When 9 is not on the right: Implications from number-form synesthesia

Abstract

Number-form synesthetes consciously experience numbers in spatially-defined locations. For non-synesthete individuals, a similar association of numbers and space appears in the form of an implicit mental number line as signified by the distance effect–reaction time decreases as the numerical distance between compared numbers increases. In the current experiment, three number-form synesthetes and two different non-synesthete control groups (Hebrew speaking and English speaking) performed a number comparison task. Synesthete participants exhibited a sizeable distance effect only when presented numbers were congruent with their number-form. In contrast, the controls exhibited a distance effect regardless of congruency or presentation type. The findings suggest that: (a) number-form synesthesia impairs the ability to represent numbers in a flexible manner according to task demands; (b) number-form synesthesia is a genuine tangible experience, triggered involuntarily; and (c) the classic mental number line can be more pliable than previously thought and appears to be independent of cultural-lingo direction.

Introduction

Number-form synesthesia is a remarkable phenomenon in which numbers are experienced consciously as existing in spatially-defined locations. Galton (1880) was the first to report this kind of condition, described by him as “the power to visualizing numerals” (p. 252). A century later, Seron, Pesenti, Noel, Deloche, and Cornet (1992) presented a few cases of individuals who were automatically able to “see” numbers in precise locations in mental space (p. 159). More recently, two newsworthy works provided some empirical data supporting the genuineness of number-form synesthesia. In those studies, participants with number-form synesthesia exhibited a significant congruency effect when asked to compare numbers presented congruently or incongruently with their relative number-form location (Piazza et al., 2006, Sagiv et al., 2006). Apparently, for participants with number-form synesthesia, numbers automatically trigger a conscious sense of spatially-defined arrays that interfere with the performance on simple number comparison tasks.

A similar, although implicit, association between numbers and space also appears in the non-synesthete population in the form of a spatial-mental number line. It has been argued that numbers are internally represented on a visuo-spatial analogue scale referred to as a ‘mental number line’ (e.g., Restle, 1970). This mental line is automatically activated each time a number comparison is required. Moyer and Landauer (1967) were the first to provide evidence for this widespread assumption. They asked participants to decide which of two presented digits, ranging from 1 to 9, was numerically larger, and found that reaction time (RT) increased as the numerical distance between digits decreased (e.g., RT for the pair “1,9” was faster than for the pair “1,2”). This effect is known as the numerical distance effect and since then, has been considered by many as an indication for the existence of the mental number line (e.g., Dehaene, 1992, Dehaene and Akhavein, 1995, Restle, 1970, Sekular et al., 1971).

Other studies focused on the spatial feature of the mental number line, and showed the spatial representation of numbers via the SNARC effect (Spatial-Numerical Association of Response Codes). When participants were asked to perform parity judgments (odd vs. even), they responded faster with the right key to large numbers (e.g., larger than 5) and with the left key to small numbers (e.g., smaller than 5) than vice versa (Dehaene, Bossini, & Giraux, 1993; for a review and meta-analysis see Wood, Nuerk, Willimes, and Fisher (2008)). This effect is assumed to support the idea of a spatial-mental number line oriented from left-to-right. Recent studies also suggested the existence of a vertical number line, organized with small numbers at the bottom and large numbers at the top. Ito and Hatta (2004) demonstrated a vertical SNARC effect by showing that participants were faster to respond to small numbers while pressing a bottom key and to large numbers while pressing a top key. Furthermore, Schwarz and Keus (2004) showed that upward saccades occur earlier with large numbers, whereas downward saccades occur earlier with small numbers. They suggested that the mental number representation is organized more like a quadratic map than a number line.

In addition to the horizontal and vertical alignments of numbers, there have been reports on other types of spatial representation. For example, Bachthold, Baumuller, and Brugger (1998) found that numbers can also be represented on a mental circle configuration rather than on a mental line. In their study, participants were instructed to imagine digits as representations of units on a clock, and decide if a digit was larger or smaller than the reference number 6. A reverse SNARC effect was observed, suggesting that the spatial-mental line can be flexibly produced and its form can be influenced by the spatial requirements of the task.

