Elsevier

Cortex

Volume 45, Issue 10, November–December 2009, Pages 1190-1199
Cortex

Special section: Research report
The ups and downs (and lefts and rights) of synaesthetic number forms: Validation from spatial cueing and SNARC-type tasks

https://doi.org/10.1016/j.cortex.2009.04.015Get rights and content

Abstract

Typically, numbers are spatially represented using a mental ‘number line’ running from left to right. Individuals with number-form synaesthesia experience numbers as occupying specific spatial coordinates that are much more complex than a typical number line. Two synaesthetes (L and B) describe experiencing the numbers 1 through 10 running vertically from bottom to top, 10–20 horizontally from left to right, 21–40 from right to left, etc. We investigated whether their number forms could bias their spatial attention using a cueing paradigm and a SNARC-type task. In both experiments, the synaesthetes' responses confirmed their synaesthetic number forms. When making odd–even judgments for the numbers 1, 2, 8, and 9, they showed SNARC-compatibility effects for up–down movements (aligned with their number form), but not left–right (misaligned) movements. We conceptually replicated these biases using a spatial cueing paradigm. Both synaesthetes showed significantly faster response times to detect targets on the bottom of the display if preceded by a low number (1, 2), and the top of the display if preceded by a high number (8, 9), whereas they showed no cueing effects when targets appeared on the left or right (misaligned with their number forms). They were however reliably faster to detect left targets following the presentation of numbers 10 and 11, and right targets following numbers 19 and 20 (since 10–20 runs from left to right). In sum, cueing and SNARC tasks can be used to empirically verify synaesthetic number forms, and show that numbers can direct spatial attention to these idiosyncratic locations.

Introduction

There is growing evidence suggesting that we represent numbers spatially in the form of a ‘mental number line’ with low numbers (1, 2) mentally represented on our left and high numbers (8, 9) on our right (Restle, 1970). Numbers have been shown to direct spatial attention to locations along this mental number line (Dehaene et al., 1993, Fischer et al., 2003, Silillas et al., 2008), and the spatial representation of numbers can influence behaviours, such as counting and arithmetic calculations (Seron et al., 1992, Ward et al., 2009). Dehaene et al. (1993) demonstrated the link between the mental number line and behaviour using a parity judgment task. In this task, participants indicated their odd/even response by pressing a left button when the centrally presented digit was ‘odd’ and a right button when the digit was ‘even’. Participants were faster when the response button was compatible with the location of the digit along the mental number line. For instance, participants were faster to make left-handed responses for small numbers versus large numbers (i.e., faster to identify the digit 1 as ‘odd’ via a left-hand response, than they were to identify the digit 9). Dehaene et al. (1993) labeled this phenomenon the Spatial Numerical Association of Response Codes (SNARC) effect, and it has been used repeatedly to demonstrate the robustness of the mental number line and its influence on behaviour (e.g., Daar and Pratt, 2008, Müller and Schwartz, 2007, Notebaert et al., 2006, Schwartz and Keus, 2004, Ito and Hatta, 2004, Shaki and Fischer, 2008, Wood et al., 1993).

Furthermore, cueing paradigms have demonstrated numerical effects on spatial attention. Fischer et al. (2003) showed that attention could be automatically directed to the left or right visual field by simply presenting a high or low digit on a computer screen. In their paradigm, the digits 1, 2, 8, or 9 were centrally presented and followed by a target (circle) to the left or right of fixation. Participants were asked to detect the presence of the target as quickly and accurately as possible by pressing a central button on the keyboard. Fischer et al. found that targets on the left side of the display were detected faster when preceded by a low number (1, 2), and right targets were detected faster when preceded by a high number (8, 9). They surmised that the presentation of the digit cues elicited shifts in spatial attention to the locations of the digits on the mental number line. Notably, this cueing of attention occurred even though the digits were not statistically predictive of the target locations. Recent electrophysiological evidence provides support for Fischer et al.'s findings and demonstrated that similar brain mechanisms are recruited during shifts of attention produced by irrelevant numerical cues compared to informative arrow cues (Ranzini et al., 2009).

