During the last decades, extensive research has investigated both the developmental
origins and the representational format of numerical information. A crucial contribution
to these issues comes from recent studies on non-verbal populations, such as non-human
animals and preverbal infants, which suggest that number is intuitively and fundamentally
spatial in nature, that a predisposition to relate numerical information to spatial
magnitude emerges very early in life, and that the association of numbers to different
spatial positions critically depends on biologically determined processing and attentional
biases.
Various sources of evidence suggest that when representing numbers human adults translate
them into corresponding spatial extensions and positions (Restle, 1970; Galton, 1880;
Dehaene et al., 1993; Fias et al., 1996). This phenomenon is referred to as number-space
mapping and accounts for various systematic behavioral effects in numerical and visuo-spatial
tasks. For instance, numerical processing modulates spatial representation according
to a cognitive illusion, whereby small numbers induce a compression and large numbers
an expansion of spatial extent (de Hevia et al., 2006, 2008; Stöttinger et al., 2012).
In particular, adult's bisection of a line flanked by two numbers is biased toward
the larger one (Fischer, 2001; de Hevia et al., 2006; Ranzini and Girelli, 2012),
and the reproduction of a spatial extension is underestimated when delimited by two
small numbers, and overestimated when delimited by two large numbers (de Hevia et
al., 2008). Other observations, such as the interference between numerical and physical
size in Stroop-like tasks and cross-dimensional mapping tasks (Stevens, 1970; Girelli
et al., 2000; Pinel et al., 2004; de Hevia et al., 2012), support the existence of
a mapping between symbolic and non-symbolic numbers and spatial magnitude.
The idea we would like to put forth is that the number-space mapping appears to be
fundamental, spontaneous, and present very early in life, as it might constitute an
innate trait of human, and possibly non-human, cognition. The notion that this mapping
is universal and spontaneous is supported by neuroanatomical evidence showing that
common parietal structures are engaged in both numerical and spatial tasks (Dehaene
et al., 2003; Fias et al., 2003). Critically, electrophysiological studies have revealed
that the posterior parietal cortex in primates, which includes quantity-selective
neurons, contains accurate information about discrete (number of items) and continuous
(length) quantity, with the same neurons coding for both non-symbolic number and spatial
length (Tudusciuc and Nieder, 2007). Therefore, in line with the well-known ATOM (A
Theory Of Magnitude) model proposed by Walsh (2003), numbers, as well as other magnitudes,
might not be represented in isolation but spontaneously connected to space representation.
Further support for an intuitive and universal number-space mapping comes from research
conducted with preschool children, preverbal infants, humans in remote cultures, and
non-human animals, where a spontaneous mapping between number and space has been observed
through a variety of experimental paradigms. When bisecting a line flanked by two
different, non-symbolic numbers, 3–5-year-old children show a signature bias toward
the larger number, just as adults do (de Hevia and Spelke, 2009; Girelli et al., 2009).
Through the habituation paradigm, infants at 8 months of age transfer the discrimination
of an ordered series of numbers to an ordered series of line lengths, and learn and
productively use a rule that establishes a positive relationship between number and
length, while failing to do so with an inverse relationship (de Hevia and Spelke,
2010; see also Lourenco and Longo, 2010). Using the number line task, which explicitly
requires the mapping of number onto space (Siegler and Opfer, 2003), adults living
in an Amazonian remote culture, with little or no education, resemble children's mappings
with non-symbolic numbers (Dehaene et al., 2008). These findings suggest that the
number-space mapping takes place well before formal education, preceding language,
and symbolic knowledge acquisition. Moreover, among other mappings between continuous
dimensions the number-space mapping seems to have a privileged status. When preschool
children create cross-dimensional matches between different instances from the dimensions
of number, line length, and level of brightness, they reliably perform mappings between
number and length, and only partially between brightness and length, but fail to map
number and brightness (de Hevia et al., 2012). Also in adults, number establishes
a stronger overlap, at both functional and neural levels, with the dimension of space
than with the dimension of brightness (Pinel et al., 2004; but see Cohen Kadosh et
al., 2008).
An instantiation of the number-space mapping is that ordered numerical magnitudes
are associated to different spatial positions along a horizontal continuum. The classical
finding for this phenomenon is the Spatial-Numerical Association of Response Codes
(SNARC) effect: generally speaking, small numbers are responded faster with the left
hand and large numbers with the right hand, suggesting a compatibility effect between
the left and right sides of one's own body and a left-to-right oriented numerical
representation (Dehaene, 1992; Dehaene et al., 1993; Fias et al., 1996). This phenomenon
has been extended to a variety of scenarios; among others, priming with a small or
large number leads to shifts of attention toward the left or right sides of the space,
respectively (Fischer et al., 2003). Critically, SNARC-like effects have been described
for non-numerical ordinal series: adults react faster using the left hand to the presentation
of the initial letters of the alphabet (Gevers et al., 2003), initial tones of a musical
scale (Rusconi et al., 2006), initial (or past) events (Santiago et al., 2007), and
initial elements in a list of unrelated words (Previtali et al., 2010), while they
are faster using the right hand for the final elements of these series. Therefore,
ordinal information in general, and not only number, triggers the use of an oriented
spatial code. Moreover, the association of number with spatial positions is amply
malleable, so that by simply varying the task requirements or setting, like conceiving
numbers as depicted in a clock-face (Bächtold et al., 1998) or exposing bilingual
participants to reading different languages (Shaki and Fischer, 2008), the association
changes. This suggests that associating numbers to spatial positions results from
a task-dependent individual's mental strategy to organize information (Fischer, 2006),
an instance of the spatial coding of ordinal information in working memory (van Dijck
and Fias, 2011).
