How is Number Associated with Space? The Role of Working Memory

Abstract

A large body of evidence demonstrates that the processing of numbers and space are tightly related.Today, the dominant explanation for this interaction is the number line hypothesis. This hypothesis claimis that the mental representation of numbers takes the form of a horizontally oriented line which is functionally homeomorphic to the way physical lines are represented. The aim of the present review is twofold. In a first step we review recent evidence on number bisection bias in neglect and on the SNARC effect challenging the homeomorphic relationship between numerical and spatial processing. For the bisection bias we present data that show a clear dissociation between number bisection and physical line bisection. Additionally, we present data on the SNARC effect showing that its origin is of a conceptual rather than visuospatial nature. In a second step, we present data that provide pointers towards a new theoretical framework which proposes that serial position in working memory may be an important determinant of the interactions between number and space. How number is associated with space? The role of working memoryIt is generally accepted that the cognitive representation and processing of number and space are tightly linked. This is evident from introspective reports, for instance by mathematicians who describe their mathematical thinking as hinging on visual imagery. Also, math instruction and education rely strongly on visuospatial tools and strategies. Remarkably, the involvement of spatial processing in mathematical cognition is not restricted to complex mathematics but even applies to the basic and elementary representation of number.Already in the 1880's Galton [e.g. 1] described the introspective reports of people who experience vivid mental number line images. Later, Seron et al. [2] showed that these were more than incidental observations and confirmed that about 14% of typical student population report mental number lines. Experiences of spatially defined mental number lines can be particularly strong and elaborated in synesthesia [3,4], a condition in which certain types of stimuli give rise to experiences in modalities that are normally not associated with such stimuli, for instance color sensations to number stimuli. Importantly, however, number-space interactions are not restricted to those who have the conscious experience of mental number lines. A number of empirical phenomena demonstrate that the involvement of space is a basic and essential aspect of number representation also in people who do not report having conscious experience of visuospatial number lines when they think about numbers.In a seminal paper, Dehaene et al. [5] showed that, when subjects respond to numbers by pressing a left or a right response key, for instance in a parity judgment task, small numbers are faster responded to with the left hand than with the right hand and that large numbers receive faster right hand than left hand responses. This effect (see Figure 1) indicating a Spatial Numerical Association ...

Small numbers in the right brain: Evidence from patients without and with spatial neglect

“…Based on the presence of number interval bisection biases in RBD patients with left spatial neglect and on the phenomenological similarity between these biases and biases usually displayed by neglect patients in the bisection of long and short visual horizontal lines (Doricchi et al, 2005b), it was proposed that numerical biases are due to the extension of visual spatial neglect to the MNL (Zorzi et al, 2002), i.e., to neglect for smaller numbers located on the left side of the MNL. This interpretation however, was not supported by several investigations showing that in RBD, neglect-like symptoms in mentalnumber space are not correlated to the severity or even the presence of left spatial neglect in the bisection of visual lines and, more generally, of neglect in visual or imagery space (Doricchi et al, 2005a(Doricchi et al, , 2009Rossetti et al, 2004Rossetti et al, , 2011Loetscher and Brugger, 2009;Loetscher et al, 2010;van Dijck et al, 2011;Aiello et al, in press;Pia et al, in press). …”

Is the SNARC Effect Related to the Level of Mathematics? No Systematic Relationship Observed despite More Power, More Repetitions, and More Direct Assessment of Arithmetic Skill

“…Implications on the current debate on the sources of the SNARC effect The current study was not designed to examine whether the foundation of the SNARC effect is more visuospatial or more verbal in nature (Fias, van Dijck, & Gevers, 2011;Gevers et al, 2010;. However, let us assume with Gevers et al (2010) that the SNARC in a parity judgement task indexes fewer spatialnumerical representations and rather more verballinguistic (or verbal working memory) capacities.…”

When time is space: Evidence for a mental time line

“…Its popularity and effectiveness induces to think that it genuinely taps into a preferential way to spatially represent time flow from left to right. In addition, it has been suggested that rightward-oriented drawings of human profiles induce a sensation of being oriented towards the future (Van Sommers, 1984). 2005; Umiltà et al, 2009, for recent reviews; but see Fias et al, 2011 for a different account). The proposal that numbers are spatially represented finds its roots in the seminal study of Galton (1880), who found that some people report vivid introspective descriptions of numbers arranged into spatial forms (notably, spatial forms were also reported for temporal sequences such as months of the calendar year).…”