Martin H. Fischer

Samuel Shaki

Frontiers in Psychology

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Fischer, Martin H.

Shaki, Samuel

publish.UP (Univ. Potsdam)

Two steps to space for numbers

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OPINION
published: 12 May 2015
doi: 10.3389/fpsyg.2015.00612
Frontiers in Psychology | www.frontiersin.org 1 May 2015 | Volume 6 | Article 612
Edited by:
Ann Dowker,
University of Oxford, UK
Reviewed by:
Marco Zorzi,
University of Padova, Italy
Katarzyna Patro,
University of Tübingen, Germany and
University of Warsaw, Poland
*Correspondence:
Martin H. Fischer,
martinf@uni-potsdam.de
Specialty section:
This article was submitted to
Developmental Psychology,
a section of the journal
Frontiers in Psychology
Received: 02 November 2014
Accepted: 24 April 2015
Published: 12 May 2015
Citation:
Fischer MH and Shaki S (2015) Two
steps to space for numbers.
Front. Psychol. 6:612.
doi: 10.3389/fpsyg.2015.00612
Two steps to space for numbers
Martin H. Fischer 1* and Samuel Shaki 2
1Division of Cognitive Sciences, Department of Psychology, University of Potsdam, Potsdam, Germany, 2Department of
Behavioral Science, Ariel University, Ariel, Israel
Keywords: spatial-nunmerical association, SNARC, mental number line, numerical cognition, spatial cognition
The study of spatial-numerical associations (SNAs) is an active research project that was triggered
by a landmark publication reporting several simple reaction time experiments: Adults classified
visually presented numbers according to their parity by using left and right response keys (Dehaene
et al., 1993). The main finding was that small numbers, such as 1 or 2, were classified faster on
the left side and larger numbers, such as 8 or 9, were classified faster on the right side. This
specific instance of a SNA has been replicated and extended in numerous studies (recent review
by Fischer and Shaki, 2014). The original interpretation of the effect assumed a “spill-over” from
reading habits into the number domain but subsequent work has pushed back the time line to
preschoolers, infants, and even neonates (for recent review, see Patro et al., 2014). Our own work
(e.g., Shaki et al., 2009; Fischer and Shaki, 2015) confirmed that reading habits contribute to the
direction and strength of SNAs but has also indicated that they are not the only and not even
the strongest determinant (e.g., Fischer et al., 2010). In the following paragraphs we propose a
processing principle for SNAs and describe two successive steps by which the mapping of numbers
onto space might occur.
Our proposed processing principle is that spatial mapping is an integral part of semantic number
processing. This is evident from the ubiquity of SNAs: They have been reported with various
stimulus formats, in many different tasks, and while studying a wide range of responses (for recent
review, see Fischer and Shaki, 2014). SNAs modulate the cortical region underlying semantic
number processing (i.e., bilateral hIPS; Cutini et al., 2012). Moreover, the association between
numbers and space is bi-directional: numerical magnitude can serve as a spatial cue and vice
versa (Stoianov et al., 2008; Shaki and Fischer, 2014a). Most studies of SNAs have used centrally
presented numbers in combination with spatial responses, whichmay have encouraged participants
to use spatial number mapping strategies (Fischer, 2006). However, today it is clear that the very
appearance of numerical stimuli is enough for SNAs to appear, even when removing, in healthy
adults (cf. Zorzi et al., 2002), spatial features from both stimuli and responses (Fischer and Shaki,
2015; Ranzini et al., 2015). Evidence for such a purely conceptual link between numbers and space
was even found in Hebrew speakers, thus requiring correction of our earlier claim of the need for
consistency of directional processing habits across stimulus domains (Shaki et al., 2009; Shaki and
Fischer, 2012, 2014b).
We note that our present proposal leaves open the issue of the origin(s) of SNAs, be they a
congenital result of hemispheric specializations, or acquired by culturally shaped spatial habits such
as reading or finger counting (Fischer, 2008; Lindemann et al., 2011; Domahs et al., 2012; Fischer
and Shaki, 2015; Rugani et al., 2015a,b). Assuming that processing number meaning is obligatorily
accompanied bymapping it onto a spatial continuum, two issues remain to be addressed to account
for a given SNA in a particular setting: The selection of the appropriate spatial dimension, and the
directionality of mapping numbers along that dimension. We now present an idea of how these
