Idiosyncratic spatial representations of the days of the week in individuals without synesthesia

Abstract

People with spatial sequence synesthesia have clear and stable mental images of spatial arrays of numbers, days of the week, and months. The shapes of the arrays vary by individual. We conducted an experiment to estimate the shapes of spatial arrays in people without synesthesia. We presented a pair of Japanese characters that represent the days of the week on a display, and asked participants without synesthesia to state which day they thought came later by pressing a key that was congruent with the spatial position of the day shown. We then estimated the shape of the spatial array in the participants' mental space (mental weekday lines) from the distribution of the reaction times. We found that these ‘estimated mental weekday lines’ differed by individual, and that the shapes (straight or bent lines, U-shapes, zigzags, or triangles) were similar to the spatial arrays found in individuals with synesthesia. We then conducted simulations using a self-organizing map and found that differences in the shapes of the spatial arrays compared with those in individuals with synesthesia could be explained by the inputs to the network. These results support the hypothesis that interactions between spatial and ordinal/cardinal representations in both synesthetes and non-synesthetes develop under the influence of self-organizing learning.

Introduction

When participants are asked to judge the parity of visually presented numbers (1–9), the response time for small numbers (1–4) is shorter when the response key is pressed with the left hand, and the response time for large numbers (6–9) is shorter when the response key is pressed with the right hand (Dehaene, Bossini, & Giraux, 1993). This phenomenon is called the spatial–numerical association of response codes (SNARC) effect and suggests that individuals have a spatial mental number line that runs from left to right. Spatial effects have also been found in other tasks such as magnitude comparison or cued detection (Dodd, Van der Stigchel, Leghari, Fung, & Kingstone, 2008; Gevers, Verguts, Reynvoet, Caessens, & Fias, 2006; Ito & Hatta, 2004; Price, 2009), as well as for sequential stimuli such as months or weekdays. Gevers, Reynvoet, and Fias (2003) asked participants to judge whether a visually presented word that represented a month came before or after July, and found that the response time for months in the first half of the year was shorter when the participants pressed the response key with their left hand (month SNARC effect). Gevers, Reynvoet, and Fias (2004) also found that the SNARC effect occurs for weekdays.

Cultural factors have been found to influence the SNARC effect. Studies using magnitude comparison tasks have revealed a reverse SNARC effect among Arabic-speaking participants who use only a right-left writing system (Zebian, 2005). English-speaking Canadians, who read both words and numbers from left to right, demonstrated a standard left-to-right SNARC effect. Conversely, Palestinians, who read both words and numbers from right to left, exhibited the reverse effect. Israelis, who read words from right to left but numbers from left to right, had no reliable spatial association (Shaki, Fischer, & Petrusic, 2009). These results indicate that reading and writing systems influence the direction of mental number lines.

However, even among participants from the same cultural context, mental number lines in a fixed direction are not always observed for the entire population. Nuerk, Wood, and Willmes (2005) found a significant SNARC effect in their study population. When they re-examined the data (Wood, Nuerk, & Willmes, 2006), they found that about 65% of the participants from their 2005 study showed a negative SNARC slope (i.e., a left–right mental number line). The proportion of individuals with a negative SNARC slope was similar to that found by Fias (2001) and Nuerk, Iversen, and Willmes (2004), indicating that about 35% of the participants did not have a left–right mental number line. Hubbard, Ranzini, Piazza, and Dehaene (2009) presented a graph showing the individual SNARC slopes of French participants (control group), which indicated that some had positive SNARC slopes (i.e., a right–left mental number line). When Price (2009) re-analyzed the data obtained by Price and Mentzoni (2008), they found a significant month SNARC effect in a parity task (asking whether the number of a month is odd or even), but did not find an effect in a magnitude judgment task (asking whether a month belongs to the first or second half of the year; this task was similar to that used in Gevers et al., 2003; see also Simner (2009)). It has not been fully investigated whether these variations among participants are due to the inevitable noise in the experiments or whether they reflect the diversity of mental number lines among non-synesthete participants.