Two main conclusions can be drawn from the findings presented so far. First, the nature of the mental number line is quite flexible and can be largely induced by a task’s spatial demands. Second, the association between numbers and space is a characteristic shared by both number-form synesthetes and the non-synesthete population. However, an important distinction must to be drawn: In contrast to the non-synesthete population who produce a mental number line implicitly, unconsciously and usually under specific experimental manipulations, number-form synesthetes visualize numbers automatically and consciously each time they see, hear or think of them (Cohen Kadosh and Henik, 2007, Galton, 1880, Seron et al., 1992).

Surprisingly, there have been very few attempts to examine the nature of the mental number line in number-form synesthesia (e.g., Piazza et al., 2006, Sagiv et al., 2006, Tang et al., 2008). The current study investigates the visuo-spatial nature of number-form synesthesia and whether this kind of synesthesia can shed some light on the processes involved in the generation of the classic mental number line. We hypothesized that the elicitation of explicit, spatially-defined configurations in number-form synesthetes would affect performance on tasks that require spatial representations of numbers. Since the distance effect is considered to be the most basic manifestation of the ability to mentally represent numbers, we used it to examine our hypothesis.

In the current experiment, three number-form synesthetes and two non-synesthete control groups—Hebrew speaking and English speaking—preformed a number comparison task. Participants were asked to decide which of two presented digits was numerically larger, by pressing the assigned keys. We manipulated the type of presentation (horizontal, vertical), the congruency of numbers within each presentation (congruent, incongruent), and the numerical distance (distance 1, 2, and 5). According to the literature, congruent trials were defined as trials in which small numbers were presented on the left or/and at the bottom (i.e., congruent with left-to-right and bottom-to-top assumed mental number lines) and incongruent trials as trials in which small numbers were presented on the right or/and at the top (i.e., incongruent with left-to-right and bottom-to-top assumed mental number lines). Naturally, for synesthete participants, congruent trials were defined as trials in which the numbers were presented congruently with their number-form and vice versa. Note that our synesthetes possess distinctive number-forms orientations, thus levels of congruency were defined differently for each one of them. Specifically, for synesthete OT numbers are represented on the horizontal meridian from right-to-left (Fig. 1A), a representation that is reversed from the standard mental number line. Hence, in his case the congruent condition was defined by trials in which small numbers were presented on the right and large numbers on the left. For synesthete SM numbers are represented on a vertical meridian from bottom-to-top (Fig. 1B), which fits the commonly represented vertical number line, thus for her the congruent condition was defined by trials in which small numbers were presented at the bottom and large numbers at the top. Synesthete RS is a pure number-form synesthete since she possesses a very simple and plain number-form aligned from left-to-right (Fig. 1C). Thus for her, as for controls, the congruent condition was defined by trials in which small numbers were presented on the left and large numbers on the right. Because of the widely accepted assumption that the non-synesthete population also represents numbers on a left-to-right mental number line—but in contrast to synesthetes, they are unaware of it—we expected RS’s behavior to be the most revealing one.

In the case of number-form synesthetes, we expected that the unique number-forms would interfere with performance when the spatial presentation of the stimuli did not match it. Namely, responding to incongruent trials would result in longer RT and a smaller distance effect compared to congruent trials. However, we expect no such differences in the controls due to the assumed flexible implicit nature of the mental number line.

We used two lingo-distinctive control groups since we were not certain whether reading habits might have an influence on the results. Dehaene et al. (1993, Experiment 7) found a revered SNARC effect in Iranian individuals, who read and write from right-to-left, and claimed that the orientation of the spatial-numerical representation is compelled by the reading direction. Note that Hebrew is written from right-to-left but mathematical expressions are processed from left-to-right. Thus, in order to avoid a lingo-cultural artifact, we compared the synesthetes with both Hebrew speaking and English speaking controls.