Review
Beyond the number domain

https://doi.org/10.1016/j.tics.2008.11.007Get rights and content

In a world without numbers, we would be unable to build a skyscraper, hold a national election, plan a wedding or pay for a chicken at the market. The numerical symbols used in all these behaviors build on the approximate number system (ANS) which represents the number of discrete objects or events as a continuous mental magnitude. Here, we first discuss evidence that the ANS bears a set of behavioral and brain signatures that are universally displayed across animal species, human cultures and development. We then turn to the question of whether the ANS constitutes a specialized cognitive and neural domain – a question central to understanding how this system works, the nature of its evolutionary and developmental trajectory and its physical instantiation in the brain.

Section snippets

Universality and domain-specificity

The case that the approximate number system (ANS) is cognitively universal is based on four sources of evidence: cognitive development 1, 2, comparative cognition 3, 4, 5, cross-cultural cognition [6] and neurobiology 7, 8, 9. Collectively, these four types of evidence have established a case for a culturally, developmentally and evolutionarily universal system for representing ‘numbers’ as mental magnitudes. Less clear, however, is whether the neural system supporting the ANS is exclusive for

A primitive system for representing ‘number’

The primary behavioral signature of the ANS is Weber's law (Box 1), which holds universally across species, human development and human cultures 1, 2, 8, 9. For example, when monkeys and college students are tested in the same numerosity comparison and addition tasks, Weber's law similarly predicts their performance 4, 19 (Figure 1). Moreover, numerical discrimination in infancy is reliably predicted by numerical ratio 20, 21, indicating that the behavioral signatures of the ANS emerge within

Cognitive similarities between number and other magnitudes

Magnitude judgments are those that invoke questions such as ‘Which is more?’ or ‘Which is bigger?’ Judgments of this nature can be applied to size, length, time, loudness, number or any uni-dimensional property of an object or set. In fact, several cognitive signatures of magnitude processing are common to numbers and many other quantitative dimensions. The shared cognitive signatures of quantitative judgments implicate both a common mental code for quantitative representation and a common

Neural overlap between number and other magnitudes

Multiple sources of evidence, including neuropsychological and neuroimaging studies of humans in addition to neurophysiological studies of non-human primates, have converged on parietal cortex, particularly the IPS, as a substrate for numerical cognition. Classically, however, parietal cortex is associated with attention, visuo-spatial reasoning and the visual guidance of motor behavior 68, 69, 70. Damage to parietal cortex can lead to hemi-spatial neglect and/or extinction in addition to an

Conclusions

A wealth of empirical data demonstrates that numerical cognition is a primitive system that is shared with other animal species and emerges early in development. These data support the hypothesis that ‘number’ is a fundamental and universal cognitive capacity. Yet, several other cognitive functions for discriminating magnitudes also seem to be widely shared with other species and develop early in ontogeny. These capacities include judgments of size, time, brightness and other continuous

Acknowledgements

We thank Sara Cordes, Emily Hopkins, Melissa Libertus, Brad Mahon, Dustin Merritt, David Paulsen and the members of the Brannon laboratory for comments on this manuscript. This work was supported by an NSF CAREER award and a McDonnell Scholar Award to E.M.B in addition to an NRSA postdoctoral fellowship to J.F.C. We also wish to thank David Van Essen for advice in using Caret (http://brainmap.wustl.edu/caret) to generate Figure 4.

References (100)

  • M. Piazza

    A magnitude code common to numerosities and number symbols in human intraparietal cortex

    Neuron

    (2007)
  • K.J. Holyoak et al.

    Subjective magnitude information in semantic orderings

    J. Learn. Verb. Learn. Behav.

    (1976)
  • W. Gevers

    The mental representation of ordinal sequences is spatially organized

    Cognition

    (2003)
  • V. Dormal

    Numerosity-duration interference: a Stroop experiment

    Acta Psychol. (Amst.)

    (2006)
  • J.D. Roitman

    Nonverbal representation of time and number in adults

    Acta Psychol. (Amst.)

    (2007)
  • W. Fias

    Irrelevant digits affect feature-based attention depending on the overlap of neural circuits

    Brain Res. Cogn. Brain Res.