Various previous studies have attempted to determine whether the SNARC effect depends on cardinal or ordinal representation (Toomarian & Hubbard, 2018). Fischer, Castel, Dodd, and Pratt (2003) found an attentional SNARC effect. In their study, a target stimulus was presented on either the left or right side of a computer screen, and an irrelevant numerical digit was presented on the center of the display before the target. They found that the response time for left-side targets was shorter when the irrelevant digit was relatively smaller, and that the response time for right-side targets was shorter when the irrelevant digit was relatively larger. Dodd et al. (2008) examined the attentional SNARC effect for numbers, letters, months, and days, and found that the effect was observed reliably only for numbers unless the participants were instructed to process the non-numerical cues (letters, months, and days) in an order-relevant fashion. Schroeder, Nuerk, and Plewnia (2017) conducted a within-subjects investigation and found a dissociation between cardinal and ordinal SNARC effects. Participants performed an order-relevant task (before/after classification) using two types of stimuli: digits and weekdays. Whereas digits contain information about magnitude (cardinal information), weekdays contain only information about order (ordinal information). The researchers found a small positive correlation between the SNARC slopes for digits and weekdays in the order-relevant task. However, the results of the regression analysis differed between digits and weekdays. These results suggest that cardinal and ordinal information is represented differently. In this study, we examined the role of cardinal and ordinal representation using a neural network simulation.

Individuals with spatial sequence synesthesia automatically “see” mental images of spatial arrays when they think of numbers, months, days, or alphabet letters. The shapes of the arrays differ dramatically between individuals. For some people, the images of numbers are aligned along a straight line from left to right, like a typical SNARC-effect mental number line. For others, however, number images appear along a slant, curve, as a zigzag line, or in a grid. Number images may even be irregular and bend back on themselves (Eagleman, 2009; Galton, 1880, Galton, 1881; Seron, Pesenti, Noël, Deloche, & Cornet, 1992; Ward, 2013). The shape of spatial arrays in spatial sequence synesthesia has been shown to be congruent with the tendency observed in psychological experiments. For example, judgments about the size of two numbers are faster when the numbers are presented on the display in the same arrangement as the synesthete's number form, compared with the opposite arrangement (Hubbard et al., 2009; Sagiv, Simner, Collins, Butterworth, & Ward, 2006). The results of parity judgments and spatial cueing tasks have also been found to be congruent with the configuration of synesthetes' number forms (Hubbard et al., 2009; Jarick, Dixon, Maxwell, Nicholls, & Smilek, 2009; Simner, 2009).

Cohen Kadosh and Henik (2007) pointed out that individuals with spatial sequence synesthesia appear to exhibit tendencies that are similar to the SNARC effect. As noted above, the prevalence of the left-right SNARC effect in non-synesthetes is about 65% (Wood et al., 2006). This is similar to the prevalence of a left-to-right array for the numbers from 1 to 10 in individuals with spatial sequence synesthesia, i.e., 66% in Seron et al. (1992) and 63% in Sagiv et al. (2006). Eagleman (2009) found that the majority (62%) of month forms (i.e., spatial arrays of months) have a left–right bias: early and later months tend to be located on the left and right, respectively. Cohen Kadosh and Henik (2007) regarded these similar percentages to be evidence of individual differences in the SNARC effect among non-synesthetes, indicating that some non-synesthetes have mental number lines with directions that differ from left-to-right. Simner (2009) proposed that synesthetic experiences might reflect mechanisms that are common to all people, such that it may be the level of awareness of these experiences that differs between synesthetes and non-synesthetes. Since synesthetes can “see” their spatial array, they can report the shape of the array. Non-synesthetes, conversely, cannot report the shape of their mental number line, and the shapes of the mental number lines in those who do not show the left-right SNARC effect are unknown. Individual differences in mental representation in individuals without synesthesia have not been fully investigated.