Contrary to what commonly hypothesized, the origins of this mapping might not be exclusively
culturally based. In favor of a culturally based position, the SNARC effect is modulated
by reading direction: in Western cultures, small numbers are associated to the left
and large numbers to the right side, while in cultures with right-to-left reading/writing
direction the association is weaker (Dehaene et al., 1993) or reversed (Shaki et al.,
2009). However, although early attempts to trace the SNARC effect in children described
its emergence at 9 years of age (Berch et al., 1999), recent studies using non-symbolic
number and non-chronometric tasks found it in 4-year-old children not formally introduced
to reading system (van Galen and Reitsma, 2008; Patro and Haman, 2012). Moreover,
the 3- and 4-year-olds who exhibit a consistent left-to-right bias in tasks such as
subtraction and addition of tokens and counting objects (e.g., counting from the left
and proceeding rightwards) are more proficient at basic numerical knowledge (Opfer
et al., 2010). These studies suggest that, much before entering school, early cultural
factors engendered by activities such as counting or “reading” illustrated books (McCrink
et al., 2011) may determine the specific orientation of children's number-space mapping.
Far from denying the strong impact of cultural conventions on the number-space mapping,
we see these forces as playing a modulating and refining role, not a fundamental one.
Our idea is that the association of numbers onto spatial positions along a spatial
magnitude might root in early biases present in the processing of magnitude information,
whether numerical or spatial, which, from early on in development, would concur in
shaping the way infants attend and represent any ordinal information, such as number.
Optimal candidates might be a biologically determined advantage for processing the
left hemispace, and an advantage in the processing of increasing order. Across the
lifespan, these biases would be modulated and refined by exposure to cultural conventions.
In fact, and of critical importance to our view, not all processing biases are determined
by culture. Let us review the seminal studies on counting abilities in newly hatched
chicks. In these studies, chicks are trained to peck at the 4th position in a series
of ten identical, equispaced and sagittally oriented locations. Afterwards, when required
to identify the correct location within a new series identical to the one used at
training, but horizontally oriented, chicks are more accurate at identifying the 4th
position from the left than from the right end, which is chosen at chance level (Rugani
et al., 2010). While cultural conventions cannot account for these findings, basic
attentional biases can. The left bias shown by chicks is thought to be due to right
hemispheric dominance in visuospatial processing, resulting in the left hemifield
guiding the birds' behavior. Chicks' hemispheric lateralization can be experimentally
manipulated by controlling the rearing environment of the eggs, thus providing a promising
animal model for investigating the neural bases of the oriented number-space mapping
(Vallortigara et al., 2010). This manipulation has been also performed in fish by
obtaining animals that differ in the direction of cerebral lateralization. When these
animals solve a bisection task, i.e., choosing the central element in a row, strong
spatial biases are found in opposite directions, either toward the right or the left,
depending on the artificially obtained direction of cerebral lateralization (Dadda
et al., 2009).
These findings from non-human, non-linguistic species substantiate the role of neural
factors and visuo-spatial processing strategies in engendering attentional biases.
One contribution to the emergence of a number-space mapping in humans is, in our view,
the biologically determined attentional bias regulating the asymmetrical exploration
of space. Although available infant literature does not clearly establish the presence
and degree of such biases, hints for this phenomenon are nonetheless informative.
First, classical studies on infants' visual exploration indicate that at birth horizontal
scans are wider and more frequent than vertical scans (Haith, 1980), suggesting that
visual exploration and stimulus detection are easier along the horizontal than the
vertical orientation. Second, a timing asymmetry may exist in the maturation of cerebral
hemispheres, with a temporal advantage for the right over the left hemisphere (Rosen
et al., 1987).
Thus, spatio-temporal constraints on brain development may determine an advantage
of the left over the right visual hemispace in early infancy. This leftward spatial
bias might constrain both the exploration of external space and the organization of
information along a representational space. In fact, attentional biases in visual
space likely extend to the mental representation of information. For instance, patients
with unilateral neglect not only fail to explore the left side of visual space, but
also the left side of a mental image (Bisiach and Luzzatti, 1978), and fail to accurately
bisect imagined numerical intervals, showing biases toward the larger number (Zorzi
et al., 2002; Vuilleumier et al., 2004). A further processing bias relevant to our
argument is the recently disclosed advantage for processing increasing magnitude information.
Four-month-old infants discriminate increasing ordered sequences of an object progressively
changing in size, but fail at detecting decreasing sequences (Macchi Cassia et al.,
2012). These finding points to the existence of an asymmetry in the processing of
ordinal information which, combined with a natural propensity to asymmetrically explore
space, might constitute one of the building blocks of a mental mapping where numbers
are associated to different spatial positions. From early on and across the lifespan,
the advantage in the horizontal scanning of the left hemispace, and the advantage
in the processing of ascending order might combine with culturally based factors,
such as exposure to reading/writing habits and the associated scanning and ordering
routines. These factors would either counteract a predetermined orientation or strengthen
it, eventually giving rise to culturally dependent strategies to represent ordinal
information, including, but not limited to, number.