Embodied Interaction Priority: Other's Body Part Affects Numeral–Space Mappings

Introduction

In the tasks of magnitude comparison or parity judgment of numbers, the left (right) hand responds to small (large) numbers faster than the right (left) hand. Such association is named as spatial–numerical association of response codes (SNARC) effect (Dehaene, Bossini, & Giraux, 1993). The SNARC effect is nowadays an established finding, and it has been consistently found across different tasks, materials, and response modalities (Antoine & Gevers, 2016; Domahs, Moeller, Huber, Willmes, & Nuerk, 2010; Gevers, Reynvoet, & Fias, 2003; Schwarz & Keus, 2004). The classical explanation about SNARC effect is mental number line (MNL) theory. Some studies have demonstrated that the MNL is innate. A recent study implies that newborn chicks can associate smaller numbers with the left space and larger numbers with the right space (Rugani, Vallortigara, Priftis, & Regolin, 2015). Conversely, there exist studies indicating that the direction of reading and writing in a specific cultural context modulates the orientation of MNL (Ito & Hatta, 2004; Shaki & Fischer, 2008; Zebian, 2005). Hence, the reversed SNARC effect occurs due to the use of a reversed spatial reference frame for their writing system. However, Fischer, Mills, and Shaki (2010) manipulated the spatial position of the number embedded in a text to explore whether the direction of SNARC effect would change or not, and the result of this study implied that reading habituation was not the only factor influencing the SNARC effect and it was a short-term problem-solving strategy involving task relevant spatial reference frame, rather than an automatically activated MNL. Bachtold et al. (1998) asked participants to imagine digits on a ruler or a clock face when they made magnitude judgment; they found classical SNARC effect when they conceived of digits on a ruler, a reversed SNARC effect was observed on a clock face. In fact, the ruler and clock face provided a spatial reference frame to participants. Medina (2007) indicated that spatial reference frame is a system representing the spatial location of entities relative to other things. These studies indicated that a relative frame of reference is needed for number representations.

The recent views consider that numeral spatial representations are similar to physical spatial information representations which depend on the specific spatial reference frames, and explain the mechanisms of numeral -spatial associations based on the influences of spatial reference frames on numeral representations. In physical spatial cognition, there are two types of spatial reference frames named as allocentric reference frames and egocentric reference frames, respectively. The allocentric reference frames mean that representing the coordinates of entities independently of our body. That is, we represent entities according to the position of absolute coordinates, environment, or objects. Mourad and Lethsteensen (2017) examined the role which spatial reference frames play in the SNARC effect, and their results implied that alignment of the spatial reference frames associated with the responses and with the representation of numerical magnitude is a necessary condition for the elicitation of the SNARC effect. In the study of patients with spatial neglect, it has been demonstrated that patients usually ignore the left side of the presented objects when they perform the line bisection task (Karnath & Rorden, 2012). Here, object-centered reference frame plays a key role in spatial judgment. In SNARC effect, the spatial alignment of keyboard as an object can provide an object-based reference frame in horizontal or vertical position. Israeli participants who write from right to left can form SNARC effect along the vertical response dimension (Shaki & Fischer, 2012). Although response dimension is inconsistent with reading or writing direction, SNARC effect was observed as well. This shows that external objects as a reference frame may influence the SNARC effect. Except object-based reference frame, in fact, an MNL from left to right seems as a world-centered reference frame irrespective of our body. In the original study, a standard SNARC effect was found whatever your hands were crossed or uncrossed (Dehaene et al., 1993). This shows that numbers can be mapped onto an external coordinate frame. Accordingly, in this study, object-based and MNL reference frame were referred to as allocentric coordinate frame.