In this study, we examined mental representations of the days of the week. We chose the days of the week as stimuli because they have an ordinal sequence. In contrast, months are not suitable for the investigation of ordinal sequence in Japanese, because the names of the months are represented by numbers (e.g. January is called “Ichi-gatsu,” which means the first month). The primary aim of the present study was to estimate the shapes of “mental weekday lines” in non-synesthetes, without depending on a specific hypothesis regarding their directionality. Most studies of mental number/month/weekday lines in non-synesthetes have focused on horizontal or vertical configurations. However, imposing such limitations on the experimental paradigm may limit exploration of the structure of mental number lines. Thus, new experimental tasks are needed to assess spatial representation without the constraint of a response arrangement. In the present study, we used a new multi-configuration comparison task to examine the structure of mental weekday lines. In this task, we presented a pair of weekdays in one of eight spatial configurations and asked participants to press the response key that corresponded to the location of the day that came afterward. This task enables assessment of the relationship between days and space without a specific hypothesis regarding directionality. The multi-configuration comparison task was developed based on the task used in Sagiv et al. (2006), where two numbers were presented on a display and the participant was asked to report which number was larger by pressing a pre-specified key. Sagiv et al. (2006) used this task to verify whether the spatial array affected the speed of numerical comparison in individuals with spatial sequence synesthesia. In their task, the response keys were assigned in advance to match the spatial array of the individual synesthete. The multi-configuration comparison task was developed to enable researchers to explore the shape of the spatial array in non-synesthetes who do not have a clear image of their mental array.

Deroy & Spence (2013) proposed that cross-modal correspondence in non-synesthetes and individuals with synesthesia are not two ends of a continuum, but separate phenomena. We agree that they are qualitatively different phenomena, in that synesthetes have a conscious image of a spatial array, while non-synesthetes does not. However, if the spatial configurations of weekdays in non-synesthetes' mental space have similar structures to those in synesthetes, then it is likely that non-synesthetes share the mechanisms that create shapes in spatial sequence synesthesia. Recently, Nair and Brang (2019) found that sounds can evoke synesthesia-like percepts in non-synesthetes after less than 5 min of visual deprivation. This result supports the notion that synesthetes and non-synesthetes share the same mechanisms of between-modality interaction.

The secondary aim of this study was to examine whether mental weekday lines estimated via a multi-configuration comparison task in non-synesthetes had similar properties to those in individuals with synesthesia. We asked each participant to complete the same experiment two months apart to examine the stability of mental weekday lines. The constancy of an array over time is one of the key properties of spatial sequence synesthesia.

Spatial sequence synesthesia is thought to be caused by a neural connection between numerical and spatial representation. The spatial effect on magnitude comparison or parity judgment also suggests the existence of a neural link between numerical and spatial representation in the brains of non-synesthetes (Dehaene, 1997). Neuroimaging studies of numerical cognition in humans and electrophysiological studies of spatial cognition in monkeys have indicated that numerical-spatial interactions arise from common parietal circuits implicated in attention for external space and internal numeric representations (Hubbard, Piazza, Pinel, & Dehaene, 2005). A framework called the self-organizing learning account of number forms (SOLA) has been proposed to explain the origin of idiosyncratic number forms in spatial sequence synesthesia. SOLA assumes that shapes in individuals with spatial sequence synesthesia are determined by self-organizing learning of associations between numerical and spatial representation (Makioka, 2009). SOLA explains three key properties of spatial sequence synesthesia: (a) within-individual consistency, (b) between-individual variation, and (c) the mixture of regularity and randomness. However, simulations using SOLA have only been conducted for numerical input and did not examine the forms associated with weeks or months. Spatial sequence synesthesia for weeks or months sometimes takes the form of a closed shape such as an ellipse, rectangular, or triangle, which are rare in number forms. The third aim of this study was to investigate whether SOLA can explain the generation process of week forms. We examined the relationships between the type of representations (magnitude or circular representation) and the shape of spatial sequence synesthesia. Using the same neural network as Makioka (2009), we compared self-organizing maps generated from two types of input representations. In addition, we investigated whether the mental space of participants without synesthesia exhibits the three key properties of spatial sequence synesthesia.