Samuel Shaki

Reading habits for both words and numbers contribute to the SNARC effect.

This study compared the spatial representation of numbers in three groups of adults: Canadians, who read both English words and Arabic numbers from left to right; Palestinians, who read Arabic words and Arabic-Indic numbers from right to left; and Israelis, who read Hebrew words from right to left but Arabic numbers from left to right. Canadians associated small numbers with left and large numbers with right space (the SNARC effect), Palestinians showed the reverse association, and Israelis had no reliable spatial association for numbers. These results suggest that reading habits for both words and numbers contribute to the spatial representation of numbers.

Reading space into numbers: a cross-linguistic comparison of the SNARC effect.

Small numbers are spontaneously associated with left space and larger numbers with right space (the SNARC effect), for example when classifying numbers by parity. This effect is often attributed to reading habits but a causal link has so far never been documented. We report that bilingual Russian-Hebrew readers show a SNARC effect after reading Cyrillic script (from left-to-right) that is significantly reduced after reading Hebrew script (from right-to-left). In contrast, they have similar SNARC effects after listening to texts in either language. These results support the view that spatially directional scanning habits contribute to the spatial association of numbers but also emphasize its flexibility.

How to Cook a SNARC: Number Placement in Text Rapidly Changes Spatial-Numerical Associations.

Most theoreticians believe that reading habits explain why Western adults associate small numbers with left space and large numbers with right space (the SNARC effect). We challenge this belief by documenting, in both English and Hebrew, that SNARC changes during reading: small and large numbers in our texts appeared near the left or right ends of the lines, positioned either spatially congruent or incongruent with reading habits. In English, the congruent group showed reliable SNARC before and after reading and the incongruent groups SNARC was significantly reduced. In Hebrew the incongruent reading condition even induced a reverse SNARC. These results show that SNARC is a fleeting aspect of number representation that captures multiple spatial associations.

The Cultural Number Line: A Review of Cultural and Linguistic Influences on the Development of Number Processing

Approximate processing of numerosities is a universal and preverbal skill, while exact number processing above 4 involves the use of culturally acquired number words and symbols. The authors first review core concepts of numerical cognition, including number representation in the brain and the influential view that numbers are associated with space along a “mental number line.” Then, they discuss how cultural influences, such as reading direction, finger counting, and the transparency of the number word system, can influence the representation and processing of numbers. Spatial mapping of numbers emerges as a universal cognitive strategy. The authors trace the impact of cultural factors on the development of number skills and conclude that a cross-cultural perspective can reveal important constraints on numerical cognition.

Spatial associations in numerical cognition—From single digits to arithmetic

The literature on spatial associations during number processing is dominated by the SNARC (spatial–numerical association of response codes) effect. We describe spatial biases found for single digits and pairs of numbers, first in the “original” speeded parity task and then extending the scope to encompass different tasks, a range of measures, and various populations. Then we review theoretical accounts before surveying the emerging evidence for similar spatial associations during mental arithmetic. We conclude that the mental number line hypothesis and an embodied approach are useful frameworks for further studies.

Direction counts: a comparative study of spatially directional counting biases in cultures with different reading directions.

Western adults associate small numbers with left space and large numbers with right space. Where does this pervasive spatial-numerical association come from? In this study, we first recorded directional counting preferences in adults with different reading experiences (left to right, right to left, mixed, and illiterate) and observed a clear relationship between reading and counting directions. We then recorded directional counting preferences in preschoolers and elementary school children from three of these reading cultures (left to right, right to left, and mixed). Culture-specific counting biases existed before reading acquisition in children as young as 3 years and were subsequently modified by early reading experience. Together, our results suggest that both directional counting and scanning activities contribute to number-space associations.

It Takes Just One Word to Quash a SNARC

Our directional reading habit seems to contribute to the widely reported association of small numbers with left space and larger numbers with right space (the spatial-numerical association of response codes, SNARC, effect). But how can this association be so flexible when reading habits are not? To address this question, we asked bilingual Russian-Hebrew readers to classify numbers by parity and alternated the number format from trial to trial between written words and Arabic digits. The number words were randomly printed in either Cyrillic or Hebrew script, thus inducing left-to-right or right-to-left reading, respectively. Classification performance indicated that the digits were spatially mapped when they followed a Russian word but not when they followed a Hebrew word. An auditory control experiment revealed left-to-right SNARC effects with different strengths in both languages. These results suggest that the SNARC effect reflects recent spatial experiences, cross-modal associations, and long-standing directional habits but not an attribute of the number concepts themselves.

On the mental representation of negative numbers: Context-dependent SNARC effects with comparative judgments

In one condition, positive and negative number pairs were compared in separate blocks of trials. In another condition, the positive and the negative number pairs were intermixed. In the intermixed condition, comparisons involving negative numbers were faster with the left hand than with the right, and comparisons were faster with the right hand than with the left hand with the positive numbers; that is, a spatial numerical association of response codes (SNARC) effect was obtained, in which the mental number line was extended leftward with the negative numbers. On the other hand, in the blocked condition, a reverse SNARC effect was obtained with the negative numbers; that is, negative number pairs have the same underlying spatial representation as the positive numbers in this context. Nongraded semantic congruity effects, obtained in both the blocked and the intermixed conditions, are consistent with the idea that magnitude information is extracted prior to the generation of discrete semantic codes.

Multiple spatial mappings in numerical cognition.

A recent cross-cultural comparison (Shaki, Fischer, & Petrusic, 2009) suggested that spatially consistent processing habits for words and numbers are a necessary condition for the spatial representation of numbers (Spatial-Numerical Association of Response Codes; SNARC effect). Here we reexamine the SNARC in Israelis who read text from right to left but numbers from left to right. We show that, despite these spatially inconsistent processing habits, a SNARC effect still emerges when the response dimension is spatially orthogonal to the conflicting processing dimension. These results clarify the cognitive conditions for spatial-numerical mappings.

Random walks on the mental number line

The direction of influence between conceptual and motor activation, and its relevance for real-life activities, is still unclear. Here, we use the frequently reported association between small/large numbers and left/right space to investigate this issue during walking. We asked healthy adults to generate random numbers as they made lateral turns and found that (1) lateral turn decisions are predicted by the last few numbers generated prior to turning; (2) the intention to turn left/right makes small/large numbers more accessible; and (3) magnitude but not order of auditorily presented numbers influences the listener’s turn selection. Our findings document a bidirectional influence between conceptual and motor activation and point to a hierarchically organized conceptual–motor activation.