The egocentric reference frame was referred to as that we regard our body as the center to judge the spatial location of entities. For example, if we represent the number 2 to our left, the egocentric system will be working. Many researches have demonstrated that egocentric reference frame played a key role in SNARC effect. There is a dynamic hierarchy of reference frames involving in SNARC effect, including hand-based, finger-based, eye-centered, and so on (Viarouge, Hubbard, & Dehaene, 2014). Crollen, Dormala, Seron, Lepore, and Collignon (2013) ask early blind participants to respond to number magnitude with either crossed or uncrossed hands. The results imply that standard SNARC effect emerges in uncrossed condition, but it finds a reversed SNARC effect in crossed hands. This manifests that hand-based reference frame is at work in early blind participants. Expect hands, other sensory modalities relative to our body have an influence on SNARC effect. From finding that finger counting may be the origin of SNARC effect (Wood & Fischer, 2008), lots of studies have investigated the effect of finger-centered reference frame on SNARC effect. Riello and Rusconi (2011) required participants to make a parity task with the index and middle fingers of either their left hand or right hand. A unimanual SNARC effect was observed when participant's right hand placed palm down, whereas when participant's hands placed palm up, a unimanual SNARC effect was presented with the left hand. Whatever your hands or fingers, they are the parts of our body. In other words, when we make a parity or magnitude task, we may identify the spatial position of numbers with respect to our body. For example, participants reported more small digits (smaller than 15) with the range of 1 to 30 when their head turn left, but they say more large digits when their head turn right (Loetscher, Schwarz, Schubiger, & Brugger, 2008). Later, using the same reporting method, a study implied that our eye movement could predict the next number generated (Loetscher, Bockisch, Nicholls, & Brugger, 2010). In addition, whole-body motion can influence numerical cognition (Hartmann, Grabherr, & Mast, 2011). All these studies show that there are multiple egocentric reference frames, such as abovementioned, hands-centered, finger-based, head-centered, eye-centered, and whole-body.

These studies of body-related accord with the view of embodied cognition, which consider the cognition processing as a dynamic interaction of cognition, body, and environment. Zhang, Chen, Wang, and Hong (2012) studied the SNARC effect from the perspective of embodied cognition in a cooperative situation, and the results turned out that only when the body position (left or right) and the reactive hand (left or right) of the participants kept consistency, the SNARC effect did appear. This indicates that the body form of the cognitive subject has an effect on the SNARC effect and affects the cognitive process of the individual. Actually, this idea based on embodied cognition was quite matching with the egocentric reference frames. A study has demonstrated that a joint SNARC effect was observed when two participants performed the parity tasks together (Atmaca, Sebanz, Prinz, & Knoblich, 2008). This declares that in social settings without communication, two individuals can share the number representation. When the subjects completed the go/no-go task in the cooperative situation, they would represent each other's behavior spontaneously, that is, the corepresentation. The subjects would still represent the stimulus while they encountered the number of stimuli that should be responded by the other actor. Common coding theory was established to explain its important role in joint action and facilitate the interaction between oneself and others. So this is a model that both egocentric reference frames and allocentric reference frames were involved. Campbell (2014) studied the SNARC effect in a new joint action situation which pairs seated opposite one another. And individuals did not show the SNARC effect when working jointly with an opposite actor; just the change in the spatial position of a companion can lead to the disappearance of the SNARC effect shows that the influence of spatial reference frames on SNARC exists. However, which reference frame is dominated when they take action together in social settings? This issue is uninvestigated. Hence, in the present study, we aim to explore the role of allocentric (object-based and MNL) and egocentric coordinate frames involved in SNARC effect in social settings without communication. And further to explore whether spatial reference frames are critical to the numeral–spatial representations and how the multiple reference frames interact with each other in the processing involved in SNARC effect by researching the effect of multiple reference frames in compatible and conflict conditions on the numeral–spatial representations.

Experiment 1

In this experiment, we examine which reference frames play a key role in cooperative task and how to corepresent the spatial–numerical mappings when allocentric dimension is consistent with egocentric and social dimension.

Method

Participants

Before this experiment, we first balanced Reaction Time (RT) difference of each pairs of participants in the experiment. Finally, a total of 40 paid participants (all are women) between the ages of 19 and 23 years took part in the experiment. All were right-handed and had normal or corrected-to-normal vision. Nobody knew the purpose of this study.