For most people, the act of thinking about a given number does not consciously trigger an awareness of that number's spatial location on the number line. Indeed Tang et al. (2008) characterize the typical left to right number line as an “unconscious, number-space relationship” (p. 1). However, for approximately 10–12% of individuals (Sagiv et al., 2006, Seron et al., 1992, Tang et al., 2008), numbers do elicit a conscious awareness of a spatial location. These people experience very vivid ‘number forms’ that are much more complex than the typical number line (Galton, 1880, Galton, 1881, Price and Mentzoni, 2008, Seron et al., 1992, Tang et al., 2008).

Most researchers have considered these atypically strong number–space associations (number forms) a variant of synaesthesia (Hubbard et al., 2005, Piazza et al., 2006, Sagiv et al., 2006, Tang et al., 2008). Synaesthesia is a fascinating phenomenon whereby an ordinary stimulus (e.g., digit 5) elicits an extraordinary experience (e.g., the colour blue). For individuals with number-form synaesthesia, the extraordinary experience involves a conscious awareness of a specific location in space triggered by the number. These synaesthetic number forms can appear as rows, scales, or grids (Seron et al., 1992), spirals or oblongs (Galton, 1880), or even as infinite tunnels. Although the spatial organization of the numbers might vary considerably from one synaesthete to the next, their number forms seem to have important commonalities. First, the number–space relations tend to be very consistent within individuals (Seron et al., 1992); if on one occasion a number-form synaesthete draws a depiction of their number form, they will draw the same atypical number form on each subsequent occasion. Second, individuals who have vivid number forms indicate that they have had them since infancy (Seron et al., 1992) and cannot recall a time when they did not experience them. Finally, the synaesthetic number forms seem to be involuntarily and automatically activated (Seron et al., 1992). That is, whenever a number is seen, heard, or thought of, the synaesthete cannot (through an act of will) prevent themselves from also experiencing the associated spatial location (Sagiv et al., 2006, Seron et al., 1992). Studies exploring these characteristics of number-form synaesthesia are just beginning to emerge.

Tang et al. (2008) used functional magnetic resonance imaging (fMRI) to investigate the brain areas underlying the number forms of synaesthetes versus the brain areas supporting the more ubiquitous left-to-right number lines. They selected synaesthetes whose number forms ran from left to right, and compared them to controls who presumably have the standard, left to right number line. Their results showed comparable brain regions involved when the task concerned processing numerical magnitude (e.g., number of items in the display). However, when the task required ordinal processing of the numbers (e.g., whether the number N was in the nth position), greater activation was found bilaterally in synaesthetes in the intraparietal sulci. These findings suggest that the number forms experienced by synaesthetes are a spatial representation of the sequential (as opposed to magnitude) aspects of numbers (Sagiv et al., 2006; also see Walsh, 2003 for a theory on magnitude processing).

This sequential interpretation of this form of synaesthesia may extend to other forms of synaesthesia as well. For instance, Smilek et al. (2007) have shown that for individuals with time–space synaesthesia, sequences such as time units (e.g., months of the year) are also assigned highly specific spatial locations. In a target detection task, Smilek et al. showed that month names could cue spatial attention to the left or right depending on the synaesthetic spatial location of the presented month. Similarly, Price and Mentzoni (2008) showed a month-SNARC effect for time–space synaesthesia. They highlighted how the idiosyncratic organization of month locations nevertheless had systematic SNARC effects. For two of their synaesthetes, early months were located on the left side of space and later months on the right side, whereas the other two synaesthetes experienced later months on the left and early months on the right. All four synaesthetes were asked to judge whether the presented month was in the first or second half of the year and make a left or rightward response to indicate their choice. The authors found a left-hand advantage for early months for synaesthetes whose early months were synaesthetically on the left, but a right hand advantage for those whose early months were synaesthetically on the right. Importantly, they did not find any hint of any month-SNARC effects in non-synaesthetes (but see, Gevers et al., 2003). Price and Mentzoni's results suggest that (at least for synaesthetes) SNARC-type tasks can be used to uncover not only interactions between numbers and space, but also a more general relationship between ordinal sequences (including time units like months of the year) and space.