    (2001)
  • M. Oliveri

    Perceiving numbers alters time perception

    Neurosci. Lett.

    (2008)
  • E. Rusconi

    Spatial representation of pitch height: the SMARC effect

    Cognition

    (2006)
  • H.S. Terrace

    The simultaneous chain: a new approach to serial learning

    Trends Cogn. Sci.

    (2005)
  • R. Cohen Kadosh

    Small is bright and big is dark in synaesthesia

    Curr. Biol.

    (2007)
  • A. Herrera

    The role of working memory in the association betwee number magnitude and space

    Acta Psychol. (Amst.)

    (2008)
  • K.J. Holyoak

    Comparative judgments with numerical reference points

    Cognit. Psychol.

    (1978)
  • K.J. Holyoak et al.

    Cognitive reference points in judgments of symbolic magnitude

    Cognit. Psychol.

    (1982)
  • L. Feigenson

    The equality of quantity

    Trends Cogn. Sci.

    (2007)
  • M. Shuman et al.

    Numerical magnitude in the human parietal lobe: tests of representational generality and domain specificity

    Neuron

    (2004)
  • O. Simon

    Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe

    Neuron

    (2002)
  • R. Cohen Kadosh

    Notation-dependent and -independent representations of number in the parietal lobes

    Neuron

    (2007)
  • D. Ansari

    Parametric effects of numerical distance on the intraparietal sulcus during passive viewing of rapid numerosity changes

    Brain Res.

    (2006)
  • P. Pinel

    Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments

    Neuron

    (2004)
  • L. Kaufmann

    Neural correlates of distance and congruity effects in a numerical Stroop task: an event-related fMRI study

    Neuroimage

    (2005)
  • C. Marshuetz

    Working memory for order and the parietal cortex: an event-related functional magnetic resonance imaging study

    Neuroscience

    (2006)
  • D.L. Harrington

    Neural representation of interval encoding and decision making

    Brain Res. Cogn. Brain Res.

    (2004)
  • S.C. Hinton

    Neural systems supporting timing and chronometric counting: an fMRI study

    Brain Res. Cogn. Brain Res.

    (2004)
  • P. Maquet

    Brain activation induced by estimation of duration: a PET study

    Neuroimage

    (1996)
  • J.F. Cantlon et al.

    Semantic congruity affects numerical judgments similarly in monkeys and humans

    Proc. Natl. Acad. Sci. U. S. A.

    (2005)
  • J.F. Cantlon et al.

    Basic math in monkeys and college students

    PLoS Biol.

    (2007)
  • M.D. Hauser et al.

    Evolutionary and developmental foundations of human knowledge: a case study of mathematics

  • P. Pica

    Exact and approximate arithmetic in an Amazonian indigene group

    Science

    (2004)
  • B. Butterworth

    The Mathematical Brain

    (1999)
  • S. Dehaene

    Three parietal circuits for number processing

    Cogn. Neuropsychol.

    (2003)
  • S. Carey et al.

    Domain-specific knowledge and conceptual change

  • J.A. Fodor

    The Modularity of Mind: An Essay on Faculty Psychology

    (1983)
  • N. Kanwisher

    Domain specificity in face perception

    Nat. Neurosci.

    (2000)
  • D. Ansari

    Effect of development and enculturation on number representation in the brain

    Nat. Rev. Neurosci.

    (2008)
  • E.M. Hubbard

    Interactions between number and space in parietal cortex

    Nat. Rev. Neurosci.

    (2005)
  • J.F. Cantlon et al.

    Shared system for ordering small and large numbers in monkeys and humans

    Psychol. Sci.

    (2006)
  • J.S. Lipton et al.

    Origins of number sense: large-number discrimination in human infants

    Psychol. Sci.

    (2003)
  • L. Cipolotti

    A specific deficit for numbers in a case of dense acalculia

    Brain

    (1991)
  • M. Cappelletti

    Dissociations in numerical abilities revealed by progressive cognitive decline in a patient with semantic dementia

    Cogn. Neuropsychol.

    (2005)
  • E. Eger

    A supramodal number representation in human intraparietal cortex

    Neuron

    (2003)
  • Cited by (0)

    View full text