Elsevier

Cortex

Volume 44, Issue 4, April 2008, Pages 353-358
Cortex

Special issue: Editorial
Numbers, space, and action – From finger counting to the mental number line and beyond

https://doi.org/10.1016/j.cortex.2008.01.002Get rights and content

Introduction

We spontaneously associate numbers with space: we think of small numbers as being lower and to the left of us, and larger numbers as being further up and to the right of us. Even though we may not notice it ourselves, this spontaneous association of numbers with space affects our behaviour in many ways: it affects response speed and accuracy when we classify numbers by parity or magnitude, and influences our spatial behaviour when we move our arms in response to numbers, or when we estimate midpoints of visually or auditorily presented number intervals. Our responses in all these and many other tasks are systematically affected by the numbers' magnitudes, an effect that has aptly been named the Spatial-Numerical Association of Response Codes (or SNARCs).

The SNARC effect is now an established finding (for reviews, see Fias and Fischer, 2005, Gevers and Lammertyn, 2005, Hubbard et al., 2005). This effect is reliably found across different tasks, materials, response modalities and populations (but see Wood et al., 2006a, Wood et al., 2006b). At the time of this writing, almost 200 studies that either carry the acronym SNARC in the title or abstract, or cite the seminal study by Dehaene et al. (1993) have been published (see Fig. 1), and the trend in our figure reveals an ever growing interest in this topic. Because of its prevalence in perception, cognition, and action, the SNARC effect has even made its entry into textbooks (e.g., Ward, 2006, p. 279).

At the same time, several basic issues surrounding the SNARC effect have not yet been resolved, for example its neuro-anatomical underpinnings (Hubbard et al., 2005) and developmental origins (Bachot et al., 2005, Berch et al., 1999), or its implications for neuropsychology (Vuilleumier et al., 2004, Priftis et al., 2006) and for cognition more generally (Proctor and Cho, 2006). These and other topics were covered in a workshop on “Numbers, Space, and Action” that was organized by Klaus Willmes, Helga Krinzinger, and ourselves and held in Aachen/Germany on 23 and 24 March 2007. The present special issue is a result of this workshop, and although many more researchers contributed to its success, space constraints forced us to select from over 30 excellent submissions a subset that we think reflects some of the most exciting new developments in this ever-growing field.

Section snippets

Why numbers, space, and action?

Why should numbers and space be associated, and how does this association determine action? Most probably the narrow vicinity of the neuroanatomical structures subserving number and space and action in the posterior parietal cortex is an important ingredient of the transactions between them (e.g., Hubbard et al., 2005). In the intraparietal cortex there are many regions highly specialized in spatial processing which are associated with perceptual as well as with motor processes (Rushworth and

Manumerical cognition and the origin of SNARC

Despite 15 years of research and a large number of published studies it is still not clear how the SNARC effect comes about. Several authors refer to an analogy with reading because the original SNARC study suggested a reversed association in Iranian adults who normally read and write from right to left: the longer these Iranians had spent in France, the stronger they presented the association large-right/small-left (Dehaene et al., 1993, Experiment 7). This observation was taken to show that

The when and where of numerical activation

Another recurring point of debate is the cognitive locus of the association between numbers, space, and action. Daar and Pratt (2008, this issue) introduce evidence from a new free response paradigm, supporting the view that the SNARC effect emerges at the response selection stage (see also Gevers et al., 2006, Keus et al., 2005). However, an SNARC-like bias also occurs in tasks without response selection (Fischer et al., 2003; see also Casarotti et al., 2007, Galfano et al., 2006, Ristic

Atomic fusion

The existence of magnitude representations in the intraparietal cortex is well established (e.g., Hubbard et al., 2005, Nieder, 2005). The notion that such representations become activated in every task involving magnitudes, regardless of whether they are times, spaces, frequencies, or numerosities, was at the heart of A Theory Of Magnitude (ATOM) proposed by Walsh (2003). Supporting this proposal, Ishihara et al. (2008, this issue) show that duration judgments also have a preferred spatial

Conclusions

Associations and dissociations between numbers, space, and action go far beyond the well known SNARC effect, the best known child of an apparently big family of interactions occurring in the parietal cortex. In general, the cross-talk seems to be determined by attention, intention, and strategic processes. As can be gleaned from this special issue, the core magnitude representation can be dissociated from, but normally interacts with different visuo-spatial representations which possibly may

Acknowledgements

We are indebted to all participants of the Workshop “Number, Space, and Action” (Aachen/Germany, March 23–24, 2007) and of the Summer School on Numeracy and Brain Development (Santorini, Greece, September 15–22, 2007; http://math.nmi.jyu.fi/numbra/) for stimulating discussions. In particular, we thank Avishai Henik and Hans-Christoph Nuerk for valuable comments. We also thank Sergio Della Sala for his support from conception to completion of this special issue.

MHF is member of the Marie Curie

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