Materials and apparatus

Arabic digits from 1 to 9 (except 5) were shown in black on white background with an Arial font (bold, size = 48 points). Left participants respond to stimulus by pressing the “A” key, right participants respond to stimulus by pressing the “L” key.

Procedure

This study adopted go-nogo paradigm (see Figure 1). Participants sat side by side assigned magnitude judgments to Arabic digits ranging from 1 to 9 (except 5), responding with the left index finger or right index finger. We designed four conditions according to the consistency between participants' position and their response hands. In the first condition, the participant who sits on left position uses left hand to respond to stimuli, participant who sits on right position uses right hand to respond to stimuli. In the second condition, participant sitting on left position uses right hand to respond to stimuli, right participant uses left hand to respond to stimuli. The last two conditions refer to partially consistent; in other words, two participants use their left hand to respond to digits in the third condition. In the fourth condition, two participants use their right hand to respond digits. Each pair of participants performed two conditions; the sequence of the two conditions was random. In our study, 20 participants performed the first two conditions; the remaining participants did the latter two conditions. In all conditions, participants performed two blocks of 80 trials each. The first block required left participant to respond to digits smaller than five, right participant responded to digits larger than five. The second block was vice versa. Each trial started with a 500-ms fixation cross, then appeared blank for 800 ms, followed by the number stimulus presented for a maximum of 1,500 ms. The stimulus disappeared from the screen until participant pressed the key. After an intertrial interval of 1,000 ms, the next trial started. Trial order was randomized within blocks (see Figure 2). OPEN IN VIEWER

Figure 1.

Two individuals sat side by side performing a go-nogo task.

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Figure 2.

Display sequence.

Results

There were 2.2% incorrect responses, which were excluded from further analyses. The mean RTs were entered into a 2 (Side: left/right) × 2 (Magnitude: small/large) × 4 (Consistency between participants' position and response hands: complete consistency/complete inconsistency/consistency between left participant's position and response hand/consistency between right participant's position and response hand) repeated measures analysis of variance (ANOVA). The main effect of Side was not significance, F(1, 38) = 0.418, p > .05, as well as the main effect of Magnitude was not significance either, F(1, 38) = 0.028, p > .05, but there was significant Side × Magnitude × Consistency interaction, F(1, 38) = 4.610, p < .05, η p 2  = 0.108. Hence, further simple effect analysis was used to investigate SNARC effect under abovementioned four conditions.

In Condition 1 (complete consistency), left actor uses left hand to respond to stimulus, right actor uses right hand to respond to stimulus. We performed a 2 (Side: left/right) × 2 (Magnitude: small/large) repeated measures ANOVA. The main effect of Side was not significant, F(1, 18) = 0.875, p > .05, and the main effect of Magnitude was not significant either, F(1, 18) = 0.323, p > .05. But the interaction effect of Side × Magnitude was significant, F(1, 18) = 7.988, p < .01, η p 2  = 0.307, indicating the presence of a standard SNARC effect in this condition (see Figure 3). OPEN IN VIEWER

In Condition 2 (complete inconsistency), left actor responds to stimulus with right hand, right actor responds to stimulus with left hand. A 2 (Side: left/right) × 2 (Magnitude: small/large) repeated measures ANOVA was performed. The main effect of Side was not significant, F(1, 18) = 0.006, p > .05, the main effect of Magnitude was not significant either, F(1, 18) = 2.433, p > .05, but the interaction effect of Side × Magnitude was significant, F(1, 18) = 12.683, p < .05, η p 2  = 0.413, confirming the presence of a reversed SNARC effect (see Figure 4). OPEN IN VIEWER

In Condition 3 (consistency between left participant's position and response hand), left actor and right actor all use their left hand to respond. A 2 (Side: left/right) × 2 (Magnitude: small/large) repeated measures ANOVA was performed. The main effect of Side was not significant, F(1, 18) = 0.05, p > .05, the main effect of Magnitude was not significant either, F(1, 18) = 0.198, p > .05, and the interaction effect of Side × Magnitude was also not significant, F(1, 18) = 0.039, p > .05 (see Figure 5). OPEN IN VIEWER

