  Specifying Executive Representations and processes in Number Generation Tasks , 2001, The Quarterly journal of experimental psychology. A, Human experimental psychology.

[3]  Klaus Willmes,et al.  Decade breaks in the mental number line? Putting the tens and units back in different bins , 2001, Cognition.

[4]  S. Kosslyn.  Measuring the visual angle of the mind's eye , 1978, Cognitive Psychology.

[5]  K. Priftis,et al.  Brain damage: Neglect disrupts the mental number line , 2002, Nature.

[6]  S. Schweinberger,et al.  Implicit perception in patients with visual neglect: Lexical specificity in repetition priming , 2001, Neuropsychologia.

[7]  Brian Butterworth,et al.  The Mathematical Brain , 1999 .

[8]  Stanislas Dehaene,et al.  The neural basis of the Weber–Fechner law: a logarithmic mental number line , 2003, Trends in Cognitive Sciences.

[9]  Peter Brugger,et al.  Stimulus-response compatibility in representational space , 1998, Neuropsychologia.

[10]  A. T. Welford,et al.  THE MEASUREMENT OF SENSORY-MOTOR PERFORMANCE : SURVEY AND REAPPRAISAL OF TWELVE YEARS' PROGRESS , 1960 .

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

[12]  Marie-Pascale Noël,et al.  Images of numbers, or “when 98 is upper left and 6 sky blue” , 1992, Cognition.

[13]  W P Banks,et al.  Two subjective scales of number , 1981, Perception & psychophysics.

[14]  S. Kosslyn.  Image and mind , 1982 .

[15]  D. H. Mating.  How Long is a Piece of String , 1968 .

[16]  S. Dehaene,et al.  Imaging unconscious semantic priming , 1998, Nature.

[17]  Marco Zorzi,et al.  A Computational Model of Number Comparison , 2020, Proceedings of the Twenty First Annual Conference of the Cognitive Science Society.

[18]  R. Shepard,et al.  Mental Rotation of Three-Dimensional Objects , 1971, Science.

[19]  FRANCIS GALTON,et al.  Visualised Numerals , 1880, Nature.

[20]  Ian H. Robertson,et al.  Unilateral Neglect: Clinical and Experimental Studies edited by Ian H. Robertson and John C. Marshall , 1994 .

[21]  J. Baird,et al.  Psychophysical study of numbers , 1975 .

[22]  E. Bisiach,et al.  Unilateral Neglect of Representational Space , 1978, Cortex.

[23]  J. Mattingley,et al.  Parietal neglect and visual awareness , 1998, Nature Neuroscience.

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

[25]  Fred Attneave,et al.  Perception and related areas. , 1962 .

[26]  John C. Baird,et al.  Psychophysical study of numbers , 1975 .

[27]  James V. Hinrichs,et al.  Two-digit number comparison: Use of place information. , 1981 .

[28]  S. Dehaene,et al.  Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. , 1990, Journal of experimental psychology. Human perception and performance.