The majority of investigations into the spatial properties associated with number sequences have focused primarily on representations that extend exclusively from left to right (with the exception of Piazza et al., 2006 and Sagiv et al., 2006). Our objective was to examine number-form synaesthetes who experience unusual mental number lines that do not run from left to right. In these experiments, we investigated two number-form synaesthetes (L and B) who report experiencing atypical number lines, such that the numbers 1 through 10 run vertically from bottom to top, and the numbers 10–20 extend horizontally from left to right (see Fig. 1 for a “birds eye” view of L's representation).

We first sought to empirically evaluate the synaesthete's atypical number forms using a SNARC-type task. If the SNARC effect is determined by the association between response codes and the spatial representation of numbers, then SNARC effects should result that correspond to L and B's idiosyncratically structured number line. That is, we should find larger SNARC effects when the synaesthetes make vertical (up and down) responses than when they make horizontal (left and right) responses because their numbers rise vertically from 1 to 9. Non-synaesthetes however, should produce the opposite pattern of results and show larger SNARC effects for horizontal than vertical responses consistent with their standard left-to-right mental number lines. Although for non-synaesthetes, some vertical SNARC effects may be present (Gevers et al., 2006, Schwartz and Keus, 2004) albeit to a smaller extent. The key here is that non-synaesthetes should show a larger SNARC effect for left–right movements than up–down movements, whereas synaesthetes should show the opposite pattern because of the vertical alignment of their atypical number forms.

Secondly, we aimed to further verify L and B's unusual number forms using the spatial cueing paradigm of Fischer et al. (2003). According to Fischer et al., low numbers directed attention to the left, and higher numbers directed attention to the right in accordance with the left–right alignment of the standard mental number line. Importantly, for the synaesthetes L and B, the left and right target locations in the Fischer task are misaligned with their synaesthetic number lines. Thus, if cued with the digits 1, 2, 8, and 9 preceding left or right targets, we expect no cueing effects to be observed. Yet, if the targets were presented on the top and bottom of the display, now aligned with L and B's number forms, we expect to find strong cueing effects (e.g., low numbers would facilitate detecting targets below fixation). Furthermore, we expect to find strong cueing effects with left–right targets when the numbers 10, 11, 19 and 20 are presented as cues, since recall that for both L and B the digits 10–20 run horizontally from left to right. Also note that while L took part in both the SNARC and Fischer cueing tasks, B could only participate in the cueing task (Experiments 2 and 3) due to injury that interfered with her making the repetitive movements required during the SNARC task.

Section snippets

Experiment 1

For the SNARC-type task, our predictions are straightforward: non-synaesthetes should show larger SNARC effects for left/right responses, whereas the synaesthetes, because of their vertical number form, should show the opposite pattern, larger SNARC effects for up/down responses.

Experiment 2

In Experiment 2, we used the Fischer cueing task to provide converging evidence for L and B's unusual number forms. As with the SNARC task, we ran versions of the Fischer task that were either aligned or misaligned with L and B's number forms. The digits 1, 2, 8, or 9 were presented at fixation, followed by target circles that appeared in boxes either to the left or the right of the display (misaligned with the synaesthetes' vertically rising number forms) or above and below fixation (aligned

Experiment 3

The Fischer task provided converging evidence for the SNARC effects shown in Experiment 1. Only when the targets were aligned with the synaesthetes' number forms, were strong cueing effects observed. The Fischer task has an advantage over the SNARC task in that two digit numbers can be used in the Fischer task, while it is impossible to demonstrate SNARC effects for two digit numbers in a parity task (participants simply ignore the leftmost digit). This allowed us to empirically validate the

General discussion

This series of experiments provides empirical confirmation of synaesthetic number forms using two types of tasks: the SNARC task (Dehaene et al., 1993) and a spatial cueing task (Fischer et al., 2003). The SNARC effect has been used widely to show the automatic response activation of implicit spatial representations of sequences in synaesthetes (Price and Mentzoni, 2008) and non-synaesthetes (e.g., Dehaene et al., 1993, Gevers et al., 2003, Gevers et al., 2006). While the ‘mental number line’

Acknowledgements

This research was supported by the Natural Sciences and Engineering Research Council of Canada, with a grant to M.J.D. and D.S., and a Postgraduate Scholarship to M.J. We wish to sincerely thank the synaesthetes who made this research possible. We also extend our appreciation to Edward Hubbard for providing helpful comments on a previous version of the manuscript.

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