two steps are taken and describe recent evidence in support of this proposal.
First, the spatial dimension selected for mapping of numbers reflects the stimulus and response
features of the current task. When lateralized response keys are provided to participants to measure
the speed of their judgments, then most participants will align their number representations along
the dimension indicated by these keys, be it horizontal, vertical, or radial. This is what the bulk of
Fischer and Shaki Two steps to space for numbers
the literature has documented (as recently reviewed by Fischer
and Shaki, 2014). In the absence of such response keys,
when responses to numbers are required by making spatially
directional arm, head, eye or whole-body movements, then the
major directions or endpoints of those movements define the
mapping dimension, again either using the horizontal (Fischer,
2003; Fischer et al., 2004; Loetscher et al., 2008; Shaki and
Fischer, 2014a) or vertical dimension (Schwarz and Keus, 2004;
Winter and Matlock, 2013). When spatially distinct responses
to the numbers are required but no response dimension is
prescribed, the resulting mapping of numbers onto space will
be more varied across participants (Fischer and Campens,
2008). Finally, even when no spatially distinct responses are
required, as for example in a simple detection task, the spatial
mapping of centrally presented numbers will still emerge through
lateralization of other stimuli, such as visually presented cues
(Fischer et al., 2003; for a recent update, see Fischer and Knops,
2014).
Finally, once a dimension for the spatial mapping of numbers
has been selected by the participant, their distribution along
this dimension still remains to be decided. For this second
step, we propose that the orientation of the SNA is influenced
by spatial experience. This rule underlines the manifold of
possible influences on the SNARC which are only beginning
to be documented and studied. Living in a three-dimensional
world, we are differentially sensitive to horizontal vs. vertical
space. For example, as a result of the embodied nature of
cognition, vertical distinctions are most salient and horizontal
ones least salient (Fischer and Brugger, 2011), leading to
faster acquisition of, and discrimination along, the vertical
than the horizontal dimension (Franklin and Tversky, 1990).
Similarly, the increasing strength of SNAs with age (Wood
et al., 2008; Hoffmann et al., 2014) indicates that they may
reflect accumulated spatial habits/experiences during life. An
example are reading habits (see the contribution of Nuerk
et al., 2015 to this research topic for a detailed description of
mechanisms). Importantly, such life-long experiences are less
powerful in determining the directionality of a SNAs compared
to more recent experiences with numbers, as demonstrated in
emerging training studies (e.g., Fischer, 2012) and by rapid
alternations of SNAs between successive trials (Fischer et al.,
2009).
In summary, the proposed two successive steps seem to
capture a wide range of observations pertaining to the ubiquity
of SNAs that have recently re-invigorated research into numerical
cognition. We hope that the present proposal will guide further
interest in the design of novel studies that aim to test specific
predictions about the origin and strength of SNAs. For example,
how can we identify the sequential nature of the mapping
process? How shall we weight the contributions of previous
experiences? Clearly, such questions identify numerical cognition
as a convenient test-bed for the study of fundamental principles
of cognition generally.
Acknowledgment
MHF is funded by DFG grant FI 1915/2-1 “Manumerical
cognition”.
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Conflict of Interest Statement: The authors declare that the research was
conducted in the absence of any commercial or financial relationships that could
be construed as a potential conflict of interest.
Copyright © 2015 Fischer and Shaki. This is an open-access article distributed
under the terms of the Creative Commons Attribution License (CC BY). The use,
distribution or reproduction in other forums is permitted, provided the original
author(s) or licensor are credited and that the original publication in this journal
is cited, in accordance with accepted academic practice. No use, distribution or
reproduction is permitted which does not comply with these terms.
Frontiers in Psychology | www.frontiersin.org 3 May 2015 | Volume 6 | Article 612


Martin H Fischer

Samuel eShaki

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