In Condition 4 (consistency between right participant's position and response hand), left actor and right actor respond to stimulus all with their right hand. A 2 (Side: left/right) × 2 (Magnitude: small/large) repeated measures ANOVA was performed. The main effect of Side was not significant, F(1, 18) = 1.310, p > .05, the main effect of Magnitude was not significant either, F(1, 18) = 0.343, p > .05, the interaction effect of Side × Magnitude was not significant, F(1, 18) = 0.014, p > .05 (see Figure 6). OPEN IN VIEWER

Experiment 2

The results of Experiment 1 indicated that the object-based reference frame is not related with SNARC effect; in other words, the horizontal layout of keyboard from left to right does not work. To further demonstrate this result, in Experiment 2, the keyboard was rotated 90° counterclockwise on the table. We aim to study the way that participants corepresent the tasks, and which reference frame is primary and dominated when allocentric reference frame is inconsistent with egocentric reference frame. In Experiment 2, left participants press “A” key (corresponding to lower key) to respond, right participants press “L” key (corresponding to up key) to respond (see Figure 7). OPEN IN VIEWER

General Discussion

The presented two experiments examined whether and how three possible reference frames affect spatial–numeral representations; a dynamic organization of reference frames including egocentric reference frame; allocentric reference frame; and social interaction dimension is indicated from the results, which shows the importance of different reference frames for the spatial mapping of numerals, and the interactions among them (see Figure 12). Different kinds of numerals can be mapped onto space referred to different reference frames (Zhang & You, 2012); as a result, the organization is dynamic and flexible, the priority and importance of the reference frames for the mappings can be set at certain conditions for certain type of numerals. Different reference frames seem not working in isolated way but interact for the observed SNARC effect. The results support the hypothesis that numerals can be flexibly mapped onto different reference frames, depending on context, instructions, and other factors, including cultural traditions such as the direction of reading and writing. In addition, we believe that the framework proposed here may provide a powerful organizing structure that can help make sense of the literature and furthermore motivate and guide future research. OPEN IN VIEWER

The present results indicate that we are very good at cooperating with a partner in tasks and our brain seems ready for the cooperation. Humans, as a kind of social animals, are more enjoyable to performing with others. Coordination takes place when two or more individuals unintentionally adjust the timing of their actions to each other so that their actions become synchronized. Evidence for the unintentional synchronization of actions comes from studies on rhythmic synchrony, showing that interaction partners coordinate their speech and body movements (McDowall, 1978), and from studies on the unintentional synchronization of rhythmic movements, such as swinging a handheld pendulum (Richardson, Marsh, & Schmidt, 2005; Schmidt & O'Brian, 1997). Corepresentation takes place when an individual shares another individual's mental representation. The corepresentation of actions and intentions in the present study suggested that other representational contents like feelings or beliefs can unintentionally come to be shared as well.

Furthermore, the present study indicates that space–number representation has a close association with hand action. This is consistent with researches which found that certain area of brain is related with the cooperation of hand gestures or actions, as grasping, space, and numeral cognition. This may be a result of evolution of humans, as the hunting is the most important activity in the evolution of the human development; the hunting is a joint performing of hand action, spatial information, and numeral information processing.

It is worth mentioned that our participants are women, which may influence our results. There are some reasons for the gender imbalance in our experiments. The proportion of girls are much higher than boys in our university, and it is hard to find male participants to take part in our experiments. For whatever reason, it is desirable to explore whether gender influence coactor SNARC effect in the further study.

To sum up, the present study provides an evidence that space–numeral association has a very close association with body, not only our own body but also our partners; body is the most important and prior reference for the spatial information and numeral information, the role of body is much more deeper than the culture functions for the association than we thought before. Body cooperation is much more important than representation cooperation; body is the primary clue for the interaction in the cooperation. The study shed light on the social effect on the spatial–numeral interactions; future study will concern how communication and social factors affect spatial–numeral representation and processing. These findings and future further studies will provide insights and foundations for the interface design of interactions.